@Preamble{
"\def \toenglish #1\endtoenglish{[{\em English:} #1\unskip]} " #
"\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}} \fi" #
"\ifx \undefined \circled \def \circled #1{(#1)} \fi" #
"\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}} \fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}} \fi" #
"\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}} \fi" #
"\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}} \fi" #
"\ifx \undefined \pkg \def \pkg #1{{{\tt #1}}} \fi" #
"\ifx \undefined \r \let \r = \ocirc \fi" #
"\ifx \undefined \reg \def \reg {\circled{R}} \fi" #
"\ifx \undefined \texttt \def \texttt #1{{\tt #1}} \fi" #
"\ifx \undefined \TM \def \TM {${}^{\sc TM}$} \fi" #
"\hyphenation{
Cor-dic
COR-DIC
Gleit-komma
Gleit-komma-zahl-en
Gleit-komma-pro-zess-or
Gleit-komma-for-mat
Mikro-rech-en-tech-nik
Mikro-rech-ner-sys-tem-en
Mikro-rech-ner
Mi-yo-shi
Quad-rat-wurz-eln
Semi-nu-mer-i-cal
Swartz-lan-der
}"
}
@String{ack-jg = "Joe Grcar,
email: \path=[email protected]="}
@String{ack-jh = "John Harrison,
email: \path=[email protected]="}
@String{ack-jr = "Jon Rokne,
Department of Computer Science,
The University of Calgary,
2500 University Drive N.W.,
Calgary, Alberta T2N 1N4,
Canada"}
@String{ack-kr = "Karin Remington,
National Institute of Standards and Technology,
Building 820, Room 365,
Gaithersburg, MD 20899, USA,
Tel: +1 301 975-5119,
FAX: +1 301 990-4127,
e-mail: \path|[email protected]|"}
@String{ack-mfc = "Michael F. Cowlishaw,
IBM UK (MP5),
PO Box 31,
Birmingham Road,
Warwick, CV34 5JL,
UK,
e-mail: \path|[email protected]|,
URL: \path|http://www2.hursley.ibm.com/decimal|"}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
e-mail: \path|[email protected]|,
\path|[email protected]|,
\path|[email protected]| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
@String{ack-nj = "Norbert Juffa,
2445 Mission College Blvd.
Santa Clara, CA 95054
USA
email: \path=[email protected]="}
@String{ack-pb = "Preston Briggs,
Tera Computer Company,
2815 Eastlake East,
Seattle, WA 98102,
USA,
Tel: +1 206 325-0800,
e-mail: \path|[email protected]|"}
@String{ack-rfb = "Ronald F. Boisvert,
Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, MD 20899, USA,
Tel: +1 301 975 3812,
e-mail: \path=[email protected]="}
@String{ack-sfo = "Stuart F. Oberman,
e-mail: \path=stuart.[email protected]="}
@String{inst-ANL = "Argonne National Laboratory"}
@String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL
60439-4801, USA"}
@String{inst-ATT-BELL = "AT\&T Bell Laboratories"}
@String{inst-ATT-BELL:adr = "Murray Hill, NJ, USA"}
@String{inst-BERKELEY = "University of California"}
@String{inst-BERKELEY:adr = "Berkeley, CA, USA"}
@String{inst-BERKELEY-CPAM = "Center for Pure and Applied Mathematics,
University of California"}
@String{inst-BERKELEY-CPAM:adr = "Berkeley, CA, USA"}
@String{inst-BERKELEY-CS = "Department of Computer Science, University
of California"}
@String{inst-BERKELEY-CS:adr = "Berkeley, CA, USA"}
@String{inst-BERKELEY-EECS = "Department of Electrical Engineering and
Computer Science, University of California,
Berkeley"}
@String{inst-BERKELEY-EECS:adr = "Berkeley, CA, USA"}
@String{inst-BERKELEY-MATH-EECS = "Department of Mathematics and Department of
Electrical Engineering and Computer Science,
University of California, Berkeley"}
@String{inst-BERKELEY-MATH-EECS:adr = "Berkeley, CA, USA"}
@String{inst-CS-PURDUE = "Department of Computer Science, Purdue
University"}
@String{inst-CS-PURDUE:adr = "West Lafayette, IN 47907-2107, USA"}
@String{inst-CSC = "Center for Scientific Computing,
Department of Mathematics, University of
Utah"}
@String{inst-CSC:adr = "Salt Lake City, UT 84112, USA"}
@String{inst-ETH = "ETH Z{\"u}rich"}
@String{inst-ETH:adr = "Z{\"u}rich, Switzerland"}
@String{inst-HP = "Hewlett--Packard Corporation"}
@String{inst-HP:adr = "Palo Alto, CA, USA"}
@String{inst-INST-ADV-STUDY = "Institute for Advanced Study"}
@String{inst-INST-ADV-STUDY:adr = "Princeton, NJ, USA"}
@String{inst-INTEL = "Intel Corporation"}
@String{inst-INTEL:adr = "Santa Clara, CA, USA"}
@String{inst-LASL = "Los Alamos Scientific Laboratory"}
@String{inst-LASL:adr = "Los Alamos, NM, USA"}
@String{inst-LORIA-INRIA-LORRAINE = "LORIA/INRIA Lorraine"}
@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
Nancy-Brabois, 615 rue du jardin
botanique, F-54602
Villers-l{\`e}s-Nancy Cedex, France"}
@String{inst-NLRC = "NASA Langley Research Center"}
@String{inst-NLRC:adr = "Hampton, VA, USA"}
@String{inst-NPL = "National Physical Laboratory"}
@String{inst-NPL:adr = "Teddington, Middlesex TW11 0LW, UK"}
@String{inst-MATHWORKS = "The MathWorks, Inc."}
@String{inst-MATHWORKS:adr = "3 Apple Hill Drive, Natick, MA 01760-2098,
USA"}
@String{inst-MRC-WISCONSIN = "Mathematics Research Center, University of
Wisconsin, Madison"}
@String{inst-MRC-WISCONSIN:adr = "Madison, WI, USA"}
@String{inst-PRINCETON = "Princeton University"}
@String{inst-PRINCETON:adr = "Princeton, NJ, USA"}
@String{inst-STAN-CS = "Stanford University, Department of
Computer Science"}
@String{inst-STAN-CS:adr = "Stanford, CA, USA"}
@String{inst-UT-CS = "Department of Computer Science,
University of Tennessee, Knoxville"}
@String{inst-UT-CS:adr = "Knoxville, TN 37996, USA"}
@String{j-ACTA-INFO = "Acta Informatica"}
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}
@String{j-ACM-J-EXP-ALGORITHMICS = "ACM Journal of Experimental Algorithmics"}
@String{j-ADA-LETT = "Ada Letters"}
@String{j-ADV-COMPUT-MATH = "Advances in Computational Mathematics"}
@String{j-ADV-SOFT-SCI-TECH = "Advances in software science and
technology"}
@String{j-ADV-THEORY-SIMUL = "Advanced Theory and Simulations"}
@String{j-ALGORITHMICA = "Algorithmica"}
@String{j-ALGORITHMS-BASEL = "Algorithms ({Basel})"}
@String{j-ALTA-FREQ = "Alta frequenza"}
@String{j-AM-J-MATH = "American Journal of Mathematics"}
@String{j-AM-SCI = "American Scientist"}
@String{j-AMER-J-PHYSICS = "American Journal of Physics"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANN-HIST-COMPUT = "Annals of the History of Computing"}
@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
Intelligence"}
@String{j-ANN-MATH-STAT = "Annals of Mathematical Statistics"}
@String{j-ANN-NUM-MATH = "Annals of Numerical Mathematics"}
@String{j-APL-QUOTE-QUAD = "ACM SIGAPL APL Quote Quad"}
@String{j-APPL-ALGEBRA-ENG-COMMUN-COMPUT = "Applicable algebra in engineering,
communication and computing"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPL-NUM-MATH = "Applied Numerical Mathematics"}
@String{j-APPL-OPTICS = "Applied Optics"}
@String{j-APPL-STAT = "Applied Statistics"}
@String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"}
@String{j-ASTA-ADV-STAT-ANAL = "AStA. Advances in Statistical Analysis"}
@String{j-ASTRON-J = "Astronomical Journal"}
@String{j-AUSTRALIAN-COMP-J = "Australian Computer Journal"}
@String{j-AUTO-CTL-COMP-SCI = "Automatic Control and Computer Sciences"}
@String{j-AUTOMATION-REMOTE-CTL = "Automation and Remote Control"}
@String{j-BELL-LABS-RECORD = "Bell Laboratories Record"}
@String{j-BELL-SYST-TECH-J = "The Bell System Technical Journal"}
@String{j-BER-WISSENSCHAFTGESCH = "{Berichte zur Wissenschaftsgeschichte}"}
@String{j-BIOL-CYBERN = "Biological Cybernetics"}
@String{j-BIOMETRICS = "Biometrics"}
@String{j-BIT = "BIT (Nordisk tidskrift for
informationsbehandling)"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BRITISH-J-HIST-MATH = "British Journal for the History of
Mathematics"}
@String{j-BRITISH-J-HIST-SCI = "British Journal for the History of Science"}
@String{j-BULL-AMS = "Bulletin of the American Mathematical
Society"}
@String{j-BULL-CALCUTTA-MATH-SOC = "Bulletin of the Calcutta Mathematical Society"}
@String{j-BYTE = "Byte Magazine"}
@String{j-C-R-ACAD-BULGARE-SCI = "Comptes rendus de l'Acad{\'e}mie bulgare
des sciences"}
@String{j-C-R-ACAD-SCI-PARIS-SER-I-MATH = "Comptes Rendus des S{\'e}ances de
l'Acad{\'e}mie des Sciences. S{\'e}rie I.
Math{\'e}matique"}
@String{j-CACM = "Communications of the Association for
Computing Machinery"}
@String{j-CAD = "Computer Aided Design"}
@String{j-CCCUJ = "C/C++ Users Journal"}
@String{j-CCPE = "Concurrency and Computation: Prac\-tice and
Experience"}
@String{j-CGF = "Com{\-}pu{\-}ter Graphics Forum"}
@String{j-COED = "CoED"}
@String{j-COLLEGE-MATH-J = "College Mathematics Journal"}
@String{j-COMBIN-PROBAB-COMPUT = "Combinatorics, Probability and Computing"}
@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
and Computation"}
@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
Methods"}
@String{j-COMP-ARCH-NEWS = "ACM SIGARCH Computer Architecture News"}
@String{j-COMP-DESIGN = "Computer Design"}
@String{j-COMP-EDU-J = "Computers in education journal"}
@String{j-COMP-GEOM = "Computational Geometry. Theory and
Applications"}
@String{j-COMP-GEOSCI = "Computers and Geosciences"}
@String{j-COMP-J = "The Computer Journal"}
@String{j-COMP-LANG-MAG = "Computer Language Magazine"}
@String{j-COMP-LANGS = "Computer Languages"}
@String{j-COMP-PHYS-COMM = "Computer Physics Communications"}
@String{j-COMP-SURV = "ACM Computing Surveys"}
@String{j-COMPUT-AIDED-ENG = "Computer-aided engineering: CAE"}
@String{j-COMPUT-EDGE = "ComputingEdge"}
@String{j-COMPUT-ELECTR-ENG = "Computers and Electrical Engineering"}
@String{j-COMPUT-MATH-APPL = "Computers and Mathematics with Applications"}
@String{j-COMPUT-PHYS = "Computers in Physics"}
@String{j-COMPUT-SCI-ENG = "Computing in Science and Engineering"}
@String{j-COMPUT-SECUR = "Computers \& Security"}
@String{j-COMPUTE = "Compute"}
@String{j-COMPUTER = "Computer"}
@String{j-COMPUTING = "Computing: Archiv fur informatik und
numerik"}
@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}
@String{j-CONG-NUM = "Congressus Numerantium"}
@String{j-CONTEMP-PHYS = "Contemporary physics"}
@String{j-CPE = "Concurrency: Prac\-tice and Experience"}
@String{j-CRYPTOLOGIA = "Cryptologia"}
@String{j-CT = "c't"}
@String{j-CUJ = "C Users Journal"}
@String{j-CYBER = "Cybernetics"}
@String{j-DDJ = "Dr. Dobb's Journal of Software Tools"}
@String{j-DEC-TECH-J = "Digital Technical Journal"}
@String{j-DEMOGRAPHY = "Demography"}
@String{j-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"}
@String{j-DIGIT-SIGNAL-PROCESS = "Digital Signal Processing"}
@String{j-DISCRETE-COMPUT-GEOM = "Discrete and Computational Geometry"}
@String{j-DOKL-AKAD-NAUK = "Doklady Akademii nauk SSSR"}
@String{j-DTRAP = "Digital Threats: Research and Practice
(DTRAP)"}
@String{j-EDN = "EDN"}
@String{j-EDUC-STUD-MATH = "Educational Studies in Mathematics"}
@String{j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI = "Electronics and communications in
Japan. Part 3, Fundamental electronic
science"}
@String{j-ELECT-LETTERS = "Electronics Letters"}
@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
Computer Science"}
@String{j-ELECTR-ENG = "Electrical Engineering (American Institute of
Electrical Engineers)"}
@String{j-ELECTRON-COMMUN-JPN = "Electronics and communications in Japan"}
@String{j-ELECTRON-ENG = "Electronic Engineering"}
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
Analysis"}
@String{j-ELECTRONIC-DESIGN = "Electronic Design"}
@String{j-ELECTRONIC-ENG-TIMES = "Electronic engineering times"}
@String{j-ELECTRONICS = "Electronics"}
@String{j-ELECTRONIK = "Elektronik"}
@String{j-ELEK-RECHENANLAGEN = "Elektronische Rechenanlagen"}
@String{j-ELEKTRONIKER = "Elektroniker (Switzerland)"}
@String{j-EMBED-SYS-PROG = "Embedded Systems Programming"}
@String{j-ENTROPY = "Entropy"}
@String{j-EURASIP-J-ADV-SIGNAL-PROCESS = "EURASIP Journal on Advances in Signal
Processing"}
@String{j-EURASIP-J-EMBED-SYS = "EURASIP Journal on Embedded Systems"}
@String{j-FIB-QUART = "Fibonacci Quarterly"}
@String{j-FORM-METHODS-SYST-DES = "Formal Methods in System Design"}
@String{j-FORTH-DIMENSIONS = "Forth Dimensions"}
@String{j-FORTRAN-FORUM = "ACM Fortran Forum"}
@String{j-FOUND-SCI = "Foundations of Science"}
@String{j-FUT-GEN-COMP-SYS = "Future Generation Computer Systems"}
@String{j-FUZZY-SETS-SYSTEMS = "Fuzzy Sets and Systems"}
@String{j-GAMM-MIT = "Mitteilungen der Gesellschaft f{\\\"u}r
Angewandte Mathematik und Mechanik"}
@String{j-GEOSCI-MODEL-DEV = "Geoscientific Model Development"}
@String{j-HIST-MATH = "Historia Mathematica"}
@String{j-HIST-SCI-2 = "Historia Scientiarum. Second Series.
International Journal of the History
of Science Society of Japan"}
@String{j-HIGH-PERFORM-SYST = "High performance systems"}
@String{j-HEWLETT-PACKARD-J = "Hewlett--Packard Journal"}
@String{j-HONEYWELL-COMP-J = "Honeywell Computer Journal"}
@String{j-IBM-JRD = "IBM Journal of Research and Development"}
@String{j-IBM-SYS-J = "IBM Systems Journal"}
@String{j-IBM-TDB = "IBM Technical Disclosure Bulletin"}
@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital
Techniques"}
@String{j-IEE-PROC-E = "IEE proceedings, E: Computers and digital
techniques"}
@String{j-IEEE-ACCESS = "IEEE Access"}
@String{j-IEEE-ANN-HIST-COMPUT = "IEEE Annals of the History of Computing"}
@String{j-IEEE-APM = "IEEE Antennas and Propagation Magazine"}
@String{j-IEEE-CGA = "IEEE Computer Graphics and Applications"}
@String{j-IEEE-COMMUN-LET = "IEEE Communications Letters"}
@String{j-IEEE-COMPUT-ARCHIT-LETT = "IEEE Computer Architecture Letters"}
@String{j-IEEE-COMPUT-SCI-ENG = "IEEE Computational Science \& Engineering"}
@String{j-IEEE-DES-TEST-COMPUT = "IEEE Design \& Test of Computers"}
@String{j-IEEE-INT-CONF-ALG-ARCH-PAR-PROC = "IEEE International Conference on
Algorithms and Architectures for Parallel
Processing"}
@String{j-IEEE-J-EMERG-SEL-TOP-CIRCUITS-SYST = "IEEE Journal on Emerging and
Selected Topics in Circuits and Systems"}
@String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"}
@String{j-IEEE-MICRO = "IEEE Micro"}
@String{j-IEEE-POT = "IEEE Potentials"}
@String{j-IEEE-J-SEL-AREAS-COMMUN = "IEEE Journal on Selected Areas in
Communications"}
@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"}
@String{j-IEEE-SIGNAL-PROCESS-MAG = "IEEE Signal Processing Magazine"}
@String{j-IEEE-SOFTWARE = "IEEE Software"}
@String{j-IEEE-SPECTRUM = "IEEE Spectrum"}
@String{j-IEEE-TIT = "IEEE Transactions on Information Theory"}
@String{j-IEEE-TRANS-ACOUST-SPEECH = "IEEE Transactions on Acoustics, Speech,
and Signal Processing"}
@String{j-IEEE-TRANS-AEROSP-ELECTRON-SYST = "IEEE Transactions on Aerospace
and Electronic Systems"}
@String{j-IEEE-TRANS-APPL-SUPERCOND = "IEEE Transactions on Applied
Superconductivity"}
@String{j-IEEE-TRANS-AUDIO-ELECTROACOUST = "IEEE Transactions on Audio and
Electroacoustics"}
@String{j-IEEE-TRANS-AUTOMAT-CONTR = "IEEE Transactions on Automatic Control"}
@String{j-IEEE-TRANS-BIOMED-ENG = "IEEE Transactions on Biomedical
Engineering"}
@String{j-IEEE-TRANS-BROADCAST = "IEEE Transactions on Broadcasting"}
@String{j-IEEE-TRANS-CAD-ICS = "IEEE Transactions on Computer-Aided Design
of Integrated Circuits and Systems"}
@String{j-IEEE-TRANS-CIRCUITS-SYST = "IEEE Transactions on Circuits and
Systems"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-1 = "IEEE Transactions on Circuits and
Systems I: Regular Papers"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL = "IEEE Transactions on
Circuits and Systems I: Fundamental
Theory and Applications"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE transactions on circuits and
systems. 2, Analog and digital signal
processing"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS = "IEEE Transactions on
Circuits and Systems II: Express Briefs"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH = "IEEE Transactions on Circuits
and Systems for Video Technology"}
@String{j-IEEE-TRANS-COMM = "IEEE Transactions on Communications"}
@String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"}
@String{j-IEEE-TRANS-CONSUMER-ELECTRONICS = "IEEE Transactions on Consumer
Electronics"}
@String{j-IEEE-TRANS-CONTROL-SYST-TECHNOL = "IEEE Transactions on Control
Systems Technology"}
@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}
@String{j-IEEE-TRANS-EMERG-TOP-COMPUT = "IEEE Transactions on Emerging Topics in
Computing"}
@String{j-IEEE-TRANS-IND-ELECTRON = "IEEE Transactions on Industrial
Electronics"}
@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}
@String{j-IEEE-TRANS-INSTRUM-MEAS = "IEEE Transactions on Instrumentation and
Measurement"}
@String{j-IEEE-TRANS-NEURAL-NETW = "IEEE Transactions on Neural Networks"}
@String{j-IEEE-TRANS-NUCL-SCI = "IEEE Transactions on Nuclear Science"}
@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
Distributed Systems"}
@String{j-IEEE-TRANS-PROF-COMMUN = "IEEE Transactions on Professional
Communication"}
@String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"}
@String{j-IEEE-TRANS-SOFTW-ENG = "IEEE Transactions on Software Engineering"}
@String{j-IEEE-TRANS-VEH-TECHNOL = "IEEE Transactions on Vehicular Technology"}
@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization and
Computer Graphics"}
@String{j-IEEE-TRANS-VLSI-SYST = "IEEE Transactions on Very Large Scale
Integration (VLSI) Systems"}
@String{j-IEEE-TRANS-WIREL-COMMUN = "IEEE Transactions on Wireless Communications"}
@String{j-IFIP-TRANS-A = "IFIP Transactions. A. Computer Science and
Technology"}
@String{j-IJQC = "International Journal of Quantum Chemistry"}
@String{j-IJSA = "The International Journal of Supercomputer
Applications"}
@String{j-IJHPCA = "The International Journal of High Performance
Computing Applications"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-INC-STAT = "The Incorporated Statistician"}
@String{j-INF-CONTROL = "Information and Control"}
@String{j-INF-PROCESS-MACH = "Information processing machines"}
@String{j-INFO-PROC = "Journal of Information Processing (of
Japan??)"}
@String{j-INFO-PROC-LETT = "Information Processing Letters"}
@String{j-INFORM-THEOR-APPL = "RAIRO. Informatique th{\'e}orique et
applications := Theoretical
informatics and applications"}
@String{j-INFORMATIK-SPEKTRUM = "Informatik Spektrum"}
@String{j-INFORMS-J-COMPUT = "INFORMS Journal on Computing"}
@String{j-INT-J-COMPUT-GEOM-APPL = "International Journal of
Computational Geometry and Applications
(IJCGA)"}
@String{j-INT-J-COMP-APPL = "International Journal of Computer
Applications"}
@String{j-INT-J-COMP-RESEARCH = "International Journal of Computer Research"}
@String{j-INT-J-CONTROL = "International Journal of Control"}
@String{j-INT-J-ELECTRON = "International Journal of Electronics
Theoretical \& Experimental"}
@String{j-INT-J-FOUND-COMP-SCI = "International Journal of Foundations of
Computer Science"}
@String{j-INT-J-INFO-SEC = "International Journal of Information
Security"}
@String{j-INT-J-NUM-METH-FLUIDS = "Int. J. Num. Meth. Fluids"}
@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
Computing"}
@String{j-INT-J-MINI-MICROCOMPUTERS = "International Journal of Mini and
Microcomputers"}
@String{j-INT-J-PAR-EMER-DIST-SYS = "International Journal of Parallel, Emergent
and Distributed Systems: IJPEDS"}
@String{j-INT-J-PARALLEL-PROG = "International Journal of Parallel
Programming"}
@String{j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER = "International Journal on
Software Tools for Technology Transfer:
STTT"}
@String{j-INT-J-SYST-SCI = "International Journal of Systems Science"}
@String{j-INTEGRATION-VLSI-J = "Integration, the VLSI journal"}
@String{j-INTEL-TECH-J = "Intel Technology Journal"}
@String{j-INTERVAL-COMP = "Interval Computations = Interval'nye
vychisleniia"}
@String{j-IRE-PROC = "IRE Proceedings"}
@String{j-IRE-TRANS-ELEC-COMPUT = "IRE Transactions on Electronic Computers"}
@String{j-ISIS = "Isis"}
@String{j-J-ACM = "Journal of the Association for Computing
Machinery"}
@String{j-J-ACOUST-SOC-AM = "Journal of the Acoustical Society of
America"}
@String{j-J-ADV-MODEL-EARTH-SYST = "Journal of Advances in Modeling Earth
Systems"}
@String{j-J-ALG = "Journal of Algorithms"}
@String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical
Association"}
@String{j-J-APPL-MATH = "Journal of Applied Mathematics"}
@String{j-J-APPL-PROBAB = "Journal of Applied Probability"}
@String{j-J-APPL-STAT = "Journal of Applied Statistics"}
@String{j-J-APPROX-THEORY = "Journal of Approximation Theory"}
@String{j-J-AUSTRALIAN-MATH-SOC = "Journal of the Australian Mathematical
Society"}
@String{j-J-AUTOM-REASON = "Journal of Automated Reasoning"}
@String{j-J-CHINESE-INST-ENG = "Journal of the Chinese Institute of Engineers
= Chung-kuo kung ch'eng hsueh kan"}
@String{j-J-COMB-THEORY-A = "Journal of Combinatorial Theory (Series A)"}
@String{j-J-COMP-SYS-SCI = "Journal of Computer and System Sciences"}
@String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-J-COMPUT-PHYS = "Journal of Computational Physics"}
@String{j-J-COMPUT-SCI = "Journal of Computational Science"}
@String{j-J-CRYPTO-ENG = "Journal of Cryptographic Engineering"}
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@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-SYNGRESS = "Syngress Publishing, Inc."}
@String{pub-SYNGRESS:adr = "Rockland, MA, USA"}
@String{pub-TEUBNER = "B. G. Teubner"}
@String{pub-TEUBNER:adr = "Stuttgart, Germany"}
@String{pub-TEWI = "te-wi"}
@String{pub-TEWI:adr = "M{\"u}nchen, Germany"}
@String{pub-TOMASH = "Tomash Publishers"}
@String{pub-TOMASH:adr = "Los Angeles, CA, USA"}
@String{pub-USENIX = "USENIX"}
@String{pub-USENIX-EL-CERRITO:adr = "P.O. Box 7, El Cerrito 94530, CA,
USA"}
@String{pub-USENIX:adr = "San Francisco, CA, USA"}
@String{pub-USGPO = "United States Government Printing Office"}
@String{pub-USGPO:adr = "Washington, DC, USA"}
@String{pub-VEB-VERLAG-TECHNIK = "VEB Verlag Technik"}
@String{pub-VEB-VERLAG-TECHNIK:adr = "Berlin, Germany"}
@String{pub-VIKING = "Viking"}
@String{pub-VIKING:adr = "New York, NY, USA"}
@String{pub-WCB = "William C. Brown Company Publishers"}
@String{pub-WCB:adr = "Dubuque, IA, USA"}
@String{pub-WEITEK = "Weitek Corporation"}
@String{pub-WEITEK:adr = "1060 E. Arques Ave., Sunnyvale, CA
94086-BRM-9759, USA"}
@String{pub-WESTERN-PERIODICALS = "Western Periodicals Co.,"}
@String{pub-WESTERN-PERIODICALS:adr = "North Hollywood, CA"}
@String{pub-WILEY = "Wiley"}
@String{pub-WILEY:adr = "New York, NY, USA"}
@String{pub-WILEY-INTERSCIENCE = "Wiley-In{\-}ter{\-}sci{\-}ence"}
@String{pub-WILEY-INTERSCIENCE:adr = "New York, NY, USA"}
@String{pub-WORLD-SCI = "World Scientific Publishing
Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road,
Singapore 9128"}
@String{ser-APPL-MATH-SER-NBS = "Applied Mathematics Series / National Bureau
of Standards"}
@String{ser-LECT-NOTES-MATH = "Lecture Notes in Mathematics"}
@String{ser-LNCS = "Lecture Notes in Computer Science"}
@String{ser-LNCSE = "Lecture Notes in Computational
Science and Engineering"}
@String{ser-PROJECT-GUTENBERG = "Project Gutenberg"}
@String{ser-SIGPLAN = "ACM SIGPLAN Notices"}
@Article{Leibniz:1703:EAB,
author = "G.-W. Leibniz",
title = "Explication de {l'Arithm{\'e}tique} Binaire.
({French}) [{Explanation} of binary arithmetic]",
journal = "M{\'e}moires de math{\'e}matique et de physique de l
Acad{\'e}mie royale des sciences",
volume = "??",
number = "??",
pages = "85--89",
month = "????",
year = "1703",
bibdate = "Fri Mar 17 08:48:17 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Leibniz is often credited with the invention of the
binary number system, but there is other work from his
era, and detailed analysis of Leibniz's use of binary
numbers. See
\cite{Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV}",
URL = "https://hal.archives-ouvertes.fr/ads-00104781/document",
acknowledgement = ack-nhfb,
language = "French",
}
@Book{Pelicano:1712:APQ,
author = "Wenceslao Josepho Pelicano",
title = "Arithmeticus Perfectus Qui tria numerare nescit,
\ldots{}. ({Latin}) [{A} Perfect Arithmetic for who
does not know how to count to three]",
publisher = "????",
address = "Prague, Czechoslovakia",
pages = "????",
year = "1712",
bibdate = "Fri Mar 17 08:56:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://play.google.com/books/reader?id=cNxdAAAAcAAJ",
acknowledgement = ack-nhfb,
longtitle = "Arithmeticus Perfectus Qui tria numerare nescit, sen
Arithmetica dualis in qua Numerando non proceditur,
nisi ad duo, \& tamen omnes questiones Arithmetic{\ae}
negoti{\^o} facile enodar possunt ad perilsturem equite
Mathematic{\ae}. ({Latin}) [{A} Perfect Arithmetic for
who does not know how to count to three, is a dual
arithmetic in which he does not proceed to numbering
except to two, and yet all the questions of arithmetic
business can easily be entangled to the peril of the
mathematician]",
}
@Article{Colson:1726:SAN,
author = "John {Colson, F.R.S.}",
title = "A Short Account of Negativo-Affirmative Arithmetick",
journal = j-PHILOS-TRANS-R-SOC-LOND,
volume = "34",
number = "392--398",
pages = "161--173",
month = "????",
year = "1726",
CODEN = "PTRSAV",
DOI = "https://doi.org/10.1098/rstl.1726.0032",
ISSN = "0370-2316 (print), 2053-9207 (electronic)",
bibdate = "Tue Jul 28 14:21:05 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith22.gforge.inria.fr/slides/s2-ercegovac.pdf",
acknowledgement = ack-nhfb,
fjournal = "Philosophical transactions of the Royal Society of
London",
journal-URL = "http://rsta.royalsocietypublishing.org/",
remark = "Early work on signed-digit arithmetic, reported by
Milo{\v{s}} Ercegovac in a talk at the ARITH'22
conference, Lyon, France, June 2015.",
}
@Unpublished{Babbage:1837:MPC,
author = "Charles Babbage",
title = "On the mathematical powers of the calculating engine",
month = dec,
year = "1837",
bibdate = "Wed Oct 13 11:09:59 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript held by Museum of the History of Science,
Oxford, UK. Reprinted in \cite[\S
2.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Book{Nystrom:1862:PNS,
author = "John W. (John William) Nystrom",
title = "Project of a new system of arithmetic, weight, measure
and coins, proposed to be called the tonal system, with
sixteen to the base",
publisher = "J. B. Lippincott and Co.",
address = "Philadelphia, PA, USA",
pages = "106",
year = "1862",
LCCN = "QC96 .N95",
bibdate = "Sat Oct 29 10:28:27 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://unifoundry.com/tonal/;
https://catalog.hathitrust.org/Record/011602816;
https://lccn.loc.gov/04025433",
acknowledgement = ack-nhfb,
author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
remark = "Thanks to Paul Hardy of Unifoundry in San Diego, CA,
USA, for information about Nystrom's promotion of
hexadecimal arithmetic, and for creating a Web site
about Nystrom's tonal system, as well as developing
Unicode-compatible fonts to represent the additional
digits needed by the system.",
subject = "Weights and measures; Numeration; base-16 arithmetic;
hexadecimal arithmetic",
}
@Article{Anonymous:1875:AOM,
author = "Anonymous",
title = "The Arithmetical Operations of Multiplication and
Division",
journal = j-SCI-AMER,
volume = "32",
number = "3",
pages = "41--42",
day = "16",
month = jan,
year = "1875",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican01161875-41",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:29:24 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Anonymous:1879:TRA,
author = "Anonymous",
title = "Three Rules for Abbreviating Multiplication",
journal = j-SCI-AMER,
volume = "41",
number = "12",
pages = "184--184",
day = "20",
month = sep,
year = "1879",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican09201879-184",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Fri May 17 10:36:54 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
URL = "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Newcomb:1881:NFU,
author = "Simon Newcomb",
title = "Note on the frequency of use of the different digits
in natural numbers",
journal = j-AM-J-MATH,
volume = "4",
number = "1/4",
pages = "39--40",
year = "1881",
CODEN = "AJMAAN",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibdate = "Thu Feb 15 16:35:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2-K",
abstract = "That the ten digits do not occur with equal frequency
must be evident to any one making much use of
logarithmic tables, and noticing how much faster the
first pages wear out than the last ones. The first
significant figure is oftener 1 than any other digit,
and the frequency diminishes up to 9.",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Mathematics",
journal-URL = "https://www.jstor.org/journal/amerjmath",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 40: ``The law of probability of the occurrence
of numbers is such that all mantissas of their
logarithms are equally probable.''",
}
@Article{Holman:1888:DPM,
author = "Silas W. Holman",
title = "Discussion of the precision of measurement",
journal = "Technol. Q.",
volume = "1",
number = "??",
pages = "194--207",
month = "????",
year = "1888",
bibdate = "Mon May 21 17:12:03 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 14]{Carter:2013:ESF}.",
}
@Book{Holman:1892:DPM,
author = "Silas W. Holman",
title = "Discussion of the Precision of Measurements: With
Examples Taken Mainly From Physics And Electrical
Engineering",
publisher = "Ferris Brothers Printers",
address = "New York, NY, USA",
pages = "????",
year = "1892",
bibdate = "Mon May 21 17:14:39 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 15]{Carter:2013:ESF}.",
}
@Article{Anonymous:1893:IDb,
author = "Anonymous",
title = "The Instantaneous Divider",
journal = j-SCI-AMER,
volume = "68",
number = "21",
pages = "325--325",
day = "27",
month = may,
year = "1893",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican05271893-325a",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:04:00 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v68/n21/pdf/scientificamerican05271893-325a.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Felt:1893:MA,
author = "Dorr E. Felt",
title = "Mechanical Arithmetic",
journal = j-SCI-AMER,
volume = "69",
number = "20",
pages = "309--310",
day = "11",
month = nov,
year = "1893",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican11111893-309b",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:04:25 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v69/n20/pdf/scientificamerican11111893-309b.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Aley:1897:DES,
author = "Robert J. Aley",
title = "A Device for Extracting the Square Root of Certain
Surd Quantities",
journal = j-AMER-MATH-MONTHLY,
volume = "4",
number = "8/9",
pages = "204--208",
month = aug # "\slash " # sep,
year = "1897",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:08 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Anonymous:1898:OFA,
author = "Anonymous",
title = "Our Fingers as an Aid in Multiplication",
journal = j-SCI-AMER,
volume = "79",
number = "17",
pages = "265--266",
day = "22",
month = oct,
year = "1898",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican10221898-265",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 19:08:57 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
URL = "http://www.nature.com/scientificamerican/journal/v79/n17/pdf/scientificamerican10221898-265.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Ludgate:1909:PAM,
author = "P. E. Ludgate",
title = "On a proposed analytical machine",
journal = j-SCI-PROC-ROY-DUBLIN-SOC,
volume = "12",
number = "9",
pages = "77--91",
year = "1909",
CODEN = "SPRDAP",
ISSN = "0371-2303",
bibdate = "Wed Oct 13 11:14:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 2.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Scientific proceedings of the Royal Dublin Society",
}
@Article{Babbage:1910:BBA,
author = "H. P. Babbage",
title = "{Babbage}: {Babbage}'s analytical engine",
journal = j-MONTHLY-NOT-ROY-ASTRON-SOC,
volume = "70",
number = "??",
pages = "517--526, 645",
year = "1910",
CODEN = "MNRAA4",
ISSN = "0035-8711 (print), 1365-2966 (electronic)",
ISSN-L = "0035-8711",
bibdate = "Wed Oct 13 11:12:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 2.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Monthly Notices of the Royal Astronomical Society",
journal-URL = "https://academic.oup.com/mnras",
}
@Article{TorresyQuevedo:1915:EAS,
author = "L. {Torres y Quevedo}",
title = "Essais sur l'automatique. Sa definition. {{\'E}}tendue
th{\'e}orique de ses applications ({French}) [{Essays}
on automation. {Its} definition. {Theoretical} extent
of its applications]",
journal = j-REV-GEN-SCI-PURES-APPL,
volume = "??",
number = "??",
pages = "601--611",
day = "15",
month = nov,
year = "1915",
ISSN = "0370-7431",
bibdate = "Wed Oct 13 11:15:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 2.5]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
fjournal = "Revue G{\'e}n{\'e}rale des Sciences Pures et
Appliqu{\'e}es",
language = "French",
}
@Article{Barrow:1924:QDD,
author = "D. F. Barrow",
title = "Questions and Discussions: Discussions: On Taking
Square Roots of Integers",
journal = j-AMER-MATH-MONTHLY,
volume = "31",
number = "10",
pages = "482--484",
month = dec,
year = "1924",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:29 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Smith:1924:FPA,
author = "David Eugene Smith",
title = "The First Printed Arithmetic ({Treviso}, 1478)",
journal = j-ISIS,
volume = "6",
number = "3",
pages = "311--331",
month = "????",
year = "1924",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:26 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211087;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/224315",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Book{Karpinski:1925:HA,
author = "Louis Charles Karpinski",
title = "The History of Arithmetic",
publisher = "Rand McNally \& Company",
address = "New York, NY, USA",
pages = "xi + 200",
year = "1925",
bibdate = "Fri Nov 28 18:09:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Cajori:1926:BRB,
author = "Florian Cajori",
title = "Book Review: {{\booktitle{The History of Arithmetic}}
by Louis Charles Karpinski}",
journal = j-ISIS,
volume = "8",
number = "1",
pages = "231--232",
month = feb,
year = "1926",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:36 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211094;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/223706",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Smith:1926:FGC,
author = "David Eugene Smith",
title = "The First Great Commercial Arithmetic",
journal = j-ISIS,
volume = "8",
number = "1",
pages = "41--49",
month = feb,
year = "1926",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:36 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211094;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/223673",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Cajori:1927:EAP,
author = "Florian Cajori",
title = "The Earliest Arithmetic Published in {America}",
journal = j-ISIS,
volume = "9",
number = "3",
pages = "391--401",
month = dec,
year = "1927",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:57:45 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i214411;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
URL = "http://www.jstor.org/stable/330806",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{J:1930:RPRb,
author = "R. A. J.",
title = "Recent Publications: Reviews: {{\em Standard Table of
Square Roots}}, by {L. M. Milne-Thomson}",
journal = j-AMER-MATH-MONTHLY,
volume = "37",
number = "6",
pages = "314--314",
month = jun # "\slash " # jul,
year = "1930",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:35:55 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Laughlin:1930:LND,
author = "Harry H. Laughlin",
title = "Large-Number Division by Calculating Machine",
journal = j-AMER-MATH-MONTHLY,
volume = "37",
number = "6",
pages = "287--293",
month = jun # "\slash " # jul,
year = "1930",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:35:55 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Garver:1932:QDNb,
author = "Raymond Garver",
title = "Questions, Discussions, and Notes: a Square Root
Method and Continued Fractions",
journal = j-AMER-MATH-MONTHLY,
volume = "39",
number = "9",
pages = "533--535",
month = nov,
year = "1932",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:47 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Polachek:1932:MMU,
author = "H. Polachek",
title = "A method of multiplication used by {Saadia Gaon} in
the 10th century",
journal = j-SCRIPTA-MATH,
volume = "1",
number = "??",
pages = "245--246",
month = "????",
year = "1932",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
jfm = "59.0019.03",
ZBmath = "2542288",
}
@Article{Simons:1932:IGA,
author = "T. E. Simons",
title = "{Isaac Greenwood}'s arithmetic",
journal = j-SCRIPTA-MATH,
volume = "1",
number = "??",
pages = "262--264",
month = "????",
year = "1932",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
jfm = "59.0026.02",
ZBmath = "2542316",
}
@Book{Couffignal:1933:MCL,
author = "L. Couffignal",
title = "Les machines {\`a} calculer, leurs principes, leur
{\'e}volution. ({French}) [{Calculating} machines,
their principles, their evolution]",
publisher = "Gauthier-Villars",
address = "Paris, France",
year = "1933",
bibdate = "Wed Oct 13 11:19:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Kalbfell:1934:QDN,
author = "D. C. Kalbfell",
title = "Questions, Discussions and Notes: On a Method for
Calculating Square Roots",
journal = j-AMER-MATH-MONTHLY,
volume = "41",
number = "8",
pages = "504--506",
month = oct,
year = "1934",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:31 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Simons:1935:EEC,
author = "L. G. Simons",
title = "An early eighteenth century {American} readyreckoner",
journal = j-SCRIPTA-MATH,
volume = "3",
number = "??",
pages = "94--96",
month = "????",
year = "1935",
ISSN = "0036-9713",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
jfm = "61.0020.03",
ZBmath = "2531128",
}
@Article{Calvert:1936:DDS,
author = "H. R. Calvert",
title = "Decimal Division of Scales before the Metric System",
journal = j-ISIS,
volume = "25",
number = "2",
pages = "433--436",
month = sep,
year = "1936",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:21:25 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211115;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/225380",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Book{LeVita:1936:ALI,
author = "Maurice H. {Le Vita}",
title = "An Arithmetic of Life Insurance",
publisher = "Life Office Management Association",
address = "New York",
pages = "xii + 132",
year = "1936",
LCCN = "HG8781 .L43",
bibdate = "Sat Aug 12 14:42:20 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hdl.handle.net/2027/mdp.39015017290688;
https://babel.hathitrust.org/cgi/pt?id=mdp.39015017290688",
abstract = "We have determined this item to be in the public
domain according to US copyright law through
information in the bibliographic record and/or US
copyright renewal records. The digital version is
available for all educational uses worldwide. Please
contact HathiTrust staff at hathitrust-help <at>
umich.edu with any questions about this item. Life
insurance--Mathematics. (LCCN)36034103.
(OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66.
Http://hdl.handle.net/2027/mdp.39015017290688.",
acknowledgement = ack-nhfb,
remark = "While not about computer arithmetic, this book is
about practical applications of arithmetic in the life
insurance industry. It considers compound interest
calculations, present values of financial instruments,
mortality tables, insurance premiums, bond returns, and
so on. In Table 1, which shows the growth of an
investment at 3 percent over 10 years, the author
[amusingly] comments ``Mathematicians have already
worked out the multiplications and have incorporated
them into a table. With the use of this table, the
result can be obtained by a single multiplication.''.
Although the MARC record indicates the book is in the
public domain, the URL only permits download of a
single page at a time, although it is possible to page
through the book.",
tableofcontents = "Preface / vii \\
Index to Tables / xi \\
Notes on the Solution of Problems / xii \\
\\
I. Interest and Discount / 1 \\
Interest \\
Discount \\
Examples \\
Observations \\
Problems \\
\\
II. The Mortality Table and Easy Problems in Rate
Calculation at Age 90 / 6 \\
Natural or Net One-Year Term Premium \\
Net One-Year Pure Endowment \\
Net Single Premium Whole Life \\
Fundamental Principle \\
Observations \\
Problems \\
\\
III. Single Premium Contracts --- Age 35 / 14 \\
Mortality Table \\
(Net) Single Premium 10-Year Term \\
(Net) Single Premium 10-Year Pure Endowment \\
(Net) Single Premium 10-Year Endowment \\
(Net) Single Premium Whole Life \\
(Net) Single Premium 10-Year Temporary Annuity \\
(Net) Single Premium Life Annuity \\
\\
IV. Development of Net Annual Premiums / 22 \\
Extension of Use of Discount \\
(Net) Annual Premium, Whole Life Policy \\
(Net) Annual Premium, 10-Payment Life \\
(Net) Annual Premium, 10-Year Term \\
(Net) Annual Premium, 10-Year Endowment \\
The ``Practical' and `More Exact' Premium \\
Alternative Method of Obtaining Net Annual Premiums \\
Problems \\
\\
V. More About Premiums / 30 \\
The Yearly Renewable Term Policy \\
Loading the Premium \\
Partial or Instalment Premiums \\
Problems \\
\\
VI. Net Level Premium Reserves / 34 \\
10-Year Term Policy \\
10-Year Endowment Policy \\
Whole Life Policy \\
10-Payment Life Policy \\
Yearly Renewable Term \\
Problems \\
\\
VII. Reserve Fund, Mortality Fund and Cost of Insurance
/ 44 \\
Reserve Credit \\
Payment of Death Claims \\
The Reserve Fund and Mortality Fund \\
Cost of Insurance \\
Problems \\
\\
VIII. Full Preliminary Term Valuation \\
Gross Level Annual Premiums \\
Preliminary Term \\
Terminal Reserves Policy P \\
Full Preliminary Term Valuation \\
Modified Preliminary Term \\
Problems \\
\\
IX. Initial, Mean, and Calendar Year Reserves \\
\\
Initial Reserve \\
Mean Reserve \\
Calendar Year Reserve \\
Initial and Mean Reserves, F.P.T. Basis \\
Problems \\
\\
X. Non-Foreiture Options; Cash VALUE; Paid-Up and
Extended Insurance; Loan Value / 61 \\
The Cash Value \\
What Happens When Policy is Surrendered \\
Non-Forfeiture Options (Option 1, Option 2, and Option
3) \\
Cash Values under F.P.T. Basis of Valuation \\
Loan Values \\
Problems \\
\\
XI. Profits to a Life Insurance Company / 67 \\
Actual and Expected Mortality \\
Actual and Expected Expenses \\
Actual and Expected Interest \\
Gain and Loss for the Year \\
Arithmetical Statement of Financial Status \\
Problems \\
\\
XII. Distribution of Surplus --- Dividend Options / 73
\\
Allocating Surplus to Policyholders \\
Share of Gain from Mortality, Loading and Interest \\
Dividend Formula \\
Variations in Dividend Formula \\
Dividend Options (Options 1 to 6) \\
Withdrawing the Dividend or Surrendering the Dividend
Credit \\
Problems \\
\\
XIII. Further Problems in Interest and Discount / 79
\\
Fundamental Principle \\
Annuity Certain (Present Value of) \\
Annuity Certain (Amount of) \\
Interest Compounded Oftener than Once a Year \\
Value of a Bond \\
Problems \\
\\
XIV. Deferred Annuity --- Certain and Continuous
Annuity --- Optional Modes of Settlement / 91 \\
Deferred Life Annuity \\
``Combination'' Annuity Contract \\
Optional Modes of Settlement \\
Problems \\
\\
XV. Mortality Rates and Mortality Tables / 94 \\
Rate of Mortality \\
Building the Table \\
Changing Number at Initial Age \\
Selection and Select Tables \\
Indicating the Age (for Mortality Analysis) \\
Select Table \\
Ultimate Tables and Select and Ultimate Tables \\
Problems \\
\\
XVI. More About Reserves / 103 \\
Fundamental Principle Amended \\
Corollary to Amended Principle \\
Prospective and Retrospective Method of Obtaining the
Reserve \\
Reserves on Single Premium Policies \\
Reserves on Substandard Policies \\
Percentage Mortality Rating Table \\
Problems. \\
\\
XVII. Modified Preliminary Term Valuation / 109 \\
M.P.T. Basis of Valuation \\
Method A: M.P.T. Whole Life Basis \\
Method B: M.P.T. 20-Payment Life Basis \\
Method C: M.P.T. Original Plan Basis \\
Illinois Standard System of Valuation \\
Ohio Standard System of Valuation \\
New Jersey Standard System of Valuation \\
Problems \\
\\
Appendices: \\
I. Miscellaneous Examples / 118 \\
II. Chart 3B --- Single Premium Life Insurance (Age 35)
/ 121 \\
III. Chart 5B -- Single Premium Life Annuity (Age 35) /
122 \\
IV. Answers to Problems and Miscellaneous Examples 123
\\
Index / 127",
usmarc540 = "[US Library of Congress record]: We have determined
this item to be in the public domain according to US
copyright law through information in the bibliographic
record and/or US copyright renewal records. The digital
version is available for all educational uses
worldwide.",
}
@Article{Phillips:1936:BC,
author = "E. W. Phillips",
title = "Binary calculation",
journal = j-J-INST-ACTUARIES,
volume = "67",
number = "??",
pages = "187--221",
year = "1936",
ISSN = "0020-2681",
bibdate = "Wed Oct 13 11:33:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Actuaries",
}
@Misc{Zuse:1936:VSD,
author = "K. Zuse",
title = "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
Rechnungen mit Hilfe von Rechenmaschinen}. ({German})
[{Procedure} for automatic execution of calculations by
calculating machines]",
howpublished = "German patent application Z23624.",
day = "11",
month = apr,
year = "1936",
bibdate = "Wed Oct 13 11:22:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Escott:1937:QDN,
author = "E. B. Escott",
title = "Questions, Discussions, and Notes: Rapid Method for
Extracting a Square Root",
journal = j-AMER-MATH-MONTHLY,
volume = "44",
number = "10",
pages = "644--646",
month = dec,
year = "1937",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:44 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Book{Millikan:1937:MMP,
author = "Robert A. Millikan and Duane E. Roller and Earnest C.
Watson",
title = "Mechanics, Molecular Physics, Heat, and Sound",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "????",
year = "1937",
bibdate = "Mon May 21 17:16:04 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Appendix: Significant Figures and Notations by
Powers of Ten.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 22]{Carter:2013:ESF}.",
}
@MastersThesis{Shannon:1937:SAR,
author = "Claude Elwood Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
type = "{Master of Science}",
school = "Department of Electrical Engineering, MIT",
address = "Cambridge, MA, USA",
pages = "72",
day = "10",
month = aug,
year = "1937",
bibdate = "Thu Nov 18 10:35:20 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Not submitted until 1940",
URL = "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
acknowledgement = ack-nhfb,
author-dates = "April 30, 1916--February 24, 2001",
remark = "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
[Shannon] also had the insight, like Atanasoff, that
the binary arithmetic that relay switches represented
would simplify information systems. His master's
thesis, written when he as twenty-one and published
when he was twenty-two, is considered to be one of the
most important, if not the most important, master's
thesis of the twentieth century.''\par
Pages 59--61 of the thesis are a section called
``Electric Adder to the Base Two'', and pages 62--68,
``A Factor Table Machine'', describe a machine that
will print a table of factors and primes of all the
integers from 1 to 100,000,000. Shannon notes on page
68: ``As to the practicality of such a device, it might
be said that J. P. Kulik spent 20 years in constructing
a table of primes up to 100,000,000 and when finished
it was found to contain so many errors that it was not
worth publishing. The machine described here could
probably be made to handle 5 numbers per second so that
the table would require only about 2 months to
construct.''",
}
@Article{Benford:1938:LAN,
author = "Frank Benford",
title = "The Law of Anomalous Numbers",
journal = j-PROC-AMER-PHIL-SOC,
volume = "78",
number = "4",
pages = "551--572",
month = mar,
year = "1938",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Thu Feb 15 16:28:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
abstract = "It has been observed that the first pages of a table
of common logarithms show more wear than do the last
pages, indicating that more used numbers begin with the
digit 1 than with the digit 9. A compilation of some
20,000 first digits taken from widely divergent sources
shows that there is a logarithmic distribution of first
digits when the numbers are composed of four or more
digits. An analysis of the numbers from different
sources shows that the numbers taken from unrelated
subjects, such as a group of newspaper items, show a
much better agreement with a logarithmic distribution
than do numbers from mathematical tabulations or other
formal data. There is here the peculiar fact that
numbers that individually are without relationship are,
when considered in large groups, in good agreement with
a distribution law---hence the name ``Anomalous
Numbers.''\par
A further analysis of the data shows a strong tendency
for bodies of numerical data to fall into geometric
series. If the series is made up of numbers containing
three or more digits the first digits form a
logarithmic series. If the numbers contain only single
digits the geometric relation still holds but the
simple logarithmic relation no longer applies.\par
An equation is given showing the frequencies of first
digits in the different orders of numbers 1 to 10, 10
to 100, etc.\par
The equation also gives the frequency of digits in the
second, third + place of a multi-digit number, and it
is shown that the same law applies to
reciprocals.\par
There are many instances showing that the geometric
series, or the logarithmic law, has long been
recognized as a common phenomenon in factual literature
and in the ordinary affairs of life. The wire gauge and
drill gauge of the mechanic, the magnitude scale of the
astronomer and the sensory response curves of the
psychologist are all particular examples of a
relationship that seems to extend to all human affairs.
The Law of Anomalous Numbers is thus a general
probability law of widespread application.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was
published in 1938 in a journal of rather limited
circulation and not usually read by mathematicians. It
so happened that it was immediately followed in the
same issue by a physics paper which became of some
importance for secret nuclear work during World War II
[H. A. Bethe, M. E. Rose, and L. P. Smith, `The
Multiple Scattering of Electrons', Proc. Amer. Phil.
Soc. 78(4), 573--585 (1938)]. That is why Benford's
paper caught the attention of physicists in the early
1940's and was much discussed. This led to the notes in
Nature by Goudsmit and Furry [3] and Furry and Hurwitz
[4] containing an effort to explain Benford's law. We
considered it at that time merely a welcome diversion
and did not expect that over thirty papers would be
devoted to this subject in subsequent years.'' The 2006
bibliography \cite{Hurlimann:2006:BLB} cites 325
publications about Benford's Law.",
}
@PhdThesis{Couffignal:1938:AMA,
author = "L. Couffignal",
title = "Sur l'analyse m{\'e}canique. Application aux machines
{\`a} calculer et aux calculs de la m{\'e}canique
c{\'e}leste. ({French}) [{On} mechanical analysis.
Application to calculating machines and to calculation
in celestial mechanics]",
publisher = "Gauthier-Villars",
school = "Facult{\'e} des Sciences de Paris",
address = "Paris, France",
year = "1938",
bibdate = "Wed Oct 13 11:17:22 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
Translated by Mr. R. Basu.",
acknowledgement = ack-nhfb,
language = "French",
}
@Book{Hardy:1938:ITN,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 403",
year = "1938",
LCCN = "QA241 .H28",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Shannon:1938:SAR,
author = "Claude E. Shannon",
title = "A Symbolic Analysis of Relay and Switching Circuits",
journal = j-TRANS-AMER-INST-ELEC-ENG,
volume = "57",
number = "??",
pages = "713--723",
month = dec,
year = "1938",
CODEN = "TAEEA5",
ISSN = "0096-3860",
bibdate = "Sat Nov 20 08:54:12 2010",
bibsource = "http://www2.research.att.com/~njas/doc/shannonbio.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Institute of Electrical
Engineers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
remark = "This is Shannon's first published paper (his Master's
thesis). In 1940, it received the Alfred Noble Prize of
the combined engineering societies of the United
States, an award given each year to a person not over
thirty for a paper published in one of the journals of
the participating societies. H. H. Goldstine
\cite{Goldstine:1972:CPN} called this work ``one of the
most important master's theses ever written \ldots{} a
landmark in that it helped to change digital circuit
design from an art to a science.''",
}
@Article{Jager:1939:AAD,
author = "Robert Jager and Boyd C. Patterson",
title = "The Artificial Arithmetick in Decimals of {Robert
Jager} ({London}, 1651)",
journal = j-ISIS,
volume = "31",
number = "1",
pages = "25--31",
month = nov,
year = "1939",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:26:49 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302217;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
URL = "http://www.jstor.org/stable/226014",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{K:1939:BRBd,
author = "M. G. K.",
title = "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
George S. Terry}",
journal = j-J-R-STAT-SOC,
volume = "102",
number = "2",
pages = "299--300",
month = "????",
year = "1939",
DOI = "https://doi.org/10.2307/2980013",
ISSN = "0952-8385",
bibdate = "Sat Jan 24 11:18:08 MST 2015",
bibsource = "http://www.jstor.org/stable/i349540;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
URL = "http://www.jstor.org/stable/2980013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society",
journal-URL = "http://www.jstor.org/journals/09528385.html",
}
@TechReport{Atanasoff:1940:CMS,
author = "J. V. Atanasoff",
title = "Computing machine for the solution of large systems of
linear algebraic equations",
type = "Unpublished memorandum",
institution = "Iowa State College",
address = "Ames, IA, USA",
month = aug,
year = "1940",
bibdate = "Wed Oct 13 11:36:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Misc{Bush:1940:AM,
author = "V. Bush",
title = "Arithmetical Machine",
howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
Samuel, 1939--1940",
year = "1940",
bibdate = "Wed Oct 13 11:37:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
Copyright interest in the unpublished writings of
Vannevar Bush has been dedicated to the public.",
acknowledgement = ack-nhfb,
}
@TechReport{Stibitz:1940:C,
author = "G. R. Stibitz",
title = "Computer",
type = "Unpublished memorandum",
institution = "Bell Telephone Laboratories",
address = "New York, NY, USA",
year = "1940",
bibdate = "Wed Oct 13 11:30:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@MastersThesis{Berry:1941:DED,
author = "Clifford Edward Berry",
title = "Design of electrical data recording and reading
mechanism",
type = "{M.S.} thesis",
school = "Iowa State College",
address = "Ames, IA, USA",
pages = "32",
year = "1941",
bibdate = "Thu Nov 18 11:18:18 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1918--1963",
historical-note = "From
http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:
``John Vincent Atanasoff received his M.S. (1926) in
Mathematics from Iowa State College (University) and
received his Ph.D. (1930) in Theoretical Physics from
the University of Wisconsin-Madison. He returned to
Iowa State in 1930 as Assistant Professor in
mathematics and physics and was promoted to Associate
Professor (1936). Atanasoff began developing concepts
for an electronic computing machine in 1937. It was
shortly thereafter that he, along with graduate student
Clifford Berry, started work on the world's first
electronic digital computer. The computer would later
be named the Atanasoff-Berry Computer (ABC).
Work on the machine stopped at the start of World War
II in 1941 and the ABC was never patented. Atanasoff
and Berry were both called to support the war effort
and left Iowa State. By the end of the decade, the ABC
was removed from the basement of Physics Hall and
dismantled.
Atanasoff and the ABC were part of a major court case
between Honeywell, Inc. and Sperry Rand Corporation
which occurred 1967-1973. The case involved the ENIAC
patent which covered basic ownership rights to the
design of electronic digital computers. During the
trial, the judge concluded that the invention of the
ENIAC was derived from the work of John Vincent
Atanasoff at Iowa State University.
A replica of the Atanasoff-Berry Computer was completed
and unveiled to the public in 1996. The ABC replica was
constructed by a team of Iowa State scientists at the
Ames Laboratory and was exhibited at museums throughout
the country over the next several years.''",
remark = "This thesis may be one of the earliest surviving
records of the ABC computer built by John Atanasoff and
Clifford Berry in the late 1930s. The one-of-a-kind ABC
was destroyed in 1948, and most of its parts were lost.
Also cited in ``Charles W. Bradley Collection on the
ENIAC Trial, 1930--1966'', (found in
http://discover.lib.umn.edu/): CWB as an attorney for
the group retained by Honeywell in the Honeywell v.
Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}
@Article{Lancaster:1942:MME,
author = "Otis E. Lancaster",
title = "Machine Method for the Extraction of Cube Root",
journal = j-J-AM-STAT-ASSOC,
volume = "37",
number = "217",
pages = "112--115",
month = mar,
year = "1942",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:24 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314096;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
URL = "http://www.jstor.org/stable/2279437",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@TechReport{Mauchly:1942:UHS,
author = "J. W. Mauchly",
title = "The use of high speed vacuum tube devices for
calculating",
type = "Privately circulated memorandum",
institution = "Moore School of Electrical Engineering, University of
Pennsylvania",
address = "Philadelphia, PA, USA",
month = aug,
year = "1942",
bibdate = "Wed Oct 13 11:52:54 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@TechReport{Rajchman:1942:REP,
author = "J. A. Rajchman and G. A. Morton and A. W. Vance",
title = "Report on Electronic Predictors for Anti-Aircraft Fire
Control",
institution = "Research Laboratories, R.C.A. Manufacturing Company,
Inc.",
address = "Camden, NJ, USA",
month = apr,
year = "1942",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Article{Crawford:1943:DNS,
author = "W. S. H. Crawford",
title = "Discussions and Notes: Square Roots from a Table of
Cosines",
journal = j-AMER-MATH-MONTHLY,
volume = "50",
number = "3",
pages = "190--191",
month = mar,
year = "1943",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:57 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@TechReport{Rademacher:1943:MTI,
author = "Hans Rademacher",
title = "Mathematical Topics of Interest in {PX}, Part Two:
Summary of Articles Dealing with Rounding off Errors",
type = "{PX} Report",
number = "14",
institution = "Moore School of Electrical Engineering, Office of the
Director Records, University of Pennsylvania",
address = "Philadelphia, PA, USA",
day = "30",
month = nov,
year = "1943",
bibdate = "Fri Jun 15 17:39:28 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited on page 34 of Haigh, Priestley, and Rope,
\booktitle{ENIAC in Action} (2016) (ISBN 0-262-03398-4)
as an annotated bibliography of rounding errors.",
}
@Article{Goudsmit:1944:SFN,
author = "S. A. Goudsmit and W. H. Furry",
title = "Significant Figures of Numbers in Statistical Tables",
journal = j-NATURE,
volume = "154",
number = "3921",
pages = "800--801",
day = "23",
month = dec,
year = "1944",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/154800a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:57:19 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
abstract = "A rough qualitative explanation of this fact can
easily be given. If we consider tables in which the
entries become rarer the larger they are, we can draw
the obvious conclusion that in any interval, say,
between 10 and 99, or 10,000 and 99,999, there are more
entries on the small side than on the large side.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Furry:1945:DND,
author = "W. H. Furry and Henry Hurwitz",
title = "Distribution of Numbers and Distribution of
Significant Figures",
journal = j-NATURE,
volume = "155",
number = "3924",
pages = "52--53",
day = "13",
month = jan,
year = "1945",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/155052a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sun Sep 18 11:51:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@TechReport{vonNeumann:1945:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
institution = "University of Pennsylvania",
day = "30",
month = jun,
year = "1945",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
remark = "This is the report that got von Neumann's name
associated with the serial, stored-program, general
purpose, digital architecture upon which 99.99\% of all
computers today are based.",
xxnote = "Report prepared for U.S. Army Ordinance Department
under Contract W-670-ORD-4926. Reprinted in
\cite[pp.~177--246]{Stern:1981:EUA},
\cite[pp.~399--413]{Randell:1982:ODC},
\cite{vonNeumann:1993:FDR}, and
\cite{Laplante:1996:GPC}.",
}
@Article{Aiken:1946:ASC,
author = "H. H. Aiken and G. M. Hopper",
title = "The {Automatic Sequence Controlled Calculator}",
journal = j-ELECTR-ENG,
volume = "65",
number = "??",
pages = "384--391, 449--454, 522--528",
year = "1946",
CODEN = "ELENAC",
ISSN = "0095-9197",
bibdate = "Wed Oct 13 11:26:29 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Electrical Engineering (American Institute of
Electrical Engineers)",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
}
@TechReport{Burks:1946:PDL,
author = "Arthur W. Burks and Herman H. Goldstine and John von
Neumann",
title = "Preliminary discussion of the logical design of an
electronic computing instrument",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "42",
day = "28",
month = jun,
year = "1946",
MRnumber = "MR22442",
bibdate = "Wed Oct 13 08:17:48 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report to the U.S. Army Ordnance Department under
contract W-36-034-OKD-7481. Reprinted in \cite[Paper
2]{Taub:1963:JNCa}, \cite{Bell:1971:CSR}, \cite[pp.
221--259]{Swartzlander:1976:CDD} and \cite[pp.
97--146]{Aspray:1987:PJN}",
URL = "https://deepblue.lib.umich.edu/handle/2027.42/3972;
https://grch.com.ar/docs/p1/Apuntes/eng/Logical%20Design%20of%20an%20Electronic%20Computing%20Instrument.pdf",
acknowledgement = ack-nhfb,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
remark = "Discusses floating-point versus fixed-point
computation, and concludes that floating-point is
probably not justifiable. They wrote:\par
``There appear to be two major purposes in a `floating'
decimal point system both of which arise from the fact
that the number of digits in a word is a constant fixed
by design considerations for each particular machine.
The first of these purposes is to retain in a sum or
product as many significant digits as possible and the
second of these is to free the human operator from the
burden of estimating and inserting into a problem
`scale factors' --- multiplicative constants which
serve to keep numbers within the limits of the
machine.\par
There is, of course, no denying the fact that human
time is consumed in arranging for the introduction of
suitable scale factors. We only argue that the time so
consumed is a very small percentage of the total time
we will spend in preparing an interesting problem for
our machine. The first advantage of the floating point
is, we feel, somewhat illusory. In order to have such a
floating point, one must waste memory capacity which
could otherwise be used for carrying more digits per
word. It would therefore seem to us not at all clear
whether the modest advantages of a floating binary
point offset the loss of memory capacity and the
increased complexity of the arithmetic and control
circuits.''",
}
@Article{Cesareo:1946:RI,
author = "O. Cesareo",
title = "The Relay Interpolator",
journal = j-BELL-LABS-RECORD,
volume = "23",
number = "??",
pages = "457--460",
year = "1946",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:31:47 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Bell Laboratories Record",
}
@Article{Comrie:1946:BDC,
author = "L. J. Comrie",
title = "{Babbage}'s Dream Come True",
journal = j-NATURE,
volume = "158",
number = "4017",
pages = "567--568",
day = "26",
month = oct,
year = "1946",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/158567a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Aug 9 07:30:09 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The black mark earned by the government of the day
more than a hundred years ago for its failure to see
Charles Babbage's difference engine brought to a
successful conclusion has still to be wiped out. It is
not too much to say that it cost Britain the leading
place in the art of mechanical computing. Babbage then
conceived and worked on his `analytical engine',
designed to store numbers and operate on them according
to a sequence of processes conveyed to the machine by
cards similar to those used in the Jacquard loom. This,
however, was never completed.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "The title in the Nature archive index is completely
wrong: it says ``A Manual of Operation for the
Automatic Sequence Controlled Calculator''. After the
critical introduction [see the abstract], the article
goes on to describe IBM's gift to Harvard of the
Automatic Sequence Controlled Calculator. It reports
about the ASCC: ``The machine contains seventy-two
storage counters, capable of holding twenty-three
digits and a sign. \ldots{} When working to the full
23-figure capacity of the machine, multiplication takes
about six seconds, and division twice as long;
additions and subtractions are done at the rate of
three a second, whatever their length.'' It then
describes the computation of logarithms via the Taylor
series expansion of $ \log (1 + x) $, and reports that
it can do exponential, trigonometric, and hyperbolic
functions as well.",
}
@TechReport{Dreyer:1946:REM,
author = "H.-J. Dreyer and A. Walther",
title = "{Der Rechenautomat Ipm. Entwicklung Mathematischer
Instrumente in Deutschland 1939 bis 1945}. ({German})
[{The} {Ipm} Calculator. {The} development of
mathematical instruments in {Germany} 1939--1945]",
type = "{Bericht}",
number = "A3",
institution = "Institut f{\"u}r Praktische Mathematik, Technische
Hochschule",
address = "Darmstadt, West Germany",
day = "19",
month = aug,
year = "1946",
bibdate = "Wed Oct 13 11:20:15 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Goldstine:1946:ENI,
author = "H. H. Goldstine and Adele Goldstine",
title = "The {Electronic Numerical Integrator and Computer
(ENIAC)}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "2",
number = "15",
pages = "97--110",
month = jul,
year = "1946",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Goldstine:1947:PCPa,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 1",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPb,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 1",
type = "Technical report",
number = "1",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "69",
day = "1",
month = apr,
year = "1947",
MRnumber = "MR22443",
bibdate = "Wed Jun 01 17:41:33 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Report prepared for U.S. Army Ordnance Department
under contract W-36-034-OKD-7481. Reprinted in
\cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p.
278]{Knuth:1998:SA} cites pp. 142--151 of this report
as the first published treatment of double-precision
arithmetic on digital computers.",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPc,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 2",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPd,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 2",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPe,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 1}, Vol. 3",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Goldstine:1947:PCPf,
author = "Herman H. Goldstine and John von Neumann",
title = "Planning and coding of problems for an electronic
computing instrument. {Part 2}, Vol. 3",
type = "Technical report",
institution = inst-INST-ADV-STUDY,
address = inst-INST-ADV-STUDY:adr,
pages = "??",
month = "????",
year = "1947",
bibdate = "Fri Nov 16 16:35:14 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{HUCL:1946:MOA,
author = "{Harvard University. Computation Laboratory}",
title = "A Manual of Operation for the {Automatic Sequence
Controlled Calculator}",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "561",
year = "1946",
LCCN = "QA3 .H3 v.1",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Its Annals v. 1",
acknowledgement = ack-nhfb,
keywords = "electronic digital computers; mathematics ---
bibliography",
}
@TechReport{Turing:1946:PEC,
author = "A. M. Turing",
title = "Proposed Electronic Calculator",
type = "Report",
number = "E882",
institution = inst-NPL,
address = inst-NPL:adr,
pages = "48",
year = "1946",
bibdate = "Fri Nov 25 16:22:27 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.emula3.com/docs/Turing_Report_on_ACE.pdf",
acknowledgement = ack-nhfb,
author-dates = "Alan Mathison Turing (23 June 1912--7 June 1954)",
xxnote = "Reprinted in \cite{Turing:1972:MTO}.",
}
@Article{Juley:1947:BC,
author = "J. Juley",
title = "The Ballistic Computer",
journal = j-BELL-LABS-RECORD,
volume = "24",
number = "??",
pages = "5--9",
year = "1947",
CODEN = "BLRCAB",
ISSN = "0005-8564",
bibdate = "Wed Oct 13 11:32:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Bell Laboratories Record",
}
@InProceedings{Mauchly:1947:PPE,
author = "J. W. Mauchly",
booktitle = "{Proceedings of a Symposium on Large Scale Digital
Calculating Machinery, 7--10 January 1947}",
title = "Preparation of problems for {EDVAC}-type machines",
publisher = "Harvard University Press",
address = "Cambridge, MA, USA",
year = "1947",
bibdate = "Wed Oct 13 11:55:58 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in {\em Annals of the Computation Laboratory
of Harvard University}, {\bf 16}, 203--207 (1948).
Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Article{Richeson:1947:FAP,
author = "A. W. Richeson",
title = "The First Arithmetic Printed in {English}",
journal = j-ISIS,
volume = "37",
number = "1--2",
pages = "47--56",
month = may,
year = "1947",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:27:09 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302230;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1940.bib",
URL = "http://www.jstor.org/stable/226161",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
remark = "From the second paragraph: ``The earliest printed work
in English to discuss arithmetic, \booktitle{The
Myrrour of the World}, came from the press of William
Caxton in 1481. This work, however, contained only one
page devoted entirely to arithmetic. It is not until
1537 that we find another book printed in English
devoted entirely to arithmetic and dealing with the
Hindu--Arabic system of numbers. This is an anonymous
publication, from a press located at St. Albans, with
the title \booktitle{An Introduction for to Lerne to
Recken with the Pen, or with the Counters},'' This book
went through eight editions between 1537 and 1629. The
article quotes book sections on integer division.",
}
@Article{vonNeumann:1947:NIM,
author = "John von Neumann and Herman H. Goldstine",
title = "Numerical Inverting of Matrices of High Order",
journal = j-BULL-AMS,
volume = "53",
number = "11",
pages = "1021--1099",
month = nov,
year = "1947",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
MRclass = "65.0X",
MRnumber = "MR0024235 (9,471b)",
MRreviewer = "E. Bodewig",
bibdate = "Thu Nov 8 14:49:36 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/auto.diff.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
in \cite[vol. 5, pp. 479--557]{Taub:1961:JNCa}.",
URL = "http://projecteuclid.org/euclid.bams/1183511222",
ZMnumber = "0031.31402",
acknowledgement = ack-nhfb # " and " # ack-jg,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
kwds = "nla, linear system, rounding error",
referred = "[Markov1999a].",
remark = "This may be the first journal publication about the
use of double-precision arithmetic on computers, used
for the accumulation of inner products and matrix
products. On pp. 1035--1038, the authors show that when
the sum of $m$ products of two $s$-digit numbers is
accumulated in precision $ 2 s $, with rounding to $s$
digits only after the final sum is complete, then the
rounding error is essentially one unit in the last
place, instead of $m$ times that value. Cited in
\cite{Sterbenz:1974:FPC}.",
}
@Article{Alt:1948:BTLa,
author = "Franz L. Alt",
title = "A {Bell Telephone Laboratories}' Computing
Machine---{I}",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "3",
number = "21",
pages = "1--13",
month = jan,
year = "1948",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Tue Oct 13 08:44:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
note = "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Eckert:1948:EC,
author = "W. J. Eckert",
title = "Electrons and computation",
journal = j-SCI-MONTHLY,
volume = "67",
number = "5",
pages = "315--323",
month = nov,
year = "1948",
CODEN = "SCMOAA",
ISSN = "0096-3771 (print), 2327-7513 (electronic)",
bibdate = "Wed Oct 13 11:27:40 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "The Scientific Monthly",
journal-URL = "http://www.jstor.org/journal/sciemont",
}
@InProceedings{Rademacher:1948:AEP,
author = "Hans A. Rademacher",
title = "On the Accumulation of Errors in Processes of
Integration on High-Speed Calculating Machines",
crossref = "Anonymous:1948:PSL",
pages = "176--187",
year = "1948",
bibdate = "Mon Jun 18 11:03:56 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From page 186, remark by John W. Mauchly: ``I just
wanted to remark that this paper is probably one of the
first to appear as a result of the interaction between
computing machines and mathematics. I think many of us
have been looking forward with certainty to the day
when the advent of computing machines would influence
the course of mathematics, and there are still many
directions in which we can look forward to further such
impacts. This reaction is not, of course, one way.
Mathematics should also influence the computing
machine.''",
}
@TechReport{Tukey:1948:NSR,
author = "John W. Tukey",
title = "A note on the square-root iteration",
type = "SRG Memorandum report",
number = "10",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "18",
year = "1948",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Turing:1948:REM,
author = "A. M. Turing",
title = "Rounding-Off Errors in Matrix Processes",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
pages = "287--308",
month = sep,
year = "1948",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "MR0028100 (10,405c)",
MRreviewer = "E. Bodewig",
bibdate = "Sat Nov 19 12:09:58 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Turing:1992:PM} with summary and
notes (including corrections)",
URL = "http://turing.ecs.soton.ac.uk/browse.php/B/18",
ZMnumber = "0033.28501",
acknowledgement = ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
mynote = "The notes are not very good. They mainly correct
errors and fill in the gaps of derivations. Much better
would have been higher level comments from a numerical
analyst, e.g. on where Turing's ideas/predictions were
wrong.",
}
@Article{Williams:1948:EDC,
author = "F. C. Williams and T. Kilburn",
title = "Electronic digital computers",
journal = j-NATURE,
volume = "162",
number = "4117",
pages = "487--487",
day = "25",
month = sep,
year = "1948",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/162487a0",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Wed Oct 13 12:00:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "Letter submitted 3 August 1948. Describes a small
prototype digital computer with 32 31-bit words for
instructions, data, and working storage.",
}
@Article{Davis:1949:MM,
author = "Harry M. Davis",
title = "Mathematical Machines",
journal = j-SCI-AMER,
volume = "180",
number = "4",
pages = "28--39",
month = apr,
year = "1949",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0449-28",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Sat May 18 16:12:10 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1940.bib",
URL = "http://www.jstor.org/stable/24967160;
http://www.nature.com/scientificamerican/journal/v180/n4/pdf/scientificamerican0449-28.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
remark = "Description of counting devices before 1950, including
an introduction to the binary number system.",
}
@Article{Hartree:1949:NSR,
author = "Douglas R. (Douglas Rayner) Hartree",
title = "Note On Systematic Roundoff Errors in Numerical
Integration",
journal = "Journal of Research of the National Bureau of
Standards",
volume = "42",
number = "??",
pages = "62--??",
month = "????",
year = "1949",
bibdate = "Wed Feb 14 19:07:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Huskey:1949:PCP,
author = "H. D. Huskey",
title = "On the Precision of a Certain Procedure of Numerical
Integration",
journal = j-J-RES-NATL-BUR-STAND,
volume = "42",
number = "1",
pages = "57--62",
month = jan,
year = "1949",
CODEN = "JRNBAG",
DOI = "https://doi.org/10.6028/jres.042.005",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
bibdate = "Fri Aug 20 09:32:34 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With an appendix by Douglas R. Hartree.",
abstract = "An example of numerical integration is given that
shows very systematic effects in the less significant
digits. This lack of randomness gives rounding-off
errors that exceed the predicted standard deviation by
a factor of three. The example considered in this paper
shows that systematic rounding-off errors can occur in
numerical in integration, irrespective of the number of
digits kept in the contributions to the integral. In
the appendix this phenomenon is examined, and criteria
are set up to detect the cases in which it may arise to
a serious extent.",
acknowledgement = ack-nhfb,
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Tukey:1949:TRA,
author = "John W. Tukey and M. F. Freeman",
title = "Transformation related to the angular and the
square-root",
type = "SRG Memorandum report",
number = "24",
institution = inst-PRINCETON,
address = inst-PRINCETON:adr,
pages = "??",
year = "1949",
bibdate = "Tue May 15 08:00:09 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Stifler:1950:HSC,
editor = "W. W. {Stifler, Jr.}",
title = "High-speed computing devices",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xiii + 451",
year = "1950",
LCCN = "QA75 .E5",
bibdate = "Fri Aug 20 10:18:44 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Supervised by Charles Brown Tompkins and C. H.
Wakelin, Engineering Research Associates. The contents
of this volume were first assembled in the form of a
report to the Office of Naval Research, prepared under
a provision of contract N6-ONR-240, Task 1. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "computers",
}
@Article{Harrison:1950:BDC,
author = "J. O. {Harrison, Jr.}",
title = "Binary--Decimal Conversion on a Desk Calculator (in
Automatic Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "4",
number = "32",
pages = "231--234",
month = oct,
year = "1950",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2002500",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Wilkes:1950:E,
author = "M. V. Wilkes and W. Renwick",
booktitle = "{Report of a Conference on High Speed Automatic
Calculating Machines, 22--25 June 1949}",
title = "The {EDSAC}",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "9--11",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 12:00:41 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Worsley:1950:ED,
author = "B. H. Worsley",
booktitle = "Report of a Conference on High Speed Automatic
Calculating Machines, {22--25 June 1949}",
title = "The {EDSAC} demonstration",
publisher = "University Mathematical Laboratory",
address = "Cambridge, UK",
pages = "12--16",
month = jan,
year = "1950",
bibdate = "Wed Oct 13 11:39:09 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:1951:R,
author = "Anonymous",
title = "{RECIPROOT}",
howpublished = "Manchester University Electronic Computer Web
document.",
day = "9",
month = jul,
year = "1951",
bibdate = "Sat Aug 19 09:57:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "To calculate square roots and reciprocal square
roots.",
URL = "https://0x5f37642f.com/documents/ManchesterRecipRoot.pdf",
acknowledgement = ack-nhfb,
remark = "Code used on Ferranti Mark I.",
}
@Article{Booth:1951:SBM,
author = "A. D. Booth",
title = "A signed binary multiplication technique",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "4",
number = "2",
pages = "236--240",
month = "????",
year = "1951",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@InCollection{Brown:1951:HRR,
author = "G. W. Brown",
title = "History of {RAND}'s random digits",
crossref = "Householder:1951:MCM",
pages = "31--32",
year = "1951",
bibdate = "Sun Sep 18 12:02:43 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.rand.org/pubs/papers/2008/P113.pdf",
acknowledgement = ack-nhfb,
}
@Article{Gill:1951:PSS,
author = "S. Gill",
title = "A process for the step-by-step integration of
differential equations in an automatic digital
computing machine",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "47",
pages = "96--108",
year = "1951",
CODEN = "PCPSA4",
ISSN = "0008-1981",
bibdate = "Tue Aug 28 05:54:12 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
[8] noticed that the rounding error in the sum of two
numbers could be estimated by subtracting one of the
numbers from the sum, and he made use of this estimate
in a Runge--Kutta code in a program library for the
EDSAC computer.''",
}
@Article{Goldstine:1951:NIM,
author = "Herman H. Goldstine and John von Neumann",
title = "Numerical Inverting of Matrices of High Order. {II}",
journal = j-PROC-AM-MATH-SOC,
volume = "2",
pages = "188--202",
year = "1951",
CODEN = "PAMYAR",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
MRclass = "65.0X",
MRnumber = "MR0041539 (12,861b)",
MRreviewer = "F. J. Murray",
bibdate = "Thu Nov 8 14:49:46 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
in \cite[Paper 15, pp. 558--572]{Taub:1963:JNCa}.",
URL = "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
ZMnumber = "043.12301",
acknowledgement = ack-nhfb,
author-dates = "John von Neumann (28 December 1903--8 February 1957)",
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
}
@Article{MacMillan:1951:FDC,
author = "Donald B. MacMillan and Richard H. Stark",
title = "``Floating Decimal'' Calculation on the {IBM} Card
Programmed Electronic Calculator (in Automatic
Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "5",
number = "34",
pages = "86--92",
month = apr,
year = "1951",
CODEN = "MTTCAS",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Rademacher:1951:AEP,
author = "Hans Rademacher",
booktitle = "Proceedings of a Symposium on Large-scale Digital
Calculating Machinery",
title = "On the accumulation of errors in processes of
integration on high-speed calculating machines",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "176--185",
year = "1951",
bibdate = "Mon Jun 18 06:50:41 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Shirley:1951:BNB,
author = "John W. Shirley",
title = "Binary Numeration before {Leibniz}",
journal = j-AMER-J-PHYSICS,
volume = "19",
number = "8",
pages = "452--454",
month = nov,
year = "1951",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.1933042",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Sat Feb 8 10:29:20 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
abstract = "Though it is frequently stated that binary numeration
was first formally proposed by Leibniz as an
illustration of his dualistic philosophy, the
mathematical papers of Thomas Hariot (1560--1621) show
clearly that Hariot not only experimented with number
systems, but also understood clearly the theory and
practice of binary numeration nearly a century before
Leibniz's time.",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
remark = "Submitted 14 November 1950.",
}
@Book{Wilkes:1951:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
pages = "167",
year = "1951",
LCCN = "QA76.5 .W55 1951",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also second edition \cite{Wilkes:1957:PPE}, and
reprint \cite{Wilkes:1982:PPE}.",
acknowledgement = ack-nhfb,
tableofcontents = "Part I \\
Chapter 1. The Design of Programs for Electronic
Computing Machines / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machines / 2 \\
1-3 Description of the EDSAC / 3 \\
1-4 The EDSAC order code / 5 \\
1-5 Notes on the order code / 6 \\
1-6 The use of conditional orders / 7 \\
1-7 Modification of orders by the program / 8 \\
1-8 Multiaddress codes / 11 \\
1-9 Binary--decimal conversion / 12 \\
1-10 Checking facilities / 14 \\
Chapter 2. Input of Orders / 15 \\
2-1 Initial orders / 15 \\
2-2 Pseudo-orders / 17 \\
2-3 Examples / 17 \\
2-4 Control combinations / 17 \\
2-5 Starting the program / 18 \\
2-6 Use of code letters / 19 \\
2-7 Constants / 20 \\
2-8 Notation / 20 \\
Chapter 3. Subroutines and Parameters / 22 \\
3-1 Open subroutines / 22 \\
3-2 closed subroutines / 22 \\
3-3 preset parameters / 23 \\
3-4 program parameters / 23 \\
Chapter 4. Library Subroutines and their Use in
Constructing Programs / 25 \\
4-1 Library catalog / 25 \\
4-2 Input and output subroutines / 25 \\
4-3 Division subroutines / 27 \\
4-4 Trigonometrical and other functions / 27 \\
4-5 Quadrature / 27 \\
4-6 Assembly subroutines / 27 \\
4-7 Integration of differential equations / 32 \\
4-8 Processes, Interpretive subroutines / 34 \\
Chapter 5. Pitfalls / 38 \\
5-1 Proofreading of programs, points to be checked / 38
\\
5-2 Location of mistakes in a program / 39 \\
5-3 Counting operations / 41 \\
Chapter 6. Use of the EDSAC \& Its Associated Equipment
/ 42 \\
6-1 Tape Punching \& editing facilities / 42 \\
6-2 Storage of library subroutines / 43 \\
6-3 EDSAC organization / 43 \\
6-4 EDSAC controls / 43 \\
Chapter 7. Examples / 45 \\
7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
7-2 Example 2. Calculation of $\pi$ by evaluation of
definite integral / 48 \\
7-3 Alternative method for Example 2 / 52 \\
7-4 Example 2, with extra print orders for checking /
53 \\
7-5 Application of checking subroutine C11 to Example 2
/ 54 \\
7-6 Example of integration of an ordinary differential
equation / 46 \\
7-7 Evaluation of a definite integral / 61 \\
7-8 Program to facilitate the solution of algebraic
equation / 66 \\
Part II. Specifications of Library Subroutines / 72 \\
A. Subroutines to carry out floating point arithmetic /
73 \\
B. Subroutines to carry out arithmetical operations on
complex numbers / 78 \\
C. Checking subroutines / 79 \\
D. Division subroutines / 82 \\
E. Exponential subroutines / 83 \\
F. General routines relating to functions / 84 \\
G. Subroutines for integration of ordinary differential
equations / 86 \\
J. Subroutines for calculating special functions
[Legendre polynomials] / 88 \\
K. Subroutines for the summation of power series / 88
\\
L. Subroutines for evaluating logarithms / 91 \\
M. Miscellaneous subroutines / 91 \\
P. Print subroutines / 92 \\
Q. Quadrature subroutines / 95 \\
R. Input subroutines / 96 \\
S. Subroutines for evaluation of fractional powers / 98
\\
T. Subroutines for calculating trigonometrical
functions / 99 \\
U. Subroutines for counting operations / 101 \\
V1. Multiplication of vector by symmetric matrix / 102
\\
V2. Addition and subtraction of $n$ dimensional vectors
/ 103 \\
Part III. Programs of Selected Library Subroutines /
104 \\
Appendix A. Keyboard perforator code, etc. / 158 \\
Appendix B. The initial orders / 159 \\
Appendix C. Control combinations / 161 \\
Appendix D. Interpretive subroutines: example of
packing of orders / 162 \\
Appendix E. Methods of counting in a simple cycle / 164
\\
Index",
}
@InProceedings{Andrews:1952:RBL,
author = "E. G. Andrews",
editor = "J. C. McPherson",
booktitle = "Proceedings of the {AIEE-IRE '51}: Papers and
discussions presented at the December 10--12, 1951,
joint {AIEE-IRE} computer conference, Philadelphia,
{PA}: Review of electronic digital computers",
title = "A review of the {Bell Laboratories}' digital computer
developments",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "vi + 114",
pages = "101--105",
year = "1952",
DOI = "https://doi.org/10.1145/1434770.1434787",
LCCN = "????",
bibdate = "Fri Dec 03 09:17:58 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Bell Laboratories Model 1--5 relay computers; complex
fixed-point decimal arithmetic; complex floating-point
decimal arithmetic",
remark-1 = "From page 101: ``The Bell Telephone Laboratories
have designed and built seven digital
computers.''",
remark-2 = "From page 101: ``George R. Stibitz \ldots{} designed
and \ldots{} called it a ``complex number computer.''",
remark-3 = "From page 101: ``This computer operated with binary
coded decimal notation, with the decimal digits 0 to 9
being represented by the binary numbers 0011 to
1100. The input and output information consisted of
eight place numbers, but the calculator carried
operations out to ten places, the two extra places
being used to improve accuracy when accumulating the
results of several problems.''",
remark-4 = "From page 104: ``Besides these advantages in operation
ease, another has been developed but it has not yet
been incorporated into a computer as far as is
known. This is the self-correcting code for numerical
data. Dr. R. W. Hamming devised this principle of
coding. A computer with this feature would show an
unattended operation performance superior to anything
we know today.'' [Refers to ``Error Detecting and Error
Correcting Codes'', The Bell System Technical Journal
{\bf 29}(2) 147--160, April 1960,
doi:10.1002/j.1538-7305.1950.tb00463.x].",
}
@Article{Davis:1952:ARS,
author = "K. Davis and R. Biddulph and S. Balashek",
title = "Automatic Recognition of Spoken Digits",
journal = j-J-ACOUST-SOC-AM,
volume = "24",
number = "6",
pages = "637--642",
month = nov,
year = "1952",
CODEN = "JASMAN",
ISSN = "0001-4966",
ISSN-L = "0001-4966",
bibdate = "Fri Nov 28 16:38:51 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Journal of the Acoustical Society of America",
journal-URL = "http://scitation.aip.org/content/asa/journal/jasa",
}
@Article{Hammersley:1952:CSS,
author = "J. M. Hammersley",
title = "The computation of sums of squares and products on a
desk calculator",
journal = j-BIOMETRICS,
volume = "8",
number = "??",
pages = "156--168",
year = "1952",
CODEN = "BIOMB6",
DOI = "https://doi.org/10.2307/3001930",
ISSN = "0006-341X (print), 1541-0420 (electronic)",
ISSN-L = "0006-341X",
MRclass = "65.0X",
MRnumber = "48908",
MRreviewer = "E. Lukacs",
bibdate = "Thu Jun 25 17:01:03 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/biometrics1950.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Biometrics",
fjournal = "Biometrics",
journal-URL = "http://www.jstor.org/journal/biometrics",
}
@Article{Irani:1952:SMT,
author = "Rida A. K. Irani",
title = "A sexagesimal multiplication table in the {Arabic}
alphabetical system",
journal = j-SCRIPTA-MATH,
volume = "18",
number = "??",
pages = "92--93",
month = "????",
year = "1952",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
MRclass = "01.0X",
MRnumber = "49109",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0046.00102",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
ZBmath = "3070983",
}
@Article{Michaelson:1952:BA,
author = "R. L. Michaelson",
title = "Binary Arithmetic",
journal = j-INC-STAT,
volume = "3",
number = "1",
pages = "35--40",
month = feb,
year = "1952",
CODEN = "????",
DOI = "https://doi.org/10.2307/2986591",
ISSN = "1466-9404",
ISSN-L = "1466-9404",
bibdate = "Thu Jan 22 18:10:18 MST 2015",
bibsource = "http://www.jstor.org/stable/i349863;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib",
URL = "http://www.jstor.org/stable/2986591",
acknowledgement = ack-nhfb,
fjournal = "The Incorporated Statistician",
journal-URL = "http://www.jstor.org/journals/14669404.html",
}
@Article{Morrill:1952:SEM,
author = "C. D. Morrill and R. V. Baum",
title = "A Stabilized Electronic Multiplier",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-1",
number = "??",
pages = "52--59",
month = dec,
year = "1952",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}
@InProceedings{Sheldon:1952:ICP,
author = "J. W. Sheldon and L. Tatum",
booktitle = "Review of Electronic Digital Computers. {Joint
AIEE--IRE Computer Conference. 10--12 December 1951}",
title = "The {IBM} card-programmed electronic calculator",
publisher = "American Institute of Electrical Engineers",
address = "New York, NY, USA",
pages = "30--36",
year = "1952",
bibdate = "Wed Oct 13 11:28:45 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
}
@Article{Brooker:1953:FOE,
author = "R. A. Brooker and D. J. Wheeler",
title = "Floating Operations on the {EDSAC} (in Automatic
Computing Machinery; Discussions)",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "7",
number = "41",
pages = "37--47",
month = jan,
year = "1953",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1953-0052901-3",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
JSTOR database",
abstract = "The difficulties which arise when programming
calculations for large automatic calculating machines
which have a fixed decimal point are discussed. This
leads to a consideration of the possibility of using
floating decimal arithmetic for certain kinds of
calculations. A method by which floating decimal
arithmetic can be carried out with any fixed
decimal-point machine is outlined and the scheme
adopted for use with the EDSAC is described in
detail.",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "floating-point decimal arithmetic",
remark-01 = "From page 38: ``The problem [of programmer-controlled
numeric scaling] does not arise with machines designed
to operate directly with numbers expressed in the
floating radix form. Numbers in this form are
represented by $a \cdot r^p$. The first machine of this
kind was the Bell Telephone Laboratories Relay Computer
Model V(1). This is a decimal machine (that is, $r =
10$) in which $1 > |a| > 0.1$, $19 > p > -19$ and $a$
is expressed to an accuracy of seven significant
figures. Since this was completed all important relay
machines have been equipped with similar facilities. No
electronic machine of this kind has yet been built but
we would remark that in our opinion an electronic
machine provided with a floating point arithmetical
unit would be a powerful computing instrument even if
it had a relatively slow store, a magnetic drum, for
example.''",
remark-02 = "From page 39: ``Two long and two short storage
locations are set aside to form a kind of `arithmetical
unit.' One long location holds the numerical part of a
number and one short location holds the exponent.
Together they form the {\em floating decimal
accumulator}. In a similar fashion the other long
location and the other short location form the {\em
floating decimal register}.''",
remark-03 = "From page 40: ``the floating decimal accumulator is
then `cleared' by replacing the number held in it by
zero, that is, by the special number $010^{-63}$.''",
remark-04 = "From page 40: `The use of two separate storage
locations for the floating decimal accumulator allows
the range and accuracy of numbers held therein to be
greater than those held in a single storage location
elsewhere. This enables products to be accumulated
without loss of accuracy due to intermediate
rounding-off errors.''",
remark-05 = "From the conclusion on page 46: ``From a direct
comparison it would seem that the floating 'orders,'
other than those used for reading and writing, are
about 60 times as slow as the machine orders and hence
that a programme using the interpretive subroutine
would be slower by the same factor. This is not
altogether true because in such a programme fewer
orders' are needed than would otherwise be necessary as
there are no scale factors to deal with and the
techniques for counting and for the modification of
orders' have been streamlined. Moreover, the time taken
by the C auxiliaries is about the same as that taken by
the corresponding subroutine in fixed decimal-point
working. These factors vary from problem to problem but
our experience has shown that the reduction in speed
varies from about 20 to 1 to about 4 to 1. The
reduction of the time taken to code a problem has to be
experienced to be believed!''",
}
@Book{IBM:1953:POT,
author = "{IBM Corporation}",
title = "Principles of Operation: Type 701 and Associated
Equipment",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "103",
year = "1953",
bibdate = "Wed Sep 14 23:17:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Samelson:1953:ORR,
author = "Klaus Samelson and Friedrich L. Bauer",
title = "{Optimale Rechengenauigkeit bei Rechenanlagen mit
gleitendem Komma}. ({German}) [{Optimal} calculation
accuracy for calculators with a floating point]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "4",
number = "4",
pages = "312--316",
month = jul,
year = "1953",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/bf02074638",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
bibdate = "Sun Aug 16 18:04:35 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Digital automatic computing machines with floating
binary point are investigated with respect to their
accuracy. It is concluded that special devices can be
designed without difficulty, which guarantee the
highest accuracy obtainable with a fixed number of
digits. For binary computers, a modification of the
usual conversion routine is necessary, which is
discussed in detail.",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik
= Journal of Applied Mathematics and Physics}",
journal-URL = "http://link.springer.com/journal/33",
keywords = "number base conversion",
language = "German",
}
@InCollection{Stiefel:1953:MCA,
author = "E. Stiefel",
booktitle = "Les machines {\`a} calculer et la pens{\'e}e humaine",
title = "La machine {\`a} calculer arithm{\'e}tique ``{Z4}'' de
l'{Ecole} {Polytechnique} {F}{\'e}d{\'e}rale {\`a}
{Zurich} ({Suisse}) et son application {\`a} la
r{\'e}solution d'une {\'e}quation aux d{\'e}riv{\'e}es
partielles de type elliptique. ({French}) [{The}
arithmetic calculator ``{Z4}'' of the {Swiss Federal
Polytechnical University in Zurich (Switzerland)} and
its application to the solution of an elliptical type
partial derivative equation]",
publisher = "Centre National de la Recherche Scientifique",
address = "Paris, France",
pages = "33--40",
year = "1953",
MRclass = "65.0X",
MRnumber = "0066093",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Colloques internationaux du Centre National de la
Recherche Scientifique, no 37",
acknowledgement = ack-nhfb,
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
language = "French",
}
@Article{Backus:1954:ISS,
author = "J. W. Backus",
title = "The {IBM 701 Speedcoding} System",
journal = j-J-ACM,
volume = "1",
number = "1",
pages = "4--6",
month = jan,
year = "1954",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf",
abstract = "The IBM 701 Speedcoding System is a set of
instructions which causes the 701 to behave like a
three-address floating point calculator. Let us call
this the Speedcoding calculator. In addition to
operating in floating point, this Speedcoding
calculator has extremely convenient means for getting
information into the machine and for printing results;
it has an extensive set of operations to make the job
of programming as easy as possible. Speedcoding also
provides automatic address modification, flexible
tracing, convenient use of auxiliary storage, and
built-in checking.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Manual{Burroughs:1954:DH,
author = "{Burroughs Corporation.ElectroData}",
title = "Datatron handbooks",
organization = "The Division",
address = "Pasadena, CA, USA",
year = "1954",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "12 volumes in 1.",
acknowledgement = ack-nhfb,
keywords = "Datatron (Computer)",
remark = "Datatron programming and coding manual --- Datatron
operation manual --- Central computer handbook ---
Paper tape system handbook --- Card converter Model 500
handbook --- Magnetic tape system handbook ---
Cardatron system handbook --- Model 560 DATAFILE
handbook --- Control console and consolette handbook
--- Floating point control unit handbook --- External
switching unit handbook --- Tape preparation unit
handbook.",
}
@Article{Freeman:1954:TSA,
author = "H. Freeman and E. Parsons",
title = "Time-Sharing Analog Multiplier ({TSAM})",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-3",
number = "1",
pages = "11--17",
month = mar,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Jul 15 15:20:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
remark = "Cited in US Patent 3,043,516 (10 July 1962): Time
Summing Device for Division, Multiplication, Root
Taking and Interpolation, by Harold W. Abbott and
Vernon P. Mathis.",
}
@Article{Gorn:1954:AAC,
author = "Saul Gorn",
title = "The Automatic Analysis and Control of Computing
Errors",
journal = j-J-SIAM,
volume = "2",
number = "2",
pages = "69--81",
month = jun,
year = "1954",
CODEN = "JSIMAV",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
journal-URL = "http://epubs.siam.org/loi/smjmap.1",
}
@Article{Kovach:1954:AMU,
author = "L. D. Kovach and W. Comley",
title = "An Analog Multiplier Using Thyrite",
journal = j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
volume = "EC-3",
number = "2",
pages = "42--45",
month = jun,
year = "1954",
CODEN = "????",
ISSN = "????",
bibdate = "Sun Jul 17 09:57:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the I.R.E. Professional Group on
Electronic Computers",
}
@Article{Mayer:1954:ODF,
author = "M. A. Mayer and B. M. Gordon and R. N. Nicola",
title = "An operational digital feedback divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-3",
number = "1",
pages = "17--20",
month = mar,
year = "1954",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Sun Jul 17 09:52:58 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Moshman:1954:GPR,
author = "Jack Moshman",
title = "The Generation of Pseudo-Random Numbers on a Decimal
Calculator",
journal = j-J-ACM,
volume = "1",
number = "2",
pages = "88--91",
month = apr,
year = "1954",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 00:18:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floating-point arithmetic",
}
@Article{Clenshaw:1955:NSC,
author = "C. W. Clenshaw",
title = "A note on the summation of {Chebyshev} series",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
number = "51",
pages = "118--120",
year = "1955",
CODEN = "MTTCAS",
DOI = "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
ISSN = "0891-6837 (print), 2326-4853 (electronic)",
ISSN-L = "0891-6837",
MRclass = "65.0X",
MRnumber = "0071856",
bibdate = "Thu Feb 08 16:17:25 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
remark = "Hidden inside \cite{Brenner:1955:TNS}, but important
in its own right for commentary on the recursive
algorithm for summation of Chebyshev series, and a
brief analysis of its accuracy.",
}
@Article{Crockett:1955:GMM,
author = "J. B. Crockett and H. Chernoff",
title = "Gradient Methods of Maximization",
journal = j-PAC-J-MATH,
volume = "5",
number = "??",
pages = "33--50",
year = "1955",
CODEN = "PJMAAI",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
bibdate = "Fri Aug 20 08:54:24 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Eckert:1955:FFS,
author = "W. J. (Wallace John) Eckert and Rebecca Bradley
Jones",
title = "Faster, faster; a simple description of a giant
electronic calculator and the problems it solves",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "160",
year = "1955",
LCCN = "QA76 .E25",
bibdate = "Fri Aug 20 08:57:56 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1902--1971",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Computers",
xxaddress = pub-MCGRAW-HILL:adr,
xxpublisher = pub-MCGRAW-HILL,
}
@Book{Hastings:1955:ADC,
author = "Cecil B. {Hastings, Jr.} and Jeanne T. Hayward and
James P. {Wong, Jr.}",
title = "Approximations for Digital Computers",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "viii + 201",
year = "1955",
LCCN = "QA76 .H33",
bibdate = "Mon Sep 30 14:51:50 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Lenaerts:1955:ASR,
author = "E. H. Lenaerts",
title = "Automatic Square Rooting",
journal = j-ELECTRON-ENG,
volume = "27",
number = "??",
pages = "287--289",
month = jul,
year = "1955",
CODEN = "ELEGAP",
ISSN = "0013-4902",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Engineering",
}
@Article{Parsons:1955:SDC,
author = "Frances L. Parsons",
title = "A Simple Desk-Calculator Method for Checking Binary
Results of Digital Computer Arithmetic Operations",
journal = j-J-ACM,
volume = "2",
number = "3",
pages = "205--207",
month = jul,
year = "1955",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Nov 09 01:00:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Book{Richards:1955:AOD,
author = "Richard Kohler Richards",
title = "Arithmetic Operations in Digital Computers",
publisher = "D. Van Nostrand",
address = "New York, NY, USA",
pages = "iv + 397",
year = "1955",
LCCN = "QA75 .R5 1955",
bibdate = "Fri Nov 28 18:46:37 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Robertson:1955:TCM,
author = "J. E. Robertson",
title = "Two's Complement Multiplication in Binary Parallel
Digital Computers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-4",
number = "3",
pages = "118--119",
month = sep,
year = "1955",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/IRETELC.1955.5407911",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:10:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Stiefel:1955:RID,
author = "Eduard Stiefel",
title = "{Rechenautomaten im Dienste der Technik. Erfahrungen
mit dem Zuse-Rechenautomaten Z4}. ({German})
[{Calculating} machines in the service of technology.
{Experience} with the {Zuse}-calculator {Z4}]",
volume = "45",
publisher = "Westdeutscher Verlag",
address = "Cologne and Opladen, West Germany",
pages = "29--45; Diskussion 47--65",
year = "1955",
MRclass = "68.0X",
MRnumber = "0073311",
MRreviewer = "H. H. Goldstine",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Arbeitsgemeinschaft f{\"{u}}r Forschung des Landes
Nordrhein-Westfalen. Heft",
acknowledgement = ack-nhfb,
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
language = "German",
}
@Article{Estrin:1956:NHS,
author = "G. Estrin and B. Gilchrist and J. H. Pomerene",
title = "A Note on High-Speed Digital Multiplication",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "3",
pages = "140--140",
month = sep,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219936",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Hildebrand:1956:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to Numerical Analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "511",
year = "1956",
LCCN = "QA300 .H5",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "See also second edition
\cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.",
subject = "Numerical analysis",
tableofcontents = "1. Introduction (significant figures, random
errors, error bounds, etc.) \\
2. Interpolation with divided differences \\
3. Lagrangian methods \\
4. Finite-difference interpolation \\
5. Operations with finite differences \\
6. Numerical solution of ordinary differential
equations \\
7. Least-squares polynomial approximation \\
8. Gaussian quadrature and related topics \\
9. Approximations of various types \\
10. Numerical solution of equations \\
Appendix: Justification of the Crout reduction",
}
@TechReport{Lazarus:1956:MI,
author = "R. B. Lazarus and N. Metropolis and W. Orvedahl and J.
H. Richardson and W. {Spack, Jr.} and R. L. Bivins and
J. V. Caulfield and I. Kral and A. F. Malmberg and G.
T. McKinley and R. E. Williamson",
title = "{MANIAC II}",
type = "Report",
number = "LA-2083",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "54",
day = "1",
month = oct,
year = "1956",
bibdate = "Tue Mar 20 11:14:15 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sgp.fas.org/othergov/doe/lanl/lib-www/la-pubs/00320765.pdf",
acknowledgement = ack-nhfb,
remark-1 = "OSTI ID: 4382471",
remark-2 = "From page 9: ``The Maniac II \ldots{} has 12,288
48-bit words. It is asynchronous and has no clock. Its
speed is that appropriate to (1) a memory cycle of 8
microseconds, (2) a basic add time of 6 microseconds,
and (3) a shift time of about 1.3 microseconds per
stage. The average multiply time is about 160
microseconds.''",
remark-3 = "From page 14, the 48-bit floating-point word consists
of a 1-bit sign, a 3-bit exponent-of-65536, a 1-bit
sign of the exponent, and a 43-bit fraction in [0,1).
The range of nonzero numbers is (0x1p-155, 0x1p112), or
roughly (2e-47, 5e33). The report notes: ``Although
such a large base implies of possibility of as many as
15 lead[ing] zeros, the large word size of 48 bits
guarantees adequate significance.''",
}
@Article{Lilamand:1956:TDM,
author = "M. Lejet Lilamand",
title = "A Time-Division Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "1",
pages = "26--34",
month = mar,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219789",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Perkins:1956:EPC,
author = "Robert Perkins",
title = "{EASIAC}, {A} Pseudo-Computer",
journal = j-J-ACM,
volume = "3",
number = "2",
pages = "65--72",
month = apr,
year = "1956",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 04 23:46:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the primary functions of the MIDAC installation
at the University of Michigan is the instruction of
beginners in the various aspects of digital machine use
including programming and coding. \ldots{} In
conducting these courses it was soon found to be
extremely difficult, in five or six instruction
periods, to bring a complete newcomer up to the point
where he can code and check out on MIDAC anything more
than a rather trivial routine. As might be expected the
difficulty centers around problems of scaling,
instruction modification and binary representation.
\ldots{} To alleviate these problems it was decided
that a new computer was needed: one designed to make
programming easier. At the cost of some of MIDAC's
speed and capacity plus two or three man-months of
programming time EASIAC, the EASy Instruction Automatic
Computer, was realized as a translation-interpretation
program in MIDAC.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "decimal floating-point arithmetic",
remark = "Early example of a decimal floating-point machine.",
}
@Article{Robertson:1956:NCD,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "??",
pages = "65--73",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 09 19:14:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Stegun:1956:PC,
author = "Irene A. Stegun and Milton Abramowitz",
title = "Pitfalls in computation",
journal = "Journal of the Society for Industrial and Applied
Mathematics",
volume = "4",
pages = "207--219",
year = "1956",
bibdate = "Tue Aug 28 06:16:28 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Sydnor:1956:AMS,
author = "R. L. Sydnor and T. R. O'Meara and J. Strathman",
title = "Analog Multipliers and Squarers Using a Multigrid
Modulator",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "2",
pages = "82--85",
month = jun,
year = "1956",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1956.5219804",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 15:46:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Weinberger:1956:OMA,
author = "A. Weinberger and J. L. Smith",
title = "A One-Microsecond Adder Using One-Megacycle
Circuitry",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-5",
number = "??",
pages = "65--73",
month = jun,
year = "1956",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 09 19:38:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Wolontis:1956:CFD,
author = "V. M. Wolontis",
title = "A Complete Floating-Decimal Interpretive System for
the {IBM 650 Magnetic Drum Calculator}",
journal = "IBM Technical Newsletter",
volume = "??",
number = "11",
pages = "xxi + 63",
month = mar,
year = "1956",
bibdate = "Mon Sep 04 13:55:28 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://babel.hathitrust.org/cgi/pt?id=coo.31924003945759&seq=7",
acknowledgement = ack-nhfb,
}
@Book{Alt:1957:EDC,
editor = "Franz L. Alt",
title = "Electronic Digital Computers: Their Use in Science and
Engineering",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 335",
year = "1957",
bibdate = "Sun Jun 17 18:53:23 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Section 2.3 discusses number representation and
decimal versus binary arithmetic.",
xxnote = "Check page count: incomplete view in Google books.
Price bibliography says 1958.",
}
@Article{Ercoli:1957:EDO,
author = "Paolo Ercoli and Roberto Vacca",
title = "Errors Due to Overflow in Arithmetic Operations
Particularly as Regards {FINAC} Electronic Computer",
journal = j-J-ACM,
volume = "4",
number = "4",
pages = "450--455",
month = oct,
year = "1957",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Dec 08 09:28:48 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Ercoli:1960:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "floating-point arithmetic; overflow",
}
@Article{Gini:1957:SFD,
author = "Corrado Gini",
title = "Sulla frequenza delle cifre iniziali dei numeri
osservati. ({Italian}) [{On} the frequency of initial
digits of observed numbers]",
journal = "Bull. Inst. Internat. Stat.",
volume = "35",
number = "??",
pages = "57--76",
year = "1957",
bibdate = "Sun Sep 18 11:54:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "29th session, 2nd delivery, Rio de Janerio.",
URL = "",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
@Article{Herzel:1957:SDD,
author = "Amato Herzel",
title = "Sulla distribuzione della cifre iniziali dei numeri
statistici. ({Italian}) [{On} the frequency of initial
digits of statistical numbers]",
journal = "Atti dell XV e XVII Riunione, Societa Italiana di
Statistica",
volume = "??",
number = "??",
pages = "??--??",
year = "1957",
bibdate = "Sun Sep 18 12:00:07 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
language = "Italian",
}
@Article{Howe:1957:TRA,
author = "R. M. Howe and E. G. Gilbert",
title = "Trigonometric Resolution in Analog Computers by Means
of Multiplier Elements",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "2",
pages = "86--92",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221576",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Kalbfell:1957:EAM,
author = "David C. Kalbfell",
title = "An Electronic Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "2",
pages = "100--103",
month = jun,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221579",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Kogbetliantz:1957:CEN,
author = "E. G. Kogbetliantz",
title = "Computation of $ e^n $ for $ - \infty < n < + \infty $
Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "110--115",
month = apr,
year = "1957",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 06 18:04:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Lehman:1957:HSD,
author = "M. Lehman",
title = "High-Speed Digital Multiplication",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "3",
pages = "204--205",
month = sep,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5222025",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Luke:1957:CLZ,
author = "Y. L. Luke",
title = "On the Computation of $ \log {Z} $ and $ \arctan {Z}
$",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "11",
number = "??",
pages = "16--18",
month = "????",
year = "1957",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Metze:1957:SPO,
author = "G. Metze",
title = "A Study of Parallel One's Complement Arithmetic Units
with Separate Carry or Borrow Storage",
type = "Report",
number = "81",
institution = "Digital Computer Laboratory, University of Illinois",
address = "Urbana, IL, USA",
pages = "77",
year = "1957",
bibdate = "Thu Nov 18 09:07:07 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Flores' book \cite[p. 485]{Flores:1963:LCA} cites this
report, and says that its conclusion is that the
disadvantages of one's complement arithmetic outweigh
the advantages.",
}
@Article{Murphy:1957:PIA,
author = "R. W. Murphy",
title = "A Positive-Integer Arithmetic for Data Processing",
journal = j-IBM-JRD,
volume = "1",
number = "2",
pages = "158--170",
month = apr,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.12.0158",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "68.0X",
MRnumber = "18,939d",
bibdate = "Tue Sep 11 15:35:33 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735;
http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdf",
abstract = "It is hypothesized that positive numbers suffice for
the expression of quantities in accounting. New
arithmetic operations are devised that yield
non-negative results in computation, and the
applicability of these operations to data processing is
studied. These operations permit a wide variety of
functions to be computed with fewer and less complex
steps and imply the feasibility of constructing less
complex data-processing machines.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
reviewer = "C. C. Gotlieb",
}
@Article{Pawlak:1957:UEN,
author = "Z. Pawlak",
title = "Use of expansions with a negative basis in the
arithmometer of a digital computer",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "5",
number = "??",
pages = "232--236",
month = "????",
year = "1957",
bibdate = "Thu Nov 06 05:56:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@TechReport{Taylor:1957:CCA,
author = "W. Bruce Taylor",
title = "{COIN} (Compile-Interpreter): an automatic
programming, fixed and floating-point library of
subroutines for the {ERA} 1103 computer",
institution = "Operations Research Office, Johns Hopkins University",
address = "Bethesda, MD, USA",
pages = "43",
year = "1957",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Staff paper / Johns Hopkins University, Operations
Research Office; ORO-SP-32 Staff paper (Johns Hopkins
University. Operations Research Office); ORO-SP-32.",
acknowledgement = ack-nhfb,
keywords = "Military art and science --- Data processing.;
Military research --- Data processing.",
remark = "Cover title. ``Operating under contract with the
Department of the Army.'' ``Project COMPLAB.''
``October 1957.'' ORO-SP-32",
}
@Article{Wadel:1957:NBN,
author = "L. B. Wadel",
title = "Negative base number systems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "??",
pages = "123--??",
month = jun,
year = "1957",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Nov 06 05:53:55 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "negative base",
}
@Article{Walker:1957:EMA,
author = "R. M. Walker and D. E. Rosenheim and P. A. Lewis and
A. G. Anderson",
title = "An Experimental 50-Megacycle Arithmetic Unit",
journal = j-IBM-JRD,
volume = "1",
number = "3",
pages = "257--278",
month = jul,
year = "1957",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.13.0257",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:35:35 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687;
http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf",
abstract = "An experimental 50-megacycle arithmetic unit has been
built which performs a repetitive multiplication
program and checks the results for errors. The unit
uses pulse circuitry which has been developed to
perform digital operations at a 50-megacycle
pulse-repetition rate. This paper describes the
arithmetic system and the circuits which perform the
required functions. These circuits include a full
binary adder, a phase-locked frequency divider which
provides a 3.125-megacycle secondary timing source, a
reshaping and retiming circuit using germanium diodes
and capacitive storage, a high-speed shift register, a
high-speed indicator register, and a binary word
generator.\par
Various novel features of a digital system operating at
these high speeds are described. These include the use
of coaxial delay lines for the distribution of signals
and as storage elements, and the use of secondary
emission tubes in amplifier and multivibrator
circuits.\par
In a 50-megacycle system the interdependence of the
space and time dimensions is marked, and although this
introduces problems which are not ordinarily
encountered in computing systems, it may be used
advantageously to provide features such as the
variable-phase clock system used in the arithmetic
unit.\par
The performance and reliability of the arithmetic unit
are discussed as well as the reliability of the
components and circuits which make up the system.
Although the techniques and circuitry discussed here
have been applied only to a relatively simple
arithmetic unit, it is felt that they could be useful
in a variety of high-speed computing and measurements
applications.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Weibel:1957:EAM,
author = "Erich S. Weibel",
title = "An Electronic Analog Multiplier Using Carriers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-6",
number = "1",
pages = "30--34",
month = mar,
year = "1957",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1957.5221558",
ISSN = "0367-9950",
bibdate = "Thu Jun 30 16:07:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Wilkes:1957:PPE,
author = "Maurice V. Wilkes and David J. Wheeler and Stanley
Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xiv + 238",
year = "1957",
LCCN = "QA76.5 .W52 1957",
bibdate = "Mon Feb 10 09:42:47 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also first edition \cite{Wilkes:1951:PPE}.",
URL = "https://b-ok.org/book/3668116/b363ff",
acknowledgement = ack-nhfb,
remark-1 = "According to \cite{Anderson:2019:SAM}, this book
discusses the computation of integer population counts
on the Electronic Delay Storage Automatic Calculator
(EDSAC) computer using a recursive divide-and-conquer
algorithm. See also somewhat negative 1958 review by
Fernando J. Corbat{\'o}
\url{https://doi.org/10.1063/1.3062687}. Floating-point
arithmetic is discussed on pages 60, 90--91, and
135--137.",
remark-2 = "From page 5: ``Each storage location in the EDSAC
holds 17 binary digits. In words representing numbers,
the binary point is regarded as being to the right of
the extreme left-hand digit; this digit (the most
significant digit) is used as a sign indicator and is
referred to as the sign digit. \ldots{} the capacity of
the accumulator is 70 digits; there is, therefore,
plenty of room to hold the full 33-digit product of two
17-digit numbers. \ldots{} A negative number $-x$
(where $O < x \leq 1$) is represented by a $1$ in the
sign-digit position, followed by the digits of $(1 -
x)$; for example, $1.1100\ldots{}$ represents $-(1 -
3/4) = -1/4$. \ldots{} Another way of explaining the
representation of negative numbers is to regard the
sign digit as an ordinary numerical digit, and to say
that $-x$ is stored as the number $(2 - x)$. Note in
particular that $1.0000\ldots{}$ represents $-1$.''
[Page 59 calls this a {\em True complements}
representation, distinguished from one's complement.]",
remark-3 = "From page 35: ``The EDSAC has a facility which enables
an even-numbered storage location and the following
odd-numbered storage to be used as a single storage
location holding 35 binary digits.'' [This suggests the
word size in 18, not 17 as page 5 suggests. The
Wikipedia article on the EDSAC reports: ``The EDSAC's
main memory consisted of 1024 locations, though only
512 locations were initially installed. Each contained
18 bits, but the topmost bit was always unavailable due
to timing problems, so only 17 bits were used.'']",
remark-4 = "From page 36: ``The multiplier register of the
arithmetical unit is of sufficient capacity to hold a
long number, and the accumulator is of sufficient
capacity to hold the complete (69) binary digit
[including the sign bit] product of two long
numbers.''",
remark-5 = "From page 36: ``In some calculations, long numbers may
not provide sufficient precision. In such cases, the
programmer may make use of what is known as
double-length or double-precision working, in which two
long storage locations are used to hold the digits of a
single number.'' [this would be a quad-word number
holding 69 bits, including the sign bit.].",
remark-6 = "From page 60: ``\ldots{} two double-length numbers,
each stored in two locations, can be added and the
result put in two locations in the store, by means of
six orders''.",
remark-7 = "From page 90: ``Each number is expressed in the form
$a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
p < 63$ and is represented in the store by $a \cdot
2^{-11} + p \cdot 2^{-6}$.''",
remark-8 = "From page 91: ``Numbers are expressed in the form $a
\cdot 10^p$, where $a$ and $p$ are packed into a single
storage location. The number of digits defining $p$ may
be varied from 4 to 15 by means of a preset parameter,
so that a suitable value for the permissible range of
variation of numbers may be selected for a given
calculation.''",
remark-9 = "From page 91: ``Although the use of floating-point
operation can simplify the programmer's task by
relieving him of undue preoccupation with scaling, it
must not be thought that it solves all his
difficulties. In particular, the loss of significant
digits resulting from the subtraction of a number from
a nearly equal number can have serious consequences
unless proper precautions are taken.''",
tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
1-1 Introduction / 1 \\
1-2 Types of automatic computing machine / 1 \\
1-3 The EDSAC / 3 \\
1-4 Store / 5 \\
1-5 Arithmetical unit / 5 \\
1-6 Form of numbers in the machine / 5 \\
1-7 Form of orders in the machine / 6 \\
1-8 Storage of orders / 6 \\
1-9 Written form of orders / 7 \\
1-10 Some simple examples / 7 \\
Exercises A / 9 \\
1-11 Jump orders / 9 \\
Exercises B / 11 \\
1-12 Repeated groups of orders / 11 \\
1-13 The use of the B-register / 15 \\
Exercises C / 18 \\
1-14 Equivalence between orders and numbers;
pseudo-orders / 18 \\
1-15 Use of the arithmetical unit for constructing or
modifying orders / 20 \\
1-16 The mix order / 23 \\
Exercises D / 24 \\
CHAPTER 2. SUBROUTINES / 25 \\
2-1 Introduction / 25 \\
2-2 Relative numbering of addresses / 25 \\
2-3 Internal and external forms of orders / 26 \\
2-4 Reading of orders from the input tape / 28 \\
2-5 Open and closed subroutines / 29 \\
2-6 Entering and leaving a closed subroutine / 29 \\
2-7 Closed B subroutines / 30 \\
2-8 Closed A subroutines / 31 \\
2-9 Use of library subroutines / 32 \\
Exercises E / 33 \\
2-10 Long numbers / 35 \\
2-11 Some further orders in the order code / 36 \\
2-12 Scale factors / 38 \\
2-13 Control combinations / 39 \\
Exercises F / 40 \\
2-14 Relative addresses in control combinations / 41
\\
2-15 Extension of the use of relative addresses / 41
\\
2-16 Setting of the constants to be added by terminal
code letters / 43 \\
2-17 Complete table of terminal code letters / 44 \\
2-18 Parameters / 45 \\
2-19 Preset parameters / 46 \\
2-20 Program parameters / 46 \\
2-21 Standard procedure for setting preset parameters /
46 \\
2-22 Interpretive subroutines / 47 \\
Exercises G / 49 \\
CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
3-1 Introduction / 51 \\
3-2 Single-address codes / 52 \\
3-3 Multi-address codes / 53 \\
3-4 Multiplication and division / 56 \\
3-5 Source-destination codes / 57 \\
3-6 Representation of negative numbers / 59 \\
3-7 Miscellaneous facilities / 60 \\
3-8 Minimum-access coding / 61 \\
3-9 The evaluation of an order code / 63 \\
3-10 Use of an auxiliary store / 64 \\
CHAPTER 4. INPUT AND OUTPUT / 66 \\
4-1 Introduction / 66 \\
4-2 Input of numbers / 66 \\
4-3 Output of numbers / 67 \\
4-4 Input of orders / 69 \\
4-5 Recognition of the code letter S / 72 \\
4-6 Economy of input and output time / 72 \\
4-7 Some features of input systems used with other
machines / 73 \\
4-8 Punched tape / 73 \\
4-9 Punched cards / 75 \\
CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
5-1 Introduction / 80 \\
5-2 Library catalog / 80 \\
5-3 Input subroutines / 81 \\
5-4 Output subroutines / 81 \\
5-5 Division subroutines / 82 \\
5-6 Trigonometric and other functions / 82 \\
5-7 The economization of a power series by the use of
Chebyshev polynomials / 83 \\
5-8 Quadrature / 86 \\
5-9 Integration of ordinary differential equations / 87
\\
5-10 Library subroutines Gl2 and G13: Runge--Kutta
processes / 88 \\
5-11 The independent variable / 88 \\
5-12 Definition of the Runge--Kutta--Gill process / 89
\\
5-13 Taylor-series method / 90 \\
5-14 Interpretive subroutines / 90 \\
5-15 Floating-point subroutines / 90 \\
CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
6-1 Introduction / 92 \\
6-2 Proofreading of programs / 93 \\
6-3 Punching / 93 \\
6-4 Locating mistakes in a program- / 94 \\
6-5 Subroutines for checking programs / 96 \\
6-6 The development of a program / 97 \\
CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
/ 99 \\
EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
EXAMPLE 2 The evaluation of a definite integral / 102
\\
EXAMPLE 3 Integration of an ordinary differential
equation / 108 \\
EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
EXAMPLE 5 Evaluation of a definite integral / 118 \\
CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
8-1 Introduction / 126 \\
8-2 Conversion versus interpretation / 127 \\
8-3 Assembly of a program / 127 \\
8-4 Floating addresses / 129 \\
8-5 Formula recognition / 136 \\
Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
139 \\
CATEGORY A. Subroutines to carry out floating-point
arithmetic / 140 \\
CATEGORY B. Subroutines to perform arithmetical
operations on complex numbers / 142 \\
CATEGORY C. Error-diagnosis subroutines / 144 \\
CATEGORY D. Division subroutines / 146 \\
CATEGORY E. Exponential subroutines / 148 \\
CATEGORY F. General subroutines relating to functions /
148 \\
CATEGORY G. Subroutines for the integration of
differential equations / 150 \\
CATEGORY L. Subroutines for evaluating logarithms / 153
\\
CATEGORY M. Miscellaneous subroutines / 154 \\
CATEGORY N. Operations on double-length numbers / 156
\\
CATEGORY P. Print subroutines / 158 \\
CATEGORY Q. Quadrature subroutines / 162 \\
CATEGORY R. Input subroutines / 164 \\
CATEGORY s. Subroutines for evaluating fractional
powers / 168 \\
CATEGORY T. Subroutines for calculating trigonometric
functions / 169 \\
CATEGORY Z. Post-mortem routines / 170 \\
PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
SUBROUTINES / 173 \\
APPENDIX 1. Input and output codes of the EDSAC / 212
\\
APPENDIX 2. Order code and controls of the EDSAC / 214
\\
APPENDIX 3. The initial input routine of the EDSAC /
218 \\
APPENDIX 4. Control combinations / 221 \\
APPENDIX 5. Specimen solutions to programming exercises
/ 223 \\
BIBLIOGRAPHY / 233 \\
INDEX / 237",
}
@TechReport{Anonymous:1958:ARM,
author = "Anonymous",
title = "Analysis and research memorandum 294",
type = "{AR} Memo",
number = "294 (AD 207929)",
institution = "Massachusetts Institute of Technology, Naval
Supersonic Laboratory",
address = "Cambridge, MA, USA",
pages = "7",
day = "23",
month = oct,
year = "1958",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Error functions.; Floating-point arithmetic.",
}
@Article{Bemer:1958:MMS,
author = "Robert W. Bemer",
title = "A Machine Method for Square-Root Computation",
journal = j-CACM,
volume = "1",
number = "1",
pages = "6--7",
month = jan,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 15 18:35:46 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Bemer:1958:SMC,
author = "R. W. Bemer",
title = "A Subroutine Method for Calculating Logarithms",
journal = j-CACM,
volume = "1",
number = "5",
pages = "5--7",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Couleur:1958:BBD,
author = "J. F. Couleur",
title = "{BIDEC} --- a Binary-to-Decimal or Decimal-to-Binary
Converter",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
pages = "313--316",
year = "1958",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Fri Nov 28 16:28:12 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "decimal floating-point arithmetic",
}
@Article{Delury:1958:CAN,
author = "Daniel B. Delury",
title = "Computation with Approximate Numbers",
journal = j-MATH-TEACH,
volume = "51",
pages = "521--530",
month = nov,
year = "1958",
ISSN = "0025-5769 (print), 2330-0582 (electronic)",
bibdate = "Fri Nov 28 11:47:47 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Mathematics Teacher",
}
@Article{Ershov:1958:PAO,
author = "Andrei P. Ershov",
title = "On Programming of Arithmetic Operations",
journal = j-CACM,
volume = "1",
number = "8",
pages = "3--6",
month = aug,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:21 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Ershov58;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Ershov58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Ershov58",
}
@Article{Gower:1958:NIM,
author = "J. C. Gower",
title = "A Note on an Iterative Method for Root Extraction",
journal = j-COMP-J,
volume = "1",
pages = "142--143",
year = "1958",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:36:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Hammer:1958:PST,
author = "Franz Hammer",
title = "{Nicht Pascal sondern der T{\"u}binger Professor
Wilhelm Schickard erfand die Rechenmaschine!}.
({German}) [{Not Pascal}, but the {T{\"u}bingen}
professor {William Schickard}, invented the
calculator!]",
journal = "{B{\"u}romarkt}",
volume = "20",
number = "??",
pages = "1023--1025",
month = "????",
year = "1958",
ISSN = "0007-3148",
ISSN-L = "0007-3148",
bibdate = "Sat Jul 27 11:05:26 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Kogbetliantz:1958:CANa,
author = "E. G. Kogbetliantz",
title = "Computation of Arctan {$N$} for $ - \infty < {N} < +
\infty $ Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "1",
pages = "43--53",
month = jan,
year = "1958",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Kogbetliantz:1958:CANb,
author = "E. G. Kogbetliantz",
title = "Computation of Arcsin {$N$} for $ 0 < {N} < 1 $ Using
an Electronic Computer",
journal = j-IBM-JRD,
volume = "2",
number = "3",
pages = "218--222",
month = jul,
year = "1958",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Metropolis:1958:SDC,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Significant Digit Computer Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "4",
pages = "265--267",
month = dec,
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222657",
ISSN = "0367-9950",
bibdate = "Wed Feb 14 19:23:38 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222657",
abstract = "The usual floating point arithmetic makes error
analysis difficult. This paper describes an alternative
system which offers a means of analyzing floating point
calculations more effectively and which also possesses
certain advantages from an equipment standpoint.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "MANIAC III",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Robertson:1958:NCDa,
author = "J. E. Robertson",
title = "A new class of digital division methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "3",
pages = "88--92",
month = sep,
year = "1958",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Robertson:1958:NCDb,
author = "James E. Robertson",
title = "A New Class of Digital Division Methods",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "3",
pages = "218--222",
month = sep,
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222579",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222579",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Schmid:1958:TFQ,
author = "Hermann Schmid",
title = "A Transistorized Four-Quadrant Time-Division
Multiplier with an Accuracy of 0.1 Per Cent",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-7",
number = "1",
pages = "41--47",
month = mar,
year = "1958",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1958.5222094",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222094",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Sisson:1958:IDR,
author = "Roger L. Sisson",
title = "An Improved Decimal Redundancy Check",
journal = j-CACM,
volume = "1",
number = "5",
pages = "10--12",
month = may,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:22:12 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "As more emphasis is placed on improving the accuracy
of data fed into automatic computing systems, more
emphasis will be placed on redundancy checking of
predictable fields within the input. Two systems (at
least) of checking a field of decimal digits have been
proposed. In both of these it is assumed that the field
to be checked is all numeric and that the redundancy
must be of only one digit.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
oldlabel = "Sisson58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sisson58",
}
@Article{Tocher:1958:TMD,
author = "K. D. Tocher",
title = "Techniques of Multiplication and Division for
Automatic Binary Computers",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "11",
number = "3",
pages = "364--384",
month = "????",
year = "1958",
CODEN = "QJMMAV",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@Article{Wadey:1958:TSR,
author = "W. G. Wadey",
title = "Two Square-Root Approximations",
journal = j-CACM,
volume = "1",
number = "11",
pages = "13--14",
month = nov,
year = "1958",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Wadey58",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}
@Article{Ashenhurst:1959:UFP,
author = "Robert L. Ashenhurst and Nicholas Metropolis",
title = "Unnormalized Floating Point Arithmetic",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "415--428",
month = jul,
year = "1959",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/320986.320996",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "68.00",
MRnumber = "MR0105833 (21 \#4568)",
MRreviewer = "H. H. Goldstine",
bibdate = "Fri Dec 08 13:06:24 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
ZMnumber = "0121.12102",
abstract = "Algorithms for floating point computer arithmetic are
described, in which fractional parts are not subject to
the usual normalization convention. These algorithms
give results in a form which furnishes some indication
of their degree of precision. An analysis of one-stage
error propagation is developed for each operation; a
suggested statistical model for long-run error
propagation is also set forth.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Buchholz:1959:FFC,
author = "Wilfried Buchholz",
title = "Fingers or Fists? (The Choice of Decimal or Binary
Representation)",
journal = j-CACM,
volume = "2",
number = "12",
pages = "3--11",
month = "????",
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:28:45 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
oldlabel = "Buchholz59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
xxnote = "Check author first name: article has W. Buchholz; I
think it should be Werner, not Wilfried.",
}
@Article{Carr:1959:EAF,
author = "John W. {Carr III}",
title = "Error Analysis in Floating Point Arithmetic",
journal = j-CACM,
volume = "2",
number = "5",
pages = "10--15",
month = may,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:23 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Carr59a",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}
@InCollection{Carr:1959:PC,
author = "John W. {Carr III}",
editor = "Eugene M. Grabbe and Simon Ramo and Dean E.
Wooldridge",
booktitle = "Handbook of Automation, Computation, and Control",
title = "Programming and Coding",
publisher = pub-WILEY,
address = pub-WILEY:adr,
bookpages = "????",
year = "1959",
LCCN = "TJ213 .G72",
bibdate = "Fri Aug 20 08:41:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Chapter 2.",
acknowledgement = ack-nhfb,
remark = "1958--1961: Volume 1. Control fundamentals. Volume 2.
Computers and data processing. Volume 3. Systems and
components. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "automation; mathematics; computers; operations
research",
}
@Article{Daggett:1959:DBC,
author = "D. H. Daggett",
title = "Decimal-Binary Conversions in {CORDIC}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "335--339",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 08 08:14:00 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
keywords = "decimal floating-point arithmetic",
}
@Article{Ercoli:1959:BAD,
author = "Paolo Ercoli and Roberto Vacca",
title = "Binary Arithmetic for Discretely Variable Word Length
in a Serial Computer",
journal = j-CACM,
volume = "2",
number = "4",
pages = "13--15",
month = apr,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "ErcoliV59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ErcoliV59",
}
@Article{Forsythe:1959:RNR,
author = "George E. Forsythe",
title = "Reprint of a Note on Rounding-Off Errors",
journal = j-SIAM-REVIEW,
volume = "1",
number = "1",
pages = "66--67",
month = jan,
year = "1959",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1001011",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65.00",
MRnumber = "MR0099119 (20 \#5563)",
bibdate = "Thu Mar 27 09:04:24 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/1/1;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
ZMnumber = "0168.14002",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "numerical analysis; random rounding-off procedure",
onlinedate = "January 1959",
received = "7 February 1958",
remark = "From a footnote on the cover page: ``This note was
written in June 1950 at the National Bureau of
Standards, Los Angeles, and a few copies were
distributed in multilithed form by that organization as
an appendix to a reproduction of a well-known article
by Rademacher [1]. The note was abstracted in Math.
Reviews, Vol. 12 (1951), p. 208. Because he receives
frequent requests for copies of the note, which are
unavailable, the author has asked the editors to
reprint it in essentially its original form.''",
}
@Article{Garner:1959:RMS,
author = "Harvey L. Garner",
title = "A Ring Model for the Study of Multiplication for
Complement Codes",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "1",
pages = "25--30",
month = mar,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222757",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Garner:1959:RNS,
author = "Harvey L. Garner",
title = "The Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "140--147",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219515",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@InProceedings{Gray:1959:NFP,
author = "H. L. Gray and C. Harrison",
booktitle = "Proceedings of the Eastern Joint Computer Conference,
Boston, {MA}, December 1--3, 1959",
title = "Normalized floating-point arithmetic with an index of
significance",
volume = "16",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "244--248",
year = "1959",
LCCN = "TK7885.A1 J6",
bibdate = "Tue Oct 09 09:43:31 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Henrici:1959:TES,
author = "Peter Henrici",
editor = "????",
booktitle = "Proceedings of the International Conference on
Information Processing, {UNESCO}",
title = "Theoretical and Experimental Studies on the
Accumulation of Error in the Numerical Solution of
Initial Value Problems for Systems of Ordinary
Differential Equations",
publisher = "????",
address = "????",
pages = "36--43",
year = "1959",
LCCN = "????",
bibdate = "Fri Aug 20 09:11:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kogbetliantz:1959:CSC,
author = "E. G. Kogbetliantz",
title = "Computation of $ \sin {N} $, $ \cos {N} $, and {$M$
th} Root of {$N$} Using an Electronic Computer",
journal = j-IBM-JRD,
volume = "3",
number = "2",
pages = "147--152",
month = apr,
year = "1959",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Lucal:1959:AOD,
author = "Harold M. Lucal",
title = "Arithmetic Operations for Digital Computers Using a
Modified Reflected Binary Code",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "4",
pages = "449--458",
month = dec,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5222057",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Muller:1959:CMG,
author = "Mervin E. Muller",
title = "A Comparison of Methods for Generating Normal Deviates
on Digital Computers",
journal = j-J-ACM,
volume = "6",
number = "3",
pages = "376--383",
month = jul,
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 1 09:33:26 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
descriptors = "RVG",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Pawlak:1959:EDC,
author = "Z. Pawlak",
title = "An electronic digital computer based on the `$ - 2 $'
system",
journal = "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
volume = "7",
number = "??",
pages = "713--722",
month = "????",
year = "1959",
bibdate = "Thu Nov 06 05:58:31 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@Article{Pfeiffer:1959:FQM,
author = "Paul E. Pfeiffer",
title = "A Four-Quadrant Multiplier Using Triangular Waves,
Diodes, Resistors, and Operational Amplifiers",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "222--227",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219526",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Rothstein:1959:RBN,
author = "Jerome Rothstein",
title = "Residues of Binary Numbers Modulo Three",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "2",
pages = "229--229",
month = jun,
year = "1959",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1959.5219529",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:56:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219529",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Sarafyan:1959:NMC,
author = "Diran Sarafyan",
title = "A New Method of Computation of Square Roots Without
Using Division",
journal = j-CACM,
volume = "2",
number = "11",
pages = "23--24",
month = nov,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:24 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Traub:1960:CNM}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Sarafyan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}
@Article{Sheridan:1959:ATC,
author = "Peter B. Sheridan",
title = "The Arithmetic Translator Compiler of the {IBM FORTRAN
Automatic Coding System}",
journal = j-CACM,
volume = "2",
number = "2",
pages = "9--21",
month = feb,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 14 15:48:22 MDT 2004",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59;
http://ei.cs.vt.edu/~cs4304/bibliography.html;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Sheridan59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sheridan59",
}
@Article{Strachey:1959:TSR,
author = "C. Strachey",
title = "On taking the square root of a complex number",
journal = j-COMP-J,
volume = "2",
number = "2",
pages = "89--89",
month = jul,
year = "1959",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/2.2.89",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:11 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
remark = "This 1/4-page note comments that if $ \sqrt {x + i y}
= u + i v $, then $ u = \sqrt {[\sqrt {x^2 + y^2} + x]
/ 2} $ and $ v = \sqrt {[\sqrt {x^2 + y^2} - x] / 2}
$, where both inner and outer square roots should be
evaluated to twice working precision.",
}
@Article{Taranto:1959:BCF,
author = "Donald Taranto",
title = "Binary Conversion, with Fixed Decimal Precision, of a
Decimal Fraction",
journal = j-CACM,
volume = "2",
number = "7",
pages = "27--27",
month = jul,
year = "1959",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:25:37 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Taranto59;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
oldlabel = "Taranto59",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Taranto59",
}
@Article{Volder:1959:CTC,
author = "J. E. Volder",
title = "The {CORDIC} Trigonometric Computing Technique",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-8",
number = "5",
pages = "330--334",
month = sep,
year = "1959",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Wensley:1959:CNA,
author = "J. H. Wensley",
title = "A Class of Non-Analytical Iterative Processes",
journal = j-COMP-J,
volume = "1",
number = "4",
pages = "163--167",
month = jan,
year = "1959",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:07 MDT 2000",
bibsource = "Compiler/semantics.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/010163.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/163.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/164.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/165.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/166.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/167.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1959:EZIa,
author = "J. H. Wilkinson",
title = "The evaluation of the zeros of ill-conditioned
polynomials. {I}",
journal = j-NUM-MATH,
volume = "1",
pages = "150--166",
month = dec,
year = "1959",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386381",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0109435 (22 \#321)",
MRreviewer = "H. Rutishauser",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1959:EZIb,
author = "J. H. Wilkinson",
title = "The evaluation of the zeros of ill-conditioned
polynomials. {II}",
journal = j-NUM-MATH,
volume = "1",
pages = "167--180",
month = dec,
year = "1959",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386382",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0109435 (22 \#321)",
MRreviewer = "H. Rutishauser",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@MastersThesis{Young:1959:SSM,
author = "John Mackay Young",
title = "A study of some methods of numerical integration using
floating point arithmetic",
type = "Thesis ({M.S. in Mathematics})",
school = "Texas A.\&M. College",
address = "College Station, TX, USA",
pages = "50",
year = "1959",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bockstaele:1960:NFA,
author = "P. Bockstaele",
title = "Notes on the First Arithmetics Printed in {Dutch} and
{English}",
journal = j-ISIS,
volume = "51",
number = "3",
pages = "315--321",
month = sep,
year = "1960",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:28:03 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302265;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1960.bib",
URL = "http://www.jstor.org/stable/226510",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Brown:1960:EDC,
author = "David T. Brown",
title = "Error Detecting and Correcting Binary Codes for
Arithmetic Operations",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-9",
number = "3",
pages = "333--337",
month = sep,
year = "1960",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1960.5219855",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:34:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219855",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Cohen:1960:EAF,
author = "Eckford Cohen",
title = "The elementary arithmetical functions",
journal = j-SCRIPTA-MATH,
volume = "25",
number = "??",
pages = "221--228",
month = "????",
year = "1960",
ISSN = "0036-9713",
ISSN-L = "0036-9713",
MRclass = "10.00",
MRnumber = "118694",
MRreviewer = "H. Bergstr{\"{o}}m",
bibdate = "Thu Oct 26 11:15:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0116.27101",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
xxpages = "221--227",
ZBmath = "3189455",
}
@Article{Croy:1960:IAD,
author = "John E. Croy",
title = "Improved Arrangement of a Decimal Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-9",
number = "2",
pages = "263--263",
month = jun,
year = "1960",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1960.5219830",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 15:34:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219830",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Ercoli:1960:LEE,
author = "Paolo Ercoli",
title = "Letter to the {Editor}: {Errors} Due to Overflow in
Arithmetic Operations",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Ercoli:1957:EDO}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Gurzi:1960:HSM,
author = "Fred Gurzi",
title = "A High-Speed Multiplication Process for Digital
Computers",
journal = j-CACM,
volume = "3",
number = "4",
pages = "241--245",
month = apr,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Gurzi60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Gurzi60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gurzi60",
}
@TechReport{Jensen:1960:CIF,
author = "B. A. Jensen",
title = "Coding instructions for floating point trigonometric,
inverse trigonometric hyperbolic and exponential
functions",
type = "Group report",
number = "30G-0009",
institution = "Massachusetts Institute of Technology, Lincoln
Laboratory",
address = "Lexington, MA, USA",
pages = "7",
year = "1960",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Trigonometrical functions --- Computer programs.",
remark = "Cover title. ``Millstone Hill Radar Station.'' ``1
November 1960.'' Air Force Contract",
}
@Article{Kanner:1960:NUA,
author = "Herbert Kanner",
title = "A Note on the Use of the Abacus in Number Conversion",
journal = j-CACM,
volume = "3",
number = "3",
pages = "167--167",
month = mar,
year = "1960",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367149.367166",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Kanner60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Conversion of integers in both directions between the
base ten and any desired base can be accomplished with
remarkable simplicity by use of the abacus. In fact,
the conversion procedures are far more cumbersome on
the electric desk calculator, for reasons which will be
apparent.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "number base conversion",
oldlabel = "Kanner60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kanner60",
}
@Article{Knuth:1960:INS,
author = "Donald E. Knuth",
title = "An Imaginary Number System",
journal = j-CACM,
volume = "3",
number = "4",
pages = "245--247",
month = apr,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B554",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Knuth60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4}
(August 1961), 355 \cite{Knuth:1961:EIN}. See
\cite{Nadler:1961:DSR} for extension to division and
square root.",
abstract = "For centuries the decimal number system reigned
supreme, except, perhaps, among the Mayan Indians,
until the advent of digital computers brought the
binary and octal systems into the limelight. This paper
introduces another number system which may prove useful
for manipulating complex numbers on machines.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Knuth60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Knuth60",
ZMreviewer = "C. B. Haselgrove",
}
@Article{Lowan:1960:PREa,
author = "Arnold N. Lowan",
title = "On the Propagation of Round-Off Errors in the
Numerical Integration of the Heat Equation",
journal = j-MATH-COMPUT,
volume = "14",
number = "70",
pages = "139--146",
month = apr,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Lowan:1960:PREb,
author = "Arnold N. Lowan",
title = "On the Propagation of Round-Off Errors in the
Numerical Treatment of the Wave Equation",
journal = j-MATH-COMPUT,
volume = "14",
number = "71",
pages = "223--228",
month = jul,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Pawlak:1960:ODC,
author = "Z. Pawlak",
title = "The organization of a digital computer based on the `$
- 2 $' system",
journal = "Bull. Acad. Pol. Sci., Ser. Tech. Sci.",
volume = "8",
number = "??",
pages = "253--258",
month = "????",
year = "1960",
bibdate = "Thu Nov 06 06:00:08 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "negative base",
}
@Article{Perlin:1960:HPC,
author = "I. E. Perlin and J. R. Garrett",
title = "High Precision Calculation of $ \operatorname {Arcsin}
x $, $ \operatorname {Arccos} x $, and $ \operatorname
{Arctan} x $ (in {Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "14",
number = "71",
pages = "270--274",
month = jul,
year = "1960",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Perry:1960:CBF,
author = "C. Perry",
title = "Conversion between floating point representations",
journal = j-CACM,
volume = "3",
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "352.68.00",
MRnumber = "22\#8714",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Pope:1960:MPA,
author = "D. A. Pope and M. L. Stein",
title = "Multiple Precision Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "652--654",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@InCollection{Reitwiesner:1960:BA,
author = "G. W. Reitwiesner",
title = "Binary arithmetic",
crossref = "Alt:1960:AC",
pages = "231--308",
year = "1960",
bibdate = "Sat May 18 14:36:56 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sarafyan:1960:DCS,
author = "Diran Sarafyan",
title = "Divisionless computation of square roots through
continued squaring",
journal = j-CACM,
volume = "3",
number = "5",
pages = "319--321",
month = may,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.00",
MRnumber = "22\#8639",
bibdate = "Fri Nov 25 18:19:26 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "M. Lotkin",
}
@Article{Silver:1960:LER,
author = "Roland Silver",
title = "Letter to the {Editor}: Rounding in Floating-Point
Arithmetic",
journal = j-CACM,
volume = "3",
number = "12",
pages = "A9--A9",
month = dec,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:29 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Sklansky:1960:CSA,
author = "J. Sklansky",
title = "Conditional Sum Addition Logic",
journal = j-TRANS-IRE,
volume = "EC-9",
number = "2",
pages = "226--230",
month = jun,
year = "1960",
bibdate = "Fri Nov 09 19:17:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the IRE",
}
@Article{Traub:1960:CNM,
author = "J. F. Traub",
title = "Comments on a recent paper [{``A New Method of
Computation of Square Roots Without Using
Division''}]",
journal = j-CACM,
volume = "3",
number = "2",
pages = "86--86",
month = feb,
year = "1960",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:25 MST 2005",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sarafyan:1959:NMC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "Traub60",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}
@Article{Wadey:1960:FA,
author = "W. G. Wadey",
title = "Floating-Point Arithmetics",
journal = j-J-ACM,
volume = "7",
number = "2",
pages = "129--139",
month = apr,
year = "1960",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.00 (68.00)",
MRnumber = "22\#6090",
bibdate = "Fri Dec 08 14:44:46 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Three types of floating-point arithmetics with error
control are discussed and compared with conventional
floating-point arithmetic. General multiplication and
division shift criteria are derived (for any base) for
Metropolis-style arithmetics. The limitations and most
suitable range of application for each arithmetic are
discussed.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
reviewer = "C. B. Haselgrove",
xxmonth = "none",
xxnumber = "none",
}
@Article{Wilkinson:1960:EAF,
author = "J. H. Wilkinson",
title = "Error Analysis of Floating-Point Computation",
journal = j-NUM-MATH,
volume = "2",
pages = "319--340",
month = dec,
year = "1960",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0116477 (22 \#7264)",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Amble:1961:AFP,
author = "O. Amble and Jan V. Garwick",
title = "On the Accuracy of Floating Point Computers {[BIT {\bf
1}(2), 1961, pp. 87--88]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "220--222",
month = sep,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933434",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
xxpages = "220--221??",
}
@TechReport{Anonymous:1961:MCM,
author = "Anonymous",
title = "Modern Computing Methods",
type = "Notes on Applied Science",
number = "16",
institution = "National Physical Laboratory",
address = "Her Majesty's Stationery Office, London",
year = "1961",
bibdate = "Fri Aug 20 10:05:25 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Avizienis:1961:SDN,
author = "Algirdas Avi{\v{z}}ienis",
title = "Signed-Digit Number Representations for Fast Parallel
Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "389--400",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219227",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Cheney:1961:DCB,
author = "Philip Warren Cheney",
title = "A Digital Correlator Based on the Residue Number
System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "1",
pages = "63--70",
month = mar,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219154",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
abstract = "A system design for a digital correlator based on the
application of the residue number system for
computation is presented. Areas of investigation
include sampling, analog-to-residue conversion, logical
design of the arithmetic units, residue-to-analog
conversion, and modes of operation of the proposed
digital correlator. The advantages of speed of
computation and simplicity of logic due to the use of a
residue number system are shown to result in a
significantly faster and simpler system than if a
conventional number system were used. The resulting
digital correlator is designed for megacycle sampling
and computation with a 0.1 per cent system precision.",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Cheney:1961:TNA,
author = "E. W. Cheney and H. L. Loeb",
title = "Two new algorithms for rational approximation",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "72--75",
month = dec,
year = "1961",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386002",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 19:01:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Clarkson:1961:DMI,
author = "W. K. Clarkson",
title = "A Divisionless Method of Integer Conversion",
journal = j-CACM,
volume = "4",
number = "7",
pages = "315--316",
month = jul,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 08:14:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Cox:1961:NMP,
author = "Albert G. Cox and H. A. Luther",
title = "A Note on Multiple Precision Arithmetic",
journal = j-CACM,
volume = "4",
number = "8",
pages = "353--353",
month = aug,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366678.366693",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Dec 03 14:07:44 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since computers have means to detect overflow on
addition or subtraction, this can be used in a multiple
precision addition-subtraction subroutine to obviate a
sign analysis. Consider all integers in the computer to
be expressed ``radix t'', that is, in the form $ a =
a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
like sign and have magnitudes less than $t$. $t$ is a
positive integer determined by the word length of the
computer. Consider the expression $ c = a \pm b = (a_0
\pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
Here $ a_i \pm b_i$ may exceed the storage capacity of
one word or may have a sign different from $c$.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Croy:1961:RTM,
author = "John E. Croy",
title = "Rapid Technique of Manual or Machine Binary-to-Decimal
Integer Conversion Using Decimal Radix Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "777--777",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219286",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Freiman:1961:SAC,
author = "C. V. Freiman",
title = "Statistical analysis of certain binary division
algorithms",
journal = j-IRE-PROC,
volume = "49",
number = "1",
pages = "91--103",
month = jan,
year = "1961",
bibdate = "Mon Sep 16 16:12:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IRE Proceedings",
xxnote = "Check author name: I have found this paper cited both
as Freiman and as Frieman?? Hennessy and Patterson
\cite{Hennessy:2002:CAQ} have Freiman.",
}
@TechReport{Garner:1961:RNS,
author = "H. L. Garner and R. F. Arnold and B. C. Benson and C.
G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
title = "Residue number systems for computers",
type = "{ASD} Technical Report",
number = "61-483",
institution = "Electronic Technology Laboratory, The University of
Michigan",
address = "Ann Arbor, MI, USA",
month = oct,
year = "1961",
bibdate = "Thu Nov 18 09:27:06 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
abstract = "The purpose of the research performed under this
contract was to investigate the feasibility of residue
number systems in their applications to digital
computers. The problems of such an application are the
ones of magnitude determination, sign determination,
overflow, scaling, and division. These problems are not
independent, but are found to be quite interrelated. A
theoretical treatment of residue number systems is
given which lays the foundation for a unified study of
the complete problem. Treatments of an organizational
nature are given which deal with multiplication,
division, and scaling. The matter of correlating the
theoretical and organizational studies to physical
realizations involving networks is treated also. The
question of whether the residue number system can be
successfully applied to general purpose computers is
still an open one. Their application to special purpose
machines is considered both feasible and practical.",
acknowledgement = ack-nhfb,
remark = "This report represents the results of research
performed by the group at The University of Michigan
under the direction of Professor H. L. Garner.
Concurrently, research on the same subject was being
conducted at Harvard University under the direction of
Professor Howard Aiken, and at the Lockheed Missile
System Division under the direction of Dr. Richard
Tanaka. There was a considerable exchange of
information among the above groups during the course of
the research effort. The efforts attained exhibit
little overlap, rather they are complementary. A
portion of this report was extracted from the doctoral
dissertation of D. P. Rozenberg. His work was supported
by this contract, and led to the Ph.D..",
}
@Article{Garwick:1961:AFP,
author = "Jan V. Garwick",
title = "The Accuracy of Floating Point Computers",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "2",
pages = "87--88",
month = jun,
year = "1961",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939221",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also comment and reply
\cite{Amble:1961:AFP,Garwick:1961:RAF}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
@Article{Garwick:1961:RAF,
author = "J. V. Garwick",
title = "Reply to {``On the Accuracy of Floating Point
Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "1",
number = "3",
pages = "222--222",
year = "1961",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Nov 16 14:36:22 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point accuracy; floating-point arithmetic",
}
@InProceedings{Henderson:1961:RCE,
author = "D. S. Henderson",
booktitle = "{Proceedings of the 1961 16th ACM national meeting}",
title = "Residue class error checking codes",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "132.101--132.104",
year = "1961",
DOI = "https://doi.org/10.1145/800029.808563",
bibdate = "Thu Aug 07 19:04:58 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error checking codes based on residues have the
advantage over parity-based codes of monitoring
arithmetic as well as transmission operations. Codes
may be devised to detect burst-type errors, to correct
single errors in a binary arithmetic operation, to
correct burst errors and finally to correct any
single-digit error in a decimal operation.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@Article{Kettel:1961:AAM,
author = "E. Kettel and W. Schneider",
title = "An Accurate Analog Multiplier and Divider",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "269--272",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219198",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Knuth:1961:EIN,
author = "Donald E. Knuth",
title = "Errata: {``An imaginary number system''}",
journal = j-CACM,
volume = "4",
number = "8",
pages = "355--355",
month = aug,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jan 09 07:10:22 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Kovatch:1961:HEA,
author = "G. Kovatch and W. E. Meserve",
title = "The {Hall-Effect} Analog Multiplier",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "3",
pages = "512--515",
month = sep,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219240",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Lehman:1961:STH,
author = "M. Lehman and N. Burla",
title = "Skip Techniques for High-Speed Carry-Propagation in
Binary Arithmetic Units",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "691--698",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219274",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{MacSorley:1961:HSA,
author = "O. L. MacSorley",
title = "High-speed arithmetic in binary computers",
journal = j-IRE-PROC,
volume = "49",
number = "??",
pages = "67--91",
month = jan,
year = "1961",
bibdate = "Sat May 18 14:34:55 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1976:CDD}.",
acknowledgement = ack-nhfb,
fjournal = "IRE Proceedings",
}
@Book{Morrison:1961:CBP,
editor = "Philip Morrison and Emily Morrison",
title = "{Charles Babbage} on the principles and development of
the calculator: and other seminal writings",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xxxviii + 400",
year = "1961",
ISBN = "0-486-24691-4 (paperback)",
ISBN-13 = "978-0-486-24691-8 (paperback)",
LCCN = "QA75 .C52 1961",
bibdate = "Sat Jan 12 22:30:15 MST 2013",
bibsource = "clio-db.cc.columbia.edu:7090/Voyager;
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$7.95",
acknowledgement = ack-nhfb,
subject = "Calculators; Babbage, Charles",
subject-dates = "Charles Babbage (26 December 1791--18 October 1871)",
tableofcontents = "Chapters from Passages from the life of a
philosopher \\
Selections from Babbage's calculating engines \\
Appendix of miscellaneous papers",
}
@Article{Nadler:1961:DSR,
author = "Morton Nadler",
title = "Division and square root in the quater-imaginary
number system",
journal = j-CACM,
volume = "4",
number = "4",
pages = "192--193",
month = apr,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.99",
MRnumber = "23\#B555",
bibdate = "Fri Nov 25 18:19:32 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1960:INS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
ZMreviewer = "C. B. Haselgrove",
}
@Article{Pinkham:1961:DFS,
author = "Roger S. Pinkham",
title = "On the Distribution of First Significant Digits",
journal = j-ANN-MATH-STAT,
volume = "32",
number = "4",
pages = "1223--1230",
month = dec,
year = "1961",
CODEN = "AASTAD",
ISSN = "0003-4851 (print), 2168-8990 (electronic)",
ISSN-L = "0003-4851",
bibdate = "Thu Feb 15 15:07:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T",
abstract = "It has been noticed by astute observers that well used
tables of logarithms are invariably dirtier at the
front than at the back. Upon reflection one is led to
inquire whether there are more physical constants with
low order first significant digits than high. Actual
counts by Benford [2] show that not only is this the
case but that it seems to be an empirical truth that
whenever one has a large body of physical data,
Farmer's Almanac, Census Reports, Chemical Rubber
Handbook, etc., the proportion of these data with first
significant digit $n$ or less is approximately $
\log_{10}(n + 1) $. Any reader formerly unaware of this
``peculiarity'' will find an actual sampling experiment
wondrously tantalizing. Thus, for example,
approximately $ 0.7 $ of the physical constants in the
Chemical Rubber Handbook begin with $4$ or less ($
\log_{10}(4 + 1) = 0.699 $). This is to be contrasted
with the widespread intuitive evaluation $ 4 / 9 $
ths.",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "From p. 1223: ``\ldots{} the proportion of these data
with first significant digit $n$ or less is
approximately $ \log_{10}(n + 1) $.''\par
\ldots{} ``The only distribution for first significant
digits which is invariant under scale change of the
underlying distribution is $ \log_{10}(n + 1) $.
Contrary to suspicion this is a non-trivial
mathematical result, for the variable $n$ is
discrete.''.\par
From p. 1230: ``The foregoing results bear on questions
of round-off in computing machines. Since $ d(u v) = u
d v + v d u $, the error resulting from multiplying two
rounded numbers will be governed primarily by the first
significant digits of the two numbers being multiplied.
Now the distribution of first significant digits,
favoring as it does low order digits, tends to produce
less error than would be the case if first significant
digits were uniform as has sometimes been
assumed.''\par
Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Rabinowitz:1961:MPD,
author = "Philip Rabinowitz",
title = "Multiple-Precision Division",
journal = j-CACM,
volume = "4",
number = "2",
pages = "98--98",
month = feb,
year = "1961",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366105.366171",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 00:29:25 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Saltman:1961:RCT,
author = "Roy G. Saltman",
title = "Reducing Computing Time for Synchronous Binary
Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "2",
pages = "169--174",
month = jun,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219186",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Spielberg:1961:ECF,
author = "Kurt Spielberg",
title = "Efficient Continued Fraction Approximations To
Elementary Functions",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "409--417",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Spielberg:1961:RPS,
author = "K. Spielberg",
title = "Representation of Power Series in Terms of
Polynomials, Rational Approximations and Continued
Fractions",
journal = j-J-ACM,
volume = "8",
number = "4",
pages = "613--627",
month = oct,
year = "1961",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Dec 09 14:01:44 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Thacher:1961:ISR,
author = "Henry C. {Thacher, Jr.}",
title = "Iterated Square Root Expansions for the Inverse Cosine
and Inverse Hyperbolic Cosine",
journal = j-MATH-COMPUT,
volume = "15",
number = "76",
pages = "399--403",
month = oct,
year = "1961",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Weik:1961:TSD,
author = "Martin H. Weik",
title = "A Third Survey of Domestic Electronic Digital
Computing Systems",
type = "Report",
number = "1115",
institution = "Ballistic Research Laboratories",
address = "Aberdeen Proving Ground, MD, USA",
pages = "1131",
month = mar,
year = "1961",
bibdate = "Fri Nov 28 19:37:51 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the results of a third survey, the
engineering and programming characteristics of two
hundred twenty-two different electronic digital
computing systems are given. The data are presented
from the point of view of application, numerical and
arithmetic characteristics, input, output and storage
systems, construction and checking features, power,
space, weight, and site preparation and personnel
requirements, production records, cost and rental
rates, sale and lease policy, reliability, operating
experience, and time availability, engineering
modifications and improvements and other related
topics. An analysis of the survey data, fifteen
comparative tables, a discussion of trends, a revised
bibliography, and a complete glossary of computer
engineering and programming terminology are included.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Wilson:1961:ARB,
author = "J. B. Wilson and R. S. Ledley",
title = "An Algorithm for Rapid Binary Division",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-10",
number = "4",
pages = "662--670",
month = dec,
year = "1961",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1961.5219271",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 14:45:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@InProceedings{Ashenhurst:1962:MIA,
author = "R. L. Ashenhurst",
title = "The {Maniac III} Arithmetic System",
crossref = "AFIPS:1962:APS",
pages = "192--202",
year = "1962",
bibdate = "Wed Feb 14 17:14:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Buchholz:1962:PCS,
editor = "Werner Buchholz",
title = "Planning a Computer System: {Project Stretch}",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 322",
year = "1962",
LCCN = "1876",
bibdate = "Fri Nov 19 10:02:31 MST 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
library.ox.ac.uk:210/ADVANCE",
note = "This important book is the primary description of the
influential IBM 7030 Stretch computer, written by its
architects. See also a detailed critical review
\cite{Strachey:1962:BRP}.",
URL = "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
acknowledgement = ack-nhfb,
remark = "The text of the book is in the public domain, with the
permission of the author in 2003.
See \cite{MacKenzie:1991:IAL} for a remark about the
noisy mode for floating-point arithmetic in the IBM
7030 Stretch. That mode is first mentioned on page 25
of this book, and described in detail on page 102,
which states:
``By definition of ordinary normalized FLP operations,
numbers are frequently extended on the right by
attaching zeros. During addition the n-digit operand
that is not preshifted is extended with n zeros, so as
to provide the extra positions to which the preshifted
operand can be added. Any operand or result that is
shifted left to be normalized requires a corresponding
number of zeros to be shifted in at the right. Both
sets of zeros tend to produce numbers smaller in
absolute value than they would have been if more digits
had been carried. In the noisy mode these numbers are
simply extended with 1's instead of zeros (1's in a
binary machine, 9's in a decimal machine). So all
numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss.
The principal weakness of the noisy-mode procedure is
that it requires two runs for the same problem. A much
less important weakness is that the loss of
significance cannot be guaranteed to show up --- it
merely has a very high probability of showing up ---
whereas built-in significance checks can be made
slightly pessimistic, so that actual significance loss
will not be greater than indicated. On the other hand,
little extra hardware and no extra storage are required
for the noisy-mode approach. Furthermore, significance
loss is relatively rare, so that running a problem
twice when Significance loss is suspected does not pose
a serious problem. What is serious is the possibility
of unsuspected significance loss.
In discussions of significance two points are often
overlooked. The first of these is trivial: the best way
of ensuring significant results is to use an adequate
number of fraction digits. The second is almost equally
mundane: for a given procedure, normalized FLP
arithmetic will ordinarily produce the greatest
precision possible for the number of fraction digits
used. Normalized FLP arithmetic has been criticized
with respect to significance loss, because such loss is
not indicated by the creation of leading zeros, as it
is with fixed-point arithmetic. In other words, the
contention is not that normalized FLP arithmetic is
more prone to significance loss than equivalent
fixed-point arithmetic, which would be untrue, but that
an equivalent indication of such loss is not provided.
Loss of significance, however, is also a serious
problem in fixed-point arithmetic; multiplication and
division do not handle it at all correctly by means of
leading zeros. (In particular, fixed-point
multiplication may lead to serious or even total
significance loss, which would not have occurred with
normalized FLP arithmetic: and although leading zeros
in addition and subtraction of fixed-point operands do
give correct significance indications, the use of other
operations and of built-in scaling loops frequently
destroys entirely the leading-zeros method of counting
significance.)''",
subject = "Computer architecture",
tableofcontents = "Foreword v \\
Preface vii \\
1. Project Stretch 1 \\
[by W. Buchholz] \\
2. Architectural Philosophy 5 \\
[by F. P. Brooks, Jr.] \\
2.1. The Two Objectives of Project Stretch 5 \\
2.2. Resources 6 \\
2.3. Guiding Principles 7 \\
2.4. Contemporary Trends in Computer Architecture 10
\\
2.5. Hindsight 15 \\
3. System Summary of IBM 7030 17 \\
[by W. Buchholz] \\
3.1. System Organization 17 \\
3.2. Memory Units 17 \\
3.3. Index Memory 19 \\
3.4. Special Registers 19 \\
3.5. Input and Output Facilities 19 \\
3.6. High-speed Disk Units 20 \\
3.7. Central Processing Unit 20 \\
3.8. Instruction Controls 21 \\
3.9. Index-arithmetic Unit 21 \\
3.10. Instruction Look-ahead 21 \\
3.11. Arithmetic Unit 22 \\
3.12. Instruction Set 24 \\
3.13. Data Arithmetic 24 \\
3.14. Radix-conversion Operations 27 \\
3.15. Connective Operations 27 \\
3.16. Index-arithmetic Operations 27 \\
3.17. Branching Operations 28 \\
3.18. Transmission Operations 28 \\
3.19. Input-Output Operations 29 \\
3.20. New Features 29 \\
3.21. Performance 32 \\
4. Natural Data Units 33 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
4.1. Lengths and Structures of Natural Data Units 33
\\
4.2. Procedures for Specifying Natural Data Units 36
\\
4.3. Data Hierarchies 39 \\
4.4. Classes of Operations 40 \\
5. Choosing a Number Base 42 \\
[by W. Buchholz] \\
5.1. Introduction 42 \\
5.2. Information Content 45 \\
5.3. Arithmetic Speed 49 \\
5.4. Numerical Data 50 \\
5.5. Nonnumerical Data 51 \\
5.6. Addresses 52 \\
5.7. Transformation 53 \\
5.8. Partitioning of Memory 54 \\
5.9. Program Interpretation 56 \\
5.10. Other Number Bases 58 \\
5.11. Conclusion 58 \\
6. Character Set 60 \\
[by R. W. Bemer and W. Buchholz] \\
6.1. Introduction 60 \\
6.2. Size of Set 62 \\
6.3. Subsets 62 \\
6.4. Expansion of Set 63 \\
6.5. Code 63 \\
6.6. Parity Bit 66 \\
6.7. Sequence 66 \\
6.8. Blank 67 \\
6.9. Decimal Digits 68 \\
6.10. Typewriter Keyboard 68 \\
6.11. Adjacency 69 \\
6.12. Uniqueness 69 \\
6.13. Signs 70 \\
6.14. Tape-recording Convention 71 \\
6.15. Card-punching Convention 71 \\
6.16. List of 7030 Character Set 72 \\
7. Variable-field-length Operation 75 \\
[by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
\\
7.1. Introduction 75 \\
7.2. Addressing of Variable-field-length Data 76 \\
7.3. Field Length 77 \\
7.4. Byte Size 78 \\
7.5. Universal Accumulator 79 \\
7.6. Accumulator Operand 79 \\
7.7. Binary and Decimal Arithmetic 80 \\
7.8. Integer Arithmetic 81 \\
7.9. Numerical Signs 82 \\
7.10. Indicators 84 \\
7.11. Arithmetical Operations 85 \\
7.12. Radix-conversion Operation 87 \\
7.13. Logical Connectives of Two Variables 87 \\
7.14. Connective Operations 89 \\
8. Floating-point Operation 92 \\
[by S. G. Campbell] \\
General Discussion \\
8.1. Problems of Fixed-point Arithmetic 92 \\
8.2. Floating-point Arithmetic 94 \\
8.3. Normalization 97 \\
8.4. Floating-point Singularities 98 \\
8.5. Range and Precision 99 \\
8.6. Round-off Error 100 \\
8.7. Significance Checks 101 \\
8.8. Forms of Floating-point Arithmetic 103 \\
8.9. Structure of Floating-point Data 104 \\
Floating-point Features of the 7030 \\
8.10. Floating-point Instruction Format 106 \\
8.11. Floating-point Data Formats 106 \\
8.12. Singular Floating-point Numbers 108 \\
8.13. Indicators 112 \\
8.14. Universal Accumulator 113 \\
8.15. Fraction Arithmetic 114 \\
8.16. Floating-point-arithmetic Operations 114 \\
8.17. Fixed-point Arithmetic Using Unnormalized \\
Floating-point Operations 118 \\
8.18. Special Functions and Forms of Arithmetic 119 \\
8.19. Multiple-precision Arithmetic 119 \\
8.20. General Remarks 121 \\
9. Instruction Formats 122 \\
[by W. Buchholz] \\
9.1. Introduction 122 \\
9.2. Earlier Instruction Languages 122 \\
9.3. Evolution of the Single-address Instruction 124
\\
9.4. Implied Addresses 125 \\
9.5. Basic 7030 Instruction Formats 126 \\
9.6. Instruction Efficiency 127 \\
9.7. The Simplicity of Complexity 131 \\
9.8. Relationship to Automatic Programming Languages
132 \\
10. Instruction Sequencing 133 \\
[by F. P. Brooks, Jr.] \\
10.1. Modes of Instruction Sequencing 133 \\
10.2. Instruction Counter 134 \\
10.3. Unconditional Branching 135 \\
10.4. Conditional Branching 136 \\
10.5. Program-interrupt System 136 \\
10.6. Components of the Program-interrupt System 137
\\
10.7. Examples of Program-interrupt Techniques 140 \\
10.8. Execute Instructions 146 \\
10.9. Execute Operations in the 7030 148 \\
11. Indexing 150 \\
[by G. P. Blaauw] \\
11.1. Introduction 150 \\
11.2. Indexing Functions 151 \\
11.3. Instruction Format for Indexing 155 \\
11.4. Incrementing 157 \\
11.5. Counting 159 \\
11.6. Advancing by One 161 \\
11.7. Progressive Indexing 161 \\
11.8. Data Transmission 162 \\
11.9. Data Ordering 163 \\
11.10. Refilling 165 \\
11.11. Indirect Addressing and Indirect Indexing 167
\\
11.12. Indexing Applications 169 \\
11.13. Record-handling Applications 172 \\
11.14. File Maintenance 175 \\
11.15. Subroutine Control 177 \\
11.16. Conclusion 178 \\
12. Input-Output Control 179 \\
[by W. Buchholz] \\
12.1. A Generalized Approach to Connecting \\
Input-Output and External Storage 179 \\
12.2. Input-Output Instructions 180 \\
12.3. Defining the Memory Area 181 \\
12.4. Writing and Reading 182 \\
12.5. Controlling and Locating 183 \\
12.6. An Alternative Approach 184 \\
12.7. Program Interruptions 184 \\
12.8. Buffering 180 \\
12.9. Interface 188 \\
12.10. Operator Control of Input-Output Units 190 \\
13. Multiprogramming 192 \\
[by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
Scalzi] \\
13.1. Introduction 192 \\
13.2. Multiprogramming Requirements 193 \\
13.3. 7030 Features that Assist Multiprogramming 195
\\
13.4. Programmed Logic 197 \\
13.5. Concluding Remarks 200 \\
13.6. References 201 \\
14. The Central Processing Unit 202 \\
[by E. Bloch] \\
14.1. Concurrent System Operation 202 \\
14.2. Concurrency within the Central Processing Unit
204 \\
14.3. Data Flow 204 \\
14.4. Arithmetic Unit 208 \\
14.5. Checking 216 \\
14.6. Component Count 216 \\
14.7. Performance 217 \\
14.8. Circuits 218 \\
14.9. Packaging 223 \\
15. The Look-ahead Unit 228 \\
[by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
15.1. General Description 228 \\
15.2. Timing-simulation Program 230 \\
15.3. Description of the Look-ahead Unit 238 \\
15.4. Forwarding 240 \\
15.5. Counter Sequences 241 \\
15.6. Recovery after Interrupt 246 \\
15.7. A Look-back at the Look-ahead 247 \\
16. The Exchange 248 \\
[by W. Buchholz] \\
16.1. General Description 248 \\
16.2. Starting a WRITE or READ Operation 250 \\
16.3. Data Transfer during Writing 250 \\
16.4. Data Transfer during Reading 251 \\
16.5. Terminating a WRITE or READ Operation 252 \\
16.6. Multiple Operations 252 \\
16.7. CONTROL and LOCATE Operations 252 \\
16.8. Interrogating the Control Word 253 \\
16.9. Forced Termination 253 \\
17. A Nonarithmetical System Extension 254 \\
[by S. G. Campbell, P. S. Herwitz, and J. H. Pomerene]
\\
17.1. Nonarithmetical Processing 254 \\
17.2. The Set-up Mode 258 \\
17.3. Byte-sequence Formation 259 \\
17.4. Pattern Selection 260 \\
17.5. Transformation Facilities 261 \\
17.6. Statistical Aids 263 \\
17.7. The BYTE-BY-BYTE Instruction 263 \\
17.8. Monitoring for Special Conditions 264 \\
17.9. Instruction Set 265 \\
17.10. Collating Operations 266 \\
17.11. Table Look-up Operations 267 \\
17.12. Example 267 \\
Appendix A. Summary Data 273 \\
A.1. List of the Larger IBM Stored-program Computers
273 \\
A.2. Instruction Formats 275 \\
A.3. List of Registers and Special Addresses 276 \\
A.4. Summary of Operations and Modifiers 277 \\
A.5. Summary of Indicators 287 \\
Appendix B. Programming Examples 292 \\
Notation 292 \\
B.1. Polynomial Evaluation 295 \\
B.2. Cube-root Extraction 296 \\
B.3. Matrix Multiplication 298 \\
B.4. Conversion of Decimal Numbers to a \\
Floating-point Normalized Vector 299 \\
B.5. Editing a Typed Message 301 \\
B.6. Transposition of a Large Bit Matrix 303 \\
Index 305",
}
@InCollection{Campbell:1962:FPO,
author = "S. G. Campbell",
editor = "Werner Buchholz",
booktitle = "Planning a Computer System: {Project Stretch}",
title = "Floating-Point Operation",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
bookpages = "322",
pages = "92--121",
year = "1962",
LCCN = "QA76.8.I2 I5",
bibdate = "Wed Feb 14 17:24:27 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "IBM 7030 (Computer); IBM Stretch",
}
@Article{Cantor:1962:LEF,
author = "D. Cantor and G. Estrin and R. Turn",
title = "Logarithmic and Exponential Function Evaluation in a
Variable Structure Digital Computer",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "155--164",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219348",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@TechReport{Descloux:1962:REF,
author = "J. Descloux",
title = "Remarks on errors in first order iterative processes
with floating-point computers",
institution = "University of Illinois Graduate College, Digital
Computer Laboratory",
address = "Urbana, IL, USA",
pages = "7",
year = "1962",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Report / University of Illinois, Digital Computer
Laboratory; no. 113 Report (University of Illinois
(Urbana-Champaign campus). Digital Computer
Laboratory); no. 113.",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
calculations.",
remark = "Supported by: National Science Foundation under grant
G16489. ``March 22, 1962.''",
}
@Article{Fischler:1962:TRA,
author = "M. A. Fischler and E. A. Poe",
title = "Threshold Realization of Arithmetic Circuits",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "287--288",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219366",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Fraser:1962:CRA,
author = "W. Fraser and J. F. Hart",
title = "On the computation of rational approximations to
continuous functions",
journal = j-CACM,
volume = "5",
number = "7",
pages = "401--403",
month = jul,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368273.368578",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:39 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
elementary functions; Remes algorithm; special
functions",
}
@Article{Grau:1962:FNR,
author = "A. A. Grau",
title = "On a floating-point number representation for use with
algorithmic languages",
journal = j-CACM,
volume = "5",
number = "3",
pages = "160--161",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "26\#4506",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithmic languages, such as ALGOL, make provision
for two types of numbers, real and integer, which are
usually implemented on the computer by means of
floating-point and fixed-point numbers respectively.
The concepts real and integer, however, are taken from
mathematics, where the set of integers forms a proper
subset of the set of real numbers. In implementation a
real problem is posed by the fact that the set of
fixed-point numbers is not a proper subset of the set
of floating-point numbers; this problem becomes very
apparent in attempts to implement ALGOL 60.
Furthermore, the {\em one\/} mathematical operation of
addition is implemented in the machine by one of {\em
two\/} machine operations, fixed-point addition or
floating-point addition.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
reviewer = "R. L. Ashenhurst",
}
@Article{Guffin:1962:CSL,
author = "Ronald M. Guffin",
title = "A Computer for Solving Linear Simultaneous Equations
Using the Residue Number System",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "2",
pages = "164--173",
month = apr,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219349",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219349",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Book{Hamming:1962:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "411",
year = "1962",
LCCN = "QA297 .H28",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis; Electronic digital computers",
}
@Article{Jones:1962:FPF,
author = "F. B. Jones and A. W. Wymore",
title = "Floating Point Feature on the {IBM Type 1620}",
journal = j-IBM-TDB,
volume = "05-62",
pages = "43--46",
month = may,
year = "1962",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 11:26:02 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
remark = "The IBM 1620 normalized variable-precision arithmetic
provides up to 100 decimal digits with an exponent
range of $ \pm 99 $.",
}
@Article{Karatsuba:1962:MMN,
author = "A. Karatsuba and Y. Ofman",
title = "Multiplication of multidigit numbers on automata",
journal = j-DOKL-AKAD-NAUK,
volume = "145",
number = "??",
pages = "293--294",
month = "????",
year = "1962",
CODEN = "DANKAS",
ISSN = "0002-3264",
bibdate = "Tue Jul 05 10:35:11 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Akademii nauk SSSR",
journal-URL = "http://istina.msu.ru/journals/366838/",
}
@Article{Keir:1962:DOD,
author = "Y. A. Keir and P. W. Cheney and M. Tannenbaum",
title = "Division and overflow detection in residue number
systems",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "4",
pages = "501--507",
month = aug,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219389",
ISSN = "0367-9950",
MRclass = "68.00",
MRnumber = "MR0150990 (27 \#976)",
MRreviewer = "N. H. Choksy",
bibdate = "Thu Jul 14 09:11:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Kesner:1962:FPA,
author = "O. Kesner",
title = "Floating-point arithmetic in {COBOL}",
journal = j-CACM,
volume = "5",
number = "5",
pages = "269--271",
month = may,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/367710.367739",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:38 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Knuth:1962:EPC,
author = "Donald E. Knuth",
title = "Evaluation of polynomials by computer",
journal = j-CACM,
volume = "5",
number = "12",
pages = "595--599",
month = dec,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355580.369074",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00 (12.00)",
MRnumber = "27 \#970",
bibdate = "Thu Dec 08 11:11:03 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
note = "See letter \cite{Knuth:1963:LEE}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "The author that Motzkin (1962) showed that Horner's
rule for polynomial evaluation may not be optimal, and
develops the idea further for arbitrary polynomials,
but also observes that the coefficients of the revised
polynomials may be difficult to find. He also asks
about, but does not answer, the question of error
analysis of the various methods.",
}
@Article{Lake:1962:LEH,
author = "G. T. Lake",
title = "Letter to the Editor: Hardware Conversion of Decimal
and Binary Numbers",
journal = j-CACM,
volume = "5",
number = "9",
pages = "468--469",
month = sep,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:16:30 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
}
@Article{Lynch:1962:WBD,
author = "W. C. Lynch",
title = "On a Wired-In Binary-to-Decimal Conversion Scheme",
journal = j-CACM,
volume = "5",
number = "3",
pages = "159--159",
month = mar,
year = "1962",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 28 18:21:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
}
@Article{MacSorley:1962:RBA,
author = "O. L. MacSorley",
title = "Review: \booktitle{An Algorithm for Rapid Binary
Division}, by {J. B. Wilson and R. S. Ledley}",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "3",
pages = "420--420",
month = jun,
year = "1962",
CODEN = "IRELAO",
ISSN = "0367-9950",
bibdate = "Sat Jul 16 20:52:08 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{McGee:1962:BM,
author = "W. C. McGee",
title = "A Binary Multiplication",
journal = j-SIAM-REVIEW,
volume = "4",
number = "3",
pages = "256--256",
month = "????",
year = "1962",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1004066",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:04:54 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/4/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1962",
}
@Article{Meggitt:1962:PDP,
author = "J. E. Meggitt",
title = "Pseudo Division and Pseudo Multiplication Processes",
journal = j-IBM-JRD,
volume = "6",
number = "2",
pages = "210--226",
month = apr,
year = "1962",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Metze:1962:CBD,
author = "Gernot Metze",
title = "A Class of Binary Divisions Yielding Minimally
Represented Quotients",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "6",
pages = "761--764",
month = dec,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219460",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219460",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Mitchell:1962:CMD,
author = "John N. Mitchell",
title = "Computer Multiplication and Division Using Binary
Logarithms",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "4",
pages = "512--517",
month = aug,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219391",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219391",
abstract = "A method of computer multiplication and division is
proposed which uses binary logarithms. The logarithm of
a binary number may be determined approximately from
the number itself by simple shifting and counting. A
simple add or subtract and shift operation is all that
is required to multiply or divide. Since the logarithms
used are approximate there can be errors in the result.
An error analysis is given and a means of reducing the
error for the multiply operation is show",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Rozier:1962:DBC,
author = "Charles P. Rozier",
title = "Decimal-to-Binary Conversion Using Octal Radix
Arithmetic",
journal = j-IRE-TRANS-ELEC-COMPUT,
volume = "EC-11",
number = "5",
pages = "708--709",
month = oct,
year = "1962",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/TEC.1962.5219436",
ISSN = "0367-9950",
bibdate = "Thu Jul 14 09:11:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219436",
acknowledgement = ack-nhfb,
fjournal = "IRE Transactions on Electronic Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}
@Article{Shanks:1962:CD,
author = "Daniel Shanks and John W. {Wrench, Jr.}",
title = "Calculation of $ \pi $ to 100,000 Decimals",
journal = j-MATH-COMPUT,
volume = "16",
number = "77",
pages = "76--99",
month = jan,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Misc{Sierra:1962:FDP,
author = "Huberto M. Sierra",
title = "Floating Decimal Point Arithmetic Control Means for
Calculator",
howpublished = "US Patent 3,037,701",
day = "5",
month = jun,
year = "1962",
bibdate = "Sat Mar 24 05:59:45 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US3037701A",
abstract = "The invention relates to digital computers and more
particularly to digital computers for making
calculations with numbers having a wide range of values
with a limited number of digit storing positions.",
acknowledgement = ack-nhfb,
remark = "US Patent filed 21 November 1956, granted to IBM on 5
June 1962, expired 5 June 1979 (17 years after grant).
This may be the earliest US patent on floating-point
arithmetic.",
}
@Article{Smith:1962:ACDa,
author = "Robert L. Smith",
title = "{Algorithm 116}: {Complex} Division",
journal = j-CACM,
volume = "5",
number = "8",
pages = "435--435",
month = aug,
year = "1962",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/368637.368661",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:40 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Spielberg:1962:PCF,
author = "Kurt Spielberg",
title = "Polynomial and Continued-Fraction Approximations for
Logarithmic Functions",
journal = j-MATH-COMPUT,
volume = "16",
number = "78",
pages = "205--217",
month = apr,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Strachey:1962:BRP,
author = "Christopher Strachey",
title = "Book Reviews: {{\booktitle{Planning a Computer System:
Project Stretch}}. Edited by Werner Buchholz. 322
pp.(London: McGraw-Hill)}",
journal = j-COMP-J,
volume = "5",
number = "2",
pages = "152--153",
month = aug,
year = "1962",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/5.2.152",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Sep 25 09:59:25 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Buchholz:1962:PCS}.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "IBM 7030 (Stretch); IBM 7950 (Harvest)",
}
@Article{Wynn:1962:AAP,
author = "P. Wynn",
title = "An Arsenal of {ALGOL} Procedures for Complex
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "4",
pages = "232--255",
month = dec,
year = "1962",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940171",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "ALGOL; complex arithmetic; confluence hypergeometric
function; continued fractions; incomplete beta
function; incomplete gamma function; Stieltjes
$S$-fractions; Weber parabolic cylinder function",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Zuse:1962:ERE,
author = "K. Zuse",
editor = "W. Hoffman",
booktitle = "{Digitale Informationswandler}",
title = "{Entwicklungslinien einer Rechenger{\"a}te-Entwicklung
von der Mechanik zur Elektronik}. ({German}) [Lines of
development of computing equipment development from
mechanics to electronics]",
publisher = "Vieweg \& Sohn, GmbH",
address = "Braunschweig, West Germany",
pages = "508--532",
year = "1962",
bibdate = "Wed Oct 13 11:23:04 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 4.3]{Randell:1982:ODC}.
Translated by Mr. and Mrs. P. Jones.",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Bemer:1963:NRT,
author = "R. W. Bemer",
title = "A Note on Range Transformations for Square Root and
Logarithm",
journal = j-CACM,
volume = "6",
number = "6",
pages = "306--307",
month = jun,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:47 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\log(x)$; $\sqrt(x)$; elementary functions",
}
@Article{Clenshaw:1963:ASF,
author = "C. W. Clenshaw and G. F. Miller and M. Woodger",
title = "Algorithms for Special Functions {I}",
journal = j-NUM-MATH,
volume = "4",
pages = "403--419",
year = "1963",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:21:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Daly:1963:HSA,
author = "W. G. Daly and J. F. Kruy",
title = "A High-Speed Arithmetic Unit Using Tunnel Diodes",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "5",
pages = "503--511",
month = oct,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263644",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037964",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Descloux:1963:NRE,
author = "J. Descloux",
title = "Note on the Round-Off Errors in Iterative Processes",
journal = j-MATH-COMPUT,
volume = "17",
number = "81",
pages = "18--27",
month = jan,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Dietmeyer:1963:CPN,
author = "Donald L. Dietmeyer",
title = "Conversion from Positive to Negative and Imaginary
Radix",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "1",
pages = "20--22",
month = feb,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263391",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:36 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037765",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "imaginary base; negative base",
}
@Article{Eisman:1963:PER,
author = "S. H. Eisman",
title = "Polynomial Evaluation Revisited",
journal = j-CACM,
volume = "6",
number = "7",
pages = "384--385",
month = jul,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Eve:1963:SAI,
author = "J. Eve",
title = "Starting Approximations for the Iterative Calculation
of Square Roots",
journal = j-COMP-J,
volume = "6",
number = "3",
pages = "274--276",
month = nov,
year = "1963",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/6.3.274",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:30 MST 2012",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://comjnl.oxfordjournals.org/content/6/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Several starting approximations are given which, in
conjunction with a well-known iterative process, lead
to square root approximations, with a relative error in
the range $ (2^{-55}, 2^{-45}) $, at the expense of
three divisions. More accurate approximations are given
which require in addition a single multiplication.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Book{Flores:1963:LCA,
author = "I. Flores",
title = "The Logic of Computer Arithmetic",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 493",
year = "1963",
LCCN = "QA76.5 .F46",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Geier:1963:ACD,
author = "A. Geier and I. Sturz",
title = "The approximate calculation of a definite integral
with automatic choice of integration steps (intervals).
The program for the computer {$ {\rm MECIPTI} $} in a
floating point regime. ({Romanian})",
journal = "An. Univ. Timi{\c{s}}oara Ser. {\c{S}}ti. Mat.-Fiz.",
volume = "1",
pages = "133--139",
year = "1963",
MRclass = "68.00",
MRnumber = "30\#3588",
bibdate = "Fri Dec 08 13:52:47 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. N. Goss",
}
@Article{Goldstein:1963:SAD,
author = "Max Goldstein",
title = "Significance arithmetic on a digital computer",
journal = j-CACM,
volume = "6",
number = "3",
pages = "111--117",
month = mar,
year = "1963",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/366274.366339",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:45 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The 7090 at NYU has been modified to include a
``Significance Mode'' of operation which is intended to
facilitate the identification of significant bits in
the results of floating-point arithmetic operations.
The manner in which floating-point arithmetic is
handled in this mode is discussed. Several numerical
experiments using this mode are described and
comparisons are made with the ordinary ``normalized
mode.'' Examples include power series evaluation,
linear equations solution, determinant evaluation and
matrix inversion.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Knuth:1963:LEE,
author = "Donald E. Knuth",
title = "Letter to the {Editor}: {Evaluation} of polynomials by
computer",
journal = j-CACM,
volume = "6",
number = "2",
pages = "51--51",
month = feb,
year = "1963",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Dec 26 16:31:38 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1962:EPC}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@Article{Krishnamurthy:1963:CMD,
author = "E. V. Krishnamurthy",
title = "On Computer Multiplication and Division Using Binary
Logarithms",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "3",
pages = "319--320",
month = jun,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263572",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037874",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lehman:1963:MAB,
author = "M. Lehman",
title = "The Minimization of Assimilations in Binary
Carry-Storage Arithmetic Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "4",
pages = "409--410",
month = aug,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263479",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037921",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lehmer:1963:RDO,
author = "D. H. Lehmer",
title = "{R63--17} Division and Overflow Detection in Residue
Number Systems",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "1",
pages = "36--37",
month = feb,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263493",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:36 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037786;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
}
@Article{Lindamood:1963:MCO,
author = "George E. Lindamood and George Shapiro",
title = "Magnitude Comparison and Overflow Detection in Modular
Arithmetic Computers",
journal = j-SIAM-REVIEW,
volume = "5",
number = "4",
pages = "342--350",
month = "????",
year = "1963",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1005095",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:07 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/5/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1963",
}
@Article{Metropolis:1963:BOU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Basic Operations in an Unnormalized Arithmetic
System",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-12",
number = "6",
pages = "896--904",
month = dec,
year = "1963",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1963.263593",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 08:10:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
ZMnumber = "0124.07910",
abstract = "A particular set of unnormalized arithmetic operations
termed ``basic'' are described, in the context of the
University of Chicago Maniac III Computer. Each basic
operation involves three operand words and generates
two result words, all in unnormalized floating point
format. The use of these operations in the
implementation of multi-precision arithmetic is
explained; in particular, it is demonstrated that
multiprecision division can be effected in a
nontentative manner with their aid.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753",
keywords = "MANIAC III",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Mood:1963:ITS,
author = "Alexander McFarlane Mood and Franklin A. Graybill",
title = "Introduction to the theory of statistics",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "443",
year = "1963",
LCCN = "HA29 .M75 1963",
bibdate = "Fri Aug 20 10:02:03 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "McGraw-Hill series in probability and statistics",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Mathematical statistics",
}
@Article{Stern:1963:CSR,
author = "T. E. Stern and R. M. Lerner",
title = "A circuit for the square root of the sum of the
squares",
journal = j-PROC-IEEE,
volume = "51",
number = "4",
pages = "593--596",
month = apr,
year = "1963",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A piecewise-linear network can produce an output
proportional to the square root of the sum of the
squares of a set of input voltages, using resistors and
diodes alone. The required relationship between
voltages can be represented by a multi- \ldots{}",
}
@Article{Stroud:1963:MPF,
author = "A. H. Stroud and D. Secrest",
title = "A multiple-precision floating-point interpretive
program for the {Control Data} 1604",
journal = j-COMP-J,
volume = "6",
number = "1",
pages = "62--66",
month = apr,
year = "1963",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:45 MDT 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tif",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Svoboda:1963:AD,
author = "A. Svoboda",
title = "An algorithm for division",
journal = j-INF-PROCESS-MACH,
volume = "9",
number = "??",
pages = "25--33",
month = "????",
year = "1963",
CODEN = "IPRMDD",
ISSN = "0373-885X",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Information processing machines",
}
@InProceedings{Wilkinson:1963:PSA,
author = "J. H. Wilkinson",
title = "Plane rotations in floating-point arithmetic",
crossref = "Metropolis:1963:PFS",
pages = "185--198",
year = "1963",
MRclass = "65.35",
MRnumber = "28\#1744",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "A. S. Householder",
}
@Article{Aiken:1964:PAC,
author = "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
title = "Proposed automatic calculating machine",
journal = j-IEEE-SPECTRUM,
volume = "1",
number = "8",
pages = "62--69",
month = aug,
year = "1964",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1964.6500770",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Tue Jan 14 11:14:17 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Previously unpublished memorandum written by Aiken and
dated by an unknown recipient as 4 November 1937.
Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
abstract = "Here presented is the memorandum that 20 years ago
initiated a series of events whose revolutionary
implications are only beginning to manifest themselves
a description of the first large-scale general-purpose
automatic digital computer. Twenty years ago, on August
7, 1944, Mark I, the first large-scale general-purpose
automatic digital computer ever to be put in operation
was dedicated at Harvard University by James B. Conant,
then president of Harvard, and the late Thomas J.
Watson, founder of IBM.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
remark = "Pages 66--69 discuss computation of the elementary
functions with minimal intermediate storage: recipes
are given for integral and fractional power, log,
exponential, trigonometric, inverse trigonometric,
hyperbolic, and inverse hyperbolic. Mention is also
made of the probability integral, elliptic functions,
and Bessel functions, but the text says they will be
discussed later (meaning, in a future publication). The
methods involve recurrences and series summations, and
thus, can be regarded as precision independent.",
}
@Manual{Anonymous:1964:PPF,
author = "Anonymous",
title = "{PINT}: {Purdue} floating point interpretive system:
for the {RPC 4000 General Precision} electronic
computer",
organization = "General Precision, Inc.",
address = "West Lafayette, IN, USA",
pages = "45",
year = "1964",
bibdate = "Mon May 06 10:24:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.; Purdue
University School of Electrical Engineering; RPC 4000
(Computer)",
remark = "Program no. H1-02.0",
}
@Article{Ashenhurst:1964:FEU,
author = "R. L. Ashenhurst",
title = "Function Evaluation in Unnormalized Arithmetic",
journal = j-J-ACM,
volume = "11",
number = "2",
pages = "168--187",
month = apr,
year = "1964",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 22:33:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Baer:1964:MPA,
author = "Robert M. Baer and Martin G. Redlich",
title = "Multiple-precision arithmetic and the exact
calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $
symbols",
journal = j-CACM,
volume = "7",
number = "11",
pages = "657--659",
month = nov,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "31\#865",
bibdate = "Mon Oct 24 09:33:02 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a system of general-purpose
multiple-precision fixed-point routines and their use
in subroutines which calculate exactly the
quantum-mechanical 3-j, 6-j and 9-j symbols of large
arguments.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@MastersThesis{Bookhart:1964:SFP,
author = "Thomas Woodward Bookhart",
title = "A study of floating point arithmetic",
type = "Thesis ({M.S. in Math.})",
school = "Georgia Institute of Technology",
address = "Atlanta, GA, USA",
pages = "51",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Number theory.;
Numerical calculations --- Computer programs.",
}
@Article{Brooker:1964:PPS,
author = "R. A. Brooker",
title = "A programming package for some general modes of
arithmetic",
journal = j-CACM,
volume = "7",
number = "2",
pages = "119--127",
month = feb,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An interpretive programming package is described for
computation with operands which may be real, complex,
single or double precision, or real multiple precision.
It also performs operations on matrices formed from
these elements. A simple language structure is used to
describe the computation.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Manual{Burroughs:1964:BBI,
author = "{Burroughs Corporation}",
title = "{Burroughs B5500} Information Processing Systems
Reference Manual",
organization = "Burroughs Corporation",
address = "Detroit, MI, USA",
year = "1964",
bibdate = "Wed Nov 22 21:15:11 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The B5500 uses a decimal integer or fixed-point
coefficient of 21 or 22 digits, with an exponent range
of $ \pm 63 $.",
}
@Article{Cody:1964:DPS,
author = "W. J. {Cody, Jr.}",
title = "Double-Precision Square Root for the {CDC-3600}",
journal = j-CACM,
volume = "7",
number = "12",
pages = "715--718",
month = dec,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355588.365122",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In January of 1960, the late Hans J. Maehly completed
a summary of approximations to the elementary functions
for the CDC-1604 computer. The approximations and
techniques suggested by Maehly are equally applicable
to the second large computer in the CDC line, the 3600.
Unlike the 1604, however, the 3600 has built-in
double-precision floating-point arithmetic. The present
work, largely inspired by the successes of Maehly and
his associates, concerns the extension of one of
Maehly's ideas to a double-precision subroutine for the
3600.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$sqrt(x)$; CDC 3600; elementary functions",
}
@Article{Cowgill:1964:LEB,
author = "D. Cowgill",
title = "Logic Equations for a Built-In Square Root Method",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "156--157",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263791",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Eve:1964:EP,
author = "J. Eve",
title = "The Evaluation of Polynomials",
journal = j-NUM-MATH,
volume = "6",
pages = "17--21",
year = "1964",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:21:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@MastersThesis{Goldschmidt:1964:ADC,
author = "Robert E. Goldschmidt",
title = "Applications of Division by Convergence",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering, Massachusetts
Institute of Technology",
address = "Cambridge, MA, USA",
pages = "44",
month = jun,
year = "1964",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dspace.mit.edu/handle/1721.1/11113",
acknowledgement = ack-sfo # " and " # ack-nhfb,
advisor = "Alfred K. Susskind",
remark = "This thesis introduced the quadratically convergent
Goldschmidt algorithm for iterative division, as an
alternative to Newton--Raphson iteration: see
\cite{Flynn:1966:VHS, Anderson:1967:ISMb,
Flynn:1970:DFI, Ito:1995:EIAb, Oberman:1996:FIR,
Ercegovac:1999:IGD, Ercegovac:2000:IGD,
Gallagher:2000:FTN, Even:2003:PEA, Markstein:2004:SDS,
Even:2005:PEA, Piso:2006:OMD, Schulte:2007:FPD,
Kong:2008:RMI, Piso:2008:FOS, Piso:2008:NRA,
Ruiz:2008:EIR, Kong:2010:RMR, Kong:2011:GDM,
Piso:2011:VLG, Panhaleux:2012:CFP} for improvements and
error analysis. For computing $ Q = N / D $,
Newton--Raphson starts with $ Y \approx 1 / D $, and
iterates $ Y \leftarrow (2 - Y D) Y $, or equivalently,
$ Y \leftarrow Y - (Y (Y D - 1)) $. With the same
starting point, Goldschmidt instead iterates $ N
\leftarrow N Y $, $ D \leftarrow D Y $, $ Y = 2 - D $,
which converges to $ Y = 1 $. When parallel multipliers
are available, the two multiplies can be done at the
same time, whereas Newton--Raphson requires two
sequential multiplies. In addition, the update $ 2 D $
can be computed in hardware by a fast bitwise two's
complement operation, instead of a slower
floating-point subtraction. The Goldschmidt algorithm
has been used in CPUs of the IBM S/360 model 91 and the
AMD K7. Unfortunately, unlike Newton--Raphson, each
iteration of the Goldschmidt algorithm increases
rounding error. Numerical tests of the Goldschmidt
algorithm show worst-case errors in ulps roughly equal
to the number of iterations. Without an FMA, the
Newton--Raphson worst case errors are about 1.7 ulps,
and with an FMA, about 1.0 ulps. In hardware in both
cases, a few bits of extra intermediate precision can
lead to correctly rounded results. Without extra
precision, additional fixups are needed for correct
rounding.",
}
@Article{Gram:1964:RZF,
author = "Christian Gram",
title = "On the Representation of Zero in Floating-Point
Arithmetic",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "4",
number = "3",
pages = "156--161",
month = sep,
year = "1964",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01956026",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68.00",
MRnumber = "29\#5412",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=4&issue=3&spage=156",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Gregory:1964:FAN,
author = "Robert T. Gregory and James L. Raney",
title = "Floating-point arithmetic with $ 84 $-bit numbers",
journal = j-CACM,
volume = "7",
pages = "10--13",
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2706",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Book{Henrici:1964:ENA,
author = "Peter Henrici",
title = "Elements of numerical analysis",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 328",
year = "1964",
LCCN = "QA297 .H4",
bibdate = "Fri Aug 20 09:17:19 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Based on the author's lecture notes for a course
entitled {\em Numerical Mathematical Analysis\/} at the
University of California, Los Angeles. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@Article{Jacobsohn:1964:SFM,
author = "D. Jacobsohn",
title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "6",
pages = "754--754",
month = dec,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263942",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:06 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038318",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Book{Khinchin:1964:CF,
author = "Aleksandr Iakovlevich Khinchin",
title = "Continued fractions",
publisher = "P. Noordhoff",
address = "Groningen, The Netherlands",
pages = "101",
year = "1964",
LCCN = "QA295 .K513 1964a",
bibdate = "Fri Nov 30 06:55:53 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated by Peter Wynn",
URL = "http://www.loc.gov/catdir/description/dover032/97008056.html;
http://www.loc.gov/catdir/toc/dover031/97008056.html",
acknowledgement = ack-nhfb,
author-dates = "1894--1959",
}
@Article{Klokacev:1964:RNF,
author = "I. V. Kloka{\v{c}}ev",
title = "A refinement of the normalized floating point number
notation on digital computers. ({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
volume = "4",
pages = "192--194",
year = "1964",
MRclass = "68.00",
MRnumber = "28\#4694",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Kundu:1964:TMD,
author = "P. Kundu and S. Banerji",
title = "Transistorized Multiplier and Divider and Its
Applications",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "3",
pages = "288--295",
month = jun,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263919",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038157",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lamson:1964:DAD,
author = "Roger C. Lamson",
title = "A Division Algorithm for a Digital Differential
Analyzer",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "54--55",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263838",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038079",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Lynn:1964:REM,
author = "M. Stuart Lynn",
title = "On the Round-Off Error in the Method of Successive
Over-Relaxation",
journal = j-MATH-COMPUT,
volume = "18",
number = "85",
pages = "36--49",
month = jan,
year = "1964",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Book{Maley:1964:MDC,
author = "Gerald A. Maley and Edward J. Skiko",
title = "Modern digital computers",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 216",
year = "1964",
LCCN = "QA76.5 .M192",
bibdate = "Thu Nov 18 10:04:00 MST 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Prentice-Hall electrical engineering series",
acknowledgement = ack-nhfb,
keywords = "binary arithmetic",
subject = "Electronic digital computers",
}
@Book{McCracken:1964:NMF,
author = "Daniel D. McCracken and William S. Dorn",
title = "Numerical methods and {FORTRAN} programming, with
applications in engineering and science",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 457",
year = "1964",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Numerical analysis --- Data processing.; {Fortran}
(Computer program language)",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Merrill:1964:IDC,
author = "Roy D. Merrill",
title = "Improving Digital Computer Performance Using Residue
Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "2",
pages = "93--101",
month = apr,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263776;
https://doi.org/10.1109/PGEC.1964.263777",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
summary = "Residue arithmetic has the interesting characteristic
that in multiplication, addition and subtraction any
digit in the result is dependent only on its two
corresponding operand digits. Consequently, for these
operations, residue arithmetic is \ldots{}",
}
@Article{Miller:1964:ESD,
author = "R. H. Miller",
title = "An example in ``significant-digit'' arithmetic",
journal = j-CACM,
volume = "7",
number = "1",
pages = "21--21",
month = jan,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Oct 24 09:33:00 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Different methods of handling the summing process for
the geometric series are shown to give results
indicating widely differing significances when carried
out in a machine incorporating ``significant-digit''
arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@MastersThesis{Moss:1964:RDC,
author = "George Joseph {Moss, Jr.}",
title = "Recording digital counter with floating point output
format",
type = "Thesis ({M.S.})",
school = "University of Maryland",
address = "College Park, MD, USA",
pages = "155",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Rice:1964:AFV,
author = "John R. Rice",
title = "The Approximation of Functions",
volume = "1",
publisher = pub-AW,
address = pub-AW:adr,
pages = "various",
year = "1964",
LCCN = "QA221 .R5 V.1-2",
bibdate = "Fri Dec 08 13:02:52 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Santos:1964:BVB,
author = "J. Santos and H. Arango",
title = "Base $3$ vs Base $2$ Synchronous Arithmetic Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "5",
pages = "608--609",
month = oct,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263734",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:57:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038256",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Stein:1964:DCM,
author = "M. L. Stein",
title = "Divide-and-Correct Methods for Multiple Precision
Division",
journal = j-CACM,
volume = "7",
number = "8",
pages = "472--474",
month = aug,
year = "1964",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@MastersThesis{Sweo:1964:SFP,
author = "David Ernest Sweo",
title = "A study of floating point arithmetic with the residue
number system",
type = "Thesis ({M.S.})",
school = "UCLA - Engineering",
address = "Los Angeles, CA, USA",
pages = "89",
year = "1964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Congruences and residues.; Electronic digital
computers --- Programming.",
}
@Article{Wallace:1964:SFM,
author = "C. S. Wallace",
title = "A Suggestion for a Fast Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-13",
number = "1",
pages = "14--17",
month = feb,
year = "1964",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1964.263830",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038071",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Wolfe:1964:RTE,
author = "Jack M. Wolfe",
title = "Reducing Truncation Errors by Programming",
journal = j-CACM,
volume = "7",
number = "6",
pages = "355--356",
month = jun,
year = "1964",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/512274.512287",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:54 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In accumulating a sum such as in a numerical
integration with a large number of intervals, the sum
itself becomes much larger than the individual addends.
This may produce a less accurate sum as the number of
intervals is increased. Separate variables can be
established as accumulators to hold partial sums within
various distinct intervals. Thus, the extensive
successive truncations are eliminated.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; truncation errors",
remark = "This algorithm is a precursor of Kahan's compensated
summation algorithm \cite{Kahan:1965:PFR}; see \cite[p.
384]{Lange:2020:NDF} for a discussion.",
}
@Article{Ashenhurst:1965:EEC,
author = "R. L. Ashenhurst and N. Metropolis",
title = "Error Estimation in Computer Calculation",
journal = j-AMER-MATH-MONTHLY,
volume = "72",
number = "2 (Part 2)",
pages = "47--58",
year = "1965",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65.80",
MRnumber = "MR0192671 (33 \#896)",
MRreviewer = "James H. Wilkinson",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in Department of Economics, Graduate School
of Business, University of Chicago, Center for
Mathematical Studies in Business and Economics, number
45.",
ZMnumber = "0216.49602",
acknowledgement = ack-jr,
fjournal = "The American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
keywords = "error estimation; floating-point arithmetic",
}
@InProceedings{Ashenhurst:1965:EIU,
author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Experimental investigation of unnormalized
arithmetic",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "3--37",
year = "1965",
bibdate = "Thu Nov 8 14:49:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARI FLP",
}
@InProceedings{Ashenhurst:1965:TAE,
author = "R. L. Ashenhurst",
editor = "L. B. Rall",
booktitle = "Error in digital computation",
title = "Techniques for automatic error monitoring and
control",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "43--59",
year = "1965",
bibdate = "Tue Oct 9 09:42:56 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARI FLP",
}
@Article{Atrubin:1965:ODR,
author = "A. J. Atrubin",
title = "A One-Dimensional Real-Time Iterative Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "394--399",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264145",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038457",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Blum:1965:EAP,
author = "B. I. Blum",
title = "An Extended Arithmetic Package",
journal = j-CACM,
volume = "8",
number = "5",
pages = "318--320",
month = may,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Combet:1965:CBT,
author = "M. Combet and H. {Van Zonneveld} and L. Verbeek",
title = "Computation of the Base Two Logarithm of Binary
Numbers",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "6",
pages = "863--867",
month = dec,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264080",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dadda:1965:SSP,
author = "Luigi Dadda",
title = "Some Schemes for Parallel Multipliers",
journal = j-ALTA-FREQ,
volume = "34",
number = "??",
pages = "349--356",
month = mar,
year = "1965",
CODEN = "ALFRAJ",
ISSN = "0002-6557",
ISSN-L = "0002-6557",
bibdate = "Fri Nov 09 10:47:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[pages
118--225]{Swartzlander:1990:CAa}.",
URL = "http://en.wikipedia.org/wiki/Dadda_multiplier;
http://en.wikipedia.org/wiki/luigi_dadda",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
fjournal = "Alta frequenza",
remark = "According to an ARITH'21 conference attendee, this is
a recommended article for understanding the Wallace and
Dadda multipliers.",
}
@Article{Deiters:1965:ODD,
author = "Robert M. Deiters",
title = "Optimum Design of a Diode Squarer by Applying the
Criterion of Square Root of the Integral of Per Cent
Error Squared",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "3",
pages = "456--463",
month = jun,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264153",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Dodd:1965:RSB,
author = "George G. Dodd",
title = "Remarks on Simulation of {Boolean} Functions",
journal = j-CACM,
volume = "8",
number = "8",
pages = "517--517",
month = aug,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:01 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently M. Morris Mano presented a method for
performing Boolean OR, AND and NOT operations by means
of arithmetic and conditional transfer operations in a
decimal computer lacking builtin logical
instructions.",
acknowledgement = ack-nhfb,
checked = "19940407",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Boolean operations; decimal arithmetic",
sjb = "Commenting on \cite{Mano:1965:PSB}.",
}
@Article{Earle:1965:LCS,
author = "J. G. Earle",
title = "Latched Carry-Save Adder",
journal = j-IBM-TDB,
volume = "7",
number = "??",
pages = "909--910",
month = mar,
year = "1965",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 09 10:49:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InCollection{Garner:1965:NSA,
author = "H. L. Garner",
title = "Number systems and arithmetic",
crossref = "Alt:1965:AC",
volume = "6",
pages = "131--194",
year = "1965",
bibdate = "Sat May 18 14:18:19 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Garner:1965:RID,
author = "H. L. Garner",
title = "{R65-22} Improving Digital Computer Performance Using
Residue Number Theory",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "277--277",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.263975",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038430;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
}
@Article{Hammel:1965:RLC,
author = "D. Hammel",
title = "{R65-54} The Logic of Computer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "670--670",
month = aug,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264031",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Hammer:1965:BRBa,
author = "Preston C. Hammer",
title = "Book Review: {{\booktitle{Experimental Arithmetic,
High Speed Computing and Mathematics}} by N. C.
Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.2307/1266139",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Sat Jun 21 13:17:45 MDT 2014",
bibsource = "http://www.jstor.org/journals/00401706.html;
http://www.jstor.org/stable/i254241;
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
URL = "http://www.jstor.org/stable/1266139",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Hammer:1965:BRBb,
author = "Preston C. Hammer",
title = "Book Review: {{\booktitle{Experimental Arithmetic,
High Speed Computing and Mathematics}} by N. C.
Metropolis, A. H. Taub, John Todd, and C. B.
Tompkins}",
journal = j-TECHNOMETRICS,
volume = "7",
number = "1",
pages = "82--82",
month = feb,
year = "1965",
CODEN = "TCMTA2",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
bibdate = "Tue Mar 20 13:44:52 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
URL = "http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9",
acknowledgement = ack-nhfb,
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html",
}
@Article{Hamming:1965:NLB,
author = "R. W. Hamming and W. L. Mammel",
title = "A Note on the Location of the Binary Point in a
Computing Machine",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "260--261",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264258",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "The authors consider the low-level multiplication
circuit efficiency of placing the binary point before
or after the first bit. If the leading bit is equally
likely to be a 0 or a 1, then their analysis shows that
it is better to place the point before the leading bit.
However, they report that a more likely distribution is
logarithmic (as predicted by Benford's Law, although
the Newcomb / Benford work is neither mentioned nor
cited), in which case there is no advantage for either
choice of placement of the binary point. The conclude
that it would be humane to place it after the leading
digit, by analogy with how people learn decimal
arithmetic.",
}
@Article{Ikebe:1965:NTP,
author = "Yasuhiko Ikebe",
title = "Note on Triple-Precision Floating-Point Arithmetic
with 132-Bit Numbers",
journal = j-CACM,
volume = "8",
number = "3",
pages = "175--177",
month = mar,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2707",
bibdate = "Fri Dec 08 14:32:51 1995",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper, Gregory and Raney described a
technique for double-precision floating-point
arithmetic. A similar technique can be developed for
triple-precision floating-point arithmetic and its is
the purpose of this note to describe this technique.
Only the multiplication and the division algorithms are
described, since the addition-subtraction algorithm can
be obtained by a trivial modification of the algorithm
in Gregory's and Raney's paper.",
acknowledgement = ack-nhfb,
checked = "19940404",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{James:1965:GSR,
author = "Wendy James and P. Jarratt",
title = "The Generation of Square Roots on a Computer with
Rapid Multiplication Compared with Division (in
{Technical Notes and Short Papers})",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "497--500",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InCollection{Kahan:1965:FPO,
author = "W. Kahan",
booktitle = "Programmer's Reference Manual",
title = "The Floating-Point Over\slash Underflow Trap Routine
{{\tt FPTRP}}",
publisher = "Institute of Computer Science, University of Toronto",
address = "Toronto, Ontario, Canada",
year = "1965",
LCCN = "????",
bibdate = "Wed Feb 14 19:11:11 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Section 4.1.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kahan:1965:PFR,
author = "W. Kahan",
title = "Pracniques: {Further} Remarks on Reducing Truncation
Errors",
journal = j-CACM,
volume = "8",
number = "1",
pages = "40--40",
month = jan,
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363707.363723",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 08 00:18:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; truncation errors",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Moller:1965:QDP}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}. See
improvement \cite{Ozawa:1993:SAE}.",
}
@Article{Kanner:1965:NBC,
author = "Herbert Kanner",
title = "Number Base Conversion in Significant Digit
Arithmetic",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "242--246",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{King:1965:LED,
author = "R. King",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Krishnamurthy:1965:DCM,
author = "E. V. Krishnamurthy",
title = "On a Divide-and-Correct Method for Variable Precision
Division",
journal = j-CACM,
volume = "8",
number = "3",
pages = "179--181",
month = mar,
year = "1965",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363791.363829",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "30\#2709",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Described in this paper is a divide-and-correct method
for variable precision division in digital computers.
Unlike the earlier methods of Stein and Pope, the
present method uses a suitably rounded form of the
normalized divisor for getting an estimate of the
quotient characters. This result is a correction of at
most plus or minus one to the estimate, to obtain the
exact quotient character. It is believed that this
method will be widely applicable for division
operations in variable word-length character-oriented
machines.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "correct rounding; floating-point arithmetic",
}
@TechReport{Lederer:1965:FPP,
author = "E. Lederer",
title = "Floating-point-Pegasus, {FLPPEG}",
type = "{ISD-Bericht}",
number = "12",
institution = "ISD, Inst. f{\"u}r Statik u. Dynamik d. Luft- u.
Raumfahrtkonstruktionen, Universit{\"a}t Stuttgart",
address = "Stuttgart, Germany",
pages = "5",
year = "1965",
bibdate = "Thu May 09 09:05:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lehman:1965:SAT,
author = "M. Lehman",
title = "Serial Arithmetic Techniques",
crossref = "AFIPS:1965:FJC",
pages = "715--725",
year = "1965",
bibdate = "Tue Jan 08 23:08:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Liddiard:1965:DPF,
author = "Lawrence Anthony Liddiard",
title = "Double precision floating point arithmetic",
type = "Thesis ({M.S.})",
school = "University of Minnesota",
address = "????",
pages = "various",
year = "1965",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Calculators.; Numerical calculations.",
}
@Book{Lyusternik:1965:HCE,
author = "L. A. Lyusternik and O. A. Chervonenkis and A. R.
Yanpolski",
title = "Handbook for Computing Elementary Functions",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "xiii + 251",
year = "1965",
LCCN = "QA221.L513",
bibdate = "Thu Sep 1 10:13:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from the Russian by G. J. Tee. Translation
edited by K. L. Stewart.",
acknowledgement = ack-nj,
}
@Article{Mano:1965:PSB,
author = "M. Morris Mano",
title = "Pracniques: {Simulation} of {Boolean} functions in a
decimal computer",
journal = j-CACM,
volume = "8",
number = "1",
pages = "39--40",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:58 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remarks \cite{Dodd:1965:RSB}.",
acknowledgement = ack-nhfb,
checked = "19940304",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
sjb = "Describes how to perform Boolean operations by means
of arithmetic and conditional transfer operations on a
decimal computer lacking any built in logical
instructions. See also \cite{Dodd:cacm:65}.",
}
@Article{Martin:1965:SHS,
author = "A. R. Martin and A. B. Rosenstein",
title = "A Shiftrix for High-Speed Multiplication",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "4",
pages = "639--643",
month = aug,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264010",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038521",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@InProceedings{Metropolis:1965:AIE,
author = "N. Metropolis",
title = "Analysis of Inherent Errors in Matrix Decomposition
Using Unnormalized Arithmetic",
crossref = "Kalenich:1965:IPP",
volume = "2",
pages = "441--442",
year = "1965",
bibdate = "Wed Feb 14 19:21:38 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0161.35502",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Metropolis:1965:AUA,
author = "N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {I}.
{Recurrence} relations",
journal = j-NUM-MATH,
volume = "7",
number = "2",
pages = "104--112",
month = apr,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "68.00",
MRnumber = "MR0178589 (31 \#2846)",
MRreviewer = "G. Dahlquist",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See erratum \cite{Metropolis:1965:BAU}.",
ZMnumber = "0128.36301",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Metropolis:1965:BAU,
author = "N. Metropolis",
title = "Berichtigung: {Algorithms} in unnormalized arithmetic.
{I}. {Recurrence} relations",
journal = j-NUM-MATH,
volume = "7",
number = "4",
pages = "354",
month = aug,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553943",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Metropolis:1965:RCU,
author = "N. Metropolis and R. L. Ashenhurst",
title = "Radix Conversion in an Unnormalized Arithmetic
System",
journal = j-MATH-COMPUT,
volume = "19",
number = "91",
pages = "435--441",
month = jul,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28196507%2919%3A91%3C435%3ARCIAUA%3E2.0.CO%3B2-D",
ZMnumber = "0146.14607",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Metze:1965:MSR,
author = "Gernot Metze",
title = "Minimal Square Rooting",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "181--185",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.263963",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Miller:1965:ASF,
author = "G. F. Miller",
title = "Algorithms for Special Functions {II}",
journal = j-NUM-MATH,
volume = "7",
pages = "194--196",
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 10:22:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Moller:1965:NQD,
author = "Ole M{\o}ller",
title = "Note on Quasi Double-Precision",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "4",
pages = "251--255",
year = "1965",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moller:1965:QDP}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Moller:1965:QDP,
author = "Ole M{\o}ller",
title = "Quasi Double-Precision in Floating Point Addition",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "5",
number = "1",
pages = "37--50",
month = mar,
year = "1965",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01975722",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.80",
MRnumber = "MR0181130 (31 \#5359)",
bibdate = "Wed Jan 4 18:52:08 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Moller:1965:NQD}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=37",
acknowledgement = ack-nj # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
remark = "Gives summation error estimate formula `s = fl(a + b);
error = (a - s) + b', also discovered independently by
\cite{Kahan:1965:PFR}. Extends Gill's earlier
fixed-point result \cite{Gill:1951:PSS}.",
}
@InCollection{Moore:1965:AACa,
author = "Ramon E. Moore",
title = "The automatic analysis and control of error in digital
computing based on the use of interval numbers",
crossref = "Rall:1965:EDCa",
chapter = "2",
bookpages = "????",
pages = "61--130",
year = "1965",
MRclass = "65.61 (65.80)",
MRnumber = "MR0176614 (31 \#886)",
MRreviewer = "T. E. Hull",
bibdate = "Thu Jun 20 10:51:40 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V1.pdf",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Moore:1965:AACb,
author = "Ramon E. Moore",
title = "Automatic local coordinate transformations to reduce
the growth of error bounds in interval computation of
solutions of ordinary differential equations",
crossref = "Rall:1965:EDCb",
chapter = "2",
pages = "103--140",
year = "1965",
MRclass = "65.80 (65.60)",
MRnumber = "MR0185839 (32 \#3299)",
MRreviewer = "T. E. Hull",
bibdate = "Thu Jun 20 10:51:40 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V2.pdf",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Morrison:1965:MCC,
author = "D. R. Morrison",
title = "A Method for Computing Certain Inverse Functions",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "10",
number = "??",
pages = "202--208",
month = "????",
year = "1965",
CODEN = "MTTCAS",
ISSN = "0891-6837",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "Math. Tables Other Aids Comput.",
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Nathan:1965:CM,
author = "Amos Nathan",
title = "The Cascade Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "2",
pages = "243--247",
month = apr,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264250",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038406",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Penney:1965:BSC,
author = "Walter Penney",
title = "A {``Binary''} System for Complex Numbers",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "247--248",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Thu Nov 03 08:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Book{Ralston:1965:FCN,
author = "Anthony Ralston",
title = "A first course in numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xix + 578",
year = "1965",
LCCN = "QA297 .R3",
bibdate = "Fri Aug 20 10:13:32 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "See also second edition
\cite{Ralston:1978:FCN,Ralston:2001:FCN}. Cited in
\cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@Article{Riordan:1965:UAT,
author = "R. H. S. Riordan and R. R. A. Morton",
title = "The Use of Analog Techniques in Binary Arithmetic
Units",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "1",
pages = "29--35",
month = feb,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264051",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038346",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Ross:1965:RTE,
author = "D. R. Ross",
title = "Reducing Truncation Errors Using Cascading
Accumulators",
journal = j-CACM,
volume = "8",
number = "1",
pages = "32--33",
month = jan,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sun Sep 18 22:55:00 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When accumulating a large number of quantities as in
numerical integration, the sum itself may become much
larger than the individual addends. This results in
truncation error. Much of this error can be eliminated
using cascading accumulators as noted in a recent
article by Wolfe. A simpler and slightly more flexible
algorithm is presented which deals also with the case
of negative addends.",
acknowledgement = ack-nhfb,
checked = "19940304",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "accurate floating-point summation",
sjb = "Refers to \cite{Wolfe:cacm:196,Wilhelm:1977:GMPb}.",
}
@Article{Schreiber:1965:BRB,
author = "Alvin L. Schreiber",
title = "Book Review: {{\booktitle{A Binary Multiplication}}
(W. C. McGee)}",
journal = j-SIAM-REVIEW,
volume = "7",
number = "1",
pages = "134--136",
month = "????",
year = "1965",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1007016",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:20 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/7/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1965",
}
@Article{Smith:1965:ASO,
author = "Francis J. Smith",
title = "An Algorithm for Summing Orthogonal Polynomial Series
and their Derivatives with Applications to
Curve-Fitting and Interpolation",
journal = j-MATH-COMPUT,
volume = "19",
number = "89",
pages = "33--36",
month = apr,
year = "1965",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Specker:1965:CAL,
author = "W. H. Specker",
title = "A Class of Algorithms for $ \ln x $, $ \exp x $, $
\sin x $, $ \cos x $, $ \tan^{-1} x $, and $ \cot^{-1}
x $",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-14",
number = "1",
pages = "85--86",
month = feb,
year = "1965",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1965.264066",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 06:26:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038361",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Swarztrauber:1965:LED,
author = "P. N. Swarztrauber",
title = "Letter to the {Editor}: On the Double-Precision Square
Root Routine",
journal = j-CACM,
volume = "8",
number = "4",
pages = "202",
month = apr,
year = "1965",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Aug 31 14:02:19 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; floating-point
arithmetic",
}
@Article{Sweeney:1965:AFP,
author = "D. W. Sweeney",
title = "An analysis of floating-point addition",
journal = j-IBM-SYS-J,
volume = "4",
number = "1",
pages = "31--42",
year = "1965",
CODEN = "IBMSA7",
DOI = "https://doi.org/10.1147/sj.41.0031",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:42:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
note = "Reprinted in
\cite[pp.~317--328]{Swartzlander:1990:CAa}.",
URL = "http://www.research.ibm.com/journal/sj/041/ibmsjIVRID.pdf",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
fjournal = "IBM Systems Journal",
remark = "Page 34, containing a critical table, was originally
missing from the PDF file, and this was finally
corrected by IBM in November 2008.",
xxmonth = "(none)",
}
@Article{Winograd:1965:TRP,
author = "Shmuel Winograd",
title = "On the Time Required to Perform Addition",
journal = j-J-ACM,
volume = "12",
number = "2",
pages = "277--285",
month = apr,
year = "1965",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Arango:1966:FCP,
author = "H. Arango and J. Santos",
title = "A Fast Carry-Propagation Circuit for Base $3$ Signed
Non redundant Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "2",
pages = "254--255",
month = apr,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264311",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038725",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Brooker:1966:MFA,
author = "R. A. Brooker and J. S. Rohl and S. R. Clark",
title = "The main features of {Atlas Autocode}",
journal = j-COMP-J,
volume = "8",
number = "4",
pages = "303--310",
month = jan,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:10 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comment \cite{Clark:1966:CMP}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/080303.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/303.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/304.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/305.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/306.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/307.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/308.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/309.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/310.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@MastersThesis{Chang:1966:DHR,
author = "Henry Kwan-cheung Chang",
title = "Design of a high rate floating point digital
accumulator",
type = "Thesis ({M.S. in Engineering})",
school = "University of California, Davis",
address = "Davis, CA, USA",
pages = "60",
year = "1966",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Dissertations, Academic --- California ---
Engineering.",
}
@Article{Chartres:1966:ACP,
author = "Bruce A. Chartres",
title = "Automatic Controlled Precision Calculations",
journal = j-J-ACM,
volume = "13",
number = "3",
pages = "386--403",
month = jul,
year = "1966",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Fri Nov 28 16:23:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recent developments in computer design and error
analysis have made feasible the use of variable
precision arithmetic and the preparation of programs
that automatically determine their own precision
requirements. Such programs enable the user to specify
the accuracy he wants, and yield answers guaranteed to
lie within the bounds prescribed. A class of such
programs, called ``contracting error programs'', is
defined in which the precision is determined by
prescribing error bounds on the data. A variant of
interval arithmetic is defined which enables a limited
class of algorithms to be programmed as contracting
error programs. A contracting error program for the
solution of simultaneous linear equations is described,
demonstrating the application of the idea to a wider
class of problems.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Clark:1966:CMP,
author = "S. R. Clark and W. F. Lunnon",
title = "Correspondence: Multiple precision arithmetic (real
and complex)",
journal = j-COMP-J,
volume = "9",
number = "2",
pages = "174--174",
month = aug,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:14 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brooker:1966:MFA}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/tiff/174.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Clark:1966:MPA,
author = "S. R. Clark and W. F. Lunnon",
title = "Multiple precision arithmetic in {Atlas Autocode}",
journal = j-COMP-J,
volume = "9",
number = "2",
pages = "174--174",
month = aug,
year = "1966",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/9.2.174",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:36 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/9/2.toc;
https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/9/2/174.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Fike:1966:SAS,
author = "C. T. Fike",
title = "Starting Approximations for Square Root Calculation on
{IBM System\slash 360}",
journal = j-CACM,
volume = "9",
number = "4",
pages = "297--299",
month = apr,
year = "1966",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/365278.365556",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
abstract = "Several starting approximations for square root
calculation by Newton's method are presented in a form
to facilitate their use in IBM System/360 square root
routines. These approximations include several for the
range [1/16, 1], which is the interval of primary
interest on IBM System/360.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; IBM S/360",
}
@Article{Filippi:1966:BEE,
author = "S. Filippi",
title = "{Die Berechnung einiger elementarer transzendenter
Funktionen mit Hilfe des Richardson-Algorithmus}
\toenglish {The Computation of Some Elementary
Transcendental Functions by Means of the Richardson
Algorithm} \endtoenglish",
journal = j-COMPUTING,
volume = "1",
number = "??",
pages = "127--132",
month = "????",
year = "1966",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Flehinger:1966:PRI,
author = "B. J. Flehinger",
title = "On the Probability that a Random Integer Has Initial
Digit `{A}'",
journal = j-AMER-MATH-MONTHLY,
volume = "73",
number = "??",
pages = "1056--1061",
year = "1966",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Feb 14 18:53:58 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
remark = "Probably November or December issue; missing from
amermathmonthly1960.bib.",
}
@Article{Flynn:1966:VHS,
author = "M. J. Flynn",
title = "Very high-speed computing systems",
journal = j-PROC-IEEE,
volume = "54",
number = "12",
pages = "1901--1909",
year = "1966",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1109/proc.1966.5273",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Wed Dec 13 08:39:04 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "floating-point arithmetic; Goldschmidt division",
}
@Article{Garner:1966:ECA,
author = "Harvey L. Garner",
title = "Error Codes for Arithmetic Operations",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "5",
pages = "763--770",
month = oct,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264566",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038884",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Grau:1966:BRB,
author = "A. A. Grau",
title = "Book Review: {{\booktitle{Rounding Errors in Algebraic
Processes}} (J. H. Wilkinson)}",
journal = j-SIAM-REVIEW,
volume = "8",
number = "3",
pages = "397--398",
month = "????",
year = "1966",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1008087",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:37 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/8/3;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1966",
}
@Article{Gregory:1966:DAU,
author = "Robert T. Gregory",
title = "On the Design of the Arithmetic Unit of a
Fixed-Word-Length Computer from the Standpoint of
Computational Accuracy",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-15",
number = "2",
pages = "255--257",
month = apr,
year = "1966",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1966.264312",
ISSN = "0367-7508",
bibdate = "Thu Jul 14 05:46:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038726",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Book{Greve:1966:HLR,
author = "J. Greve and H. Gumin and E. Hochsteller",
title = "{Herrn von Leibniz' Rechnung mit Null und Ein}.
({German}) [{Mister von Leibniz'} calculation with zero
and one]",
publisher = "{Siemens AG}",
address = "Berlin and M{\"u}nchen, West Germany",
pages = "59",
year = "1966",
bibdate = "Fri Mar 17 08:31:51 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Gottfried Wilhelm Freiherr von Leibnitz",
language = "German",
}
@InProceedings{Harding:1966:ISF,
author = "L. J. {Harding, Jr.}",
editor = "????",
booktitle = "{SHARE} {XXVII}, Toronto, Canada, August 1966",
title = "Idiosyncracies of {System\slash 360} Floating-Point",
publisher = "????",
address = "????",
pages = "??--??",
year = "1966",
LCCN = "????",
bibdate = "Wed Feb 14 19:04:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Harding:1966:MSF,
author = "L. J. {Harding, Jr.}",
title = "Modifications of {System\slash 360} Floating-Point",
number = "SSD 157, C4470",
howpublished = "SHARE Secretarial Distribution",
pages = "11--27",
month = "????",
year = "1966",
bibdate = "Wed Feb 14 19:05:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Henrici:1966:TPM,
author = "Peter Henrici",
title = "Test of probabilistic models for the propagation of
roundoff errors",
journal = j-CACM,
volume = "9",
number = "6",
pages = "409--410",
month = jun,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:07 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Hull:1966:TPM,
author = "T. E. Hull and J. R. Swenson",
title = "Tests of Probabilistic Models for Propagation of
Roundoff Errors",
journal = j-CACM,
volume = "9",
number = "2",
pages = "108--113",
month = feb,
year = "1966",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.80",
MRnumber = "32\#3297",
bibdate = "Fri Nov 25 18:20:04 MST 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In any prolonged computation it is generally assumed
that the accumulated effect of roundoff errors is in
some sense statistical. The purpose of this paper is to
give precise descriptions of certain probabilistic
models for roundoff error, and then to describe a
series of experiments for testing the validity of these
models. It is concluded that the models are in general
very good. Discrepancies are both rare and mild. The
test techniques can also be used to experiment with
various types of special arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic; rounding errors",
}
@Manual{IBM:1966:ISM,
key = "IBM",
title = "{IBM System\slash 360 Model 91}: Functional
Characteristics",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1966",
bibdate = "Fri Aug 20 09:34:43 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "File No. S360-01, Form A22-6907-2.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{Isaacson:1966:ANM,
author = "Eugene Isaacson and Herbert Bishop Keller",
title = "Analysis of numerical methods",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 541",
year = "1966",
LCCN = "QA297 .I8",
bibdate = "Fri Aug 20 09:37:14 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}. Reprinted in
\cite{Isaacson:1994:ANM}.",
subject = "Numerical analysis",
}
@Misc{Kahan:1966:ISS,
author = "W. Kahan",
title = "{7094 II} System Support for Numerical Analysis",
howpublished = "SHARE Secretary Distribution 159, C4537",
pages = "1--54",
year = "1966",
bibdate = "Wed Nov 07 08:39:33 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InCollection{Kogbetliantz:1966:GEF,
author = "E. G. Kogbetliantz",
title = "Generation of Elementary Functions",
crossref = "Ralston:1966:MMD",
pages = "7--35",
year = "1966",
bibdate = "Sat Dec 09 14:09:27 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Kuki:1966:EGS,
author = "H. Kuki and E. Hanson and J. J. Ortega and J. C.
Butcher and P. G. Anderson",
title = "Evaluation Guidelines {SHARE Numerical Analysis
Project (N.A.P.)}",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 150, part II",
number = "C4304",
pages = "1--42",
year = "1966",
bibdate = "Fri Aug 20 09:45:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Lam:1966:COG,
author = "Lay-yong Lam",
title = "On the {Chinese} origin of the {Galley} method of
arithmetical division",
journal = j-BRITISH-J-HIST-SCI,
volume = "3",
number = "part 1, 9",
pages = "66--69",
year = "1966",
CODEN = "BJHSAT",
DOI = "https://doi.org/10.1017/S0007087400000200",
ISSN = "0007-0874 (print), 1474-001X (electronic)",
ISSN-L = "0007-0874",
MRclass = "01.10",
MRnumber = "0204243 (34 \#4087)",
MRreviewer = "I. N. Veselovski{\u\i}",
bibdate = "Wed Sep 22 18:01:23 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
ZMnumber = "0143.24202",
acknowledgement = ack-nhfb,
fjournal = "British Journal for the History of Science",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BJH",
keywords = "history",
}
@Article{Mancino:1966:MPF,
author = "O. G. Mancino",
title = "Multiple precision floating-point conversion from
decimal-to-binary and vice versa",
journal = j-CACM,
volume = "9",
number = "5",
pages = "347--348",
month = may,
year = "1966",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355592.365635",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:06 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal-to-binary and binary-to-decimal floating-point
conversion is often performed by using a table of the
powers $ 10^i $ ($i$ a positive integer) for converting
from base $ 10$ to base $2$, and by using a table of
the coefficients of a polynomial approximation of $
10^x (0 \leq x < 1)$ for converting from base $2$ to
base $ 10$. These tables occupy a large storage region
in the case of a nonsingle precision conversion. This
paper shows that a single small table suffices for a
floating-point conversion from decimal to binary, and
vice versa, in any useful precision.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; Multiple precision
arithmetic; number base conversion",
}
@Unpublished{Mazor:1966:FSI,
author = "Stan Mazor",
title = "{Fairchild Symbol II} Decimal Floating Point Unit",
year = "1966",
bibdate = "Wed Nov 22 21:18:53 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in \cite[p. 106]{Cowlishaw:2003:DFP}.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Book{Moore:1966:IA,
author = "Ramon E. Moore",
title = "Interval analysis",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 145",
year = "1966",
LCCN = "QA297 .M63",
bibdate = "Sat Feb 14 08:15:54 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Nickel:1966:NFA,
author = "K. Nickel",
title = "{{\"U}ber die Notwendigkeit einer Fehlerschranken-
Arithmetik f{\"u}r Rechenautomaten}",
journal = j-NUM-MATH,
volume = "9",
pages = "69--79",
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Parker:1966:SNS,
author = "Francis D. Parker",
title = "The structure of number systems",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 137",
year = "1966",
LCCN = "QA241 .P3; QA241 .P239",
bibdate = "Fri Nov 9 19:10:47 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "Teachers' mathematics reference series",
acknowledgement = ack-nhfb,
subject = "Number theory",
}
@Book{Richards:1966:EDS,
author = "R. K. (Richard Kohler) Richards",
title = "Electronic Digital Systems",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "ix + 637",
year = "1966",
LCCN = "TK7888.3 .R52",
bibdate = "Mon Oct 24 05:33:53 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
author-dates = "1921--",
remark = "According to \cite[pp. 168--170]{Smiley:2010:MWI},
this was the first book to draw attention to the
pre-World War II work by John Atanasoff (1903--1995)
and Clifford Berry (1918--1963) at Iowa State College
of Agricultural and Mechanic Arts (renamed on 4 July
1959 to Iowa State University of Science and
Technology), and to name their computer the ABC.
Richards is quoted with ``The ancestry of all
electronic digital systems appears to be traceable to a
computer which will be called the Atanasoff--Berry
Computer.'' The book provided important evidence in the
priority dispute and courtroom battles over who
invented the computer (Atanasoff and Berry versus
Mauchly and Eckert). Berry died in unresolved
circumstances: suicide or murder?",
subject = "Electronic digital computers",
tableofcontents = "1: History and Introduction / 1 \\
2: Theory of Digital Systems / 50 \\
3: The Stored-Program Concept / 109 \\
4: Automatic Programming / 293 \\
5: Digital Data Transmission / 362 \\
6: Combined Analog and Digital Techniques / 451 \\
7: Telephone and Message Switching Systems / 481 \\
8: The Relationship between Thinking and Digital
Systems / 519 \\
9: Miscellaneous Digital Systems / 541 \\
10: Digital System Reliability / 571 \\
11: The Automatic Design of Digital Systems / 610 \\
Index / 631",
}
@Article{Saidan:1966:EEA,
author = "A. S. Saidan",
title = "The Earliest Extant {Arabic} Arithmetic:
{{\booktitle{Kitab al-Fusul fi al Hisab al-Hindi}}} of
{Abu al-Hasan, Ahmad ibn Ibrahim al-Uqlidisi}",
journal = j-ISIS,
volume = "57",
number = "4",
pages = "475--490",
month = "Winter",
year = "1966",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:22:16 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211145;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1960.bib",
URL = "http://www.jstor.org/stable/228518",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Smith:1966:CP,
author = "John Smith",
title = "The Challenge of {Pi}",
journal = j-IEEE-SPECTRUM,
volume = "3",
number = "10",
pages = "5--5",
month = oct,
year = "1966",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1966.5217340",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 08:45:04 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Computer errors; Digital arithmetic; Educational
institutions; Hardware; Physics computing; Power
engineering computing; Programming profession;
Registers; Testing; Upper bound",
remark = "Report of a computation of $ \pi $ to 17,935 places
using base-1,000,000 arithmetic. A footnote reports
``The AIL result to 17,940 places was identical with
the reference to 17,935 places. Reference: D. Shanks
and J. W. Wrench, Jr., `Calculation of Pi to 100,000
Decimals', Mathematics of Computation, January 1962,
Vol. 16, No. 77, pp. 67--99.''",
}
@Article{Spielberg:1966:CEU,
author = "K. Spielberg",
title = "Computation of $ e^x $ with the use of large tables",
journal = j-IBM-SYS-J,
volume = "5",
number = "2",
pages = "102--114",
year = "1966",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:43:03 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Systems Journal",
xxmonth = "(none)",
}
@Article{Tienari:1966:SPM,
author = "M. Tienari and V. Suokonautio",
title = "A Set of Procedures Making Real Arithmetic of
Unlimited Accuracy Possible Within {Algol 60}",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "4",
pages = "332--338",
month = jul,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01966093",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Sep 12 08:07:38 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=4&spage=332",
acknowledgement = ack-nj,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{vanWijngaarden:1966:NAI,
author = "A. {van Wijngaarden}",
title = "Numerical Analysis as an Independent Science",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "6",
number = "1",
pages = "66--81",
month = mar,
year = "1966",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939551",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:09 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=1&spage=66",
abstract = "The paper describes how a number of well-known
mathematical concepts ought to be modified in order to
make sense within the scope of numerical analysis. It
is also shown how obvious difficulties can be overcome
in a logical way. All algorithms suggested are given as
ALGOL procedures.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Watson:1966:SCC,
author = "R. W. Watson and C. W. Hastings",
title = "Self-Checked Computation using Residue Arithmetic",
journal = j-PROC-IEEE,
volume = "54",
number = "12",
pages = "1920--1931",
month = dec,
year = "1966",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 09 19:37:52 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Whitney:1966:PCR,
author = "D. E. Whitney",
title = "Propagation and control of roundoff error in the
matrix exponential method",
journal = j-PROC-IEEE,
volume = "54",
number = "10",
pages = "1483--1484",
month = oct,
year = "1966",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@TechReport{Wiegel:1966:MBA,
author = "R. E. Wiegel",
title = "Methods of Binary Addition",
type = "Technical report",
number = "195",
institution = "Department of Computer Science, University of
Illinois",
address = "Urbana, IL, USA",
month = feb,
year = "1966",
bibdate = "Fri Nov 09 19:40:18 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Adams:1967:SCP,
author = "Duane A. Adams",
title = "A stopping criterion for polynomial root finding",
journal = j-CACM,
volume = "10",
number = "10",
pages = "655--658",
month = oct,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "39\#2314",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When searching for the root of a polynomial, it is
generally difficult to know just when to accept a
number as an adequate approximation to the root. In
this paper an algorithm is presented which allows one
to terminate the iteration process on the basis of
calculated bounds for the roundoff error which occurs
in evaluating the polynomial. This stopping criterion
has been tested on numerous examples and has been found
to serve as a satisfactory means for accepting a
complex number as a zero of a real polynomial.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Anderson:1967:ISMb,
author = "S. F. Anderson and J. G. Earle and R. E. Goldschmidt
and D. M. Powers",
title = "The {IBM System\slash 360 Model 91}: Floating-point
execution unit",
journal = j-IBM-JRD,
volume = "11",
number = "1",
pages = "34--53",
month = jan,
year = "1967",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.111.0034",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 11 15:36:09 MDT 2012",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392016",
abstract = "The principal requirement for the Model 91
floating-point execution unit was that it be designed
to support the instruction-issuing rate of the
processor. The chosen solution was to develop separate,
instruction-oriented algorithms for the add, multiply,
and divide functions. Linked together by the
floating-point instruction unit, the multiple execution
units provide concurrent instruction execution at the
burst rate of one instruction per cycle.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@TechReport{Clark:1967:PSF,
author = "N. A. Clark and W. J. Cody and K. E. Hillstrom and E.
A. Thieleker",
title = "Performance Statistics of the {FORTRAN IV (H)} Library
for the {IBM System\slash 360}",
type = "Technical Report",
number = "ANL-7231",
institution = inst-ANL,
address = inst-ANL:adr,
year = "1967",
bibdate = "Fri Aug 20 08:47:24 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in SHARE Secretary Distribution, SDD 169,
C4473, pp. 12 46.",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Cody:1967:CFI,
author = "W. J. Cody",
title = "Critique of the {FORTRAN IV (H)} Library for the {IBM
System\slash 360}",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 169",
number = "C4473",
pages = "4--11",
year = "1967",
bibdate = "Fri Aug 20 08:52:04 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@InProceedings{Cody:1967:IMD,
author = "W. J. Cody",
title = "The influence of machine design on numerical
algorithms",
crossref = "AFIPS:1967:ACP",
pages = "305--309",
year = "1967",
bibdate = "Sat Sep 24 00:18:32 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Cody:1967:LEA,
author = "William J. {Cody, Jr.}",
title = "Letter to the {Editor}: Another Aspect of Economical
Polynomials",
journal = j-CACM,
volume = "10",
number = "9",
pages = "531--531",
month = sep,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363566.363577",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Nov 17 10:20:03 1994",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fike:1967:MEP}.",
abstract = "In his paper ``Methods of Evaluating Polynomial
Approximations in Function Evaluation Routines'' [Comm.
ACM 10, (March 1967)], C. T. Fike fails to discuss one
very important aspect of the ``economical'' methods for
polynomials. Since these evaluation methods involve a
decreased number of arithmetic operations over the
usual Horner's method (or at least replace a
multiplication by an addition) the implication is that
they are faster to execute. Dr. Fike points out that
these methods can be poorly conditioned for particular
polynomials, thus requiring extended precision or
fixed-point arithmetic to maintain accuracy and costing
more in time than Horner's method. But even if we
assume the methods are well conditioned, the need to
store away and retrieve intermediate results in some
machines with only one floating-point arithmetic
register can wipe out the time savings effected by a
reduction in the number of arithmetic operations. On
many of today's high-performance computers the time
required to store away and retrieve a result is about
the same as the time required for a floating-point
addition. It is no longer sufficient to estimate the
efficiency of a method by a count of arithmetic
operations alone.",
acknowledgement = ack-wjc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic",
}
@Article{Crisansan-Zverca:1967:PED,
author = "Mariana Cri{\c{s}}an-Zverca",
title = "Pseudo-operations of an electronic digital machine
with floating point. ({Romanian})",
journal = j-STUD-CERCET-MAT,
volume = "19",
pages = "1413--1424",
year = "1967",
ISSN = "0039-4068, 0567-6401",
MRclass = "68.00",
MRnumber = "40\#3753",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Studii {\c{s}}i cercet{\u{a}}ri Matematice",
}
@Article{Curry:1967:ART,
author = "E. Curry",
title = "The analysis of round-off and truncation errors in a
hybrid control system",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "12",
number = "5",
pages = "601--604",
month = oct,
year = "1967",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "The round-off and truncation errors of a
digital-analog (hybrid) servo system are studied in
terms of the least upper bound and second moment, or
variance. The study was applied to the azimuth function
of a guided missile launcher system and a \ldots{}",
}
@Article{DeRegt:1967:NRA,
author = "M. P. DeRegt",
title = "Negative radix arithmetic",
journal = j-COMP-DESIGN,
volume = "6",
number = "??",
pages = "52--63",
month = may,
year = "1967",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Thu Nov 06 06:07:24 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Design",
keywords = "negative base",
}
@Article{Ferrari:1967:DMU,
author = "Domenico Ferrari",
title = "A Division Method Using a Parallel Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "224--226",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264580",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See correction \cite{Ferrari:1969:CDM}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039036",
abstract = "The use of a parallel multiplier for performing
high-speed binary division requires that an algorithm
be devised that obtains the quotient by means of
multiplications and additions. Furthermore, its
hardware implementation must be as simple and as fast
as possible. A suitable algorithm, which applies to a
first approximation to the reciprocal of the divisor,
has already been proposed [1]. A similar algorithm is
presented in this paper. The comparison between the two
methods for equal numbers of multiplications shows that
the latter is more accurate. Conversely, a given
accuracy can often be obtained with a higher speed. The
generation of a piecewise-linear initial approximation
is also discussed.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Fike:1967:LER,
author = "C. T. Fike",
title = "Letter to the {Editor}: {A} rational approximation
optimal by {Moursund}'s criterion",
journal = j-CACM,
volume = "10",
number = "11",
pages = "683--684",
month = nov,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363790.363795",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:16 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "elementary function; square root",
remark = "Gives a starting value for $ \sqrt {x} $ ($x$ on $ [1
/ 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x +
0.84106293)$, with an error of $ 2^{-12.496}$.",
}
@Article{Fike:1967:MEP,
author = "C. T. Fike",
title = "Methods of Evaluating Polynomial Approximations in
Function Evaluation Routines",
journal = j-CACM,
volume = "10",
number = "3",
pages = "175--178",
month = mar,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363162.363200",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:12 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remark on efficiency \cite{Cody:1967:LEA}.",
abstract = "The method of nested multiplication is commonly used
in function evaluation routines to evaluate
approximation polynomials. New polynomial evaluation
methods have been developed in recent years which
require fewer multiplications than nested
multiplication and may therefore be preferable for use
in function evaluation routines. Although some of these
methods do not appear to be practically useful because
of rounding-error difficulties, several methods of
evaluating low-degree polynomials have been found to be
satisfactory. Three such methods are described and
illustrated.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Fike:1967:RAO,
author = "C. T. Fike",
title = "A Rational Approximation Optimal by {Moursund}'s
Criterion (letter to the editor)",
journal = j-CACM,
volume = "10",
number = "11",
pages = "683--684",
month = nov,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Filho:1967:AGF,
author = "A. M. S. Filho and G. Schwachheim",
title = "Algorithm 309: Gamma Function with Arbitrary
Precision",
journal = j-CACM,
volume = "10",
number = "8",
pages = "511--512",
month = aug,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Book{Forsythe:1967:CSL,
author = "George E. Forsythe and Cleve B. Moler",
title = "Computer Solution of Linear Algebraic Systems",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 148",
year = "1967",
LCCN = "QA297 .F57 1967",
MRclass = "65.35",
MRnumber = "MR0219223 (36 \#2306)",
MRreviewer = "N. Gastinel",
bibdate = "Tue May 25 08:52:32 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
ZMnumber = "0154.40401",
acknowledgement = ack-nhfb,
keywords = "numerical analysis; software",
remark = "Translated to Russian (1969), Japanese (1969), and
German (1971). Cited in \cite{Sterbenz:1974:FPC}.",
subject = "numerical analysis; data processing; matrices",
tableofcontents = "Reader's background and purpose of book \\
Vector and matrix norms \\
Diagonal form of a matrix under orthogonal equivalence
\\
Proof of diagonal-form theorem \\
Types of computational problems in linear algebra \\
Types of matrices encountered impractical problems \\
Sources of computational problems of linear algebra \\
Condition of a linear system \\
Gaussian elimination and LU decomposition \\
Need for interchanging rows \\
Scaling equations and unknowns \\
The Crout and Doolittle variants \\
Iterative improvement \\
Computing the determinant \\
Nearly singular matrices \\
Algol 60 program \\
Fortran, extended Algol, and PL/1 programs \\
Matrix inversion \\
An example: Hilbert matrices \\
Floating-point round-off analysis \\
Rounding error in Gaussian elimination \\
Convergence of iterative improvement \\
Positive definite matrices; band matrices \\
Iterative methods for solving linear systems \\
Nonlinear systems of equations",
}
@Article{Freeman:1967:CMS,
author = "Herbert Freeman",
title = "Calculation of Mean Shift for a Binary Multiplier
Using $2$, $3$, or $4$ Bits at a Time",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "6",
pages = "864--866",
month = dec,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264752",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:06 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039205",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Freiman:1967:CDU,
author = "C. V. Freiman and others",
title = "Composite Division Unit",
journal = j-IBM-TDB,
volume = "9",
number = "8",
pages = "994--995",
month = jan,
year = "1967",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Tue Jan 08 22:40:53 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Friedland:1967:AAV,
author = "Paul Friedland",
title = "{Algorithm 312}: {Absolute} Value and Square Root of a
Complex Number",
journal = j-CACM,
volume = "10",
number = "10",
pages = "665--665",
month = oct,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363717.363780",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\abs(z)$; $\sqrt(z)$; elementary functions",
}
@Article{Goldberg:1967:BED,
author = "I. Bennett Goldberg",
title = "$ 27 $ Bits Are Not Enough For $8$-Digit Accuracy",
journal = j-CACM,
volume = "10",
number = "2",
pages = "105--106",
month = feb,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363067.363112",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:11 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "From the inequality $ 10^8 < 2^{27} $, we are likely
to conclude that we can represent 8-digit decimal
floating-point numbers accurately by 27-bit [binary]
floating-point numbers. However, we need 28 significant
bits to represent some 8-digit numbers accurately. In
general, we can show that if $ 10^p < 2^{q - 1} $, then
$q$ significant bits are always enough for $p$-digit
decimal accuracy. Finally, we can define a compact
27-bit floating-point representation that will give 28
significant bits, for numbers of practical
importance.",
acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic",
received = "August 1966 (revised October 1966)",
}
@Book{Gschwind:1967:DDC,
author = "H. W. Gschwind",
title = "Design of Digital Computers: An Introduction",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 530",
year = "1967",
LCCN = "TK7888.3 .G72",
bibdate = "Fri Nov 09 18:56:39 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Hertz:1967:CHF,
author = "Theodore M. Hertz",
title = "Computer Having Floating Point Multiplication",
howpublished = "US Patent 3,304,417.",
day = "14",
month = feb,
year = "1967",
bibdate = "Sat Mar 24 06:05:12 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Filed 1 October 1962.",
URL = "https://patentimages.storage.googleapis.com/47/86/c8/897ec6540ff584/US3304417.pdf;
https://patents.google.com/patent/US3304417",
abstract = "Prior art digital computers utilized fixed point
arithmetic processes in executing computer operations.
In performing fixed point arithmetic processes a
computer assumes the binary point (analogous to a
decimal point) to be between the sign of a number and
the most significant digit of the number. Thus the
number is considered to have an absolute value of less
than one. As explained in patent application filed
September 24, 1962, Serial No. 225,676, now abandoned,
for a ``Computer Having Floating Point Addition and
Floating Point Subtraction'' invented by me, in order
to execute fixed point addition and subtraction
operations, numbers to be operated upon by a computer
must first be appropriately scaled prior to computation
in order to obtain the scaling of the numbers is
accomplished prior to entering them into the computer
or by shifting them through programming afterwards.
Fixed point multiplication needs to have numbers scale
prior to performing computations with them. In
multiplication, shifting of the result through
programming is desirable in order to prevent loss of
significant portions which should be retained for use
in later computations. Particularly is it true where
after a multiplication operation has been performed,
the product must be added or subtracted from or with
other numbers, in which case scaling would first have
to be done before the additional computation could be
made.",
acknowledgement = ack-nhfb,
}
@Article{Howell:1967:MPA,
author = "K. M. Howell",
title = "Multiple precision arithmetic techniques",
journal = j-COMP-J,
volume = "9",
number = "4",
pages = "383--387",
month = feb,
year = "1967",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:19 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/090383.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/383.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/384.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/385.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/386.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/387.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Jarden:1967:EAL,
author = "Dov Jarden",
title = "Existence of Arbitrarily Long Sequences of Consecutive
Members in Arithmetic Progressions Divisible by
Arbitrarily Many Different Primes",
journal = j-FIB-QUART,
volume = "5",
number = "3",
pages = "280--??",
month = oct,
year = "1967",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:54 MDT 2011",
bibsource = "http://www.fq.math.ca/5-3.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/5-3/jarden1.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Krishnamurthy:1967:NRD,
author = "E. V. Krishnamurthy and S. K. Nandi",
title = "On the Normalization Requirement of Divisor in
Divide-and-Correct Methods",
journal = j-CACM,
volume = "10",
number = "12",
pages = "809--813",
month = dec,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Kuki:1967:CAE,
author = "H. Kuki",
title = "Comments on the {ANL} Evaluation of the {OS\slash 360
FORTRAN} Math Function Library",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 169",
number = "C4773",
pages = "47--53",
year = "1967",
bibdate = "Fri Aug 20 09:42:04 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Lewis:1967:CFP,
author = "H. R. {Lewis, Jr.} and E. J. {Stovall, Jr.}",
title = "Comments on a Floating-Point Version of {Nordsieck}'s
Scheme for the Numerical Integration of Differential
Equations",
journal = j-MATH-COMPUT,
volume = "21",
number = "98",
pages = "157--161",
month = apr,
year = "1967",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Long:1967:LAS,
author = "C. T. Long and J. H. Jordan",
title = "A Limited Arithmetic on Simple Continued Fractions",
journal = j-FIB-QUART,
volume = "5",
number = "2",
pages = "113--128",
month = apr,
year = "1967",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:52 MDT 2011",
bibsource = "http://www.fq.math.ca/5-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/5-2/long.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Mandelbaum:1967:CLS,
author = "David Mandelbaum",
title = "A Comparison of Linear Sequential Circuits and
Arithmetic Sequences",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "151--157",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264810",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:01 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039022",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@Article{Massell:1967:RAP,
author = "E. Massell",
title = "{R67-41} An Analog Photoresistive Multiplier",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "3",
pages = "380--380",
month = jun,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264730",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See comment \cite{Azgapetian:1968:CAP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039094",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
}
@InProceedings{Matula:1967:BCM,
author = "David W. Matula",
booktitle = "{Proceedings of the AFIPS 1967 Spring Joint Computer
Conference}",
title = "Base Conversion Mappings",
volume = "30",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "311--318",
year = "1967",
bibdate = "Wed Feb 14 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Book{McCalla:1967:INM,
author = "Thomas Richard McCalla",
title = "Introduction to Numerical Methods and {Fortran}
Programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 359",
month = jan,
year = "1967",
ISBN = "0-471-58125-9",
ISBN-13 = "978-0-471-58125-3",
LCCN = "QA297 .M25",
bibdate = "Sat Sep 27 17:58:26 MDT 1997",
bibsource = "http://www.amazon.com/exec/obidos/ISBN=0471581259/wholesaleproductA/;
http://www.cbooks.com/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$27.95",
URL = "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0471581259",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.; FORTRAN
(Computer program language); Numerical analysis.",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{McKeeman:1967:RER,
author = "W. M. McKeeman",
title = "Representation Error for Real Numbers in Binary
Computer Arithmetic",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "5",
pages = "682--683",
month = oct,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264781",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039164",
abstract = "Real numbers can be represented in a binary computer
by the form $ i \cdot B^e $ where $i$ is the integer
part, $B$ the base, and $e$ the exponent. The accuracy
of the representation will depend upon the number of
bits allocated to the integer part and exponent part as
well as what base is chosen. If $ L(i) $ and $ L(e) $
are the number of bits allocated to the magnitudes of
the integer and exponent parts and we define $ I =
2^{L(i)} $ and $ E = 2^{L(e)} $, the exponent range is
given by $ B^{\pm E} $, the maximum relative
representation error is given by $ B / 2 I $, and the
average relative representation error is given by $ (B
- 1) / (4 I \ln B) $. The formulas provide quantitative
comparison for the effectiveness of alternative formats
for real number representations.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
remark = "McKeeman discusses the maximum and average relative
errors in binary (with and without a hidden bit),
octal, and hexadecimal bases for floating-point
arithmetic with a 48-bit computer word. Errors are
smallest with binary and a hidden bit.",
}
@Article{Menzel:1967:AUA,
author = "M. Menzel and N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {II}.
{Unrestricted} polynomial evaluation",
journal = j-NUM-MATH,
volume = "10",
number = "5",
pages = "451--462",
month = nov,
year = "1967",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162878",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.80",
MRnumber = "MR0255093 (40 \#8300)",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0225.65059",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Minsky:1967:CFI,
author = "Marvin Lee Minsky",
title = "Computation: Finite and Infinite Machines",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xvii + 317",
year = "1967",
LCCN = "QA267 .M55",
bibdate = "Thu Oct 17 06:05:56 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1927--2016",
tableofcontents = "Physical machines and their abstract counterparts
\\
Part 1: Finite-state machines \\
Neural networks. Automata made up of parts \\
The memories of events in finite-state machines \\
Part 2: Infinite machines \\
Computability, effective procedures, and algorithms.
Infinite machines \\
Turing machines \\
Universal Turing machines \\
Limitations of effective computability: some problems
not solvable by instruction-obeying machines \\
The computable real numbers \\
The relations between Turing machines and recursive
functions \\
Models similar to digital computers \\
Part 3: Symbol-manipulation systems and computability
\\
The symbol-manipulation systems of post \\
Post's normal-form theorem \\
Very simple bases for computability \\
Solutions to selected problems",
}
@Article{Moler:1967:IRF,
author = "C. B. Moler",
title = "Iterative Refinement in Floating Point",
journal = j-J-ACM,
volume = "14",
number = "2",
pages = "316--321",
month = apr,
year = "1967",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue Nov 1 09:43:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "ir, nla, lud, iterative refinement",
}
@Article{Mosteller:1967:DSR,
author = "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
title = "The Distribution of Sums of Rounded Percentages",
journal = j-DEMOGRAPHY,
volume = "4",
number = "2",
pages = "850--858",
month = jun,
year = "1967",
CODEN = "????",
ISSN = "0070-3370 (print), 1533-7790 (electronic)",
ISSN-L = "0070-3370",
bibdate = "Thu Nov 24 08:03:16 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Diaconis:1979:RP} for further work.",
URL = "http://muse.jhu.edu/journals/dem/;
http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
http://www.jstor.org/stable/2060324",
abstract = "When percentages are computed for counts in several
categories or for several positive measurements0 each
taken as a fraction of their sum, the rounded
percentages often fail to add to 100 percent. We
investigate how frequently this failure occurs and what
the distributions of sums of rounded percentages are
for (1) an empirical set of data, (2) the multinomial
distribution in small samples, (3) spacings between
points dropped on an interval --- the broken-stick
model; and (4) for simulation for several categories.
The several methods produce similar distributions.We
find that the probability that the sum of rounded
percentages adds to exactly 100 percent is certain for
two categories, about three-fourths for three
categories, about two-thirds for four categories, and
about [Formula: see text] for larger numbers of
categories, c, on the average when categories are not
improbable.",
acknowledgement = ack-nhfb,
fjournal = "Demography",
pubmedid = "21318695",
}
@Article{Moursund:1967:OSV,
author = "David G. Moursund",
title = "Optimal starting values for {Newton--Raphson}
calculation of $ \sqrt {x} $",
journal = j-CACM,
volume = "10",
number = "7",
pages = "430--432",
month = jul,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363427.363454",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "39\#2297",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letter \cite{Fike:1967:LER}.",
abstract = "The problem of obtaining starting values for the
Newton-Raphson calculation of $ \sqrt {x} $ on a
digital computer is considered. It is shown that the
conventionally used best uniform approximations to $
\sqrt {x} $ do not provide optimal starting values. The
problem of obtaining optimal starting values is stated,
and several basic results are proved. A table of
optimal polynomial starting values is given.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions",
remark = "Title of article has incorrect $ \sqrt (x^{1 / 2}) $:
the article discusses computation of {\tt sqrt(x)}.",
}
@Article{Nandi:1967:STD,
author = "Salil K. Nandi and E. V. Krishnamurthy",
title = "A simple technique for digital division",
journal = j-CACM,
volume = "10",
number = "5",
pages = "299--301",
month = may,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:13 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Sandberg:1967:FPR,
author = "I. W. Sandberg",
title = "Floating-Point-Roundoff Accumulation in Digital-Filter
Realizations",
journal = j-BELL-SYST-TECH-J,
volume = "46",
number = "8",
pages = "1775--1791",
month = oct,
year = "1967",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4608.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-8-1775.pdf",
abstract = "In this paper, several results are presented
concerning the effects of roundoff in the
floating-point realization of a general discrete filter
governed ideally by a stable difference equation of the
form\par
$$ w_n = \sum_{k = 0}^M b_k x_{n - k} - \sum {k = 1}^N
a_k w_{n - k}, \qquad n \geq N \qquad (1) $$ \par
in which $ \{ w_n \} $ and $ \{ x_n \} $ are output and
input sequences, respectively.\par
In particular, for a large class of filters it is
proved that there is a function $ f(K) $ with $ f(K)
\to 0 $ as $ K \to \infty $ and a constant $c$, both
dependent on the $ b_k $, the $ a_k $, the order in
which the products on the right side of (1) are summed
in the machine, and $t$, the number of bits allotted to
the mantissa, such that\par
$$ \langle e \rangle_K \leq c \langle y \rangle_K +
f(K) $$ \par
for all $ K \geq N $, in which, with the computed
output sequence of the realized filter,\par
$$ \langle y \rangle_K = \left (\frac {1}{K + 1}
\sum_{n = 0}^K |y_n|^2 \right)^{1 / 2} $$ \par
and\par
$$ \langle e \rangle_K = \left (\frac {1}{K + 1}
\sum_{n = 0}^K |w_n - y_n|^2 \right)^{1 / 2} $$
\par
Bounds on $ f(K) $ and $c$ are given that are not
difficult to evaluate, and which, in many realistic
cases, are informative. For example, for the
second-order bandpass filter:\par
$$ w_n = x_n - a_1 w_{n - 1} - a_2 w_{n - 2}, \qquad n
\geq 2 \qquad (2) $$ \par
with $ a_1 $ and $ a_2 $ chosen so that its poles arc
at approximately $ \pm 45^\circ $ and at distance
approximately (but not less than) $ 0.001 $ from the
unit circle, we find that $c$, an upper bound on the
``asymptotic output error-to-signal ratio'', is not
greater than $ 0.58 \times 10^{-4} $, assuming that $ t
= 27 $, that the terms on the right side of (2) are
summed in the machine in the order indicated (from
right to left), and that the $ x_n $ in (2) are machine
numbers. If the $ x_n $ are not machine numbers, and
hence must be quantized before processing, then $ c
\leq 0.76 \times 10^{-4} $.\par
In addition to error bounds, an inequality is derived
which, if satisfied, rules out certain types of
generally undesirable behavior such as self-sustained
output limit cycles due to roundoff effects. This
inequality is satisfied for the example described
above.",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Sasaki:1967:ASR,
author = "Akio Sasaki",
title = "Addition and Subtraction in the Residue Number
System",
journal = j-IEEE-TRANS-ELEC-COMPUT,
volume = "EC-16",
number = "2",
pages = "157--164",
month = apr,
year = "1967",
CODEN = "IEECA8",
DOI = "https://doi.org/10.1109/PGEC.1967.264811",
ISSN = "0367-7508",
bibdate = "Wed Jul 13 21:15:01 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039023;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4039015",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Electronic Computers",
keywords = "residue arithmetic; residue number system",
summary = "Improved residue expression and new arithmetic
algorithms for addition and subtraction are proposed.
In the proposed system positive and negative integers
of any magnitude can be handled regardless of the
particular choice of the set of relatively \ldots{}",
}
@Book{Szabo:1967:RAA,
author = "Nicholas S. Szab{\'o} and Richard I. Tanaka",
title = "Residue arithmetic and its applications to computer
technology",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvi + 236",
year = "1967",
LCCN = "QA247.35 .S95",
bibdate = "Fri Jun 24 16:02:00 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "McGraw-Hill series in information processing and
computers",
acknowledgement = ack-nhfb,
remark = "Based on the authors' Report on residue (modular)
arithmetic survey.",
subject = "Modular arithmetic; Algorithms; Computer programming",
}
@Article{Tomasulo:1967:EAE,
author = "R. M. Tomasulo",
title = "An Efficient Algorithm for Exploiting Multiple
Arithmetic Units",
journal = j-IBM-JRD,
volume = "11",
number = "1",
pages = "25--33",
month = jan,
year = "1967",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Fri Aug 26 10:27:10 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Book{Wilkinson:1967:BZW,
author = "J. H. Wilkinson",
title = "Bledy Zaokragle{\'n} w Procesach Algebraicznych.
({Polish}) [{Rounding} errors in algebraic Processes]",
publisher = "PWW",
address = "Warszawa, Poland",
pages = "????",
year = "1967",
bibdate = "Thu Aug 25 09:28:02 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Polish translation of \cite{Wilkinson:1963:REA}",
acknowledgement = ack-nhfb,
language = "Polish",
}
@Article{Winograd:1967:TRP,
author = "Shmuel Winograd",
title = "On the Time Required to Perform Multiplication",
journal = j-J-ACM,
volume = "14",
number = "4",
pages = "793--802",
month = oct,
year = "1967",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321420.321438",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Feb 8 10:29:30 2020",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Yarbrough:1967:PCC,
author = "Lynn Yarbrough",
title = "Precision calculations of $e$ and $ \pi $ constants",
journal = j-CACM,
volume = "10",
number = "9",
pages = "537--537",
month = sep,
year = "1967",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363566.363578",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:15 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point arithmetic; number base conversion",
remark = "Gives decimal, octal, and hexadecimal values of $e$
and $ \pi $ to 100 digits, and notes ``The difficulty
arises because assemblers and compilers are hardly ever
designed to convert decimal constants to a precision of
more than a dozen or so digits. Thus, if calculations
to greater precision are to be done, constants usually
must be input in octal or other binary-derived
representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Atkins:1968:HRD,
author = "D. E. Atkins",
title = "Higher-radix division using estimates of the divisor
and partial remainders",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "10",
pages = "925--934",
month = oct,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226439",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Azen:1968:DMS,
author = "S. Azen and S. Derr",
title = "On the Distribution of the Most Significant
Hexadecimal Digit",
type = "Technical Report",
number = "RM 5496 PR",
institution = "Rand Report",
address = "Santa Monica, CA, USA",
year = "1968",
bibdate = "Wed Feb 14 17:22:53 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Azgapetian:1968:CAP,
author = "V. Azgapetian",
title = "Comment on {``An Analog Photoresistive Multiplier''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "2",
pages = "188--188",
month = feb,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229083",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Massell:1967:RAP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687312",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brennan:1968:FTA,
author = "J. F. Brennan",
title = "The Fastest Time of Addition and Multiplication",
journal = "IBM Research Reports",
volume = "4",
number = "1",
pages = "??--??",
month = "????",
year = "1968",
bibdate = "Fri Nov 09 10:43:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Dean:1968:GRB,
author = "K. J. Dean",
title = "Generator for the reciprocals of binary numbers",
journal = j-PROC-IEE,
volume = "115",
number = "6",
pages = "787",
month = jun,
year = "1968",
CODEN = "PIEEAH",
DOI = "https://doi.org/10.1049/piee.1968.0142",
ISSN = "0020-3270 (print), 2053-7891 (electronic)",
ISSN-L = "0020-3270",
bibdate = "Thu Apr 10 13:07:02 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Institution of Electrical
Engineers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5247218",
}
@Article{Dietmeyer:1968:GPI,
author = "D. L. Dietmeyer and J. R. Duley",
title = "Generating prime implicants via ternary encoding and
decimal arithmetic",
journal = j-CACM,
volume = "11",
number = "7",
pages = "520--523",
month = jul,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/363397.363565",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Aug 07 17:25:16 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal arithmetic, ternary encoding of cubes, and
topological considerations are used in an algorithm to
obtain the extremals and prime implicants of Boolean
functions. The algorithm, which has been programmed in
the FORTRAN language, generally requires less memory
than other minimization procedures, and treats DON'T
CARE terms in an efficient manner.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "cubical complexes; extremal; minimization; prime
implicants; switching function; ternary encoding",
}
@Article{Elliott:1968:EAA,
author = "David Elliott",
title = "Error analysis of an algorithm for summing certain
finite series",
journal = j-J-AUSTRALIAN-MATH-SOC,
volume = "8",
number = "2",
pages = "213--221",
month = may,
year = "1968",
CODEN = "JAUMAX",
DOI = "https://doi.org/10.1017/s1446788700005267",
ISSN = "0004-9735 (print), 2059-9234 (electronic)",
ISSN-L = "0004-9735",
MRclass = "65.25",
MRnumber = "0230452",
MRreviewer = "U. C. Guha",
bibdate = "Fri Feb 9 15:20:35 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Australian Mathematical Society",
remark = "Analysis of Clenshaw algorithm for Chebyshev summation
\cite{Clenshaw:1955:NSC}, and report of region of
instability of that procedure",
}
@Book{Fike:1968:CEM,
author = "C. T. Fike",
title = "Computer Evaluation of Mathematical Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 227",
year = "1968",
LCCN = "QA297 .F5",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Fraser:1968:AUA,
author = "M. Fraser and N. Metropolis",
title = "Algorithms in unnormalized arithmetic. {III}. {Matrix}
inversion",
journal = j-NUM-MATH,
volume = "12",
number = "5",
pages = "416--428",
month = dec,
year = "1968",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.80",
MRnumber = "MR0255094 (40 \#8301)",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0184.37503",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Harman:1968:ADI,
author = "M. G. Harman",
title = "An Attempt to Design an Improved Multiplication
System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "11",
pages = "1090--1090",
month = nov,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226864",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687268",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Hart:1968:CAa,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-88275-642-7",
ISBN-13 = "978-0-88275-642-4",
LCCN = "QA 297 C64 1978",
bibdate = "Tue Dec 14 22:55:11 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "Reprinted 1978 with corrections.",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
2: General Methods of Computing Functions / 10 \\
3: Least Maximum Approximations / 42 \\
4: The Choice and Application of Approximations / 58
\\
5: Description and Use of the Tables / 82 \\
6: Function Notes / 89 \\
7: Tables of Coefficients / 155 \\
Appendix A: Conversion Algorithms / 307 \\
Appendix B: Bibliography of Approximations / 313 \\
Appendix C: Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
tableofcontents = "1: The Design of a Function Subroutine / 1 \\
1.1 Introduction / 1 \\
1.2 General Considerations in Writing a Function
Subroutine / 2 \\
1.3 Relation of the Function Subroutine to the Computer
System / 3 \\
1.4 The Three Main Types of Function Subroutine / 4 \\
1.5 Special Programming Techniques / 7 \\
1.6 Subroutine Errors / 7 \\
1.7 Final Steps / 9 \\
2: General Methods of Computing Functions / 10 \\
2.1 Introduction / 10 \\
2.2 Application of Infinite Expansions / 11 \\
2.3 Recurrence and Difference Relations / 23 \\
2.4 Iterative Techniques / 27 \\
2.5 Integral Representations / 28 \\
2.6 Differential Equations / 29 \\
2.7 Tabular Data / 32 \\
2.8 Convergence Acceleration / 33 \\
3: Least Maximum Approximations / 42 \\
3.1 Introduction / 42 \\
3.2 Properties of Least Maximum Approximations / 43 \\
3.3 Nearly Least Maximum Approximations / 46 \\
3.4 Rational Approximation / 51 \\
3.5 Segmented Approximation / 54 \\
3.6 Computation of the Tables / 55 \\
4: The Choice and Application of Approximations / 58
\\
4.1 Introduction / 5 8 \\
4.2 Domain Considerations / 58 \\
4.3 Machine Considerations / 62 \\
4.4 Conditioning of Approximations / 65 \\
4.5 Polynomial Forms / 67 \\
4.6 Rational Forms / 73 \\
4.7 Transformation Algorithms / 78 \\
5: Description and Use of the Tables / 82 \\
5.1 Introduction / 22 \\
5.2 Function Notes / 82 \\
5.3 Accuracy of the Coefficients / 83 \\
5.4 How to Use the Tables / 86 \\
5.5 Preparation of the Tables / 88 \\
6: Function Notes / 89 \\
6.1 Square Root, Cube Root / 89 \\
6.2 Exponential and Hyperbolic Functions / 96 \\
6.3 The Logarithm Function / 105 \\
6.4 Trigonometric Functions / 112 \\
6.5 The Inverse Trigonometric Functions / 120 \\
6.6 The Gamma Function and Its Logarithm / 130 \\
6.7 The Error Function / 136 \\
6.8 Bessel Functions / 141 \\
6.9 Complete Elliptic Integrals / 150 \\
7: Tables of Coefficients / 155 \\
Appendix A: Conversion Algorithms / 307 \\
Appendix B: Bibliography of Approximations / 313 \\
Appendix C: Decimal and Octal Constants / 333 \\
References / 336 \\
Index / 341",
}
@Book{Hart:1968:CAb,
author = "John F. Hart and E. W. Cheney and Charles L. Lawson
and Hans J. Maehly and Charles K. Mesztenyi and John R.
Rice and Henry G. {Thatcher, Jr.} and Christoph
Witzgall",
title = "Computer Approximations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 343",
year = "1968",
ISBN = "0-471-35630-1",
ISBN-13 = "978-0-471-35630-1",
LCCN = "QA297 .C64",
bibdate = "Sat Jan 14 14:53:06 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "The SIAM series in applied mathematics",
acknowledgement = ack-nhfb,
}
@Book{IBM:1968:ISP,
author = "{IBM Corporation}",
title = "{IBM System}\slash 360 Principles of Operation",
publisher = pub-IBM,
address = pub-IBM:adr,
edition = "Eighth",
pages = "175",
year = "1968",
LCCN = "QA76.8.I12 I59 1968",
bibdate = "Wed Sep 14 23:12:39 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:1968:ISS,
author = "W. Kahan",
title = "{7094-II} system support for numerical analysis",
howpublished = "SHARE Secretarial Distribution SSD-159.",
year = "1968",
bibdate = "Mon Sep 16 16:14:28 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaneko:1968:PSA,
author = "T. Kaneko and B. Liu",
title = "Round-off error of floating-point digital filters",
crossref = "Anonymous:1968:PSA",
pages = "219--227",
year = "1968",
MRclass = "65.80",
MRnumber = "41\#7878",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Matula:1968:BCT,
author = "David W. Matula",
title = "The Base Conversion Theorem",
journal = j-PROC-AM-MATH-SOC,
volume = "19",
number = "3",
pages = "716--723",
month = jun,
year = "1968",
CODEN = "PAMYAR",
DOI = "https://doi.org/10.1090/s0002-9939-1968-0234908-9",
ISSN = "0002-9939 (print), 1088-6826 (electronic)",
ISSN-L = "0002-9939",
bibdate = "Fri Apr 21 07:26:39 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A demonstration that, in converting numbers from base
$ \beta $ to base $ \nu $, where $ \beta^i \neq \nu^j $
for any positive integers $ i, j $, a one-to-one
mapping exists only if $ \nu^{m - 1} \geq \beta^n - 1
$. Here $m$ is the number of digits in base $ \nu $ and
$n$ that in base $ \beta $.\par
The implications of this result are discussed in the
author's earlier paper [Proc. Amer. Fed. Information
Processing Soc. 30 (1967), 311--318].",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/proc",
received = "9 February 1967",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Matula:1968:C,
author = "David W. Matula",
title = "In-and-out conversions",
journal = j-CACM,
volume = "11",
number = "1",
pages = "47--50",
month = jan,
year = "1968",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362851.362887",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.80",
MRnumber = "39\#2360",
bibdate = "Fri Nov 25 18:20:17 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Goldberg:1967:BED,Matula:1968:BCT}",
abstract = "By an in-and-out conversion we mean that a
floating-point number in one base is converted into a
floating-point number in another base and then
converted back to a floating-point number in the
original base. For all combinations of rounding and
truncation conversions the question is considered of
how many significant digits are needed in the
intermediate base to allow such in-and-out conversions
to return the original number (when possible), or at
least significant digit.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "floating-point numbers; number base conversion;
rounding error; significance; truncation error",
received = "April 1967 (revised August 1967)",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Metropolis:1968:ANA,
author = "N. Metropolis",
title = "Algorithms in un-normalized arithmetic: Polynomial
evaluation and matrix decomposition",
journal = "Colloques internationaux, Centre National de la
Recherche Scientifique, Paris",
volume = "165",
pages = "293--303",
year = "1968",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0207.15804",
acknowledgement = ack-nhfb,
classmath = "*65H05 (Single nonlinear equations (numerical
methods)) 65F05 (Direct methods for linear systems)",
}
@Article{Nathan:1968:IVS,
author = "A. Nathan and J. Molcho",
title = "Improved Voltage Selector and Cascade Multiplier
Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "4",
pages = "380--382",
month = apr,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229386",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687350",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Nickel:1968:EBC,
author = "K. Nickel",
booktitle = "Proceedings of the {IFIP} Congress",
title = "Error Bounds and Computer Arithmetic",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "54--60",
year = "1968",
LCCN = "????",
bibdate = "Fri Aug 20 10:09:47 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Nievergelt:1968:CCP,
author = "J. Nievergelt",
title = "Computers and computing --- Past present Future",
journal = j-IEEE-SPECTRUM,
volume = "5",
number = "1",
pages = "57--61",
month = jan,
year = "1968",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1968.5215633",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 09:30:58 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Computer science; Concurrent computing; Digital
arithmetic; Hardware; History; Instruments;
Maintenance; Manufacturing; Programming; Relays",
}
@Article{Padegs:1968:SAS,
author = "A. Padegs",
title = "Structural aspects of the {SYSTEM\slash 360 Model 85},
Part {III}: Extensions to floating-point architecture",
journal = j-IBM-SYS-J,
volume = "7",
number = "1",
pages = "22--29",
year = "1968",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Tue Mar 19 17:38:46 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Systems Journal",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Phillips:1968:EME,
author = "G. M. Phillips",
title = "Estimate of the maximum error in best polynomial
approximations",
journal = j-COMP-J,
volume = "11",
pages = "110--111",
year = "1968",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:39:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Rao:1968:ECL,
author = "T. R. N. Rao",
title = "Error-Checking Logic for Arithmetic-Type Operations of
a Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "9",
pages = "845--849",
month = sep,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229144",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687471",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ross:1968:UMF,
author = "Richard D. Ross",
title = "{University of Mississippi} floating point subroutines
({UMFS})",
institution = "Computer Center, University of Mississippi",
address = "University",
pages = "31",
year = "1968",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic data processing.",
remark = "Cover title.",
}
@Article{Sasaki:1968:BIA,
author = "A. Sasaki",
title = "The Basis for Implementation of Additive Operations in
the Residue Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "11",
pages = "1066--1073",
month = nov,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/TC.1968.226466",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687264;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35582",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A new residue number system algebra has been
previously proposed by the author. The algebra has
solved an essential theoretical barrier in the residue
number system and has enabled one to pursue additive
operations in the residue \ldots{}",
}
@Article{Schmookler:1968:HSB,
author = "M. S. Schmookler",
title = "High Speed Binary to Decimal Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
pages = "506--508",
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.226913",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 28 19:09:15 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This note describes several methods of performing
fast, efficient, binary-to-decimal conversion. With a
modest amount of circuitry, an order of magnitude speed
improvement can is obtained. This achievement offers a
unique advantage to general-purpose computers requiring
special hardware to translate between binary and
decimal numbering systems.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Book{Scott:1968:OET,
author = "Th{\'e}odore G. Scott",
title = "Ordinateurs {\'e}lectroniques, techniques de
programmation: Computer programming techniques",
publisher = "Tournai, Ed. Gamma",
address = "Paris, France",
pages = "662",
year = "1968",
bibdate = "Thu May 09 09:52:34 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cinq volumes. Version fran{\c{c}}aise de Juliette
Charbonneau-Kohiyama.",
acknowledgement = ack-nhfb,
contents = "1. Pr{\'e}sentation du Tutac. Etude du registre - base
et de ses fonctions. Le registre base. - 2. Les sous
programmes. L'entr{\'e}e. La sorite. - 3. La bande
magn{\'e}tique. La d{\'e}tection des erreurs. - 4. Les
calculs en virgule flottante. L'{\'e}dition des
programmes. - 5. La programmation symbolique. Le
language Cobol. Fortran et Algol",
}
@Manual{Smith:1968:CC,
author = "Smith, Robert E. (Robert Elijah)",
title = "Competence course",
organization = "Control Data Corp.",
address = "Minneapolis, MN, USA",
pages = "vi + 296",
year = "1968",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; FORTRAN (Computer program
language)",
remark = "``Computer programming using FORTRAN and card inputs
without key punching!'' Cover title: Competence course,
FORTRAN computer programming. At head of title: School
computer-use plan.",
}
@Book{Stuart:1968:FP,
author = "Fredric Stuart",
title = "{Fortran} programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 353",
year = "1968",
ISBN = "0-471-83477-7",
ISBN-13 = "978-0-471-83477-9",
LCCN = "QA76.5 .S8",
bibdate = "Sat Jan 27 13:40:57 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
{Fortran} (Computer program language)",
remark = "Cited in \cite{Sterbenz:1974:FPC}, but given year
1969.",
}
@Article{Tung:1968:DAS,
author = "Chin Tung",
title = "A Division Algorithm for Signed-Digit Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-17",
number = "9",
pages = "887--889",
month = sep,
year = "1968",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1968.229150",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 17:40:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687477",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Urabe:1968:RED,
author = "Minoru Urabe",
title = "Roundoff Error Distribution in Fixed-Point
Multiplication and a Remark about the Rounding Rule",
journal = j-SIAM-J-NUMER-ANAL,
volume = "5",
number = "2",
pages = "202--210",
month = jun,
year = "1968",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Veltkamp:1968:APV,
author = "G. W. Veltkamp",
title = "{ALGOL} procedures voor het berekenen van een inwendig
product in dubbele precisie. ({Dutch}) [{ALGOL}
procedures for calculating an inner product in double
precision]",
type = "Technical report",
number = "22",
institution = "RC-Informatie, Technische Hogeschool Eindhoven",
address = "Eindhoven, The Netherlands",
year = "1968",
bibdate = "Tue Dec 26 14:53:03 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Dutch",
}
@Article{Vitenko:1968:OAA,
author = "{\=I}. V. V{\=\i}ten'{k}o",
title = "Optimal algorithms for addition and multiplication on
machines with floating point. ({Russian})",
journal = "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz",
volume = "8",
pages = "1076--1084",
year = "1968",
MRnumber = "40\#2250",
bibdate = "Sat Dec 16 16:45:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
reviewer = "J. Kuntzmann",
}
@TechReport{Yohe:1968:CPA,
author = "J. M. Yohe",
title = "Computer Programming for Accuracy",
type = "{MRC} Technical Summary Report",
number = "866",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
month = apr,
year = "1968",
bibdate = "Sun Dec 30 21:42:55 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In most computations, it is tacitly assumed that the
results produced by the program are 'accurate enough'.
This assumption is not always valid. In this report, we
discuss several possible sources of error in digital
computation, and we list several steps which can be
taken to guard against some types of error and
determine an upper bound for the effects of other
types. We illustrate these techniques with our
experience in writing a program to locate zeros of the
Riemann zeta function.",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1969:VPD,
author = "Anonymous",
title = "Video Probability Distributions",
journal = j-IEEE-SPECTRUM,
volume = "6",
number = "4",
pages = "5--5",
month = apr,
year = "1969",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1969.5214042",
ISSN = "1939-9340",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 11:58:06 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Arithmetic; Circuit noise; Detectors; Distribution
functions; Gaussian noise; Probability distribution;
Signal to noise ratio; Tail; Testing; Voltage",
}
@InProceedings{Babuska:1969:NSM,
author = "Ivo Babu{\v{s}}ka",
title = "Numerical stability in mathematical analysis",
crossref = "Morrell:1969:IPP",
pages = "11--23",
year = "1969",
bibdate = "Tue Nov 22 05:36:22 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Banerji:1969:SDR,
author = "D. K. Banerji and J. A. Brzozowski",
title = "Sign Detection in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "4",
pages = "313--320",
month = apr,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1969.222658",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671251;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35034",
abstract = "This paper is concerned with the sign detection
problem in residue number systems. The proposed
solution is applicable only to nonredundant systems. It
is shown that under rather general conditions an
explicit, closed formula for the sign function can be
obtained. In a special case, when one of the moduli is
$2$, the sign function becomes an EXCLUSIVE-OR
function. A sign detection algorithm is proposed and
methods of implementing the algorithm are presented.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
}
@Manual{BrinchHansen:1969:RCR,
author = "Per {Brinch Hansen}",
title = "{RC-4000 Computer} Reference Manual",
number = "RCSL No: 55-D1",
organization = "A/S Regnecentralen",
address = "Copenhagen, Denmark",
pages = "85",
month = jun,
year = "1969",
bibdate = "Sat Mar 09 14:14:25 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bitsavers.org/pdf/regnecentralen/RC_4000_Reference_Manual_Jun69.pdf;
https://www.math.utah.edu/~beebe/RC-4000",
acknowledgement = ack-nhfb,
remark = "The RC-4000 has a 24-bit word, and supplies 12-bit and
24-bit integer arithmetic, and 48-bit floating-point
arithmetic. The latter has a signed 36-bit normalized
two's-complement binary fraction stored at the left of
a double word, followed by a 12-bit two's-complement
signed exponent. The representable range is therefore
[-0x1p-2049, +0x1p2047), or about [-1.547e-617,
1.615e+161]. The sign, and zero value, can be
determined by examining only the first word. Its
floating-point arithmetic can exactly represent 35-bit
integer arithmetic.",
tableofcontents = "1. RC 4000 Specifications / 9 \\
2. Design Considerations / 11 \\
2.1. Word Length / 11 \\
2.2. Register Structure / 11 \\
2.3. Address Modification / 11 \\
2.4. Monitor Control / 12 \\
2.5. Input/Output Control / 13 \\
3. Data and Instruction Formats / 15 \\
3.1. Data Formats / 15 \\
3.2. Storage Addressing / 15 \\
3.3. Working Registers / 16 \\
3.4. Instruction Format / 17 \\
3.5. Address Modify Instruction / 18 \\
4. Integer Arithmetic / 19 \\
4.1. Number Representation / 19 \\
4.2. Byte Arithmetic / 19 \\
4.3. Multiplication and Division / 20 \\
4.4. Overflow and Carry Indication / 21 \\
5. Floating-Point Arithmetic / 22 \\
5.1. Number Representation / 22 \\
5.2. Arithmetic Operations / 23 \\
5.3. Normalization and Rounding / 23 \\
5.4. Precision Modes / 24 \\
5.5. Underflow, Overflow, and Non-Normalized Operands /
25 \\
5.6. Number Conversion / 26 \\
5.7. Exact Arithmetic with Floating-Point Instructions
/ 26 \\
6. Protection System / 28 \\
6.1. Storage Protection / 28 \\
6.2. Privileged Instructions / 29 \\
6.3. Summary of Protection System / 29 \\
6.4. An Example of Protected Areas / 30 \\
7. Interruption System / 32 \\
7.1. Interruption Logic / 32 \\
7.2. Interruption Conditions / 33 \\
8. Low-Speed Data Channel / 35 \\
8.1. Main Characteristics / 35 \\
8.2. Input/Output Instruction / 35 \\
8.3. Channel Operation / 36 \\
8.4. Disconnected and Busy Indication / 37 \\
8.5. Device Commands / 37 \\
8.6. Read / 37 \\
8.7. Sense / 37 \\
8.8. Write / 38 \\
8.9. Control / 39 \\
8.10. Summary of Low-Speed Channel / 39 \\
9. High-Speed Data Channel / 41 \\
10. Standard Peripheral Devices / 43 \\
10.1. Console Devices / 43 \\
10.2. Interval Timer / 43 \\
11. Operator Control Panel / 44 \\
11.1. Indicators and Control Keys / 44 \\
11.2. Machine Errors / 44 \\
11.3. Reset Control / 44 \\
11.4. Start Control / 45 \\
11.5. Autoload Control / 45 \\
11.6. Local/Remote Indication / 46 \\
12. Technical Control Panel / 47 \\
12.1. Operating Modes / 47 \\
12.2. Instruction Step Keys / 47 \\
12.3. Register Setting and Display / 47 \\
12.4. Microinstruction Selection and Display / 48 \\
12.5. Parity Control / 48 \\
13. Instruction Set / 49 \\
14. Definition of Instructions / 51 \\
14.1. Algol Notation / 51 \\
14.2. Register Structure / 51 \\
14.3. Elementary Operations / 54 \\
14.4. Control Panel Functions / 55 \\
14.5. Instruction Fetch Cycle / 55 \\
14.6. Protection Procedures / 56 \\
14.7. Arithmetic Procedures / 57 \\
14.8. Instruction Execution / 58 \\
Appendix / 79 \\
A.1. Reserved Storage Locations / 79 \\
A.2. Numeric Instruction Codes / 80 \\
A.3. Instruction Execution Times / 81 \\
Index / 83",
}
@Article{Brown:1969:CB,
author = "W. S. Brown and P. L. Richman",
title = "The Choice of Base",
journal = j-CACM,
volume = "12",
number = "10",
pages = "560--561",
month = oct,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68.00",
MRnumber = "43\#5755",
bibdate = "Mon Mar 24 21:38:51 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A digital computer is considered, whose memory words
are composed of $N$ $r$-state devices plus two sign
bits (two state devices). The choice of base $ \beta $
for the internal representation floating-point numbers
on such a computer is discussed. It is shown that in a
certain sense $ \beta = r $ is best.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Bell Telephone Labs. Inc., Murray Hill, NJ, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "accuracy; base choice; digital arithmetic;
floating-point; number representations",
}
@InProceedings{Clark:1969:SCE,
author = "N. W. Clark and W. J. Cody",
title = "Self-contained exponentiation",
crossref = "AFIPS:1969:ACPb",
volume = "35",
pages = "701--706",
year = "1969",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Cody:1969:PTF,
author = "W. J. Cody",
title = "Performance testing of function subroutines",
crossref = "AFIPS:1969:ACPa",
volume = "34",
pages = "759--763",
year = "1969",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Duke:1969:DFP,
author = "K. A. Duke",
title = "Decimal Floating Point Processor",
journal = j-IBM-TDB,
volume = "11-69",
pages = "862--862",
month = nov,
year = "1969",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 11:29:48 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
remark = "Decimal arithmetic with unnormalized binary integers
of unspecified length for coefficient and exponent.",
}
@MastersThesis{Duncan:1969:FFA,
author = "Daniel D. A. Duncan",
title = "{FLOP}: a floating-point arithmetic package",
type = "Thesis ({M.S.})",
school = "University of Southwestern Louisiana",
address = "Lafayette, LA, USA",
pages = "108",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Arithmetic --- Foundations.; FLOP
(Computer program language).; Transformations
(Mathematics).",
}
@Article{Dunworth:1969:ECB,
author = "A. Dunworth and J. I. Roche",
title = "The Error Characteristics of the Binary Rate
Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "8",
pages = "741--745",
month = aug,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222757",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671350",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ehrman:1969:SFP,
author = "J. R. Ehrman",
title = "A Study of Floating-Point Conversions in Some
{OS\slash 360} Components",
number = "SDD 196, C5207",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "1--6",
year = "1969",
bibdate = "Wed Feb 14 18:50:19 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Fenstad:1969:NSM,
author = "Jens Erik Fenstad",
title = "Non-standard models for arithmetic and analysis",
journal = j-LECT-NOTES-MATH,
volume = "118",
pages = "30--47",
year = "1969",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0060250",
ISBN = "3-540-04907-X (print), 3-540-36246-0 (e-book)",
ISBN-13 = "978-3-540-04907-4 (print), 978-3-540-36246-3
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Thu May 8 17:39:14 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0060250/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0060247",
book-URL = "http://www.springerlink.com/content/978-3-540-36246-3",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Fenwick:1969:BMO,
author = "P. M. Fenwick",
title = "Binary Multiplication with Overlapped Addition
Cycles",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "1",
pages = "71--74",
month = jan,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222527",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671120",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ferrari:1969:CDM,
author = "D. Ferrari",
title = "Correction to {``A Division Method Using a Parallel
Multiplier''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "10",
pages = "960--960",
month = oct,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222555",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Ferrari:1967:DMU}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671148",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Field:1969:OFP,
author = "J. A. Field",
title = "Optimizing floating-point arithmetic via post addition
shift probabilities",
crossref = "AFIPS:1969:ACPa",
pages = "597--??",
year = "1969",
bibdate = "Tue Oct 09 07:54:02 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Flores:1969:BRB,
author = "Ivan Flores",
title = "Book Review: {{\booktitle{Residue Arithmetic and Its
Application to Computer Technology}} (Nicholas S. Szabo
and Richard I. Tanaka)}",
journal = j-SIAM-REVIEW,
volume = "11",
number = "1",
pages = "103--104",
month = "????",
year = "1969",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1011027",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:04 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/11/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1969",
}
@Book{Froberg:1969:INA,
author = "Carl Erik Fr{\"o}berg",
title = "Introduction to numerical analysis",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xii + 433",
year = "1969",
LCCN = "QA297 .F6813 1969",
bibdate = "Fri Aug 20 09:03:07 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Translation of Swedish original {\em L{\"a}robok i
numerisk analys}. Cited in \cite{Sterbenz:1974:FPC}.",
subject = "Numerical analysis",
}
@PhdThesis{Glaser:1969:HMN,
author = "Anton Glaser",
title = "History of Modern Numeration Systems",
type = "{Educat.D.} thesis",
school = "Temple University",
address = "Philadelphia, PA, USA",
pages = "261",
year = "1969",
bibdate = "Fri Mar 17 08:18:07 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See subsequent books
\cite{Glaser:1971:HBO,Glaser:1981:HBO}.",
URL = "https://www.proquest.com/pqdtglobal/docview/302503306/A48758ED17C34A1APQ/1",
acknowledgement = ack-nhfb,
remark = "ProQuest dissertation number 7016666.",
}
@Article{Hammersley:1969:NAP,
author = "P. Hammersley",
title = "Note on {Algorithm 34}: Procedures for the Basic
Arithmetical Operations in Multi-Length Working",
journal = j-COMP-J,
volume = "12",
number = "1",
pages = "102--103",
month = feb,
year = "1969",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:33 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/102.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/103.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Holzwarth:1969:VBB,
author = "A. Holzwarth",
title = "{Ein Verfahren zur Bestimmung bester
Tscheb\-y\-scheff- Ap\-prox\-i\-ma\-tion\-en der
Quadratwurzelfunktion} \toenglish {A Method for
Determination of Best Chebyshev Approximations to the
Square Root Function} \endtoenglish",
journal = j-COMPUTING,
volume = "4",
number = "2",
pages = "168--177",
year = "1969",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
affiliation = "T{\"u}bingen, West Germany",
classification = "C4130",
description = "Chebyshev approximation; numerical analysis",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Howell:1969:ASLa,
author = "Jo Ann Howell and Robert T. Gregory",
title = "An algorithm for solving linear algebraic equations
using residue arithmetic. {I}",
journal = j-BIT,
volume = "9",
pages = "200--224",
year = "1969",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261775 (41 \#6388a)",
bibdate = "Thu Nov 8 14:50:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Howell:1969:ASLb,
author = "Jo Ann Howell and Robert T. Gregory",
title = "An algorithm for solving linear algebraic equations
using residue arithmetic. {II}",
journal = j-BIT,
volume = "9",
pages = "324--337",
year = "1969",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261776 (41 \#6388b)",
MRreviewer = "J. Legras",
bibdate = "Thu Nov 8 14:50:18 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@MastersThesis{Huey:1969:DFP,
author = "Ben Milton Huey",
title = "Design of a floating point processor for the {PDP-9}
computer",
type = "Thesis ({M.S. - Electrical Engineering})",
school = "University of Arizona",
address = "Tucson, AZ, USA",
pages = "175",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer storage devices.; Hybrid computers.",
}
@Article{Huttenhoff:1969:AUC,
author = "J. H. Huttenhoff and R. R. Shively",
title = "Arithmetic Unit of a Computing Element in a Global,
Highly Parallel Computer",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "8",
pages = "695--698",
month = aug,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222751",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671344",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{King:1969:LEN,
author = "Richard F. King and David L. Phillips",
title = "The Logarithmic Error and {Newton}'s Method for the
Square Root",
journal = j-CACM,
volume = "12",
number = "2",
pages = "87--88",
month = feb,
year = "1969",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362848.362861",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2333",
bibdate = "Fri Nov 25 18:20:24 MST 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The problem of obtaining optimal starting values for
the calculation of the square root using Newton's
method is considered. It has been pointed out elsewhere
that if relative error is used as the measure of
goodness of fit, optimal results are not obtained when
the initial approximation is a best fit. It is shown
here that if, instead, the so-called logarithmic error
is used, then a best initial fit is optimal for both
types of error. Moreover, use of the logarithmic error
appears to simplify the problem of determining the
optimal initial approximation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4120 (Functional analysis)",
corpsource = "Argonne Nat. Lab., Argonne, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "$\sqrt(x)$; elementary functions; function evaluation;
iterative methods",
}
@Article{Kirsch:1969:ACA,
author = "Arnold Kirsch",
title = "An analysis of commercial arithmetic",
journal = j-EDUC-STUD-MATH,
volume = "1",
number = "3",
pages = "300--311",
month = jan,
year = "1969",
CODEN = "EDSMAN",
DOI = "https://doi.org/10.1007/BF00558315",
ISSN = "0013-1954 (print), 1573-0816 (electronic)",
ISSN-L = "0013-1954",
bibdate = "Sat Jan 14 17:12:11 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/educstudmath.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/BF00558315",
acknowledgement = ack-nhfb,
fjournal = "Educational Studies in Mathematics",
journal-URL = "http://link.springer.com/journal/10649",
}
@MastersThesis{Knight:1969:FPS,
author = "Douglas Wayne Knight",
title = "A floating point software package in {BCD} format for
small, fixed word length, digital computers",
type = "Thesis ({M.S.})",
school = "Arizona State University, Electrical Engineering",
address = "Tempe, AZ, USA",
pages = "151",
year = "1969",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Knuth:1969:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
MRclass = "68.00 (65.00)",
MRnumber = "44 \#3531",
MRreviewer = "M. Muller",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Benford's Law is discussed on pp. 219--229. Cited in
\cite{Sterbenz:1974:FPC}.",
tableofcontents = "3: Random Numbers \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 9 \\
3.2.1. The Linear Congruential Method / 9 \\
3.2.1.1. Choice of modulus / 11 \\
3.2.1.2. Choice of multiplier / 15 \\
3.2.1.3. Potency / 21 \\
3.2.2. Other Methods / 25 \\
3.3. Statistical Tests / 34 \\
3.3.1. General Test Procedures for Studying Random Data
/ 35 \\
3.3.2. Empirical Tests / 54 \\
*3.3.3. Theoretical Tests / 69 \\
3.3.4. The Spectral Test / 82 \\
3.4. Other Types of Random Quantities / 100 \\
3.4.1. Numerical Distributions / 101 \\
3.4.2. Random Sampling and Shuffling / 121 \\
*3.5. What is a Random Sequence? / 127 \\
3.6. Summary / 155 \\
4: Arithmetic \\
4.1. Positional Number Systems / 162 \\
4.2. Floating-Point Arithmetic / 180 \\
4.2.1. Single-Precision Calculations / 180 \\
4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
*4.2.3. Double-Precision Calculations / 210 \\
4.2.4. Statistical Distribution / 218 \\
4.3. Multiple-Precision Arithmetic / 229 \\
4.3.1. The Classical Algorithms / 229 \\
*4.3.2. Modular Arithmetic / 248 \\
*4.3.3. How Fast Can We Multiply? / 258 \\
4.4. Radix Conversion / 280 \\
4.5. Rational Arithmetic / 290 \\
4.5.1. Fractions / 290 \\
4.5.2. The Greatest Common Divisor / 293 \\
*4.5.3. Analysis of Euclid's Algorithm / 316 \\
4.5.4. Factoring into Primes / 339 \\
4.6. Polynomial Arithmetic / 360 \\
4.6.1. Division of Polynomials / 363 \\
*4.6.2. Factorization of Polynomials / 381 \\
4.6.3. Evaluation of Powers / 398 \\
4.6.4. Evaluation of Polynomials / 422 \\
*4.7. Manipulation of Power Series / 444 \\
Answers to Exercises / 452 \\
Appendix A: MIX / 565 \\
1. Description of MIX / 565 \\
2. The MIX Assembly Language / 584 \\
Appendix B: Tables of Numerical Quantities / 596 \\
1. Fundamental Constants (decimal) / 596 \\
2. Fundamental Constants (octal) / 597 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 598 \\
Appendix C: Index to Notations / 600 \\
Index and Glossary / 605",
xxyear = "{\noopsort{1968c}}1969",
}
@Book{Knuth:ACP69-2,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 624",
year = "1969",
ISBN = "0-201-03802-1",
ISBN-13 = "978-0-201-03802-6",
LCCN = "QA76.5 .K57",
MRclass = "68.00 (65.00)",
MRnumber = "44 \#3531",
MRreviewer = "M. Muller",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Benford's Law is discussed on pp. 219--229.",
tableofcontents = "3: Random Numbers \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 9 \\
3.2.1. The Linear Congruential Method / 9 \\
3.2.1.1. Choice of modulus / 11 \\
3.2.1.2. Choice of multiplier / 15 \\
3.2.1.3. Potency / 21 \\
3.2.2. Other Methods / 25 \\
3.3. Statistical Tests / 34 \\
3.3.1. General Test Procedures for Studying Random Data
/ 35 \\
3.3.2. Empirical Tests / 54 \\
*3.3.3. Theoretical Tests / 69 \\
3.3.4. The Spectral Test / 82 \\
3.4. Other Types of Random Quantities / 100 \\
3.4.1. Numerical Distributions / 101 \\
3.4.2. Random Sampling and Shuffling / 121 \\
*3.5. What is a Random Sequence? / 127 \\
3.6. Summary / 155 \\
4: Arithmetic \\
4.1. Positional Number Systems / 162 \\
4.2. Floating-Point Arithmetic / 180 \\
4.2.1. Single-Precision Calculations / 180 \\
4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
*4.2.3. Double-Precision Calculations / 210 \\
4.2.4. Statistical Distribution / 218 \\
4.3. Multiple-Precision Arithmetic / 229 \\
4.3.1. The Classical Algorithms / 229 \\
*4.3.2. Modular Arithmetic / 248 \\
*4.3.3. How Fast Can We Multiply? / 258 \\
4.4. Radix Conversion / 280 \\
4.5. Rational Arithmetic / 290 \\
4.5.1. Fractions / 290 \\
4.5.2. The Greatest Common Divisor / 293 \\
*4.5.3. Analysis of Euclid's Algorithm / 316 \\
4.5.4. Factoring into Primes / 339 \\
4.6. Polynomial Arithmetic / 360 \\
4.6.1. Division of Polynomials / 363 \\
*4.6.2. Factorization of Polynomials / 381 \\
4.6.3. Evaluation of Powers / 398 \\
4.6.4. Evaluation of Polynomials / 422 \\
*4.7. Manipulation of Power Series / 444 \\
Answers to Exercises / 452 \\
Appendix A: MIX / 565 \\
1. Description of MIX / 565 \\
2. The MIX Assembly Language / 584 \\
Appendix B: Tables of Numerical Quantities / 596 \\
1. Fundamental Constants (decimal) / 596 \\
2. Fundamental Constants (octal) / 597 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 598 \\
Appendix C: Index to Notations / 600 \\
Index and Glossary / 605",
xxyear = "{\noopsort{1968c}}1969",
}
@Article{Linhardt:1969:DDT,
author = "R. J. Linhardt and H. S. Miller",
title = "Digit-by-Digit Transcendental-Function Computation",
journal = j-RCA-REV,
volume = "30",
number = "2",
pages = "209--247",
month = jun,
year = "1969",
CODEN = "RCARCI",
ISSN = "0033-6831",
bibdate = "Fri Sep 16 10:31:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "RCA review",
}
@Article{Liu:1969:EAD,
author = "B. Liu and T. Kaneko",
title = "Error analysis of digital filters realized with
floating-point arithmetic",
journal = j-PROC-IEEE,
volume = "57",
number = "10",
pages = "1735--1747",
month = oct,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Liu:1970:CEA}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "This paper calculates the error at the output of a
digital filter using floating-point arithmetic
operations due to roundoff accumulation and input
quantization. Expressions are derived for the mean
square error for each of the three canonical forms
\ldots{}",
}
@InProceedings{Matula:1969:TAM,
author = "David W. Matula",
title = "Towards an Abstract Mathematical Theory of
Floating-Point Arithmetic",
crossref = "AFIPS:1969:ACPa",
pages = "765--772",
year = "1969",
bibdate = "Fri Oct 19 23:01:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Posnov:1969:FPR,
author = "N. N. Posnov and M. K. Buza and V. K. Kravcov",
title = "The floating point in a residue class number system.
({Russian})",
journal = "Vestnik Beloruss. Gos. Univ. Ser. I",
volume = "3",
pages = "21--27",
year = "1969",
MRclass = "10A10",
MRnumber = "45 3303e",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
reviewer = "J. B. Roberts",
}
@Book{Rice:1969:AFV,
author = "John R. Rice",
title = "The Approximation of Functions",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
pages = "various",
year = "1969",
LCCN = "QA221 .R5 V.1-2",
bibdate = "Fri Dec 08 13:02:54 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rigby:1969:DFP,
author = "G. W. Rigby",
title = "To draw a floating point number on the graph
plotter({PRP 2})",
type = "Group Research report",
institution = "British Steel Corporation",
address = "London, UK",
year = "1969",
bibdate = "Thu May 09 08:32:48 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Rosen:1969:ECH,
author = "Saul Rosen",
title = "Electronic Computers: a Historical Survey",
journal = j-COMP-SURV,
volume = "1",
number = "1",
pages = "7--36",
month = mar,
year = "1969",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356540.356543",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Mon Sep 19 18:18:44 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The first large scale electronic computers were built
in connection with university projects sponsored by
government military and research organizations. Many
established companies, as well as new companies,
entered the computer field during the first generation,
1947-1959, in which the vacuum tube was almost
universally used as the active component in the
implementation of computer logic. The second generation
was characterized by the transistorized computers that
began to appear in 1959. Some of the computers built
then and since are considered super computers; they
attempt to go to the limit of current technology in
terms of size, speed, and logical complexity. From 1965
onward, most new computers belong to a third
generation, which features integrated circuit
technology and multiprocessor multiprogramming
systems.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
keywords = "computer history; electronic computers; magnetic drum
computers; super computers; time-sharing;
transistorized computers; university computer projects;
vacuum tube computers",
}
@Article{S:1969:BRQ,
author = "D. S.",
title = "Book Review: {{\em Square Roots of Integers $2$ to $
15 $ in Various Bases $2$ to $ 10 $: $ 88062 $ Binary
Digits or Equivalent} by W. A. Beyer, N. Metropolis,
and J. R. Neergaard}",
journal = j-MATH-COMPUT,
volume = "23",
number = "107",
pages = "679--679",
month = jul,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Mar 20 13:34:21 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0025-5718%28196907%2923%3A107%3C679%3ASROI2T%3E2.0.CO%3B2-C",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Shea:1969:NDN,
author = "Dale D. Shea",
title = "On the Number of Divisions Needed in Finding the
Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "7",
number = "4",
pages = "337--340",
month = nov,
year = "1969",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:19 MDT 2011",
bibsource = "http://www.fq.math.ca/7-4.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/7-4/shea.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Sterbenz:1969:OSA,
author = "P. H. Sterbenz and C. T. Fike",
title = "Optimal Starting Approximations for {Newton}'s
Method",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "313--318",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Svoboda:1969:DAS,
author = "A. Svoboda",
title = "Decimal Adder with Signed Digit Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "3",
pages = "212--215",
month = mar,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222633",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 20:44:42 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Article{Troelstra:1969:EA,
author = "A. S. Troelstra",
title = "Elementary arithmetic",
journal = j-LECT-NOTES-MATH,
volume = "95",
pages = "12--13",
year = "1969",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0080646",
ISBN = "3-540-04614-3 (print), 3-540-36130-8 (e-book)",
ISBN-13 = "978-3-540-04614-1 (print), 978-3-540-36130-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Thu May 8 17:39:14 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0080646",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0080643",
book-URL = "http://www.springerlink.com/content/978-3-540-36130-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Turner:1969:CSI,
author = "L. Richard Turner",
title = "Comment on Some {IBM} Software",
journal = "{SHARE Secretary Distribution}",
volume = "SSD 199",
number = "C5279",
pages = "40--43",
year = "1969",
bibdate = "Fri Aug 20 10:23:55 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Turner:1969:DSC,
author = "L. Richard Turner",
title = "Difficulty in {\tt sin\slash cos} Routine",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "13--13",
month = oct,
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Feb 15 15:23:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Turner:1969:IOC,
author = "L. R. Turner",
title = "Input-Output Conversion in {System\slash 360}",
number = "SSD 194, C5173",
institution = "SHARE Secretary Distribution",
address = "????",
pages = "1--8",
year = "1969",
bibdate = "Thu Feb 15 15:21:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Usow:1969:SSC,
author = "Karl H. Usow",
title = "{SIGNUM} subroutine certification committee",
journal = j-SIGNUM,
volume = "4",
number = "3",
pages = "15--18",
month = oct,
year = "1969",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Mar 5 17:26:29 MST 2007",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@TechReport{Veltkamp:1969:APV,
author = "G. W. Veltkamp",
title = "{ALGOL} procedures voor het rekenen in dubbele lengte.
({Dutch}) [{ALGOL} procedures for double-length
arithmetic]",
type = "Technical report",
number = "21",
institution = "RC-Informatie, Technische Hogeschool Eindhoven",
address = "Eindhoven, The Netherlands",
year = "1969",
bibdate = "Tue Dec 26 14:53:03 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Dutch",
}
@Article{Weinstein:1969:CCR,
author = "C. Weinstein and A. V. Oppenheim",
title = "Correction to {``A comparison of roundoff noise in
floating point and fixed point digital filter
realizations''}",
journal = j-PROC-IEEE,
volume = "57",
number = "8",
pages = "1466--1466",
month = aug,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Weinstein:1969:CRN}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Weinstein:1969:CRN,
author = "C. Weinstein and A. V. Oppenheim",
title = "A comparison of roundoff noise in floating point and
fixed point digital filter realizations",
journal = j-PROC-IEEE,
volume = "57",
number = "6",
pages = "1181--1183",
month = jun,
year = "1969",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Weinstein:1969:CCR}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "A statistical model for roundoff noise in floating
point digital filters, proposed by Kaneko and Liu, is
tested experimentally for first- and second-order
digital filters. Good agreement between theory and
experiment is obtained. The model is used to \ldots{}",
}
@Article{Weinstein:1969:RNF,
author = "C. Weinstein",
title = "Roundoff noise in floating point fast {Fourier}
transform computation",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "17",
number = "3",
pages = "209--215",
month = sep,
year = "1969",
CODEN = "ITADAS",
ISSN = "0018-9278 (print), 1558-2582 (electronic)",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
summary = "A statistical model for roundoff errors is used to
predict output noise-to-signal ratio when a fast
Fourier transform is computed using floating point
arithmetic. The result, derived for the case of white
input signal, is that the ratio of mean-square
\ldots{}",
}
@Article{Whipple:1969:CHR,
author = "W. L. Whipple",
title = "Comments on {``Higher-Radix Division Using Estimates
of the Divisor and Partial Remainders''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-18",
number = "2",
pages = "183--183",
month = feb,
year = "1969",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1969.222623",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 16:55:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
note = "See \cite{Atkins:1968:HRD}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671216",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Young:1969:SCN,
author = "David M. Young and Alvis E. McDonald",
title = "On the surveillance and control of number range and
accuracy in numerical computation (with discussion)",
crossref = "Morrell:1970:IPP",
pages = "145--152",
year = "1969",
MRclass = "65.80",
MRnumber = "40\#8303",
bibdate = "Thu Jan 18 13:48:21 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}, but given year
1968.",
}
@Article{Atkins:1970:DAU,
author = "D. E. Atkins",
title = "Design of the Arithmetic Units of {ILLIAC III}: Use of
Redundancy and Higher Radix Methods",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "720--723",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223022",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 09 19:03:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Atkins.pdf",
abstract = "In keeping with the experimental nature of the
Illinois Pattern Recognition Computer (ILLIAC III), the
arithmetic units are intended to be a practical testing
ground for recent theoretical work in computer
arithmetic. This paper describes the use of redundant
number systems and the design of a structure with which
multiplication and division are executed radix 256. The
heart of the unit is the stored-sign subtracter, a
recently discovered member of the family of borrow-save
subtracters and carry-save adders. A cascade of these
subtracters, controlled by a multiplier recoder,
provides multiplication. The same structure, controlled
by a ``model division'' (a quotient recoder), performs
division.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "arithmetic unit; computer arithmetic; division; higher
radix arithmetic; ILLIAC III; multiplication; redundant
number systems; signed-digit subtracter; stored-sign
subtracter; stored-sign subtracter. Arithmetic unit",
remark = "Despite statements elsewhere that the ILLIAC III used
base 256, that is incorrect. The original manuals for
the machine clearly show an IBM System/360-style
base-16 encoding. This paper reveals the source of the
confusion: the multiplier uses a Wallace recoding
scheme, first defined for radix 4, but extended for the
ILLIAC III to radix 256. Thus, multiplication is done 8
bits at a time. Division is done 4 bits at a time.",
}
@Article{Avizienis:1970:UAB,
author = "Algirdas Avi{\v{z}}ienis and Chin Tung",
title = "A Universal Arithmetic Building Element ({ABE}) and
Design Methods for Arithmetic Processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "733--745",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223023",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Avizienis.pdf",
abstract = "The advent of large-scale integration of logic
circuits requires the definition of digital computer
structure in terms of large functional arrays of logic
of very few types. This paper describes a
single-package arithmetic processor called the
arithmetic building element (ABE). The ABE accepts
operands in either conventional or signed-digit radix-r
representation and produces signed-digit results, which
the ABE can reconvert to conventional form. Radix 16 is
chosen for illustrations. Arrays of ABE's may be
arranged to implement unit-time parallel addition,
all-combinational multiplication, and more complex
functions which are presently computed by subroutines.
To facilitate such arithmetic design, a graph model is
developed which permits a translation of the given
arithmetical algorithm into an interconnection diagram
of ABE's. The design procedure is illustrated by an
array for polynomial evaluation. Speed, cost, and
roundoff error of the array are considered. A computer
program has been written for the automatic translation
of the algorithm graph to an interconnection graph, and
for the evaluation of the cost and speed for a given
polynomial degree and a given precision requirement.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Behringer:1970:BFI,
author = "F. A. Behringer",
title = "{Eine bedingte Form der Integral-Ungleichun von
Gronwal, leichte Verallgemeinerung eins
Stabilit{\"a}tsatzes von Perron und {\"u}berlauffreie
Skalierung von Analogrechenschaltungen}. ({German})
[{A} conditional version of the integral inequality of
{Gronwall}, a slight generalization of a stability
theorem of {Perron}, and overflow-free scaling of
analogue computer set-ups]",
journal = j-COMPUTING,
volume = "5",
number = "4",
pages = "333--348",
year = "1970",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "Tech. Hochschule, M{\"u}nchen, West Germany",
classification = "C5460",
description = "analogue computer methods; differential equations",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Beyer:1970:GST,
author = "W. A. Beyer and N. Metropolis and J. R. Neergaard",
title = "The Generalized Serial Test Applied to Expansions of
Some Irrational Square Roots in Various Bases",
journal = j-MATH-COMPUT,
volume = "24",
number = "111",
pages = "745--747",
month = jul,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.15",
MRnumber = "MR0273773 (42 \#8649)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28197007%2924%3A111%3C745%3ATGSTAT%3E2.0.CO%3B2-2",
ZMnumber = "0227.10044",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Beyer:1970:SSD,
author = "W. A. Beyer and N. Metropolis and J. R. Neergaard",
title = "Statistical Study of Digits of Some Square Roots of
Integers in Various Bases",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "455--473",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "62.70",
MRnumber = "MR0272129 (42 \#7010)",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://links.jstor.org/sici?sici=0025-5718%28197004%2924%3A110%3C455%3ASSODOS%3E2.0.CO%3B2-I",
ZMnumber = "0208.19505",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Brent:1970:ABN,
author = "R. Brent",
title = "On the Addition of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "758--759",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223027",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Brent.pdf",
abstract = "An upper bound is derived for the time required to add
numbers modulo $ 2^n $, using circuit elements with a
limited fan-in and unit delay, and assuming that all
numbers have the usual binary encoding. The upper bound
is within a factor $ (1 + \epsilon) $ of Winograd's
lower bound (which holds for all encodings), where $
\epsilon \rightarrow 0 $ as $ n \rightarrow \infty $,
and only $ O(n \log n) $ circuit elements are
required.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "addition; ARITH-1; binary numbers; computational
complexity; group multiplication; logic circuits;
logical design",
}
@TechReport{deLugish:1970:CAA,
author = "B. G. de Lugish",
title = "A Class of Algorithms for Automatic Evaluation of
Certain Elementary Function in a Binary Computer",
type = "Report",
number = "399",
institution = "Department of Computer Science, University of
Illinois",
pages = "??",
month = jun,
year = "1970",
bibdate = "Fri Sep 02 22:49:20 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Flynn:1970:DFI,
author = "M. J. Flynn",
title = "On Division by Functional Iteration",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "702--706",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223019",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Swartzlander:1990:CAa}.",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Flynn.pdf",
abstract = "In order to avoid the time delays associated with
linearly convergent division based on subtraction,
other iterative schemes can be used. These are based on
(1) series expansion of the reciprocal, (2)
multiplicative sequence, or (3) additive sequence
convergent to the quotient. These latter techniques are
based on finding the root of an arbitrary function at
either the quotient or reciprocal value. A
Newton--Raphson iteration or root finding iteration can
be used.
The most useful techniques are quadratically convergent
(i.e., $ \mathrm {error}_{i + 1} = O((\mathrm
{error}_i)^2) $). These techniques generally require
two arithmetic operations (add or multiply) to double
the precision of the quotient.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Forsythe:1970:PCW,
author = "George E. Forsythe",
title = "Pitfalls in Computation, or Why a Math Book Isn't
Enough",
journal = j-AMER-MATH-MONTHLY,
volume = "77",
number = "9",
pages = "931--956",
month = nov,
year = "1970",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "Contributed Item",
MRnumber = "MR1536090",
bibdate = "Tue Nov 22 09:08:17 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
ZMnumber = "0207.15401",
acknowledgement = ack-nhfb,
classmath = "*65G50 Roundoff error 65Y20 Complexity and performance
of numerical algorithms",
fjournal = "The American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@TechReport{Gardiner:1970:SDA,
author = "V. Gardiner and N. Metropolis",
title = "Significant Digit Arithmetic on a {CDC 6600}",
type = "Technical Report",
number = "LA--4470",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "4",
day = "1",
month = jan,
year = "1970",
bibdate = "Tue Mar 20 11:46:17 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4093265&query_id=0",
acknowledgement = ack-nhfb,
}
@Article{Good:1970:CIA,
author = "Donald I. Good and Ralph L. London",
title = "Computer Interval Arithmetic: Definition and Proof of
Correct Implementation",
journal = j-J-ACM,
volume = "17",
number = "4",
pages = "603--612",
month = oct,
year = "1970",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sun Nov 6 11:55:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Habibi:1970:FM,
author = "A. Habibi and P. A. Wintz",
title = "Fast Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "2",
pages = "153--157",
month = feb,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222881",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671474",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hall:1970:GPQ,
author = "E. L. Hall and D. D. Lynch and S. J. Dwyer",
title = "Generation of Products and Quotients Using Approximate
Binary Logarithms for Digital Filtering Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "2",
pages = "97--105",
month = feb,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222874",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671467",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hamming:1970:DN,
author = "R. W. Hamming",
title = "On the Distribution of Numbers",
journal = j-BELL-SYST-TECH-J,
volume = "49",
number = "8",
pages = "1609--1625",
month = oct,
year = "1970",
CODEN = "BSTJAN",
DOI = "https://doi.org/10.1002/j.1538-7305.1970.tb04281.x",
ISSN = "0005-8580 (print), 2376-7154 (electronic)",
ISSN-L = "0005-8580",
bibdate = "Tue Nov 9 11:15:55 MST 2010",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/bstj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
abstract = "This paper examines the distribution of the mantissas
of floating-point numbers and shows how the arithmetic
operations of a computer transform various
distributions toward the limiting distribution $$ r(x)
= 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
$b$ is the base of the number system). The paper also
gives a number of applications to hardware, software,
and general computing which show that this distribution
is not merely an amusing curiosity. A brief examination
of the distribution of exponents is included.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Hansen:1970:APN,
author = "Rodney T. Hansen",
title = "Arithmetic of Pentagonal Numbers",
journal = j-FIB-QUART,
volume = "8",
number = "1",
pages = "83--86",
month = feb,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:23 MDT 2011",
bibsource = "http://www.fq.math.ca/8-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-1/hansen.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Harris:1970:NND,
author = "V. C. Harris",
title = "Note on the Number of Divisions Required in Finding
the Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "8",
number = "1",
pages = "104--??",
month = feb,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:23 MDT 2011",
bibsource = "http://www.fq.math.ca/8-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-1/harris2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@MastersThesis{Harvey:1970:SSP,
author = "Michael P. Harvey",
title = "A system study and problem solution in polynomial
evaluation",
type = "Thesis ({M.S.})",
school = "California State College",
address = "Long Beach, CA, USA",
pages = "vi + 119",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Numerical
calculations.; Polynomials.",
remark = "Title on spine: Automated floating point polynomial
evaluation.",
}
@TechReport{Hillstrom:1970:PSF,
author = "K. E. Hillstrom",
title = "Performance Statistics for the {FORTRAN IV (H)} and
{PL/I} (Version 5) Libraries in the {IBM OS\slash 360
Release 18}",
type = "Report",
number = "ANL-7666",
institution = inst-ANL,
address = inst-ANL:adr,
year = "1970",
bibdate = "Fri Aug 20 09:29:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Hornbuckle:1970:LMA,
author = "G. D. Hornbuckle and E. I. Ancona",
title = "The {LX-1} Microprocessor and Its Application to
Real-Time Signal Processing",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "710--720",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223021",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Hornbuckle.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Howell:1970:SLE,
author = "Jo Ann Howell and Robert T. Gregory",
title = "Solving linear equations using residue arithmetic ---
{Algorithm II}",
journal = j-BIT,
volume = "10",
pages = "23--37",
year = "1970",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "MR0261777 (41 \#6389)",
MRreviewer = "J. Legras",
bibdate = "Thu Nov 8 14:50:19 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Kailas:1970:AMC,
author = "M. V. Kailas",
title = "Another method of converting from hexadecimal to
decimal",
journal = j-CACM,
volume = "13",
number = "3",
pages = "193--193",
month = mar,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There is a simple paper-and-pencil method of
converting a hexadecimal number N to decimal.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "digital arithmetic",
}
@Article{Knuth:1970:VNF,
author = "Donald E. Knuth",
title = "{Von Neumann}'s First Computer Program",
journal = j-COMP-SURV,
volume = "2",
number = "4",
pages = "247--260",
month = dec,
year = "1970",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/356580.356581",
ISSN = "0010-4892",
ISSN-L = "0360-0300",
bibdate = "Sat Mar 23 15:03:00 2002",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/compsurv.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/HBP/ACMCS.bib;
https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite{Aspray:1987:PJN}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Krishnamurthy:1970:OIS,
author = "E. V. Krishnamurthy",
title = "On Optimal Iterative Schemes For High-Speed Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "3",
pages = "227--231",
month = mar,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222901",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jan 08 23:09:36 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Krishnamurthy:1970:RTT,
author = "E. V. Krishnamurthy",
title = "On Range-Transformation Techniques for Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "2",
pages = "157--160",
month = feb,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222882",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671475",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ling:1970:HSC,
author = "H. Ling",
title = "High-Speed Computer Multiplication Using a
Multiple-Bit Decoding Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "706--709",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223020",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Ling.pdf",
abstract = "This paper presents a method of performing the binary
multiplication beyond the scheme of multiple ADD and
SHIFT. The binary multiplication algorithm will be
discussed first, followed by block decoding method,
logic implementation, hardware consideration, and two
examples which are at the end of the discussion.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Linz:1970:AFP,
author = "Peter Linz",
title = "Accurate Floating-Point Summation",
journal = j-CACM,
volume = "13",
number = "6",
pages = "361--362",
month = jun,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.25",
MRnumber = "44\#3468",
MRreviewer = "R. P. Brent",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1970.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes an alternate method for summing a
set of floating-point numbers. Comparison of the error
bound for this method with that of the standard
summation method shows that it is considerably less
sensitive to propagation of round-off error.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "New York University, NY, USA",
descriptors = "Simulation; statistics; numeric calculation",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "accurate floating-point summation; computers, data
processing; digital arithmetic; floating point
arithmetic; floating-point addition; mathematics;
numerical methods; round-off error; round-off errors;
round-off propagation; summation",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Liu:1970:CEA,
author = "B. Liu and T. Kaneko",
title = "Correction to {``Error analysis of digital filters
realized with floating-point arithmetic''}",
journal = j-PROC-IEEE,
volume = "58",
number = "3",
pages = "376--376",
month = mar,
year = "1970",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Liu:1969:EAD}.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@Article{Long:1970:LAS,
author = "C. T. Long and J. H. Jordan",
title = "A Limited Arithmetic on Simple Continued Fractions ---
{II}",
journal = j-FIB-QUART,
volume = "8",
number = "2",
pages = "135--157",
month = mar,
year = "1970",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:25 MDT 2011",
bibsource = "http://www.fq.math.ca/8-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/8-2/long.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@TechReport{Malcolm:1970:AFA,
author = "Michael Malcolm",
title = "An algorithm for floating-point accumulation of sums
with small relative error",
number = "STAN-CS-70-163",
institution = "Computer Science Department, Stanford University",
address = "Stanford, CA, USA",
pages = "21",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Algorithms.;
FORTRAN (Computer program language); Numerical
calculations --- Computer programs.",
remark = "Reproduced by National Technical Information Service.
AD 708 691.",
}
@MastersThesis{Marasa:1970:AAE,
author = "John D. Marasa",
title = "Accumulated arithmetic error in floating-point and
alternative logarithmic number systems",
type = "Thesis ({M.S.})",
school = "Washington University, Sever Institute of Technology,
Department of Applied Mathematics and Computer
Science",
address = "St. Louis, MO, USA",
pages = "vii + 88",
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Programming (Mathematics)",
}
@Article{Matula:1970:ECA,
author = "David W. Matula",
title = "The emergence of computational arithmetic as a
component of the computer science curriculum",
journal = j-SIGCSE,
volume = "2",
number = "3",
pages = "41--44",
month = nov,
year = "1970",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/873641.873650",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sun Nov 18 08:53:42 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse1970.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Matula:1970:FFP,
author = "D. W. Matula",
title = "A Formalization of Floating-Point Numeric Base
Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "681--692",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223017",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:35 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671610;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Matula.pdf",
abstract = "The process of converting arbitrary real numbers into
a floating-point format is formalized as a mapping of
the reals into a specified subset of real numbers. The
structure of this subset, the set of $n$ significant
digit base $b$ floating-point numbers, is analyzed and
properties of conversion mappings are determined. For a
restricted conversion mapping of the $n$ significant
digit base $b$ numbers to the $m$ significant-digit
base $d$ numbers, the one-to-one, onto, and
order-preserving properties of the mapping are
summarized. Multiple conversions consisting of a
composition of individual conversion mappings are
investigated and some results of the invariant points
of such compound conversions are presented. The
hardware and software implications of these results
with regard to establishing goals and standards for
floating-point formats and conversion procedures are
considered.",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Mifsud:1970:MDA,
author = "C. J. Mifsud",
title = "A multiple-precision division algorithm",
journal = j-CACM,
volume = "13",
number = "11",
pages = "666--668",
month = nov,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Mar 25 13:26:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See addendum \cite{Mifsud:1973:AMP}.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Mitre Corp., McLean, VA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "digital arithmetic",
}
@Article{Nickel:1970:KBS,
author = "K. Nickel",
title = "{Das Kahan--Babu{\v{s}}kasche Summierungsverfahren in
Triplex-ALGOL 60}. ({German}) [{The
Kahan--Babu{\v{s}}ka} summation method in
{Triplex-ALGOL 60}]",
journal = j-Z-ANGE-MATH-MECH,
volume = "50",
pages = "369--373",
year = "1970",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Tue Aug 28 06:12:04 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
keywords = "accurate floating-point summation",
language = "German",
}
@Article{Ninomiya:1970:BRS,
author = "Ichizo Ninomiya",
title = "Best Rational Starting Approximations and Improved
{Newton} Iteration for the Square Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "391--404",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb # " and " # ack-nj,
ajournal = "Math. Comput.",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Nagoya University, Chikua ku, Japan",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computing procedure; function approximation; iterative
methods; Newton iteration; rational approximation;
square root",
treatment = "T Theoretical or Mathematical",
}
@Article{Oppenheim:1970:RDF,
author = "A. Oppenheim",
title = "Realization of digital filters using
block-floating-point arithmetic",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "18",
number = "2",
pages = "130--136",
month = jun,
year = "1970",
CODEN = "ITADAS",
ISSN = "0018-9278 (print), 1558-2582 (electronic)",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
summary = "Recently, statistical models for the effects of
roundoff noise in fixed-point and floating-point
realizations of digital filters have been proposed and
verified, and a comparison between these realizations
presented. In this paper a structure for \ldots{}",
}
@Article{Phillips:1970:GLE,
author = "David L. Phillips",
title = "Generalized Logarithmic Error and {Newton}'s Method
for the $m$ th Root",
journal = j-MATH-COMPUT,
volume = "24",
number = "110",
pages = "383--389",
month = apr,
year = "1970",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Rao:1970:BEC,
author = "T. R. N. Rao",
title = "Biresidue Error-Correcting Codes for Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "5",
pages = "398--402",
month = may,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222937",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:32 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Rao:1970:BLR,
author = "T. R. N. Rao and A. K. Trehan",
title = "Binary Logic for Residue Arithmetic Using Magnitude
Index",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "752--757",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223026",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Rao.pdf",
abstract = "We consider a residue number system using n pairwise
relatively prime moduli $ m_1, \ldots {}, m_n $ to
represent any integer $X$ in the range $ M / 2 \leq X >
M / 2 $, when $ M = \prod m_i $. The moduli $ m_i $ are
chosen to be of the $ 2 - 1 $ type, in order that the
residue arithmetic can be implemented by means of
binary registers and binary logic. Further, for each
residue number $X$, a magnitude index $ P_x $ is
maintained for all arithmetic operations. We
investigate the properties of such a system and derive
the addition, subtraction, multiplication, sign
determination, and overflow detection algorithms. The
proposed organization is found to improve the operation
times for sign detection and overflow detection
operations, while rendering multiplication to be a
difficult operation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1; base extension; index generation logic;
magnitude index; modular adders; naturalized form;
overflow detection; residue multiplication; residue
number system; scale by 2; sign determination",
}
@Article{Robertson:1970:CBM,
author = "J. E. Robertson",
title = "The Correspondence Between Methods of Digital Division
and Multiplier Recoding Procedures",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "692--701",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223018",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Robertson.pdf",
abstract = "This paper relates previous analyses of the binary SRT
division to the theory of multiplier recoding. Since
each binary quotient digit has three possible values,
the quotient resulting from the SRT division is in
recoded form; in this paper it is shown that the
recoding is a function of the divisor, and the method
for determining the characteristic Boolean function of
the recoding is presented. The relationship between the
division and the recoding is established by scaling the
division in such a way that the scaled ``visor''
becomes a constant. Higher radix results are also
discussed.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@TechReport{Rothmaier:1970:BQN,
author = "B. Rothmaier",
title = "{Die Berechnung der Quadratwurzel nebst Schranken auf
Dualmaschinen} \toenglish {The Computation of the
Square Root together with [Interval] Bounds on Binary
Machines} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/17",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Rothmaier:1970:DSB,
author = "B. Rothmaier",
title = "{Dokumentation der Standardfunktionen des
Betriebssystems Hydra X8} \toenglish {Documentation} of
the Elementary Functions of the Operating System {Hydra
X8} \endtoenglish",
type = "{Interner Bericht}",
number = "Nr. 70/8",
institution = "Institut f{\"u}r Informatik, Universit{\"a}t
Karlsruhe",
pages = "??",
year = "1970",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Shively:1970:PFI,
author = "Richard R. Shively",
title = "Preface: {First IEEE Conference on Computer
Arithmetic, Minneapolis, Minnesota, June 16, 1969}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "679--680",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223016",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671609;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Shively.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1",
}
@Article{Sikdar:1970:DMM,
author = "K. Sikdar",
title = "Determination of Multipliers Mapping an Arbitrary
Integer into a Range of Certain Type",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "12",
pages = "1221--1222",
month = dec,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222863",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671456",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Svoboda:1970:ADC,
author = "A. Svoboda",
title = "Adder With Distributed Control",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "749--751",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223025",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Svoboda.pdf",
abstract = "An adder is described for addition of a large number
of binary numbers $ x_j, j = 1, 2, \ldots {}, m $,
where $ x_j = \sum_i x_{j, i} 2^i, x_{j, i} = 0, 1, i =
0, 1, \ldots {}, n - 1 $. The adder's algorithm has two
parts: (1) the bits $ x_{j, i} $ are added
independently for each binary order $ i : s_i = \sum_j
x_{j, i} \leq m $ and the result expressed in the
binary form $ s_i = \sum_k a_{i, k} 2^k, a_{i, k} = 0,
1, k = 0, 1, \ldots {}, p - 1 $ (where $ 2^{p - 1} \leq
m < 2^p $) ; (2) the sum $ y = \sum_j x_j $ is formed
by adding terms $ s_{i, k} {2^{i + k}} $ as
contributions of the bit $ s_{i, k} $ to the total $y$.
A hardware implementation of this algorithm is
suggested where the sum $ s_i $ is obtained by a
sequential circuit which reorders the values $ x_{j,
i}' $ so that their sum $ s_i $, remains unchanged and
so that after the reordering the new values $ x_{j, i}'
$ obey the conditions $ x_{j + 1, i} \leq x_{j, i} $
for every $ j = 1, 2, \ldots {}, m - 1 $. The
implementation with integrated circuits should be quite
rewarding because the control of the circuit is done
with independent control elements distributed all over
the chip.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "adder; adder for large number of numbers; ARITH-1;
distributed control; reordering",
}
@Article{Taub:1970:ECS,
author = "D. M. Taub and C. E. Owen and B. P. Day",
title = "Experimental Computer for Schools",
journal = "Proceedings of the IEE",
volume = "117",
number = "2",
pages = "303--312",
month = feb,
year = "1970",
bibdate = "Fri Nov 28 19:30:38 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The computer is a small desk-top machine designed for
teaching schoolchildren how computers work. It works in
decimal notation and has a powerful instruction set
which includes 3-address floating-point instructions
implemented as `extracode' subroutines. Addressing can
be absolute, relative or indirect. For input it uses a
capacitive touch keyboard, and for output and display a
perfectly normal TV receiver is used. Another
input/output device is an ordinary domestic tape
recorder, used mainly for long term storage of
programs. To make the operation of the machine easy to
follow, it can be made to stop at certain stages in the
processing of an instruction and automaticaly display
the contents of all registers and storage locations
relevant at that time. The paper gives a description of
the machine and a discussion of the factors that hav
influenced its design.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "IBM Schools computer with scaled integer format, six
decimal digits and exponent range of $ [ - 6, 0] $.",
}
@Book{Thornton:1970:DCC,
author = "James E. Thornton",
title = "Design of a Computer: the {Control Data 6600}",
publisher = pub-SF,
address = pub-SF:adr,
pages = "v + 181",
year = "1970",
ISBN = "0-07-057302-6, 0-07-057303-4",
ISBN-13 = "978-0-07-057302-4, 978-0-07-057303-1",
LCCN = "TK7889.C6 T5 1970",
bibdate = "Wed Sep 14 22:45:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://archive.computerhistory.org/resources/text/CDC/cdc.6600.thornton.design_of_a_computer_the_control_data_6600.1970.102630394.pdf",
acknowledgement = ack-nhfb,
remark = "See Table V: Nonstandard Floating Point Arithmetic on
page 79 for the rules governing Indefinite, Infinity,
and Negative Zero operands.",
tableofcontents = "I: Introduction / 1 \\
A. Justification for Large Computers / 1 \\
B. Building Blocks / 4 \\
C. The Approach / 5 \\
II: Organization of the 6600 / 9 \\
A. General / 9 \\
B. Peripheral Subsystem / 10 \\
C. Central Processor-CPU / 12 \\
D. Central Storage / 15 \\
E. Extended Core Storage / 17 \\
III: Basic Circuit Properties / 19 \\
A. The Silicon Transistor / 19 \\
B. DCTL Logic Circuits / 21 \\
C. Logic Symbols / 24 \\
D. Transmission Lines / 28 \\
E. Packaging / 32 \\
IV: Central Storage System / 37 \\
A. Storage Module / 37 \\
B. Theory of Interleaved Storage / 44 \\
C. Stunt Box / 47 \\
D. Storage Bus System / 51 \\
E. Extended Core Storage / 53 \\
F. ECS Coupler and Controller / 55 \\
V: Central Processor Functional Units / 57 \\
A. Boolean Unit / 59 \\
B. Fixed Add Unit / 63 \\
C. Data Trunks / 69 \\
D. Shift Unit / 71 \\
E. Add Unit / 77 \\
F. Multiply Unit / 88 \\
G. Divide Unit / 101 \\
H. Increment Unit / 105 \\
I. Branch Unit / 111 \\
J. ECS Coupler-Controller / 114 \\
VI: Central Processor Control / 117 \\
A. Exchange Jump / 117 \\
B. Instruction Fetch / 120 \\
C. Instruction Issue / 123 \\
D. Scoreboard / 125 \\
Register Entry/Exit Control / 134 \\
F. Summary / 137 \\
VII: Peripheral Subsystem / 141 A. Peripheral
Processors / 141 \\
B. Dead Start / 154 \\
C. Disk Storage / 157 \\
VIII: Systems Operation / 163 \\
A. Files / 163 \\
B. Tables / 165 \\
C. Circular Buffer for 1/0 / 166 \\
D. Job Processing / 167 \\
E. System Monitor MTR / 168 \\
F. Control Points / 169 \\
G. Summary / 171 \\
Appendix / 173 \\
Index / 177",
}
@Article{Tienari:1970:SMR,
author = "Martti Tienari",
title = "A Statistical Model of Roundoff Error for Varying
Length Floating-Point Arithmetic",
journal = j-BIT,
volume = "10",
number = "3",
pages = "355--365",
month = sep,
year = "1970",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934204",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68.00 (65.00)",
MRnumber = "42\#7108",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=3&spage=355",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
reviewer = "R. W. Hamming",
}
@Article{Tung:1970:SDD,
author = "Chin Tung",
title = "Signed-Digit Division Using Combinational Arithmetic
Nets",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "8",
pages = "746--748",
month = aug,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.223024",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 15 07:59:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Tung.pdf",
abstract = "To meet the challenge created by the advent of large-
scale integration, a unique microelectronic arithmetic
building element and combinational arithmetic nets,
composed of the building elements, have been studied
and proposed for arithmetic processor design. A fast
division algorithm, particularly suitable for floating-
point arithmetic, has also been developed for
signed-digit arithmetic. This algorithm is
characterized by the need of preprocessing the divisor
and then exact generation of quotient digits. This
paper describes the implementation of this division
algorithm with the arithmetic building element and
combinational arithmetic nets. The intention here is to
explore the feasibility of applying large-scale
integration technology to arithmetic processors.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-1; arithmetic building element; combinational
arithmetic net; division; large-scale integration;
microelectronic block; signed-digit number system",
}
@Article{Usow:1970:CB,
author = "K. H. Usow",
title = "Certification Bibliography",
journal = j-SIGNUM,
volume = "5",
number = "2",
pages = "14--15",
month = mar,
year = "1970",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Fri Aug 20 10:26:49 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Waksman:1970:WAI,
author = "A. Waksman",
title = "On {Winograd}'s Algorithm for Inner Products",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "4",
pages = "360--361",
month = apr,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222926",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 09 18:54:12 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This correspondence demonstrates an improvement on
Winograd's algorithm for inner products as applied to
the multiplication of two matrices.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "fast matrix multiplication; product of matrices;
sufficient number of arithmetical operations",
}
@Article{Wilson:1970:OSA,
author = "M. Wayne Wilson",
title = "Optimal Starting Approximations for Generating Square
Root for Slow or No Divide",
journal = j-CACM,
volume = "13",
number = "9",
pages = "559--560",
month = sep,
year = "1970",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "44\#2338",
MRreviewer = "J. E. {Dennis, Jr.}",
bibdate = "Thu Sep 1 10:15:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "On computing machines with slow or no division, it is
preferable to use an iterative scheme for the square
root different from the classical Heron scheme. The
problem of optimal initial approximants is considered,
and some optimal polynomial initial approximations are
tabulated.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, Houston, TX, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "CACMA; digital arithmetic; ele; iterative methods;
mathematics; numerical methods; optimisation",
}
@TechReport{Yohe:1970:ACB,
author = "J. M. Yohe",
title = "Accurate Conversion Between Number Bases",
type = "{MRC} Technical Summary Report",
number = "1109",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
month = oct,
year = "1970",
bibdate = "Sun Dec 30 21:39:41 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The author presents and proves algorithms for taking a
number expressed in base gamma and finding, for a
predetermined floating point representation in base
beta, its least upper bound, greatest lower bound, and
closest approximation.",
acknowledgement = ack-nhfb,
}
@TechReport{Yohe:1970:BPF,
author = "J. M. Yohe",
title = "Best possible floating point arithmetic",
type = "{MRC} Technical Summary Report",
number = "1054",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "ii + 27",
month = mar,
year = "1970",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The report presents an algorithm for floating point
arithmetic, using single-length arithmetic registers,
which yields the most accurate approximation which can
be expressed in the given floating point format, the
greatest lower bound, or the least upper bound for the
result of the operation, whichever is specified by the
programmer. This makes the algorithm particularly
useful for implementation of interval arithmetic.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "March 1970. Sponsored by Army Research Office, Durham,
N.C.",
}
@Article{Yong:1970:GBA,
author = "Lam Lay Yong",
title = "The Geometrical Basis of the {Ancient Chinese}
Square-Root Method",
journal = j-ISIS,
volume = "61",
number = "1",
pages = "92--102",
month = "Spring",
year = "1970",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:28:39 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302287;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
URL = "http://www.jstor.org/stable/229151",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{Zohar:1970:NRC,
author = "S. Zohar",
title = "Negative Radix Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "3",
pages = "222--226",
month = mar,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222900",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Pawlak:1971:ACN,Wadel:1971:CNR}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671493",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Book{Zuse:1970:CML,
author = "Konrad Zuse",
title = "{Der Computer, mein Lebenswerk}",
publisher = "Verlag moderne Industrie",
address = "M{\"u}nchen, Germany",
pages = "221",
year = "1970",
LCCN = "QA76.2.Z8 A3",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "computer engineers --- Germany --- biography;
computers --- Germany --- history; Zuse, Konrad",
}
@Article{Abdelmalek:1971:REA,
author = "Nabih N. Abdelmalek",
title = "Round-off Error Analysis for {Gram--Schmidt} Method
and Solution of Linear Least Squares Problems",
journal = j-BIT,
volume = "11",
number = "4",
pages = "345--367",
month = dec,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939404",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:12 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=4&spage=345",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Alway:1971:GFA,
author = "G. G. Alway",
title = "A general factorising algorithm",
journal = j-COMP-J,
volume = "14",
number = "2",
pages = "166--168",
month = may,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:53 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/140166.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/166.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/167.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/168.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Nat. Phys. Lab., Teddington, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "computer algorithm; digital arithmetic; general
factorising algorithm; primality of large numbers",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Banerji:1971:RAC,
author = "D. K. Banerji",
title = "Residue arithmetic in computer design",
institution = "University of Waterloo",
address = "Waterloo, ON, Canada",
year = "1971",
bibdate = "Thu Nov 18 09:13:45 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://books.google.com/books?id=YNVcPgAACAAJ",
acknowledgement = ack-nhfb,
}
@Article{Bataille:1971:GCW,
author = "M. Bataille",
title = "The {Gamma 60}: The computer that was ahead of its
time",
journal = j-HONEYWELL-COMP-J,
volume = "5",
number = "3",
pages = "99--105",
month = "????",
year = "1971",
CODEN = "HNCJA3",
ISSN = "0046-7847",
bibdate = "Thu Nov 25 09:37:15 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Honeywell Computer Journal",
keywords = "decimal floating-point arithmetic",
remark = "The Gamma 60 decimal floating-point system provides 11
to 19 decimal digits with an exponent range of $ \pm 40
$.",
}
@Book{Bell:1971:CSR,
editor = "C. Gordon Bell and Allen Newell",
booktitle = "Computer Structures: Readings and Examples",
title = "Computer Structures: Readings and Examples",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xix + 668",
year = "1971",
ISBN = "0-07-004357-4",
ISBN-13 = "978-0-07-004357-2",
LCCN = "TK7888.3 .B4",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
acknowledgement = ack-nhfb,
shorttableofcontents = "Part 1 The Structure of Computers \\
Chapter 1 Introduction \\
Chapter 2 The PMS and ISP Descriptive Systems \\
Chapter 3 The Computer Space \\
Part 2 The Instruction-set Processor: Main-line
computers \\
Section 1 Processors with One Address per Instruction
\\
Chapter 4 Preliminary Discussion of the Logical Design
of an Electronic Computing Instrument \\
Chapter 5 The DEC PDP-8 \\
Chapter 6 The Whirlwind I Computer \\
Chapter 7 Some Aspects of the Logical Design of a
Control Computer: A Case Study \\
Chapter 8 The UNIVAC System \\
Section 2 Processors with a General-Register State \\
Chapter 9 The Design Philosophy of Pegasus, A
Quantity-production Computer \\
Chapter 10 An 8-bit-character Computer \\
Part 3 The Instruction-Set Processor Level: Variations
in the Processor \\
Section 1 Processors with Greater than One Address per
Instruction \\
Chapter 11 The Pilot ACE \\
Chapter 12 ZEBRA, A Simple Binary Computer \\
Chapter 13 UNIVAC Scientific (1103A) Instruction Logic
\\
Chapter 14 Instruction Logic of the MIDAC \\
Chapter 15 Instruction Logic of the Soviet Strela
(Arrow) \\
Section 2 Processors Constrained by a Cyclic, Primary
Memory \\
Chapter 16 The LGP-30 and LGP-21 \\
Chapter 17 IBM 650 Instruction Logic \\
Section 3 Processors for Variable-length-string Data
\\
Chapter 18 The IBM 1401 \\
Section 4 Desk Calculator Computers: Keyboard
Programmable Processors with Small Memories \\
Chapter 19 The OLIVETTI Programma 101 Desk Calculator
\\
Chapter 20 The HP Model 9100A Computing Calculator \\
Section 5 Processors with Stack Memories (Zero
Addresses per Instruction) \\
Chapter 21 Design of an Arithmetic Unit Incorporating a
Nesting Store \\
Chapter 22 Design of the B 5000 System \\
Section 6 Processors with Multiprogramming Ability \\
Chapter 23 One-level Storage System \\
Chapter 24 A User Machine in a Time-sharing System \\
Part 4 The Instruction-set Processor Level:
Special-function Processors \\
Section 1 Processors to Control Terminals and Secondary
Memories (Input-output Processors) \\
Chapter 25 The DEC 338 Display Processor \\
Section 2 Processors for Array Data \\
Chapter 26 NOVA: A List-oriented Computer \\
Chapter 27 The ILLIAC IV Computer \\
Section 3 Processors Defined by a Microprogram \\
Chapter 28 Microprogramming and the Design of the
Control Circuits in an Electronic Computer \\
Chapter 29 The Design of a General-Purpose
Microprogram-controlled Computer with Elementary
Structure \\
Section 4 Processors Based on a Programming Language
\\
Chapter 30 A Command Structure for Complex Information
Processing \\
Chapter 31 System Design of a FORTRAN Machine \\
Chapter 32 A Microprogrammed Implementation of EULER on
IBM System/360 Model 30 \\
Part 5 The PMS Level \\
Section 1 Computers with One Central Processor \\
Section 2 Computers with One Central Processor and
Multiple Input/Output Processors \\
Chapter 33 The IBM 1800 \\
Chapter 34 The Engineering Design of the Stretch
Computer \\
Chapter 35 PILOT, The NBS Multicomputer System \\
Section 3 Computers for Multiprocessing and Parallel
Processing \\
Chapter 36 D825 --- A Multiple-computer System for
Command and Control \\
Chapter 37 A Survey of Problems and Preliminary Results
Concerning Parallel Processing and Parallel Processors
\\
Section 4 Network Computers and Computer Networks \\
Chapter 38 The RW-400: A New Polymorphic Data System
\\
Chapter 39 Parallel Operation in the Control Data 6600
\\
Chapter 40 Computer Network Examples / 504 \\
Part 6 Computer Families \\
Section 1 The IBM 701--7094 II Sequence, a Family by
Evolution \\
Chapter 41 The IBM 7094 I, 11 / 517 \\
Section 2 The SDS 910--9300 Series, a Planned Family\\
Chapter 42 The SDS 910-9300 Series \\
Section 3 The IBM System/360 --- A Series of Planned
Machines Which Span a Wide Performance Range \\
Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure System Implementations
\\
Chapter 44 The Structure of System/360, Part II ---
System Implementations \\
Appendix PMS and ISP Notations",
subject-dates = "John von Neumann (28 December 1903--8 February 1957);
James H. Wilkinson (27 September 1919--5 October 1986);
Sir Maurice Vincent Wilkes (26 June 1913--29 November
2010)",
tableofcontents = "[NB: Bracketed chapter entries are subject cross
references] \\
Preface / v \\
Contributors / xiii \\
Acknowledgments / x \\
\\
Part 1 The Structure of Computers \\
\\
Chapter 1 Introduction / 3 \\
Chapter 2 The PMS and ISP Descriptive Systems / 15 \\
Chapter 3 The Computer Space / 37 \\
\\
Part 2 The Instruction-set Processor: Main-line
computers \\
\\
Section 1 Processors with One Address per Instruction /
89 \\
\\
Chapter 4 Preliminary Discussion of the Logical Design
of an Electronic Computing Instrument --- Arthur W.
Burks, Herman H. Goldstine, and John von Neumann / 92
\\
Chapter 5 The DEC PDP-8 / 120 \\
Chapter 6 The Whirlwind I Computer --- R. R. Everett /
137 \\
[Chapter 33 The IBM 1800] \\
Chapter 7 Some Aspects of the Logical Design of a
Control Computer: A Case Study --- R. L. Alonso, H.
Blair-Smith, and A. L. Hopkins / 146 \\
[Chapter 42 The SDS 910-9300 Series] \\
[Chapter 16 The LGP-30 and LGP-21] \\
[Chapter 17 IBM 650 Instruction Logic ---John W. Carr
III] \\
[Chapter 41 The IBM 7094 I, II] \\
Chapter 8 The UNIVAC System --- J. Presper Eckert, Jr,
James B. Weiner, H. Frazer Welsh, and Herbert F.
Mitchell / 157 \\
[Chapter 23 One-level Storage System --- T. Kilburn, D.
B. G. Edwards, M. J. Lanigan, and F. H. Summer] \\
[Chapter 34 The Engineering Design of the Stretch
Computer --- Erich Bloch] \\
\\
Section 2 Processors with a General-Register State \\
\\
Chapter 9 The Design Philosophy of Pegasus, A
Quantity-production Computer --- W. S. Elliott, C. E.
Owen, C. H. Devonald, and B. G. Maudsley / 171 \\
[Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure --- G. A. Blaauw and
F. P. Brooks, Jr.] \\
Chapter 10 An 8-bit-character Computer / 184 \\
[Chapter 39 Parallel Operation in the Control Data 6600
--- James E. Thornton] \\
\\
Part 3 The Instruction-Set Processor Level: Variations
in the Processor \\
\\
Section 1 Processors with Greater than One Address per
Instruction / 191 \\
\\
Chapter 11 The Pilot ACE --- J. H. Wilkinson / 193 \\
Chapter 12 ZEBRA, A Simple Binary Computer --- W. L.
van der Poel / 200 \\
Chapter 13 UNIVAC Scientific (1103A) Instruction Logic
--- John W. Carr III / 205 \\
[Chapter 38 The RW-400: A New Polymorphic Data System
--- R. E. Porter] \\
Chapter 14 Instruction Logic of the MIDAC --- John W.
Carr III / 209 \\
Chapter 15 Instruction Logic of the Soviet Strela
(Arrow) ---John W. Carr III / 213 \\
\\
Section 2 Processors Constrained by a Cyclic, Primary
Memory / 216 \\
\\
[Chapter 19 The OLIVETTI Programma 101 Desk Calculator]
\\
[Chapter 12 ZEBRA, A Simple Binary Computer --- W. L.
van der Poel] \\
Chapter 16 The LGP-30 and LGP-21 / 217 \\
[Chapter 11 The Pilot ACE --- J. H. Wilkinson] \\
[Chapter 8 The UNIVAC System --- J. Presper Eckert,
Jr., James R. Weiner, H. Frazer Welsh, and Herbert F.
Mitchell] \\
[Chapter 9 The Design Philosophy of Pegasus, A
Quantity-production Computer --- W. S. Elliott, C. E.
Owen, C. H. Devonald, and B. G. Maudsley] \\
Chapter 17 IBM 650 Instruction Logic --- John W. Carr
III / 220 \\
[Chapter 26 NOVA: A List-oriented Computer --- Joseph
E. Wirsching] \\
\\
Section 3 Processors for Variable-length-string Data /
224 \\
\\
Chapter 18 The IBM 1401 / 228 \\
[Chapter 10 An 8-bit-character Computer] \\
\\
Section 4 Desk Calculator Computers: Keyboard
Programmable Processors with Small Memories / 235 \\
\\
Chapter 19 The OLIVETTI Programma 101 Desk Calculator /
237 \\
Chapter 20 The HP Model 9100A Computing Calculator ---
Richard E. Monnier, Thomas E. Osborne, and David S.
Cochran / 243 \\
\\
Section 5 Processors with Stack Memories (Zero
Addresses per Instruction) / 257 \\
\\
Chapter 21 Design of an Arithmetic Unit Incorporating a
Nesting Store --- R. H. Allmark and J. R. Lucking / 262
\\
Chapter 22 Design of the B 5000 System --- William
Lonergan and Paul King / 267 \\
[Chapter 36 D825 --- A Multiple-computer System for
Command and Control --- James P. Anderson, Samuel A.
Hoffman, Joseph Shifman, and Robert J. Williams] \\
[Chapter 30 A Command Structure for Complex Information
Processing --- J. C. Shaw, A. Newell, H. A. Simon, T.
O. Ellis] \\
[Chapter 32 Microprogrammed Implementation of EULER on
IBM System/360 Model 30 --- Helmut Weber] \\
\\
Section 6 Processors with Multiprogramming Ability /
274 \\
\\
Chapter 23 One-level Storage System --- T. Kilburn, D.
B. G. Edwards, M. J. Lanigan, and F. H. Sumner / 276
\\
[Chapter 21 Design of the B 5000 System --- William
Lonergan and Paul King] \\
Chapter 24 A User Machine in a Time-sharing System ---
B. W. Lampson, W. W. Lichtenberger, and M. W. Pirtle /
291 \\
\\
Part 4 The Instruction-set Processor Level:
Special-function Processors \\
\\
Section 1 Processors to Control Terminals and Secondary
Memories (Input-output Processors) / 303 \\
\\
[Chapter 41 The IBM 7094 I, II] \\
[Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure ---- G. A. Blaauw and
F. P. Brooks, Jr.] \\
[Chapter 33 The IBM 1800] \\
Chapter 25 The DEC 338 Display Processor / 305 \\
\\
Section 2 Processors for Array Data / 315 \\
\\
Chapter 26 NOVA: A List-oriented Computer --- Joseph E.
Wirsching / 316 \\
Chapter 27 The ILLIAC IV Computer --- George H. Barnes,
Richard M. Brown, Maso Kato, David J. Kuck, Daniel L.
Slotnick, and Richard E. Stokes / 320 \\
\\
Section 3 Processors Defined by a Microprogram / 334
\\
\\
Chapter 28 Microprogramming and the Design of the
Control Circuits in an Electronic Computer --- M. V.
Wilkes and J. B. Stringer / 335 \\
Chapter 29 The Design of a General-Purpose
Microprogram-controlled Computer with Elementary
Structure --- Thomas W. Kampe / 341 \\
[Chapter 20 The HP Model 9100A Computing Calculator
---Richard E. Monnier, Thomas E. Osborne, and David S.
Cochran] \\
[Chapter 32 A Microprogrammed Implementation of EULER
on IBM System/360 Model 30 --- Helmut Weber] \\
\\
Section 4 Processors Based on a Programming Language /
348 \\
\\
Chapter 30 A Command Structure for Complex Information
Processing --- J. C. Shaw, A.Newell, H. A. Simon, and
T.O. Ellis / 349 \\
\\
Chapter 31 System Design of a FORTRAN Machine ---
Theodore R. Bashkow, Azra Sasson, and Arnold Kronfeld /
363 \\
Chapter 32 A Microprogrammed Implementation of EULER on
IBM System/360 Model 30 --- Helmut Weber / 382 \\
\\
Part 5 The PMS Level \\
\\
Section 1 Computers with One Central Processor / 395
\\
\\
[Chapter 6 The Whirlwind I Computer --- R. R. Everett]
\\
[Chapter 42 The SDS 910-9300 Series] \\
\\
Section 2 Computers with One Central Processor and
Multiple Input/Output Processors / 396 \\
\\
[Chapter 5 The DEC PDP-8] \\
Chapter 33 The IBM 1800 / 399 \\
[Chapter 41 The IBM 7094 I, II] \\
[Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure -- G. A. Blaauw and F.
P. Brooks, Jr.] \\
Chapter 34 The Engineering Design of the Stretch
Computer -- Erich Bloch / 421 \\
Chapter 35 PILOT, The NBS Multicomputer System --- A.
L. Leiner, W. A. Notz, J. L. Smith, and A. Weinberger /
440 \\
\\
Section 3 Computers for Multiprocessing and Parallel
Processing / 446 \\
\\
Chapter 36 D825 --- A Multiple-computer System for
Command and Control --- James P. Anderson, Samuel A.
Hoffman, Joseph Shifman, and Robert J. Williams / 447
\\
[Chapter 22 Design of the B 5000 System ---- William
Lonergan and Paul King] \\
Chapter 37 A Survey of Problems and Preliminary Results
Concerning Parallel Processing and Parallel Processors
--- M. Lehman / 456 \\
\\
Section 4 Network Computers and Computer Networks / 470
\\
\\
Chapter 38 The RW-400: A New Polymorphic Data System
--- R. E. Porter / 477 \\
Chapter 39 Parallel Operation in the Control Data 6600
--- James E. Thornton / 489 \\
Chapter 40 Computer Network Examples / 504 \\
\\
Part 6 Computer Families \\
\\
Section 1 The IBM 701--7094 II Sequence, a Family by
Evolution / 515 \\
\\
Chapter 41 The IBM 7094 I, 11 / 517 \\
\\
Section 2 The SDS 910--9300 Series, a Planned Family /
542 \\
\\
Chapter 42 The SDS 910-9300 Series / 543 \\
\\
Section 3 The IBM System/360 --- A Series of Planned
Machines Which Span a Wide Performance Range / 561 \\
\\
Chapter 43 The Structure of System/360, Part I ---
Outline of the Logical Structure --- G. A. Blaauw and
F. P. Brooks, Jr. / 588 \\
Chapter 44 The Structure of System/360, Part II ---
System Implementations --- W. Y. Stevens / 602 \\
\\
Appendix PMS and ISP Notations / 607 \\
\\
General Conventions / 607 \\
\\
1 Basic Semantics / 608 \\
2 Metanotation / 608 \\
3 Basic Syntax / 609 \\
4 Commands: Assignments, Abbreviation, Variables, Forms
/ 609 \\
5 Indefinite Expressions / 610 \\
6 Lists and Sets / 611 \\
7 Definite Expressions / 611 \\
8 Attributes / 612 \\
9 Null Symbol and Optional Expression / 613 \\
10 Names / 613 \\
11 Numbers / 614 \\
12 Quantities, Dimensions, and Units / 615 \\
13 Boolean and Relations / 615 \\
\\
PMS Conventions / 615 \\
\\
1 Dimensions / 616 \\
2 General Units / 616 \\
3 Information Units / 616 \\
4 Component / 617 \\
5 Link (L) / 619 \\
6 Memory (M) / 620 \\
7 Switch (S) / 623 \\
8 Control (K) / 624 \\
9 Transducer (T) / 625 \\
10 Data-operations (D) / 626 \\
11 Processor (P) / 626 \\
12 Computer (C) / 628 \\
\\
ISP Conventions / 628 \\
\\
1 Data-types / 629 \\
2 Instruction / 631 \\
3 Operations / 632 \\
4 Processors / 635 \\
\\
Bibliography / 638 \\
Name Index / 653 \\
Machine and Organization Index / 656 \\
Subject Index / 661",
}
@Article{Berg:1971:SAO,
author = "R. O. Berg and L. L. Kinney",
title = "Serial Adders with Overflow Correction",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "668--671",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223321",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671914",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Caprani:1971:ILR,
author = "Ole Caprani",
title = "Implementation of a Low Round-Off Summation Method",
journal = j-BIT,
volume = "11",
number = "3",
pages = "271--275",
month = sep,
year = "1971",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01931808",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Sat Nov 14 09:14:57 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=3&spage=271",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
}
@Misc{Chen:1971:BAU,
author = "Tien Chi Chen",
title = "Binary arithmetic unit implementing a multiplicative
iteration for the exponential, logarithm, quotient and
square root functions",
howpublished = "United States Patent 3,631,230",
day = "28",
month = dec,
year = "1971",
bibdate = "Tue Jan 08 21:54:11 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/3631230.html",
abstract = "Apparatus and a method is described for efficiently
achieving arithmetic evaluations for functions such as
exponential, logarithm, quotient, and square root with
a minimum use of multiplications or divisions.
Basically, use is made of the fact that $ x(1 \pm
2^{-m}) $ can be evaluated by a shift followed by an
add. A pair of numbers $ (x_k, y_k) $ can represent a
function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
y_n) = y_n $ for logarithm, quotient and square root.
Then, multiplication by shifting is applied to $ x_k $
with suitable adjustments on $ y_k $, until $ x_k $ is
close to unity, at which time $ y_k $ represents the
desired answer. The exponential is computed by
essentially reversing the logarithm procedure. A
termination algorithm further improves accuracy. The
apparatus involves two registers for $ x_k $ and $ y_k
$, a local memory, an adder and a shift register.",
acknowledgement = ack-nhfb,
}
@Article{Chen:1971:BMS,
author = "Tien Chi Chen",
title = "A Binary Multiplication Scheme Based on Squaring",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "678--680",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223325",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671918",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Chen:1971:DNC,
author = "Tien Chi Chen",
title = "Decimal Number Compression",
howpublished = "Internal IBM memo to Dr. Irving T. Ho.",
pages = "4",
day = "29",
month = mar,
year = "1971",
bibdate = "Fri Nov 28 16:24:59 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The fact that four bits can represent 16 different
states, but a decimal digit exploits only 10 of then
(0--9) has been a valid criticism against decimal
arithmetic.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Chen:1971:EAA,
author = "Tien Chi Chen",
title = "Efficient Arithmetic Apparatus and Method",
journal = j-IBM-TDB,
volume = "14",
number = "1",
pages = "328--330",
month = jun,
year = "1971",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Tue Jan 08 22:33:33 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InCollection{Clark:1971:SCP,
author = "N. W. Clark and W. J. Cody and H. Kuki",
title = "Self-Contained Power Routines",
crossref = "Rice:1971:MS",
pages = "399--415",
year = "1971",
bibdate = "Thu Sep 15 18:56:49 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Cody:1971:DHC,
author = "W. J. Cody",
title = "Desirable Hardware Characteristics for Scientific
Computation",
journal = j-SIGNUM,
volume = "6",
number = "1",
pages = "16--31",
month = jan,
year = "1971",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1052614.1052616",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:49:57 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
xxtitle = "Hardware characteristics (pages missing from print)",
}
@InCollection{Cody:1971:SEF,
author = "W. J. Cody",
title = "Software for the Elementary Functions",
crossref = "Rice:1971:MS",
pages = "171--186",
year = "1971",
bibdate = "Thu Sep 15 18:56:47 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dekker:1971:FPT,
author = "Theodorus J. Dekker",
title = "A Floating-Point Technique for Extending the Available
Precision",
journal = j-NUM-MATH,
volume = "18",
number = "3",
pages = "224--242",
month = jun,
year = "1971",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01397083",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "68A55",
MRnumber = "MR0299007 (45 \#8056)",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib;
Parallel/par.lin.alg.bib",
URL = "http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN362160546_0018",
abstract = "A technique is described for expressing multilength
floating-point arithmetic in terms of singlelength
floating point arithmetic, i.e. the arithmetic for an
available (say: single or double precision)
floating-point number system. The basic algorithms are
exact addition and multiplication of two singlelength
floating-point numbers, delivering the result as a
doublelength floating-point number. A straight-forward
application of the technique yields a set of algorithms
for doublelength arithmetic which are given as ALGOL 60
procedures.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Math. Centre, Amsterdam, Netherlands",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "accurate floating-point summation; ALGOL 60
procedures; available precision; digital arithmetic;
double precision; multilength; single; single length
floating point arithmetic; subroutines",
remark = "Report MR 118/70, Computation Department, Mathematical
Centre, Amsterdam. Part of this research was done while
the author was visiting Bell Telephone Laboratories,
Murray Hill, New Jersey.",
treatment = "T Theoretical or Mathematical",
}
@Article{DeLong:1971:UPA,
author = "Howard DeLong",
title = "Unsolved Problems in Arithmetic",
journal = j-SCI-AMER,
volume = "224",
number = "3",
pages = "50--60",
month = mar,
year = "1971",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0371-50",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 12:00:01 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1970.bib",
URL = "http://www.nature.com/scientificamerican/journal/v224/n3/pdf/scientificamerican0371-50.pdf",
acknowledgement = ack-nhfb,
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
}
@Article{Dutka:1971:SRD,
author = "Jacques Dutka",
title = "The Square Root of $2$ to $ 1, 000, 000 $ Decimals",
journal = j-MATH-COMPUT,
volume = "25",
number = "116",
pages = "927--930",
month = oct,
year = "1971",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Gentleman:1971:OMC,
author = "W. Morven Gentleman",
title = "Optimal multiplication chains for computing a power of
a symbolic polynomial",
journal = j-SIGSAM,
volume = "??",
number = "18",
pages = "23--30",
month = apr,
year = "1971",
CODEN = "SIGSBZ",
DOI = "https://doi.org/10.1145/1093425.1093426",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Tue Jun 17 19:14:25 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper shows that in a certain model of symbolic
manipulation of algebraic formulae, the simple method
of computing a power of a symbolic polynomial by
repeated multiplication by the original polynomial is,
in essence, the optimal method.",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "18",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@TechReport{Ghest:1971:TCD,
author = "R. C. Ghest",
title = "A Two's Complement Digital Multiplier, the {Am25S05}",
type = "Technical report",
institution = "Advanced Micro Devices",
address = "Sunnyvale, CA, USA",
pages = "????",
year = "1971",
bibdate = "Fri Nov 09 18:50:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ginsberg:1971:NID,
author = "Myron Ginsberg",
booktitle = "Proceedings of the First Annual Rocky Mountain
Symposium on Microprocessors",
title = "Numerical influences on the design of floating-point
arithmetic for microcomputers",
publisher = "????",
address = "????",
pages = "24--72",
year = "1971",
bibdate = "Fri Nov 09 18:52:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Glaser:1971:HBO,
author = "Anton Glaser",
title = "History of Binary and Other Nondecimal Numeration",
publisher = "Anton Glaser",
address = "Southampton, PA, USA",
pages = "ix + 196",
year = "1971",
ISBN = "0-9600324-1-X",
ISBN-13 = "978-0-9600324-1-9",
LCCN = "QA141.2 .G55",
bibdate = "Fri Mar 17 08:12:27 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "See also revised edition \cite{Glaser:1981:HBO}.",
acknowledgement = ack-nhfb,
author-dates = "1924--",
remark = "Based on the author's thesis, Temple University, with
title: History of modern numeration systems.",
subject = "Numeration; History",
tableofcontents = "Before Leibniz \\
Leibniz (1646--1716) \\
The rest of the 1700s \\
The nineteenth century \\
The twentieth century up to the computer age \\
Applications to computers \\
Contemporary literature",
}
@Article{Golub:1971:CAC,
author = "G. H. Golub and L. B. Smith",
title = "{Chebyshev} Approximation of Continuous Functions by a
{Chebyshev} System of Functions",
journal = j-CACM,
volume = "14",
number = "11",
pages = "737--746",
month = nov,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Aug 15 09:54:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM Algorithm 414.",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@TechReport{Haavie:1971:SMA,
author = "T. H{\aa}vie",
title = "Some Methods for Automatic Integration and their
Implementation on the {CERN CDC 65\slash 6600}
Computers",
type = "Report",
number = "CERN 71-26",
institution = "CERN",
address = "Geneva, Switzerland",
day = "1",
month = dec,
year = "1971",
bibdate = "Thu Jan 04 13:15:46 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://cds.cern.ch/record/190218/files/CERN-71-26.pdf",
abstract = "Two schemes for automatic integration using modified
Romberg and Clenshaw--Curtis quadratures are discussed.
The experience gained testing FORTRAN routines, using
both rounded and unrounded arithmetic, on a set of 20
test examples are reported.",
acknowledgement = ack-nhfb,
keywords = "automatic integration; CDC arithmetic; Clenshaw\slash
Curtis; Romberg; rounding corrections",
onlinedate = "iv + 43",
remark = "The report gives results, and recommendations, for
default (unrounded) and rounded arithmetic computation
in the peculiar arithmetic of the CDC 6000\slash 7000
family computers, for single precision (48-bit
significand, about 14 decimal digits) and double
precision (96-bit significand, almost 29 decimal
digits). Unlike Wirth's compiler work
\cite{Wirth:1972:PCG}, it does not get down to
instruction set details, or discuss the problems of
integer arithmetic.",
}
@Article{Honey:1971:CCD,
author = "D. W. Honey",
title = "Correspondence: Calculation of a double-length square
root from a double length number using single precision
techniques",
journal = j-COMP-J,
volume = "14",
number = "4",
pages = "443--443",
month = nov,
year = "1971",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:58 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Kagan:1971:FPS,
author = "Claude A. R. Kagan",
title = "Floating point sub-language of a string language",
journal = j-SIGPLAN,
volume = "6",
number = "10",
pages = "20--22",
month = nov,
year = "1971",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/1317448.1317449",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Dec 2 08:35:10 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan1970.bib",
URL = "https://dl.acm.org/citation.cfm?id=1317449",
abstract = "The facilities for floating point computation within
the framework of a string language currently operating
on the PDP-10 at the Western Electric Company
Engineering Research Center are considered to be a
sublanguage. This sublanguage is accessed through use
of the * (asterisk) as a function marker in lieu of the
colon, and such use causes execution of all of the
available arithmetic functions as well as a family of
additional functions whose names are the same as those
used in Fortran. The list of functions that will
execute in this sublanguage is displayed through
execution of ** (LF), expression.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@InProceedings{Kahan:1971:SEA,
author = "W. M. Kahan",
title = "A Survey of Error Analysis",
crossref = "Freiman:1971:PIC",
pages = "1214--1239",
year = "1971",
MRclass = "65G05",
MRnumber = "MR0458845 (56 \#17045)",
bibdate = "Tue Aug 28 05:24:53 2001",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Information Processing 71",
URL = "http://dblp.uni-trier.de/db/conf/ifip/ifip71-2.html#Kahan71",
acknowledgement = ack-jr # " and " # ack-nhfb,
keywords = "accurate floating-point summation",
remark = "This paper contains the modified compensating
summation algorithm wherein `e = (temp - s) + y' is
replaced by `f = 0; if (sign(temp) == sign(y)) {f =
(0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
cited in e.g.,
\cite{Dalhquist:1974:NM,Higham:1993:AFP}.",
}
@Article{Kan:1971:EAD,
author = "E. Kan and J. Aggarwal",
title = "Error analysis of digital filter employing
floating-point arithmetic",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "18",
number = "6",
pages = "678--686",
month = nov,
year = "1971",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Kan:1973:CEA}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The error accumulation in a digital filter employing
floating-point arithmetic is studied. Sources of errors
are considered to originate from (1) roundoff in the
arithmetic operations, (2) quantization of both the
input and the initial states, and (3) \ldots{}",
}
@Article{Kingsbury:1971:DFU,
author = "N. G. Kingsbury and P. J. W. Rayner",
title = "Digital filtering using logarithmic arithmetic",
journal = j-ELECT-LETTERS,
volume = "7",
number = "2",
pages = "56--58",
day = "28",
month = jan,
year = "1971",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19710039",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Mon May 30 07:32:20 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Krishnamurthy:1971:CTW,
author = "E. V. Krishnamurthy",
title = "Complementary Two-Way Algorithms for Negative Radix
Conversions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "543--550",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223288",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671881",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Krishnamurthy:1971:EIR,
author = "E. V. Krishnamurthy",
title = "Economical Iterative and Range-Transformation Schemes
for Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "470--472",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223270",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671863",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kuki:1971:FEP,
author = "H. Kuki and J. Ascoly",
title = "{FORTRAN} extended-precision library",
journal = j-IBM-SYS-J,
volume = "10",
number = "1",
pages = "39--61",
year = "1971",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Thu Sep 15 18:51:32 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Systems Journal",
xxmonth = "(none)",
}
@InCollection{Kuki:1971:MFS,
author = "H. Kuki",
title = "Mathematical Function Subprograms for Basic System
Libraries\emdash Objectives, Constraints, and
Trade-Off",
crossref = "Rice:1971:MS",
pages = "187--199",
year = "1971",
bibdate = "Fri Sep 16 16:27:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
}
@Article{Kulisch:1971:AAR,
author = "U. Kulisch",
title = "An axiomatic approach to rounded computations",
journal = j-NUM-MATH,
volume = "18",
number = "1",
pages = "1--17",
month = feb,
year = "1971",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01398455",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The present paper is intended to give an axiomatic
approach to rounded computations. A rounding is defined
as a monotone mapping of an ordered set into a subset,
which in general is called a lower respectively an
upper screen. The first chapter deals with roundings in
ordered sets. In the second chapter further properties
of roundings in linearly ordered sets are studied. The
third chapter deals with the two most important
applications, the approximation of the real arithmetic
on a finite screen and the approximation of the real
interval arithmetic on an upper screen. Beyond these
examples various further applications are possible.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Kupka:1971:SRA,
author = "I. Kupka",
title = "Simulation of real arithmetic and real functions in
finite sets",
journal = j-NUM-MATH,
volume = "17",
number = "2",
pages = "143--152",
year = "1971",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C1220 (Simulation, modelling and identification);
C4110 (Error analysis in numerical methods)",
corpsource = "Univ. Hamburg, West Germany",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "error estimation; errors; estimation theory; finite
set; floating point arithmetic; real functions;
simulation",
language = "German",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Lindsay:1971:RAF,
author = "D. S. Lindsay",
title = "A rounded arithmetic {FORTRAN} compiler for {CDC 6000}
machines",
type = "Report",
number = "????",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
pages = "????",
month = dec,
year = "1971",
bibdate = "Thu Jan 04 13:08:56 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "rounding corrections",
remark = "No copy of this report seems to be available online;
it is cited in \cite[p. 34]{Wirth:1972:PCG}. See the
remarks in that entry about the challenges of the CDC
arithmetic system.",
}
@Article{Majithia:1971:CAN,
author = "J. C. Majithia and R. Kitai",
title = "A Cellular Array for the Nonrestoring Extraction of
Square Roots",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1617--1618",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223191",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Majithia:1971:IAM,
author = "J. C. Majithia and R. Kitai",
title = "An Iterative Array for Multiplication of Signed Binary
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "2",
pages = "214--216",
month = feb,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671809",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Malcolm:1971:AFP,
author = "Michael A. Malcolm",
title = "On Accurate Floating-Point Summation",
journal = j-CACM,
volume = "14",
number = "11",
pages = "731--736",
month = nov,
year = "1971",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362854.362889",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05 (68-XX)",
MRnumber = "47 4434",
MRreviewer = "P. Brock",
bibdate = "Mon Jan 22 07:01:06 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Malcolm71;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Stanford University, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "accurate floating-point summation; digital arithmetic;
error analysis",
oldlabel = "Malcolm71",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm71",
}
@TechReport{Malcolm:1971:ARP,
author = "Michael A. Malcolm",
title = "Algorithm to reveal properties of floating-point
arithmetic",
institution = "Stanford University",
address = "Stanford, Ca.",
pages = "8",
year = "1971",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AD-727 104",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Floating-point arithmetic.",
remark = "``STAN-CS-71-211.''",
}
@Article{Morris:1971:TFP,
author = "R. Morris",
title = "Tapered Floating Point: a New Floating-Point
Representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1578--1579",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223174",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671767",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Mullet:1971:NME,
author = "Gary M. Mullet and Tracy W. Murray",
title = "A New Method for Examining Rounding Error in
Least-Squares Regression Computer Programs",
journal = j-J-AM-STAT-ASSOC,
volume = "66",
number = "335",
pages = "496--498",
month = sep,
year = "1971",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:44 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314211;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
URL = "http://www.jstor.org/stable/2283514",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Nicoud:1971:IAR,
author = "Jean-Daniel Nicoud",
title = "Iterative Arrays for Radix Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1479--1489",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223160",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Oct 10 13:44:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The general study of the conversion of a number from
the radix p to the radix q number system leads to four
different algorithms for integers, and to four similar
ones for fractions. Most transform algorithms can be
implemented by iterative arrays of cells characterized
by simple equations. Such arrays are very attractive
with present-time large-scale integration technology.
Two kinds of cells, that is, two iterative arrays, are
sufficient for the near instantaneous conversion of
fixed-point numbers from radix p to radix q, or vice
versa. For the important special case of binary-decimal
conversion, the structure of the cells is studied, and
different realizations using the BCD code are
described. One of them is specially suited for an LSI
realization in MOS technology. The advantages of other
codes are discussed. In particular, the use of the
biquinary code allows the realization of the fastest
cells, with only one gate delay for each line of
cells.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "base conversion; binary-decimal conversion; cellular
arrays; code conversion; iterative arrays; large-scale
integration; MOS technology; number systems; radix
conversion algorithms",
}
@Article{Paker:1971:BFP,
author = "Y. Paker",
title = "A Binary Floating-Point Resistor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "1",
pages = "7--11",
month = jan,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223074",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671667",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Paus:1971:FPA,
author = "Dag Paus",
title = "Floating point arithmetikk til {Nord-2B}",
type = "Hovedoppgave i fysikk",
institution = "Universitetet i Oslo",
address = "Oslo, Norway",
pages = "156",
year = "1971",
bibdate = "Thu May 09 08:11:14 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Norwegian",
}
@Article{Pawlak:1971:ACN,
author = "Z. Pawlak",
title = "Another Comment on {``Negative Radix Conversion''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "587--587",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223301",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Wadel:1971:CNR,Zohar:1970:NRC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671894",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Pezaris:1971:BBA,
author = "S. D. Pezaris",
title = "A 40ns 17-bit by 17-bit array multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "442--447 (??)",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223261",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:12:55 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Pezaris:1971:NBB,
author = "S. D. Pezaris",
title = "A 40-ns 17-Bit by 17-Bit Array Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "4",
pages = "442--447",
month = apr,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223261",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671854",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Rhyne:1971:SPN,
author = "V. T. Rhyne",
title = "A Simple Postcorrection for Nonrestoring Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "2",
pages = "213--214",
month = feb,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223215",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671808",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Rothmaier:1971:BEF,
author = "B. Rothmaier",
title = "{Die Berechnung der elementaren Funktionen mit
beliebiger Genauigkeit} \toenglish {The Computation of
Elementary Functions with Arbitrary Accuracy}
\endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1971",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sarkar:1971:EPP,
author = "B. P. Sarkar and E. V. Krishnamurthy",
title = "Economic Pseudodivision Processes for Obtaining Square
Root, Logarithm, and Arctan",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1589--1593",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223178",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671771",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Schmookler:1971:HSD,
author = "Martin S. Schmookler and Arnold Weinberger",
title = "High speed decimal addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "8",
pages = "862--867",
month = aug,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223362",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 28 19:10:32 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Parallel decimal arithmetic capability is becoming
increasingly attractive with new applications of
computers in a multiprogramming environment. The direct
production of decimal sums offers a significant
improvement in addition over methods requiring decimal
correction. These techniques are illustrated in the
eight-digit adder which appears in the System/360 Model
195.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Article{Schonhage:1971:SMG,
author = "A. Sch{\"o}nhage and V. Strassen",
title = "{Schnelle Multiplikation gro{\ss}er Zahlen}.
({German}) [{Fast} multiplication of large numbers]",
journal = j-COMPUTING,
volume = "7",
number = "3--4",
pages = "281--292",
year = "1971",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Thu Jan 04 08:42:36 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "Check pages??",
acknowledgement = ack-ec # " and " # ack-nhfb,
affiliation = "University, Konstanz, West Germany",
classification = "C5230",
description = "digital arithmetic",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "algorithm; binary numbers; logical nets; multitape
Turing machines; product",
language = "German",
}
@Article{Shepherd:1971:RSL,
author = "B. J. Shepherd",
title = "Right Shift for Low-Cost Multiply and Divide",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "12",
pages = "1586--1589",
month = dec,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223177",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671770",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Stein:1971:IMA,
author = "Marvin L. Stein and William D. Munro",
title = "Introduction to machine arithmetic",
publisher = pub-AW,
address = pub-AW:adr,
pages = "viii + 295",
year = "1971",
LCCN = "QA76.5 .S752",
bibdate = "Fri Nov 9 19:20:08 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers; Arithmetic",
}
@Article{Stein:1971:SMA,
author = "M. L. Stein and W. D. Munro",
title = "Scaling Machine Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "6",
pages = "675--678",
month = jun,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223324",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671917",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wadel:1971:CNR,
author = "L. B. Wadel",
title = "Comment on {``Negative Radix Conversion''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-20",
number = "5",
pages = "587--587",
month = may,
year = "1971",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1971.223300",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 06:38:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Pawlak:1971:ACN,Zohar:1970:NRC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671893",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Walker:1971:BS,
author = "R. J. Walker",
title = "Binary Summation",
journal = j-CACM,
volume = "14",
number = "6",
pages = "417--417",
month = jun,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:27:52 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Walker71;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Cornell University, Ithaca, NY, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "binary summation; digital arithmetic; floating point;
roundoff errors; space; storage",
oldlabel = "Walker71",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Walker71",
}
@InProceedings{Walther:1971:UAE,
author = "J. S. Walther",
title = "A unified algorithm for elementary functions",
crossref = "AFIPS:1971:ACP",
volume = "38",
pages = "379--385",
year = "1971",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Wlodarski:1971:FLN,
author = "J. Wlodarski",
title = "{Fibonacci} and {Lucas} Numbers Tend to Obey
{Benford's Law}",
journal = j-FIB-QUART,
volume = "9",
number = "1",
pages = "87--88",
month = feb,
year = "1971",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:05:33 MDT 2011",
bibsource = "http://www.fq.math.ca/9-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@InProceedings{Yohe:1971:R,
author = "J. M. Yohe",
booktitle = "Proceedings of the 1971 Army Numerical Analysis and
Computers Conference",
title = "Rounding",
publisher = "US Army Research Office",
address = "Durham, NC, USA",
pages = "213--223",
year = "1971",
LCCN = "????",
bibdate = "Sun Dec 30 21:37:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ARO-D Report 71-4",
acknowledgement = ack-nhfb,
}
@MastersThesis{Abdelmagid:1972:DFP,
author = "Mohamed Nabil Fouad Abdelmagid",
title = "Design of a floating point arithmetic unit",
type = "Thesis ({M.S.})",
school = "Illinois Institute of Technology",
address = "Chicago, IL.",
pages = "v + 60",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Ahmad:1972:ISH,
author = "M. Ahmad",
title = "Iterative schemes for high speed division",
journal = j-COMP-J,
volume = "15",
number = "4",
pages = "333--336",
month = nov,
year = "1972",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:07 MDT 2000",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/150333.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/333.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/334.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/335.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/336.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Manchester, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; digital computers; high speed
division; iterative methods; iterative schemes;
multiplicative",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Bandyopadhyay:1972:IAM,
author = "S. Bandyopadhyay and S. Basu and A. K. Choudhury",
title = "An Iterative Array for Multiplication of Signed Binary
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "921--922",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009055",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009055",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Banerji:1972:TAR,
author = "D. K. Banerji and J. A. Brzozowski",
title = "On Translation Algorithms in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1281--1285",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1972.223499",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672092;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35066",
abstract = "This paper considers translation problems in residue
number systems. The conversion from a fixed-base
representation to a residue representation can be done
using residue adders only; we show that relatively
simple combinational logic can be used to replace one
level of residue addition. In the reverse translation
problem, we examine the conditions under which base
extension can be used to compute the fixed-base digits
from a residue code number, and we study the efficiency
of the algorithm.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "base extension; input translation; modular arithmetic;
output translation; residue arithmetic; residue number
systems",
}
@Article{Brakefield:1972:OFP,
author = "James C. Brakefield",
title = "An optimal floating point format",
journal = j-COMP-ARCH-NEWS,
volume = "1",
number = "4",
pages = "16--17",
month = oct,
year = "1972",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:41:08 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Chen:1972:ACE,
author = "Tien Chi Chen",
title = "Automatic Computation of Exponentials, Logarithms,
Ratios and Square Roots",
journal = j-IBM-JRD,
volume = "16",
number = "4",
pages = "380--388",
month = jul,
year = "1972",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65D20",
MRnumber = "49 \#1738",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/164/chen.pdf",
abstract = "It is shown how a relatively simple device can
evaluate exponentials, logarithms, ratios and square
roots for fraction arguments, employing only shifts,
adds, high-speed table lookups, and bit counting. The
scheme is based on the cotransformation of a number
pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
invariant; when $x$ is driven towards a known value $
x_w $, $y$ is driven towards the result. For an $N$-bit
fraction about $ N / 4 $ iterations are required, each
involving two or three adds; then a termination
algorithm, based on an add and an abbreviated multiply,
completes the process, for a total cost of about one
conventional multiply time. Convergence, errors and
simulation using APL are discussed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "IBM, San Jose, CA, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "adds; APL; bit counting; convergence;
cotransformation; digital arithmetic; errors;
exponentials; high speed table; iteration; logarithms;
lookups; ratios; shifts; simulation; square roots;
termination algorithm",
reviewer = "F. Gotze",
treatment = "P Practical",
}
@Article{Chiang:1972:NAB,
author = "A. C. L. Chiang and I. S. Reed",
title = "Notes on the Arithmetic {BN} Modulo {A} Codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "891--894",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009046",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009046",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chien:1972:ECH,
author = "R. T. Chien and Se June Hong",
title = "Error Correction in High-Speed Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "5",
pages = "433--438",
month = may,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223538",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672131",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chinal:1972:SCP,
author = "J. P. Chinal",
title = "Some Comments on Postcorrections for Nonrestoring
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1385--1394",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223511",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672104",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{DeMori:1972:PSS,
author = "R. {De Mori} and A. Serra",
title = "A Parallel Structure for Signed-Number Multiplication
and Addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "12",
pages = "1453--1454",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223525",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672118",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fenwick:1972:BRD,
author = "Peter M. Fenwick",
title = "A Binary Representation for Decimal Numbers",
journal = j-AUSTRALIAN-COMP-J,
volume = "4",
number = "4",
pages = "146--149",
month = nov,
year = "1972",
CODEN = "ACMJB2",
ISSN = "0004-8917",
bibdate = "Fri Nov 28 11:31:38 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Australian Computer Journal",
keywords = "decimal floating-point arithmetic",
}
@Article{Fettweis:1972:CBM,
author = "A. Fettweis",
title = "On the connection between multiplier word length
limitation and roundoff noise in digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "19",
number = "5",
pages = "486--491",
month = sep,
year = "1972",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "It is shown that for digital filters there exists a
direct and an indirect connection between the
generation of roundoff noise by a multiplier and the
effect that the coefficient word length limitation of
this multiplier has upon the response \ldots{}",
}
@Article{Franklin:1972:ZDA,
author = "J. W. Franklin",
title = "Zoned Decimal Arithmetic",
journal = j-IBM-TDB,
volume = "15",
number = "7",
pages = "2123--2124",
month = dec,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Book{Goldstine:1972:CPN,
author = "Herman H. Goldstine",
title = "The Computer: {From Pascal} to {von Neumann}",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xii + 378",
year = "1972",
ISBN = "0-691-02367-0; 0-691-08104-2",
ISBN-13 = "978-0-691-02367-0; 978-0-691-08104-5",
bibdate = "Mon Jun 06 19:17:03 2005",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/TUBScsd/1972.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Second printing, 1973. Paperback edition 1980. Fifth
printing, 1993 with new preface. Reprint 2000 by Books
on Demand, Ann Arbor, MI, USA.",
acknowledgement = ack-nhfb,
descriptor = "Computer, ENIAC, Entwicklung, Geschichte, Pascal, Von
Neumann",
kwds = "book, history, computer",
}
@TechReport{Gosper:1972:HCF,
author = "R. W. Gosper",
title = "{HAKMEM} 101: Continued Fractions",
type = "Memo",
number = "AIM 239",
institution = "MIT AI Laboratory",
address = "Cambridge, MA, USA",
pages = "37--44",
year = "1972",
bibdate = "Fri Nov 30 06:37:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.inwap.com/pdp10/hbaker/hakmem/cf.html#item101a",
acknowledgement = ack-nhfb,
remark = "From the document: ``The familiar transcendental
functions of rational arguments also have simple
continued fractions, but these are generally not
regular and cannot be reconstructed from numerical
values by a simple algorithm, since nonregular
representations aren't unique. The point is, however,
that numbers like e, pi, sqrt(2), sin .5, sqrt(7)
arctan sqrt(7), etc. can be expressed to unlimited
precision by simple programs which produce the terms on
demand.'' Also: ``Rational number arithmetic often
loses because numerators and denominators grow so large
as to require icky multiprecision. Algorithms for
arithmetic on continued fractions seem generally
unknown. The next items describe how to arithmetically
combine continued fractions to produce new ones, one
term at a time.'' and ``Continued fractions let us
perform numerical calculations a little at a time
without ever introducing any error, such as roundoff or
truncation. As if this weren't enough, the calculations
provide automatic error analysis, and obviate most
forms of successive approximation.''",
}
@Article{Gregory:1972:CFP,
author = "James Gregory",
title = "A Comparison of Floating Point Summation Methods",
journal = j-CACM,
volume = "15",
number = "9",
pages = "838--838",
month = sep,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:46:23 MST 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Gregory72;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Argonne Nat. Lab., IL, USA",
descriptors = "Simulation; statistics; numeric calculation",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "accurate floating-point summation; comparison; digital
arithmetic; error; error propagation; floating point
summation methods; truncation",
oldlabel = "Gregory72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gregory72",
}
@Article{Gregory:1972:URA,
author = "Robert Todd Gregory",
title = "The use of residue arithmetic with automatic digital
computers",
journal = "Delta (Waukesha)",
volume = "3",
number = "2",
pages = "1--27",
year = "1972\slash 1973",
MRclass = "68A10",
MRnumber = "MR0321348 (47 \#9881)",
MRreviewer = "A. D. Booth",
bibdate = "Thu Nov 8 14:50:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hallin:1972:PAF,
author = "T. G. Hallin and M. J. Flynn",
title = "Pipelining of Arithmetic Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "880--886",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009044",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 18:57:52 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Heising:1972:MM,
author = "W. Heising and M. O. Rabin and Shmuel Winograd",
title = "Multiplication Method",
journal = j-IBM-TDB,
volume = "15",
number = "4",
pages = "1147--1148",
month = sep,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Manual{IBM:1972:ISR,
author = "{International Business Machines Corporation}",
title = "{IBM System\slash 360} reference data: direct
evaluation of floating point numbers in hexadecimal:
debugging aid",
organization = "IBM Corporation",
address = "White Plains, NY, USA",
pages = "18",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "IBM 360 (Computer)",
remark = "``GX20-1787-0.''",
}
@Article{Kamal:1972:HSM,
author = "A. A. Kamal and M. A. N. Ghannam",
title = "High-Speed Multiplication Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1017--1021",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009082",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009082",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Liu:1972:REF,
author = "B. Liu and M. {Van Valkenburg}",
title = "On roundoff error of fixed-point digital filters using
sign-magnitude truncation",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "19",
pages = "536--537",
month = sep,
year = "1972",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "This correspondence gives the statistical mean squared
error at the output of a digital filter due to roundoff
accumulation when fixed-point arithmetic with
sign-magnitude truncation is \ldots{}",
}
@Article{Loevenbruck:1972:CNR,
author = "A. P. Loevenbruck",
title = "Conversion of Number Representations",
journal = j-IBM-TDB,
volume = "15",
number = "7",
pages = "2148--2151",
month = dec,
year = "1972",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Majithia:1972:CAE,
author = "J. C. Majithia",
title = "Cellular Array for Extraction of Squares and Square
Roots of Binary Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "9",
pages = "1023--1024",
month = sep,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009084",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Malcolm:1972:ARP,
author = "Michael A. Malcolm",
title = "Algorithms to Reveal Properties of Floating-Point
Arithmetic",
journal = j-CACM,
volume = "15",
number = "11",
pages = "949--951",
month = nov,
year = "1972",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/355606.361870",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Malcolm72;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Gentleman:1974:MAR}.",
abstract = "Two algorithms are presented in the form of Fortran
subroutines. Each subroutine computes the radix and
number of digits of the floating-point numbers and
whether rounding or chopping is done by the machine on
which it is run. The methods are shown to work on any
``reasonable'' floating-point computer.",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723",
corpsource = "Stanford University, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "chopping; computer programming; computer programming
languages --- Fortran; digital arithmetic; digits;
floating point arithmetic; Fortran subroutines;
mathematical techniques --- Digital Arithmetic; number
of; properties; radix; rounding",
oldlabel = "Malcolm72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm72",
}
@Article{Mandelbaum:1972:ECR,
author = "David Mandelbaum",
title = "Error correction in residue arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
pages = "538--545",
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009006",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "94A10 (94A20)",
MRnumber = "MR0345709 (49 \#10440)",
MRreviewer = "P. Deussen",
bibdate = "Thu Nov 8 14:50:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Manos:1972:CCA,
author = "Paul Manos and L. Richard Turner",
title = "Constrained {Chebyshev} approximations to some
elementary functions suitable for evaluation with
floating-point arithmetic",
type = "{NASA} Technical Note",
number = "TN D-6698",
institution = "NASA",
address = "Washington, DC, USA",
pages = "iii + 68",
month = mar,
year = "1972",
bibdate = "Mon May 22 11:27:24 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
acknowledgement = ack-nhfb,
}
@MastersThesis{Maple:1972:FPA,
author = "Christopher Marion Maple",
title = "A floating point analog to digital and digital to
analog converter",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering",
address = "Cambridge, MA, USA",
pages = "18",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Marino:1972:NAA,
author = "D. Marino",
title = "New Algorithms for the Approximate Evaluation in
Hardware of Binary Logarithms and Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "21",
number = "12",
pages = "1416--1421",
month = dec,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223516",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 08:05:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Matula:1972:NTF,
author = "David W. Matula",
title = "Number Theoretic Foundations of Finite Precision
Arithmetic",
crossref = "Zaremba:1972:ANT",
pages = "479--489",
year = "1972",
bibdate = "Fri Oct 19 22:58:55 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "base conversion; finite-precision rational arithmetic;
number theory; overflow; radix conversion; tape
updating problem",
}
@TechReport{Metropolis:1972:ABCa,
author = "N. Metropolis",
title = "Analyzed Binary Computing",
type = "Technical Report",
number = "LA-DC--72-783; CONF-720916--2",
institution = inst-LASL,
address = inst-LASL:adr,
pages = "4",
day = "12",
month = sep,
year = "1972",
bibdate = "Tue Mar 20 11:25:24 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4647144&query_id=0",
acknowledgement = ack-nhfb,
}
@InProceedings{Metropolis:1972:ABCb,
author = "N. Metropolis",
title = "Analyzed Binary Computing",
crossref = "IEEE:1972:IAD",
pages = "81--84",
year = "1972",
bibdate = "Wed Mar 21 09:24:37 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A single format for the representation of numbers in a
computer is proposed to accommodate both exact and
inexact quantities. A consistent set of rules is
described for addition (subtraction), multiplication
and division of such quantities, both within their
separate types, as well as in combination. Error
correlation aside, the propagation of inherent errors
is monitored in operations with at least one imprecise
value. A definitive algorithm must, of course take into
account any correlations of inherent errors; these
correlations must be recognized and incorporated into
the algorithm by the numerical analyst, not by the
logical designer of the computer.",
acknowledgement = ack-nhfb,
}
@InProceedings{Metropolis:1972:ABCc,
author = "Nicholas C. Metropolis",
title = "Analyzed binary computing",
crossref = "IEEE:1972:ITS",
pages = "1--14",
year = "1972",
DOI = "https://doi.org/10.1109/ARITH.1972.6153912",
bibdate = "Tue Mar 5 08:31:37 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912",
acknowledgement = ack-nhfb,
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6148543",
}
@MastersThesis{Miller:1972:DFD,
author = "Peter Edwin Miller",
title = "The design of a floating-point, double-precision
arithmetic unit for the {Digital Equipment
Corporation}'s {PDP-9} computer",
type = "Thesis ({M.S.})",
school = "Ohio State University",
address = "Columbus, OH, USA",
pages = "83",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Arithmetic --- Computer programs; PDP-9 (Computer)",
}
@InProceedings{Neely:1972:CSN,
author = "Peter M. Neely",
title = "On conventions for systems of numerical
representation",
crossref = "ACM:1972:PAA",
pages = "644--561",
year = "1972",
bibdate = "Fri Nov 28 11:28:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Present conventions for numeric representation are
considered inadequate to serve the needs of applied
computing. Thus an augmented digital number system is
proposed for use in programming languages and in
digital computers. Special symbols are proposed for
numbers too large, too small or too close to zero to be
represented in the normal digital number system, or
which are undefined. Properties of mappings among and
between digital number systems are used to justify the
augments chosen. Finally a suggestion is made for a new
floating point word format that will serve all the
above needs and will greatly extend the exponent range
of floating point numbers.",
acknowledgement = ack-nhfb,
}
@Article{Oberman:1972:FRM,
author = "R. M. M. Oberman",
title = "A Flexible Rate Multiplier Circuit with Uniform Pulse
Distribution Outputs",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "896--899",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009048",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009048",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Paris:1972:MA,
author = "J. B. Paris",
title = "On models of arithmetic",
journal = j-LECT-NOTES-MATH,
volume = "255",
pages = "251--280",
year = "1972",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0059548",
ISBN = "3-540-05744-7 (print), 3-540-37162-1 (e-book)",
ISBN-13 = "978-3-540-05744-4 (print), 978-3-540-37162-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "02H05 (02H13)",
MRnumber = "0392552 (52 \#13369)",
MRreviewer = "W. Marek",
bibdate = "Fri May 9 19:07:09 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0059548/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0059533",
book-URL = "http://www.springerlink.com/content/978-3-540-37162-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Pettus:1972:IDC,
author = "C. Pettus",
title = "Indeterminate $ 0 \div 0 $ check in {APL}",
journal = j-SIGPLAN,
volume = "7",
number = "4",
pages = "40--41",
month = apr,
year = "1972",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 25 06:58:23 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One unique feature of the APL system is the definition
$ (0 \div 0) = 1 $. Although there is obvious merit in
this decision, in real analysis $ (0 \div 0) $ is
indeterminate. If one wishes to be alerted to the fact
that a denominator is zero and does not want the result
$1$ if the numerator is also zero, one can replace the
expression $ X \div Y $ with $ X \times \div Y $. Then
if $X$ and $Y$ are both zero, a Domain Error will be
reported instead of yielding.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "floating-point arithmetic; zero divide",
}
@Article{Phillips:1972:ICF,
author = "C. Phillips",
title = "Instabilities caused by floating-point arithmetic
quantization",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "17",
number = "2",
pages = "242--243",
month = apr,
year = "1972",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "It is shown that an otherwise stable digital control
system may become unstable due to signal quantization
if the controller operates on floating-point
arithmetic. Sufficient conditions for instability are
developed \ldots{}",
}
@Article{Pichat:1972:CSA,
author = "M. Pichat",
title = "Correction d'une Somme en Arithm{\'e}tique {\`a}
Virgule Flottante. ({French}) {[Correction of a Sum in
Floating-Point Arithmetic]}",
journal = j-NUM-MATH,
volume = "19",
number = "5",
pages = "400--406",
year = "1972",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Sep 17 18:30:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From Douglas Priest:
(\path=Douglas.[email protected]=) writing in Usenet
newsgroup sci.math.num-analysis on 13 Sep 1994 16:04:56
GMT: ``\ldots{} An iterative algorithm for computing a
protracted sum to working precision by repeatedly
applying the sum-and-roundoff method.''",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Conservatoire Nat. Arts M{\'e}tiers, Paris, France",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "accurate floating-point summation; correct rounding;
correction; digital arithmetic; floating point
arithmetic; rounding off law; sum; truncature with
guard digit",
language = "French",
treatment = "T Theoretical or Mathematical",
xxmonth = "(none)",
xxnumber = "(none)",
}
@Article{Ramamoorthy:1972:SPI,
author = "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
title = "Some Properties of Iterative Square-Rooting Methods
Using High-Speed Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "8",
pages = "837--847",
month = aug,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1972.5009039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:45 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Randell:1972:ATO,
author = "Brian Randell",
title = "On {Alan Turing} and the origins of digital
computers",
type = "Technical report",
number = "33",
institution = "University of Newcastle upon Tyne, Computing
Laboratory",
address = "Newcastle upon Tyne, UK",
pages = "36",
year = "1972",
LCCN = "TK7888.3 .R35",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "University of Newcastle upon Tyne. Computing
Laboratory. Technical report series",
acknowledgement = ack-nhfb,
subject = "Von Neumann, John; Turing, Alan Mathison; Electronic
digital computers; History",
subject-dates = "1903--1957 (John von Neumann); 1912--1954 (Alan
Turing)",
}
@TechReport{Randell:1972:ODC,
author = "Brian Randell",
title = "The origins of digital computers: a bibliography",
type = "Technical report",
number = "38",
institution = "Computing Laboratory, University of Newcastle upon
Tyne",
address = "Newcastle upon Tyne, UK",
pages = "iii + 59",
year = "1972",
LCCN = "TK7888.3 .R35",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "University of Newcastle upon Tyne, Computing
laboratory. Technical report series",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers; History; Bibliography",
}
@Article{Richman:1972:AEA,
author = "Paul L. Richman",
title = "Automatic Error Analysis for Determining Precision",
journal = j-CACM,
volume = "15",
number = "9",
pages = "813--817",
month = sep,
year = "1972",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05",
MRnumber = "47 2808",
bibdate = "Mon Jan 22 07:15:56 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Richman72;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The problem considered is that of evaluating a
rational expression to within any desired tolerance on
a computer which performs variable-precision
floating-point arithmetic operations. An automatic
error analysis technique is given for determining,
directly from the results of a trial low-precision
interval arithmetic calculation, just how much
precision and data accuracy are required to achieve a
desired final accuracy. The technique given generalize
easily to the evaluation of many nonrational
expressions.",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods); C5230 (Digital
arithmetic methods)",
classification = "921",
corpsource = "Bell Telephone Labs. Inc., Denver, CO, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "automatic error analysis; control; digital arithmetic;
error analysis; floating point arithmetic; interval
arithmetic; mathematical techniques; precision;
precision control",
oldlabel = "Richman72",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman72",
}
@PhdThesis{Ripley:1972:PFP,
author = "Jerald Lester Ripley",
title = "On proofs of floating-point program correctness and a
measure of their relative efficiency",
type = "Thesis ({Ph.D.})",
school = "University of Oklahoma",
address = "????",
pages = "vi + 105",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Numerical calculations.",
}
@Article{Rohl:1972:NCA,
author = "J. S. Rohl and J. A. Linn",
title = "A Note on Compiling Arithmetic Expressions",
journal = j-COMP-J,
volume = "15",
number = "1",
pages = "13--14",
month = feb,
year = "1972",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/15.1.13",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:49 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/15/1.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/15/1/13.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/150013.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/13.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/14.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6150C (Compilers, interpreters
and other processors)",
corpsource = "Univ. Manchester, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic expressions; compilers; compiling; data
handling; digital arithmetic; minimisation;
minimization; program; single accumulator; storing;
temporary",
treatment = "T Theoretical or Mathematical",
}
@Article{Samet:1972:CDL,
author = "P. A. Samet and D. W. Honey",
title = "Calculation of a Double-Length Square Root from
Double-Length Number using Single Precision
Techniques",
journal = j-COMP-J,
volume = "15",
number = "2",
pages = "116--116",
month = may,
year = "1972",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/15.2.116",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:49 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/15/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Coll., London, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; double length; precision
techniques; single; square root",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Schulenberg:1972:RSS,
author = "Craig Schulenberg and James E. Kernan",
title = "Results of space shuttle computer floating-point
precision study",
type = "Report",
number = "E-2637",
institution = "M.I.T. Charles Stark Draper Laboratory",
address = "Cambridge",
pages = "various",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic data processing --- Space trajectories.;
Reusable space vehicles.",
remark = "At head of title: Apollo guidance, navigation and
control.",
}
@Article{Schurmann:1972:MEA,
author = "A. Schurmann",
title = "On the minimum error in addition processes of positive
floating-point numbers",
journal = j-ZASTOS-MAT,
volume = "13",
pages = "351--366",
year = "1972--1973",
CODEN = "ZAMTAK",
MRclass = "65G05",
MRnumber = "48 3242",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Zastosowania Matematyki",
reviewer = "A. D. Booth",
}
@Article{Shaham:1972:NDA,
author = "Z. Shaham and Z. Riesel",
title = "A Note on Division Algorithms Based on
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "5",
pages = "513--514",
month = may,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223557",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 18:58:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672150",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Stallings:1972:CPM,
author = "W. T. Stallings and T. L. Boullion",
title = "Computation of Pseudoinverse Matrices Using Residue
Arithmetic",
journal = j-SIAM-REVIEW,
volume = "14",
number = "1",
pages = "152--163",
month = "????",
year = "1972",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1014005",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:35 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/14/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1972",
}
@Article{Stefanelli:1972:SHS,
author = "R. Stefanelli",
title = "A Suggestion for a High-Speed Parallel Binary
Divider",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-21",
number = "1",
pages = "42--55",
month = jan,
year = "1972",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1972.223430",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jan 08 22:42:31 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "family of four procedures to compute the inverse $ 1 /
X $ of a given binary number $X$ normalized between 0.5
and 1 is described. The quotient is obtained in
redundant binary form, i.e., in a base 2 code in which
digits can assume any positive or negative integer
value. All methods here described can be implemented by
combinatorial networks; the dividers realized in this
way are very fast because all carry propagations take
place at the same time.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InCollection{Tung:1972:A,
author = "C. Tung",
title = "Arithmetic",
crossref = "Cardenas:1972:CS",
pages = "??--??",
year = "1972",
bibdate = "Sat May 18 14:39:14 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Urabae:1972:CEA,
author = "Minoru Urabae",
title = "Component-wise error analysis of iterative methods
practiced on a floating-point system",
type = "{MRC} Technical Summary Report",
number = "1268",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "57",
year = "1972",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Error analysis (Mathematics); Floating-point
arithmetic.; Iterative methods (Mathematics)",
remark = "``Received August 11, 1972.'' Sponsored by Army
Research Office, Durham, N.C.",
}
@Article{Varian:1972:LEB,
author = "Hal R. Varian",
title = "Letter to the {Editor}: {Benford's Law}",
journal = j-AMER-STAT,
volume = "26",
number = "3",
pages = "65--66",
month = jun,
year = "1972",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Mar 30 11:34:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
abstract = "Around 1938 the physicist Frank Benford observed a
rather strange fact: tables of logarithms in libraries
tend to be dirtier at the beginning than at the end.
This indicated to Benford that people had more occasion
to calculate with numbers beginning with 1 or 2 than
with 8 or 9.\par
Benford also found that the frequency of the digit p
being the first digit of a decimal number was very
closely approximated by $ \log (p + 1) - \log p $
[i.e., $ \log (1 + 1 / p) $ ]. This has become known as
Benford's law.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@TechReport{Wirth:1972:PCG,
author = "Niklaus Wirth",
title = "On ``{Pascal}'', Code Generation, and the {CDC 6000}
Computer",
type = "Report",
number = "STAN-CS-72-257",
institution = inst-STAN-CS,
address = inst-STAN-CS:adr,
pages = "i + 38",
month = feb,
year = "1972",
bibdate = "Thu Jan 04 12:57:12 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "``PASCAL'' is a general purpose programming language
with characteristics similar to ALGOL 60, but with an
enriched set of program- and data structuring
facilities. It has been implemented on the CDC 6000
computer. This paper discusses selected topics of code
generation, in particular the selection of instruction
sequences to represent simple operations on arithmetic,
Boolean, and powerset operands. Methods to implement
recursive procedures are briefly described, and it is
hinted that the more sophisticated solutions are not
necessarily also the best. The CDC 6000 architecture
appears as a frequent source of pitfalls and nuisances,
and its main trouble spots are scrutinized and
discussed.",
acknowledgement = ack-nhfb,
author-dates = "15 February 1934--1 January 2024",
remark = "This report contains an interesting discussion of the
problems for compiler writers with a hardware
arithmetic design that subsumes integer arithmetic
inside one's complement floating-point arithmetic, and
is unable to detect integer overflow. The CDC 6000 and
7000, and Burroughs 5000 and 6000 families, share some
of these difficulties.",
}
@Book{Young:1972:SNM,
author = "David M. Young and Robert Todd Gregory",
title = "A Survey of Numerical Mathematics",
publisher = pub-AW,
address = pub-AW:adr,
pages = "x + 492 (A1--A18 and B1--B14 and I1--I19)",
year = "1972",
ISBN = "0-201-08773-1, 0-486-65691-8 (Dover paperback)",
ISBN-13 = "978-0-201-08773-4, 978-0-486-65691-5 (Dover
paperback)",
LCCN = "QA297 .Y63 1972",
MRclass = "65-02",
MRnumber = "53 11954a",
bibdate = "Wed Jan 17 10:57:04 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "D. Greenspan",
tableofcontents = "1: Numerical Analysis as a Subject Area \\
1.1 Introduction \\
1.2 Some pitfalls in computation \\
1.3 Mathematical and computer aspects of an algorithm
\\
1.4 Numerical instability of algorithms and
ill-conditioned problems \\
1.5 Typical problems of interest to the numerical
analyst \\
1.6 Iterative methods \\
2: Elementary Operations with Automatic Digital
Computers \\
2.1 Introduction \\
2.2 Binary arithmetic \\
2.3 Conversion from base $D$ to base $B$ representation
\\
2.4 Representation of integers on a binary computer \\
2.5 Floating-point representations \\
2.6 Computer-representable numbers \\
2.7 Floating-point arithmetic operations \\
2.8 Fortran analysis of a floating-point number \\
2.9 Calculation of elementary functions \\
3: Surveillance of Number Ranges \\
3.1 Introduction \\
3.2 Allowable number ranges \\
3.3 Basic real arithmetic operations \\
3.4 The quadratic equation \\
3.5 Complex arithmetic operations \\
4: Solution of Equations \\
4.1 Introduction \\
4.2 Attainable accuracy \\
4.3 Graphical methods \\
4.4 The method of bisection \\
4.5 The method of false position \\
4.6 The secant method \\
4.7 General properties of iterative methods \\
4.8 Generation of iterative methods \\
4.9 The Newton method \\
4.10 Muller's method \\
4.11 Orders of convergence of iterative methods \\
4.12 Acceleration of the convergence \\
4.13 Systems of nonlinear equations \\
5: Roots of Polynomial Equations \\
5.1 Introduction \\
5.2 General properties of polynomials \\
5.3 The Newton method and related methods \\
5.4 Muller's method and Cauchy's method \\
5.5 Location of the roots \\
5.6 Root acceptance and refinement \\
5.7 Matrix related methods: the modified Bernoulli
method \\
5.8 Matrix related methods: the IP method \\
5.9 Polyalgorithms \\
5.10 Other methods \\
6: Interpolation and Approximation \\
6.1 Introduction \\
6.2 Linear interpolation \\
6.3 Convergence and accuracy of linear interpolation
\\
6.4 Lagrangian interpolation \\
6.5 Convergence and accuracy of Lagrangian
interpolation \\
6.6 Interpolation with equal intervals \\
6.7 Hermite interpolation \\
6.8 Limitations on polynomial interpolation: smooth
interpolation \\
6.9 Inverse interpolation \\
6.10 Approximation by polynomials \\
6.11 Least squares approximation by polynomials \\
6.12 Rational approximation \\
6.13 Trigonometric interpolation and approximation \\
6.14 Interpolation in two variables \\
7: Numerical Differentiation and Quadrature \\
7.1 Introduction \\
7.2 The method of undetermined weights \\
7.3 Numerical differentiation \\
7.4 Numerical quadrature --- equal intervals \\
7.5 The Euler--MacLaurin formula \\
7.6 Romberg integration \\
7.7 Error determination \\
7.8 Numerical quadrature --- unequal intervals \\
8: Ordinary Differential Equations \\
8.1 Introduction \\
8.2 Existence and uniqueness \\
8.3 Analytic methods \\
8.4 Integral equation formulation --- the Picard method
of successive approximations \\
8.5 The Euler method \\
8.6 Methods based on numerical quadrature \\
8.7 Error estimation for predictor-corrector methods
\\
8.8 A numerical example \\
8.9 Runge--Kutta methods \\
8.10 Methods based on numerical differentiation \\
8.11 Higher-order equations and systems of first-order
equations \\
8.12 The use of high-speed computers \\
Appendix A \\
Appendix B \\
Appendix C \\
Bibliography \\
Index",
}
@Article{Aird:1973:SUM,
author = "T. Aird and D. Dodson and E. Houstis and J. Rice",
title = "Statistics on the Use of Mathematical Subroutines from
a Computer Center Library",
journal = j-SIGNUM,
volume = "8",
number = "4",
pages = "8--9",
month = oct,
year = "1973",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@MastersThesis{Anjoorian:1973:EME,
author = "Harry Anjoorian",
title = "An example of microprogrammed extended-precision
floating-point arithmetic",
type = "Thesis ({M.A.})",
school = "California State University, Chico",
address = "Chico, CA, USA",
pages = "ix + 94",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Electronic
digital computers --- Design and construction.",
}
@Article{Atkins:1973:PCA,
author = "David E. {Atkins, III} and Harvey L. Garner",
title = "Preface: Computer Arithmetic: An Introduction and
Overview [{Second IEEE Symposium on Computer
Arithmetic, May 15--16, 1972, University of
Maryland}]",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "549--551",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009104",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009104;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Atkins.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Avizienis:1973:AAE,
author = "Algirdas Avi{\v{z}}ienis",
title = "Arithmetic Algorithms for Error-Coded Operands",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "567--572",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009108",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Avizienis.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Book{Barna:1973:ICD,
author = "Arpad Barna and Dan I. Porat",
title = "Integrated Circuits in Digital Electronics",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 483",
year = "1973",
ISBN = "0-471-05050-4",
ISBN-13 = "978-0-471-05050-6",
LCCN = "TK7868.D5 B43",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Barsi:1973:ECP,
author = "F. Barsi and P. Maestrini",
title = "Error Correcting Properties of Redundant Residue
Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "3",
pages = "307--315",
month = mar,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223711",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672304;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35074",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The error correcting properties of the redundant
residue number systems (RNS) are investigated through a
more natural a approach than was previously known. The
necessary and sufficient condition for the correction
of a given error affecting a single \ldots{}",
}
@Article{Baugh:1973:TCP,
author = "C. R. Baugh and B. A. Wooley",
title = "A Two's Complement Parallel Array Multiplication
Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "12",
pages = "1045--1047",
month = dec,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223648",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments
\cite{Blankenship:1974:CTC,Kroft:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672241",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Besslich:1973:MDS,
author = "P. W. Besslich and S. Raman",
title = "Multiplication, Division and Square Root Extraction
Methods for Electronic Desk Calculators",
journal = "Journal of the Institution of Telecommunication
Engineers (India)",
volume = "19",
number = "4",
month = apr,
year = "1973",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Brent:1973:PAV,
author = "Richard P. Brent",
title = "On the Precision Attainable with Various
Floating-Point Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "601--607",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009113",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Brent.pdf",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Brent:1973:PEA,
author = "R. Brent and D. Kuck and K. Maruyama",
title = "The Parallel Evaluation of Arithmetic Expressions
Without Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "5",
pages = "532--534",
month = may,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223757",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672350",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cappa:1973:AIA,
author = "M. Cappa and V. C. Hamacher",
title = "An Augmented Iterative Array for High-Speed Binary
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "172--175",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223680",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Gardiner:1974:CAI}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672273",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cody:1973:SDN,
author = "William J. {Cody, Jr.}",
title = "Static and Dynamic Numerical Characteristics of
Floating-Point Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "598--601",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009112",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Dorr:1973:REC,
author = "Fred W. Dorr and Cleve B. Moler",
title = "Roundoff error on the {CDC 6600\slash 7600}
computers",
journal = j-SIGNUM,
volume = "8",
number = "2",
pages = "24--26",
month = apr,
year = "1973",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:49:59 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. California, Los Alamos, NM, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic; CDC 6600/7600 computers; computer; digital
arithmetic; program; roundoff error",
treatment = "P Practical; X Experimental",
}
@Article{Du:1973:CSS,
author = "Min-Wen Du and C. Dennis Weiss",
title = "Circuit Structure and Switching Function
Verification",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "618--625",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009116",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Ercegovac:1973:REC,
author = "Milo{\v{s}} D. Ercegovac",
title = "Radix-16 Evaluation of Certain Elementary Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "561--566",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009107",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@TechReport{Erkio:1973:EAV,
author = "Hannu Erkio",
title = "An extension of {ALGOL} with variable precision
floating-point arithmetic",
type = "Series {A}. Report",
number = "1973/2",
institution = "University of Helsinki, Department of Computer
Science",
address = "Helsinki",
pages = "ii + 20",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ALGOL (Computer program language); Floating-point
arithmetic",
}
@Article{Fettweis:1973:RNA,
author = "A. Fettweis",
title = "Roundoff noise and attenuation sensitivity in digital
filters with fixed-point arithmetic",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "20",
number = "2",
pages = "174--175",
month = mar,
year = "1973",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "A general expression is established which relates the
output roundoff noise generated by a fixed-point
multiplier in a digital filter to the sensitivity of
the filter attenuation with respect to the
corresponding multiplier coefficient. It confirms
\ldots{}",
}
@Article{Gelenbe:1973:UAE,
author = "Erol Gelenbe",
title = "A Unified Approach to the Evaluation of a Class of
Replacement Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "611--618",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009115",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Gelenbe.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Green:1973:NTF,
author = "D. H. Green and R. G. Kelsch",
title = "Nonlinear Ternary Feedback Shift Registers",
journal = j-COMP-J,
volume = "16",
number = "4",
pages = "360--367",
month = nov,
year = "1973",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:52:16 MDT 2000",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/160360.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/360.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/361.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/362.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/363.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/364.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/365.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/366.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/367.tif",
acknowledgement = ack-nhfb,
classcodes = "B1260 (Pulse circuits); B1265 (Digital electronics);
C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
classification = "722",
corpsource = "Univ. Manchester Inst. Sci. Technol., UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic; coding theory; communications; computers,
digital; digital arithmetic; digital computers;
feedback shift registers; functions; nonlinear;
polynomial domain representation; shift registers;
ternary",
treatment = "T Theoretical or Mathematical",
}
@Book{Hamming:1973:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "ix + 721",
year = "1973",
ISBN = "0-07-025887-2",
ISBN-13 = "978-0-07-025887-7",
LCCN = "QA297 .H28 1973",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing",
}
@Article{Hwang:1973:RRS,
author = "W. G. Hwang and John Todd",
title = "A recurrence relation for the square root",
journal = j-J-APPROX-THEORY,
volume = "9",
pages = "299--306",
year = "1973",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1016/0021-9045(73)90075-0",
ISSN = "0021-9045,1096-0430",
ISSN-L = "0021-9045",
MRclass = "65H05",
MRnumber = "373270",
MRreviewer = "L. Fox",
bibdate = "Sat Oct 21 14:25:01 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0271.65032",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007)",
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
received = "19 April 1971",
ZBmath = "3426800",
}
@Article{Jacobsohn:1973:CDA,
author = "David H. Jacobsohn",
title = "A Combinatoric Division Algorithm for Fixed-Integer
Divisors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "608--610",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009114",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Jacobsohn.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@TechReport{Kahan:1973:IAL,
author = "W. Kahan",
title = "Implementation of algorithms (lecture notes by {W. S.
Haugeland} and {D. Hough})",
type = "Technical report",
number = "20",
institution = "Department of Computer Science",
address = "Berkeley, CA, USA",
year = "1973",
bibdate = "Tue Aug 28 05:28:07 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
remark = "This paper contains the modified compensating
summation algorithm wherein `e = (temp - s) + y' is
replaced by `f = 0; if (sign(temp) == sign(y)) {f =
(0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
cited in e.g.,
\cite{Dalhquist:1974:NM,Higham:1993:AFP}. Kahan remarks
``The mysterious constant 0.46, which could perhaps be
any number between 0.25 and 0.50, and the fact that the
proof requires a consideration of known machines
designs, indicate that this algorithm is not an advance
in computer science.''",
}
@Article{Kan:1973:CEA,
author = "E. Kan and J. Aggarwal",
title = "Correction to {``Error Analysis of Digital Filters
Employing Floating-Point Arithmetic''}",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "20",
number = "5",
pages = "617--618",
month = sep,
year = "1973",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kan:1971:EAD}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
}
@Article{Kanani:1973:NCS,
author = "Dhirubhai V. Kanani and Kenneth H. O'Keefe",
title = "A Note on Conditional-Sum Addition for Base $ - 2 $
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "626--626",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009117",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:26 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009117;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Kanani.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; negative base",
}
@Article{Kaneko:1973:LCO,
author = "T. Kaneko",
title = "Limit-cycle oscillations in floating-point digital
filters",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "21",
number = "2",
pages = "100--106",
month = apr,
year = "1973",
CODEN = "ITADAS",
ISSN = "0018-9278 (print), 1558-2582 (electronic)",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
summary = "In a digital filter realized with fixed-point
arithmetic, there is a peculiar phenomenon known as
limit-cycle oscillation, which is due to roundoff
errors. For floating-point arithmetic, it has been
conjectured that its amplitude is negligibly small,
\ldots{}",
}
@Article{Kaneko:1973:LRE,
author = "Toyohisa Kaneko and Bede Liu",
title = "On Local Roundoff Errors in Floating-Point
Arithmetic",
journal = j-J-ACM,
volume = "20",
number = "3",
pages = "391--398",
month = jul,
year = "1973",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321765.321771",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "49 8318",
bibdate = "Tue Oct 09 10:18:49 2007",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A bound on the relative error in floating-point
addition using a single-precision accumulator with
guard digits is derived. It is shown that even with a
single guard digit, the accuracy can be almost as good
as that using a double-precision accumulator. A
statistical model for the roundoff error in
double-precision multiplication and addition is also
derived. The model is confirmed by experimental
measurements.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
reviewer = "V. V. Ivanov",
}
@TechReport{Kent:1973:PDS,
author = "Jan G. Kent",
title = "Procedures for the description and simulation of
floating point instructions",
type = "Report",
number = "426",
institution = "Norwegian Computing Center",
address = "Oslo, Norway",
month = sep,
year = "1973",
bibdate = "Sat Jan 09 06:27:20 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Kent:1973:TDA,
author = "Jan G. Kent",
title = "Theoretical definition, analysis and comparison of
floating point instructions",
type = "Report",
number = "425",
institution = "Norwegian Computing Center",
address = "Oslo, Norway",
month = sep,
year = "1973",
bibdate = "Sat Jan 09 06:27:20 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Kielbasinski:1973:SAC,
author = "Andrzej Kie{\l}basi{\'n}ski",
title = "Summation algorithm with corrections and some of its
applications",
journal = j-MATH-STOS,
volume = "1",
pages = "22--41",
year = "1973",
bibdate = "Tue Aug 28 06:06:57 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "In Polish.",
acknowledgement = ack-nhfb,
fjournal = "Math. Stos.",
keywords = "accurate floating-point summation",
remark = "The author's name is correct [verified by a Polish
colleague who knows the author]: some references have
it incorrectly as Kie{\l}baszi{\'n}ski.",
}
@Article{Kinoshita:1973:GDS,
author = "E. Kinoshita and H. Kosako and Y. Kojima",
title = "General Division in the Symmetric Residue Number
System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "134--142",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223674",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672267;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35073",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "In the residue number system, the arithmetic
operations of addition, subtraction, and multiplication
are executed in the same period of time without the
need for interpositional carry. There is a hope for
high-speed operation if residue arithmetic \ldots{}",
}
@Article{Kreifelts:1973:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
Gleitkomma-Arithmetik} \toenglish {Optimal Choice of
Basis for a Floating-Point Arithmetic} \endtoenglish",
journal = j-COMPUTING,
volume = "11",
number = "??",
pages = "353--363",
month = "????",
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Kreifelts:1973:OBG,
author = "Thomas Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine
Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
Basis for a Floating-Point Arithmetic]",
journal = j-COMPUTING,
volume = "11",
number = "4",
pages = "353--363",
month = dec,
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
note = "See correction \cite{Kreifelts:1975:OBF}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Inst. Numerische Datenverarbeitung, Bonn, West
Germany",
classification = "723; 921; C5230",
description = "digital arithmetic",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "base; computer programming; correct rounding; floating
point arithmetic; mathematical techniques; optimal
choice; rounding errors",
language = "German",
}
@Article{Kuki:1973:SSA,
author = "H. Kuki and W. J. Cody",
title = "A Statistical Study of the Accuracy of Floating Point
Number Systems",
journal = j-CACM,
volume = "16",
number = "4",
pages = "223--230",
month = apr,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "68A20 (65G05)",
MRnumber = "51 2344",
MRreviewer = "I. Kaufmann",
bibdate = "Wed Aug 31 13:47:33 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents the statistical results of tests
of the accuracy of certain arithmetic systems in
evaluating sums, products and inner products, and
analytic error estimates for some of the computations.
The arithmetic systems studied are 6-digit hexadecimal
and 22-digit binary floating point number
representations combined with the usual chop and round
modes of arithmetic with various numbers of guard
digits, and with a modified round mode with guard
digits. In a certain sense, arithmetic systems
differing only in their use of binary or hexadecimal
number representations are shown to be approximately
statistically equivalent in accuracy. Further, the
usual round mode with guard digits is shown to be
statistically superior in accuracy to the usual chop
mode in all cases save one. The modified round mode is
found to be superior to the chop mode in all cases.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723",
corpsource = "Univ. Chicago, IL, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "accuracy; arithmetic; computer programming; digital
arithmetic; error analysis; floating point arithmetic;
floating point number systems; guard digits; number
representation; rounding; statistical study",
oldlabel = "KukiC73",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/KukiC73",
}
@Article{Larson:1973:HSM,
author = "R. H. Larson",
title = "High Speed Multiply Using Four Input Carry Save
Adder",
journal = j-IBM-TDB,
volume = "??",
number = "??",
pages = "2053--2054",
month = dec,
year = "1973",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Jun 24 20:46:32 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Larson:1973:MSM,
author = "R. H. Larson",
title = "Medium Speed Multiply",
journal = j-IBM-TDB,
volume = "??",
number = "??",
pages = "2055--2055",
month = dec,
year = "1973",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Jun 24 20:42:28 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@PhdThesis{Lee:1973:SFP,
author = "Keng Ho Lee",
title = "Survey of floating-point software arithmetics and
basic library mathematical functions",
type = "Thesis ({Ph.D.})",
school = "Glasgow University",
address = "Glasgow, Scotland",
year = "1973",
bibdate = "Thu May 09 08:34:15 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Majithia:1973:NBL,
author = "J. C. Majithia and D. Levan",
title = "A note on base-2 logarithm computations",
journal = j-PROC-IEEE,
volume = "61",
number = "10",
pages = "1519--1520",
month = oct,
year = "1973",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 18:05:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "The well-known methods of iteration used suitably can
yield a more accurate and rapidly convergent
computation for the values of many functions. One
typical example is the base-2 logarithm-antilogarithm
computation. Some recently proposed techniques
\ldots{}",
}
@TechReport{Malcolm:1973:MAP,
author = "Michael A. Malcolm",
title = "A machine-independent {ALGOL} procedure for accurate
floating-point summation",
type = "Technical report",
number = "STAN-CS-73-374",
institution = "Stanford University, Computer Science Department",
address = "Stanford, CA, USA",
pages = "6",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ALGOL (Computer program language)",
}
@PhdThesis{Malcolm:1973:PAF,
author = "Michael A. Malcolm",
title = "Part {I}: On accurate floating-point summation; Part
{II}: Computation of nonlinear spline functions",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, Stanford University",
address = "Stanford, CA, USA",
pages = "ix + 129",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Interpolation;
spline theory",
}
@Article{Marasa:1973:SSC,
author = "John D. Marasa and David W. Matula",
title = "A simulated study of correlated error propagation in
various finite-precision arithmetics",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "587--597",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009111",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 05:07:23 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Marasa.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Article{Metropolis:1973:ABC,
author = "Nicholas C. Metropolis",
title = "Analyzed Binary Computing",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "573--576",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009109",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Mar 21 09:24:37 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A single format for the representation of numbers in a
computer is proposed to accommodate both exact and
inexact quantities. A consistent set of rules is
described for addition (subtraction), multiplication,
and division of such quantities, both within their
separate types, as well as in combination. Error
correlation aside, the propagation of inherent errors
is monitored in operations with at least one imprecise
value. A definitive algorithm must, of course take into
account any correlations of inherent errors; these
correlations must be recognized and incorporated into
the algorithm by the numerical analyst, not by the
logical designer of the computer.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; control of propagated errors; floating-point
representation; representation error; significant digit
arithmetic",
}
@Article{Metropolis:1973:SAC,
author = "N. Metropolis and Gian-Carlo Rota and S. Tanny",
title = "Significance arithmetic: the carrying algorithm",
journal = j-J-COMB-THEORY-A,
volume = "14",
pages = "386--421",
month = may,
year = "1973",
CODEN = "JCBTA7",
ISSN = "0097-3165 (print), 1096-0899 (electronic)",
ISSN-L = "0097-3165",
MRclass = "10A30 (02E10)",
MRnumber = "MR0321857 (48 \#222)",
MRreviewer = "R. L. Goodstein",
bibdate = "Thu Nov 8 14:50:22 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0259.00001",
abstract = "It has been remarked that, in mathematics, a
notational deficiency is often a symptom of conceptual
obscurity. The starting point of this work is one such
deficiency. In ordinary binary arithmetic, a number
ending in a string of ones, such as $ 0.0110111 \ldots
{} $ is equal to the number obtained by replacing the
digit zero next to the string of ones by the digit one,
and the string of succeeding ones by zeros; in the
example, $ 0.0111000 $",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory. Series A",
journal-URL = "http://www.sciencedirect.com/science/journal/00973165",
}
@Article{Mifsud:1973:AMP,
author = "Charles J. Mifsud and Michael J. Bohlen",
title = "Addendum to a Multiple-Precision Division Algorithm",
journal = j-CACM,
volume = "16",
number = "10",
pages = "628--??",
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:04:18 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#MifsudB73;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Mifsud:1970:MDA}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "MifsudB73",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/MifsudB73",
}
@Article{Newbery:1973:EAF,
author = "A. C. R. Newbery",
title = "Error Analysis for {Fourier} Series Evaluation",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "639--644",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Univ. Kentucky, Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "error analysis; evaluation; floating point; Fourier
series evaluation; numerical methods; polynomials;
recursive method; series (mathematics); trigonometric
polynomials",
treatment = "T Theoretical or Mathematical",
}
@Article{OKeefe:1973:RBE,
author = "Kenneth H. O'Keefe and John L. Wright",
title = "Remarks on Base Extension for Modular Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "9",
pages = "833--835",
month = sep,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009173",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009173",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Parker:1973:DHF,
author = "Tony Edwin Parker",
title = "Design of a hardware floating point processor for the
{PDP-8s}",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering",
address = "Cambridge, MA, USA",
pages = "19",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Paterson:1973:NNM,
author = "Michael S. Paterson and Larry J. Stockmeyer",
title = "On the Number of Nonscalar Multiplications Necessary
to Evaluate Polynomials",
journal = j-SIAM-J-COMPUT,
volume = "2",
number = "1",
pages = "60--66",
month = mar,
year = "1973",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Mon Nov 29 10:57:40 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/2/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Theory/Matrix.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
kwds = "na, polynomial, complexity",
xxnote = "Cited in \cite{govl:89}.",
}
@Article{Pittnauer:1973:AA,
author = "E. Pittnauer",
title = "{Eine Aussage {\"u}ber Alternanten} \toenglish {??}
\endtoenglish",
journal = j-NUM-MATH,
volume = "23",
number = "??",
pages = "427--432",
month = "????",
year = "1973",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Pittnauer:1973:NPK,
author = "E. Pittnauer",
title = "{Numerische Polynomapproximation mit Knotenpolynomen}
\toenglish {Numerical Polynomial Approximations with
Knot Polynomials} \endtoenglish",
journal = j-NUM-MATH,
volume = "21",
number = "3",
pages = "256--263",
year = "1973",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
xxmonth = "(none)",
}
@Book{Randell:1973:ODC,
editor = "Brian Randell",
title = "The origins of digital computers: selected papers",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 464",
year = "1973",
ISBN = "0-387-06169-X, 3-540-06169-X",
ISBN-13 = "978-0-387-06169-6, 978-3-540-06169-4",
LCCN = "TK7888.3 .R36",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "See also later editions
\cite{Randell:1975:ODC,Randell:1982:ODC}.",
}
@Article{Richman:1973:VPE,
author = "Paul L. Richman",
title = "Variable-Precision Exponentiation",
journal = j-CACM,
volume = "16",
number = "1",
pages = "38--40",
month = jan,
year = "1973",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65D20",
MRnumber = "51 4631",
MRreviewer = "V. V. Ivanov",
bibdate = "Mon Jan 22 07:15:57 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Richman73;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A previous paper presented an efficient algorithm,
called the Recomputation Algorithm, for evaluating a
rational expression to within any desired tolerance on
a computer which performs variable-precision arithmetic
operations. The Recomputation Algorithm can be applied
to expressions involving any variable-precision
operations having $ O(10^( - p) + \sum_i|E_i|) $ error
bounds, where $p$ denotes the operation's precision and
$ E_i $ denotes the error in the operation's $i$-th
argument. \par
This paper presents an efficient variable-precision
exponential operation with an error bound of the above
order. Other operations such as log, sin, and cos,
which have simple series expansions, can be handled
similarly.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723; 921",
corpsource = "Bell Telephone Labs. Inc., Denver, CO, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "computer programming; digital arithmetic; error
analysis; exponential function; exponentiation;
interval arithmetic; mathematical programming; variable
precision; variable-precision",
oldlabel = "Richman73",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman73",
}
@Article{Robertson:1973:SIC,
author = "James E. Robertson and Kishor S. Trivedi",
title = "The status of investigations into computer hardware
design based on the use of continued fractions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "555--560",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009106",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 8 14:50:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; continued fractions",
}
@Article{Roy:1973:ARC,
author = "P. K. Sinha Roy and C. L. Sheng",
title = "Author's Reply to Comments on {``Decomposition Method
of Determining Maximum Compatibles''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "627--627",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009119",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Sureshchander:1973:CDM}.",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@MastersThesis{Rubinfield:1973:FM,
author = "Louis P. Rubinfield",
title = "A floating-point macromodule",
type = "Thesis ({M.S.})",
school = "Washington University, Department of Electrical
Engineering",
address = "St. Louis, MO, USA",
pages = "vii + 111",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Design and
construction.",
}
@Article{Sankar:1973:AAN,
author = "P. V. Sankar and S. Chakrabarti and E. V.
Krishnamurthy",
title = "Arithmetic Algorithms in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "120--125",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223671",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672264",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Sankar:1973:DDA,
author = "P. V. Sankar and S. Chakrabarti and E. V.
Krishnamurthy",
title = "Deterministic Division Algorithm in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "125--128",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223672",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672265",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Schatte:1973:VMG,
author = "Peter Schatte",
title = "{Zur Verteilung der Mantisse in der
Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
({German}) [Distribution of the mantissa in the
floating-point representation of a random variable]",
journal = j-Z-ANGE-MATH-MECH,
volume = "53",
number = "??",
pages = "553--565",
month = "????",
year = "1973",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Mon Nov 14 16:35:28 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
language = "German",
}
@Article{Schmid:1973:BLIa,
author = "H. Schmid",
title = "{BCD} logic {I}: {BCD} -- logic of many uses",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "13",
pages = "90--95",
month = jun,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 08 08:17:30 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLIb,
author = "H. Schmid",
title = "{BCD} logic {II}: {BCD} multiplication",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "14",
pages = "62--69",
month = jul,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLIc,
author = "H. Schmid",
title = "{BCD} logic {III}: {BCD} division",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "15",
pages = "86--92",
month = jul,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLId,
author = "H. Schmid",
title = "{BCD} logic {IV}: {BCD} decimal-point location",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "16",
pages = "80--84",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
keywords = "decimal floating-point arithmetic",
}
@Article{Schmid:1973:BLVa,
author = "H. Schmid",
title = "{BCD} logic {V}: {BCD} square root",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "17",
pages = "62--69",
month = aug,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLVb,
author = "H. Schmid",
title = "{BCD} logic {VI}: {BCD} logarithms and exponentials",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "18",
pages = "118--123",
month = sep,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Schmid:1973:BLVc,
author = "H. Schmid",
title = "{BCD} logic {VII}: {BCD} trig and hyperbolic
functions",
journal = j-ELECTRONIC-DESIGN,
volume = "21",
number = "19",
pages = "68--73",
month = sep,
year = "1973",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Sentance:1973:FAB,
author = "W. A. Sentance",
title = "A Further Analysis of {Benford's Law}",
journal = j-FIB-QUART,
volume = "11",
number = "5",
pages = "490--494",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/11-5.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Shea:1973:NDN,
author = "Dale D. Shea",
title = "On the Number of Divisions Needed in Finding the
Greatest Common Divisor",
journal = j-FIB-QUART,
volume = "11",
number = "5",
pages = "508--510",
month = dec,
year = "1973",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:46 MDT 2011",
bibsource = "http://www.fq.math.ca/11-5.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/11-5/shea.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Singh:1973:MOA,
author = "S. Singh and R. Waxman",
title = "Multiple Operand Addition and Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "2",
pages = "113--120",
month = feb,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223670",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672263",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Sites:1973:FPS,
author = "Richard L. Sites",
title = "Floating point significance interrupt proposal",
journal = j-COMP-ARCH-NEWS,
volume = "2",
number = "1",
pages = "10--12",
month = jan,
year = "1973",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:28 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The purpose of this proposal is to aid numerical
analysts in observing the significance of results in
floating-point calculations. This proposal is not a
cure-all, but it does attempt to a first, high-payoff
step in understanding and analyzing floating-point
algorithms. This proposal is specifically for IBM
360/370 architecture, but the ideas are applicable to
all machines.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "The author observes that register clearing by
subtraction is common, and is one of the reasons that
``all IBM language processors execute with significance
masked off.'' He proposes suppressing the significance
interrupt in subtractions when both operands are
equal.",
}
@Article{Sjoding:1973:NVR,
author = "T. Sjoding",
title = "Noise variance for rounded two's complement product
quantization",
journal = j-IEEE-TRANS-AUDIO-ELECTROACOUST,
volume = "21",
number = "4",
pages = "378--380",
month = aug,
year = "1973",
CODEN = "ITADAS",
ISSN = "0018-9278 (print), 1558-2582 (electronic)",
ISSN-L = "0018-9278",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Audio and Electroacoustics",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
summary = "The Halyo-McAlpine discrete model for product
quantization is reconstructed using an error variable
set having an even number of members. It is shown in
this case that the noise variance associated with a
continuous model becomes an upper rather \ldots{}",
}
@Article{Spira:1973:CTA,
author = "Philip M. Spira",
title = "Computation Times of Arithmetic and {Boolean}
functions in $ (d, r) $ circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "552--555",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009105",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Spira.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
}
@Book{Stone:1973:DMS,
author = "Harold S. Stone",
title = "Discrete mathematical structures and their
applications",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
pages = "401",
year = "1973",
LCCN = "QA162 .S877d; QA162 .S77",
bibdate = "Fri Nov 9 19:24:02 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "The SRA computer science series",
acknowledgement = ack-nhfb,
subject = "Algebra, Abstract; Group theory; Machine theory",
tableofcontents = "Foundations of discrete mathematics. \\
Groups. \\
The P\'olya theory of enumeration. \\
Applications of group theory to computer design. \\
Group codes. \\
Semigroups. \\
Finite-state machines. \\
Rings and fields. \\
Linear -finite-state machines. \\
Boolean algebra with applications to computer design.",
}
@Article{Sureshchander:1973:CDM,
author = "Sureshchander",
title = "Comments on {``Decomposition Method of Determining
Maximum Compatibles''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "627--627",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009118",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:18:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Roy:1973:ARC}.",
URL = "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2",
xxnote = "Author has only a single name",
}
@Article{Swartzlander:1973:QSM,
author = "E. E. {Swartzlander, Jr.}",
title = "The Quasi-Serial Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "4",
pages = "317--321",
month = apr,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1973.223717",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672310",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Tanny:1973:SSA,
author = "Stephen Michael Tanny",
title = "Studies in Significance Arithmetic",
type = "{Ph.D.} thesis",
school = "Massachusetts Institute of Technology",
address = "Cambridge, MA, USA",
pages = "195",
year = "1973",
bibdate = "Tue Oct 22 06:18:19 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/302720894",
acknowledgement = ack-nhfb,
remark = "Full text is not available in ProQuest.",
}
@Article{Urabe:1973:CEA,
author = "Minoru Urabe",
title = "Component-wise error analysis of iterative methods
practiced on a floating-point system",
journal = j-MEM-FAC-SCI-KYUSHU-UNIV-A,
volume = "27",
pages = "23--64",
year = "1973",
CODEN = "MFKAAF",
ISSN = "0373-6385 (print), 1883-2172 (electronic)",
ISSN-L = "0373-6385",
MRclass = "65H10",
MRnumber = "48 1457",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Memoirs of the Faculty of Science, Kyushu Imperial
University. Series A, Mathematics = Kyushu Teikoku
Daigaku Rigakubu kiyo",
reviewer = "D. C. Handscomb",
}
@PhdThesis{Wiatrowski:1973:DFP,
author = "Claude A. Wiatrowski",
title = "Design of a floating-point processor for digital
simulation",
type = "Thesis ({Ph.D.} - Electrical Engineering)",
school = "University of Arizona",
address = "Tucson, AZ, USA",
pages = "107",
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Computer storage
devices.",
}
@Article{Yau:1973:ECR,
author = "S. S.-S. Yau and Yu-Cheng Liu",
title = "Error Correction in Redundant Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "1",
pages = "5--11",
month = jan,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1973.223594",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672187;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35069",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Two error-correcting algorithms for redundant residue
number systems are presented, one for single
residue-error correction and the other for burst
residue-error correction. Neither algorithm requires
table lookup, and hence their implementation \ldots{}",
}
@TechReport{Yohe:1973:FFPa,
author = "J. M. Yohe",
title = "Foundations of floating point computer arithmetic",
type = "{MRC} Technical Summary Report",
number = "1302",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "25",
month = jan,
year = "1973",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A formal structure, within which computer arithmetic
operations may be defined, is described. Several
floating point arithmetic schemes are defined within
this context. The structure described in the paper
includes, as a sub-structure, the significance spaces
of Matula.",
acknowledgement = ack-nhfb,
keywords = "Computers.; Floating-point arithmetic.",
remark = "January 1973. Sponsored by Army Research Office,
Durham, NC, USA.",
}
@Article{Yohe:1973:IBS,
author = "J. M. Yohe",
title = "Interval Bounds for Square Roots and Cube Roots",
journal = j-COMPUTING,
volume = "11",
number = "1",
pages = "51--57",
year = "1973",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:51 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-jr # " and " # ack-nhfb,
affiliation = "Univ. Wisconsin, Madison, WI, USA",
classification = "C5230",
description = "digital arithmetic; error analysis",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "binary computers; cube roots; error analysis; interval
bounds; machine representable number; optimal upward
directed rounding; smallest machine representable
interval; square roots",
}
@Article{Yohe:1973:RFP,
author = "J. Michael Yohe",
title = "Roundings in Floating-Point Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "6",
pages = "577--586",
month = jun,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009110",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009110;
http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Yohe.pdf",
abstract = "In this paper we discuss directed roundings and
indicate how hardware might be designed to produce
proper upward directed, downward directed, and certain
commonly used symmetric roundings. Algorithms for the
four binary arithmetic operations and for rounding are
presented, together with proofs of their correctness;
appropriate formulas for a priori error analysis of
these algorithms are presented. Some of the basic
applications of directed roundings are surveyed.",
acknowledgement = ack-jr # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-2; correct rounding; floating-point arithmetic",
}
@Book{Zacher:1973:HDG,
author = "H. J. Zacher",
title = "{Die Hauptschriften zur Dyadik von G. W. Leibniz: Ein
Beitr. zur Geschichte des bin{\"a}ren Zahlen-systems}.
({German}) [{The} main writings on the dyadic by {G. W.
Leibniz}: a contribution to the history of the binary
number system]",
publisher = "V. Klostermann",
address = "Frankfurt am Main, West Germany",
pages = "viii + 384",
year = "1973",
LCCN = "QA141.4.Z3; QA141.4.Z3 1973",
bibdate = "Fri Mar 17 09:19:21 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Ver{\"o}ffentlichungen des Leibniz-Archivs",
acknowledgement = ack-nhfb,
language = "German",
remark = "Selected original texts and correspondence in French,
German or Latin.",
subject = "Leibniz, Gottfried Wilhelm; Freiherr von; Yi jing;
Freiherr von,; Binary system (Mathematics); History;
Sources; Syst{\'e}me binaire (Math{\'e}matiques);
Histoire; Binary system (Mathematics)",
}
@Article{Zohar:1973:DCR,
author = "Shalhav Zohar",
title = "{A/D} Conversion for Radix ($ - 2$)",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-22",
number = "7",
pages = "698--701",
month = jul,
year = "1973",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1973.5009137",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 16:45:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009137",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
}
@Article{Agrawal:1974:NCL,
author = "D. P. Agrawal",
title = "Negabinary carry-look-ahead adder and fast
multiplier",
journal = j-ELECT-LETTERS,
volume = "10",
number = "??",
pages = "312--313",
month = jul,
year = "1974",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Thu Nov 06 06:16:38 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "negative base",
}
@Article{Banerji:1974:NIM,
author = "D. K. Banerji",
title = "A Novel Implementation Method for Addition and
Subtraction in Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "1",
pages = "106--109",
month = jan,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.223790",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672383;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "This correspondence describes an implementation scheme
for the operations of addition and subtraction in the
residue number systems. The method is based on the
property that the set of residues modulo m form a
finite group under addition and \ldots{}",
}
@Article{Banerji:1974:URA,
author = "D. K. Banerji",
title = "On the Use of Residue Arithmetic for Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1315--1317",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223855",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672448",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Barsi:1974:EDC,
author = "F. Barsi and P. Maestrini",
title = "Error Detection and Correction by Product Codes in
Residue Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "9",
pages = "915--924",
month = sep,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.224055",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:35 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672648;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35088",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The arithmetic error detecting and correcting
capabilities of product (AN) codes in residue number
systems (RNS) are described. The redundancy necessary
and sufficient to allow single residue digit error
detection or correction is determined, under \ldots{}",
}
@Article{Bauer:1974:CGR,
author = "F. L. Bauer",
title = "Computational Graphs and Rounding Error",
journal = j-SIAM-J-NUMER-ANAL,
volume = "11",
number = "1",
pages = "87--96",
month = mar,
year = "1974",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0711010",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65G05",
MRnumber = "356482",
MRreviewer = "L. B. Rall",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database; Theory/auto.diff.bib",
note = "In memoriam George Forsythe.",
URL = "https://www.jstor.org/stable/2156433",
ZMID = "03527739",
ZMnumber = "0337.65028",
acknowledgement = ack-nhfb,
author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
March 2015)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
referred = "[Char91a]; [Irim91a].",
}
@Article{Blankenship:1974:CTC,
author = "P. E. Blankenship",
title = "Comments on {``A Two's Complement Parallel Array
Multiplication Algorithm''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1327--1327",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223862",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Baugh:1973:TCP,Kroft:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672455",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Boyes:1974:BNS,
author = "J. D. Boyes",
title = "Binary Noise Sources Incorporating Modulo-{$N$}
Dividers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "5",
pages = "550--552",
month = may,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223980",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672573",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brent:1974:FEP,
author = "Barry Brent",
title = "Functional Equations with Prime Roots from Arithmetic
Expressions for {$ G_\alpha $}",
journal = j-FIB-QUART,
volume = "12",
number = "2",
pages = "199--207",
month = apr,
year = "1974",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:50 MDT 2011",
bibsource = "http://www.fq.math.ca/12-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/12-2/brent1.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Brown:1974:BDE,
author = "D. A. H. Brown",
title = "Biquinary Decimal Error Detection Codes with One, Two
and Three Check Digits",
journal = j-COMP-J,
volume = "17",
number = "3",
pages = "201--204",
month = aug,
year = "1974",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/201.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/202.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/203.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/204.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "722; 723",
corpsource = "Royal Radar Establ., Malvern, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "biquinary decimal error detection codes; check digits;
computer systems, digital; computers --- Debugging;
decimal floating-point arithmetic; digital arithmetic;
error detection codes; polynomial coding",
treatment = "T Theoretical or Mathematical",
}
@Article{Brown:1974:SEC,
author = "D. A. H. Brown",
title = "Some Error Correcting Codes for Certain Transposition
and Transcription Errors in Decimal Integers",
journal = j-COMP-J,
volume = "17",
number = "1",
pages = "9--12",
month = feb,
year = "1974",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Nov 28 16:12:29 2003",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/10.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/11.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/12.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/9.tif",
acknowledgement = ack-mfc # " and " # ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
classification = "731",
corpsource = "Royal Radar Establ., Malvern, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithm; block; codes, symbolic; cyclic; decimal
floating-point arithmetic; decimal integers; digital
arithmetic; error correcting codes; error correction
codes; modulus 11; transcription; transposition",
treatment = "P Practical",
}
@Article{Carta:1974:HLR,
author = "David G. Carta",
title = "Help!!: {The} Lost Reference: ({A} Modified {Newton}
Method for Square Roots)",
journal = j-SIGNUM,
volume = "9",
number = "4",
pages = "9--9",
month = oct,
year = "1974",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1206085.1206086",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Jun 17 18:47:00 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Around 1970 I saw a journal article describing a
modified Newton iteration for square roots. It involved
changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
(x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
0.5 $, thereby increasing the asymptotic rate of
convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
1} = 0.25 e_n^2 $.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Catlin:1974:MR,
author = "Paul A. Catlin",
title = "On the Multiplication of Recurrences",
journal = j-FIB-QUART,
volume = "12",
number = "4",
pages = "365--367",
month = dec,
year = "1974",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:58:54 MDT 2011",
bibsource = "http://www.fq.math.ca/12-4.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/12-4/catlin2.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Chakrabarti:1974:DCA,
author = "S. Chakrabarti",
title = "Divide-and-Correct Algorithm for Division in a
Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "9",
pages = "981--983",
month = sep,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.224066",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:35 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672659",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chan:1974:REM,
author = "O. Chan and E. Jury",
title = "Roundoff error in multidimensional generalized
discrete transforms",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "21",
number = "1",
pages = "100--108",
month = jan,
year = "1974",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The analysis of rounding error in the one-dimensional
fast Fourier transform (FFT) is extended to a class of
generalized orthogonal transforms [1] with a common
fast algorithm similar to the FFT algorithm. This class
includes the BInary FOurier \ldots{}",
}
@Book{Dahlquist:1974:NM,
author = "Germund Dahlquist and {\AA}ke Bj{\"o}rck and Ned
Anderson",
title = "Numerical Methods",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xviii + 573",
year = "1974",
ISBN = "0-13-627315-7",
ISBN-13 = "978-0-13-627315-8",
LCCN = "QA297 .D131 1969",
bibdate = "Tue Dec 14 22:44:59 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Translated by Ned Anderson.",
series = "Prentice-Hall Series in Automatic Computation",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: Some General Principles of Numerical
Calculation / 1 \\
2: How to Obtain and Estimate Accuracy in Numerical
Calculations / 21 \\
3: Numerical Uses of Series / 60 \\
4: Approximation of Functions / 81 \\
5: Numerical Linear Algebra / 137 \\
6: Nonlinear Equations / 218 \\
7: Finite Differences with Applications to Numerical
Integration, Differentiation, and Interpolation / 255
\\
8: Differential Equations / 330 \\
9: Fourier Methods / 405 \\
10: Optimization / 422 \\
11: The Monte Carlo Method and Simulation / 448 \\
12: Solutions to Problems / 465 \\
13: Bibliography and Published Algorithms / 536 \\
Index by Subject to Algorithms, 1960--1970 / 548 \\
Appendix Tables / 563 \\
Index / 565",
tableofcontents = "Preface / xvii \\
Conventions / xix \\
1: Some General Principles of Numerical Calculation / 1
\\
1.1. Introduction / 1 \\
1.2. Some Common Ideas and Concepts in Numerical
Methods / 2 \\
1.3. Numerical Problems and Algorithms / 13 \\
1.3.1. Definitions / 13 \\
1.3.2. Recursive Formulas; Homer's Rule / 14 \\
1.3.3. An Example of Numerical Instability / 16 \\
2: How to Obtain and Estimate Accuracy in Numerical
Calculations / 21 \\
2.1. Basic Concepts in Error Estimation / 21 \\
2.1.1. Introduction / 21 \\
2.1.2. Sources of Error / 22 \\
2.1.3. Absolute and Relative Errors / 23 \\
2.1.4. Rounding and Chopping / 24 \\
2.2 Propagation of Errors / 26 \\
2.2.1. Simple Examples of Error Analysis / 26 \\
2.2.2. The General Formula for Error Propagation;
Maximum Error and Standard Error / 29 \\
2.2.3. On the Practical Application of Error Estimation
/ 34 \\
2.2.4. The Use of Experimental Perturbations / 36 \\
2.2.5. Automatic Control of Accuracy / 37 \\
2.3. Number Systems; Floating and Fixed Representation
/ 42 \\
2.3.1. The Position System / 42 \\
2.3.2. Floating and Fixed Representation / 43 \\
2.3.3. Floating Decimal Point / 44 \\
2.3.4. Fixed Decimal Point / 46 \\
2.3.5. Round-off Errors in Computation with Floating
Arithmetic Operations / 46 \\
2.4. Backward Error Analysis; Condition Numbers / 51
\\
2.4.1. Backward Error Analysis / 51 \\
2.4.2. Condition Numbers for Problems and Algorithms /
53 \\
2.4.3. Geometrical Illustration of Error Analysis / 56
\\
3: Numerical Uses of Series / 60 \\
3.1. Elementary Uses of Series / 60 \\
3.1.1. Simple Examples / 60 \\
3.1.2. Estimating the Remainder / 62 \\
3.1.3. Power Series / 65 \\
3.2. Acceleration of Convergence / 71 \\
3.2.1. Slowly Converging Alternating Series / 71 \\
3.2.2. Slowly Converging Series with Positive Terms /
73 \\
3.2.3. Other Simple Ways to Accelerate Convergence / 74
\\
3.2.4. Ill-Conditioned Series / 75 \\
3.2.5. Numerical Use of Divergent Series / 77 \\
4: Approximation of Functions / 81 \\
4.1. Basic Concepts in Approximation / 81 \\
4.1.1. Introduction / 81 \\
4.1.2. The Idea of a Function Space / 84 \\
4.1.3. Norms and Seminorms / 85 \\
4.1.4. Approximation of Functions as a Geometric
Problem in Function Space / 87 \\
4.2. The Approximation of Functions by the Method of
Least Squares / 88 \\
4.2.t. Statement of the Problems / 88 \\
4.2.2. Orthogonal Systems / 89 \\
4.2.3. Solution of the Approximation Problem / 92 \\
4.3. Polynomials / 97 \\
4.3.1. Basic Terminology; the Weierstrass Approximation
Theorem / 97 \\
4.3.2. Triangle Families of Polynomials / 98 \\
4.3.3. A Triangle Family and Its Application to
Interpolation / 99 \\
4.3.4. Equidistant Interpolation and the Runge
Phenomenon / 101 \\
4.4. Orthogonal Polynomials and Applications / 104 \\
4.4.1. Tchebycheff Polynomials / 104 \\
4.4.2. Tchebycheff Interpolation and Smoothing / 106
\\
4.4.3. General Theory of Orthogonal Polynomials / 108
\\
4.4.4. Legendre Polynomials and Gram Polynomials / 113
\\
4.5. Complementary Observations on Polynomial
Approximation / 117 \\
4.5.1. Summary of the Use of Polynomials / 117 \\
4.5.2. Some Inequalities for $E_n(f)$ with Applications
to the Computation of Linear Functionals / 120 \\
4.5.3. Approximation in the Maximum Norm / 124 \\
4.5.4. Economization of Power Series; Standard
Functions / 125 \\
4.5.5. Some Statistical Aspects of the Method of Least
Squares / 126 \\
4.6. Spline Functions / 131 \\
5: Numerical Linear Algebra / 137 \\
5,1. Introduction / 137 \\
5.2. Basic Concepts of Linear Algebra / 138 \\
5.2.1. Fundamental Definitions / 138 \\
5.2.2. Partitioned Matrices / 140 \\
5.2.3. Linear Vector Spaces / 141 \\
5.2.4. Eigenvalues and Similarity Transformations / 142
\\
5.2.5. Singular-Value Decomposition and Pseudo-Inverse
/ 143 \\
5.3. Direct Methods for Solving Systems of Linear
Equations / 146 \\
5.3.1. Triangular Systems / 146 \\
5.3.2. Gaussian Elimination / 147 \\
5.3.3. Pivoting Strategies / 150 \\
5.3.4. $L U$-Decomposition / 152 \\
5.3.5. Compact Schemes for Gaussian Elimination / 157
\\
5.3.6. Inverse Matrices / 159 \\
5.4. Special Matrices / 162 \\
5.4.1. Symmetric Positive-Definite Matrices / 162 \\
5.4.2. Band Matrices / 165 \\
5.4.3. Large-Scale Linear Systems / 168 \\
5.4.4. Other Sparse Matrices / 169 \\
5.5. Error Analysis for Linear Systems / 174 \\
5.5.1. An Ill-Conditioned Example / 174 \\
5.5.2. Vector and Matrix Norms / 175 \\
5.5.3. Perturbation Analysis / 176 \\
5.5.4. Rounding Errors in Gaussian Elimination / 177
\\
5.5.5. Scaling of Linear Systems / 181 \\
5.5.6. Iterative Improvement of a Solution / 183 \\
5.6. Iterative Methods / 188 \\
5.7. Overdetermined Linear Systems / 196 \\
5.7.1. The Normal Equations / 197 \\
5.7.2. Orthogonalization Methods / 201 \\
5.7.3. Improvement of Least-Squares Solutions / 204 \\
5.7.4. Least-Squares Problems with Linear Constraints /
205 \\
5.8. Computation of Eigenvalues and Eigenvectors / 208
\\
5.8.1. The Power Method / 209 \\
5.8.2. Methods Based on Similarity Transformations /
211 \\
5.8.3. Eigenvalues by Equation Solving / 215 \\
5.8.4. The $Q R$-Algorithm / 216 \\
6: Nonlinear Equations / 218 \\
6.1. Introduction / 218 \\
6.2. Initial Approximations; Starting Methods / 219 \\
6.2.1. Introduction / 219 \\
6.2.2. The Bisection Method / 220 \\
6.3. Newton--Raphson's Method / 222 \\
6.4. The Secant Method / 227 \\
6.4.1. Description of the Method / 227 \\
6.4.2. Error Analysis for the Secant Method / 228 \\
6.4.3. Regula Falsi / 230 \\
6.4.4. Other Related Methods / 230 \\
6.5. General Theory of Iteration Methods / 233 \\
6.6. Error Estimation and Attainable Accuracy in
Iteration Methods / 238 \\
6.6.1. Error Estimation / 238 \\
6.6.2. Attainable Accuracy; Termination Criteria / 240
\\
6.7. Multiple Roots / 242 \\
6.8. Algebraic Equations / 243 \\
6.8.1. Introduction / 243 \\
6.8.2. Deflation / 245 \\
6.8.3. Ill-Conditioned Algebraic Equations / 246 \\
6.9. Systems of Nonlinear Equations / 248 \\
6.9.1. Iteration / 249 \\
6.9.2. Newton--Raphson's Method and Some Modifications
/ 249 \\
6.9.3. Other Methods / 251 \\
7: Finite Differences with Applications to Numerical
Integration, Differentiation, and Interpolation / 255
\\
7.1. Difference Operators and Their Simplest Properties
/ 255 \\
7.2. Simple Methods for Deriving Approximation Formulas
and Error Estimates / 263 \\
7.2.1. Statement of the Problems and Some Typical
Examples / 263 \\
7.2.2, Repeated Richardson Extrapolation / 269 \\
7.3. Interpolation / 275 \\
7.3.1. Introduction / 275 \\
7.3.2. When is Linear Interpolation Sufficient? / 276
\\
7.3.3. Newton's General Interpolation Formula / 277 \\
7.3.4. Formulas for Equidistant Interpolation / 279 \\
7.3.5. Complementary Remarks on Interpolation / 282 \\
7.3.6. Lagrange's Interpolation Formula / 284 \\
7.3.7. Hermite Interpolation / 285 \\
7.3.8. Inverse Interpolation / 286 \\
7.4. Numerical Integration / 290 \\
7.4.1. The Rectangle Rule, Trapezoidal Rule, and
Romberg's Method / 291 \\
7.4.2. The Truncation Error of the Trapezoidal Rule /
293 \\
7.4.3. Some Difficulties and Possibilities in Numerical
Integration / 294 \\
7.4.4. The Euler--Maclaurin Summation Formula / 297 \\
7.4.5. Uses of the Euler--Maclaurin Formula / 300 \\
7.4.6. Other Methods for Numerical Integration / 302
\\
7.5. Numerical Differentiation / 307 \\
7.6. The Calculus of Operators / 311 \\
7.6.1. Operator Algebra / 311 \\
7.6.2. Operator Series with Applications / 312 \\
7.7. Functions of Several Variables / 318 \\
7.7.1. Working with One Variable at a Time / 319 \\
7.7.2. Rectangular Grids / 319 \\
7.7.3. Irregular Triangular Grids / 322 \\
8: Differential Equations / 330 \\
8.1. Theoretical Background / 330 \\
8.1.1. Initial-Value Problems for Ordinary Differential
Equations / 330 \\
8.1.2. Error Propagation / 333 \\
8.1.3. Other Differential Equation Problems / 337 \\
8.2. Euler's Method, with Repeated Richardson
Extrapolation / 338 \\
8.3. Other Methods for Initial-Value Problems in
Ordinary Differential Equations / 342 \\
8.3.1. The Modified Midpoint Method / 342 \\
8.3.2. The Power-Series Method / 345 \\
8.3.3. Runge--Kutta Methods / 346 \\
8.3.4. Implicit Methods / 347 \\
8.3.5. Stiff Problems / 349 \\
8.3.6. Control of Step Size / 350 \\
8.3.7. A Finite-Difference Method for a Second-Order
Equation / 352 \\
8.4. Orientation on Boundary and Eigenvalue Problems
for Ordinary Differential Equations / 359 \\
8.4.1. Introduction / 359 \\
8.4.2. The Shooting Method / 359 \\
8.4.3. The Band Matrix Method / 361 \\
8.4.4. Numerical Example of an Eigenvalue Problem / 363
\\
8.5. Difference Equations / 367 \\
8.5.1. Homogeneous Linear Difference Equations with
Constant Coefficients / 368 \\
8.5.2. General Linear Difference Equations / 370 \\
8.5.3. Analysis of a Numerical Method with the Help of
a Test Problem / 372 \\
8.5.4. Linear Multistep Methods / 375 \\
8.6. Partial Differential Equations / 383 \\
8.6.1. Introduction / 383 \\
8.6.2. An Example of an Initial-Value Problem / 384 \\
8.6.3. An Example of a Boundary-Value Problem / 389 \\
8.6.4. Methods of Undetermined Coefficients and
Variational Methods / 392 \\
8.6.5. Finite-Element Methods / 395 \\
8.6.6. Integral Equations / 397 \\
9: Fourier Methods / 405 \\
9.1. Introduction / 405 \\
9.2. Basic Formulas and Theorems in Fourier Analysis /
406 \\
9.2.1. Functions of One Variable / 406 \\
9.2.2. Functions of Several Variables / 411 \\
9.3. Fast Fourier Analysis / 413 \\
9.3.1. An Important Special Case / 413 \\
9.3.2. Fast Fourier Analysis, General Case / 414 \\
9.4. Periodic Continuation of a Nonperiodic Function /
417 \\
9.5. The Fourier Integral Theorem / 419 \\
10: Optimization / 422 \\
10.1. Statement of the Problem, Definitions, and Normal
Form / 422 \\
10.2. The Simplex Method / 426 \\
10.3. Duality / 435 \\
10.4. The Transportation Problem and Some Other
Optimization Problems / 436 \\
10.5. Nonlinear Optimization Problems / 438 \\
10.5.1. Basic Concepts and Introductory Examples / 438
\\
10.5.2. Line Search / 440 \\
10.5.3. Algorithms for Unconstrained Optimization / 441
\\
10.5.4. Overdetermined Nonlinear Systems / 443 \\
10.5.5. Constrained Optimization / 444 \\
11: The Monte Carlo Method and Simulation / 448 \\
11.1. Introduction / 448 \\
11.2. Random Digits and Random Numbers / 449 \\
11.3. Applications; Reduction of Variance / 455 \\
11.4. Pseudorandom Numbers / 463 \\
12: Solutions to Problems / 465 \\
13: Bibliography and Published Algorithms / 536 \\
13.1. Introduction / 536 \\
13.2. General Literature in Numerical Analysis / 536
\\
13.3. Tables, Collections of Formulas, and Problems /
539 \\
13.4. Error Analysis and Approximation of Functions /
540 \\
13.5. Linear Algebra and Nonlinear Systems of Equations
/ 541 \\
13.6. Interpolation, Numerical Integration, and
Numerical Treatment of Differential Equations / 543 \\
13.7. Optimization; Simulation / 545 \\
13.8. Reviews, Abstracts and Other Periodicals / 547
\\
13.9. Survey of Published Algorithms / 548 \\
Index by Subject to Algorithms, 1960--1970 / 548 \\
Appendix Tables / 563 \\
Index / 565",
}
@Article{Davis:1974:USN,
author = "R. L. Davis",
title = "Uniform Shift Networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "317--322",
month = mar,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224214",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 10:48:43 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fateman:1974:PMP,
author = "Richard J. Fateman",
title = "Polynomial Multiplication, Powers, and asymptotic
Analysis: {Some} Comments",
journal = j-SIAM-J-COMPUT,
volume = "3",
number = "3",
pages = "196--213",
month = "????",
year = "1974",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Mon Nov 29 10:57:57 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/3/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Theory/auto.diff.bib; Theory/Comp.Alg.1.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
referred = "[Bren78a].",
}
@Article{Fettweis:1974:PFP,
author = "A. Fettweis",
title = "On properties of floating-point roundoff noise",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "22",
number = "2",
pages = "149--151",
month = apr,
year = "1974",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The probability density and related properties of the
relative error due to rounding after floating-point
arithmetic operations can be computed from the
distributions of the mantissa and its absolute error.
Various results obtained, in particular, \ldots{}",
}
@Article{Fischer:1974:FLI,
author = "Michael J. Fischer and Larry J. Stockmeyer",
title = "Fast on-line integer multiplication",
journal = j-J-COMP-SYS-SCI,
volume = "9",
number = "3",
pages = "317--331",
month = dec,
year = "1974",
CODEN = "JCSSBM",
DOI = "https://doi.org/10.1016/S0022-0000(74)80047-4",
ISSN = "0022-0000 (print), 1090-2724 (electronic)",
ISSN-L = "0022-0000",
bibdate = "Tue Jan 29 15:25:28 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcompsyssci.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022000074800474",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computer and System Sciences",
journal-URL = "http://www.sciencedirect.com/science/journal/00220000",
}
@MastersThesis{Fischer:1974:FPP,
author = "David Michael Fischer",
title = "Floating point processor for teleoperator studies",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Mechanical Engineering",
address = "Cambridge, MA, USA",
pages = "35 + 14",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Gardiner:1974:CAI,
author = "A. B. Gardiner",
title = "Comments on {``An Augmented Iterative Array for High
Speed Division''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "3",
pages = "326--327",
month = mar,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223931",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Cappa:1973:AIA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672524",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gentleman:1974:MAR,
author = "W. Morven Gentleman and Scott B. Marovich",
title = "More on Algorithms that Reveal Properties of Floating
Point Arithmetic Units",
journal = j-CACM,
volume = "17",
number = "5",
pages = "276--277",
month = may,
year = "1974",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/360980.361003",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:43:47 MST 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#GentlemanM74;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Malcolm:1972:ARP}.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Univ. Waterloo, Ont., Canada",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "algorithms; base of the arithmetic; digital
arithmetic; floating point arithmetic units; high
level; languages; trailing digits",
oldlabel = "GentlemanM74",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GentlemanM74",
}
@Book{Hildebrand:1974:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "xiii + 669",
year = "1974",
ISBN = "0-07-028761-9",
ISBN-13 = "978-0-07-028761-7",
LCCN = "QA297 .H54 1974",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "Reprinted in \cite{Hildebrand:1987:INA}.",
subject = "Numerical analysis",
}
@Article{Hill:1974:RFF,
author = "Bruce M. Hill",
title = "The rank-frequency form of {Zipf}'s law",
journal = j-J-AM-STAT-ASSOC,
volume = "69",
number = "348",
pages = "1017--1026",
month = dec,
year = "1974",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62E15",
MRnumber = "0426242 (54 \#14188)",
MRreviewer = "S. M. Samuels",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
ZMnumber = "Zbl 0301.60011",
acknowledgement = ack-nhfb,
classification = "B0240 (Probability and statistics); C1140
(Probability and statistics)",
corpsource = "Department of Statistics, University of Michigan, Ann
Arbor, MI, USA",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Bose--Einstein allocation; distribution; random
processes; rank frequency form; statistics; Zipf's
law",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Hull:1974:LFM,
author = "T. E. Hull and J. J. Hofbauer",
title = "Language facilities for multiple precision floating
point computation, with examples, and the description
of a preprocessor",
type = "Technical report",
number = "63",
institution = "University of Toronto, Department of Computer
Science",
address = "Toronto, ON, Canada",
pages = "vi + 84",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; Electronic digital
computers --- Programming",
}
@Article{Kinoshita:1974:FPA,
author = "Eisuke Kinoshita and Hideo Kosako and Yoshiaki
Kojima",
title = "Floating-Point Arithmetic Algorithms in the Symmetric
Residue Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "1",
pages = "9--20",
month = jan,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1974.223772",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68A10",
MRnumber = "50 9042",
bibdate = "Tue Jul 12 11:27:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672365;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
reviewer = "M. S. Cheema",
summary = "The residue number system is an integer number system
and is inconvenient to represent numbers with
fractional parts. In the symmetric residue system, a
new representation of floating-point numbers and
arithmetic algorithms for its addition, \ldots{}",
}
@Article{Kroft:1974:CTC,
author = "D. Kroft",
title = "Comments on {``A Two's Complement Parallel Array
Multiplication Algorithm''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1327--1328",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223863",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Baugh:1973:TCP,Blankenship:1974:CTC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672456",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kulisch:1974:PCC,
author = "U. Kulisch",
title = "Formalization and implementation of floating-point
arithmetics",
crossref = "Panagiotopoulos:1974:PCC",
pages = "328--369",
year = "1974",
MRclass = "65G05",
MRnumber = "57 14392",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. H. Bartels",
}
@Article{Ling:1974:CSA,
author = "Robert F. Ling",
title = "Comparison of several algorithms for computing sample
means and variances",
journal = j-J-AM-STAT-ASSOC,
volume = "69",
number = "348",
pages = "859--866",
month = dec,
year = "1974",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.1080/01621459.1974.10480219",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:46 MST 2012",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1974.bib;
http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314230;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib;
Theory/Matrix.bib",
URL = "http://www.jstor.org/stable/2286154;
https://www.tandfonline.com/doi/abs/10.1080/01621459.1974.10480219;
https://www.tandfonline.com/doi/pdf/10.1080/01621459.1974.10480219",
acknowledgement = ack-nhfb,
country = "USA",
date = "13/05/93",
descriptors = "Simulation; statistics; numeric calculation",
enum = "7605",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "mean; standard deviation; stat; updating; variance",
location = "SEL: Wi",
remark = "This is an early paper on the numerical difficulties
associated with two important statistical algorithms.
See also entry \cite{McCullough:2019:WTS} in
fparith.bib that shows that even after 45 years, some
statistics code in database software remains poor.",
revision = "16/01/94",
xxtitle = "Comparison of Several Algorithms for Computing Means
and Variances",
}
@Article{Linnainmaa:1974:ASK,
author = "Seppo Linnainmaa",
title = "Analysis of Some Known Methods of Improving the
Accuracy of Floating-Point Sums",
journal = j-BIT,
volume = "14",
number = "2",
pages = "167--202",
month = jun,
year = "1974",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932946",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "MR0483373 (58 \#3381)",
bibdate = "Fri Dec 08 13:05:19 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=2&spage=167",
acknowledgement = ack-nj,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
reviewer = "H. Ratschek",
}
@InCollection{Metropolis:1974:SAA,
author = "N. Metropolis and Gian-Carlo Rota",
booktitle = "Studies in numerical analysis (papers in honour of
{Cornelius Lanczos} on the occasion of his 80th
birthday)",
title = "Significance arithmetic---on the algebra of binary
strings",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "241--251",
year = "1974",
MRclass = "02F43 (68A15)",
MRnumber = "MR0354335 (50 \#6815)",
MRreviewer = "Stephen Tanny",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0311.65031",
acknowledgement = ack-nhfb,
}
@InProceedings{Miller:1974:CCN,
author = "Webb Miller",
title = "Computational complexity and numerical stability",
crossref = "ACM:1974:CRS",
pages = "317--322",
year = "1974",
bibdate = "Wed Nov 24 12:46:29 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Manual{Moon:1974:MRM,
author = "David A. Moon",
title = "{MacLISP} Reference Manual",
organization = "MIT Project MAC",
address = "Cambridge, MA, USA",
month = apr,
year = "1974",
bibdate = "Wed Jan 29 16:47:55 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "From \cite{Steele:2004:RHP}: ``In early 1971, he
[White] began to analyze the machine-language algorithm
used in the implementation of MacLisp (described in
this report) to convert PDP-10 floating-point numbers
into decimal notation.''",
}
@Article{Neumaier:1974:REV,
author = "A. Neumaier",
title = "{Rundungsfehleranalyse Einiger Verfahren Zur Summation
Endlicher Summen}. ({German}) [{Rounding} error
analysis of a method for summation of finite sums]",
journal = j-Z-ANGE-MATH-MECH,
volume = "54",
pages = "39--51",
year = "1974",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
keywords = "accurate floating-point summation",
language = "German",
}
@Article{Newbery:1974:EAP,
author = "A. C. R. Newbery",
title = "Error Analysis for Polynomial Evaluation",
journal = j-MATH-COMPUT,
volume = "28",
number = "127",
pages = "789--793",
month = jul,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290B (Error analysis in numerical methods); B0290D
(Functional analysis); C4110 (Error analysis in
numerical methods); C4120 (Functional analysis)",
corpsource = "Univ. Kentucky, Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "analysis; Chebyshev; computable error bound; error
analysis; floating point error; function evaluation;
Horner's scheme; polynomial evaluation; polynomials",
treatment = "T Theoretical or Mathematical",
}
@MastersThesis{Prezas:1974:FPA,
author = "Pericles Panos Prezas",
title = "Floating point arithmetic unit",
type = "Thesis ({M.S.})",
publisher = "The author",
school = "Illinois Institute of Technology",
address = "Chicago, IL.",
pages = "ix + 77",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Rauscher:1974:MUX,
author = "Tomlinson G. Rauscher",
title = "Microprogramming the {AN\slash UYK-17(XB-1)(V)} signal
processing element signal processing arithmetic unit",
journal = j-SIGMICRO,
volume = "5",
number = "2",
pages = "29--63",
month = apr,
year = "1974",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1217157.1217160",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:17 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/1217157.1217160",
abstract = "The AN/UYK-17(XB-1)(V) Signal Processing Element (SPE)
is a high performance computer system being developed
at the Naval Research Laboratory for radar, sonar, and
communication applications. To perform signal
processing tasks efficiently, the SPE comprises
multiple functional units that execute different
processes in parallel. Due to the inherent parallelism
in signal processing tasks, horizontal microprograms
are used to control the functional units [references 5
and 6]. This report overviews the SPE, describes the
Signal Processing Arithmetic Unit (SPAU) in detail,
discusses ANIMIL --- the microprogramming language for
representing SPAU microprograms, and illustrates the
use of the ANIMIL translator with a simple
microprogram. Companion documents describe the SPAU
simulator program (reference 3) and the formal syntax
and semantics of the ANIMIL language (reference 4).",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Renner:1974:RRN,
author = "K. Renner and S. Gupta",
title = "Reduction of roundoff noise in wave digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "21",
number = "2",
pages = "305--310",
month = mar,
year = "1974",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Roundoff noise generated by arithmetic operations in a
digital-filter computational sequence is undesirable in
that it serves to distort the true signal at the
output. Furthermore, coefficient wordlength is directly
related to the generated noise. \ldots{}",
}
@Book{Scaife:1974:SNA,
editor = "B. K. P. Scaife",
title = "Studies in numerical analysis",
publisher = "The Royal Irish Academy",
address = "Dublin, Ireland",
pages = "xxii + 333",
year = "1974",
MRclass = "65-06",
MRnumber = "MR0347039 (49 \#11759)",
bibdate = "Thu Nov 8 19:02:54 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Papers in honour of Cornelius Lanczos on the occasion
of his 80th birthday",
acknowledgement = ack-nhfb,
}
@Book{Schmid:1974:DC,
author = "Hermann Schmid",
title = "Decimal Computation",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 266",
year = "1974",
ISBN = "0-471-76180-X",
ISBN-13 = "978-0-471-76180-8",
LCCN = "QA75 .S34",
bibdate = "Thu Sep 1 10:14:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted \cite{Schmid:1983:DC}.",
acknowledgement = ack-nj,
keywords = "decimal floating-point arithmetic",
}
@Article{Sites:1974:SBD,
author = "R. L. Sites",
title = "Serial Binary Division by Ten",
journal = j-IEEE-TRANS-COMPUT,
volume = "23",
number = "12",
pages = "1299--1301",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223849",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 07 18:02:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A technique is presented for dividing a positive
binary integer by ten, in which the bits of the input
are presented serially, low-order bit first. A complete
division by ten is performed in two word times
(comparable to the time needed for two serial
additions). The technique can be useful in serial
conversions from binary to decimal, or in scaling
binary numbers by powers of 10.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal arithmetic",
}
@Book{Sterbenz:1974:FPC,
author = "Pat H. Sterbenz",
title = "Floating Point Computation",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 316",
year = "1974",
ISBN = "0-13-322495-3",
ISBN-13 = "978-0-13-322495-5",
LCCN = "QA76.8.I12 S771 1974",
MRclass = "68A05 (65G05)",
MRnumber = "50 1556",
bibdate = "Sat May 29 08:01:36 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
series = "Prentice-Hall Series in Automatic Computation.",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Compiling (Electronic computers); Computation by
computer systems --- Floating point representation;
Floating-point arithmetic; IBM 360 (Computer) ---
Programming",
remark = "From p. 116: ``There is general agreement that the
mantissas of floating-point numbers are not uniformly
distributed. [See Hamming (1962)
[\cite{Hamming:1962:NMS}], Pinkham (1961)
[Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
Instead, it is customary to assume that they are
distributed logarithmically, that is, that the
probability density function is
$$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
\leq m \leq 1. $$
This assumption is based on the following observations:
First, this distribution reproduces itself under
multiplication, but a uniform distribution does not.
[See Hamming (1962) [\cite{Hamming:1962:NMS}] and
Exercise 20.] A second justification is based on the
fact that many of the numbers that arise in computation
represent measurable quantities such as lengths,
forces, etc., and it is reasonable to believe that the
distribution of the mantissas of such quantities is
independent of the units in which they are measured.
Pinkham (1961) shows that this leads to the conclusion
that the distribution of mantissas must be
logarithmic.''",
reviewer = "F. J. Murray",
tableofcontents = "Preface / ix \\
1. Floating-Point Number Systems / 1 \\
1.1 Fixed-Point Calculation / 1 \\
1.2 Floating-Decimal Representation of Numbers / 4 \\
1.3 Floating-Decimal Arithmetic / 6 \\
1.4 Floating-Point Number Systems / 9 \\
1.5 FP(r, p, c) and FP(r, p, R) / 12 \\
1.6 Laws of Algebra / 14 \\
1.7 Inequalities in FP(r,p, c) / 21 \\
1.8 FP(r, p, clq) / 22 \\
1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\
1.10 Division / 33 \\
Exercises / 35 \\
2. Floating-Point Overflow and Underflow / 39 \\
2.1 Bounds for Exponents / 39 \\
2.2 $\Omega$-Zero Fixup / 41 \\
2.3 Interrupt / 44 \\
2.4 Messages and Tests / 46 \\
2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\
2.6 Example / 50 \\
2.7 Counting Mode / 57 \\
2.8 Gradual Underflow / 59 \\
2.9 Imprecise Interrupt / 61 \\
2.10 Changing the Treatment of Spill / 62 \\
2.11 Virtual Overflow and Underflow / 64 \\
2.12 Division by Zero and Indeterminant Forms / 66 \\
Exercises / 67 \\
3. Error Analysis / 71 \\
3.1 Significant Digits / 71 \\
3.2 Relative Error / 73 \\
3.3 Relative Error in FP(r,p, clq) / 75 \\
3.4 Approximate Laws of Algebra / 80 \\
3.5 Propagation of Rounding Error / 87 \\
3.6 X**N / 92 \\
3.7 Condition / 98 \\
3.8 Error Analysis of a Program / 103 \\
3.9 Backward Error Analysis / 105 \\
3.10 Examples / 107 \\
3.11 Changing the Problem / 109 \\
3.12 Statistical Error Analysis / 113 \\
Exercises / 117 \\
4. Example / 123 \\
4.1 Quadrature / 123 \\
4.2 Power Series / 130 \\
4.3 Exact Sums and Differences in FP(r, p, clq) / 137
\\
4.4 Dismantling Floating-Point Numbers / 143 \\
Exercises / 146 \\
5. Double-Precision Calculation / 154 \\
5.1 Programs Using Double-Precision Arithmetic / 155
\\
5.2 Implicit Typing of Names / 162 \\
5.3 Routines to Perform Double-Precision Arithmetic /
163 \\
5.4 Double-Precision Multiplication / 165 \\
5.5 Double-Precision Addition and Subtraction / 168 \\
5.6 Double-Precision Division / 171 \\
5.7 Writing Double-Precision Programs Without Language
Support / 178 \\
5.8 Uses of Double-Precision / 180 \\
5.9 Higher-Precision Arithmetic / 185 \\
Exercises / 186 \\
6. Rounding / 189 \\
6.1 General Considerations / 189 \\
6.2 Uses of Rounding / 191 \\
6.3 Implementation of Rounding / 192 \\
6.4 Bias Removal / 194 \\
6.5 Other ``Rounding'' Procedures / 197 \\
Exercises / 198 \\
7. Automatic Analysis of Error / 201 \\
7.1 Introduction / 201 \\
7.2 Significance Arithmetic / 202 \\
7.3 Noisy Mode / 205 \\
7.4 Interval Arithmetic / 207 \\
7.5 Rerunning the Program in Higher-Precision / 213 \\
Exercises / 222 \\
8. Radix Conversion / 224 \\
8.1 Equivalent Number of Digits / 224 \\
8.2 Properties of Conversion Transformations / 228 \\
8.3 Conversion Techniques / 232 \\
Exercises / 238 \\
9/ Carefully Written Programs / 240 \\
9.1 Introduction / 240 \\
9.2 Average Problem / 240 \\
9.3 Quadratic Equation / 246 \\
Exercises / 252 \\
10. Checking and Testing / 255 \\
10.1 Range Checking / 255 \\
10.2 Mathematical Checks / 256 \\
10.3 Testing / 259 \\
Exercises / 261 \\
11. Language Features for Floating-Point Computation /
263 \\
11.1 Introduction / 263 \\
11.2 Predictability, Controllability, Observability /
264 \\
11.3 Ease of Programming / 265 \\
11.4 Machine Independence / 267 \\
Exercises / 269 \\
12. Floating-Point Hardware / 271 \\
12.1 Choice of Radix / 271 \\
12.2 The Representation of Floating-Point Numbers / 273
\\
12.3 FP(r, p, c) and FP(r, p, R) / 277 \\
12.4 Unnormalized Numbers and Unnormalized Arithmetic /
278 \\
Exercises / 282 \\
13. Complex Numbers / 285 \\
13.1 Programs Using Complex Numbers / 285 \\
13.2 Relative Error / 286 \\
13.3 Complex Arithmetic / 287 \\
Exercises / 297 \\
Bibliography / 301 \\
Glossary of Symbols / 309 \\
Index / 311",
}
@Article{Suter:1974:MAA,
author = "B. W. Suter",
title = "The Modular Arithmetic of Arbitrarily Long Sequences
of Digits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-23",
number = "12",
pages = "1301--1303",
month = dec,
year = "1974",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1974.223850",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 11:27:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672443",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Syslo:1974:RAP,
author = "M. M. Syslo",
title = "Remarks on addition processes of positive
floating-point numbers",
journal = j-ZASTOS-MAT,
volume = "14",
pages = "415--417",
year = "1974",
CODEN = "ZAMTAK",
MRclass = "65G05",
MRnumber = "50 8953",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Zastosowania Matematyki",
reviewer = "Sven-{\AA}ke Gustafson",
}
@PhdThesis{Thompson:1974:IUF,
author = "Jackie Lloyd Thompson",
title = "An implementation of user-oriented floating point
arithmetic",
type = "Dissertation ({Ph.D.} in {Computing Science})",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "150",
year = "1974",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Tsao:1974:DSD,
author = "Nai Kuan Tsao",
title = "On the Distributions of Significant Digits and
Roundoff Errors",
journal = j-CACM,
volume = "17",
number = "5",
pages = "269--271",
month = may,
year = "1974",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65G05",
MRnumber = "49 6595",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Mon Jan 22 07:26:38 MST 2001",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Generalized logarithmic law is derived for the
distribution of the first $t$ significant digits of a
random digital integer. This result is then used to
determine the distribution of the roundoff errors in
floating-point operations, which is a mixture of
uniform and reciprocal distributions.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "921",
corpsource = "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "Benford's Law; digital arithmetic; digital integer;
distributions; error analysis; floating point
operations; Law of Anomalous Numbers; logarithmic law;
mathematical techniques; mean value; random;
reciprocal; roundoff errors; significant digits;
uniform distribution; variance; Zipf's Law",
oldlabel = "Tsao74",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}
@Article{Tsao:1974:SPE,
author = "Nai-Kuan Tsao",
title = "Some a Posteriori Error Bounds in Floating-Point
Computations",
journal = j-J-ACM,
volume = "21",
number = "1",
pages = "6--17",
month = jan,
year = "1974",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "49 8319",
bibdate = "Fri Dec 08 13:06:33 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
reviewer = "N. N. Abdelmalek",
}
@Article{Walker:1974:FGU,
author = "A. J. Walker",
title = "Fast generation of uniformly distributed pseudorandom
numbers with floating-point representation",
journal = j-ELECT-LETTERS,
volume = "10",
number = "25--26",
pages = "533--534",
day = "12",
month = dec,
year = "1974",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19740423",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Dec 30 16:39:46 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4245313",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Agrawal:1975:AAN,
author = "D. P. Agrawal",
title = "Arithmetic Algorithms in a Negative Base",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "998--1000",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224109",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672702",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Agrawal:1975:OAL,
author = "Dharma P. Agrawal",
title = "Optimum Array-Like Structures for High-Speed
Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "208--219",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Agrawal.pdf",
abstract = "Array-like structures for high-speed multiplication,
division, square and square-root operations have been
described in this paper. In these designs the division
and square-rooting time have been made to approach to
that of multiplication operation. These structures are
optimum from speed and versatility point of view. Most
of the cellular arrays described in the literature are
adequately slow. The time delay is particularly
significant in the division and square-rooting
operations due to the ripple effect of the carries.
Though the carry-save technique has been widely
utilized for multiplication operation, it has been only
recently employed by Cappa et al. in the design of a
nonrestoring divider array. This requires sign-bit
detection that makes the array non-uniform. Such an
array has been named as an array-like structure. The
carry-save method has been extended here for restoring
division operation. Due to sign-detection and overflow
correction requirements, the restoring method is
slightly complex. But the main advantage of such
restoring array is in its simple extension for
multiplication operation. The array for the two
operations, when pipelined, will have more computing
power than all other multiplier-divider arrays.
Suggestions have also been included for further speed
improvement.\par
The technique applied for division operation is as well
applicable for the square-rooting and an array-like
structure for square-square-rooting operations has also
been given. For performing any one of the four
operations, the only manipulation to be done is to
combine the two arrays; one for multiplication-division
and another for square-square-rooting. Possible.
methods of combining the two arrays have been indicated
and their relative advantages and disadvantages have
been mentioned. Finally, a generalized pipeline
array-like structure with complete internal details and
for 4-bit operation, has been shown. Due consideration
has also been given to the possibility of
large-scale-integration of different arrays presented
in this paper.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Atkins:1975:HRN,
author = "Daniel E. Atkins",
title = "Higher Radix, Non-restoring Division: History and
recent Developments",
crossref = "IEEE:1975:SCA",
pages = "158--167",
year = "1975",
bibdate = "Wed Nov 14 17:43:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Atkins.pdf",
abstract = "This paper reviews work related to the theory and
application of higher-radix. non-restoring division as
originally defined by Robertson in 1958.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Atkins:1975:IRR,
author = "D. E. Atkins",
title = "Introduction to the Role of Redundancy in Computer
Arithmetic",
journal = j-COMPUTER,
volume = "8",
number = "6",
pages = "74--77",
month = jun,
year = "1975",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1975.219001",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat May 7 16:08:43 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Avizienis:1975:RNR,
author = "Algirdas Avi{\v{z}}ienis",
title = "Redundancy in Number Representations as an Aspect of
Computational Complexity of Arithmetic Functions",
crossref = "IEEE:1975:SCA",
pages = "87--89",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Avizienis.pdf",
abstract = "Recent research has led to the derivation of bounds
for the time required to perform arithmetic operations
by means of logical elements with a limited number of
inputs [1--4]. The model of a $ (d, r) $ logical
circuit $C$ employed in these studies consists of a set
of $ (d, r) $ logical elements and a rule of
interconnection with designated sets of input and
output lines. The $ (d, r) $ logical element has $r$
input lines and one output line; these lines can assume
one of $d$ distinct states. The $ (d, r) $ logical
element has a unit time delay; that is, the state of
the output line at the time $ t + 1 $ is a function of
the states of the input lines at time $t$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Baker:1975:MER,
author = "P. W. Baker",
title = "More Efficient Radix-2 Algorithms for Some Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "11",
pages = "1049--1054",
month = nov,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224132",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Banerji:1975:CLS,
author = "D. K. Banerji",
title = "On Combinational Logic for Sign Detection in Residue
Number Systems",
crossref = "IEEE:1975:SCA",
pages = "113--116",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Banerji.pdf",
abstract = "This paper is concerned with the algebraic sign
detection of a number in a residue number system. The
proposed solution is applicable only to nonredundant
systems. The method utilizes a systematic decomposition
of the sign function $S$ that is based on some special
properties of $S$. Starting with the canonical
sum-of-products expression for $S$, we transform the
expression to a form whose realization is simpler than
the canonical form realization and, if possible, also
simpler than the minimal sum-of-products realization.
In some cases, the proposed method yields savings as
high as 85\% compared to the minimal sum-of-products
realization for $S$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Basu:1975:SPN,
author = "D. Basu and T. Jayashree",
title = "On a Simple Postcorrection for Nonrestoring Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1019--1020",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224116",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672709",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Benedek:1975:DLB,
author = "M. Benedek",
title = "Developing Large Binary to {BCD} Conversion
Structures",
crossref = "IEEE:1975:SCA",
pages = "188--196",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Benedek.pdf",
abstract = "Static binary to BCD conversion has been described in
many papers during the last decade, but none of the
methods presented were practical for the conversion of
large number of binary bits.\par
In this paper it is intended to further develop static
conversions by the expansion of the original BIDEC
method (Ref. 1). There are quite a few static
conversion schemes published which use other methods of
conversion. The static method, developed from the
BIDEC, lends itself best for the expansion to larger
structures as in its original ``correct and shift''
form there were no basic limitations on the size of the
binary words to be converted. with the appearance of
large bipolar ROMs and the even larger but somewhat
slower MOS ROMs there is a renewed interest in large
structures for fast binary to BCD conversions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Bivins:1975:SAA,
author = "R. L. Bivins and N. Metropolis",
title = "Significance Arithmetic: Application to a Partial
Differential Equation",
crossref = "IEEE:1975:SCA",
pages = "64--66",
year = "1975",
DOI = "https://doi.org/10.1109/ARITH.1975.6156973",
bibdate = "Mon Mar 19 18:17:32 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also available as Los Alamos Technical Report
LA-UR-75-1763 CONF-751103-1.",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bivins.pdf",
abstract = "The methods of significance arithmetic are applied to
the numerical solution of a nonlinear partial
differential equation. The authors approach permits the
use of initial values having imprecision considerably
greater than that of rounding error; moreover, the
intermediate and final quantities are monitored so that
at any stage the precision of such quantities is
available. An algorithm is found that represents
faithfully the solution to a difference equation
approximation to Burger's equation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; significance arithmetic",
}
@InProceedings{Bohlender:1975:FPC,
author = "G. Bohlender",
title = "Floating-Point Computation of Functions with Maximum
Accuracy",
crossref = "IEEE:1975:SCA",
pages = "14--23",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bohlender.pdf",
abstract = "Algorithms are given which compute multiple sums and
products and arbitrary roots of floating-point numbers
with maximum accuracy. The summation algorithm can be
applied to compute scalar products, matrix products,
etc. For all these functions, simple error formulas and
the smallest floating-point intervals containing the
exact result can be obtained.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@TechReport{Brent:1975:FMP,
author = "R. P. Brent",
title = "A {Fortran} Multiple-Precision Arithmetic Package",
type = "Technical report",
institution = "Department of Computer Science, Australian National
University",
address = "Canberra, Australia",
year = "1975",
bibdate = "Fri Jan 06 07:38:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; multiple-precision
arithmetic",
}
@TechReport{Brent:1975:MZM,
author = "R. P. (Richard P.) Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "26",
year = "1975",
bibdate = "Sat Jan 11 10:14:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Iterative methods (Mathematics)",
searchkey = "ti:elementary n1 function",
}
@Article{Brubaker:1975:MUL,
author = "T. A. Brubaker and J. C. Becker",
title = "Multiplication Using Logarithms Implemented with
Read-Only Memory",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "8",
pages = "761--765",
month = aug,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224307",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672900",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Caprani:1975:REF,
author = "Ole Caprani",
title = "Round-off Errors in Floating-Point Summation",
journal = j-BIT,
volume = "15",
number = "1",
pages = "5--9",
month = mar,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932993",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "58 19088",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
xxtitle = "Roundoff errors in floating-point summation",
}
@Article{Chen:1975:SER,
author = "Tien Chi Chen and Irving T. Ho",
title = "Storage-Efficient Representation of Decimal Data",
journal = j-CACM,
volume = "18",
number = "1",
pages = "49--52",
month = jan,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "94A15 (68A20)",
MRnumber = "50 16105",
MRreviewer = "R. N. Goss",
bibdate = "Mon Jan 22 06:30:44 MST 2001",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#ChenH75;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Collection of articles honoring {Alston S.
Householder}. See comment \cite{Smith:1975:CPC}.",
abstract = "Usually $n$ decimal digits are represented by $ 4 n $
bits in computers. Actually, two BCD digits can be
compressed optimally and reversibly into $7$ bits, and
three digits into $ 10 $ bits, by a very simple
algorithm based on the fixed-length combination of two
variable field-length encodings. In over half of the
cases the compressed code results from the conventional
BCD code by simple removal of redundant $0$ bits. A
long decimal message can be subdivided into three-digit
blocks, and separately compressed; the result differs
from the asymptotic minimum length by only $ 0.34 $
percent. The hardware requirement is small, and the
mappings can be done manually.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques)",
classification = "722; 921",
corpsource = "IBM San Jose Res. Lab., CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "asymptotic minimum; binary coded decimal; codes;
compressed code; data compression; data storage units;
decimal data; decimal floating-point arithmetic; fixed
length combination; hardware; length; length encodings;
mathematical techniques --- Digital Arithmetic;
representation; storage efficient; variable field",
oldlabel = "ChenH75",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ChenH75",
}
@InProceedings{Chinal:1975:LMA,
author = "Jean P. Chinal",
title = "The Logic of Modulo $ 2^k + 1 $ Adders",
crossref = "IEEE:1975:SCA",
pages = "126--136",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_2.pdf",
abstract = "The design of modulo $ 2^k + 1 $ adders for arbitrary
$k$ is considered, with the objective of achieving a
logic structure as regular as possible so as to allow a
convenient implementation in large-scale integration
technology (LSI). It is shown how the design problem
can be reduced. to the recursive generation of a
subtract signal and to the merging, in various degrees,
of the corresponding logic with the logic of an
ordinary adder or, alternately, of a so-called {\em
signed-carry adder\/} which is defined and designed
itself in general, with both recursive and explicit
carry schemes. Modulo $ 2^k + 1 $ adder designs are
given, one with conventional adder, another based on
signed-carry adder and a third, derived from the
signed-carry scheme, where subtract signal generation
and carry logic are merged. This last scheme can be set
up with two backward recursion chains and five or six
forward ones. Two more basic variants are finally
indicated for this integrated scheme, aiming at
reducing as much as possible the residual logic
structure irregularity presented by the most
significant position in the word.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Chinal:1975:MA,
author = "Jean P. Chinal",
title = "Mirror Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "98--107",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_1.pdf",
abstract = "Mirror coding for signed numbers is defined by means
of a set of primitive powers of two $ \{ + 2^n, - 2^{n
- 1}, \ldots {}, - 2^0 \} $ where signs of the usual
set used in 2's complement representation are reversed.
Use of the mirror representation is shown as an
alternate design approach and is illustrated by a
special purpose adder design in mirror code, by an
alternate proof of a basic property of signed-digit
arithmetic and as another interpretation of cells used
in some array multipliers for signed numbers. Lastly,
the concept is used to define a variable mode redundant
coding, allowing simple sign-flipping without
overflow.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Cobb:1975:IPS,
author = "Gary W. Cobb",
title = "The Impact of Parallelism on Software",
crossref = "IEEE:1975:SCA",
pages = "220--222",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Cobb.pdf",
abstract = "There seems to be a tug-of-war raging between computer
procurement technical evaluation committees, computer
designers and scholars of computer science and
numerical analysis over the issue of parallelism in
computations. Caught in the middle seems to be the user
community and the compiler writers. For the scope of
this paper, the term ``user community'' will be assumed
to be Fortran programmers who are involved in solving
problems that require large computer resources, e.g.,
plasma research, weather prediction, ray tracing,
seismic analysis, econometric modeling, weapons
research, reactor calculation, etc.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{DeMori:1975:MMM,
author = "Renato {De Mori} and Michele Elia and Angelo Serra",
title = "Minimization Methods for Macrocellular Arithmetic
Networks",
crossref = "IEEE:1975:SCA",
pages = "232--240",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_DeMori.pdf",
abstract = "This paper presents a new method to study arithmetic
combinatorial circuits. Using polynomial associated to
the input-output sequences and to the system, it is
possible to solve the problem of minimization of the
number of the component blocks. Particularly, the
important case of the multiple outputs elementary units
can be treated.\par
Applications of the introduced procedures to multiplier
and to fast networks for performing convolution are
presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Deverell:1975:PIA,
author = "J. Deverell",
title = "Pipeline Iterative Arithmetic Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "317--322",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224214",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 18:46:50 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Elias:1975:UCS,
author = "P. Elias",
title = "Universal codeword sets and representations of the
integers",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "21",
number = "2",
pages = "194--203",
month = mar,
year = "1975",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/tit.1975.1055349",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Fri Dec 15 15:10:16 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}
@PhdThesis{Ercegovac:1975:GMEa,
author = "Milo{\v{s}} Dragutin Ercegovac",
title = "A General Method for Evaluation of Functions and
Computations in a Digital Computer",
type = "{Ph.D.} Thesis",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana-Champaign, IL, USA",
pages = "viii + 109",
month = jul,
year = "1975",
bibdate = "Mon Feb 10 07:18:12 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/302756306",
acknowledgement = ack-nhfb,
advisor = "James E. Robertson",
}
@InProceedings{Ercegovac:1975:GMEb,
author = "Milo{\v{s}} D. Ercegovac",
title = "A General Method for Evaluation of Functions in a
Digital Computer",
crossref = "IEEE:1975:SCA",
pages = "147--157",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ercegovac.pdf",
abstract = "This paper presents a recently discovered general
computational method, amenable for efficient
implementation in digital computing systems. The method
provides a unique, simple and fast algorithm for
solving many computational problems, such as the
evaluation of polynomials, rational functions and
arithmetic expressions, or solving a class of systems
of linear equations, or performing the basic
arithmetics. In particular, the method is well suited
for fast evaluation of commonly used mathematical
functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@MastersThesis{Fawcett:1975:MCR,
author = "B. K. Fawcett",
title = "Maximal Clocking Rates for Pipelined Digital Systems",
type = "{M.S.} thesis",
school = "Department of Electrical Engineering, University of
Illinois at Urbana-Champaign",
address = "Urbana-Champaign, IL, USA",
year = "1975",
bibdate = "Fri Nov 09 10:50:56 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Foster:1975:CNM,
author = "Caxton Foster and Edward Riseman and Fred Stockton and
Conrad Wogrin",
title = "{CHARGOGGAGGOGGMANCHAUGAGOGGCHAUBUNAGUNGAMAUG}: a
Novel Multiply-by-Three Circuit",
crossref = "IEEE:1975:SCA",
pages = "185--187",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Foster.pdf",
abstract = "Recently, while considering the connection of a 48 bit
word computer to a 16 bit computer, we felt the need
for a fast and inexpensive device that would multiply a
binary address by a factor of three. Since $ 3 N = N +
2 N $, there is an obvious solution of providing a
normal adder circuit and presenting one set of inputs
with $N$ and the other with $N$-shifted left one place.
But, there is a great deal of redundancy here since
knowing one input we have complete knowledge of the
other.\par
Seeking to take advantage of this redundancy, we have
spent some twenty man hours and have saved one gate per
stage over a conventional full adder. Since the
ultimate circuit is to be a ``one-of'' this is scarcely
economic, but it has been fun. Before going further,
the interested reader may enjoy puzzling over the
problem for himself. We make no pretense of minimality,
but we have a circuit with 6 gates per stage and a
propagation delay of one gate per stage.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
remark = "Footnote to title: The title of this paper refers to
the Indian name of a lake in Massachusetts which
reputedly means ``You fish on your side, I fish on my
side, nobody fish in the middle.'",
}
@InProceedings{Gabrielian:1975:FSN,
author = "Armen Gabrielian",
title = "Formal Systems of Numerals",
crossref = "IEEE:1975:SCA",
pages = "76--81",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gabrielian.pdf",
abstract = "A new system of numerals is introduced for
representing numbers in base $ 2^N $, for $ N \leq 8 $.
The new notation greatly simplifies arithmetical
operations on numbers. For example, for $ N = 3 (4) $
one obtains a notation for octal (hexadecimal) numbers
in which one can perform addition and multiplication
much more easily than in the standard notation. For $ N
= 8 $ one obtains a practical way of representing
numbers to the base 256. A simplification of the
decimal notation is also presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{George:1975:ARR,
author = "James E. George",
title = "Algorithms to Reveal the Representation of Characters,
Integers, and Floating-Point Numbers",
journal = j-TOMS,
volume = "1",
number = "3",
pages = "210--216",
month = sep,
year = "1975",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355644.355647",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Gibson:1975:SCT,
author = "J. A. Gibson and R. W. Gibbard",
title = "Synthesis and Comparison of Two's Complement Parallel
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1020--1027",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224117",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672710",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Ginsberg:1975:DUFa,
author = "Myron Ginsberg and Dennis J. Frailey",
title = "The design and use of a floating-point (software)
simulator for testing the arithmetic behavior of
mathematical software",
type = "Technical report",
number = "CP 74028",
institution = "Department of Computer Science, Institute of
Technology, Southern Methodist University",
address = "Dallas",
edition = "Revised Oct. 1975.",
pages = "26",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units --- Testing.;
Computer programs --- Testing.; Floating-point
arithmetic.",
}
@InProceedings{Ginsberg:1975:DUFb,
author = "Myron Ginsberg and Dennis J. Frailey",
title = "The Design and Use of a Floating-Point (Software)
Simulator for Testing the Arithmetic Behavior of
Mathematical Software",
crossref = "IEEE:1975:SCA",
pages = "56--63",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ginsberg.pdf",
abstract = "An important aspect of any evaluative procedure for
developing high quality mathematical software is
testing the effects of arithmetic behavior on
algorithmic implementations. This paper describes a
proposed design approach and various applications of a
high-level language floating-point simulator which has
two inputs: the program to be tested and a description
of the floating-point arithmetic under which the
routine is to be executed. A brief discussion of the
motivation for this approach is given along with a
review of existing efforts to study the influences of
computer arithmetic on the accuracy and reliability of
mathematical. software. An overview of the simulator's
structure is presented as well as suggestions for
experiments to assist in determining the effects of
floating-point behavior across several different
computer architectures. Present and future uses of the
simulator are also indicated.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Goodman:1975:REP,
author = "R. Goodman and A. Feldstein",
title = "Round-Off Error in Products",
journal = j-COMPUTING,
volume = "15",
number = "3",
pages = "263--273",
month = sep,
year = "1975",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02242373",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jan 2 17:40:52 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Department of Math., University of Miami, Coral
Gables, FL, USA",
classification = "921; C5230",
description = "digital arithmetic",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput (Vienna/NY)",
keywords = "digit by digit deviation; floating point numbers;
fraction; logarithmic distribution; mathematical
techniques; mean; multiplication; products; roundoff
errors; variance",
}
@InProceedings{Goyal:1975:DAE,
author = "Lakshmi N. Goyal",
title = "Design of an Arithmetic Element for Serial Processing
in an Iterative Structure",
crossref = "IEEE:1975:SCA",
pages = "223--231",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Goyal.pdf",
abstract = "This paper describes the arithmetic and logic design
of the digit processing logic of an arithmetic element.
The arithmetic element is used in an iterative
structure and arithmetic processing takes place
serially on a digit by digit basis with the most
significant digit first. Starting from the arithmetic
specification of the digit processing logic, the
arithmetic design (namely, the choice of number system,
number representation and the digit algorithm) is
developed. Algebraic and logic designs of the logic
necessary to execute the digit algorithm and its
implication for LSI implementation are discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Grant:1975:TAS,
author = "J. A. Grant and G. D. Hitchins",
title = "Two Algorithms for the Solution of Polynomial
Equations to Limiting Machine Precision",
journal = j-COMP-J,
volume = "18",
number = "3",
pages = "258--264",
month = aug,
year = "1975",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/18.3.258",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:56 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/18/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/18/3/258.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/258.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/259.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/260.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/261.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/262.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/263.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/264.tif",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
classification = "723; 921",
corpsource = "Department of Math., University of Bradford, Bradford,
UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithms; complex coefficients; computer programming
--- Subroutines; limiting machine; mathematical
techniques; polynomial equations; polynomials;
precision; real coefficients",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Gregory:1975:BCR,
author = "Robert Todd Gregory and David W. Matula",
title = "Base Conversion in Residue Number Systems",
crossref = "IEEE:1975:SCA",
pages = "117--125",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gregory.pdf",
abstract = "We are concerned in this paper with the representation
of an integer in a (multiple-modulus) residue number
system and, in particular, with an algorithm for
changing the base vector of the residue number system.
Szabo and Tanaka [1, p.47] describe such an algorithm
when each modulus of the second base vector is
relatively prime to each modulus of the first base
vector. However, we show that a much simpler algorithm
exists if we allow the moduli of the second base vector
to have factors in common with the moduli of the first
base vector (even though the moduli of the second base
vector are pairwise relatively prime among
themselves).",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Hunter:1975:QMP,
author = "G. Hunter",
title = "A quantitative measure of precision",
journal = j-COMP-J,
volume = "18",
number = "3",
pages = "231--233",
month = aug,
year = "1975",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/231.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/232.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/233.tif",
abstract = "The precision $ z_b $ of a real number is defined
quantitatively in terms of the fractional error in the
number, and the base of the arithmetic in which it is
represented. The definition is an extension of the
traditional rough measure of precision as the number of
signification digits in the number. In binary
arithmetic the integral part of $ z_b $ is the number
of binary digits required to store the number.
Conversion of the precision from one base to another
(such as binary/decimal) is discussed, and applied to
consideration of the intrinsic precision of
input/output routines and floating point arithmetic.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "723; 921",
corpsource = "York University, Department of Chem., Downsview, Ont.,
Canada",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary arithmetic; digital arithmetic; digits;
floating; fractional error; input/output routines;
mathematical techniques; point arithmetic; precision;
real number; significant",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kehl:1975:MMA,
author = "T. H. Kehl and Kenneth Burkhardt",
title = "A Minicomputer Microprogrammable, Arithmetic
Processor",
crossref = "IEEE:1975:SCA",
pages = "174--178",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kehl.pdf",
abstract = "Except for a few notable examples, all computers have
been designed as ``adder-central'' architectures.
``Adder-central,'' as used here, refers to an
organization which places the Arithmetic Logic Unit
(ALU) at that junction of the system through which all
data must flow --- thus creating a bottleneck. In the
early days, when adders were expensive, cost
considerations precluded more than one ALU. Nowadays
powerful ALU's are available at very low cost and a
designer, even of minicomputers, can consider placing
more than one ALU in a system.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Keir:1975:CNR,
author = "Roy A. Keir",
title = "Compatible number representations",
crossref = "IEEE:1975:SCA",
pages = "82--87",
year = "1975",
bibdate = "Fri Nov 28 11:38:18 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_2.pdf",
abstract = "A compatible number system for mixed fixed-point and
floating-point arithmetic is described in terms of
number formats and opcode sequences (for hardwired or
microcoded control). This inexpensive system can be as
fast as fixed-point arithmetic on integers, is faster
than normalized arithmetic in floating point, gets
answers identical to those of normalized arithmetic,
and automatically satisfies the Algol-60 mixed-mode
rules. The central concept is the avoidance of
meaningless ``normalization'' following arithmetic
operations. Adoption of this system could lead to
simpler compilers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; decimal floating-point arithmetic",
}
@InProceedings{Keir:1975:PCR,
author = "Roy A. Keir",
title = "Programmer-controlled roundoff and the selection of a
stable roundoff rule",
crossref = "IEEE:1975:SCA",
pages = "73--76",
year = "1975",
bibdate = "Fri Nov 28 18:11:30 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_1.pdf",
abstract = "The author suggests that every computer with
floating-point addition and subtraction should have PSW
controllable roundoff facilities. Yohe's catalog should
be included. There should also be a stable roundoff
mode using the round-to-off [{\em -odd\/}] or
round-to-even rule based on whether the radix is
divisible by four or only by two.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "ARITH-3",
}
@Article{Keir:1975:SSR,
author = "R. A. Keir",
title = "Should the stable rounding rule be radix-dependent?",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "6",
pages = "188--189",
day = "??",
month = jul,
year = "1975",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Tue Nov 17 10:49:43 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Department of Computer Sci., University of Utah, Salt
Lake City, UT, USA",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "digital arithmetic; drift; floating point addition;
radices; round to even rule; round to odd rule; stable
rounding rule",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Kent:1975:CSU,
author = "Jan G. Kent",
title = "Comparison Sets: a Useful Partitioning of the Space of
Floating-Point Operand Pairs",
crossref = "IEEE:1975:SCA",
pages = "36--39",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kent.pdf",
abstract = "In this paper the definition of comparison sets and a
discussion of their usefulness are presented based on
the research work reported in (14). In addition some
new results concerning the distribution of floating
point (FLP) operand pairs over comparison sets are
given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Klatte:1975:CPI,
author = "R. Klatte and Ch. Ullrich",
title = "Consequences of a Properly Implemented Computer
Arithmetic for Periodicities of Iterative Methods",
crossref = "IEEE:1975:SCA",
pages = "24--32",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Klatte.pdf",
abstract = "In ordered sets it is possible to show under certain
assumptions two basic theorems concerning the cycle
length of sequences of iterates generated by monotone
operators. These results are applied to different
iterative methods, where the conclusions are valid for
the sequences of iterates produced by the numerical
computations only, if the used computer arithmetic is
properly implemented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; cycle, weakly cyclic vector function;
floating-point arithmetic; Rounding invariant
structures",
}
@InProceedings{Kornerup:1975:UND,
author = "Peter Kornerup",
title = "A Unified Numeric Data Type in {Pascal}",
crossref = "IEEE:1975:SCA",
pages = "40--47",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kornerup.pdf",
abstract = "It is proposed to substitute the standard data type
{\em real\/} of a high level language, with a unified
data representation which can include a variety of
interpretations as well as formats, in order to allow
experiments with an environment containing a spectrum
of non-standard arithmetics, as well as
standard.\par
The implementation of a system is described where
syntactic extensions to a language are made to support
a microprogrammed virtual arithmetic unit which can
treat variants such as integers, normalized, and
unnormalized floating point numbers and intervals,
within a unified representation.\par
More specifically Pascal is chosen as the base
language, because it allows the user to define new data
types, and the extension then mainly consists in
substituting the simple (unstructured) data type {\em
real\/} with a skeletal structured type (which will be
called {\em numeric\/}).\par
The system is intended to be implemented on a
microprogrammable processor (called MATHILDA) with a 64
bit wide datapath. The language Pascal has already been
partially implemented based on a stack machine
specifically designed for that language, and realized
by interpretation in microcode. The present compiler
was constructed with the aid of a parser-generator
system, which will allow the language extensions to be
made with a moderate effort.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Kreifelts:1975:OBF,
author = "T. Kreifelts",
title = "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
(Berichtigung)} \toenglish {Optimal Basis Choice for a
Floating-Point Arithmetic (Correction)} \endtoenglish",
journal = j-COMPUTING,
volume = "14",
number = "??",
pages = "313--314",
month = "????",
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@InProceedings{Krishnamurthy:1975:MPU,
author = "E. V. Krishnamurthy",
title = "Matrix Processors Using $p$-{ADIC} Arithmetic for
Exact Linear Computations",
crossref = "IEEE:1975:SCA",
pages = "92--97",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Krishnamurthy.pdf",
abstract = "A unique code (called Hensel's code) is derived for a
rational number, by truncating its infinite $p$-adic
expansion. The four basic arithmetic algorithms for
these codes are described and their application to
rational matrix computations is demonstrated by solving
a system of linear equations exactly, using the
Gaussian elimination procedure.\par
A comparative study of the computational complexity
involved in this arithmetic and the multiple prime
module arithmetic is made with reference to matrix
computations. On this basis, a multiple $p$-adic scheme
is suggested for the design of a highly parallel matrix
processor.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Ku:1975:FPC,
author = "W. Ku and Siu-Ming Ng",
title = "Floating-point coefficient sensitivity and roundoff
noise of recursive digital filters realized in ladder
structures",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "22",
number = "12",
pages = "927--936",
month = dec,
year = "1975",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Coefficient sensitivity and roundoff error with
floating-point rounding have been investigated for
several digital ladder filter structures. It is found
that in all the cases studied, the ladder structures
first proposed by Fettweis show a much lower \ldots{}",
}
@InProceedings{Kuck:1975:RRN,
author = "D. J. Kuck and D. S. Parker and A. H. Sameh",
title = "{ROM}-Rounding: a New Rounding Scheme",
crossref = "IEEE:1975:SCA",
pages = "67--72",
year = "1975",
bibdate = "Thu Sep 01 12:13:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kuck.pdf",
abstract = "ROM-rounding is introduced and is shown to compare
favorably with existing floating-point rounding methods
on design considerations and on performance over a
series of error tests. The error-retarding value of
guard digits, of rounding the aligned operand, and of
rounding in general are discussed.",
acknowledgement = ack-nj,
keywords = "ARITH-3",
}
@Article{Kulisch:1975:FIF,
author = "U. Kulisch",
title = "Formalization and implementation of floating-point
arithmetics",
journal = j-COMPUTING,
volume = "14",
number = "4",
pages = "323--348",
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (68A10)",
MRnumber = "53 14897",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "A. D. Booth",
}
@InProceedings{Kulisch:1975:MFC,
author = "U. Kulisch",
title = "Mathematical Foundation of Computer Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "1--13",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kulisch.pdf",
abstract = "During the last years a number of papers concerning a
mathematical foundation of computer arithmetic have
been written. Some of these papers are still
unpublished. The papers consider the spaces which occur
in numerical computations on computers in dependence of
a properly defined computer arithmetic. The following
treatment gives a summary of the main ideas of these
papers. Many of the proofs had to be sketched or
completely omitted. In such cases the full information
can be found in the references.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Lacroix:1975:PEM,
author = "Arild Lacroix",
title = "Limit cycles in floating point digital filters",
crossref = "Swamy:1975:PEM",
pages = "475--479",
year = "1975",
MRclass = "94A05",
MRnumber = "55 12278",
bibdate = "Fri Dec 08 12:19:10 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Krzysztof Sapiecha",
}
@Article{Landauro:1975:ODC,
author = "A. Landauro and J. Lienard",
title = "On Overflow Detection and Correction in Digital
Filters",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1226--1228",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224168",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672761",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lang:1975:DPA,
author = "Allan L. Lang and Bruce D. Shriver",
title = "The Design of a Polymorphic Arithmetic Unit",
crossref = "IEEE:1975:SCA",
pages = "48--55",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lang.pdf",
abstract = "This paper presents results which stem from a research
effort concerned with the specification and design of
arithmetic units which can execute nonstandard integer
and floating-point arithmetic. An arithmetic unit is
proposed whose characteristics are based on user
specifications and subsequently is termed a Polymorphic
Arithmetic Unit (PAU). The user binds the identity of
the PAU by specifying the contents of various
descriptors and semantic interpretation tables which
the PAU accesses during its execution. This capability
removes several of the restrictions found in
commercially available arithmetic units and potentially
assists in making mathematically software portable.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Laurie:1975:PIR,
author = "D. P. Laurie",
title = "Propagation of Initial Rounding Error in
{Romberg}-Like Quadrature",
journal = j-BIT,
volume = "15",
number = "3",
pages = "277--282",
month = sep,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933660",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=3&spage=277",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Lemeire:1975:CEI,
author = "Frans Lemeire",
title = "Computation of Equivalent Inherent Rounding Errors in
the Solution of a Set of Linear Equations",
journal = j-BIT,
volume = "15",
number = "1",
pages = "65--71",
month = mar,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932997",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=1&spage=65",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Linnainmaa:1975:TAS,
author = "Seppo Linnainmaa",
title = "Towards Accurate Statistical Estimation of Rounding
Errors in Floating-Point Computations",
journal = j-BIT,
volume = "15",
number = "2",
pages = "165--173",
month = jun,
year = "1975",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932690",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "58 19090",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=2&spage=165",
abstract = "A new method of estimating a posteriori the
statistical characteristics of the rounding errors of
an arbitrary algorithm is presented. This method is
based on a discrete model of the distribution of
rounding errors which makes more accurate estimates
possible. The analysis is given for both rounding and
truncating arithmetic. Finally, some experimental
results are reported.",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@InProceedings{Lipovski:1975:RND,
author = "G. J. Lipovski",
title = "On Residue Number {A/D} and {D/A} Converters",
crossref = "IEEE:1975:SCA",
pages = "197--199",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lipovski.pdf",
abstract = "A very simple analog to digital converter and digital
to analog converter is described for residue number
digital processing. These simple devices make it
feasible to replace analog components with
comparatively inexpensive digital processors that use
residue, or modulus, arithmetic capable of operating at
very high speeds. Using off-the-shelf integrated
circuits, addition, subtraction or multiplication of
about 15 bits of accuracy can easily be done in as
little as fifty nanoseconds. Any function using these
operations (polynomial expansions, linear filters, Fast
Fourier Transforms) can be economically implemented in
a pipeline or other structure to get very fast systems.
Moreover, a stage in the pipeline can correct for
nonlinearities in the A/D or D/A converters. The simple
devices described herein make residue arithmetic
digital processors extremely attractive for use in fast
analog systems.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; residue number system",
}
@Article{Liu:1975:REF,
author = "B. Liu and T. Kaneko",
title = "Roundoff error in fast {Fourier} transforms",
journal = j-PROC-IEEE,
volume = "63",
number = "6",
pages = "991--992",
month = jun,
year = "1975",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "The finite word length used in the computer causes
round-off error in the calculation of Fourier
coefficients. When the fast Fourier transform method is
used, the statistical mean-square error has been
previously determined [3] for the case of the
\ldots{}",
}
@Article{Lorez:1975:BGB,
author = "H. Lorez and F. J. Urbanek and H. Will and R. Weiss
and W. Baron and others",
title = "{Buchbesprechungen} ({German}) {Book Reviews}",
journal = j-COMPUTING,
volume = "14",
number = "3",
pages = "315--322",
month = sep,
year = "1975",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kreifelts:1973:OBG}.",
acknowledgement = ack-nj,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Book{Luke:1975:MFT,
author = "Yudell L. Luke",
title = "Mathematical Functions and Their Approximations",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 568",
year = "1975",
ISBN = "0-12-459950-8, 1-4832-6245-6 (e-book)",
ISBN-13 = "978-0-12-459950-5, 978-1-4832-6245-1 (e-book)",
LCCN = "QA55 .L96 1975",
bibdate = "Fri Jun 30 05:58:16 MDT 2023",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
URL = "https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5",
acknowledgement = ack-nhfb,
libnote = "Not in my library.",
remark = "An updated version of part of Handbook of mathematical
functions with formulas, graphs, and mathematical
tables, edited by M. Abramowitz and I. A. Stegun.
Includes indexes.",
subject = "Mathematics; Tables; Fonctions (Math{\'e}ematiques);
Math{\'e}ematiques; Calculus; Mathematical Analysis;
Mathematics; Approximation; Funktion; Mathematik;
Spezielle Funktion",
tableofcontents = "Preface / xv \\
\\
I. The Gamma Function and Related Functions \\
\\
1.1 Definitions and Elementary Properties / 1 \\
1.2 Power Series and Other Series Expansions / 1 \\
1.3 Asymptotic Expansions / 7 \\
1.4 Rational Approximations for y (z) / 13 \\
1.5 Inequalities / 17 \\
1.6 Bibliographic and Numerical Data / 20 \\
1.6.1 General References / 20 \\
1.6.2 Description of and References to Tables / 21 \\
1.6.3 Description of and References to Other
Approximations and Expansions / 22 \\
\\
II. The Binomial Function \\
\\
2.1 Power Series / 24 \\
2.2 Expansions in Series of Jacobi and Chebyshev
Polynomials / 24 \\
2.3 Expansions in Series of Bessel Functions / 26 \\
2.4 Pad{\'e} Approximations / 27 \\
24.1 $(1 + 1 / z)^{-c}$ / 27 \\
2.4.2 The Square Root / 28 \\
2.4.3 Pad{\'e} Coefficients / 30 \\
2.4.4 The Function $e^{-w}$ / 31 \\
2.5 Inequalities / 34 \\
\\
III. Elementary Functions \\
\\
3.1 Logarithmic Functions / 36 \\
3.1.1 Power Series / 36 \\
3.1.2 Expansion in Series of Chebyshev Polynomials / 38
\\
3.1.3 Pad{\'e} Approximations / 39 \\
3.1.4 Inequalities / 41 \\
3.2 Exponential Function / 42 \\
3.2.1 Series Expansions / 42 \\
3.2.2 Expansions in Series of Jacobi and Chebyshev
Polynomials and Bessel Functions / 42 \\
3.2.3 Pad{\'e} Approximations / 46 \\
3.2.4 Inequalities / 51 \\
3.3 Circular and Hyperbolic Functions / 52 \\
3.3.1 Power Series / 52 \\
3.3.2 Expansions in Series of Jacobi and Chebyshev
Polynomials and Bessel Functions / 52 \\
3.3.3 Rational and Pad{\'e} Approximations / 57 \\
3.3.4 Inequalities / 60 \\
3.4 Inverse Circular and Hyperbolic Functions / 61 \\
3.4.1 Power Series / 61 \\
3.4.2 Expansions in Series of Chebyshev Polynomials /
63 \\
3.4.3 Pad{\'e} Approximations / 68 \\
3.4.4 Inequalities / 72 \\
3.5 Bibliographic and Numerical Data / 74 \\
3.5.1 Description of and References to Tables / 74 \\
3.5.2 Description of and References to Other
Approximations and Expansions / 74 \\
\\
IV. Incomplete Gamma Functions \\
\\
4.1 Definitions and Series Expansions / 77 \\
4.2 Differential Equations and Difference Equations /
78 \\
4.3 Pad{\'e} Approximations / 79 \\
4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\
4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\
4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq
\pi$ / 84 \\
4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu,
z)$ / 89 \\
4.4 Inequalities / 95 \\
4.4.1 $H(\nu, z)$ / 95 \\
4.4.2 $\Gamma(\nu, z)$ / 96 \\
4.5 Notes on the Computation of the Incomplete Gamma
Function / 97 \\
4.6 Exponential Integrals / 103 \\
4.6.1 Relation to Incomplete Gamma Function and Other
Properties / 103 \\
4.6.2 Expansions in Series of Chebyshev Polynomials /
104 \\
4.6.3 Rational and Pad Approximations / 106 \\
4.7 Cosine and Sine Integrals / 115 \\
4.7.1 Relation to Exponential Integral and Other
Properties / 115 \\
4.7.2 Expansions in Series of Chebyshev Polynomials /
116 \\
4.8 Error Functions / 119 \\
4.8.1 Relation to Incomplete Gamma Function and Other
Properties / 119 \\
4.8.2 Expansions in Series of Chebyshev Polynomials and
Bessel Functions / 122 \\
4.8.3 Pad{\'e} Approximations / 124 \\
4.8.4 Trapezoidal Rule Approximations / 134 \\
4.8.5 Inequalities / 137 \\
4.9 Fresnel Integrals / 139 \\
4.9.1 Relation to Error Functions and Other Properties
/ 139 \\
4.9.2 Expansions in Series of Chebyshev Polynomials /
140 \\
4.10 Bibliographic and Numerical Data / 143 \\
4.10.1 References / 143 \\
4.10.2 Description of and References to Tables / 143
\\
4.10.3 Description of and References to Other
Approximations and Expansions / 149 \\
\\
V. The Generalized Hypergeometric Function $_pF_g$ and
the $G$-Function \\
\\
5.1 Introduction / 154 \\
5.2 The $_pF_q$ / 155 \\
5.2.1 Power Series / 155 \\
5.2.2 Derivatives and Contiguous Relations / 159 \\
5.2.3 Integral Representations and Integrals Involving
the $_pF_q$ / 160 \\
5.2.4 Evaluation for Special Values of the Variable and
Parameters / 163 \\
5.3 The $G$-Function / 170 \\
5.3.1 Definition and Relation to the $_pF_q$ / 170 \\
5.3.2 Elementary Properties / 176 \\
5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ /
178 \\
5.4 The Confluence Principle / 179 \\
5.5 Multiplication Theorems / 184 \\
5.6 Integrals Involving $G$-Functions / 186 \\
5.7 Differential Equations / 190 \\
5.7.1 The $_pF_q$ / 190 \\
5.7.2 The $G$-Function / 192 \\
5.8 Series of $G$-Functions / 194 \\
5.8.1 Introduction / 194 \\
5.8.2 Notation / 194 \\
5.8.3 Expansion Theorems / 197 \\
5.9 Asymptotic Expansions / 199 \\
5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\
5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\
5.9.3 $_pF_q(z)$ / 206 \\
5.10 Expansions in Series of Generalized Jacobi,
Generalized Laguerre and Chebyshev Polynomials / 213
\\
5.10.1 Expansions for $G$-Functions / 213 \\
5.10.2 Expansions for $_pF_q$ / 220 \\
5.11 Expansions in Series of Bessel Functions / 223 \\
5.12 Polynomial and Rational Approximations / 224 \\
5.13 Recurrence Formulas for Polynomials and Functions
Occurring in Approximations to Generalized
Hypergeometric Functions / 234 \\
5.13.1 Introduction / 234 \\
5.13.2 Recursion Formulas for Extended Jacobi and
Laguerre Functions / 235 \\
5.13.3 Recursion Formulas for the Numerator and
Denominator Polynomials in the Rational Approximations
for the Generalized Hypergeometric Function / 244 \\
5.13.4 Recursion Formula for Coefficients in the
Expansion of the $G$-Function in Series of Extended
Jacobi Polynomials / 247 \\
5.14 Inequalities / 252 \\
\\
VI. The Gaussian Hypergeometric Function $_2F_1$ \\
\\
6.1 Introduction / 257 \\
6.2 Elementary Properties / 257 \\
6.2.1 Derivatives / 257 \\
6.2.2 Contiguous Relations / 258 \\
6.2.3 Integral Representations / 259 \\
6.3 Differential Equations / 260 \\
6.4 Kummer Solutions and Transformation Formulae / 262
\\
6.5 Analytic Continuation / 263 \\
6.6 The Complete Solution and Wronskians / 265 \\
6.7 Quadratic Transformations / 270 \\
6.8 The $_2F_1$ for Special Values of the Argument /
271 \\
6.9 Expansion in Series of Chebyshev Polynomials / 274
\\
6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho
+ 1;-1/z)$ / 274 \\
6.11 Inequalities / 278 \\
6.12 Bibliographic and Numerical Data / 279 \\
6.12.1 References / 279 \\
6.12.2 Description of and References to Tables / 279
\\
\\
VII. The Confluent Hypergeometric Function \\
\\
7.1 Introduction / 284 \\
7.2 Integral Representations / 284 \\
7.3 Elementary Relations / 285 \\
7.3.1 Derivatives / 285 \\
7.3.2 Contiguous Relations / 285 \\
7.3.3 Products of Confluent Functions / 286 \\
7.4 Differential Equations / 287 \\
7.5 The Complete Solution and Wronskians / 288 \\
7.6 Asymptotic Expansions / 291 \\
7.7 Expansions in Series of Chebyshev Polynomials / 293
\\
7.8 Expansions in Series of Besse! Functions / 294 \\
7.9 Inequalities / 295 \\
7.10 Other Notations and Related Functions / 295 \\
7.11 Bibliographic and Numerical Data / 296 \\
7.11.1 References / 296 \\
7.11.2 Description of and References to Tables and
Other Approximations / 296 \\
\\
VIII. Identification of the $_pF_q$, and $G$-Functions
with the Special Functions \\
\\
8.1 Introduction / 298 \\
8.2 Named Special Functions Expressed as $_pF_q$'s /
298 \\
8.2.1 Elementary Functions / 298 \\
8.2.2 The Incomplete Gamma Function and Related
Functions / 298 \\
8.2.3 The Gaussian Hypergeometric Function / 298 \\
8.2.4 Legendre Functions / 299 \\
8.2.5 Orthogonal Polynomials / 299 \\
8.2.6 Complete Elliptic Integrals / 299 \\
8.2.7 Confluent Hypergeometric Functions, Whittaker
Functions and Bessel Functions / 300 \\
8.3 Named Functions Expressed in Terms of the
$G$-Function / 300 \\
8.4 The $G$-Function Expressed as a Named Function /
306 \\
\\
IX. Bessel Functions and Their Integrals \\
\\
9.1 Introduction / 311 \\
9.2 Definitions, Connecting Relations and Power Series
/ 311 \\
9.3 Difference--Differential Formulas / 313 \\
9.4 Products of Bessel Functions / 314 \\
9.5 Asymptotic Expansions for Large Variable / 315 \\
9.6 Integrals of Bessel Functions / 315 \\
9.7 Expansions in Series of Chebyshev Polynomials / 316
\\
9.8 Expansions in Series of Bessel Functions / 360 \\
9.9 Rational Approximations / 361 \\
9.9.1 Introduction / 361 \\
9.9.2 $I_\nu(z)$, $z$ Small / 361 \\
9.9.3 $K_\nu(z)$, $z$ Large / 366 \\
9.10 Computation of Bessel Functions by Use of
Recurrence Formulas / 380 \\
9.10.1 Introduction / 380 \\
9.10.2 Backward Recurrence Schemata for Generating
$I_\nu(z)$ / 380 \\
9.10.3 Closed Form Expressions / 382 \\
9.10.4 Expressions for $J_\nu(z)$ / 389 \\
9.10.5 Numerical Examples / 392 \\
9.11 Evaluation of Bessel Functions by Application of
Trapezoidal Type Integration Formulas / 395 \\
9.12 Inequalities / 399 \\
9.13 Bibliographic and Numerical Data / 403 \\
9.13.1 References / 403 \\
9.13.2 Description of and References to Tables / 404
\\
9.13.3 Description of and References to Other
Approximations and Expansions / 410 \\
\\
X. Lommel Functions, Struve Functions, and Associated
Bessel Functions \\
\\
10.1 Definitions, Connecting Relations and Power Series
/ 413 \\
10.2 Asymptotic Expansions / 415 \\
10.3 Expansions in Series of Chebyshev Polynomials and
Bessel Functions / 415 \\
10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$
and the Errors in These Approximations / 422 \\
10.5 Bibliographic and Numerical Data / 426 \\
10.5.1 References / 426 \\
10.5.2 Description of and References to Tables / 426
\\
\\
XI. Orthogonal Polynomials \\
\\
11.1 Introduction / 428 \\
11.2 Orthogonal Properties / 428 \\
11.3 Jacobi Polynomials / 436 \\
11.3.1 Expansion Formulae / 436 \\
11.3.2 Difference--Differential Formulae / 439 \\
11.3.3 Integrals / 439 \\
11.3.4 Expansion of $x^\rho$ in Series of Jacobi
Polynomials / 440 \\
11.3.5 Convergence Theorems for the Expansion of
Arbitrary Functions in Series of Jacobi Polynomials /
442 \\
11.3.6 Evaluation and Estimation of the Coefficients in
the Expansion of a Given Function $f(x)$ in Series of
Jacobi Polynomials / 443 \\
11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
453 \\
11.5 The Chebyshev Polynomials $T_n^*(x)$ and
$U_n^*(x)$ / 459 \\
11.6 Coefficients for Expansion of Integrals of
Functions in Series of Chebyshev Polynomials of the
First Kind / 464 \\
11.6.1 Introduction / 464 \\
11.6.2 Series of Shifted Chebyshev Polynomials / 464
\\
11.6.3 Series of Chebyshev Polynomials of Even Order /
468 \\
11.6.4 Series of Chebyshev Polynomials of Odd Order /
468 \\
11.7 Orthogonality Properties of Chebyshev Polynomials
with Respect to Summation / 469 \\
11.8 A Nesting Procedure for the Computation of
Expansions in Series of Functions Where the Functions
Satisfy a Linear Finite Difference Equation / 475 \\
\\
XII. Computation by Use of Recurrence Formulas \\
\\
12.1 Introduction / 483 \\
12.2 Homogeneous Difference Equations / 483 \\
12.3 Inhomogeneous Difference Equations / 487 \\
\\
XIII. Some Aspects of Rational and Polynomial
Approximations \\
\\
13.1 Introduction / 490 \\
13.2 Approximations in Series of Chebyshev Polynomials
of the First Kind / 490 \\
13.3 The Pad{\'e} Table / 493 \\
13.4 Approximation of Functions Defined by a
Differential Equation --- The $\tau$-Method / 495 \\
13.5 Approximations of Functions Defined by a Series /
499 \\
13.6 Solution of Differential Equations in Series of
Chebyshev Polynomials of the First Kind / 500 \\
\\
XIV. Miscellaneous Topics \\
\\
14.1 Introduction / 505 \\
14.2 Bernoulli Polynomials and Numbers / 505 \\
14.3 $D$ and $\delta$ Operators / 507 \\
14.4 Computation and Check of the Tables / 509 \\
14.5 Mathematical Constants / 512 \\
14.6 Late Bibliography / 516 \\
\\
Bibliography / 517 \\
\\
Notation Index / 545 \\
\\
Subject Index / 551",
}
@Article{Martinson:1975:DMF,
author = "L. Martinson and R. Smith",
title = "Digital matched filtering with pipelined floating
point fast {Fourier} transforms ({FFT}'s)",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "23",
number = "2",
pages = "222--234",
month = apr,
year = "1975",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A special floating point arithmetic technique for fast
Fourier transform (FFT) processors has been developed.
The implementation of a high-speed pipeline FFT matched
filter using the method employs significantly fewer
components than a fixed-point \ldots{}",
}
@InProceedings{Matula:1975:FSF,
author = "D. W. Matula",
title = "Fixed-Slash and Floating-Slash Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "90--91",
year = "1975",
bibdate = "Wed Nov 14 17:45:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Matula.pdf",
abstract = "A finite precision rational number system provides for
representation of a collection of rational numbers
subject to limitations on numerator and denominator
magnitude. In fixed-point and floating-point radix
number systems, only rationals of the form $ i /
\beta^j $, where $ \beta $ is the base, can be
realized. In contrast, a finite precision rational
number system will allow representation of practically
all simple fractions encountered in applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{McDonald:1975:TCQ,
author = "T. G. McDonald and R. K. Guha",
title = "The Two's Complement Quasi-Serial Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1233--1235",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224170",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672763",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Meo:1975:ANT,
author = "A. R. Meo",
title = "Arithmetic Networks and Their Minimization Using a New
Line of Elementary Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "258--280",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224207",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672800",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Miller:1975:SRA,
author = "Webb Miller",
title = "Software for Roundoff Analysis",
journal = j-TOMS,
volume = "1",
number = "2",
pages = "108--128",
month = jun,
year = "1975",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355637.355639",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G05",
MRnumber = "53 \#9622",
bibdate = "Fri Aug 26 23:44:16 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
reviewer = "James H. Wilkinson",
}
@Article{Nance:1975:IFR,
author = "Richard E. Nance and Claude {Overstreet, Jr.}",
title = "Implementation of {Fortran} Random Number Generators
on Computers with One's Complement Arithmetic",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "4",
number = "3",
pages = "235--243",
month = "????",
year = "1975",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657508810126",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Thu Jan 05 10:58:18 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00949657508810126",
abstract = "Random number generators can be programmed in FORTRAN
using several methods on 1's complement machines. We
have presented several methods for the SRU 1107--1108
and CDC 6000 and CYBER series, the two most popular
that utilize 1's complement arithmetic. We believe the
logical mask method to be the most efficient technique
based on execution time on both machines. This method
requires only a little more than one-half the time of
the signed residue method on the SRU 1107--1108 and a
little more than two thirds the time of the unsigned
residue method on the CDC 6000--CYBER. A fast composite
generator in FORTRAN uses the logical mask method
combined with the FLD function to implement the table
approach of MacLaren and Marsaglia (1965). This
generator proves to be more than twice as fast as a
previous one for the SRU 1108, Marsaglia and Bray
(1968)",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
onlinedate = "20 Mar 2007",
}
@Article{Nelson:1975:PPF,
author = "James M. Nelson and Charles E. Cohn",
title = "Parallel Processing in {FORTRAN} with Floating-Point
Hardware",
journal = j-SPE,
volume = "5",
number = "1",
pages = "65--68",
month = jan # "\slash " # mar,
year = "1975",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Newbery:1975:PES,
author = "A. C. R. Newbery",
title = "Polynomial Evaluation Schemes",
journal = j-MATH-COMPUT,
volume = "29",
number = "132",
pages = "1046--1050",
month = oct,
year = "1975",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290D (Functional analysis); C4120 (Functional
analysis)",
corpsource = "Department of Computer Sci., University of Kentucky,
Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "floating; function evaluation; point arithmetic;
polynomial evaluation algorithm; polynomials; round off
error",
treatment = "T Theoretical or Mathematical",
}
@Manual{NSC:1975:IFP,
author = "{National Semiconductor Corporation}",
title = "{IMP-16F\slash 400} floating point firmware technical
description",
type = "Publication - National Semiconductor Corporation no.
4200072A",
organization = "National Semiconductor Corporation",
address = "Santa Clara, CA, USA",
pages = "16",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors --- Handbooks, manuals, etc.;
Microprogramming --- Handbooks, manuals, etc.",
remark = "At head of title: Integrated microprocessor-16.",
}
@Article{OKeefe:1975:NFB,
author = "K. H. O'Keefe",
title = "A Note on Fast Base Extension for Residue Number
Systems with Three Moduli",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "11",
pages = "1132--1133",
month = nov,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/PGEC.1967.264810;
https://doi.org/10.1109/T-C.1975.224147",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672740;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35091",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "An algorithm is given for the base-extension (BE)
computation in residue number systems that requires the
standard four steps (for systems with three moduli) but
which saves hardware. Furthermore, for the particular
moduli m-1, m, and m+1 it is \ldots{}",
}
@InCollection{Phillips:1975:BC,
author = "E. William Phillips",
title = "Binary Calculation",
crossref = "Randell:1975:ODC",
pages = "293--304",
year = "1975",
bibdate = "Wed Oct 13 09:51:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "The 1936 epigraph credited to this author in
\cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
aim is to persuade all of the civilized world to
abandon the decimal numeration and to use octonal in
its place; to discontinue counting in tens and to count
in eights instead. However, it seems unlikely that the
whole civilized world will be persuaded to complete
this change during the next twelve months, having
previously declined similar invitations.''",
}
@InProceedings{Rao:1975:TIS,
author = "T. R. N. Rao and D. W. Matula",
title = "The {Third IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "IEEE:1975:SCA",
pages = "v--v",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Reiser:1975:EDF,
author = "John F. Reiser and Donald E. Knuth",
title = "Evading the Drift in Floating-Point Addition",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "3",
pages = "84--87",
month = jan,
year = "1975",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/0020-0190(75)90022-8",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sun Dec 04 12:21:37 1994",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib",
note = "See erratum \cite{Reiser:1975:EED}.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
remark = "From p. 87: ``Actually Tannery's and Scarborough's
contradictory arguments [round-up and round-to-even]
are both incorrect; for example, the logarithmic law of
distribution of leading digits [3] [Benford's Law]
implies that the least significant digit of a
floating-point number will be odd slightly less often
than it will be even, assuming that $b$ is even and $ p
> 1$. The real justification for stable rounding is
that it eliminates drift.''",
}
@Article{Reiser:1975:EED,
author = "John F. Reiser and Donald E. Knuth",
title = "Erratum: {``Evading the Drift in Floating-Point
Addition''}",
journal = j-INFO-PROC-LETT,
volume = "3",
number = "5",
pages = "164--164",
month = may,
year = "1975",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/0020-0190(75)90031-9",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sun Dec 04 12:21:42 1994",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Reiser:1975:EDF}.",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Rokne:1975:ACI,
author = "J. Rokne and P. Lancaster",
title = "Algorithm 86. Complex Interval Arithmetic",
journal = j-COMP-J,
volume = "18",
number = "1",
pages = "83--85",
month = feb,
year = "1975",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C7310 (Mathematics
computing)",
corpsource = "Univ. Calgary, Alta., Canada",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithm; complex interval arithmetic; digital
arithmetic; floating point; real numbers; subroutines",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Rubinfield:1975:PMB,
author = "L. P. Rubinfield",
title = "A Proof of the Modified {Booth}'s Algorithm for
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "10",
pages = "1014--1015",
month = oct,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224114",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672707",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Senzig:1975:CA,
author = "Don Senzig",
title = "Calculator Algorithms",
journal = "IEEE Compcon Reader Digest",
pages = "139--141",
year = "1975",
bibdate = "Fri Nov 28 19:19:40 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 75CH0920-9C.",
abstract = "This paper discusses algorithms for generating the
trigonometric, exponential, and hyperbolic functions
and their inverses. No invention is claimed here. The
algorithm for logarithm was used by Briggs in compiling
his table of logarithms in the 1600's. Other earlier
references are [cited]. The development presented here
is, perhaps, more direct than those given in the above
references but leads to the same result.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Shimizu:1975:REF,
author = "Tatsujiro Shimizu and Tsunemichi Oohashi",
title = "Rounding errors in floating point addition",
journal = "TRU Math.",
volume = "11",
pages = "41--50",
year = "1975",
MRclass = "65G05",
MRnumber = "55 4646",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "R. P. Brent",
}
@InProceedings{Shriver:1975:BCA,
author = "B. D. Shriver and E. K. Reuter",
title = "A Bibliography on Computer Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "241--249",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Biography.pdf",
abstract = "This bibliography on computer arithmetic uses, by and
large, the format and abbreviations employed by
Computing Reviews. It is presented in alphabetical
order only and not by individual topics. The topics
included, however, span the abstract and implementation
problems associated with finite precision computer
arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Shriver:1975:UUN,
author = "Bruce D. Shriver and Peter Kornerup",
title = "The {UNRAU} --- a {Unified Numeric Representation
Arithmetic Unit}",
crossref = "IEEE:1975:SCA",
pages = "179--184",
year = "1975",
bibdate = "Wed Nov 14 17:46:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Shriver.pdf",
abstract = "A companion paper entitled, ``A Unified Numeric Data
Type in Pascal'', proposes the substitution of the
standard data type {\em real\/} of the language Pascal
with a unified data representation termed {\em
numeric}. The {\em numeric\/} data type can represent a
variety of arithmetic operands such as integers,
normalized floating point numbers, and centered-radius
intervals.\par
This paper describes an arithmetic unit which is
capable of executing the standard arithmetic operations
(addition, subtraction, multiplication, and division)
on pairs of operands specified to be of the {\em
numeric\/} data type. This arithmetic unit, called the
UNRAU --- Unified Numeric Representation Arithmetic
Unit, supports operations on operands externally
represented as 5-tuples $ (t, a, e, f, r) $. The UNRAU
provides for automatic conversion among the various
data types and can also be used to perform an explicit
conversion on a single operand.\par
It is intended to implement the UNRAU on a dynamically
microprogrammable microprocessor to determine what host
facilities are required to efficiently realize such an
arithmetic unit and to experiment with the high level
language support of such a unit.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Smith:1975:CPC,
author = "Alan Jay Smith",
title = "Comments on a paper by {T. C. Chen} and {I. T. Ho}",
journal = j-CACM,
volume = "18",
number = "8",
pages = "463--463",
month = aug,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:22:40 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Smith75a;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Chen:1975:SER}.",
acknowledgement = ack-nhfb,
classcodes = "C6130 (Data handling techniques)",
corpsource = "University of California, Berkeley, CA, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "advantages; alternatives; binary coded decimal; codes;
coding; compression of numbers; data handling; decimal
data; decimal floating-point arithmetic; decoding;
deletions; Huffman codes; insertions; permutations;
storage efficient representation; variable length
codes",
oldlabel = "Smith75a",
treatment = "G General Review; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Smith75a",
}
@Article{Smith:1975:SCO,
author = "Cyril Stanley Smith",
title = "A {Seventeenth-Century} Octonary Arithmetic",
journal = j-ISIS,
volume = "66",
number = "3",
pages = "390--394",
month = sep,
year = "1975",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:29:19 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i302314;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
URL = "http://www.jstor.org/stable/228846",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Book{Smith:1975:SAP,
author = "Jon M. Smith",
title = "Scientific Analysis on the Pocket Calculator",
publisher = pub-Wiley,
address = pub-Wiley:adr,
pages = "xii + 380",
year = "1975",
ISBN = "0-471-79997-1",
ISBN-13 = "978-0-471-79997-9",
LCCN = "QA75 .S555",
bibdate = "Wed Jun 12 16:56:02 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Part I: Introduction to Pocket Calculator Analysis
\\
1: The Pocket Calculator / 3 \\
2: Difference Tables, Data Analysis, and Function
Evaluation / 53 \\
Part II: Numerical Evaluation of Functions on the
Pocket Calculator \\
3: Elementary Analysis with the Pocket Calculator / 81
\\
4: Numerical Evaluation of Advanced Functions / 114 \\
Part III: Advanced Analysis on the Pocket Calculator
\\
5: Fourier Analysis / 139 \\
6: Numerical Integration / 154 \\
7: Linear Systems Simulation / 180 \\
8: Chebyshev and Rational Polynomial Approximations for
Analytic Substitution / 198 \\
9: Determining the Roots of a Function / 224 \\
10: Statistics and Probability / 242 \\
Part IV: The Programmable Pocket Calculator \\
11: The Programmable Pocket Calculator / 283 \\
12: Optimization / 300 \\
Appendix 1: Some Tricks of the Pocket Calculator Trade
/ 323 \\
Appendix 2: Matrix Analysis on the Pocket Calculator /
333 \\
Appendix 3: Complex Numbers and Functions / 336 \\
Appendix 4: Key Stroke Sequences for Complex Variable
Analysis and Hyperbolic Inverse Functions / 340 \\
Index",
}
@Article{Soule:1975:AAB,
author = "Stephen Soule",
title = "Addition in an Arbitrary Base Without Radix
Conversion",
journal = j-CACM,
volume = "18",
number = "6",
pages = "344--346",
month = jun,
year = "1975",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 07:23:30 MST 2001",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Theory/Seiferas/1975.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Soule75;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a generalization of an old
programming technique; using it, one may add and
subtract numbers represented in any radix, including a
mixed radix, and stored one digit per byte in bytes of
sufficient size. Radix conversion is unnecessary, no
looping is required, and numbers may even be stored in
a display (I/O) format. Applications to Cobol, MIX, and
hexadecimal sums are discussed.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
classification = "723; 921",
corpsource = "University of Calgary, Calgary, Alta., Canada",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "add; addition; arbitrary base; arbitrary radix
arithmetic; Cobol display arithmetic; computer systems
programming; data handling; decimal arithmetic; decimal
floating-point arithmetic; digital arithmetic;
mathematical techniques --- Digital Arithmetic; MIX
arithmetic; mixed radix arithmetic; numbers;
programming; radix conversion; subtract; subtraction;
without radix conversion",
oldlabel = "Soule75",
treatment = "A Application; T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Soule75",
}
@InProceedings{Stephenson:1975:CSP,
author = "Charles Stephenson",
title = "Case Study of the Pipelined Arithmetic Unit for the
{TI Advanced Scientific Computer}",
crossref = "IEEE:1975:SCA",
pages = "168--173",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Stephenson.pdf",
abstract = "Many scientific applications today require computers
which are very fast and capable of processing large
amounts of data. Some advances in scientific processing
have been slowed due to the lack of supercomputer
capabilities which are required primarily in the area
of Central Processor speed and the availability of
large amounts of high speed memory. Particularly in the
fields of modeling and simulation, additional speed and
memory capacity are desired to allow increased
resolution of the experiment. Technological
developments: In such things as integrated circuits,
multilayer printed circuit boards, memory speeds, and
others have contributed to the ability of computer
manufacturers to serve this market. In addition to
these developments, however, large advances had to be
realized from the standpoint of the basic computer
architecture. The concept of pipelining has provided an
answer to the large data execution rate required.
Pipelined capabilities in the form of arithmetic units
and special purpose functional units are included in
machines such as the CDC 7600, IBM 360/195, CDC
STAR-100, etc. The Texas Instruments Advanced
Scientific Computer (ASC) uses the pipeline concept
throughout the Central Processor and carries the
concept throughout the Central Processor and carries
the concept further to include vector instructions in
response to the high execution rates required. 3",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Sterbenz:1975:UA,
author = "Pat H. Sterbenz",
title = "Understandable Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "33--35",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Sterbenz.pdf",
abstract = "Since the floating-point operations form the basic
steps in our programs, the programmer has to understand
the results that will be produced by these operations.
This paper discusses operations which have been or
might be implemented in the hardware. The emphasis is
on making the results easy for the user to
understand.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Book{Stone:1975:ICA,
editor = "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
and Samuel H. Fuller and others",
title = "Introduction to computer architecture",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
pages = "x + 565",
year = "1975",
ISBN = "0-574-18405-8",
ISBN-13 = "978-0-574-18405-4",
LCCN = "QA76.5 .I7; QA76.9.A73 I57; QA76.5 .I63; QA76.9.A73
I57 1975",
bibdate = "Fri Nov 9 19:22:07 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "SRA computer science series",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers",
}
@InProceedings{Svoboda:1975:SCA,
author = "Antonin Svoboda",
title = "Self-Checking Adder for Large Scale Integration",
crossref = "IEEE:1975:SCA",
pages = "108--112",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Svoboda.pdf",
abstract = "The testing of LSI chips is expensive and
unsatisfactory. On the other hand there are cases (as
in space ship computers) where a damaged chip must be
localized and replaced. The use of self-checking chips
seems to be one of several possible solutions of this
problem. The theory of the structure of self-checking
logical circuit is covered by literature at least at
the fundamental form (see References). However, even
when the design principles are supposed to be known,
their application to the actual creation of a
self-checking circuit of an average complexity is and
will remain an art. The reason is quite simple and
fundamental optimization of design criteria
(engineering qualifications, performance and physical
properties of components of the circuits are entities
possessing different physical dimensions --- it is
impossible to qualify, for instance, two circuits A, B
designed for the same task by comparing their speeds
and costs if A is faster than B but B is cheaper than
A) will never be objective and independent of the
talent or whim of the circuit designer.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Swartzlander:1975:SLN,
author = "E. E. {Swartzlander, Jr.} and A. G. Alexopoulos",
title = "The Sign\slash Logarithm Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "12",
pages = "1238--1242",
month = dec,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224172",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Hongyuan:1986:CSL}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672765",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Toma:1975:CLA,
author = "C. I. Toma",
title = "Cellular Logic Array for High-Speed Signed Binary
Number Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "9",
pages = "932--935",
month = sep,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224340",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672933",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Trivedi:1975:LAD,
author = "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
title = "On-Line Algorithms for Division and Multiplication",
crossref = "IEEE:1975:SCA",
pages = "161--177",
year = "1975",
bibdate = "Fri Dec 08 10:45:59 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_2.pdf",
abstract = "In this paper we are considering problems of division
and multiplication in a computational environment in
which all but basic arithmetic operations satisfy
``on-line'' property: to generate $ j^{\mbox {th}} $
digits of the result it is necessary and sufficient to
have argument(s) available up to the $ (j +
\delta)^{\mbox {th}} $ digit, where the index
difference $ \delta $ is a small positive
constant.
Such an environment, due to its potential to perform a
sequence of operations in an overlapped fashion, could
conveniently speed up an arithmetic multiprocessor
structure it could be useful in certain real-time
applications, with inherent on-line properties. The
on-line property implies a left-to-right digit-by-digit
type of algorithm and consequently, a redundant
representation, at least of the results. For addition
and subtraction such algorithms satisfying on-line
property can be easily specified. Multiplication
requires a somewhat more elaborate approach and there
are several possible ways of defining an on-line
algorithm. However, the existence of an on-line
division algorithm is not obvious and its analysis
appears interesting.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@InProceedings{Trivedi:1975:UCF,
author = "Kishor S. Trivedi",
title = "On the Use of Continued Fractions for Digital Computer
Arithmetic",
crossref = "IEEE:1975:SCA",
pages = "137--146",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_1.pdf",
abstract = "Recently, there has been some interest in the use of
continued fractions for digital hardware calculations.
We require that the coefficients of the continued
fractions be integral powers of two. As a result well
known continued fraction expansions of functions cannot
be used. Methods of expansion of a large number of
functions are presented.\par
We show that the problem of selection of coefficients
of the continued fractions does not have practical
solution in most of the cases we have considered. We
conjecture that the solution of a polynomial equation
is the only problem that can be solved in our
formulation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@MastersThesis{Tzaferos:1975:EBD,
author = "Konstantina Tzaferos",
title = "Error bounds due to index of significance
specifications in floating-point operations with
encoded mantissa lengths",
type = "Thesis ({M.S.})",
school = "California State University, Chico",
address = "Chico, CA, USA",
pages = "vi + 43",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@Manual{Wadsworth:1975:MLP,
author = "Nat Wadsworth",
title = "Machine Language Programming for the 8008 (and Similar
Microcomputers)",
organization = "Scelbi Computer Consulting. Inc.",
address = "1322 Rear --- Boston Post Road, Milford, CT 0646,
USA",
pages = "172 (chapter numbering)",
year = "1975",
bibdate = "Fri Dec 01 15:53:00 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.scelbi.com/files/docs/books/Machine%20Language%20Programming%20For%20The%208008.pdf",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; multiple-precision
arithmetic",
remark = "Chapter 5 discusses implementation of floating-point
arithmetic in software on the Intel 8008, with
assembly-code routines for each operation.",
}
@Article{Wakerly:1975:DUM,
author = "J. F. Wakerly",
title = "Detection of Unidirectional Multiple Errors Using
Low-Cost Arithmetic Codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "2",
pages = "210--212",
month = feb,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224187",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672780",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Weinberger:1975:HSZ,
author = "Arnold Weinberger",
title = "High-Speed Zero-Sum Detection",
crossref = "IEEE:1975:SCA",
pages = "200--207",
year = "1975",
bibdate = "Wed Nov 14 17:44:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Weinberger.pdf",
abstract = "A common requirement accompanying high-speed parallel
addition is the early detection that the sum is equal
to zero. Normally, this condition is detected from the
sum, generally at least two logic gate levels after the
sum.\par
This paper derives expressions for detecting a zero-sum
condition concurrently with or even earlier than the
determination of the sum digits proper. As a result, a
branch operation based on detecting a zero-sum can be
executed earlier.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3",
}
@Article{Wilkinson:1975:PAA,
author = "J. H. Wilkinson",
title = "The {Pilot ACE at the NPL}",
journal = j-RADIO-ELECTRON-ENG,
volume = "45",
number = "7",
pages = "336--340",
month = jul,
year = "1975",
CODEN = "RDEEA4",
ISSN = "0033-7722",
bibdate = "Mon Nov 1 18:34:26 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Radio and Electronic Engineer",
}
@TechReport{Wozniakowski:1975:NSI,
author = "H. Wozniakowski",
title = "Numerical stability of iterations for solution of
nonlinear equations and large linear systems",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "16",
year = "1975",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Differential equations, Nonlinear.; Floating-point
arithmetic.; Iterative methods (Mathematics); Linear
systems.",
}
@Article{Yamashita:1975:EEF,
author = "Shin-ichiro Yamashita",
title = "On the error estimation in floating-point arithmetic",
journal = "Information Processing in Japan",
volume = "15",
pages = "64--69",
year = "1975",
MRclass = "65G05",
MRnumber = "54 4081",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Artenio De Matteis",
}
@Article{Yuen:1975:FPR,
author = "C. K. Yuen",
title = "On the Floating Point Representation of Complex
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "8",
pages = "846--848",
month = aug,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224321",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Bauer:1977:CFP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672914",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Yuen:1975:NBA,
author = "C. K. Yuen",
title = "A Note on Base $ - 2 $ Arithmetic Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-24",
number = "3",
pages = "325--329",
month = mar,
year = "1975",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1975.224216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 07:57:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{Agrawal:1977:CNB}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672809",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "negative base",
received = "25 January 1974; revised 3 June 1978",
remark-1 = "From page 328: ``[In base $-2$,] the product of two
$n$-bit numbers may have $2 n + 1$ bits.''",
remark-2 = "From page 329: ``In general circumstances, however, it
is at present difficult to see base $-2$ as a strong
competitor against positive base arithmetic. We have
seen that arithmetic operations are usually more
complex, and fast adders are difficult to design. The
range of base $-2$ numbers is not symmetrical: either
there are twice as many positive numbers as negative
ones, or vice versa.''",
remark-3 = "The appendix on page 329 shows a simple algorithm for
converting between numbers with base $b$ and base
$-b$.",
}
@Article{Asai:1976:RRC,
author = "H. Asai",
title = "A recursive radix conversion formula and its
application to multiplication and division",
journal = j-COMPUT-MATH-APPL,
volume = "2",
number = "3--4",
pages = "255--265",
month = "????",
year = "1976",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:13 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122176900183",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Assmus:1976:NFS,
author = "E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and
Howard E. Sachar",
title = "A New Form of the Square Root Bound",
journal = j-SIAM-J-APPL-MATH,
volume = "30",
number = "2",
pages = "352--354",
month = mar,
year = "1976",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classification = "B0250 (Combinatorial mathematics); C1160
(Combinatorial mathematics)",
corpsource = "Department of Math., Lehigh University, Bethlehem, PA,
USA",
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
keywords = "combinatorial mathematics; linear codes; square root
bound; sufficient combinatorial conditions",
treatment = "T Theoretical or Mathematical",
}
@Article{Baker:1976:SFB,
author = "P. W. Baker",
title = "Suggestion for a fast binary sine\slash cosine
generator",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "??",
pages = "1134--1137",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674566",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 05:24:26 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brent:1976:FMP,
author = "Richard P. Brent",
title = "Fast Multiple-Precision Evaluation of Elementary
Functions",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "242--251",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321941.321944",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "68A20 (68A10)",
MRnumber = "52 \#16111",
MRreviewer = "Amnon Barak",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Let $ f(x) $ be one of the usual elementary functions
($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $,
etc.), and let $ M(n) $ be the number of
single-precision operations required to multiply
$n$-bit integers. It is shown that $ f(x) $ can be
evaluated, with relative error $ O(2 - n) $, in $
O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
$, for any floating-point number $x$ (with an $n$-bit
fraction) in a suitable finite interval. From the
Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
that an $n$-bit approximation to $ f(x) $ may be
evaluated in $ O(n \log_(n) \log \log (n)) $
operations. Special cases include the evaluation of
constants such as $ \pi $ $e$, and $ e^\pi $. The
algorithms depend on the theory of elliptic integrals,
using the arithmetic-geometric mean iteration and
ascending Landen transformations.",
acknowledgement = ack-nhfb,
classification = "723",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
journalabr = "J Assoc Comput Mach",
keywords = "computational complexity; computer arithmetic;
computer programming",
}
@InProceedings{Brent:1976:MPZ,
author = "Richard P. Brent",
title = "Multiple-precision zero-finding methods and the
complexity of elementary function evaluation",
crossref = "Traub:1976:ACC",
pages = "151--176",
year = "1976",
MRclass = "68A20",
MRnumber = "54 \#11843",
MRreviewer = "Claus-Peter Schnorr",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Carter:1976:ANT,
author = "Allison Birchard Carter",
title = "Applications of number theory to the avoidance of
round-off in digital computer systems",
type = "Thesis ({M.S.})",
school = "University of Florida",
address = "Gainesville, FL, USA",
pages = "v + 74",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers.; Floating-point
arithmetic.; Number theory.",
}
@Article{Cohen:1976:EFD,
author = "Daniel I. A. Cohen",
title = "An explanation of the first digit phenomenon",
journal = j-J-COMB-THEORY-A,
volume = "20",
number = "3",
pages = "367--370",
month = may,
year = "1976",
CODEN = "JCBTA7",
ISSN = "0097-3165 (print), 1096-0899 (electronic)",
ISSN-L = "0097-3165",
bibdate = "Thu Feb 15 16:29:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Combinatorial Theory. Series A",
journal-URL = "http://www.sciencedirect.com/science/journal/00973165",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Davies:1976:IPS,
author = "M. Davies and B. Dawson",
title = "The incrementation parameter in square root
iteration",
journal = j-J-INST-MATH-APPL,
volume = "17",
number = "2",
pages = "219--223",
year = "1976",
CODEN = "JMTAA8",
ISSN = "0020-2932",
MRclass = "65H05",
MRnumber = "55 \#9514",
MRreviewer = "Luciano Biasini",
bibdate = "Fri Apr 5 07:38:01 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0319.65039",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Book{DEC:1976:DHM,
author = "{Digital Equipment Corporation}",
title = "{DECsystem}-10\slash 20 Hardware Manual",
publisher = pub-DP,
address = pub-DP:adr,
edition = "Fourth",
pages = "various",
month = mar,
year = "1976",
bibdate = "Fri Dec 08 13:03:19 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also published as Stanford Artificial Intelligence
Laboratory Operating Note 75, November 1976.",
acknowledgement = ack-nhfb,
}
@Misc{DeSandre:1976:FPF,
author = "Giovanni {De Sandre} and Angelo Subrizi and Franco
Bretti",
title = "Fixed point to floating point conversion in an
electronic computer",
howpublished = "US Patent US3961170.",
day = "1",
month = jun,
year = "1976",
bibdate = "Sat Mar 24 06:14:58 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Patent filed 17 April 1974.",
URL = "https://patents.google.com/patent/US3961170A;
https://tinyurl.com/ybz9rrqy",
abstract = "In a digital electronic computer which comprises a
memory including a first and a second register, the
first register is receptive of a number to be converted
from fixed to floating point notation and the second
register is receptive of a significant zero digit with
an associated decimal point. Shifting means including a
register is operable to shift the contents of either
register and aligning means is operable to cause
shifting of the second register until the decimal point
stored therein is aligned with the decimal point in the
first register. Indicating means indicates whether the
number stored in the first register is greater or less
than one and the shifting means next begins shifting
the contents of one or the other of the registers when
the number is indicated greater or less than one
respectively. A control means includes a detecting
means for stopping the shifting means when the decimal
point of the second register becomes aligned with the
location of the next higher order with respect to the
highest significant digit of the first register. The
control means also includes counting means which is
incremented or decremented by one for each shifting
operation in dependence on the direction of shifting.
The resultant numbers in the first and second registers
represent the mantissa and exponent respectively, of
the desired floating point number.",
acknowledgement = ack-nhfb,
}
@Article{Detlefsen:1976:CRN,
author = "Michael Detlefsen and Douglas K. Erlandson and J.
Clark Heston and Charles M. Young",
title = "Computation with {Roman} numerals",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "15",
number = "2",
pages = "141--148",
month = jun,
year = "1976",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/BF00348497",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "00A05 (01A20)",
MRnumber = "0453407 (56 \#11671)",
MRreviewer = "Richard L. Francis",
bibdate = "Fri Feb 4 21:50:12 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=15&issue=2;
https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=15&issue=2&spage=141",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
MRtitle = "Computation with {Roman} numerals",
}
@MastersThesis{Dickinson:1976:PAA,
author = "Fred Kenneth Dickinson",
title = "Pseudo-round: an alternative approach for
floating-point representation",
type = "Thesis ({M.S.})",
school = "Southwest Texas State University",
address = "San Marcos, TX, USA",
pages = "vi + 53",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Numerical calculations ---
Computer programs.",
}
@Article{Fateman:1976:MAP,
author = "R. J. Fateman",
title = "{Macsyma} Arbitrary Precision Floating Point
Arithmetic Package --- Philosophy and an Overview of
its Implementation",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "802--802",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Feldstein:1976:CED,
author = "Alan Feldstein and Richard Goodman",
title = "Convergence Estimates for the Distribution of Trailing
Digits",
journal = j-J-ACM,
volume = "23",
number = "2",
pages = "287--297",
month = apr,
year = "1976",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321941.321948",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An analysis is made of the distribution of trailing
digits (tail end digits) of positive real
floating-point numbers represented in arbitrary base $
\beta $ and randomly chosen from a logarithmic
distribution. The analysis shows that the $n$ th digit
for $ n \geq 2 $ is actually approximately uniformly
distributed. The approximation depends upon both $n$
and the base beta. It becomes better as $n$ increases,
and it is exact in the limit as $ n \rightarrow \infty
$. A table of this distribution is presented for
various $ \beta $ and $n$, along with a table of the
maximum digit by digit deviation $ \Delta $ of the
logarithmic distribution from the uniform distribution.
Various asymptotic results for $ \Delta $ are
included.",
acknowledgement = ack-nhfb,
classification = "723",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
journalabr = "J Assoc Comput Mach",
keywords = "Benford's Law; computer arithmetic; computer
programming; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Garner:1976:SSR,
author = "H. L. Garner",
title = "A Survey of Some Recent Contributions to Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "12",
pages = "1277--1282",
month = dec,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674595",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Goldstein:1976:FCF,
author = "M. J. Goldstein",
title = "Further Comparison of Floating Point Summation
Methods",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "805--805",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "accurate floating-point summation",
}
@Article{Goodman:1976:EGD,
author = "R. Goodman and A. Feldstein",
title = "Effect of Guard Digits and Normalization Options on
Floating Point Multiplication",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "806--806",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Goodman:1976:REF,
author = "Richard Goodman",
title = "On round-off error in fixed-point multiplication",
journal = j-BIT,
volume = "16",
number = "1",
pages = "41--51",
month = mar,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940776",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=1&spage=41",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "fixed-point arithmetic; floating-point arithmetic;
rounding errors",
}
@Article{Goyal:1976:NAR,
author = "L. N. Goyal",
title = "A Note on {Atrubin}'s Real-Time Iterative Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "5",
pages = "546--548",
month = may,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674646",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674646",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hannington:1976:FPM,
author = "G. Hannington and D. G. Whitehead",
title = "A Floating-Point Multiplexed {DDA} System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "11",
pages = "1074--1077",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674557",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments \cite{McCrea:1978:CFP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674557",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Higbie:1976:VFP,
author = "L. C. Higbie",
title = "Vector Floating-Point Data Format",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "1",
pages = "25--32",
month = jan,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.5009201",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009201",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{IBM:1976:ISP,
author = "{IBM Corporation}",
title = "{IBM System}\slash 370: Principles of Operation:
Systems",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "326",
year = "1976",
LCCN = "QA76.8.I122 I57 1976",
bibdate = "Fri Sep 16 16:30:13 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Jayashree:1976:BMU,
author = "T. Jayashree and D. Basu",
title = "On Binary Multiplication Using the Quarter Square
Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "9",
pages = "957--960",
month = sep,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674723",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674723",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kulisch:1976:FIF,
author = "U. Kulisch and G. Bohlender",
title = "Formalization and implementation of floating-point
matrix operations",
journal = j-COMPUTING,
volume = "16",
number = "3",
pages = "239--261",
year = "1976",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (68A10)",
MRnumber = "53 7010",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "F. Szidarovszky",
}
@Book{Kulisch:1976:GNR,
author = "Ulrich W. Kulisch",
title = "{Grundlagen des numerischen Rechnens: mathematische
Begr{\"u}ndung der Rechnerarithmetik} \toenglish
{Fundamental Principles of Numerical Computation:
Mathematical Foundations of Computer Arithmetic}
\endtoenglish",
volume = "19",
publisher = pub-BIB-INST,
address = pub-BIB-INST:adr,
pages = "467",
year = "1976",
ISBN = "3-411-01517-9",
ISBN-13 = "978-3-411-01517-7",
LCCN = "QA162 .K85",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Reihe Informatik",
acknowledgement = ack-nhfb,
keywords = "Algebra, Abstract.; Floating-point arithmetic.;
Mathematics --- Data processing.",
}
@Article{Lacroix:1976:LCF,
author = "Arild Lacroix",
title = "Limit cycles in floating point digital filters",
journal = "AE{\"U}---Arch. Elektron. {\"U}bertragungstech.",
volume = "30",
number = "7/8",
pages = "277--284",
year = "1976",
MRclass = "94A05",
MRnumber = "56 15123",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Linnainmaa:1976:TEA,
author = "Seppo Linnainmaa",
title = "{Taylor} expansion of the accumulated rounding error",
journal = j-BIT,
volume = "16",
number = "2",
pages = "146--160",
month = jun,
year = "1976",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01931367",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:14 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=146",
abstract = "The article describes analytic and algorithmic methods
for determining the coefficients of the Taylor
expansion of an accumulated rounding error with respect
to the local rounding errors, and hence determining the
influence of the local errors on the accumulated error.
Second and higher order coefficients are also
discussed, and some possible methods of reducing the
extensive storage requirements are analyzed.",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@MastersThesis{Lipschutz:1976:OPS,
author = "David Lipschutz",
title = "Optimization of a practical system for high fidelity
digital audio",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "53",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Francis F. Lee.",
acknowledgement = ack-nhfb,
keywords = "Computer sound processing.; Digital electronics.;
Floating-point arithmetic.; High-fidelity sound
systems.; Noise --- Psychological aspects.",
}
@Article{Majithia:1976:SCC,
author = "J. C. Majithia",
title = "Some Comments Concerning Design of Pipeline Arithmetic
Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "11",
pages = "1132--1134",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674565",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:06:10 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Maples:1976:FPI,
author = "Michael D. Maples",
title = "Floating-point package for {INTEL} 8008 and 8080
microprocessors",
institution = "Lawrence Livermore Laboratory, University of
California/Livermore; National Technical Information
Service [distributor]",
address = "Livermore, CA, USA",
pages = "8 + A-33",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Intel 8080
(Microprocessor); Microprocessors.",
remark = "Prepared for U.S. Energy Research and Development
Administration, under Contract No. W-7405-Eng-43.
Microfiche reproduction: Springfield, Va.: National
Technical Information Service, 1976. --- 1 microfiche;
10 x 15 cm.",
}
@PhdThesis{Martinez:1976:SSS,
author = "Ralph Martinez",
title = "A semi-portable simulation system using both fixed and
floating point derivative blocks",
type = "Thesis ({Ph.D.} - Electrical Engineering)",
school = "University of Arizona",
address = "Tucson, AZ, USA",
pages = "xii + 169",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital computer simulation.; Dynamics --- Data
processing.",
}
@TechReport{Metropolis:1976:MSA,
author = "N. Metropolis",
title = "Methods of significance arithmetic",
type = "Technical report",
number = "LA-UR-76-661;CONF-760428-1",
institution = inst-LASL,
address = inst-LASL:adr,
day = "1",
month = jan,
year = "1976",
bibdate = "Tue Mar 20 11:16:47 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Presented at the Conference on the state of the art in
numerical analysis, 12 April 1976, University of York,
England, UK",
URL = "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=7189580&query_id=0",
abstract = "A preliminary report is given of two applications of
the methods of significance arithmetic. These are a
simple nonlinear partial differential equation and
matrix inversion.",
acknowledgement = ack-nhfb,
remark = "OSTI ID: 7189580",
}
@Article{Miller:1976:AGF,
author = "Webb Miller and David L. Spooner",
title = "Automatic Generation of Floating-Point Test Data",
journal = j-IEEE-TRANS-SOFTW-ENG,
volume = "SE-2",
number = "3",
pages = "223--226",
month = sep,
year = "1976",
CODEN = "IESEDJ",
DOI = "https://doi.org/10.1109/TSE.1976.233818",
ISSN = "0098-5589 (print), 1939-3520 (electronic)",
ISSN-L = "0098-5589",
MRclass = "68A05",
MRnumber = "55 1787",
bibdate = "Thu Feb 1 08:07:37 MST 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranssoftweng1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1702369",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Software Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
keywords = "floating-point testing",
remark = "Special section on testing",
reviewer = "George Marsaglia",
}
@Article{Mohn:1976:IPA,
author = "K. Mohn and R. V. Roman",
title = "An interactive polynomial approximation algorithm",
journal = j-COMP-J,
volume = "19",
number = "1",
pages = "74--78",
month = feb,
year = "1976",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 15 18:39:43 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Ni:1976:EAT,
author = "Ming Duenn Ni and J. K. Aggarwal",
title = "Error analysis of two-dimensional recursive digital
filters employing floating-point arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "7",
pages = "755--759",
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674684",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65D99 (93E10)",
MRnumber = "55 6802",
bibdate = "Sat Dec 16 16:45:24 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
reviewer = "Sven-{\AA}ke Gustafson",
}
@TechReport{Paoni:1976:PFI,
author = "C. Paoni and M. Maples",
title = "A {PLM} floating-point interface program",
institution = "Lawrence Livermore Laboratory; National Technical
Information Service",
address = "Livermore, CA, USA",
pages = "iii + 39",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Parker:1976:STR,
author = "Douglass Stott Parker",
title = "The statistical theory of relative errors in
floating-point computation",
type = "Thesis ({M.S.})",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "62",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Report no. UIUCDCS-R-76-787",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Roundoff errors.",
}
@Article{Patel:1976:ASB,
author = "M. R. Patel and K. H. Bennett",
title = "Analysis of Speed of a Binary Multiplier Using a
Variable Number of Shifts Per Cycle",
journal = j-COMP-J,
volume = "19",
number = "3",
pages = "254--257",
month = aug,
year = "1976",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/19.3.254",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:58 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/19/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/19/3/254.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/254.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/255.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/256.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/257.tif",
acknowledgement = ack-nhfb,
classcodes = "C5210 (Logic design methods); C5230 (Digital
arithmetic methods)",
classification = "723",
corpsource = "Department of Computer Sci., University of Keele,
Keele, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary multiplication; binary multiplier; computers,
digital; digital arithmetic; logic design;
multiplication; multiplying circuits; shift per cycle;
speed",
}
@Article{Paul:1976:SEF,
author = "George Paul and M. Wayne Wilson",
title = "Should the Elementary Function Library Be Incorporated
Into Computer Instruction Sets?",
journal = j-TOMS,
volume = "2",
number = "2",
pages = "132--142",
month = jun,
year = "1976",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355681.355684",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 00:30:21 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@PhdThesis{Pichat:1976:CEE,
author = "Mich{\`e}le Pichat",
title = "Contributions {\`a} l'{\`e}tude des erreurs d'arrondi
en arithm{\`e}tique {\`a} virgule flottante. ({French})
[Contributions to the error analysis of rounding errors
in floating-point arithmetic]",
type = "Th{\`e}se",
school = "Universit{\'e} de Grenoble 1",
address = "Grenoble, France",
year = "1976",
bibdate = "Thu May 27 07:44:27 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://tel.archives-ouvertes.fr/tel-00287209/",
acknowledgement = ack-nhfb,
language = "French",
}
@TechReport{Randell:1976:ODC,
author = "Brian Randell",
title = "The origins of digital computers: supplementary
bibliography to {``Origins of digital computers:
selected papers''}",
type = "Technical report",
number = "91",
institution = "Computing Laboratory, University of Newcastle upon
Tyne",
address = "Newcastle upon Tyne, UK",
pages = "3 + 37",
year = "1976",
LCCN = "Z5642.2 .R36 1979",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "electronic digital computers; history; calculators",
}
@Article{Rankin:1976:FPR,
author = "Roy Rankin and Steve Wozniak",
title = "Floating Point Routines for the 6502",
journal = j-DDJ,
volume = "1",
number = "??",
pages = "17--19",
month = aug,
year = "1976",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Sat Jan 15 06:04:06 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.6502.org/source/floats/wozfp1.txt",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "HP 2100; MOS Technology",
}
@Article{Riesel:1976:FPU,
author = "Zvi H. Riesel",
title = "The floating point unit of the {Golem B} computer",
journal = j-RADIO-ELECTRON-ENG,
volume = "46",
number = "7",
pages = "355--359",
month = jul,
year = "1976",
CODEN = "RDEEA4",
DOI = "https://doi.org/10.1049/ree.1976.0057",
ISSN = "0033-7722",
bibdate = "Fri Dec 03 15:11:57 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Golem B computer is a fast machine using
emitter-coupled logic and multi-layer circuits. The
autonomous floating point arithmetic unit obtains its
instructions and operands from buffers loaded ahead of
need. Its main part, for 56-bit fractions, uses two
4-operand adder complexes with stored carries. In
multiplication instructions, 4 bits of the multiplier
are used to form a new partial product in each pass
through an adder complex. Division instructions use a
base-4 non-restoring algorithm. Addition favours the
case of equal or nearly equal exponents, but 112 sum
bits are accumulated for all exponent differences. An
effort has been made to provide instructions and number
formats that will aid the writing of compilers and
operating systems.",
acknowledgement = ack-nhfb,
fjournal = "The Radio and Electronic Engineer",
keywords = "adder complex; autonomous floating point arithmetic
unit; buffers; division instructions; emitter coupled
logic; exponent differences; Golem B computer; multi
layer circuits; multiplication instructions; partial
product",
}
@Article{Ris:1976:UDF,
author = "Frederic N. Ris",
title = "A Unified Decimal Floating-Point Architecture For the
Support of High-Level Languages",
journal = j-SIGNUM,
volume = "11",
number = "3",
pages = "18--23",
month = oct,
year = "1976",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:03 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper summarizes a proposal for a decimal
floating-point arithmetic interface for the support of
high-level languages, consisting both of the arithmetic
operations observed by application programs and
facilities to produce subroutine libraries accessible
from these programs. What is not included here are the
detailed motivations, examinations of alternatives, and
implementation considerations which will appear in the
full work.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods); C6120 (File
organisation)C6140D (High level languages)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic operations; decimal floating point
arithmetic; digital arithmetic; high level languages;
one level store",
remark = "Normalized decimal floating-point arithmetic with a
fractional coefficient, three directed rounding modes,
and a trap mechanism. Three precisions are provided,
with up to 31 decimal digits, and an exponent range of
$ \pm 9999 $. Cowlishaw \cite{Cowlishaw:2003:DFP} says
that this is the first implementation of the Chen-Ho
\cite{Chen:1975:SER} compressed format, allowing
storage of 31 digits and 4 exponent digits in a 128-bit
value. More modern encodings get 34 digits in the same
number of bits, at somewhat reduced exponent range ($ [
- 6143, 6144] $).",
treatment = "P Practical; T Theoretical or Mathematical",
}
@TechReport{Rosser:1976:CRE,
author = "J. Barkley Rosser and J. Michael Yohe",
title = "Cancellation and Rounding Errors",
type = "Technical Summary Report",
number = "1588",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
month = apr,
year = "1976",
bibdate = "Sun Dec 30 21:30:27 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The fact that a calculating machine can usually hold
only an approximation to the number that one is
concerned with leads to cancellation errors and
rounding errors. These concepts are defined precisely
and examples are given. Suggestions are given for
reducing (when possible) the size of errors arising
from these two effects.",
acknowledgement = ack-nhfb,
}
@Article{Rowland:1976:BRB,
author = "John H. Rowland",
title = "Book Review: {{\booktitle{Floating-Point Computation}}
(Pat H. Sterbenz)}",
journal = j-SIAM-REVIEW,
volume = "18",
number = "1",
pages = "138--139",
month = "????",
year = "1976",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1018026",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:52:30 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/18/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1976",
}
@Article{Rudeanu:1976:SRF,
author = "S. Rudeanu",
title = "Square Roots and Functional Decompositions of
{Boolean} Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "5",
pages = "528--532",
month = may,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674641",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674641",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Sanderson:1976:PCT,
author = "James George Sanderson",
title = "A proof of convergence for the tridiagonal {QL}
algorithm in floating-point arithmetic",
type = "Thesis ({Ph.D.})",
school = "University of New Mexico",
address = "Albuquerque, NM, USA",
pages = "vi + 69",
year = "1976",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Arithmetic --- Foundations.",
}
@Article{Shi:1976:SLC,
author = "S.-Y. Shi",
title = "Shortcut to Logarithms Combines Table Lookup and
Computation",
journal = j-COMP-DESIGN,
volume = "15",
number = "5",
pages = "184--186",
month = may,
year = "1976",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Thu Sep 08 08:07:38 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@PhdThesis{Slekys:1976:DCN,
author = "Arunas George Slekys",
title = "Design of complex number digital arithmetic units
based on a modified bi-imaginary number system",
type = "{Ph.D. thesis}",
school = "University of California, Los Angeles",
address = "Los Angeles, CA, USA",
pages = "223",
year = "1976",
bibdate = "Sat Aug 22 09:03:47 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "ProQuest order number AAI7707685.",
}
@Book{Spaniol:1976:AR,
author = "Otto Spaniol",
title = "{Arithmetik in Rechenanlagen: Logik und Entwurf}
\toenglish {Computer Arithmetic: Logic and Design}
\endtoenglish",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
pages = "208",
year = "1976",
ISBN = "3-519-02332-6",
ISBN-13 = "978-3-519-02332-6",
LCCN = "QA76.6 .S66",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "For an English translation, see
\cite{Spaniol:1981:CAL}.",
price = "DM24.80",
acknowledgement = ack-nj,
}
@TechReport{Warren:1976:MDT,
author = "H. S. {Warren, Jr.} and A. S. Fox and P. W.
Markstein",
title = "Modulus Division on a Two's Complement Machine",
type = "Research Report",
number = "RC7712",
institution = "IBM",
address = "Yorktown Heights, NY, USA",
month = jun,
year = "1976",
bibdate = "Fri Nov 09 19:32:44 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxnote = "Check: Waser/Flynn book dates this as 1979.",
}
@Article{Wyatt:1976:PEP,
author = "W. T. {Wyatt Jr.} and D. W. Lozier and D. J. Orser",
title = "A Portable Extended Precision Arithmetic Package and
Library With {Fortran} Precompiler",
journal = j-TOMS,
volume = "2",
number = "3",
pages = "209--231",
month = sep,
year = "1976",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 12 08:07:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1976-2-3/p209-lozier/",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Yau:1976:DMA,
author = "S. S. Yau and J. Chung",
title = "On the Design of Modulo Arithmetic Units Based on
Cyclic Groups",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "11",
pages = "1057--1067",
month = nov,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674555",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674555",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Zohar:1976:RTR,
author = "S. Zohar",
title = "Rounding and Truncation in Radix (-2) Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-25",
number = "5",
pages = "464--469",
month = may,
year = "1976",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1976.1674634",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 12 06:24:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674634",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Agrawal:1977:CNB,
author = "D. P. Agrawal",
title = "Comments on {``A Note on Base-$2$ Arithmetic
Logic''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "5",
pages = "511--511",
month = may,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674869",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Yuen:1975:NBA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674869",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Albrecht:1977:GC,
author = "Rudolf Albrecht and Ulrich Kulisch",
title = "{Grundlagen der Computer-Arithmetik}",
publisher = "Springer-Verlag",
address = "Wien, Austria",
pages = "viii + 150",
year = "1977",
ISBN = "0-387-81410-8",
ISBN-13 = "978-0-387-81410-0",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Computing: Supplementum; 1 Computing
(Springer-Verlag). Supplementum; 1.",
acknowledgement = ack-nhfb,
keywords = "Algebra, Abstract.; Floating-point arithmetic.;
Mathematics --- Data processing.",
remark = "``Diese Artikel stellen eine Auswahl von Vortragen
dar, die auf einer vom 4. bis 8. August 1975 im
`Mathematischen Forschungsinstitut Oberwolfach'
stattgefundenen Tagung gehalten wurden.''",
}
@Book{Albrecht:1977:GCA,
editor = "R. Albrecht and U. Kulisch",
title = "{Grundlagen der Computer-Arithmetik} \toenglish
{Foundations of Computer Arithmetic} \endtoenglish",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 150",
year = "1977",
ISBN = "0-387-81410-8",
ISBN-13 = "978-0-387-81410-0",
LCCN = "QA162 .G78",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Diese Artikel stellen eine Auswahl von Vortragen dar,
die auf einer vom 4. bis 8. August 1975 im
`Mathematischen Forschungsinstitut Oberwolfach'
stattgefundenen Tagung gehalten wurden.",
acknowledgement = ack-nhfb,
}
@Article{Alexander:1977:SRR,
author = "V. L. Alexander",
title = "Square Root Routine",
journal = j-IBM-TDB,
volume = "20",
number = "3",
pages = "1222",
month = aug,
year = "1977",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Anonymous:1977:CAF,
author = "Anonymous",
title = "Computer Arithmetic: Foreword and Survey",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "609--609",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674892",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674892",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Manual{AppleComputer:1977:ARM,
author = "{Apple Computer, Inc}",
title = "{APPLESOFT} reference manual: extended precision
floating point {BASIC} language",
organization = "Apple Computer, Inc.",
address = "Cupertino, CA, USA",
pages = "75",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Apple computer --- Programming.; BASIC (Computer
program language) --- Programming.; Microcomputers ---
Programming.",
}
@Article{Barak:1977:MAT,
author = "A. B. Barak",
title = "Multiplicative Algorithms for Ternary Arithmetic Using
Binary Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "8",
pages = "823--826",
month = aug,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674922",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674922",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bauer:1977:CFP,
author = "Henry R. Bauer",
title = "Comments on {``On the Floating Point Representation of
Complex Numbers''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "2",
pages = "191--191",
month = feb,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.5009301",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Yuen:1975:FPR}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009301",
abstract = "A recent paper [Burroughs B7700 Information Processing
Systems Reference Manual, p. 2-9, 1973, Burroughs
Corporation] discussed an integrated notation for
complex numbers. A second choice of the radix point
position will increase the number of values near the
origin. An argument is also made for unnormalized
notation of both parts of a complex number.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bivins:1977:SAA,
author = "Robert L. Bivins and Nicholas C. Metropolis",
title = "Significance Arithmetic: Application to a Partial
Differential Equation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "639--642",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674896",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "http://dblp.uni-trier.de/db/journals/tc/tc26.html#BivinsM77;
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/iel5/12/35159/01674896.pdf?tp=&isnumber=35159&arnumber=1674896&punumber=12",
ZMnumber = "0405.65056",
abstract = "The methods of significance arithmetic are applied to
the numerical solution of a nonlinear
partial-differential equation. Our approach permits the
use of initial values having imprecision considerably
greater than that of rounding error; moreover, the
intermediate and final quantities are monitored so that
at any stage the precision of such quantities is
available. An algorithm is found that represents
faithfully the solution to a difference-equation
approximation to Burgers' equation.",
acknowledgement = ack-jr,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bohlender:1977:FPC,
author = "Gerd Bohlender",
title = "Floating-Point Computation of Functions with Maximum
Accuracy",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "621--632",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674894",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65D15 (68A99)",
MRnumber = "56 9908",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "accurate floating-point summation",
reviewer = "Bernard H. Rosman",
}
@MastersThesis{Brinkmann:1977:FPT,
author = "Hubert Eldie Brinkmann",
title = "A floating-point processor for the {Texas Instruments}
model {980A} computer",
type = "Electrical Engineering Thesis ({M.S.})",
publisher = "Brinkmann",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "x + 68",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors.; Microprogramming.; Miniature
computers --- Programming.",
}
@InProceedings{Brown:1977:MSI,
author = "W. S. Brown",
title = "A realistic model of floating-point computation",
crossref = "Rice:1977:MSI",
number = "39",
pages = "343--360",
year = "1977",
DOI = "https://doi.org/10.1016/B978-0-12-587260-7.50017-0",
MRclass = "68A05",
MRnumber = "58 3605",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
URL = "https://www.sciencedirect.com/science/article/abs/pii/B9780125872607500170",
acknowledgement = ack-nhfb,
reviewer = "Costica Cazacu",
}
@Article{Collins:1977:APS,
author = "George E. Collins and David R. Musser",
title = "Analysis of the {Pope--Stein} Division Algorithm",
journal = j-INFO-PROC-LETT,
volume = "6",
number = "5",
pages = "151--155",
day = "??",
month = oct,
year = "1977",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/0020-0190(77)90012-6",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Tue Nov 17 10:49:43 MST 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classification = "C4240 (Programming and algorithm theory)",
corpsource = "Computer Sci. Dept., University of Wisconsin, Madison,
WI, USA",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190/",
keywords = "algorithm; algorithm theory; digital arithmetic;
integer division; multiple precision integer division;
trial quotient digits",
treatment = "T Theoretical or Mathematical",
}
@Article{Colquhoun:1977:FAS,
author = "D. G. Colquhoun",
title = "A Fast Approximation to the Sine Function",
journal = j-SPE,
volume = "7",
number = "2",
pages = "227--229",
month = mar # "--" # apr,
year = "1977",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Fri Dec 08 13:06:08 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Book{DEC:1977:VAH,
author = "{Digital Equipment Corporation}",
title = "{VAX-11}\slash 780 Architecture Handbook",
publisher = pub-DP,
address = pub-DP:adr,
pages = "328",
year = "1977",
LCCN = "QA76.8 .V12D5 B 2 829 348",
bibdate = "Thu Sep 15 18:50:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@InProceedings{Dekker:1977:MRR,
author = "T. J. Dekker",
title = "Machine Requirements for Reliable Portable Software",
crossref = "Cowell:1977:PMS",
pages = "22--36",
year = "1977",
bibdate = "Wed Nov 07 08:38:01 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Derenzo:1977:AHC,
author = "Stephen E. Derenzo",
title = "Approximations for Hand Calculators Using Small
Integer Coefficients",
journal = j-MATH-COMPUT,
volume = "31",
number = "137",
pages = "214--222",
month = jan,
year = "1977",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb # " and " # ack-nj,
ajournal = "Math. Comput.",
classcodes = "B0290D (Functional analysis); B0290F (Interpolation
and function approximation); C4120 (Functional
analysis); C4130 (Interpolation and function
approximation); C7310 (Mathematics computing)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximations; function approximation; function
evaluation; hand calculators; programmable calculators;
small integer coefficients",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Egbert:1977:PCAa,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {I}: Square Roots",
journal = j-HEWLETT-PACKARD-J,
volume = "28",
number = "9",
pages = "22--24",
month = may,
year = "1977",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C5420 (Mainframes and minicomputers); C7310
(Mathematics computing)",
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
keywords = "electronic calculators; HP personal calculator; square
root algorithm",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Egbert:1977:PCAb,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {II}: Trigonometric
Functions",
journal = j-HEWLETT-PACKARD-J,
volume = "28",
number = "10",
pages = "17--20",
month = jun,
year = "1977",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
}
@Article{Egbert:1977:PCAc,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {III}: Inverse
Trigonometric Functions",
journal = j-HEWLETT-PACKARD-J,
volume = "29",
number = "3",
pages = "22--23",
month = nov,
year = "1977",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
}
@Article{Ercegovac:1977:GHO,
author = "Milo{\v{s}} D. Ercegovac",
title = "A General Hardware-Oriented Method for Evaluation of
Functions and Computations in a Digital Computer",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "667--680",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674900",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674900",
abstract = "A parallel computational method, amenable for
efficient hardware-level implementation, is described.
It provides a simple and fast algorithm for the
evaluation of polynomials, certain rational functions
and arithmetic expressions, solving a class of systems
of linear equations, or performing the basic arithmetic
operations in a fixed-point number representation
system. The time required to perform the computation is
of the order of $m$ carry-free addition operations, $m$
being the number of digits in the solution. In
particular, the method is suitable for fast evaluation
of mathematical functions in hardware.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Arithmetic expressions; digital computer arithmetic;
E-method; evaluation of real-valued functions;
fixed-point representation; hardware-level
implementation; integral powers; linear systems;
on-line algorithms; parallel computation; polynomials;
rational functions; redundant number systems",
}
@Article{Evans:1977:AAT,
author = "Gillian R. Evans",
title = "From abacus to algorism: Theory and practice in
medieval arithmetic",
journal = j-BRITISH-J-HIST-SCI,
volume = "10",
number = "2",
pages = "114--131",
month = jul,
year = "1977",
CODEN = "BJHSAT",
DOI = "https://doi.org/10.1017/S0007087400015375",
ISSN = "0007-0874 (print), 1474-001X (electronic)",
ISSN-L = "0007-0874",
MRclass = "01A35 (Mathematics in the medieval)",
MRnumber = "522510 (80e:01006)",
MRreviewer = "M. Folkerts",
bibdate = "Thu Sep 23 07:34:43 MDT 2010",
bibsource = "http://journals.cambridge.org/action/displayJournal?jid=BJH;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
URL = "http://www.jstor.org/stable/4025865",
ZMnumber = "0358.01003",
abstract = "This paper deals primarily with the change in
practical procedures of calculation which took place
during the course of the twelfth century in Western
Europe. At the beginning of the period, the abacus was
in relatively common use; towards the end, it was being
superseded by the method of calculation which was known
as the algorism. Certain differences of theory are
apparent. Among the textbooks which were most
influential in bringing about the change was
Sacrobosco's Algorithmus Vulgaris. Authors of both
abacus and algorism treatises give an account of
number-symbols and discuss elementary number theory
briefly, but the algorism treatise show how much more
confident the authors were in using Arabic numerals.
The algorisms employ a symbol for zero; although it has
antecedents in some abacus treatises, its usefulness
was clearly not fully perceived by the authors, because
the columns of the abacus made it unnecessary to use a
counter to indicate that the number under consideration
was, for example, 306, not 36. The algorisms deal with
a far wider range of operations; while the abacus
treatises confine themselves to multiplication and
division of whole numbers and fractions, the algorisms
have addition, subtraction, doubling, halving,
multiplication, division, the extraction of roots and
progression, as well as numeration. Changes in
technical terminology are discussed. There are two
appendices, one dealing with the compilation of
arithmetical texts in Bodleian Library Oxford,
MS.~Laud.~Misc.~644, and the other on the arithmetical
sense of the term equipollentia, which was a technical
term of dialectic.",
acknowledgement = ack-nhfb,
fjournal = "British Journal for the History of Science",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BJH",
ZMreviewer = "Gillian R. Evans",
}
@Article{Feldman:1977:EEA,
author = "Michael B. Feldman",
title = "Embedding extended arithmetic in {SNOBOL4}",
journal = j-SIGPLAN,
volume = "12",
number = "1",
pages = "67--72",
month = jan,
year = "1977",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:13:59 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
corpsource = "George Washington University, Washington, DC, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "complex numbers; data structure; data structures;
digital arithmetic; embedded; extended arithmetic;
procedure oriented languages; rotational numbers;
SNOBOL4",
treatment = "P Practical",
}
@Book{Forsythe:1977:CMM,
author = "George E. (George Elmer) Forsythe and Michael A.
Malcolm and Cleve B. Moler",
title = "Computer Methods for Mathematical Computations",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xi + 259",
year = "1977",
ISBN = "0-13-165332-6",
ISBN-13 = "978-0-13-165332-0",
LCCN = "QA297 .F5681",
MRclass = "65-01",
MRnumber = "MR0458783 (56 \#16983)",
MRreviewer = "Sven-{\AA}ke Gustafson",
bibdate = "Tue May 25 09:01:08 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from
\path=math.liu.se= in \path=pub/references=",
price = "US\$16.95",
series = "Prentice-Hall series in automatic computation",
ZMnumber = "0361.65002",
acknowledgement = ack-nhfb,
classmath = "*65-01 Textbooks (numerical analysis) 68-01 Textbooks
(computer science)",
keywords = "Fortran (computer program language); numerical
analysis -- data processing",
remark = "Subroutines and exercises for the computer solution of
problems involving matrices, integrals, differential
equations, spline functions, zeros and extrema of
functions, least squares, and Monte Carlo techniques.",
subject = "Numerical analysis; Data processing; Computer
programs; Problems, exercises, etc; FORTRAN (Computer
program language)",
tableofcontents = "Introduction \\
Floating-point computation \\
Linear systems of equations \\
Interpolation \\
Numerical integration \\
Initial value problems in ordinary differential
equations \\
Solution of nonlinear equations \\
Optimization \\
Least squares and the singular value decomposition \\
Random number generation and Monte Carlo methods",
}
@TechReport{Frenckner:1977:MFP,
author = "K. Frenckner and M. Persson and S. Romberger and Y.
Sundblad",
title = "Microprogrammed floating-point arithmetic for the
{Varian-73} computer",
type = "Technical report",
number = "TRITA-NA-7702",
institution = "Kungl. Tekniska H{\"o}gskolan",
address = "Stockholm, Sweden",
pages = "37",
month = jun,
year = "1977",
bibdate = "Fri May 25 05:52:09 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0028467",
acknowledgement = ack-nhfb,
}
@TechReport{Ginsberg:1977:NID,
author = "Myron Ginsberg",
title = "Numerical influences on the design of floating-point
arithmetic for microcomputers",
type = "Technical report",
number = "CS 7708",
institution = "Department of Computer Science, Southern Methodist
University",
address = "Dallas, TX, USA",
pages = "72",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic --- Data processing.",
}
@TechReport{Goldsmith:1977:ICF,
author = "Theodore C. Goldsmith",
title = "An integrated circuit floating point accumulator",
type = "{NASA} technical note",
number = "NASA TN D-8509 NASA",
institution = "National Aeronautics and Space Administration; for
sale by the National Technical Information Service",
address = "Washington, DC, USA",
pages = "26",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.14:D-8509",
remark = "Issued June 1977.",
}
@Article{Goodman:1977:EGD,
author = "R. Goodman and A. Feldstein",
title = "Effect of Guard Digits and Normalization Options on
Floating Point Multiplication",
journal = j-COMPUTING,
volume = "18",
number = "2",
pages = "93--106",
month = "????",
year = "1977",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "55 11596",
bibdate = "Fri Dec 08 12:02:42 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "N. N. Abdelmalek",
}
@Article{Goodwin:1977:CUO,
author = "D. T. Goodwin",
title = "Conditions for Underflow and Overflow of an Arithmetic
Stack",
journal = j-COMP-J,
volume = "20",
number = "1",
pages = "56--62",
month = feb,
year = "1977",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/20.1.56",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:59 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/20/1.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/20/1/56.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/56.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/57.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/58.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/59.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/60.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/61.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/62.tif",
acknowledgement = ack-nhfb,
classcodes = "C4210 (Formal logic)",
classification = "721; 723",
corpsource = "Department of Computer Sci., University of Keele,
Keele, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arbitrary string; arithmetic stack; automata theory
--- Context Free Languages; behaviour; computer
metatheory; computer operating systems --- Program
Compilers; context free language; context-free
languages; loading; overflow; underflow",
treatment = "T Theoretical or Mathematical",
}
@Article{Gregory:1977:BCR,
author = "Robert Todd Gregory and David W. Matula",
title = "Base conversion in residue number systems",
journal = j-BIT,
volume = "17",
number = "3",
pages = "286--302",
month = sep,
year = "1977",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932149",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "10A30 (68A10)",
MRnumber = "MR0476627 (57 \#16186)",
MRreviewer = "L. Carlitz",
bibdate = "Wed Jan 4 18:52:15 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=17&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=17&issue=3&spage=286",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Interval arithmetic; residue arithmetic",
}
@Article{Hashizume:1977:FPA,
author = "B. Hashizume",
title = "Floating Point Arithmetic",
journal = j-BYTE,
volume = "2",
number = "11",
pages = "76--78, 180--188",
month = nov,
year = "1977",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Hastings:1977:FPH,
author = "Jordan Towner Hastings",
title = "Floating point half-word packing for {Control Data
Corporation 6000/7000 series} hardware",
journal = j-SPE,
volume = "7",
number = "1",
pages = "146--147",
month = jan,
year = "1977",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380070111",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "27 Oct 2006",
}
@PhdThesis{Hough:1977:EAI,
author = "David Granville Hough",
title = "Explaining and ameliorating the ill-condition of zeros
of polynomials",
type = "{Ph.D.} Thesis",
school = "Electronics Research Lab., University of California,
Berkeley",
address = "Berkeley, CA, USA",
pages = "303",
month = feb,
year = "1977",
bibdate = "Thu Jan 12 09:05:57 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://wwwlib.umi.com/dissertations/fullcit/7731401",
acknowledgement = ack-nhfb,
}
@Article{Jenkins:1977:URN,
author = "W. Jenkins and B. Leon",
title = "The use of residue number systems in the design of
finite impulse response digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "24",
number = "4",
pages = "191--201",
month = apr,
year = "1977",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/PGEC.1967.264810",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23467",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "A technique is presented for implementing a finite
impulse response (FIR) digital filter in a residue
number system (RNS). For many years residue number
coding has been recognized as a system which provides a
capability for the implementation of \ldots{}",
}
@InProceedings{Jullien:1977:HRD,
author = "G. Jullien and W. Miller and J. Soltis and A.
Baraniecka and B. Tseng",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '77}",
title = "Hardware realization of digital signal processing
elements using the residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "506--510",
year = "1977",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19770117",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In the past, hardware realization of digital signal
processing elements have been based upon binary
arithmetic concepts. Because of the dependence between
digits in binary arithmetic operations, the hardware
required to construct arithmetic elements \ldots{}",
}
@TechReport{Kahan:1977:CYC,
author = "W. M. Kahan and B. N. Parlett",
title = "Can You Count on Your Calculator?",
type = "Memorandum",
number = "UCB/ERL M77/21",
institution = "Electronics Research Laboratory, College of
Engineering, University of California, Berkeley",
address = "Berkeley, CA, USA",
pages = "ii + 28",
day = "6",
month = apr,
year = "1977",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "German Transl. Published In: Jahrbuch {\"U}berblicke
Mathematik 1978, Ed. by B. Fuchssteiner and others,
Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich,
199--216, 1978",
URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-jr,
}
@Article{Kent:1977:HSF,
author = "J. G. Kent",
title = "Highlights of a Study of Floating-Point Instructions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "660--666",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674899",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The research work that this paper is based on resulted
in the development of tools for the theoretical
definition, analysis and comparison of floating-point
instructions as mathematical mappings. These tools can
be used to study the properties of most floating-point
instructions and their operands.",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kent:1977:HST,
author = "S. A. Kent",
title = "A High-Speed Threshold Gate Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "12",
pages = "1279--1283",
month = dec,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674790",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674790",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kornerup:1977:UNR,
author = "P. Kornerup and B. D. Shriver",
title = "A Unified Numeric Representation Arithmetic Unit and
Its Language Support",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "651--659",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674898",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674898",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Krishnamurthy:1977:MPU,
author = "E. V. Krishnamurthy",
title = "Matrix Processors Using $p$-adic Arithmetic for Exact
Linear Computations",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "633--639",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674895",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674895",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kuck:1977:ARM,
author = "David J. Kuck and Douglass S. {Parker Jr.} and Ahmed
H. Sameh",
title = "Analysis of Rounding Methods in Floating-Point
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "643--650",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674897",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65G05",
MRnumber = "57 7979",
bibdate = "Fri Dec 08 12:00:49 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
reviewer = "V. V. Ivanov",
}
@Article{Kulisch:1977:MFC,
author = "Ulrich Kulisch",
title = "Mathematical foundations of computer arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "610--620",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674893",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat May 18 14:33:16 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lee:1977:FNS,
author = "S. C. Lee and A. D. Edgar",
title = "The {Focus} Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "11",
pages = "1167--1170",
month = nov,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674770",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See comments
\cite{Lee:1979:AFN,Swartzlander:1979:CFN}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674770",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ligomenides:1977:SSF,
author = "P. A. Ligomenides",
title = "The Skip-and-Set Fast-Division Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "10",
pages = "1030--1032",
month = oct,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674740",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 10:17:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674740",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Luke:1977:ACM,
author = "Yudell L. Luke",
title = "Algorithms for the Computation of Mathematical
Functions",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiii + 284",
year = "1977",
ISBN = "0-12-459940-0",
ISBN-13 = "978-0-12-459940-6",
LCCN = "QA351 .L7961",
bibdate = "Wed Dec 15 10:38:19 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / xi \\
1: Basic Formulas / 1 \\
1.1 Introduction / 1 \\
1.2 The Generalized Hypergeometric Function and the
$G$-Function / 1 \\
1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1,
q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev
Polynomials of the First Kind / 4 \\
1.4 Efficient Evaluation of Series of Chebyshev
Polynomials / 17 \\
1.5 Rational Approximations for Generalized
Hypergeometric Functions / 20 \\
1.6 The Pad{\'e} Table / 27 \\
1.7 Computations of and Checks on Coefficients and
Tables / 29 \\
1.8 Tables of the Functions $e^{-\zeta}$, and
$e^{-\xi}$ / 35 \\
2: Identification of Functions / 41 \\
2.1 Introduction / 41 \\
2.2 The Generalized Hypergeometric Function $_pF_q(z)$
/ 41 \\
2.3 The G-Function / 47 \\
2.4 Miscellaneous Functions / 48 \\
3: General Remarks on the Algorithms and Programs / 49
\\
3.1 Introduction / 49 \\
3.2 Precision and Complex Arithmetic / 49 \\
4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\
5: Coefficients for the Expansion of the Confluent
Hypergeometric Function $_1F_1(a;c;z)$ in Ascending
Series of Chebyshev Polynomials / 70 \\
6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\
7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$
in Ascending Series of Chebyshev Polynomials / 82 \\
8: Coefficients for the Expansion of the Confluent
Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$
in Descending Series of Chebyshev Polynomials / 88 \\
9: Coefficients for the Expansion of the Functions
$G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$,
in Descending Series of Chebyshev Polynomials / 101 \\
10: Differential and Integral Properties of Expansions
in Series of Chebyshev Polynomials of the First Kind /
116 \\
11: Expansion of Exponential Type Integrals in Series
of Chebyshev Polynomials of the First Kind / 126 \\
11.1 Introduction / 126 \\
11.2 The Representation for $g(x)$ / 127 \\
11.3 The Representation for $G(x)$ / 129 \\
11.4 Exponential Type Integrals Involving Logarithms /
133 \\
11.5 Numerical Examples / 135 \\
11.6 Errata / 139 \\
12: Conversion of a Power Series into a Series of
Chebyshev Polynomials of the First Kind / 154 \\
13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159
\\
14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174
\\
15: Rational Approximations for $_1F_1(a;c;-z)$ / 182
\\
16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192
\\
17: Rational Approximations for Bessel Functions of the
First Kind / 203 \\
18: Pad{\'e} Approximations for $I_{\nu +
1}(z)/I_\nu(z)$ / 220 \\
19: Evaluation of Bessel Functions of the First Kind by
Use of the Backward Recurrence Formula \\
19.1 Introduction / 230 \\
19.2 Backward Recurrence Schemata for $I_\nu(z)$ and
$J_\nu(z)$ / 230 \\
19.3 Numerical Examples / 240 \\
19.4 Mathematical Description of Programs / 243 \\
19.4.1 Evaluation of Functions Related to $I_{m +
\nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\
19.4.2 Evaluation of Functions Related to $e^{-l}I_{m +
\nu}(z)$ / 245 \\
20: Rational Approximations for $z^aU(a;1 + a - b;z)$ /
252 \\
21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265
\\
Appendices \\
Bibliography / 280 \\
Notation Index / 281 \\
Subject Index / 283",
wrongisbn = "0-12-459940-6",
}
@TechReport{Maag:1977:SRE,
author = "Werner Maag and Rudolf Wehrli",
title = "Survey on rounding effects in floating-point
arithmetic",
type = "Report",
institution = "CM Sch{\"a}nis AG",
address = "Sch{\"a}nis, Switzerland",
pages = "73",
year = "1977",
bibdate = "Thu May 09 09:10:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Merzbach:1977:GSF,
author = "Uta C. Merzbach",
title = "{Georg Scheutz} and the first printing calculator",
volume = "36",
publisher = "Smithsonian Institution Press",
address = "Washington, DC, USA",
pages = "iii + 74",
year = "1977",
LCCN = "QA75 .M46",
bibdate = "Mon Jan 21 21:21:54 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Smithsonian studies in history and technology",
acknowledgement = ack-nhfb,
subject = "Calculators; History; Scheutz, George",
subject-dates = "1785--1873",
}
@InCollection{Metropolis:1977:MSA,
author = "N. Metropolis",
title = "Methods of significance arithmetic",
crossref = "Jacobs:1977:SAN",
pages = "179--192",
year = "1977",
MRclass = "65G05 (68A99)",
MRnumber = "MR0451673 (56 \#9955)",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Thu Nov 8 14:50:25 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Metropolis:1977:SAP,
author = "N. Metropolis and Stephen M. Tanny",
title = "Significance arithmetic: the probability of carrying",
journal = j-COMPUT-MATH-APPL,
volume = "3",
number = "1",
pages = "77--81",
year = "1977",
CODEN = "CMAPDK",
ISSN = "0886-9561",
ISSN-L = "0898-1221",
MRclass = "65G05 (10A30 65C10)",
MRnumber = "MR0458846 (56 \#17046)",
MRreviewer = "Artenio De Matteis",
bibdate = "Thu Nov 8 14:50:26 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0371.60015",
abstract = "This article develops a number of probabilistic
results related to a combinatorial representation of
the real number system. This representation employs an
algorithmic definition of the arithmetic operations
analogous to that used by a computer. A carry function
for each place is defined and the distribution of these
functions is characterized in terms of classical
combinatorial polynomials",
acknowledgement = ack-nhfb,
fjournal = "Computers \& Mathematics with Applications. An
International Journal. Part B",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Mitra:1977:CDI,
author = "Debasis Mitra",
title = "Criteria for Determining if a High-Order Digital
Filter Using Saturation Arithmetic is Free of Overflow
Oscillations",
journal = j-BELL-SYST-TECH-J,
volume = "56",
number = "9",
pages = "1679--1699",
month = nov,
year = "1977",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:56 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1977/BSTJ.1977.5609.html;
http://www.alcatel-lucent.com/bstj/vol56-1977/bstj-vol56-issue09.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol56/bstj56-9-1679.pdf;
http://www.alcatel-lucent.com/bstj/vol56-1977/articles/bstj56-9-1679.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Ninke:1977:SRB,
author = "W. H. Ninke and G. R. Ritchie",
title = "Shift Register Binary Rate Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "3",
pages = "276--278",
month = mar,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674819",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674819",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Oliver:1977:EAM,
author = "J. Oliver",
title = "An Error Analysis of the Modified {Clenshaw} Method
for Evaluating {Chebyshev} and {Fourier} Series",
journal = j-J-INST-MATH-APPL,
volume = "20",
number = "3",
pages = "379--391",
year = "1977",
CODEN = "JMTAA8",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65G05 (41A50)",
MRnumber = "57 #4508",
MRreviewer = "David L. Elliott",
bibdate = "Fri Apr 5 07:38:01 MST 2002",
bibsource = "https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
ZMnumber = "0397.65013",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
xxtitle = "An error analysis of the modified {Clenshaw} methods
for evaluating {Chebyshev} and {Fourier} series",
}
@Article{Oliver:1977:SRE,
author = "J. Oliver",
title = "On the sensitivity to rounding errors of {Chebyshev}
series approximations",
journal = j-J-COMPUT-APPL-MATH,
volume = "3",
number = "2",
pages = "89--98",
month = jun,
year = "1977",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X77900031",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Palmer:1977:ISF,
author = "J. Palmer",
title = "The {Intel} Standard for Floating Point Arithmetic",
crossref = "IEEE:1977:ICS",
pages = "107--112",
year = "1977",
bibdate = "Fri Nov 09 19:09:10 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Papantoni-Kazakos:1977:CRE,
author = "P. Papantoni-Kazakos",
title = "Consideration of round off errors in the design of
mean square estimators",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "22",
number = "2",
pages = "276--279",
month = apr,
year = "1977",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "In this correspondence, a search for the optimal
polynomial mean-square (ms) estimator is undertaken;
when the input is a vector with fixed dimensionality
and at the calculation of the estimator characteristics
the round off errors are considered. \ldots{}",
}
@Article{Randell:1977:CGC,
author = "B. Randell",
title = "{Colossus}: Godfather of the Computer",
journal = j-NEW-SCIENTIST,
volume = "73",
number = "1038",
pages = "346--348",
day = "10",
month = feb,
year = "1977",
CODEN = "NWSCAL",
ISSN = "0262-4079, 0028-6664",
ISSN-L = "0262-4079",
bibdate = "Wed Oct 13 11:51:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[\S 7.5]{Randell:1982:ODC}.",
acknowledgement = ack-nhfb,
fjournal = "New Scientist",
journal-URL = "http://www.sciencedirect.com/science/journal/02624079",
}
@Article{Reimer:1977:AFO,
author = "M. Reimer",
title = "{Auswertungsalgorithmen fast-optimaler numerischer
Stabilit{\"a}t f{\"u}r Polynome} \toenglish {Algorithms
of Near-optimal Numerical Stability for the Evaluation
of Polynomials} \endtoenglish",
journal = j-COMPUTING,
volume = "17",
number = "4",
pages = "289--296",
month = "????",
year = "1977",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Ris:1977:UDF,
author = "Frederic N. Ris",
title = "A unified decimal floating-point architecture for the
support of high-level languages",
journal = j-SIGPLAN,
volume = "12",
number = "9",
pages = "60--70",
month = sep,
year = "1977",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:14:09 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "architecture; decimal floating-point arithmetic;
digital arithmetic; high level languages; procedure
oriented languages; unified",
treatment = "P Practical",
}
@Article{Rjabko:1977:AHM,
author = "B. Ja. Rjabko",
title = "An analogue of {Haffmen}'s method for the optimal
summation of floating point numbers. ({Russian})",
journal = "Diskret. Analiz",
volume = "30",
pages = "38--45, 77",
year = "1977",
MRclass = "68C05 (68E99)",
MRnumber = "80c:68023",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
reviewer = "Vladimir Sleinikov",
xxjournal = "Metody Diskret. Anal. v Reshenii Kombinatornykh
Zadach",
}
@Article{Sanyal:1977:AND,
author = "S. Sanyal",
title = "An algorithm for nonrestoring division",
journal = j-COMP-DESIGN,
volume = "16",
number = "5",
pages = "124--127",
month = may,
year = "1977",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@MastersThesis{Simmons:1977:SRA,
author = "David Michael Simmons",
title = "Signal-to-noise ration analysis of block floating
point {FFTS}",
type = "Electrical Engineering Thesis ({M.S.})",
school = "University of Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "114",
year = "1977",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Soderstrand:1977:HSL,
author = "M. A. Soderstrand",
title = "A high-speed low-cost recursive digital filter using
residue number arithmetic",
journal = j-PROC-IEEE,
volume = "65",
number = "7",
pages = "1065--1067",
month = jul,
year = "1977",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1109/PGEC.1967.264810",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31255",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "residue arithmetic; residue number system",
summary = "Use of table look-up multiplication by fractional
coefficients allows implementation of high-speed,
low-cost recursive digital filters using residue number
arithmetic. An 8-bit equivalent filter based on the
lossless discrete integrator (LDI) \ldots{}",
}
@Article{Soderstrand:1977:MRN,
author = "M. A. Soderstrand and E. L. Fields",
title = "Multipliers for residue-number-arithmetic digital
filters",
journal = j-ELECT-LETTERS,
volume = "13",
number = "6",
pages = "164--166",
day = "17",
month = mar,
year = "1977",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19770117",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4249252",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A recently proposed residue-number-arithmetic digital
filter offers major cost and speed advantages over
binary-arithmetic digital filters, but suffers one
major drawback. The filter coefficients must be
constant, since the lack of a fast method of \ldots{}",
}
@Article{Steer:1977:DHS,
author = "D. G. Steer and S. R. Penstone",
title = "Digital Hardware for Sine-Cosine Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "12",
pages = "1283--1286",
month = dec,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674791",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Stenzel:1977:CHS,
author = "W. J. Stenzel",
title = "A Compact High-Spped Multiplication Scheme",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "10",
pages = "948--957",
month = oct,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674730",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:20:56 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Stoutemyer:1977:AEA,
author = "David R. Stoutemyer",
title = "Automatic Error Analysis Using Computer Algebraic
Manipulation",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "26--43",
month = mar,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355719.355721",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Sep 02 22:30:11 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper shows how the inherent error and the
fixed-point or floating-point roundoff of chopoff error
of an expression can be determined automatically using
a computer algebra language such as {REDUCE}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Thong:1977:ARE,
author = "Tran Thong and Bede Liu",
title = "Accumulation of roundoff errors in floating point
{FFT}",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "24",
number = "3",
pages = "132--143",
month = mar,
year = "1977",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
MRclass = "65G05",
MRnumber = "55 1722",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
reviewer = "Sven-{\AA}ke Gustafson",
summary = "A statistical model for roundoff error is used to
predict the output noise to signal ratio of the two
common FFT algorithms, the decimation in time and the
decimation in frequency algorithms. A unified approach
is used to obtain the error in both algorithms
\ldots{}",
}
@Article{Tran-Thong:1977:FPF,
author = "Tr{\^a}{\`n}-Th{\^o}{\'n}g and Bede Liu",
title = "Floating Point Fast {Fourier} Transform Computation
Using Double Precision Floating Point Accumulators",
journal = j-TOMS,
volume = "3",
number = "1",
pages = "54--59",
month = mar,
year = "1977",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355719.355723",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65T05",
MRnumber = "55 \#11658",
bibdate = "Sat Aug 27 22:12:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Most commonly available fast Fourier transform (FFT)
subroutines use single precision chopping arithmetic,
and the resulting normalized roundoff error, in
computing an $N$-point transform with $ N = \prod_{i =
1}^M a_i $ is $ O(M^2) $. This paper proposes a
modification of these subroutines for use on computers
with a hardwired double precision arithmetic unit. The
resulting normalized roundoff error is $ O(M) $ and is
independent of the $ a_i $. The modification leads to a
negligible increase in storage. For most computers, the
increase in the execution time is small. For certain
computers, such as IBM System/360 models 91 and 195,
the modification can result in a decrease in the
execution time.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "computer arithmetic; double-length summation; fast
Fourier transform; roundoff error",
}
@Article{Trivedi:1977:LAD,
author = "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
title = "On-line algorithms for division and multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "681--687",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674901",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 30 07:29:16 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Trivedi:1977:UCF,
author = "K. S. Trivedi",
title = "On the Use of Continued Fractions for Digital Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "7",
pages = "700--704",
month = jul,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674903",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See corrections \cite{Trivedi:1978:CUC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674903",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ushijima:1977:SEP,
author = "Kazuo Ushijima",
title = "Step to an Efficient Program for Floating-point
Summation",
journal = j-SPE,
volume = "7",
number = "6",
pages = "759--769",
month = nov # "\slash " # dec,
year = "1977",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Williams:1977:SIA,
author = "R. P. Williams",
title = "Serial Integer Arithmetic with Magnetic Bubbles",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "3",
pages = "260--264",
month = mar,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674814",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 21:56:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674814",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wozniakowski:1977:NSC,
author = "H. Wo{\'z}niakowski",
title = "Numerical Stability of the {Chebyshev} Method for the
Solution of Large Linear Systems",
journal = j-NUM-MATH,
volume = "28",
number = "2",
pages = "191--209",
year = "1977",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4110 (Error analysis in numerical methods); C4140
(Linear algebra)",
corpsource = "Department of Computer Sci., Carnegie-Mellon
University, Pittsburgh, PA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Chebyshev approximation; Chebyshev method; computed
residuals; error analysis; floating point arithmetic;
iterative methods; large linear systems; linear
systems; numerical stability; rounding error analysis",
treatment = "T Theoretical or Mathematical",
}
@Article{Yuen:1977:NRD,
author = "C. K. Yuen",
title = "A New Representation for Decimal Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-26",
number = "12",
pages = "1286--1288",
month = dec,
year = "1977",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1977.1674792",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 07 18:00:38 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A new representation for decimal numbers is proposed.
It uses a mixture of positive and negative radixes to
ensure that the maximum value of a four bit decimal
digit is 9. This eliminates the more complex carry
generation process required in BCD addition.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal arithmetic",
}
@InProceedings{Abu-El-Haija:1978:AER,
author = "A. Abu-El-Haija and A. Peterson",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '78}",
title = "An approach to eliminate roundoff errors in digital
filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "75--78",
year = "1978",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Roundoff noise and limit cycle oscillations due to
postmultiplication rounding can seriously limit the
application of recursive digital filters in practice,
particularly for poles near the unit circle or near z =
+1. Rounding is usually performed by \ldots{}",
}
@InProceedings{Agrawal:1978:AIR,
author = "Dharma P. Agrawal",
title = "On Arithmetic Inter-relationships and Hardware
Interchangeability of Negabinary and Binary Systems",
crossref = "IEEE:1978:PSC",
pages = "88--96",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal.pdf",
abstract = "Recent use of the negabinary system in the application
oriented digital hardware, has encouraged the search
for suitable arithmetic algorithms in $ - 2 $ base.
These algorithms have been directly utilized in
designing logic circuits and several logic
implementations have been reported in the literature.
The main objective of this paper is to show the close
relationship between $ + 2 $ base addition and $ - 2 $
base negative addition. Two possible ways of utilizing
binary adders for performing negabinary addition and
their underlying theories are presented. Two similar
techniques of using negabinary adders for binary
addition are also considered in detail. An interesting
aspect of this investigation about negabinary base is
that negative addition (rather than just addition)
seems to be the primitive operation from logic
complexity and interchangeability of $ + 2 $ and $ - 2
$ adders point of view.\par
The technique of adding two numbers in one system by
the adders of the other system is extended here for
multiple operand addition. This requires inclusion of
an additional correction factor. Further, the additive
algorithms of this work lead to four simple conversion
processes of number from one system to another. This
paper seems to be a realistic step towards the use of
similar hardware for $ + 2 $ and $ - 2 $ bases and
hence this allows an instantaneous flexibility on the
selection of number system. It is believed that this
paper will attract more attention on the use of $ - 2 $
base system for the design of special purpose digital
machines and process controllers.",
acknowledgement = ack-nhfb,
keywords = "Addition; ARITH-4; base conversion; binary numbers;
even positioned bits; multiple addition; negabinary
system; negative addition; negative radix; odd
positioned bits.",
}
@InProceedings{Agrawal:1978:MAL,
author = "Dharma P. Agrawal and T. R. N. Rao",
title = "On Modular $ (2^n + 1) $ Arithmetic Logic",
crossref = "IEEE:1978:PSC",
pages = "104--108",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal_Rao.pdf",
abstract = "A novel format for representing modulo $ (2^n + 1) $
numbers, is shown to be helpful in achieving modular
addition and complementation. Logic for fast addition
using carry-look-ahead and modular complementation is
also presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Article{Andrews:1978:EFM,
author = "M. Andrews and S. F. McCormick and G. D. Taylor",
title = "Evaluation of Functions on Microcomputers: Square
Root",
journal = j-COMPUT-MATH-APPL,
volume = "4",
number = "4",
pages = "359--367",
year = "1978",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:40:29 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@Article{Andrews:1978:IAN,
author = "M. Andrews",
title = "Influence of architecture on numerical algorithms",
journal = j-MICROPROC-MICROSYS,
volume = "2",
number = "3",
pages = "130--137",
month = jun,
year = "1978",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Andrews:1978:UEF,
author = "M. Andrews and T. Mraz",
title = "Unified elementary function generator",
journal = j-MICROPROC-MICROSYS,
volume = "2",
number = "5",
pages = "270--273",
month = oct,
year = "1978",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Manual{Apple:1978:AIR,
key = "Apple",
title = "{Applesoft II} reference manual: extended
floating-point {BASIC}",
organization = "Apple Computer, Inc.",
address = "Cupertino, CA, USA",
pages = "63",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Apple II (Computer) --- Programming; BASIC (Computer
program language)",
}
@InProceedings{Atkins:1978:CTA,
author = "D. E. Atkins and S. C. Ong",
title = "A Comparison of Two Approaches to Multi-Operand Binary
Addition",
crossref = "IEEE:1978:PSC",
pages = "125--139",
year = "1978",
bibdate = "Wed Nov 14 17:47:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Atkins.pdf",
abstract = "This paper presents the results of one phase of a
study concerning methods for addition of $ P > 2 $
numbers, each encoded as a vector of digits (digit
vector) of length $N$. Such multi-operand addition has
been studied most often in the context of reducing a
set of partial products to a single result in the
implementation of multiplication. More generalized
multi-operand addition, most notably in the form of
inner product calculations is, however, central to
numerous scientific applications of digital computers.
Although multioperand addition is trivially
accomplished by accumulation (iteration in time) in any
general purpose machine, demands for very high-speed
computation, typified by 2- and 3-D signal processing
prompt implementation of dedicated, hardware-intensive
structures for multi-operand addition. This study, for
example, is motivated in part by requirements for rapid
simultaneous addition of up to 100, 16-bit operands in
the design of a dedicated processor for real-time
reconstruction of 3-D images of the beating heart and
breathing lungs.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@TechReport{Banerji:1978:HSD,
author = "Dilip K. Banerji and To-Yat Cheung and V. Ganesan",
title = "A high speed division method in residue arithmetic",
institution = "Department of Computer Science, University of Ottawa",
address = "Ottawa, ON, Canada K1N 6N5",
pages = "7",
year = "1978",
bibdate = "Thu Nov 18 09:44:27 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://books.google.com/books?id=q8fBIwAACAAJ",
acknowledgement = ack-nhfb,
remark = "Credited to CH1630-3/81/0000/0158 IEEE 1981; where did
this appear?",
}
@Article{Baraniecka:1978:DTR,
author = "A. Baraniecka and G. Jullien",
title = "On decoding techniques for residue number system
realizations of digital signal processing hardware",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "25",
number = "11",
pages = "935--936",
month = nov,
year = "1978",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19770117",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23475",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "In a recent issue of this journal, a hardware
implementation of the Chinese Remainder Theorem was
proposed for the translation of residue coded outputs
into natural integer for an FIR filter realization. The
method requires a modulo M adder- \ldots{}",
}
@Book{Bareiss:1978:PEA,
author = "Erwin H. Bareiss and Jesse L. Barlow",
title = "Probabilistic error analysis of computer arithmetics",
publisher = "Department of Electrical Engineering and Computer
Science, Northwestern University",
address = "Evanston, IL, USA",
pages = "97",
year = "1978",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 12:09:29 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Barsi:1978:ACR,
author = "F. Barsi and P. Maestrini",
title = "Arithmetic Codes in Residue Number Systems with
Magnitude Index",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "12",
pages = "1185--1188",
month = dec,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675023",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675023;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35165",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The idea of adding a magnitude index to the residue
representation of numbers is reconsidered. The range of
a given residue number system is supposed to be divided
into intervals of equal width, and the magnitude index
of a number X is defined as an \ldots{}",
}
@Manual{BellHowellCo:1978:BHF,
author = "{Bell and Howell Co} and {Apple Computer, Inc}",
title = "[{Bell and Howell} floating point {Basic} programming
reference manual]",
organization = "Bell and Howell, Audio-Visual Products Division",
address = "Chicago, IL, USA",
pages = "xiii + 168",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Apple II (Computer) --- Programming.; BASIC (Computer
program language)",
remark = "Cover title. ``Reprinted with permission of Apple
Computer, Inc.'' Companion volume: Floating point Basic
tutorial manual. Quick reference guide on folded,
inserted leaf.",
}
@Article{Blue:1978:PFP,
author = "James L. Blue",
title = "A Portable {Fortran} Program to Find the {Euclidean}
Norm of a Vector",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "15--23",
month = mar,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355769.355771",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "68A10",
MRnumber = "57 \#18205",
bibdate = "Sat Aug 27 23:14:36 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "BLAS; floating-point arithmetic; floating-point
overflow; floating-point underflow; nla; norm;
software",
reviewer = "A. D. Booth",
}
@TechReport{Boehmer:1978:TAF,
author = "K. Boehmer and J. M. Yohe",
title = "{Triplex} Arithmetic for {Fortran}",
type = "MRC Technical Summary",
number = "1901",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
pages = "38",
month = dec,
year = "1978",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intarith.bib",
abstract = "Triplex arithmetic is a variant of interval arithmetic
in which a 'main' value is computed in addition to the
endpoints of the containing interval. The 'main' value
is, in general, the value that would have been computed
had properly-rounded real arithmetic been used to
compute the results of the calculation; it may in some
sense, be regarded as the 'most probable' value of the
result of the calculation. The endpoints of the
interval define the worst-case range of the possible
values of the computation. This report describes a
FORTRAN implementation of triplex arithmetic in both
single and multiple precision. The package described in
this report is designed to be used with the AUGMENT
precompiler: this makes triplex arithmetic particularly
easy to use.",
acknowledgement = ack-jr,
keywords = "Approximation theory.; Equations, Abelian.; Spline
theory.",
}
@PhdThesis{Bohlender:1978:GBM,
author = "G. Bohlender",
title = "{Genaue Berechnung mehrfacher Summen, Produkte und
Wurzeln von Gleitkommazahlen und allgemeine Arithmetik
in h{\"o}heren Programmiersprachen} \toenglish
{Accurate Computation of Multiple Sums, Products and
Roots of Floating-Point Numbers and General Arithmetic
in High-Level Programming Languages} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1978",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "accurate floating-point summation",
}
@Article{Boney:1978:MRW,
author = "J. Boney",
title = "Math in the Real World",
journal = j-BYTE,
volume = "3",
number = "9",
pages = "114--119",
month = sep,
year = "1978",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:14:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Brady:1978:MBL,
author = "W. G. Brady",
title = "More on {Benford}'s Law",
journal = j-FIB-QUART,
volume = "16",
number = "1",
pages = "51--52",
month = feb,
year = "1978",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:24 MDT 2011",
bibsource = "http://www.fq.math.ca/16-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@TechReport{Brent:1978:AIB,
author = "R. P. Brent and J. A. Hooper and J. M. Yohe",
title = "An {Augment} Interface for {Brent}'s {Multiple
Precision Arithmetic Package}",
type = "MRC Technical Summary",
number = "1868",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
year = "1978",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published In: ACM Trans. Math. Software 6, 146--149,
1980",
acknowledgement = ack-jr,
}
@Article{Brent:1978:AMF,
author = "Richard P. Brent",
title = "Algorithm 524: {MP}, {A Fortran} Multiple-Precision
Arithmetic Package [{A1}]",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "71--81",
month = mar,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355769.355776",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 05 22:49:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Brent:1979:RMF,Brent:1980:AIB}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Brent:1978:FMP,
author = "Richard P. Brent",
title = "{A Fortran} Multiple-Precision Arithmetic Package",
journal = j-TOMS,
volume = "4",
number = "1",
pages = "57--70",
month = mar,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355769.355775",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 23:13:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Case:1978:AIS,
author = "Richard P. Case and Andris Padegs",
title = "Architecture of the {IBM System}\slash 370",
journal = j-CACM,
volume = "21",
number = "1",
pages = "73--96",
month = jan,
year = "1978",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Jan 29 18:00:28 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@TechReport{Cherry:1978:BAP,
author = "Lorinda L. Cherry and Robert Morris",
title = "{BC} --- An Arbitrary Precision Desk Calculator
Language",
type = "Technical Memorandum",
number = "1053",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
pages = "2 + 14",
day = "12",
month = nov,
year = "1978",
bibdate = "Tue Jun 06 08:07:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
abstract = "BC is a language and a compiler for doing arbitrary
precision arithmetic on the PDP-11 under the UNIX
time-sharing system. The output of the compiler is
interpreted and executed by a collection of routines
which can input, output. and do arithmetic on
indefinitely large integers and on scaled fixed-point
numbers.\par
These routines are themselves based on a dynamic
storage allocator. Overflow does not occur until all
available core storage is exhausted.\par
The language has a complete control structure as well
as immediate-mode operation. Functions can be defined
and saved for later execution.\par
Two five hundred-digit numbers can be multiplied to
give a thousand digit result in about ten
seconds.\par
A small collection of library functions is also
available, including sin. cos, arctan, log,
exponential, and Bessel functions of integer
order.\par
Some of the uses of this compiler are\par
* to do computation with large integers.\par
* to do computation accurate to many decimal
places,\par
* conversion of numbers from one base to another
base.",
abstract-2 = "BC is a language and a compiler for doing arbitrary
precision arithmetic on the PDP-11 und UNIX
Time-Sharing System.",
acknowledgement = ack-nhfb,
author-dates = "Lorinda L. Cherry (18 November 1944--February 2022);
Robert Morris (25 July 1932--26 June 2011)",
remark = "Available in PDF file of \cite[pp.
383--398]{Dolotta:1977:DPU}.",
}
@InProceedings{Chow:1978:LDR,
author = "Catherine Y. Chow and James E. Robertson",
title = "Logical Design of a Redundant Binary Adder",
crossref = "IEEE:1978:PSC",
pages = "109--115",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Chow.pdf",
abstract = "This paper investigates the logical design of a
redundant binary adder with two input digits and one
output digit, all in the digit set $ \{ \bar {1}, 0, 1
\} $. Redundant binary arithmetic structures in which
all digit sets are $ \{ \bar {1}, 0, 1 \} $ were first
discussed by Avizienis in 1961. Borovec studied the
logical design of a class of such binary adders and
subtracters in 1968. At that time, a variation of the
adder\slash subtracter was overlooked. This paper
studies the logical design of this variation. The sum
digit is still a function only of the digits in three
adjacent digital positions of the operands. ``Coupled
don't cares'' are encountered, but have not introduced
too much difficulty. The nine distinct formats (under
permutation and negation) of representing three values
with two bits given by Robertson are used. The simplest
adder\slash subtracter designs from this variation are
less complex than the simplest designs previously
known.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Cohen:1978:MAI,
author = "Danny Cohen",
title = "Mathematical Approach to Iterative Computation
Networks",
crossref = "IEEE:1978:PSC",
pages = "226--237",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Cohen.pdf",
abstract = "This paper deals with design principles for iterative
computation networks. Such computation networks are
used for performing repetitive computations which
typically are not data dependent. Most of the signal
processing algorithms. like FFT and filtering, belong
to this class.\par
The main idea in this paper is the development of
mathematical notation for expressing such designs. This
notation captures the important features and properties
of these computation networks, and can be used both for
analyzing and for designing computational networks.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@TechReport{Coonen:1978:SPS,
author = "Jerome T. Coonen",
title = "Specification for a proposed standard for floating
point arithmetic",
type = "Memorandum",
number = "ERL M78/72",
institution = "University of California, Berkeley",
address = "Berkeley, CA, USA",
year = "1978",
bibdate = "Wed Nov 24 09:10:35 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Corsini:1978:USM,
author = "P. Corsini and G. Frosini",
title = "Uniform Shift Multiplication Algorithms Without
Overflow",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "3",
pages = "256--258",
month = mar,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675081",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675081",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Crary:1978:APT,
author = "F. D. Crary and J. M. Yohe",
title = "The {Augment} Precompiler as a Tool for the
Development of Special Purpose Arithmetic Packages",
type = "MRC Technical Summary",
number = "1892",
institution = inst-MRC-WISCONSIN,
address = inst-MRC-WISCONSIN:adr,
year = "1978",
bibdate = "Fri Jan 12 11:37:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-jr,
}
@InProceedings{Dadda:1978:MAB,
author = "Luigi Dadda",
title = "Multiple Addition of Binary Serial Numbers",
crossref = "IEEE:1978:PSC",
pages = "140--148",
year = "1978",
bibdate = "Wed Nov 14 17:48:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Dadda.pdf",
abstract = "It is shown how circuits for the addition of several
serial binary numbers can be obtained as a combination
of parallel counters and memory cells.\par
The various schemes belong to one of three different
classes, characterized by the way in which carries,
produced by parallel counters, are treated.\par
A comparison is made between the various schemes, in
terms of speed and complexity.",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-4",
}
@Article{Debnath:1978:EMO,
author = "R. C. Debnath and D. A. Pucknell",
title = "Erratum: On multiplicative overflow detection in
residue number system",
journal = j-ELECT-LETTERS,
volume = "14",
number = "12",
pages = "385",
day = "8",
month = jun,
year = "1978",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19780260",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Debnath:1978:MOD}",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4241130",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
}
@Article{Debnath:1978:MOD,
author = "R. C. Debnath and D. A. Pucknell",
title = "On multiplicative overflow detection in residue number
system",
journal = j-ELECT-LETTERS,
volume = "14",
number = "5",
pages = "129--130",
month = "????",
year = "1978",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19780088",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See erratum \cite{Debnath:1978:EMO}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4240881",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A general method for the detection of multiplicative
overflow has been developed. The method has been found
suitable in 16--15-mod residue system from the
consideration of cost and speed. A circuit for
16--15-mod-multiplicative overflow detection \ldots{}",
}
@Misc{DEC-ES:1978:VIS,
author = "{Digital Equipment Corporation.Educational Services}",
title = "{VAX-11} instruction set",
publisher = "Digital Equipment Corporation",
address = "Maynard, MA, USA",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "13 videocassettes (ca. 585 min.)",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; VAX-11 (Computer)
--- Programming.",
remark = "Accompanied by 11 volumes of print materials, 1981.
[1] Instruction formats and addressing modes, lesson 1
--- [2] Instruction formats and addressing modes,
lessons 2 and 3 --- [3] Integer, logical, and branch
instructions, lessons 1 and 2 --- [4] Integer, logical,
and branch instructions, lessons 3 and 4 --- [5]
Character string instructions, lessons 1 and 2 --- [6]
Character string instructions, lessons 3 and 4 --- [7]
Decimal string instructions, lessons 1 and 2 --- [8]
Decimal string instructions, lessons 3, 4, and 5 ---
[9] Special instructions --- [10] Procedures and
subroutine instructions --- [11] Stack and address
instructions --- [12] Variable bit field instructions
--- [13] Floating point instructions. Provides an
introduction to the VAX-11 computer system.",
}
@Article{Diamond:1978:SRI,
author = "Harold G. Diamond",
title = "Stability of Rounded Off Inverses Under Iteration",
journal = j-MATH-COMPUT,
volume = "32",
number = "141",
pages = "227--232",
month = jan,
year = "1978",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database; Parallel/par.lin.alg.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Department of Math., University of Illinois, Urbana,
IL, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "function approximation; iterative methods; positive
integer; rounded off inverse stability",
treatment = "T Theoretical or Mathematical",
}
@Article{Egbert:1978:PCA,
author = "W. E. Egbert",
title = "Personal Calculator Algorithms {IV}: Logarithmic
Functions",
journal = j-HEWLETT-PACKARD-J,
volume = "29",
number = "8",
pages = "29--32",
month = apr,
year = "1978",
CODEN = "HPJOAX",
ISSN = "0018-1153",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Hewlett-Packard Journal: technical information from
the laboratories of Hewlett-Packard Company",
}
@InProceedings{Ercegovac:1978:AME,
author = "M. D. Ercegovac and M. M. Takata",
title = "An Arithmetic Module for Efficient Evaluation of
Functions",
crossref = "IEEE:1978:PSC",
pages = "190--199",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac_Takata.pdf",
abstract = "The organization and design of an arithmetic module
(Basic Byte-Slice Module --- BBM) is presented. A
network of BBWs implements an efficient digit-by-digit
method for fast evaluation of polynomial and rational
functions. Verification of the BBW design, its
feasibility in present LSI technologies and its
performance are discussed. The proposed BBW is
characterized by a small number of input\slash output
terminals, a uniform internal structure, and simple
control and inter-module communication requirements.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Ercegovac:1978:FIS,
author = "Milo{\v{s}} D. Ercegovac and Algirdas Avizienis",
title = "The {Fourth IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "IEEE:1978:PSC",
pages = "v--v",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Ercegovac:1978:LSR,
author = "Milo{\v{s}} D. Ercegovac",
title = "An On-Line Square Rooting Algorithm",
crossref = "IEEE:1978:PSC",
pages = "183--189",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
abstract = "An on-line algorithm for computing square roots in a
radix 2, normalized floating-point number system with
the redundant digit set $ \{ - 1, 0, 1 \} $ is
described. The algorithm has on-line delay of one and
it is amenable for modular implementation. A systematic
approach, used in deriving this algorithm, is presented
in detail.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@TechReport{Espelid:1978:FPS,
author = "Terje O. Espelid",
title = "On floating-point summation",
type = "Report",
number = "67",
institution = "Department of Applied Mathematics, University of
Bergen",
address = "Bergen, Norway",
pages = "24",
year = "1978",
bibdate = "Thu May 09 08:03:27 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Periodical{FloatingPointSystems:1978:P,
author = "{Floating Point Systems, Inc}",
title = "To the point",
publisher = "Floating Point Systems",
address = "Portland, OR, USA",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
alttitle = "To the point (Portland, Or.)",
keywords = "Floating Point Systems, Inc. --- Periodicals.",
remark = "``Employee newsletter.'' Title from caption.",
}
@Article{Fox:1978:AFP,
author = "P. A. Fox and A. D. Hall and N. L. Schryer",
title = "{Algorithm 528}: Framework for a Portable Library
[{Z}]",
journal = j-TOMS,
volume = "4",
number = "2",
pages = "177--188",
month = jun,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355780.355789",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 23:30:46 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remarks \cite{Fox:1979:RFP,Gay:1999:SAF}.",
acknowledgement = ack-nhfb,
annote = "The three program packages presented here provide a
framework for a portable FORTRAN subroutine library.
They were developed for the BELL Laboratories library
PORT(1). The packages are: machine-dependent constants,
automatic error handling, and dynamic storage
allocation using a stack.",
country = "USA",
date = "19/03/80",
descriptors = "Reliability; program construction; mathematical
method; FORTRAN; portability; error handling; memory
management; library",
enum = "988",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
language = "English",
location = "RWTH-AC-DFV: TELL",
references = "1",
revision = "20/03/92",
}
@Article{Fox:1978:PMS,
author = "P. A. Fox and A. D. Hall and N. L. Schryer",
title = "The {PORT} Mathematical Subroutine Library",
journal = j-TOMS,
volume = "4",
number = "2",
pages = "104--126",
month = jun,
year = "1978",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355780.355783",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Aug 27 23:13:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The development at Bell Laboratories of PORT, a
library of portable Fortran programs for numerical
computation, is discussed. Portability is achieved by
careful language specification, together with the key
technique of specifying computer classes by means of
predefined machine constants. The library is built
around an automatic error-handling facility and a
dynamic storage allocation scheme, both of which are
implemented portably. These, together with the modular
structure of the library, lead to simplified calling
sequences and ease of use.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "dynamic storage allocation; error handling; libraries;
numerical analysis; portability",
}
@Manual{FPS:1978:AAP,
key = "FPS",
title = "{AP-120B} Array Processor handbook",
organization = "Floating Point Systems, Inc.",
address = "Portland, OR, USA",
pages = "????",
year = "1978",
bibdate = "Fri Nov 09 10:52:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Fraley:1978:ZIR,
author = "B. Fraley",
title = "Zeros and Infinities Revisited and Gradual Underflow",
type = "Technical report",
institution = "HP Laboratories",
address = "3500 Deer Creek Road, Palo Alto, CA 94304, USA",
pages = "????",
day = "28",
month = dec,
year = "1978",
bibdate = "Fri Nov 09 10:53:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Frankowski:1978:RME,
author = "Krzysztof S. Frankowski",
title = "A Realistic Model for Error Estimates in the
Evaluation of Elementary Functions",
crossref = "IEEE:1978:PSC",
pages = "70--74",
year = "1978",
bibdate = "Thu Sep 01 11:22:03 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Frankowski.pdf",
abstract = "Floating point error analysis, as described by J. H.
Wilkinson (1963) has two known drawbacks: it is too
pessimistic and too cumbersome for everyday use. This
paper describes a realistic model for error analysis,
gives examples of simple formulae frequently used in
the calculation of elementary functions, and analyses
the error generated in single precision computations
with these formulae, using the proposed model for error
analysis. The paper also presents error bounds for
various polynomial evaluations, as predicted by the
model. Model verification is done using double
precision arithmetic.",
acknowledgement = ack-nj,
keywords = "ARITH-4",
}
@InProceedings{Gajski:1978:DAE,
author = "Daniel D. Gajski and L. P. Rubinfield",
title = "Design of Arithmetic Elements for {Burroughs
Scientific Processor}",
crossref = "IEEE:1978:PSC",
pages = "245--256",
year = "1978",
bibdate = "Fri Nov 09 10:54:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Gajski.pdf",
abstract = "The design criteria and implementation of the
Arithmetic Element (AE) of the Burroughs Scientific
Processor, a vector machine intended for scientific
computation requiring speed of up to 50 million
floating-point operations per second, is discussed. An
array of 16 AEs operate in lockstep mode, executing the
same instruction on 16 sets of data. The 16 AEs are one
stage in a pipeline which consists of 17 memory
modules, an input alignment network, and an output
alignment net-work. The AE itself is not pipelined. It
can perform over one hundred different operations
including a floating-point addition\slash subtraction
and multiplication, division, square root, among the
others. Eight registers are provided for the storage of
intermediate values and results. Modulo 3 residue
arithmetic is used for checking hardware failures.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Garcia:1978:AES,
author = "Oscar N. Garcia and Harvey Glass and Stanley C.
Haines",
title = "An Approximate and Empirical Study of the Distribution
of Adder Inputs and Maximum Carry Length Propagation",
crossref = "IEEE:1978:PSC",
pages = "97--103",
year = "1978",
bibdate = "Wed Nov 14 17:49:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Garcia.pdf",
abstract = "This paper investigates, using sampled data, the
commonly used hypothesis that integer operands reaching
the adder of a computer are uniformly distributed.
Questions raised on the validity of that hypothesis are
reinforced and their impact on the calculation of the
average of the worst case length of carry propagation
is considered. An approximate formula is developed for
the worst case carry chain length when the arithmetic
operands are restricted in magnitude.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; average worst case carry chain; binary
addition; carry propagation",
}
@Article{Garner:1978:TCA,
author = "H. L. Garner",
title = "Theory of Computer Addition and Overflows",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "4",
pages = "297--301",
month = apr,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675101",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675101",
abstract = "Computer addition is a groupoid. If an additive
identity exists it is unique. If(and only if) addition
is defined with the compute through the overflow (CTO)
property, then a finite ring of integers is the
homomorphic image of the computer number system and
addition. Stated another way, the necessary and
sufficient condition for CTO is a congruence relation
on the integers. Also, if the number system has CTO
capabilities for addition, it also has extended CTO
properties for addition. A technique is presented for
determining the correct sum in the extended compute
through overflow (ECTO) mode of computation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "additive identity; compute through overflow (CTO);
computer arithmetic; models of computer arithmetic;
number systems; overflow behavior",
}
@InCollection{Gautschi:1978:QNC,
author = "Walter Gautschi",
booktitle = "Recent advances in numerical analysis ({Proc. Sympos.,
Math. Res. Center, University of Wisconsin, Madison,
Wis., 1978})",
title = "Questions of numerical conditions related to
polynomials",
volume = "41",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "45--72",
year = "1978",
MRclass = "65D99",
MRnumber = "519056",
MRreviewer = "Gerhard Merz",
bibdate = "Fri Feb 9 15:26:45 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Publ. Math. Res. Center University of Wisconsin",
acknowledgement = ack-nhfb,
}
@Article{Good:1978:CMA,
author = "I. J. Good",
title = "{C 24}. {A} method for avoiding overflows and
underflows",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "8",
number = "2",
pages = "162--163",
year = "1978",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657808810261",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:10:43 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@Article{Goodman:1978:ITD,
author = "R. Goodman and J. Bustoz and A. Feldstein",
title = "Improved Trailing Digits Estimates Applied to Optimal
Computer Arithmetic",
journal = j-SIAM-REVIEW,
volume = "20",
number = "3",
pages = "625--625",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Book{Hamacher:1978:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xiv + 465",
year = "1978",
ISBN = "0-07-025681-0",
ISBN-13 = "978-0-07-025681-1",
LCCN = "QA76.9.A73 H35",
bibdate = "Sat May 18 14:24:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
}
@InProceedings{Horspool:1978:EAU,
author = "R. Nigel Horspool and Eric C. R. Hehner",
title = "Exact Arithmetic Using a Variable-Length $p$-adic
Representation",
crossref = "IEEE:1978:PSC",
pages = "10--14",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Horspool.pdf",
abstract = "The $p$-adic number system is introduced and developed
into a form suitable for performing exact arithmetic in
computers. The proposed representation has several
desirable attributes: the four standard arithmetic
operations have a simple consistent form, the
programmer has the ability to choose the precise degree
of accuracy in his calculations and the variable-length
nature of the representation achieves compact
encodings",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Hull:1978:DFP,
author = "T. E. Hull",
title = "Desirable Floating-Point Arithmetic and Elementary
Functions for Numerical Computation",
crossref = "IEEE:1978:PSC",
pages = "63--69",
year = "1978",
DOI = "https://doi.org/10.1109/arith.1978.6155780",
bibdate = "Thu Sep 01 12:14:34 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hull.pdf",
abstract = "The purpose of this paper is to summarize proposed
specifications for floating-point arithmetic and
elementary functions. The topics considered are: the
base of the number system, precision control, number
representation, arithmetic operations, other basic
operations, elementary functions, and exception
handling. The possibility of doing without fixed-point
arithmetic is also discussed.\par
The specifications are intended to be entirely at the
level of a programming language such as Fortran. The
emphasis is on convenience and simplicity from the
user's point of view. The specifications are not
complete in every detail, but it is intended that they
be complete ``in spirit'' --- some further details,
especially syntactic details, would have to be
provided, but the proposals are otherwise relatively
complete.",
acknowledgement = ack-nj,
keywords = "ARITH-4; decimal floating-point arithmetic",
remark = "Refined and implemented later by
\cite{Cohen:1983:CCP}. The paper begins with the
quote
``\ldots{} the expression $ 25 + 1 / 3 $ yields the
value $ 5.333333 $ in PL/I, and $ .333334 $ in PL/C
\ldots{}'', Conway and Gries, An Introduction to
Programming, 1975, p. 24.",
}
@InProceedings{Hwang:1978:IRR,
author = "Kai Hwang and T. P. Chang",
title = "An Interleaved Rational\slash Radix Arithmetic System
for High-Precision Computations",
crossref = "IEEE:1978:PSC",
pages = "15--24",
year = "1978",
bibdate = "Wed Nov 14 17:49:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hwang.pdf",
abstract = "A new interleaved rational\slash radix number system
is proposed for upgrading the precision of normalized
Floating-Point (FLP) arithmetic operations without
increasing the basic word length. A complete set of
rational rounding and arithmetic algorithms are
developed. The Average Relative Representation Error
(ARRE) of the proposed flexible FLP system is computed
through a series of simulation studies on CDC 6500. Our
results show a 10\% improvement of representation
accuracy when compared with the ARRE of conventional
FLP system. The architecture of a rational FLP
arithmetic processor is also presented. Tradeoffs
between operating speed and computing accuracy are
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; Farey rational numbers",
}
@Manual{Intel:1978:FAL,
author = "{Intel Corporation}",
title = "8080\slash 8085 floating-point arithmetic library:
user's manual",
organization = "Intel Corporation",
address = "Santa Clara, CA, USA",
pages = "various",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Intel 8080 (Microprocessor) --- Programming.; Intel
8085 (Microprocessor) --- Programming.",
remark = "``Manual order number: 9800452B.''",
}
@InProceedings{Jullien:1978:ARN,
author = "G. A. Jullien and W. C. Miller",
title = "Application of the Residue Number System to Computer
Processing of Digital Signals",
crossref = "IEEE:1978:PSC",
pages = "220--225",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Jullien.pdf",
abstract = "The residue number system offers parallel processing,
digital hardware implementations for the binary
operations of addition, subtraction and multiplication.
This paper discusses the use of the residue number
system in implementing digital signal processing
functions, in which these binary operations abound. The
paper covers implementations using arrays of read only
memories, and briefly discusses the use of parallel
microprocessor structures. ROM array implementations of
scaling operations are also presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; residue number system",
}
@Article{Jullien:1978:RNS,
author = "G. A. Jullien",
title = "Residue Number Scaling and Other Operations Using
{ROM} Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "4",
pages = "325--336",
month = apr,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675105",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675105;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35168",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Over the last two decades there has been considerable
interest in the implementation of digital computer
elements using hardware based on the residue number
system. This paper considers implementing such systems
with arrays of look-up tables placed \ldots{}",
}
@Article{Kahan:1978:KSI,
author = "W. Kahan and B. N. Parlett",
title = "{K{\"o}nnen Sie sich auf Ihren Rechner verlassen?}
({German}) [Can you count on your calculator?]",
journal = "{Jahrbuch {\"U}berblicke Mathematik}",
volume = "??",
pages = "199--216",
year = "1978",
bibdate = "Fri Nov 11 06:36:51 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0397.65081",
acknowledgement = ack-nhfb,
classmath = "*65Y99 Computer aspects of numerical algorithms 65D20
Computation of special functions 00A99 Miscellaneous
topics in general mathematics",
keywords = "Automated Algorithms; Error of Computation; Pocket
Calculator",
language = "German",
}
@InProceedings{Koren:1978:UAC,
author = "Israel Koren and Yoram Maliniak",
title = "A Unified Approach to a Class of Number Systems",
crossref = "IEEE:1978:PSC",
pages = "25--28",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Koren.pdf",
abstract = "A unified approach to a broad class of number systems
is proposed in this paper. This class contains all
positive and negative radix systems and other
well-known number systems. The proposed approach
enables us to develop a single set of algorithms for
arithmetic operations and conversion methods between
number systems.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Kornerup:1978:FAF,
author = "Peter Kornerup and David W. Matula",
title = "A Feasibility Analysis of Fixed-Slash and
Floating-Slash Arithmetic",
crossref = "IEEE:1978:PSC",
pages = "{39--47}",
year = "1978",
bibdate = "Wed Nov 14 17:50:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Kornerup.pdf",
abstract = "An investigation of the feasibility of a finite
precision approximate rational arithmetic based on
fixed-slash representation of rational numbers is
presented. Worst-case and average-case complexity
analyses of the involved rounding algorithm (an
extended shift-subtract gcd algorithm) are presented.
The results are applied to a proposed hardware
realization of a fixed-slash arithmetic unit.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Krishnamurthy:1978:MPP,
author = "E. V. Krishnamurthy and H. Venkateswaran",
title = "Multivariable Polynomial Processing --- Applications
to Interpolation",
crossref = "IEEE:1978:PSC",
pages = "81--87",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Krishnamurthy.pdf",
abstract = "A data-structure suitable for multivariable polynomial
processing in introduced. Using this data structure,
arithmetic algorithms are described for addition,
subtraction and multiplication of multivariable
polynomials; also algorithms are described for forming
the inner product and tensor product of vectors, Those
components are multivariable polynomials. Application
of these algorithms for multivariable cardinal spline
approximation is described in detail.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Book{Kuck:1978:SCC,
author = "David J. Kuck",
title = "The structure of computers and computations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xxii + 611",
year = "1978",
ISBN = "0-471-02716-2 (vol. 1), 0-471-08138-8",
ISBN-13 = "978-0-471-02716-4 (vol. 1), 978-0-471-08138-8",
LCCN = "QA76.9.A73 K83",
bibdate = "Mon May 20 05:05:46 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Chapter 3 for floating-point arithmetic
discussion.",
acknowledgement = ack-nhfb,
}
@InProceedings{Liddiard:1978:RSF,
author = "L. A. Liddiard",
title = "Required Scientific Floating Point Arithmetic",
crossref = "IEEE:1978:PSC",
pages = "56--62",
year = "1978",
bibdate = "Thu Sep 01 11:06:57 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Liddiard.pdf",
abstract = "Previous papers in computer arithmetic have shown that
correct rounded floating point with good arithmetic
properties can be attained using guard digits and
careful algorithms on the floating point fractions.
This paper combines that body of knowledge with
proposed exponent forms that are closed with respect to
inversion and detection and recovery of exponent under-
and overflow. In addition radix 2 is shown to be the
only base radix meeting minimal variation of precision,
a condition necessary for the safe use of floating
point. An effort is made to establish objective
criteria in answer to the question ``What is the best
division of the computer word into exponent and
fraction parts?''. Combining the previous results
allows a required scientific floating point arithmetic
to be portrayed and compared with available arithmetic
on current computers.",
acknowledgement = ack-nj,
keywords = "ARITH-4; arithmetic properties; correct rounding;
exponent over; Floating point exponents; floating-point
arithmetic; optimal base radix",
}
@InProceedings{Lillevik:1978:CDA,
author = "Sigurd L. Lillevik and P. David Fisher",
title = "Computational Design Alternatives with
Microprocessor-Based Systems",
crossref = "IEEE:1978:PSC",
pages = "267--272",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lillevik.pdf",
abstract = "This paper examines and characterizes four elemental
hardware computational design alternatives (CDA's) and
presents a structured approach to computational section
design which incorporates a rigorous, theoretic
foundation. The DIRECT CDA incorporates a single
microprocessor ($ \mu $P) and memory. The AU CDA
contains a $ \mu $P, memory, and arithmetic unit. $ \mu
$P, memory, and calculator chip comprise the CALC CDA.
Finally, several $ \mu $P's and memories in a
Master\slash Slave arrangement implement the multiple-$
\mu $P m$ \mu $P CDA. A common set of attributes ---
precision, speed and cost --- facilitates comparison.
Using these attributes, Multiattribute Utility Theory
assesses a numeric quantity, the utility, to represent
each CDA's relative usefulness. Thus, design involves
selecting the CDA with the greatest utility.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Lim:1978:HSM,
author = "Raymond S. Lim",
title = "High-Speed Multiplication and Multiple Summand
Addition",
crossref = "IEEE:1978:PSC",
pages = "149--153",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lim.pdf",
abstract = "The problem of high-speed multiplication is considered
from the viewpoint of summand generation and summand
summation. The goal is to obtain at least a
2's-complement, 32-bit floating-point (sign plus 24-bit
fraction) multiplication in 10 to 20 ns using ECL LSI
packages. Summand generation is implemented by $ m
\times m $-bit multipliers. The optimum values for $m$
are 9, 13, 17, or 21. Summand summation is implemented
by a row of $ (p, 2) $ column-summing counters. The $
(0, 2) $, $ (5, 2) $, and $ (7, 2) $ counters are
optimum choices. These counters compress $p$ inputs
into two outputs plus nonpropagating carry bits, where
these bits are added to the next higher-order stage
with at most two full adder delays.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Article{Liu:1978:ECC,
author = "Chao-Kai Liu and Tse Lin Wang",
title = "Error-Correcting Codes in Binary-Coded-Decimal
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "11",
pages = "977--984",
month = nov,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1674987",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 07 17:26:15 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error-correcting coding schemes devised for binary
arithmetic are not in general applicable to BCD
arithmetic. In this paper, we investigate the new
problem of using such coding schemes in BCD systems. We
first discuss the general characteristics of arithmetic
errors and define the arithmetic weight and distance in
BCD systems. We show that the distance is a metric
function. Number theory is used to construct a class of
single-error-correcting codes for BCD arithmetic. It is
shown that the generator of these codes possesses a
very simple form and the structure of these codes can
be analytically determined.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "BCD arithmetic; decimal arithmetic",
}
@Article{Logan:1978:FDP,
author = "Jonothan L. Logan and Samuel A. Goudsmit",
title = "The First Digit Phenomenon",
journal = j-PROC-AMER-PHIL-SOC,
volume = "122",
number = "4",
pages = "193--197",
day = "18",
month = aug,
year = "1978",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Fri Mar 30 11:20:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This paper contains derivations of both Stigler's Law
and Benford's Law, and receives strong criticism in
\cite{Raimi:1985:FDP}. This paper contains an important
historical note that is recorded in entry
\cite{Benford:1938:LAN}.",
URL = "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
http://www.jstor.org/stable/986530",
abstract = "Forty years ago an article appeared in these
Proceedings, which has since then attracted much
attention of mathematicians and some physicists. It was
written by Frank Benford, a physicist from the General
Electric Company at Schenectady. He had examined a
large number of numerical tables, the kind that are
printed in almanacs, and in scientific and technical
handbooks. He noticed a most unusual and unexpected
property of many of these tables. Consider, for
example, the numbers representing the populations of
states or all the countries in the world, or their
areas, their budgets, their numbers of hospital beds,
etc. One would expect that on the average just as many
of these entries would begin with the digit $1$ as with
$2$ or $3$ or $4$, and so on. But Benford noticed that
small values of the first digits occur far more
often.",
acknowledgement = ack-nhfb,
author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
the concept of electron spin, a critical step forward
in the quantum mechanics of many-electron systems.
Surprisingly, that work did not get them the Nobel
Prize, but it did spur Wolfgang Pauli to present his
Exclusion Principle in 1925, for which he received the
1945 Nobel Prize in Physics. After World War II,
Goudsmit was the scientific head of the Alsos mission
to capture German nuclear scientists. In the 1950s, he
founded the journal Physical Review Letters. During the
1960s and 1970s, he was Editor-in-Chief of the main
American physics journal, the Physical Review.",
}
@InProceedings{Matula:1978:BDS,
author = "David W. Matula",
title = "Basic Digit Sets for Radix Representation of the
Integers",
crossref = "IEEE:1978:PSC",
pages = "1--9",
year = "1978",
bibdate = "Wed Nov 14 17:51:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula.pdf",
abstract = "Let $Z$ denote the set of integers. A digit set $ D
\in Z $ is basic for base $ \beta \in Z $ if the set of
polynomials $ \{ d_m \beta^m + d_{m - 1} \beta^{m - 1}
+ \ldots {} + d_1 \beta + d_0 | d_i \in D \} $ contains
a unique representation for every $ n \in Z $. We give
necessary and sufficient conditions for D to be basic
for $ \beta $. We exhibit efficient procedures for
verifying that $D$ is basic for $S$, and for computing
the representation of any $ n \in Z $ when a
representation exists. There exist $D$, $S$ with $D$
basic for $S$ where $ \max \{ |d| \vert d \in D \} > |
\beta | $, and more generally, an infinite class of
basic digit sets is shown to exist for every base $S$
with $ \beta \geq 3 $. The natural extension to
infinite precision radix representation using basic
digit sets is considered and a summary of results is
presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; base; digit representation; finite and
infinite precision; non-standard number",
}
@InProceedings{Matula:1978:FAF,
author = "David W. Matula and Peter Kornerup",
title = "A Feasibility Analysis of Fixed-Slash and
Floating-Slash Number Systems",
crossref = "IEEE:1978:PSC",
pages = "{29--38}",
year = "1978",
bibdate = "Wed Nov 14 17:52:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula_Kornerup.pdf",
abstract = "Design and analysis of finite precision rational
number systems based on fixed-slash and floating-slash
representation is pursued. Natural formats for binary
fixed-slash and binary floating-slash number
representation in computer words are described.
Compatibility with standard integer representation is
obtained. Redundancy in the representation is shown to
be minimal. Arithmetic register requirements are
considered. Worst case and average case rounding errors
are determined, and the concept of adaptive variable
precision in the rounding is developed.",
acknowledgement = ack-nhfb,
keywords = "adaptive variable precision; adjacent fractions;
ARITH-4; binary numeric word format; Farey fractions;
finite precision; fixed-slash numbers; floating-slash
numbers; integer compatibility; mediant roundings;
range of number system; rational arithmetic;
redundancy; worst case and average case rounding
error",
}
@Article{McCrea:1978:CFP,
author = "P. G. McCrea and P. C. Maxwell and P. W. Baker",
title = "Comments on {``A Floating-Point Multiplexed DDA
System''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "12",
pages = "1226--1226",
month = dec,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675033",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Hannington:1976:FPM}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675033",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Mitra:1978:ITD,
author = "S. K. Mitra and G. K. Sorknes",
title = "On the Implementation of a Two-Dimensional {FIR}
Filter Using a Single Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "8",
pages = "762--764",
month = aug,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675186",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675186",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Morris:1978:DID,
author = "Robert Morris and Lorinda Cherry",
title = "{DC} --- An Interactive Desk Calculator",
type = "Technical Memorandum",
number = "1056",
institution = inst-ATT-BELL,
address = inst-ATT-BELL:adr,
pages = "8",
day = "15",
month = nov,
year = "1978",
bibdate = "Tue Jun 06 08:07:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
abstract = "DC is an arbitrary precision arithmetic package
implemented on the UNIX time-sharing system in the form
of an interactive desk calculator. It works like a
stacking calculator using reverse Polish notation.
Ordinarily DC operates on decimal integers, but one may
specify an input base, output base, and a number of
fractional digits to be maintained.",
abstract-2 = "DC is an interactive desk calculator program
implemented on the UNIX Time-Sharing System \ldots{}
arbitrary-precision integer arithmetic.",
acknowledgement = ack-nhfb,
author-dates = "Lorinda L. Cherry (18 November 1944--February 2022);
Robert Morris (25 July 1932--26 June 2011)",
remark = "Available in PDF file of \cite[pp.
399--406]{Dolotta:1977:DPU}.",
}
@Article{Murphy:1978:SRP,
author = "T. R. Murphy and P. L. Rickard",
title = "Square-Root Procedure for Floating-Point Numbers",
journal = j-IBM-TDB,
volume = "21",
number = "2",
pages = "785",
month = jul,
year = "1978",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Nussabaumer:1978:FMN,
author = "H. J. Nussabaumer",
title = "Fast Multipliers for Number Theoretic Transforms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "8",
pages = "764--765",
month = aug,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675187",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675187",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{OLeary:1978:DHS,
author = "G. P. O'Leary",
title = "The design of a high-speed arithmetic processor",
crossref = "COMPSAC:1978:CPC",
pages = "175--176",
year = "1978",
bibdate = "Wed Sep 07 22:19:45 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Olver:1978:NAE,
author = "F. W. J. Olver",
title = "New Approach to Error Arithmetic",
journal = j-SIAM-REVIEW,
volume = "20",
number = "3",
pages = "632--632",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Patel:1978:ASB,
author = "M. R. Patel and K. H. Bennett",
title = "Analysis of Speed of a Binary Divider Using a Variable
Number of Shifts Per Cycle",
journal = j-COMP-J,
volume = "21",
number = "3",
pages = "246--252",
month = aug,
year = "1978",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/21.3.246",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:03 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/21/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/21/3/246.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/246.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/247.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/248.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/249.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/250.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/251.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/252.tif",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods)",
classification = "721",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "analysis; computers, digital; cycle; digital
arithmetic; discrete time; discrete time systems;
finite state system model; ICL 2980; optimisation;
optimum hardware configuration; Patel and Bennett
(1976); speed of a binary divider; variable number of
shifts per",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Payne:1978:DPF,
author = "M. Payne and W. Strecker",
title = "Draft Proposal for Floating Point Standard",
type = "Technical report",
institution = "Digital Equipment Corporation",
address = "Maynard, MA, USA",
day = "11",
month = dec,
year = "1978",
bibdate = "Fri Nov 09 19:11:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Preston:1978:NAT,
author = "F. S. Preston",
title = "A New Algorithm for the Tangent",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "2",
pages = "167",
month = feb,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675052",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Ralston:1978:FCN,
author = "Anthony Ralston and Philip Rabinowitz",
title = "A first course in numerical analysis",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "xix + 556",
year = "1978",
ISBN = "0-07-051158-6",
ISBN-13 = "978-0-07-051158-3",
LCCN = "QA297 .R3 1978",
bibdate = "Fri Aug 20 10:13:32 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$19.50",
series = "International series in pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "See also first edition \cite{Ralston:1965:FCN}.
Reprinted in \cite{Ralston:2001:FCN}.",
subject = "Numerical analysis",
}
@Article{Rashed:1978:LRI,
author = "Roshd{\=\i} R{\=a}shed",
title = "{L}'Extraction de la Racine $ n^{\rm \scriptstyle
i{\grave e}me} $ et {l'Invention} des Fractions
D{\'e}cimales ({XI}$^e$--{XII}$^e$ Si{\`e}cles).
({French}) [{The} extraction of the n$^{{\rm th}}$ root
and the invention of decimal fractions (11$^{{\rm
th}}$--12$^{{\rm th}}$ centuries)]",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "18",
number = "3",
pages = "191--243",
month = sep,
year = "1978",
CODEN = "AHESAN",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A35",
MRnumber = "0484970 (58 \#4829)",
MRreviewer = "H. L. L. Busard",
bibdate = "Fri Feb 4 21:50:14 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=18&issue=3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=18&issue=3&spage=191",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
language = "French",
MRtitle = "{L}'extraction de la racine {$n$}i{\`e}me et
l'invention des fractions d{\'e}cimales ({XIe--XIIe}
si{\`e}cles)",
MRyear = "1977/78",
}
@InProceedings{Reuter:1978:SEU,
author = "Eric K. Reuter and John P. Jeter and J. Wayne Anderson
and Bruce D. Shriver",
title = "Some Experiments Using Interval Arithmetic",
crossref = "IEEE:1978:PSC",
pages = "75--80",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Reuter.pdf",
abstract = "This paper reviews past experiences and discusses
future work in the area of interval arithmetic at the
University of Southwestern Louisiana (USL). Two
versions of interval arithmetic were developed and
implemented at USL. An interval data type declaration
and the necessary mathematical functions for this data
type were added to Fortran via the preprocessor Augment
(4,5). In the first version the endpoints of the
intervals were represented as single precision floating
point numbers. In the other version, the endpoints were
represented to 56 decimal digits. Production
engineering programs were run as benchmarks (8). The
accumulation of computational and algorithmic error
could be observed as a widening of the intervals. The
benchmarks were also run in normal single and double
precision arithmetic. In some instances, the result
obtained from a single or double precision calculation
was not bounded by the corresponding interval result
indicating some problem with the algorithm. The
widening of an interval does not necessarily indicate a
data sensitivity nor error in an algorithm. However,
these large intervals can be used as indicator of no
problems. As could be expected, the 56-decimal digit
precision interval gave better results in terms of
smaller intervals due to the increased amount of
precision. The obvious problem with this version is
that the amount of overhead required for its execution
is high.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Manual{Richardson:1978:ATB,
author = "Caryl Richardson and Jef Raskin",
title = "The {Apple} tutorial: based on the {Apple} {II} Basic
programming manual",
organization = "Bell and Howell, Audio-Visual Products Division",
address = "Chicago, IL, USA",
pages = "vii + 157",
year = "1978",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Apple II (Computer) --- Programming.; BASIC (Computer
program language)",
remark = "Cover title: Floating point Basic tutorial manual.
``Reprinted with the permission of Apple Computer
Inc.'' Companion volume: Bell and Howell floating point
Basic programming reference manual.",
}
@Article{Ruckdeschel:1978:FA,
author = "F. Ruckdeschel",
title = "Functional Approximations",
journal = j-BYTE,
volume = "3",
number = "11",
pages = "34--46",
month = nov,
year = "1978",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Russell:1978:CCS,
author = "Richard M. Russell",
title = "The {Cray-1} Computer System",
journal = j-CACM,
volume = "21",
number = "1",
pages = "63--72",
month = jan,
year = "1978",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Dec 08 13:08:43 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "grecommended91, existing classic architecture, maeder
biblio: parallel hardware and devices, implementation,
ginsberg biblio: bhibbard enm, j\-lb",
remark = "The original paper describing the Cray-1. This paper
is reproduced in Kuhn and Padua's (1981, IEEE) survey
``Tutorial on Parallel Processing.'' Also reproduced in
``Computer Structures: Principles and Examples'' by
Daniel P. Siewiorek, C. Gordon Bell, and Allen Newell,
McGraw-Hill, 1982, pp. 743-752. Reproduced in Dharma P.
Agrawal's (ed.) ``Advanced Computer Architecture,''
IEEE, 1986, pp. 15--24. Literature search yields:
00712248 E. I. Monthly No: EI7804023850 E. I. Yearly
No: EI78014612 Title: Cray-1 Computer System. Author:
Russell, Richard M. Corporate Source: Cray Res Inc,
Minneapolis, Minn Source: Communications of the ACM v
21 n 1 Jan 1978 p 63--72 Publication Year: 1978 CODEN:
CACMA2 ISSN: 0001-0782 Language: ENGLISH Journal
Announcement: 7804 Abstract: The CRAY-1 is described,
the evolution of its architecture is discussed, and an
account is given of some of the problems that were
overcome during its manufacture. The CRAY-1 is the only
computer to have been built to date that satisfies
ERDA's Class VI requirement (a computer capable of
processing from 20 to 60 million floating point
operations per second). The CRAY-1's Fortran compiler
(CFT) is designed to give the scientific user immediate
access to the benefits of the CRAY-1's vector
processing architecture. An optimizing compiler, CFT,
``vectorizes'' innermost DO loops. Compatible with the
ANSI 1966 Fortran Standard and with many commonly
supported Fortran extensions, CFT does not require any
source program modifications or the use of additional
nonstandard Fortran statements to achieve
vectorization. 6 refs. Descriptors: *COMPUTER
ARCHITECTURE; COMPUTER SYSTEMS, DIGITAL Classification
Codes: 722 (Computer Hardware); 723 (Computer Software)
72 (COMPUTERS \& DATA PROCESSING)",
}
@Book{Schmid:1978:EDS,
author = "Hermann Schmid",
title = "{Elektronische Dezimalrechner, Schaltungen und
Verfahren} \toenglish {Electronic Decimal Computers,
Wiring and Methods} \endtoenglish",
publisher = pub-OLDENBOURG,
address = pub-OLDENBOURG:adr,
pages = "275",
year = "1978",
ISBN = "3-486-20211-1",
ISBN-13 = "978-3-486-20211-3",
LCCN = "????",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Schreiber:1978:TMF,
author = "F. A. Schreiber and R. Stefanelli",
title = "Two Methods for Fast Binary-{BCD} Conversion",
crossref = "IEEE:1978:PSC",
pages = "200--207",
year = "1978",
bibdate = "Sat Nov 12 21:58:26 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Schreiber.pdf",
abstract = "Two methods for performing binary--BCD conversion of
positive integers are discussed. The principle which
underlies both methods in the repeated division by five
and then by two, obtained the first by means of
subtractions performed from left to right, the second
by shifting bits before next subtraction.\par
It is shown that these methods work in a time which is
linear with the length in bit of the number to be
converted.\par
A ROM solution is proposed and its complexity is
compared with that of other methods.",
acknowledgement = ack-nj,
keywords = "ARITH-4",
}
@Book{Seck:1978:WSA,
editor = "Friedrich Seck",
title = "{Wilhelm Schickard, 1592--1635: Astronom, Geograph,
Orientalist, Erfinder der Rechenmaschine}. ({German})
[{Wilhelm Schickard}, 1592--1635: Astronomer,
Geographer, Orientalist, Inventor of the calculator]",
volume = "25",
publisher = "Mohr",
address = "T{\"u}bingen, West Germany",
pages = "422",
year = "1978",
ISBN = "3-16-939772-9",
ISBN-13 = "978-3-16-939772-3",
LCCN = "QB36.S312 W54",
bibdate = "Sat Jul 27 11:00:08 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib;
z3950.loc.gov:7090/Voyager",
series = "Contubernium",
acknowledgement = ack-nhfb,
language = "German",
remark = "Includes texts in Latin.",
subject = "Schickard, Wilhelm; Astronomers; Germany; Biography;
Middle East specialists",
subject-dates = "1592--1635",
}
@Article{Shen:1978:CSA,
author = "D. T. Shen and A. Weinberger",
title = "4-2 carry-save adder implementation using send
circuits",
journal = j-IBM-TDB,
volume = "20",
number = "9",
pages = "??--??",
month = feb,
year = "1978",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Mon Dec 24 10:18:16 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InProceedings{Slekys:1978:MBI,
author = "Arunas G. Slekys and Algirdas Avi{\v{z}}ienis",
title = "A Modified Bi-Imaginary Number Systems",
crossref = "IEEE:1978:PSC",
pages = "48--55",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Slekys.pdf",
abstract = "In this paper the properties of $p$-imaginary number
systems are reviewed and a modified bi-imaginary number
system is introduced as a special case with $ p = 2 $.
Major properties, including conversion of integer and
floating point operands represented in a radix $ + p $
system, range, sign and zero tests, and shifting are
discussed. The ability to represent the operands as
vectors of radix-2 digits suggests advantages in
implementing machine-usable arithmetic algorithms.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@Article{Sripad:1978:QEF,
author = "A. Sripad and D. Snyder",
title = "Quantization errors in floating-point arithmetic",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "26",
number = "5",
pages = "456--463",
month = oct,
year = "1978",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "In this paper, the quantization of the mantissa in a
normalized floating-point number is investigated. A
necessary and sufficient condition is given for the
mantissa to have a reciprocal probability density. A
model to represent a floating-point quantity \ldots{}",
}
@InProceedings{Svoboda:1978:ACF,
author = "Antonin Svoboda",
title = "Arithmetic Circuit Fault Detection by Modular
Encoding",
crossref = "IEEE:1978:PSC",
pages = "208--219",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Svoboda.pdf",
abstract = "Design principles of self checking digital circuits
are in the focus of the general interest and many
papers exist treating that subject. The use of special
data encoding techniques, suitable algorithms of
arithmetic, special hardware elements have been
proposed long ago. The purpose of this paper is to show
that the design can produce rather simple self checking
circuit when the design principles are chosen which
collaborate harmoniously:\par
(1) decimal numerical system is used\par
(2) decimal digit $ d \in \{ 0, 1, \ldots {}, 9 \} $ is
represented in the Diamond Code by the 5-bit binary
number $ f = 3 d + 2 $ \par
(3) decimal digit' addition algorithm introduced here
is simple and effective so that 10 decimal digits can
be added in parallel\par
(4) implementation of the addition algorithm by
conventional Full Adders results in a single fault
detecting circuit.\par
The design of a decimal adder for 10 decimal numbers,
each with 10 digits. is described here as an
illustration. It shows the way how to design other
decimal arithmetic circuits which are single fault
detecting, for instance a multiplier (derived from the
adder for 10 decimal numbers).",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; decimal arithmetic",
}
@InProceedings{Swartzlander:1978:MAS,
author = "E. E. {Swartzlander, Jr.}",
title = "Merged Arithmetic for Signal Processing",
crossref = "IEEE:1978:PSC",
pages = "239--244",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Swartzlander.pdf",
abstract = "The concept of merged arithmetic is introduced and
applied to signal processing. The basic idea involves
synthesizing a composite arithmetic function (e.g., a
complex multiply) directly instead of decomposing it
into multiply and add operations as is conventional
practice. This approach results in a simpler design
which is also faster.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Tan:1978:TIH,
author = "Kwang G. Tan",
title = "The theory and implementation of high-radix division",
crossref = "IEEE:1978:PSC",
pages = "154--163",
year = "1978",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Tan.pdf",
abstract = "This report derives the theory of high-radix division
in terms of the properties of the overlapped regions of
the P-D plot. The minimum precision requirements in
quotient selection are discussed. The methods of
implementations in hardware and in read-only memory are
explored.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-4",
}
@Article{Trivedi:1978:CUC,
author = "K. S. Trivedi",
title = "Corrections to {``On the Use of Continued Fractions
for Digital Computer Arithmetic''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-27",
number = "3",
pages = "288--288",
month = mar,
year = "1978",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1978.1675093",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 08:13:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Trivedi:1977:UCF}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675093",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Trivedi:1978:HRL,
author = "Kishor S. Trivedi and Joseph G. Rusnak",
title = "Higher Radix On-Line Division",
crossref = "IEEE:1978:PSC",
pages = "164--174",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Trivedi.pdf",
abstract = "We present a formal proof of correctness of the
on-line division algorithm specified in an earlier
paper [1]. We also derive two radix 4 on-line division
algorithms, with non-redundant and redundant operands
respectively.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Tseng:1978:EAF,
author = "B. Tseng and W. Miller and G. Jullien and J. Soltis
and A. Baraniecka",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '78}",
title = "An error analysis of a {FFT} implementation using the
residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "800--803",
year = "1978",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19780088",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper considers an implementation of the FFT
based upon the residue number system. This system
offers the advantages of using integer based arithmetic
operations and a simple hardware realization involving
table look-up arrays. The proposed \ldots{}",
}
@Article{Wang:1978:EPF,
author = "J. Y. Wang",
title = "The Evaluation of Periodic Functions with Large Input
Arguments",
journal = j-SIGNUM,
volume = "13",
number = "4",
pages = "7--9",
month = dec,
year = "1978",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Waser:1978:HMM,
author = "Shlomo Waser",
title = "High-speed monolithic multipliers for real-time
digital signal processing",
journal = j-COMPUTER,
volume = "11",
number = "10",
pages = "19--29",
month = oct,
year = "1978",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Thu Dec 12 07:20:54 MST 1996",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An analysis is made of arithmetic requirements for
signal processing and monolithic multipliers are
characterized. It is shown that real-time digital
signal processing requires very fast multiplication,
which is now becoming possible using mathematical
techniques to take advantage of single-chip
multipliers.",
acknowledgement = ack-nhfb,
classification = "713; 721; 723",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabr = "Computer",
keywords = "signal processing",
}
@Article{Waser:1978:SAH,
author = "S. Waser",
title = "State of the Art in High-Spped Arithmetic {ICs}",
journal = j-COMP-DESIGN,
volume = "??",
number = "??",
pages = "??--??",
month = jul,
year = "1978",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Fri Nov 09 19:34:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Design",
}
@InProceedings{Waser:1978:SAI,
author = "Shlomo Waser",
title = "Survey of Arithmetic Integrated Circuits",
crossref = "IEEE:1978:PSC",
pages = "257--266",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Waser.pdf",
abstract = "The purpose of this report is to provide the
state-of-the-art of high performance arithmetic
integrated circuits (ICs). The survey concentrates on
arithmetic ICs that are designed to improve execution
speed over software techniques, therefore, no
calculator chips are surveyed.\par
In order to understand the difficulties encountered in
fabricating high speed arithmetic ICs, we start the
article with a discussion on semiconductor technology.
Next, we survey the various arithmetic elements that
are available in monolithic form: ALUs, Data Slices,
Multipliers, Floating Point Processors, and ROMs.
Finally, we conclude with a comment on digital signal
processing and a discussion of the future trends in
arithmetic ICs.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4",
}
@InProceedings{Weinberger:1978:PAU,
author = "Arnold Weinberger",
title = "Parallel Adders Using Standard {PLAs}",
crossref = "IEEE:1978:PSC",
pages = "116--124",
year = "1978",
bibdate = "Thu Nov 15 10:49:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Weinberger.pdf",
abstract = "PLA adders are described that add in one cycle and
require a reasonable number of product terms for an 8,
16, or even a 32-bit adder. A procedure is also
described for minimizing the number of product terms
for any size adder.",
acknowledgement = ack-nhfb,
keywords = "adder; ARITH-4; carry-look-ahead; input decoders;
output exclusive-ors; product term minimization;
Programmable Logic Array (PLA)",
}
@Article{Wittmayer:1978:APP,
author = "W. R. Wittmayer",
title = "Array Processor Provides High Throughput Rate",
journal = j-COMP-DESIGN,
volume = "??",
number = "??",
pages = "93--100",
month = mar,
year = "1978",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Fri Nov 09 19:45:09 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Design",
}
@Article{Wozniakowski:1978:REA,
author = "H. Wo{\'z}niakowski",
title = "Round-off error analysis of iterations for large
linear systems",
journal = j-NUM-MATH,
volume = "30",
number = "3",
pages = "301--314",
year = "1978",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Department of Computer Sci., Carnegie-Mellon
University, Pittsburgh, PA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "equations; error analysis; floating point arithmetic;
Gauss Seidel iteration; iteration round off error
analysis; iterative methods; residual vector; sparse
linear systems",
treatment = "A Application; T Theoretical or Mathematical",
}
@InProceedings{Wrathall:1978:CGI,
author = "Celia Wrathall and Tien Chi Chen",
title = "Convergence Guarantee and Improvements for a fast
Hardware Exponential and Logarithm Evaluation Scheme",
crossref = "IEEE:1978:PSC",
pages = "175--182",
year = "1978",
bibdate = "Thu Sep 01 11:46:12 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Wrathall.pdf",
abstract = "In one iteration, Chen's algorithm for evaluating
exponentials and logarithms advances by 2 bits on the
average, yet may not advance at all. Analysis reveals
that the no-advance situation actually paves the way
for sizable advance in the next iteration, and the
guaranteed advance, after a one iteration overhead, is
one bit per iteration.\par
Two new schemes raise the guaranteed advance to 1.5
bits per iteration, after a two-iteration overhead,
while maintaining the original requirement of one
stored constant per operand bit.\par
Adopting as a figure of merit the following
quantity\par
$$ Q = \textrm {advance per iteration} \over \textrm
{memory words per operand hit} $$ \par
for the steady-state iterations, the new schemes
appears to be better than other methods heretofore
proposed.",
acknowledgement = ack-nj,
keywords = "ARITH-4",
}
@Article{Abu-El-Haija:1979:AER,
author = "A. Abu-El-Haija and A. Peterson",
title = "An approach to eliminate roundoff errors in digital
filters",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "27",
number = "2",
pages = "195--198",
month = apr,
year = "1979",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "``Second-order quantizers'' are introduced which can
be used for implementing recursive digital filters with
practically no roundoff errors or limit-cycle
oscillations. Based on the idea of changing the
transfer function used to compute roundoff \ldots{}",
}
@Article{Aggarwal:1979:REM,
author = "Vijay B. Aggarwal and James W. Burgmeier",
title = "A round-off error model with applications to
arithmetic expressions",
journal = j-SIAM-J-COMPUT,
volume = "8",
number = "1",
pages = "60--72",
month = "????",
year = "1979",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68C01 (65G05)",
MRnumber = "81b:68031",
bibdate = "Mon Nov 29 10:58:59 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{Agrawal:1979:HSA,
author = "D. P. Agrawal",
title = "High-Speed Arithmetic Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "3",
pages = "215--224",
month = mar,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675322",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:36 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675322",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Alt:1979:SRD,
author = "H. Alt",
title = "Square Rooting Is as Difficult as Multiplication",
journal = j-COMPUTING,
volume = "21",
number = "3",
pages = "221--232",
year = "1979",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68C25",
MRnumber = "82m:68081",
bibdate = "Tue Jan 2 17:40:54 MST 2001",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Math. \& Information, University of Saarlandes,
Saarbrucken, West Germany",
classification = "723; C5230",
description = "digital arithmetic",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "algorithm; computer programming; square rooting",
}
@Article{Atkins:1979:FSC,
author = "D. E. Atkins",
title = "{Fourth Symposium on Computer Arithmetic}: crunching
with quality and {LSI}",
journal = j-COMPUTER,
volume = "12",
number = "4",
pages = "94--97",
month = apr,
year = "1979",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Thu Dec 12 07:20:54 MST 1996",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Computer arithmetic problems --- faster computation
rates and more efficient representations of real
numbers --- are considered in the paper. Floating-point
arithmetic standardization, novel implementation of
basic arithmetic operators, evaluation of elementary
functions --- these are the main considerations of the
conference review.",
acknowledgement = ack-nhfb,
classification = "722; 723",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabr = "Computer",
keywords = "computer arithmetic; computer systems, digital; data
processing --- data description; mathematical
techniques --- digital arithmetic",
}
@MastersThesis{Barlow:1979:PEA,
author = "Jesse Louis Barlow",
title = "Probabilistic error analysis of computer arithmetics",
type = "{M.S. (Computer Science)}",
school = "Northwestern University",
address = "Evanston, IL, USA",
pages = "????",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; Numbers, Real.; Numerical
calculations --- Computer programs.",
}
@MastersThesis{Biddulph:1979:MFC,
author = "Thomas P. Biddulph",
title = "A modified {FORTRAN\slash 77} compiler that will
implement the proposed {IEEE\slash KCS} floating point
standard via calls to emulation routines",
type = "{Master of Science, Plan II}",
school = "Department of Electrical Engineering and Computer
Sciences",
address = "Berkeley, CA, USA",
pages = "????",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Brent:1979:RLP,
author = "R. P. Brent and H. T. Kung",
title = "A regular layout for parallel adders",
institution = "Computer Science Department, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "20",
year = "1979",
bibdate = "Thu Nov 18 09:31:44 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://books.google.com/books?id=mutgGwAACAAJ",
abstract = "With VLSI architecture the chip area is a better
measure of cost than the conventional gate count. We
show that addition of n-bit binary numbers can be
performed on a chip in time proportional to $ \log n $
and with area proportional to $ n \log n $.",
acknowledgement = ack-nhfb,
}
@Article{Brent:1979:RMF,
author = "R. P. Brent",
title = "Remark on ``{Algorithm} 524: {MP}, {A Fortran}
Multiple-Precision Arithmetic Package [{A1}]''",
journal = j-TOMS,
volume = "5",
number = "4",
pages = "518--519",
month = dec,
year = "1979",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355853.355868",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 05 22:49:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brent:1978:AMF,Brent:1980:AIB}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Brown:1979:EPB,
author = "W. S. Brown and S. I. Feldman",
title = "Environment parameters and basic functions for
floating-point computation",
crossref = "ACM:1979:PSC",
pages = "42--45",
year = "1979",
bibdate = "Fri Nov 28 17:31:00 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bustoz:1979:ITD,
author = "Joaqu{\'i}n Bustoz and Alan Feldstein and Richard
Goodman and Seppo Linnainmaa",
title = "Improved Trailing Digits Estimates Applied to Optimal
Computer Arithmetic",
journal = j-J-ACM,
volume = "26",
number = "4",
pages = "716--730",
month = oct,
year = "1979",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Oct 26 23:35:40 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "New results are given on the distribution of trailing
digits for logarithmically distributed numbers and on
error in floating-point multiplication. Some of the
results have application to computer design. In
particular, there are certain values of the base
(indeed, $ \beta = 2, 4, 6 $, and sometimes, $8$, but
{\em not} $ 16 $) which, when carefully balanced with
other design parameters, minimize the mean
multiplicative error. For these special minimizing
situations, it suffices to have only one guard $ \beta
$ it provided that postnormalization occurs after
symmetric rounding.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "computer arithmetic; floating-point multiplication;
floating-point numbers; floating-point precision and
significance; fraction error; guard digits;
logarithmically distributed numbers; mean and standard
deviation of error; nonleading digits; normalization
options; roundoff error; trailing digits; uniformly
distributed numbers",
}
@Article{Chen:1979:PMB,
author = "I-Ngo Chen and R. Willoner",
title = "An {$ O(n) $} Parallel Multiplier with Bit-Sequential
Input and Output",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "10",
pages = "721--727",
month = oct,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675239",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675239",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cody:1979:IPI,
author = "W. J. Cody",
title = "Impact of The Proposed {IEEE} Floating Point Standard
on Numerical Software",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "29--30",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C4100 (Numerical analysis); C5230 (Digital arithmetic
methods); C7310 (Mathematics computing)",
corpsource = "Appl. Math. Div., Argonne Nat. Lab., Argonne, IL,
USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "digital arithmetic; floating point; IEEE; numerical
analysis; numerical software; standard; standards",
treatment = "P Practical",
xxnumber = "si-2",
}
@Article{Coonen:1979:PSB,
author = "Jerome Coonen and William Kahan and John Palmer and
Tom Pittman and David Stevenson",
title = "A Proposed Standard for Binary Floating Point
Arithmetic: Draft 5.11",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "4--12",
month = oct,
year = "1979",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057520.1057521",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic; binary; digital arithmetic; floating
point; IEEE Computer Society; Microprocessor; standard;
standards; Standards Subcommittee",
treatment = "P Practical",
xxnumber = "si-2",
}
@TechReport{Coonen:1979:SPS,
author = "Jerome T. Coonen",
title = "Specifications for a Proposed Standard for
Floating-Point Arithmetic",
type = "Memorandum",
number = "{UCB\slash ERL M78\slash 72}",
institution = "University of California, Berkeley",
address = "Berkeley, CA, USA",
day = "25",
month = jan,
year = "1979",
bibdate = "Mon Dec 24 08:33:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cybenko:1979:REP,
author = "G. Cybenko",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '79}",
title = "Round-off error propagation in {Durbin}'s,
{Levinson}'s, and {Trench}'s algorithms",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "498--501",
year = "1979",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The subject matter of this paper concerns the
round-off error propagation in order $n^2$ algorithms
for solving problems involving Toeplitz matrices. Since
linear predictive techniques owe much of their appeal
to the computational efficiency \ldots{}",
}
@Article{Diaconis:1979:RP,
author = "Persi Diaconis and David Freedman",
title = "On Rounding Percentages",
journal = j-J-AM-STAT-ASSOC,
volume = "74",
number = "366",
pages = "359--364",
month = jun,
year = "1979",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Nov 23 11:24:59 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
note = "The authors extend prior work on correctness of sums
of rounded percentages \cite{Mosteller:1967:DSR}, and
criticize biased rounding practices in
\cite{Benford:1938:LAN}.",
URL = "http://www.jstor.org/stable/2284288",
acknowledgement = ack-nhfb,
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "Benford's Law; correct rounding; floating-point
arithmetic",
remark = "When percentage-column entries are rounded, their sum
may differ from 100\%. The authors use a prior proof
\cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded
values, the probability of a correct sum is $ \sqrt {6
/ (\pi n)} \approx 1.382 / \sqrt {n} $. They show that
rounding may produce large changes in computed
chi-squared values, and they conclude their article
with this recommendation: ``it is important to
calculate with many-digit accuracy when computing $
\chi^2 $ for large sample sizes.''",
}
@Article{Edgar:1979:FMN,
author = "Albert D. Edgar and Samuel C. Lee",
title = "{FOCUS} Microcomputer Number System",
journal = j-CACM,
volume = "22",
number = "3",
pages = "166--177",
month = mar,
year = "1979",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:37:26 MST 2001",
bibsource = "Compendex database;
http://dblp.uni-trier.de/db/journals/cacm/cacm22.html#EdgarL79;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "FOCUS is a number system and supporting computational
algorithms especially useful for microcomputer control
and other signal processing applications. FOCUS has the
wide-ranging character of floating-point numbers with a
uniformity of state distributions that give FOCUS
better than a twofold accuracy advantage over an equal
word length floating-point system. FOCUS computations
are typically five times faster than single precision
fixed-point or integer arithmetic for a mixture of
operations, comparable in speed with hardware
arithmetic for many applications. Algorithms for 8-bit
and 16-bit implementations of FOCUS are included.",
acknowledgement = ack-nhfb,
classcodes = "C5230 (Digital arithmetic methods); C5250
(Microcomputer techniques)",
classification = "723",
corpsource = "University of Oklahoma, Norman, OK, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "algorithms; arithmetic; computational; computers,
microprocessor; digital arithmetic; floating point
numbers; FOCUS; microcomputer; microcomputer control;
microcomputers; number system; signal processing",
oldlabel = "EdgarL79",
treatment = "P Practical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/EdgarL79",
}
@InProceedings{Eggers:1979:HFP,
author = "Thomas W. Eggers and Judson S. Leonard and Mary H.
Payne",
title = "Handling of floating point exceptions",
crossref = "ACM:1979:PSC",
pages = "100--108",
year = "1979",
bibdate = "Fri Nov 28 17:31:00 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Feldman:1979:IPS,
author = "Stuart I. Feldman",
title = "The Impact of the Proposed Standard for Floating Point
Arithmetic on Languages and Systems",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "31--32",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods); C6140D (High level
languages)",
corpsource = "Bell Labs., Murray Hill, NJ, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic; digital arithmetic; floating point;
languages; programming languages; proposed; standard;
standards; systems",
xxnumber = "si-2",
}
@MastersThesis{Fogler:1979:BFP,
author = "Robert Joseph Fogler",
title = "On a block floating point implementation of an
intrusion-detection algorithm",
type = "Thesis ({M.S.})",
school = "Kansas State University",
address = "Manhattan, KS, USA",
pages = "71",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic alarm systems.; Signal processing.",
}
@Article{Fox:1979:RFP,
author = "Phyllis Fox",
title = "Remark on ``{Algorithm} 528: Framework for a Portable
Library [{Z}]''",
journal = j-TOMS,
volume = "5",
number = "4",
pages = "524--524",
month = dec,
year = "1979",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355853.355871",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Aug 30 00:28:06 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fox:1978:AFP}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Fraley:1979:PED,
author = "Bob Fraley and Steve Walther",
title = "Proposal to Eliminate Denormalized Numbers",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "22--23",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Hewlett--Packard Labs., Palo Alto, CA, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "denormalized numbers; digital arithmetic; expense;
floating point",
treatment = "P Practical",
xxnumber = "si-2",
}
@Article{Gargantini:1979:NSS,
author = "Irene Gargantini",
title = "The Numerical Stability of Simultaneous Iterations Via
Square-Rooting",
journal = j-COMPUT-MATH-APPL,
volume = "5",
number = "1",
pages = "25--31",
month = "????",
year = "1979",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(81)90136-X",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812218190136X",
acknowledgement = ack-jr # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@TechReport{Ginsberg:1979:MFE,
author = "Myron Ginsberg",
title = "Monitoring floating-point error propagation in
scientific computation",
type = "Technical report",
number = "CSE 7910",
institution = "Department of Computer Science and Engineering,
Southern Methodist University",
address = "Dallas, TX, USA",
pages = "32",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
}
@Article{Gregory:1979:EFC,
author = "Robert Todd Gregory",
title = "Error-free computation with finite number systems",
journal = j-SIGNUM,
volume = "14",
number = "3",
pages = "9--16",
month = sep,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "University of Tennessee, Knoxville, TN, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "automatic digital computer; computer-representable
numbers; error free computation; finite; finite number
systems; floating point numbers; machine; numerical
methods; real numbers",
treatment = "T Theoretical or Mathematical",
}
@PhdThesis{Gruener:1979:ARD,
author = "K. Gr{\"u}ner",
title = "{Allgemeine Rechnerarithmetik und deren
Implementierung mit optimaler Genauigkeit} \toenglish
{General Computer Arithmetic and its Implementation
with Optimal Accuracy} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1979",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Hardy:1979:ITN,
author = "G. H. (Godfrey Harold) Hardy and E. M. (Edward
Maitland) Wright",
title = "An Introduction to the Theory of Numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
edition = "Fifth",
pages = "xvi + 426",
year = "1979",
ISBN = "0-19-853170-2, 0-19-853171-0 (paperback)",
ISBN-13 = "978-0-19-853170-8, 978-0-19-853171-5 (paperback)",
LCCN = "A241 .H28 1979",
bibdate = "Fri Nov 30 06:49:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Reprinted in 1988 and 1998 with corrections.",
}
@InProceedings{Hastings:1979:SMM,
author = "C. Hastings",
title = "Shift Matrices: The Missing Teeth in the Number
Cruncher",
crossref = "Anonymous:1979:WCR",
pages = "??--??",
year = "1979",
bibdate = "Fri Nov 09 18:59:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Paper number 18/3.",
acknowledgement = ack-nhfb,
}
@Article{Heath:1979:RDF,
author = "J. Heath and H. {Nagle, Jr.} and S. Shiva",
title = "Realization of digital filters using input-scaled
floating-point arithmetic",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "27",
number = "5",
pages = "469--477",
month = oct,
year = "1979",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See note \cite{Heath:1986:NRD}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "Fixed-point and floating-point realizations of digital
filters are abundant in the literature of digital
signal processing. A block-floating-point realization
which has some advantages of both fixed-point and
floating-point has been reported and \ldots{}",
}
@Article{Hehner:1979:NRR,
author = "E. C. R. Hehner and R. N. S. Horspool",
title = "A new representation of the rational numbers for fast
easy arithmetic",
journal = j-SIAM-J-COMPUT,
volume = "8",
number = "2",
pages = "124--134",
month = "????",
year = "1979",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68C05 (10A30 68A05)",
MRnumber = "80h:68027",
MRreviewer = "P. J. Weinberger",
bibdate = "Mon Nov 29 10:59:01 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See corrigendum \cite{Hehner:1980:CNR}.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@InProceedings{Hull:1979:DFP,
author = "T. E. Hull",
title = "Desirable floating-point arithmetic and elementary
functions for numerical computation",
crossref = "ACM:1979:PSC",
pages = "96--99",
year = "1979",
bibdate = "Mon Jan 08 11:06:31 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The purpose of this talk is to summarize proposed
specifications for floating-polar arithmetic and
elementary functions. The topics considered are: the
base of the number system, precision control, number
representation, arithmetic operations, ocher basic
operations, elementary functions, and exception
handling. The possibility of doing without fixed-point
arithmetic is also mentioned. The specifications are
intended to be entirely at the level of a programming
language such as Fortran. The emphasis is on
convenience and simplicity from the user's point of
view. Conforming to such specifications would have
obvious beneficial implications for the portability of
numerical software, and for proving programs correct,
as well as attempting to provide facilities which are
most suitable for the user. The specifications are not
complete in every detail, but it is intended that they
be complete ``in spirit'' --- some further details,
especially syntactic details, would have to be
provided, but the proposals are otherwise relatively
complete.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Book{Hwang:1979:CAP,
author = "Kai Hwang",
title = "Computer Arithmetic: Principles, Architecture, and
Design",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 423",
year = "1979",
ISBN = "0-471-03496-7",
ISBN-13 = "978-0-471-03496-4",
LCCN = "TK7888.3 .H9",
bibdate = "Sat May 18 14:15:19 2002",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Hwang:1979:GMT,
author = "Kai Hwang",
title = "Global and Modular Two's Complement Cellular Array
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "4",
pages = "300--306",
month = apr,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675350",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675350",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{IEEE:1979:PIF,
author = "Anonymous",
title = "The Proposed {IEEE} floating-point standard",
journal = j-SIGNUM,
pages = "32",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Floating-point arithmetic --- Standards.",
}
@Manual{IntelCorporation:1979:FAL,
author = "Intel Corporation",
title = "8080\slash 8085 floating-point arithmetic library
user's manual",
organization = "The Corporation",
address = "Santa Clara, CA, USA",
pages = "v + 20",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Assembly language (Computer program language).; Intel
8080 (Microprocessor) --- Programming.; INTEL 8085
(Computer) --- Programming.; PL/M-80 (Computer program
language).",
remark = "``Manual Order Number: 9800452-03''.",
}
@Article{Jenkins:1979:RAR,
author = "W. Jenkins",
title = "Recent advances in residue number techniques for
recursive digital filtering",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "27",
number = "1",
pages = "19--30",
month = feb,
year = "1979",
CODEN = "IETABA",
DOI = "https://doi.org/10.1049/el:19780088",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26137",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
keywords = "residue arithmetic; residue number system",
summary = "A new algorithm for scaling in residue number systems
(RNS's) is presented for applying residue number theory
to recursive digital filtering. The algorithm provides
an efficient method for scaling the output of each
recursive filter section for use \ldots{}",
}
@Article{Johnson:1979:RAF,
author = "Donald B. Johnson and Webb Miller and Brian Minnihan
and Celia Wrathall",
title = "Reducibility Among Floating-Point Graphs",
journal = j-J-ACM,
volume = "26",
number = "4",
pages = "739--760",
month = oct,
year = "1979",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "80i:65045",
bibdate = "Fri Dec 08 11:55:10 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The graph-theoretic models of this paper can be used
to compare the rounding-error behavior of numerical
programs. The models follow the approach, popularized
by Wilkinson, of assuming independent rounding errors
in each arithmetic operation. Models constructed on
this assumption are more tractable than would be the
case under more realistic assumptions. There are
identified two easily tested conditions on programs
which guarantee that error analyses are relatively
insensitive to the particular graph model employed. The
development has the additional benefit of sometimes
providing an elementary proof that one program is
comparable in stability to another. Examples of such
results are given.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Kahan:1979:PCK,
author = "William M. Kahan",
title = "Personal Calculator Has Key to Solve Any Equation $
f(x) = 0 $",
journal = j-HEWLETT-PACKARD-J,
volume = "30",
number = "12",
pages = "20--26",
month = dec,
year = "1979",
CODEN = "HPJOAX",
ISSN = "0018-1153",
MRclass = "65-01 (65G05 65H05)",
MRnumber = "MR574853 (81k:65002)",
MRreviewer = "R. P. Brent",
bibdate = "Tue Mar 25 14:12:15 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hpj.bib",
note = "Lecture notes for Math 128.",
URL = "http://www.cs.berkeley.edu/~wkahan/Math128/SOLVEkey.pdf",
acknowledgement = ack-nhfb,
classcodes = "C5420 (Mainframes and minicomputers); C7310
(Mathematics computing)",
corpsource = "Univ. of California, Berkeley, CA, USA",
fjournal = "Hewlett--Packard Journal",
keywords = "electronic calculators; equation solving; finding;
handheld calculator; HP 34C; linear algebra; personal
calculator; root; SOLVE",
reviewer = "R. P. Brent",
treatment = "P Practical",
}
@Article{Kahan:1979:PFP,
author = "W. Kahan and J. Palmer",
title = "On a Proposed Floating-Point Standard",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "13--21",
month = oct,
year = "1979",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057520.1057522",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Wed Mar 19 23:00:11 MST 1997",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
abstract = "A standard for binary floating-point arithmetic is
being proposed and there is a very real possibility
that it will be adopted by many manufacturers and
implemented on a wide range of computers. This
development matters to all of us concerned with
numerical software. One of the principal motivations
for the standard is to distribute more evenly the
burden of portability between hardware and software. At
present, any program intended to be portable must be
designed for a mythical computer that enjoys no
capability not supported by every computer on which the
program will be run. That mythical computer is so much
grubbier than almost any real computer that a portable
program will frequently be denigrated as ``suboptimal''
and then supplanted by another program supposedly
``optimal'' for the real computer in question but often
inferior in critical respects like reliability. A
standard --- almost any reasonable standard --- will
surely improve the situation. A standard environment
for numerical programs will promote fair comparisons
and sharing of numerical codes, thereby lowering costs
and prices. Furthermore, we have chosen repeatedly to
enrich that environment in order that applications
programs be simpler and more reliable. Thus will the
onus of portability be shared among hardware
manufacturers and software producers.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "University of California, Berkeley, CA, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "arithmetic; digital arithmetic; floating point;
proposal; standard; standards",
treatment = "P Practical",
xxnumber = "si-2",
}
@PhdThesis{Kent:1979:TPS,
author = "Jan Kent",
title = "The theoretical and practical study of floating point
instructions: Consisting of Theoretical definition,
analysis and comparison of floating point instruction,
and procedures for the description and simulation of
floating point instructions",
type = "{Dr. Avhandling}",
school = "Universitetet i Oslo",
address = "Oslo, Norway",
year = "1979",
bibdate = "Thu May 09 08:05:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxnote = "Bibsys library catalog gave both 1977 and 1979 as
year??",
}
@TechReport{Kolze:1979:BFP,
author = "Thomas Joseph Kolze",
title = "Block floating point {FFT} statistical noise analysis
program",
type = "Technical report",
number = "CSR-79-2",
institution = "Department of Electrical Engineering, University of
Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "vii + 180",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Communications and signal processing research.",
acknowledgement = ack-nhfb,
keywords = "Radio noise --- Computer programs.; Signals and
signaling --- Computer programs.",
}
@MastersThesis{Kolze:1979:SNA,
author = "Thomas Joseph Kolze",
title = "Statistical noise analysis of a block floating point
{FFT} and an example application",
type = "Electrical Engineering Thesis ({M.S.})",
school = "University of Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "viii + 88",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Kornerup:1979:NRA,
author = "Peter Kornerup",
title = "A note on rational arithmetic",
journal = j-SIGMICRO,
volume = "10",
number = "2",
pages = "28--28",
month = jun,
year = "1979",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1218003.1218004",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:24 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
note = "See \cite{Thacker:1979:MPR,Thacker:1979:R}.",
URL = "https://dl.acm.org/doi/10.1145/1218003.1218004",
abstract = "A recent paper in SIGMICRO [1] contained a comparison
of the accuracy of floating point vs. rational
representations, which is very unfair to the latter.
The format chosen for rational numbers utilizes 16 bits
for numerators and 16 bits for denominators. This
implies that the spacing between consecutive numbers in
the system is in most cases of the order $ 2 {-32} $.
Only around simple rational numbers (e.g. 1/1, 2/3) is
the spacing of the order $ 2 {-16}. $ However the
rounding algorithm presented in [1] will almost
certainly introduce a rounding error of the order $ 2
{-16} $, i.e. introduce an error which in most cases is
of the order $ 2^{16} $ larger than necessary.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Kusterer:1979:SEP,
author = "Roland Kusterer and Manfred Reimer",
title = "Stable Evaluation of Polynomials in Time $ \log n $",
journal = j-MATH-COMPUT,
volume = "33",
number = "147",
pages = "1019--1031",
month = jul,
year = "1979",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-1979-0528054-X;
https://doi.org/10.2307/2006075",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G05 (68C25)",
MRnumber = "80d:65050 (528054)",
MRreviewer = "C. W. Clenshaw",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Math. Inst., University of Dortmund, Dortmund, West
Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithm; approximation theory; number of
multiplications to evaluate a polynomial; polynomials",
reviewer-dates = "Charles William Clenshaw (15 March 1926--23
September 2004)",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Lautz:1979:JLD,
author = "G{\"u}nter Lautz",
title = "{300 Jahre leibnizsches dualzahlensystem}. ({German})
[300 years of the {Leibniz} binary number system]",
journal = j-BIOL-CYBERN,
volume = "35",
number = "3",
pages = "175--181",
month = dec,
year = "1979",
CODEN = "BICYAF",
DOI = "https://doi.org/10.1007/bf00337062",
ISSN = "0340-1200 (print), 1432-0770 (electronic)",
ISSN-L = "0340-1200",
bibdate = "Fri Mar 17 08:46:29 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "300 years ago G. W. Leibniz has invented his binary
number system, now widely used in computer sciences.
The paper recapitulates some informations about the
contents of the first private notes from 1679, partly
reproduced in facsimiles, and the scientific background
of that time. The circumstances and the genesis of the
first treatise on this matter, published in 1703/5 by
Leibniz at the Academy of Sciences, Paris, are
discussed in detail.",
acknowledgement = ack-nhfb,
fjournal = "Biological cybernetics",
journal-URL = "http://link.springer.com/journal/422",
language = "German",
}
@Article{Lee:1979:AFN,
author = "S. C. Lee and A. D. Edgar",
title = "Addendum to {``The Focus Number System''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "9",
pages = "693--693",
month = sep,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675442",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Lee:1977:FNS,Swartzlander:1979:CFN}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675442",
abstract = "In 1971 Kingsbury and Rayner, publishing under the
title ``Digital Filtering Using Logarithmic
Arithmetic'' disclosed a sign-plus-logarithm number
system, and a means of performing addition through
single dimensional lookup using the formula $ c = b +
F(a b) $. The system was demonstrated on a computer. In
1975 Swartzlander and Alexopoulos disclosed Kingsbury's
logarithmic arithmetic as ``The Sign\slash Logarithm
Number System''. In 1977, without knowledge of prior
art, we reinvented the wheel a third time, dubbing it
``Focus,'' after the focus of resolution around the
zero origin [3]. We wish now to acknowledge Kingsbury
and Rayner as the pioneer authors, and also
Swartzlander and Alexopoulos as prior to our
publication.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{McDonnell:1979:FR,
author = "Eugene McDonnell",
title = "Fuzzy residue",
journal = j-APL-QUOTE-QUAD,
volume = "9",
number = "4",
pages = "42--46",
year = "1979",
CODEN = "APLQD9",
DOI = "https://doi.org/10.1145/390009.804437",
ISSN = "0163-6006 (print), 1558-3392 (electronic)",
ISSN-L = "0163-6006",
bibdate = "Thu Aug 07 19:13:11 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Certain pairs of arguments to the residue function, as
implemented on many APL systems, give results which
make it seem as if the ordinary decimal relationships
we remember from grade school no longer hold. As far as
we can tell, it looks as if a given modulus should
divide the right argument, but the implementation tells
us it doesn't. A definition for a fuzzed residue
function is proposed which resolves the difficulties
users have complained of. However, certain points of
continuing difficulty remain, where the limitations of
machine arithmetic continue to defeat the attempt to
model the real number system. The representation
function is defined in terms of the residue function,
and so is affected by the change in residue. The nature
of this effect is also discussed in this paper.",
acknowledgement = ack-nhfb,
fjournal = "APL Quote Quad",
}
@Book{Oberman:1979:DCB,
author = "R. M. M. (Roelof Maarten Marie) Oberman",
title = "Digital circuits for binary arithmetic",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 340",
year = "1979",
ISBN = "0-470-26373-3",
ISBN-13 = "978-0-470-26373-0",
LCCN = "TK7868.L6 O23 1979",
bibdate = "Wed Nov 14 17:33:15 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "A Halsted Press book.",
subject = "logic circuits; digital integrated circuits; switching
theory",
}
@Article{Oliver:1979:REP,
author = "J. Oliver",
title = "Rounding error propagation in polynomial evaluation
schemes",
journal = j-J-COMPUT-APPL-MATH,
volume = "5",
number = "2",
pages = "85--97",
month = jun,
year = "1979",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:18 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0771050X79900020",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Payne:1979:DPB,
author = "Mary Payne and William Strecker",
title = "Draft Proposal for a Binary Normalized Floating Point
Standard",
journal = j-SIGNUM,
volume = "14",
number = "3S (Special issue)",
pages = "24--28",
month = oct,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:07 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Digital Equipment Corp., Maynard, MA, USA",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "binary; digital arithmetic; floating point;
normalized; proposal; standard; standards",
treatment = "P Practical",
xxnumber = "si-2",
}
@TechReport{Randell:1979:ABO,
author = "Brian Randell",
title = "An annotated bibliography on the origins of digital
computers",
type = "Technical report",
number = "140",
institution = "Computing Laboratory, University of Newcastle upon
Tyne",
address = "Newcastle upon Tyne, UK",
pages = "146",
year = "1979",
LCCN = "Z5642.2 .R36 1979",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "Electronic digital computers; History; Bibliography;
Calculators",
}
@InCollection{Rauch:1979:EAA,
author = "E. Rauch",
title = "{Einige Aspekte der Auswahl und Realisierung
numerischer Verfahren in anwendungsorientierten
Systemen} \toenglish {Several Aspects of the Choice and
Realisation of Numerical Procedures in
Application-Oriented Systems} \endtoenglish",
crossref = "Meinardus:1979:ATP",
pages = "??--??",
year = "1979",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Redinbo:1979:FFA,
author = "G. R. Redinbo",
title = "Finite Field Arithmetic on an Array Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "7",
pages = "461--471",
month = jul,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675390",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675390",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Reid:1979:FMF,
author = "John Reid",
title = "Functions for Manipulating Floating-Point Numbers",
journal = j-SIGNUM,
volume = "14",
number = "4",
pages = "11--13",
month = dec,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-nj,
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Computer Sci. and Systems Div., AERE, Harwell, UK",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "complex numbers; digital arithmetic; floating;
FORTRAN; point arithmetic; portability; precision",
treatment = "P Practical",
}
@Article{Reinsch:1979:PPC,
author = "Christian H. Reinsch",
title = "Principles and Preferences for Computer Arithmetic",
journal = j-SIGNUM,
volume = "14",
number = "1",
pages = "12--27",
month = mar,
year = "1979",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:06 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Leibniz-Rechenzentrum, Munich, West Germany",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "computer arithmetic; digital arithmetic",
treatment = "T Theoretical or Mathematical",
}
@Article{Rink:1979:CEF,
author = "R. Rink and H. Chong",
title = "Covariance equation for a floating-point regulator
system",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "24",
number = "6",
pages = "980--982",
month = dec,
year = "1979",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "Derived are linear equations that can be solved for
the steady-state covariance matrix of the plant and
observer states of a closed-loop regulator system which
employs finite wordlength A/D conversion and
floating-point computation in the observer/ \ldots{}",
}
@Article{Rink:1979:PSR,
author = "R. Rink and Hoi Chong",
title = "Performance of state regulator systems with
floating-point computation",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "24",
number = "3",
pages = "411--421",
month = jun,
year = "1979",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Rink:1980:CPS}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
summary = "The performance of a digital state regulator system
having an A/D converter of finite wordlength and a
floating-point estimator/ controller computer of finite
mantissa-length is analyzed. An upper bound on the
mean-square state error, as a function \ldots{}",
}
@Article{Robertson:1979:VPA,
author = "D. A. Robertson",
title = "Variable precision arithmetic on {CDC 6000\slash 7000}
machines",
journal = j-SPE,
volume = "9",
number = "3",
pages = "247--248",
month = mar,
year = "1979",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380090310",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "27 Oct 2006",
}
@MastersThesis{Scharf:1979:HRW,
author = "Stuart Lee Scharf",
title = "A hardware realization of the {Winograd Fourier}
Transform Algorithm",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical and Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "109",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by James H. McClellan.",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Computer engineering.; Floating-point
arithmetic.; Fourier transformations --- Computer
programs.",
}
@InProceedings{Shapiro:1979:ELM,
author = "G. Shapiro",
title = "Exploit {LSI} Memory Components Today, Instead of
Waiting for Arithmetic Devices",
crossref = "Anonymous:1979:WCR",
pages = "??--??",
year = "1979",
bibdate = "Fri Nov 09 19:15:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Paper 18/5.",
acknowledgement = ack-nhfb,
}
@Book{Shauman:1979:OMA,
author = "Aleksandr Mikhailovich Shauman",
title = "Osnovy mashinnoi arifmetiki \toenglish {Principles of
Machine Arithmetic} \endtoenglish",
publisher = "Izd-vo LGU (Leningrad State University Publishers)",
address = "Leningrad, USSR",
pages = "311",
year = "1979",
LCCN = "QA76.6 .S516",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Electronic
digital computers --- Programming.; Floating-point
arithmetic.",
remark = "At head of title: Leningradskii Gosudarstvennyi
universitet imeni A. A. Zhdanova. Bibliography: p.
306-[309]",
}
@Article{Sheue:1979:TCM,
author = "A. E. Sheue",
title = "Two's-Complement Multiplication",
journal = j-SIGMICRO,
volume = "10",
number = "1",
pages = "21--23",
month = mar,
year = "1979",
CODEN = "SIGMDJ",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIG Micro Newsletter",
}
@Article{Swartzlander:1979:CFN,
author = "E. E. {Swartzlander, Jr.}",
title = "Comment on {``The Focus Number System''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "9",
pages = "693--693",
month = sep,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675441",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
note = "See \cite{Lee:1977:FNS,Lee:1979:AFN}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675441",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Thacker:1979:MPR,
author = "William I. Thacker and G. W. Gorsline",
title = "Micro programming rational arithmetic operations",
journal = j-SIGMICRO,
volume = "10",
number = "1",
pages = "10--13",
month = mar,
year = "1979",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1217236.1217238",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:24 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
note = "See critical comments \cite{Kornerup:1979:NRA} and
response \cite{Thacker:1979:R}.",
URL = "https://dl.acm.org/doi/10.1145/1217236.1217238",
abstract = "For many years, real number arithmetic, whether
accomplished in hardware, software, or firmware, has
utilized a floating point scheme. This paper summarizes
the results of a study assessing rational
representation as a possible replacement for floating
point representation. The Hewlett-Packard 2100A
microprogrammable computer was used as the test
vehicle. Both accuracy and speed comparisons were used
to judge the usefulness of the substitution.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Thacker:1979:R,
author = "W. I. Thacker and G. W. Gorsline",
title = "Response",
journal = j-SIGMICRO,
volume = "10",
number = "2",
pages = "29--29",
month = jun,
year = "1979",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1218003.1218005",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:24 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
note = "See \cite{Thacker:1979:MPR,Kornerup:1979:NRA}.",
URL = "https://dl.acm.org/doi/10.1145/1218003.1218005",
abstract = "Within the context of our study; that is, the direct
substitution of a pure rational scheme for a floating
point scheme of arithmetic and storage within an extant
FORTRAN system with no changes to the compiler (and
thus to the storage space available for a single
numerical quantity), we continue to claim that our
results are valid. We again wish to note that our
investigation was limited to the pure rational scheme
using the same storage space available to a floating
point scheme.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Tseng:1979:IFS,
author = "Ben-Dau Tseng and G. A. Jullien and W. C. Miller",
title = "Implementation of {FFT} Structures Using the Residue
Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-28",
number = "11",
pages = "831--845",
month = nov,
year = "1979",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1979.1675263",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 06:49:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675263;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35176",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "This paper considers the implementation of a fast
Fourier transform (FFT) structure using arrays of
read-only memories. The arithmetic operations are based
entirely on the residue number system. The most
important aspect of the structure relates to \ldots{}",
}
@Article{Ukkonen:1979:AER,
author = "Esko Ukkonen",
title = "An analysis of the effect of rounding errors on the
flow of control in numerical processes",
journal = j-BIT,
volume = "19",
number = "1",
pages = "116--133",
month = mar,
year = "1979",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01931229",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "81a:65048",
bibdate = "Wed Jan 4 18:52:16 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=1&spage=116",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@InProceedings{vanHulzen:1979:NMS,
author = "J. A. {van Hulzen}",
title = "A note on methods for solving systems of polynomial
equations with floating point coefficients",
crossref = "Ng:1979:SAC",
pages = "346--357",
year = "1979",
MRclass = "65H10",
MRnumber = "81h:65049",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Frederick N. Fritsch",
}
@Article{Wichmann:1979:ID,
author = "B. A. Wichmann",
title = "Integer division",
journal = j-SPE,
volume = "9",
number = "6",
pages = "507--508",
month = jun,
year = "1979",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380090610",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "27 Oct 2006",
}
@Article{Wichmann:1979:PCG,
author = "B. A. Wichmann and J. {Du Croz}",
title = "A program to calculate the {GAMM} measure",
journal = j-COMP-J,
volume = "22",
number = "4",
pages = "317--322",
month = nov,
year = "1979",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C4240 (Programming and algorithm theory); C7430
(Computer engineering)",
classification = "723",
corpsource = "Computing Services Unit, Nat. Phys. Lab., Teddington,
UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "analysis; complete computer programs; computer
performance; computer programs; computer selection and;
confidence check; error; evaluation; floating point
calculation; FORTRAN program; GAMM measure; performance
evaluation",
treatment = "P Practical",
}
@MastersThesis{Wilbanks:1979:MFI,
author = "Thomas D. Wilbanks",
title = "Microcoding floating-point instructions for a
bit-slice processor",
type = "Thesis ({M.S.})",
school = "University of South Carolina",
address = "Columbia, SC, USA",
pages = "vi + 131",
year = "1979",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Bit slice microprocessors.; Microprocessors ---
Programming.",
}
@InProceedings{Winnigstad:1979:ULC,
author = "C. N. Winnigstad",
title = "Using {LSI} to Crunch Numbers at High Speed: An
Overview",
crossref = "Anonymous:1979:WCR",
pages = "??--??",
year = "1979",
bibdate = "Fri Nov 09 19:43:13 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Yohe:1979:INA,
author = "J. M. Yohe",
title = "Implementing Nonstandard Arithmetics",
journal = j-SIAM-REVIEW,
volume = "21",
number = "1",
pages = "34--56",
month = "????",
year = "1979",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1021003",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb # " and " # ack-jr,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Agrawal:1980:NBA,
author = "D. P. Agrawal",
title = "On Negabinary-Binary Arithmetic Relationships and
Their Hardware Reciprocity",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "11",
pages = "1032--1035",
month = nov,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675502",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675502",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Albrecht:1980:RAO,
author = "R. Albrecht",
title = "Roundings and Approximations in Ordered Sets",
crossref = "Alefeld:1980:FNC",
pages = "17--31",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rounding error",
}
@Article{Ambikairajah:1980:TPM,
author = "E. Ambikairajah and M. J. Carey",
title = "Technique for Performing Multiplication on a 16-bit
Microprocessor Using an Extension of {Booth}'s
Algorithm",
journal = j-ELECT-LETTERS,
volume = "16",
number = "2",
pages = "53--54",
month = jan,
year = "1980",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Baraniecka:1980:RNS,
author = "A. Baraniecka and G. Jullien",
title = "Residue number system implementations of number
theoretic transforms in complex residue rings",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "28",
number = "3",
pages = "285--291",
month = jun,
year = "1980",
CODEN = "IETABA",
DOI = "https://doi.org/10.1109/TC.1979.1675263",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26146",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
keywords = "residue arithmetic; residue number system",
summary = "This paper discusses the implementation of number
theoretic transforms defined in complex residue rings.
A selection of transform parameters for lookup table
and microprocessor realizations are discussed. When the
length of the convolution is \ldots{}",
}
@Article{Bareiss:1980:RED,
author = "E. H. Bareiss and J. L. Barlow",
title = "Roundoff error distribution in fixed point
multiplication",
journal = j-BIT,
volume = "20",
number = "2",
pages = "247--250",
month = jun,
year = "1980",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933198",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "81j:65066",
MRreviewer = "Seppo Linnainmaa",
bibdate = "Wed Jan 4 18:52:16 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=2&spage=247",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Barsi:1980:ECC,
author = "Ferruccio Barsi and Piero Maestrini",
title = "Error codes constructed in residue number systems with
non-pairwise-prime moduli",
journal = j-INF-CONTROL,
volume = "46",
number = "1",
pages = "16--25",
month = jul,
year = "1980",
CODEN = "IFCNA4",
DOI = "https://doi.org/10.1016/S0019-9958(80)90471-4",
ISSN = "0019-9958 (print), 1878-2981 (electronic)",
ISSN-L = "0019-9958",
bibdate = "Thu Nov 18 09:54:38 2010",
bibsource = "http://www.sciencedirect.com/science/journal/00199958;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Codes constructed in a Residue Number System (RNS) of
moduli $ m_1, m_2, \ldots {}, m_n $ are non-binary,
arithmetic codes whose codewords are vectors where the
$i$ th component is $ m_i $-valued $ (1 \leq i \leq n)
$. A new class of codes in RNS is described, where
redundancy is introduced by removing the constraint
that the moduli of the RNS be pairwise prime. The
error-detecting and correcting capabilities of such
codes are discussed and a simple approach to error
detection, localization and correction is presented.
Although the codes under consideration are quite
inefficient in some respects, it is shown that codes is
examined in more detail. Codes in this subclass,
besides correcting all single errors, also correct
almost all of double errors and localize some errors of
higher multiplicity, with less redundancy than required
to construct optimal 2-correcting codes in RNS.",
acknowledgement = ack-nhfb,
fjournal = "Information and Control",
journal-URL = "http://www.sciencedirect.com/science/journal/00199958",
}
@Article{Brent:1980:AIB,
author = "Richard P. Brent and Judith A. Hooper and J. Michael
Yohe",
title = "An {AUGMENT} Interface for {Brent}'s Multiple
Precision Arithmetic Package",
journal = j-TOMS,
volume = "6",
number = "2",
pages = "146--149",
month = jun,
year = "1980",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355887.355889",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 05 22:49:19 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brent:1978:AMF,Brent:1979:RMF}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "arithmetic, multiple precision, extended precision,
floating point, portable software, software package,
precompiler interface, AUGMENT interface",
}
@InProceedings{Brent:1980:UAE,
author = "R. P. Brent",
title = "Unrestricted Algorithms for Elementary and Special
Functions",
crossref = "Lavington:1980:IPP",
pages = "613--619",
year = "1980",
bibdate = "Thu Sep 01 11:55:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Brown:1980:EPB,
author = "W. S. Brown and S. I. Feldman",
title = "Environment Parameters and Basic Functions for
Floating-Point Computation",
journal = j-TOMS,
volume = "6",
number = "4",
pages = "510--523",
month = dec,
year = "1980",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355921.355924",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Sep 1 10:15:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "environment parameters, floating-point arithmetic,
software portability",
}
@TechReport{Brown:1980:SRM,
author = "W. S. Brown",
title = "A Simple But Realistic Model of Floating-Point
Computation",
type = "Computer Science Technical Report",
number = "83",
institution = "Bell Laboratories",
address = "Murray Hill, NJ, 07974, USA",
month = may,
year = "1980",
bibdate = "Wed Oct 13 06:30:12 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised November 1980.",
acknowledgement = ack-nhfb,
remark = "See \cite[pp. 1.9--1.10]{Coonen:1984:CPS} for negative
comments about the model in this report.",
}
@Article{Burmeister:1980:OIE,
author = "W. Burmeister",
title = "Optimal interval enclosing of certain sets of
matrices, with application to monotone enclosing of
square roots",
journal = j-COMPUTING,
volume = "25",
number = "3",
pages = "283--295",
year = "1980",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65F30 (15A57)",
MRnumber = "82e:65044",
bibdate = "Tue Jan 2 17:40:54 MST 2001",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "Sektion Math., Tech. University of Dresden, Dresden,
East Germany",
classification = "C4140",
description = "matrix algebra",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "cone; elementwise inclusion; interval enclosing;
matrix interval; optimal bounds; partial ordering",
}
@Article{Chang:1980:CAE,
author = "T. Chang",
title = "Comments on {``An} approach to eliminate roundoff
errors in digital filters''",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "28",
number = "2",
pages = "244--244",
month = apr,
year = "1980",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
}
@InProceedings{Cheng:1980:ASC,
author = "S. Cheng and K. Rallapalli",
title = "Am9512: Single Chip Floating-Point Processor",
crossref = "Electro:1980:ECR",
pages = "14/4/1--6",
year = "1980",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
remark = "The Am 9512 floating-point processor is claimed on at
least one Web page to be compatible with the Intel
8232, and that page claims the 8232 has IEEE
floating-point, while the earlier 8231 and 8231A were
some other format (see \cite{Intel:19xx:IAP} for a
brief description of the 8231A 32-bit floating-point
encoding).",
}
@PhdThesis{Chow:1980:VPP,
author = "Catherine Yuk-Fun Chow",
title = "A variable precision processor module",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "vi + 183",
month = jul,
year = "1980",
LCCN = "QA76 .I4 no. 1032",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "UIUCDCS-R 80-1032",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Floating-point arithmetic.; Parallel processing
(Electronic computers)",
}
@Article{Cluley:1980:DCB,
author = "J. C. Cluley",
title = "Digital Circuits for Binary Arithmetic",
journal = j-COMP-J,
volume = "23",
number = "3",
pages = "269--269",
month = aug,
year = "1980",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/23.3.269",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:08 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/23/3.toc;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/23/3/269.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Book{Cody:1980:SME,
author = "W. J. Cody and W. Waite",
title = "Software Manual for the Elementary Functions",
publisher = pub-PH,
address = pub-PH:adr,
pages = "x + 269",
year = "1980",
ISBN = "0-13-822064-6",
ISBN-13 = "978-0-13-822064-8",
LCCN = "QA331 .C635 1980",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Coonen:1980:IGP,
author = "Jerome T. Coonen",
title = "An Implementation Guide to a Proposed Standard for
Floating-Point Arithmetic",
journal = j-COMPUTER,
volume = "13",
number = "1",
pages = "68--79",
month = jan,
year = "1980",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/MC.1980.1653344",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sun May 02 09:17:48 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See errata in \cite{Coonen:1981:EIG}. See
\cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Dao:1980:CNA,
author = "T. T. Dao and M. Davio and C. Gossart",
title = "Complex Number Arithmetic with Odd-Valued Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "7",
pages = "604--611",
month = jul,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675631",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675631",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{DeVaal:1980:SZI,
author = "C. {De Vaal} and R. Nouta",
title = "On the suppression of zero-input parasitic
oscillations in floating point wave digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "27",
number = "2",
pages = "144--145",
month = feb,
year = "1980",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Fettweis [1] has given a condition which guarantees,
if satisfied, the absence of zero-input parasitic
oscillations in wave digital filters. In this paper a
method is given which can be used to implement this
condition in the case of floating point \ldots{}",
}
@Article{Etzel:1980:RRN,
author = "M. Etzel and W. Jenkins",
title = "Redundant residue number systems for error detection
and correction in digital filters",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "28",
number = "5",
pages = "538--545",
month = oct,
year = "1980",
CODEN = "IETABA",
DOI = "https://doi.org/10.1109/TC.1979.1675263",
ISSN = "0096-3518",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26148",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
keywords = "residue arithmetic; residue number system",
summary = "In spite of rapid advances during the last few years
in the design and realization of digital filters, very
little attention has been given to the problems of
error detection and correction in digital filters. This
paper describes how redundant \ldots{}",
}
@InProceedings{Farrell:1980:PFP,
author = "L. Farrell",
title = "8232: a Peripheral for Floating-Point Arithmetic",
crossref = "IEEE:1980:PMA",
pages = "13--18",
year = "1980",
bibdate = "Wed Sep 07 22:25:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Unpublished{Fraley:1980:PSB,
author = "R. A. Fraley and J. S. Walther",
title = "A Proposed Standard for Binary Floating-Point
Arithmetic, Alternative 3, Draft 1",
day = "4",
month = jan,
year = "1980",
bibdate = "Thu Nov 25 10:19:54 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in \cite{Payne:1980:VFPb}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Fraley:1980:STO,
author = "R. A. Fraley and J. S. Walther",
title = "Safe Treatment of Overflow and Underflow Conditions",
crossref = "Electro:1980:ECR",
pages = "18/2/1--5",
year = "1980",
bibdate = "Wed Sep 07 21:38:30 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Gajski:1980:PC,
author = "D. D. Gajski",
title = "Parallel Compressors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "5",
pages = "393--398",
month = may,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675589",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 10:56:18 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gargantini:1980:PSR,
author = "Irene Gargantini",
title = "Parallel Square-Root Iterations for Multiple Roots",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "3",
pages = "279--288",
month = "????",
year = "1980",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122180900358",
acknowledgement = ack-jr # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@Article{Ginsberg:1980:MFE,
author = "Myron Ginsberg",
title = "Monitoring floating-point error propagation in
scientific computation",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "1",
pages = "23--43",
year = "1980",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65G10 (65-04)",
MRnumber = "82a:65031",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxnote = "Special Issue",
}
@Article{Ginsberg:1980:MFP,
author = "Myron Ginsberg",
title = "Monitoring Floating-Point Error Propagation in
Scientific Computation",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "1",
pages = "23--43",
month = "????",
year = "1980",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65G10 (65-04)",
MRnumber = "82a:65031",
bibdate = "Wed Mar 1 18:51:18 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122180900577",
acknowledgement = ack-jr # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
xxnote = "Special Issue",
}
@Article{Goodwin:1980:PNU,
author = "D. T. Goodwin",
title = "Partial Non-Underflow and Non-Overflow of an
Arithmetic Stack",
journal = j-COMP-J,
volume = "23",
number = "2",
pages = "153--160",
month = may,
year = "1980",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/23.2.153",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "68B20",
MRnumber = "81i:68039",
bibdate = "Tue Dec 4 14:48:08 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/23/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/23/2/153.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/153.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/154.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/155.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/156.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/157.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/158.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/159.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/160.tif",
acknowledgement = ack-nhfb,
classcodes = "C6150J (Operating systems)",
classification = "723",
corpsource = "Department of Computer Sci., University of Keele,
Newcastle-under-Lyme, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic stack; computer programming; high level
language compile time; overflow; stack; storage
allocation; underflow",
reviewer = "K. S. Fu",
treatment = "P Practical",
}
@Book{Gosling:1980:DAU,
author = "John B. Gosling",
title = "Design of Arithmetic Units for Digital Computers",
publisher = pub-MAC,
address = pub-MAC:adr,
pages = "x + 139",
year = "1980",
ISBN = "0-387-91171-5, 0-333-26397-9, 0-333-26398-7",
ISBN-13 = "978-0-387-91171-7, 978-0-333-26397-6,
978-0-333-26398-3",
LCCN = "QA76.6.G668, TK7888.3 .G64 1980",
bibdate = "Wed Sep 07 20:43:22 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Grappel:1980:IZP,
author = "R. Grappel and J. Hemenway",
title = "Increase {Z8000} power with floating-point routines",
journal = j-EDN,
volume = "25",
number = "8",
pages = "179--185",
month = apr,
year = "1980",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Book{Gregory:1980:ECW,
author = "Robert Todd Gregory",
title = "Error-Free Computation: Why it is Needed and Methods
for Doing it",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "vi + 152",
year = "1980",
ISBN = "0-89874-240-4",
ISBN-13 = "978-0-89874-240-4",
LCCN = "QA297.5 .G73",
MRclass = "65G05",
MRnumber = "MR586772 (83f:65061)",
bibdate = "Sat Sep 03 10:09:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Approximation theory --- Data processing;
Floating-point arithmetic",
tableofcontents = "1: Mathematics vs. Numerical Mathematics \\
2: Ill-Conditioned Problems vs. Numerically Unstable
Algorithms \\
3: A Scaling Problem \\
4: ?? \\
5: ?? \\
Index",
}
@Article{Gruner:1980:IUC,
author = "K. Gr{\"u}ner",
title = "Implementation of Universal Computer Arithmetic with
Optimal Accuracy",
journal = j-COMPUTING,
volume = "24",
number = "2--3",
pages = "181--193",
year = "1980",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G99 (68A05)",
MRnumber = "83c:65118",
bibdate = "Tue Jan 2 17:40:54 MST 2001",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
INSPEC Axiom database (1968--date); MathSciNet
database",
acknowledgement = ack-nhfb,
affiliation = "University of Karlsruhe, Karlsruhe, West Germany",
classification = "C4240",
description = "computational complexity",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer programming; fast
algorithms; intervals; mapping properties; matrices;
numerical computations; universal computer arithmetic;
vectors; word length",
}
@TechReport{Hamacher:1980:DCV,
author = "V. Carl Hamacher",
title = "Design of a {CPU} for variable precision, decimal
arithmetic",
type = "Technical Report",
number = "ABC",
institution = "Department of Electrical Engineering, University of
Toronto",
address = "Toronto, ON, Canada",
month = "????",
year = "1980",
bibdate = "Sun Dec 30 15:37:50 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@Article{Havender:1980:DBF,
author = "J. W. Havender",
title = "Decimal-to-binary floating point number conversion
mechanism",
journal = j-IBM-TDB,
volume = "23",
number = "2",
pages = "706--708",
month = jul,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point numbers may be converted from decimal
to binary using a high speed natural logarithm and
exponential function calculation mechanism and a fixed
point divide/multiply unit.\par
The problem solved is to convert numbers expressed in a
radix 10 floating point form to numbers expressed in a
radix 2 floating point form.",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Article{Havender:1980:DBN,
author = "J. W. Havender",
title = "Decimal-to-binary Number Conversion",
journal = j-IBM-TDB,
volume = "23",
number = "3",
pages = "1126--1127",
month = aug,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Article{Haviland:1980:CAP,
author = "G. L. Haviland and A. A. Tuszynski",
title = "A {CORDIC} Arithmetic Processor Chip",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "2",
pages = "68--79",
month = feb,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675529",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 00:47:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Head:1980:MM,
author = "A. K. Head",
title = "Multiplication modulo $n$",
journal = j-BIT,
volume = "20",
number = "1",
pages = "115--116",
month = mar,
year = "1980",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933594",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68-04 (65G10)",
MRnumber = "81g:68001",
MRreviewer = "K. Kilberth",
bibdate = "Wed Jan 4 18:52:16 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=1&spage=115",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Hehner:1980:CNR,
author = "E. C. R. Hehner and R. N. S. Horspool",
title = "Corrigendum: {``A new representation of the rational
numbers for fast easy arithmetic'' [SIAM J. Comput.
{\bf 8} (1979), no. 2, 124--134, MR 80h:68027]}",
journal = j-SIAM-J-COMPUT,
volume = "9",
number = "1",
pages = "217--217",
month = "????",
year = "1980",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68C05 (10A30)",
MRnumber = "81f:68044",
bibdate = "Mon Nov 29 10:59:12 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/9/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Hehner:1979:NRR}.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{Henrich:1980:FPA,
author = "C. J. Henrich",
title = "Floating-point arithmetic: can it be trusted?",
journal = j-MINI-MICRO-SYSTEMS,
volume = "13",
number = "11",
pages = "143--151",
month = nov,
year = "1980",
CODEN = "XWJXEH",
ISSN = "1000-1220",
bibdate = "Wed Sep 14 19:14:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mini-Micro Systems",
}
@InProceedings{Henrici:1980:MPR,
author = "Peter Henrici",
booktitle = "Interval mathematics, 1980 ({Freiburg}, 1980)",
title = "A model for the propagation of rounding error in
floating arithmetic",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "49--73",
year = "1980",
DOI = "https://doi.org/10.1016/B978-0-12-518850-0.50009-3",
ISBN = "0-12-518850-1",
ISBN-13 = "978-0-12-518850-0",
MRclass = "65G05",
MRnumber = "651358",
bibdate = "Mon Jan 28 07:08:10 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/B9780125188500500093",
abstract = "The subject of propagation of rounding error, while of
undisputed importance in numerical analysis, is
notorious for the difficulties that it presents when it
is to be taught in the classroom in such a manner that
the student is neither insulted by lack of mathematical
content nor bored by lack of transparence and clarity.
On examination of some classical approaches, it appears
that the effect of tedium is often achieved by the
attempt of being absolutely rigorous. Absolute rigor in
error analysis is a triviality. Perhaps, what is
required in error analysis is not so much rigor but
rather an understanding why some algorithms work and
others do not. This chapter presents a model for the
propagation of rounding error in floating arithmetic
that aims at such an understanding. To bring to light
the essential consequences of floating arithmetic, the
model makes certain idealizing or simplifying
assumptions that are not always satisfied on real-life
computers. The model nevertheless furnishes realistic
descriptions of the numerical performance of a large
class of algorithms that can be described in terms of
operations on real numbers.",
acknowledgement = ack-nhfb,
author-dates = "Peter Karl Henrici (13 September 1923--13 March
1987)",
}
@PhdThesis{Holm:1980:FAP,
author = "John Erick Holm",
title = "Floating-point arithmetic and program correctness
proofs",
type = "Thesis ({Ph.D.})",
school = "Cornell University",
address = "Ithaca, NY, USA",
pages = "vii + 133",
month = aug,
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
}
@Article{Horna:1980:FAC,
author = "O. A. Horna",
title = "Fast algorithms for the computation of binary
logarithms",
journal = "COMSAT Technical Review",
volume = "10",
number = "1",
pages = "91--101",
month = "Spring",
year = "1980",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Hough:1980:APS,
author = "D. Hough",
title = "Applications of a Proposed Standard for Floating-Point
Arithmetic",
crossref = "Electro:1980:ECR",
pages = "18/3/1--6",
year = "1980",
bibdate = "Wed Sep 07 21:39:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Hull:1980:PPI,
author = "Thomas E. Hull and Christian H. Reinsch and John R.
Rice",
title = "Principles, Preferences and Ideals for Computer
Arithmetic",
type = "Technical report",
number = "TR-339",
institution = inst-CS-PURDUE,
address = inst-CS-PURDUE:adr,
pages = "13",
day = "1",
month = jun,
year = "1980",
bibdate = "Sun Dec 30 13:46:29 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-339.pdf",
abstract = "This paper presents principles and preferences for the
implementation of computer arithmetic and ideals for
the arithmetic facilities in future programming
languages. The implementation principles and
preferences are for the current approaches to the
design of arithmetic units. The ideals are for the long
term development of programming languages, with the
hope that arithmetic units will be built to support the
requirements of programming languages.",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
keywords = "decimal floating-point arithmetic",
}
@Article{Jenkins:1980:CRN,
author = "W. K. Jenkins",
title = "Complex residue number arithmetic for high-speed
signal processing",
journal = j-ELECT-LETTERS,
volume = "16",
number = "17",
pages = "660--661",
day = "14",
month = aug,
year = "1980",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
MRclass = "94A05",
MRnumber = "MR583226 (81h:94003)",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4244229",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "Complex residue number arithmetic is developed for
high-speed processing of complex waveforms. An
important feature of complex residue arithmetic is that
complex multiplication can be implemented by a real
index calculus, thereby providing a highly \ldots{}",
}
@Article{Johannes:1980:DSE,
author = "J. D. Johannes and C. Dennis Pegden and F. E. Petry",
title = "Decimal Shifting for an Exact Floating Point
Representation",
journal = j-COMPUT-ELECTR-ENG,
volume = "7",
number = "3",
pages = "149--155",
month = sep,
year = "1980",
CODEN = "CPEEBQ",
ISSN = "0045-7906 (print), 1879-0755 (electronic)",
ISSN-L = "0045-7906",
bibdate = "Fri Nov 28 11:42:59 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Electrical Engineering",
keywords = "decimal floating-point arithmetic",
}
@Article{Johnson:1980:DQS,
author = "E. L. Johnson",
title = "A Digital Quarter Square Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "3",
pages = "258--261",
month = mar,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675558",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675558",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Jullien:1980:IMM,
author = "G. A. Jullien",
title = "Implementation of Multiplication, Modulo a Prime
Number, with Applications to Number Theoretic
Transforms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "10",
pages = "899--905",
month = oct,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675473",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675473",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kahan:1980:HCE,
author = "William M. Kahan",
title = "Handheld Calculator Evaluates Integrals",
journal = j-HEWLETT-PACKARD-J,
volume = "31",
number = "8",
pages = "23--32",
month = aug,
year = "1980",
CODEN = "HPJOAX",
ISSN = "0018-1153",
MRclass = "65-04 (65D30)",
MRnumber = "MR590837 (82d:65001)",
MRreviewer = "S. Dubuc",
bibdate = "Tue Mar 25 14:12:15 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hpj.bib",
note = "Lecture notes for Math 128.",
URL = "http://www.cs.berkeley.edu/~wkahan/Math128/INTGTkey.pdf",
acknowledgement = ack-nhfb,
classcodes = "C4160 (Numerical integration and differentiation);
C5230 (Digital arithmetic methods)",
corpsource = "Hewlett--Packard Co., Palo Alto, CA, USA",
fjournal = "Hewlett--Packard Journal",
keywords = "34C; digital arithmetic; handheld calculator; HP;
integrals; integration; numerical integration;
numerical methods",
reviewer = "S. Dubuc",
treatment = "G General Review; P Practical",
}
@Unpublished{Kahan:1980:SPI,
author = "W. Kahan",
title = "Software $ \sqrt x $ for the Proposed {IEEE}
Floating-Point Standard",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
day = "25",
month = aug,
year = "1980",
bibdate = "Mon Apr 25 18:24:02 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript",
acknowledgement = ack-nhfb,
}
@InProceedings{Kleinsteiber:1980:IHM,
author = "James R. Kleinsteiber",
title = "{IBM} 4341 hardware/microcode trade-off decisions",
crossref = "Johnson:1980:MPA",
pages = "190--192",
year = "1980",
bibdate = "Thu Aug 07 18:22:42 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The design of IBM's 4341 Processor, as with other
processors, involved many cost/performance tradeoffs.
The designer is continually under pressure to increase
processor speed without increasing cost or to decrease
processor cost without decreasing performance. This
paper will examine some of the engineering decisions
that were made in the attempt to make the 4341 a
high-performing yet low cost processor. These decisions
include searching for, or developing, algorithms that
make the best use of hardware properties, such as data
path width, arithmetic/logical operations and special
functions. Functions were sought such that a small
amount of added hardware would go a long way towards
improving system performance. Hardware designers,
microcoders and performance analysis people worked
together to implement instructions, functions and
algorithms with the proper mixture of hardware
functions and microcode in order to build a viable
processor. Some specific functions will be covered to
examine a few of the decisions. The TEST UNDER MASK
performance problem will be discussed with its
resulting implementation decision. The method of using
EXCLUSIVE OR to clear storage and the resulting
algorithm design will be shown. Other topics to be
discussed include multiple hardware functions and the
resulting effect on floating point, fixed point and
decimal multiply; the divide function and its effect on
floating point and fixed point divide; and the effect
of an 8-byte data path for decimal arithmetic.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@InProceedings{Kulisch:1980:AOI,
author = "U. W. Kulisch and W. L. Miranker",
title = "Arithmetic Operations in Interval Spaces",
crossref = "Alefeld:1980:FNC",
pages = "51--67",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic",
}
@Article{Ladner:1980:PPC,
author = "Richard E. Ladner and Michael J. Fischer",
title = "Parallel Prefix Computation",
journal = j-J-ACM,
volume = "27",
number = "4",
pages = "831--838",
month = oct,
year = "1980",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/322217.322232",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Oct 26 22:55:08 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Par.Arch.Indep.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "The prefix problem is to compute all the products $
x_1 * x_2 * \cdots * x_k $ for $ 1 \leq k \leq n $,
where $*$ is an associative operation. A recursive
construction is used to obtain a product circuit for
solving the prefix problem which has depth exactly $
\lceil \log n \rceil $ and size bounded by $ 4 n $ An
application yields fast, small Boolean circuits to
simulate finite-state transducers. By simulating a
sequential adder, a Boolean circuit which has depth $ 2
\lceil \log_2 n \rceil + 2 $ and size bounded by $ 14 n
$ is obtained for $n$-bit binary addition. The size can
be decreased significantly by permitting the depth to
increase by an additive constant.",
acknowledgement = ack-nhfb,
ajournal = "J. Assoc. Comput. Mach.",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "https://dl.acm.org/loi/jacm",
}
@Article{Lemaire:1980:INR,
author = "C. A. Lemaire and J. C. Svercek",
title = "Improved Non-restoring Division",
journal = j-IBM-TDB,
volume = "23",
number = "3",
pages = "1149--1151",
month = aug,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Book{Levy:1980:CPA,
author = "Henry M. Levy and Richard H. {Eckhouse, Jr.}",
title = "Computer Programming and Architecture--the {VAX-11}",
publisher = pub-DP,
address = pub-DP:adr,
pages = "xxi + 407",
year = "1980",
ISBN = "0-932376-07-X",
ISBN-13 = "978-0-932376-07-7",
LCCN = "QA76.8 .V37 L48 1980",
bibdate = "Wed Dec 15 10:38:14 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Macke:1980:DMF,
author = "Edward T. Macke",
title = "Design of a modular floating point arithmetic unit",
type = "Thesis ({M.S.})",
school = "Washington University, Department of Electrical
Engineering",
address = "St. Louis, MO, USA",
pages = "ix + 174",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors --- Design
and construction.",
}
@InProceedings{Matula:1980:FFP,
author = "D. W. Matula",
title = "Foundations of Finite Precision Rational Arithmetic",
crossref = "Alefeld:1980:FNC",
pages = "85--111",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rational arithmetic",
}
@InProceedings{McMinn:1980:IND,
author = "C. McMinn",
title = "The {Intel 8087}: a Numeric Data Processor",
crossref = "Electro:1980:ECR",
pages = "14/5/1--8",
year = "1980",
bibdate = "Mon Sep 12 08:30:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Mead:1980:IVS,
author = "Carver Mead and Lynn Conway",
title = "Introduction to {VLSI} systems",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xvi + 396",
year = "1980",
ISBN = "0-201-04358-0",
ISBN-13 = "978-0-201-04358-7",
LCCN = "TK7874 .M371",
bibdate = "Mon Sep 16 16:25:00 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Meinardus:1980:OPN,
author = "G{\"u}nter Meinardus and G. D. Taylor",
title = "Optimal Partitioning of {Newton}'s Method for
Calculating Roots",
journal = j-MATH-COMPUT,
volume = "35",
number = "152",
pages = "1221--1230",
month = oct,
year = "1980",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65H05 (41A30)",
MRnumber = "81j:65069",
MRreviewer = "Derek W. Arthur",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4130 (Interpolation and function approximation)",
corpsource = "Fachbereich Math., University of Siegen, Siegen, West
Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "cube root; domain interval; function approximation;
iterative methods; method; Newton; optimal
partitioning; reciprocal square root; square root;
subinterval",
treatment = "A Application; T Theoretical or Mathematical",
}
@Article{Metropolis:1980:SIN,
author = "N. Metropolis",
title = "Summation of imprecise numbers",
journal = j-COMPUT-MATH-APPL,
volume = "6",
number = "3",
pages = "297--299",
year = "1980",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(80)90037-1",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65U05",
MRnumber = "MR604094 (82d:65092)",
bibdate = "Sat Feb 8 10:29:40 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
ZMnumber = "0458.65029",
abstract = "An algorithm is presented for computer summation of
imprecise numbers that may have quite disparate
magnitudes and variances. Each number is represented by
its expected value and variance. Exact numbers form a
subset and are treated in a consistent manner.
Cancellation effects are minimized.",
acknowledgement = ack-nhfb,
fjournal = "Computers \& Mathematics with Applications. An
International Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Moore:1980:MIA,
author = "R. E. Moore",
title = "Microprogrammed interval arithmetic",
journal = j-SIGNUM,
volume = "15",
number = "2",
pages = "30--30",
month = jun,
year = "1980",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Nave:1980:NDP,
author = "R. Nave and J. Palmer",
title = "A numeric data processor",
crossref = "IEEE:1980:IIS",
pages = "108--109",
year = "1980",
bibdate = "Wed Sep 07 22:22:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{North:1980:BRS,
author = "J. D. North",
title = "Book Review: a {Sixteenth Century} Polymath,
{{\booktitle{Wilhelm Schickard, 1592--1635: Astronom,
Geograph, Orientalist, Erfinder der Rechenmaschine}}}",
journal = j-J-HIST-ASTRON,
volume = "11",
number = "2",
pages = "138--140",
month = jun,
year = "1980",
CODEN = "JHSAA2",
DOI = "https://doi.org/10.1177/002182868001100210",
ISSN = "0021-8286 (print), 1753-8556 (electronic)",
ISSN-L = "0021-8286",
bibdate = "Mon Sep 29 17:17:57 MDT 2014",
bibsource = "http://jha.sagepub.com/content/11/2.toc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jhistastron.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal for the History of Astronomy",
journal-URL = "https://journals.sagepub.com/home/JHA",
}
@InProceedings{Oberaigner:1980:AMG,
author = "W. Oberaigner",
title = "Algorithms for Multiplication with Given Precision",
crossref = "Alefeld:1980:FNC",
pages = "121--129",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic",
}
@InProceedings{Palmer:1980:IND,
author = "J. Palmer",
title = "The {Intel} 8087 Numeric Data Processor",
crossref = "Anonymous:1980:CPA",
pages = "174--181",
year = "1980",
bibdate = "Mon Sep 12 08:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Palmer:1980:LIN,
author = "J. Palmer",
title = "An {LSI} Implementation of a New System for
Floating-Point Arithmetic",
crossref = "Electro:1980:ECR",
pages = "18/4/1--8",
year = "1980",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Misc{Palmer:1980:UND,
author = "John F. Palmer and Bruce W. Ravenel and Rafi Nave",
title = "{US4338675}: Numeric data processor",
howpublished = "U.S. Patent",
day = "13",
month = feb,
year = "1980",
bibdate = "Sat Nov 09 10:23:07 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published July 6, 1982. This patent was reissued on
July 2, 1991 as patent USRE33629.",
abstract = "A floating point, integrated, arithmetic circuit is
organized around a file format having a floating point
numeric domain exceeding that of any single or double
precision floating point numbers, long or short integer
words or BCD data upon which it must operate. As a
result the circuit has a greater reliability, range and
precision than ever previously achieved without
entailing additional circuit complexity. Reliability is
further enhanced by a systematic three bit rounding
field, and by including means for detecting every error
or exception condition with an optional expected
response provided thereto by hardware. As a result of
such organization, an unexpected increase of capacity
is achieved wherein transcendental functions can be
computed totally in hardware, and whereby mixed mode
arithmetic can be implemented without difficulty. The
numeric processor also includes a programmable shifter
capable of arbitrary numbers of bit and byte shifts in
a single clock cycle, as well as an arithmetic unit
capable of implementing multiplication, division,
modulo reduction and square roots directly in
hardware.",
acknowledgement = ack-nhfb,
}
@InProceedings{Payne:1980:VFPa,
author = "M. Payne and D. Bhandarkar",
title = "{VAX} Floating Point: a Solid Foundation for Numerical
Computation",
crossref = "Electro:1980:ECR",
pages = "18/1/1--12",
year = "1980",
bibdate = "Wed Sep 07 21:37:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Payne:1980:VFPb,
author = "Mary Payne and Dileep Bhandarkar",
title = "{VAX} floating point: a solid foundation for numerical
computation",
journal = j-COMP-ARCH-NEWS,
volume = "8",
number = "4",
pages = "22--33",
month = jun,
year = "1980",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/641845.641849",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Sat Jun 24 12:02:21 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Pedersen:1980:HBM,
author = "P. W. Pedersen",
title = "Hvordan beregner man kvadratroden? \toenglish {How do
you calculate the square root?} \endtoenglish",
journal = "Elektronik (Denmark)",
volume = "??",
number = "4",
pages = "18--21",
month = apr,
year = "1980",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Purtilo:1980:IAP,
author = "Jim Purtilo",
title = "On implementing arbitrary precision arithmetic in
{NIL}: an exercise in data abstraction",
journal = j-SIGSAM,
volume = "14",
number = "1",
pages = "14--18",
month = feb,
year = "1980",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Wed Oct 5 08:31:56 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "??",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Rallapalli:1980:CMF,
author = "K. Rallapalli and J. Kroeger",
title = "Chips make fast math a snap for microprocessors",
journal = j-ELECTRONICS,
volume = "53",
number = "10",
pages = "153--157",
month = apr,
year = "1980",
ISSN = "0883-4989",
bibdate = "Wed Sep 07 22:27:11 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@Article{Reid:1980:CDP,
author = "John Reid",
title = "Complex double precision in association with {Fortran
77}",
journal = j-SIGNUM,
volume = "15",
number = "1",
pages = "16--17",
month = mar,
year = "1980",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:08 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages)",
corpsource = "Computer Sci. and Systems Div., AERE Harwell, UK",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "compilers; complex double precision arithmetic;
digital arithmetic; FORTRAN; FORTRAN 77; portability",
treatment = "P Practical",
}
@Article{Reid:1980:FMF,
author = "J. K. Reid",
title = "Functions for manipulating floating-point numbers",
journal = j-SIGPLAN,
volume = "15",
number = "6",
pages = "68--76",
month = jun,
year = "1980",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Apr 25 11:46:37 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Computer Sci. and Systems Div., AERE, Harwell, Didcot,
UK",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "complete computer programs; digital arithmetic;
floating point numbers; function manipulation;
portability; software portability",
treatment = "T Theoretical or Mathematical",
}
@Article{Rink:1980:CPS,
author = "R. Rink",
title = "Correction to {``Performance of state regulator
systems with floating-point computation''}",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "25",
number = "3",
pages = "612--612",
month = jun,
year = "1980",
CODEN = "IETAA9",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Rink:1979:PSR}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
}
@PhdThesis{Rump:1980:KFM,
author = "Siegfried M. Rump",
title = "{Kleine Fehlerschranken bei Matrixproblemen}.
({German}) [Small error bounds for matrix problems]",
type = "{Ph.D.} Thesis",
school = "Institut f{\"u}r Angewandte Mathematik der
Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "vi + 131 + 49",
year = "1980",
bibdate = "Fri Jan 06 07:57:41 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ti3.tuhh.de/rump/Research/topics.php#PhD",
acknowledgement = ack-nhfb,
keywords = "accurate dot products; accurate floating-point
summation; long accumulator",
language = "German",
}
@InProceedings{Scherer:1980:SNR,
author = "R. Scherer and K. Zeller",
title = "Shorthand Notation for Rounding Errors",
crossref = "Alefeld:1980:FNC",
pages = "165--168",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rounding error",
}
@Manual{SOITA:1980:AIE,
key = "SOITA",
title = "{Applesoft II}: extended floating-point {BASIC}: quick
reference guide",
organization = "Southwestern Ohio Instructional Television
Association",
address = "Oxford, OH, USA",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 pamphlet",
series = "SOITA \#2008",
acknowledgement = ack-nhfb,
keywords = "Apple II (Computer) --- Programming; BASIC (Computer
program language)",
}
@Article{Speiser:1980:RCZ,
author = "A. P. Speiser",
title = "The Relay Calculator {Z4}",
journal = j-ANN-HIST-COMPUT,
volume = "2",
number = "3",
pages = "242--245",
month = jul # "\slash " # sep,
year = "1980",
CODEN = "AHCOE5",
DOI = "https://doi.org/10.1109/MAHC.1980.10026",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:17 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1980/pdf/a3242.pdf;
http://www.computer.org/annals/an1980/a3242abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Article{Stevenson:1980:RPI,
author = "David Stevenson",
title = "A report on the proposed {IEEE Floating Point Standard
(IEEE task p754)}",
journal = j-COMP-ARCH-NEWS,
volume = "8",
number = "5",
pages = "11--12",
month = aug,
year = "1980",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Wed Nov 24 10:59:34 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Book{Stone:1980:ICA,
editor = "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
and Samuel H. Fuller and others",
title = "Introduction to computer architecture",
publisher = "Science Research Associates",
address = "Chicago, IL, USA",
edition = "Second",
pages = "673",
year = "1980",
ISBN = "0-574-21225-6",
ISBN-13 = "978-0-574-21225-2",
LCCN = "QA76.9.A73 I57 1980",
bibdate = "Fri Nov 9 19:22:07 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
price = "US\$16.95 (est.)",
series = "The SRA computer science series",
acknowledgement = ack-nhfb,
subject = "Computer architecture",
}
@InProceedings{Stone:1980:TFP,
author = "H. S. Stone",
title = "Towards a Floating-Point Standard",
crossref = "Electro:1980:ECR",
pages = "18/0/1--5",
year = "1980",
bibdate = "Wed Sep 07 21:33:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Stummel:1980:REA,
author = "F. Stummel",
title = "Rounding Error Analysis of Elementary Numerical
Algorithms",
crossref = "Alefeld:1980:FNC",
pages = "169--195",
year = "1980",
bibdate = "Tue Aug 28 06:19:13 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rounding error",
}
@Article{Swartzlander:1980:AUH,
author = "E. E. {Swartzlander, Jr.} and B. K. Gilbert",
title = "Arithmetic for Ultra-High-Speed Tomography",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "5",
pages = "341--353",
month = may,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675584",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675584",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Swartzlander:1980:CA,
editor = "Earl E. {Swartzlander, Jr.}",
title = "Computer Arithmetic",
publisher = pub-DOWDEN,
address = pub-DOWDEN:adr,
pages = "xiii + 378",
year = "1980",
ISBN = "0-87933-350-2",
ISBN-13 = "978-0-87933-350-8",
LCCN = "QA76.6 .C633",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Benchmark papers in electrical engineering and
computer science; 21",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "Computer arithmetic.; Electronic digital computers ---
Programming.; Floating-point arithmetic.",
}
@Article{Swartzlander:1980:MA,
author = "E. E. {Swartzlander, Jr.}",
title = "Merged Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "10",
pages = "946--950",
month = oct,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675482",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:31:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675482",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Thornton:1980:CP,
author = "James E. Thornton",
title = "The {CDC 6600} Project",
journal = j-ANN-HIST-COMPUT,
volume = "2",
number = "4",
pages = "338--348",
month = oct # "\slash " # dec,
year = "1980",
CODEN = "AHCOE5",
DOI = "https://doi.org/10.1109/MAHC.1980.10044",
ISSN = "0164-1239",
bibdate = "Fri Nov 1 15:29:17 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1980/pdf/a4338.pdf;
http://www.computer.org/annals/an1980/a4338abs.htm",
abstract = "This article is an account of the development of the
Control Data 6600 computer first developed in 1964. Of
historical interest is the design team approach adopted
by Control Data in which a small staff of engineers was
isolated from the main operations of the company. Some
review is made of the design process as well as the
unique features of the machine. The article also
includes some comments in retrospect about the results
of certain of the initial design objectives.",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@MastersThesis{Ting:1980:MCU,
author = "I-chyng Ting",
title = "A microprocessor-based controller using floating-point
arithmetic",
type = "Thesis ({M.S.})",
school = "Auburn University",
address = "Auburn, AL, USA",
pages = "ix + 167",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
}
@MastersThesis{Tucker:1980:IAD,
author = "Richard Wesley Tucker",
title = "Implementation of arithmetic for the data flow machine
processing unit",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical and Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "i + 58",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Jack B. Dennis.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors ---
Programming.; Val (Computer program language).",
}
@InProceedings{Ulrich:1980:IMS,
author = "Ch. Ulrich",
title = "Iterative Methods in the Spaces of Rounded
Computations",
crossref = "Alefeld:1980:FNC",
pages = "197--209",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; rounding error",
}
@InProceedings{Undheim:1980:CFP,
author = "T. Undheim",
title = "Combinatorial Floating Point Processor as an Integral
Part of the Computer",
crossref = "Electro:1980:ECR",
pages = "14/1/1--6",
year = "1980",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Verma:1980:MPF,
author = "S. B. Verma and Maithili Sharan",
title = "Multiple Precision Floating-point Computation in
{FORTRAN}",
journal = j-SPE,
volume = "10",
number = "3",
pages = "163--173",
month = mar,
year = "1980",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Thu Sep 8 08:20:53 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@TechReport{Virkkunen:1980:UAF,
author = "V.-E. Juhani Virkkunen",
title = "A unified approach to floating-point rounding with
applications to multiple-precision summation",
type = "{Diss. Helsingfors}",
institution = "Department of Computer Science, University of
Helsinki",
address = "Helsinki, Finland",
pages = "66",
year = "1980",
ISBN = "951-45-1948-5",
ISBN-13 = "978-951-45-1948-2",
bibdate = "Thu May 09 08:25:02 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{vonGudenberg:1980:EAR,
author = "J. Wolff {von Gudenberg}",
title = "{Einbettung allgemeiner Rechnerarithmetik in Pascal
mittels eines Operatorkonzepts und Implementierung der
Standardfunktionen mit optimaler Genauigkeit}
\toenglish {Embedding a General Computer Arithmetic in
Pascal by Means of an Operator Concept and the
Implementation of Elementary Functions with Optimal
Accuracy} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1980",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Waldecker:1980:NSR,
author = "D. E. Waldecker",
title = "Nonrestoring Square Root with Simplified Answer
Generation",
journal = j-IBM-TDB,
volume = "22",
number = "11",
pages = "4807--4808",
month = apr,
year = "1980",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Waser:1980:EGP,
author = "S. Waser",
title = "{Entwicklung von Gleitkomma-Prozessoren} \toenglish
{Development of Floating-Point Processors}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "29",
number = "9",
pages = "50--54",
month = apr,
year = "1980",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@MastersThesis{Watkins:1980:MFU,
author = "Timothy Ervin Watkins",
title = "A microprogrammed {FFT} utilizing floating point
hardware",
type = "Thesis ({M.S.})",
school = "UCLA",
address = "Los Angeles, CA, USA",
pages = "v + 56",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Fourier transformations
--- Computer programs.; Microprogramming.",
}
@MastersThesis{Wong:1980:IOF,
author = "Clement Sau-Fai Wong",
title = "Input\slash output and floating-point arithmetic
package",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vi + 61",
year = "1980",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer input-output equipment.; Electronic digital
computers --- Programming.; Floating-point arithmetic.;
Microcomputers.",
}
@InProceedings{Yohe:1980:FPE,
author = "J. M. Yohe",
title = "Floating point exception handling for interval
arithmetic",
crossref = "Nickel:1980:IMP",
pages = "547--554",
year = "1980",
MRclass = "65G10",
MRnumber = "83c:65115",
bibdate = "Fri Dec 08 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Yohe:1980:PSI,
author = "J. M. Yohe",
title = "Portable Software for Interval Arithmetic",
crossref = "Alefeld:1980:FNC",
pages = "211--229",
year = "1980",
bibdate = "Tue Oct 23 08:17:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A portable multiple precision interval arithmetic
package for FORTRAN has been developed by substituting
the multiple precision arithmetic package of Richard P.
Brent for the underlying arithmetic in the author's
earlier single precision interval arithmetic package.
This package, like the earlier version, offers a
complete range of operations and functions for interval
calculations.\par
In this paper, we outline the design philosophy of the
earlier package and show how this design facilitated
the incorporation of the Brent package. We discuss
several desirable host system features and possible
adaptations of the interval package, and explain how
the design of the package would allow it to serve in
differing environments with only relatively minor
changes.\par
Since the package may be of direct use to many
individuals, we also discuss its installation on other
host systems and its use via the AUGMENT precompiler
for Fortran.",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; multiple precision arithmetic",
}
@Article{Zeman:1980:HSM,
author = "J. Zeman and H. T. {Nagle, Jr.}",
title = "A High-Speed Microprogrammable Digital Signal
Processor Employing Distributed Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-29",
number = "2",
pages = "134--144",
month = feb,
year = "1980",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1980.1675537",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 19:15:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675537",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Agrawal:1981:NAM,
author = "D. P. Agrawal and R. C. Joshi",
title = "Negabinary Addition and Multiplication Using Binary
Circuits",
crossref = "IEEE:1981:PSC",
pages = "270--273",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Agrawal_Joshi.pdf",
abstract = "This paper deals with design techniques that allow
adoption of off-the-shelf binary arithmetic circuits to
perform multi-operand addition and multiplication of
negabinary numbers. The multiple operands could be
easily added with augmented binary adders connected in
the form of a tree. The same hardware could be used to
perform multiplication. But, from an LSI implementation
viewpoint, the use of cellular array structures is
explored and necessary challenges to design a combined
binary/negabinary multiplier unit, are also outlined.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Andrews:1981:EFM,
author = "M. Andrews and D. Jaeger and S. F. McCormick and G. D.
Taylor",
title = "Evaluation of Functions on Microcomputers: $ \exp (x)
$",
journal = j-COMPUT-MATH-APPL,
volume = "7",
number = "6",
pages = "503--508",
year = "1981",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:40:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@MastersThesis{Arnold:1981:PFP,
author = "Jeffrey M. Arnold",
title = "{PSI}, a floating point processor for the {NU}
Computer",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical and Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "42",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Stephen A. Ward.",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Intel 8086 (Microprocessor); Microprocessors --- Design
and construction.",
}
@InProceedings{Arora:1981:CSR,
author = "R. K. Arora and Saroj Kaushik",
title = "Conversion Scheme in Residue Code",
crossref = "IEEE:1981:PSC",
pages = "152--156",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Arora_Kaushik.pdf",
abstract = "In this paper, an implementation scheme involving
decoders and residue adders has been suggested to
convert input data in fixed radix representation to
residue representation. A method dealing with the
reverse process is also demonstrated. A comparison has
been made with the methods known hitherto.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; residue number system",
}
@InProceedings{Atkins:1981:FIS,
author = "D. E. Atkins and K. S. Trivedi",
title = "The {Fifth IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "IEEE:1981:PSC",
pages = "iv--iv",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Trivedi_Atkins.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Avizienis:1981:LCR,
author = "Algirdas Avi{\v{z}}ienis",
title = "Low-Cost Residue and Inverse Residue Error-Detecting
Codes for Signed-Digit Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "165--168",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Avizienis.pdf",
abstract = "Low-cost residue and inverse residue codes for error
detection in signed-digit arithmetic are defined in
this paper. Checking algorithms are presented for both
digit-serial and parallel computation of the residues.
Residue digit operations are defined for two-operand
addition, multi-operand addition, multiplication,
conversion, and reconversion algorithms. All algorithms
employ the same Arithmetic Building Element ``ABE''
that has been previously developed for signed-digit
arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Banerji:1981:HSD,
author = "Dilip K. Banerji and To-Yat Cheung and V. Ganesan",
title = "A High-Speed Division Method in Residue Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "158--164",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Banerji_Cheung_Ganesan.pdf",
abstract = "This paper is concerned with the operation of division
in residue number systems. Residue codes are introduced
and the basic residue arithmetic operations are
defined. Previous results on residue division are
outlined. A well-known integer division algorithm is
used and adapted for residue division. A new method is
proposed for choosing an approximate divisor,
approximate dividends, and the partial quotients. The
proposed method yields correct quotients faster than
the existing methods and is general in its application
i.e., it is not restricted by the choice of moduli as
long as they are relatively prime.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Barlow:1981:DAA,
author = "Jesse Barlow",
title = "On the Distribution af Accumulated Roundoff Error in
Floating Point Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "100--105",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Barlow.pdf",
abstract = "This paper discusses longstanding problems in the
probabilistic error analysis of numerical algorithms
when they are performed in floating point
arithmetic.\par
Local roundoff error in floating point addition is
characterized and its mean and variance are
approximated. We apply these results to finding
distributions for the roundoff error accumulated in
sums and long inner products.\par
We state theorems which resolve questions left open in
Bustoz et al. [5] and Hamming [11]. These theorems are
proven in [3].",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@PhdThesis{Barlow:1981:PEA,
author = "Jesse Louis Barlow",
title = "Probabilistic error analysis of floating point and
{CRD} arithmetics",
type = "{Ph.D.} (Electrical Engineering and Computer
Science)",
school = "Northwestern University",
address = "Evanston, IL, USA",
pages = "????",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bashe:1981:AIE,
author = "C. J. Bashe and W. Buchholz and G. V. Hawkins and J.
J. Ingram and N. Rochester",
title = "The Architecture of {IBM}'s Early Computers",
journal = j-IBM-JRD,
volume = "25",
number = "5",
pages = "363--375",
month = sep,
year = "1981",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Mon Jan 24 21:36:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@MastersThesis{Benjamin:1981:FPF,
author = "Bruce P. Benjamin",
title = "Fixed point to floating point converter",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "60",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bhuyan:1981:MAP,
author = "L. Bhuyan and D. P. Agrawal",
title = "Multiple Addition and Parallel Counter in Generalized
Binary and Negabinary Systems",
crossref = "IEEE:1981:PSC",
pages = "264--269",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Bhuyan_Agrawal.pdf",
abstract = "This paper explores the possibility of utilizing
counters for reducing the partial products generated
from multiplication of two numbers represented in a
generalized binary system. Algorithm for multi operand
addition of Koren's generalized number system are
worked out. A carry look-ahead adder is developed and
hardware aspects of possible counters for this class of
binary number system are discussed. Negabinary counters
are also introduced in line with those proposed for
binary multiplication by Stenzel et al.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Bice:1981:AAS,
author = "P. K. Bice",
title = "Algorithm adds square root to micro's arithmetic
capability",
journal = j-ELECTRONIC-DESIGN,
volume = "29",
number = "11",
pages = "146",
month = may,
year = "1981",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronic Design",
}
@Article{Blikle:1981:CTI,
author = "Andrzej Blikle",
title = "The Clean Termination of Iterative Programs",
journal = j-ACTA-INFO,
volume = "16",
number = "2",
pages = "199--217",
month = oct,
year = "1981",
CODEN = "AINFA2",
ISSN = "0001-5903 (print), 1432-0525 (electronic)",
ISSN-L = "0001-5903",
MRclass = "68B10",
MRnumber = "83c:68015",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
ftp://ftp.ira.uka.de/pub/bibliography/Misc/HBP/ACTAI.bib;
ftp://ftp.ira.uka.de/pub/bibliography/Misc/leavens.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
catcode = "D.2; D.2.4; F.3",
content = "Most correctness proofs assume that elementary
instructions represent total functions. In fact this is
not always the case: for instance, in dealing with real
numbers, Brown's model of floating point computation
[1], a model which has been accepted by the designers
of ADA, uses interval analysis. If the interval of x
overlaps the interval of y, the Boolean value of x r y
is not well defined.\par
In this paper the author studies the clean termination
(i.e., without abortion) of iterative programs, not
supposing that the test functions are total. The
relational approach to computing, which the author has
largely worked out (cf. Sanderson [2] for an account
from the starting point) is very well suited for that
design. A general theorem links the ``global
correctness'' of a program with a ``well-founded''
breakdown of the program relation. Next the author
gives new validation rules, in which a Z b depart from
the usual meaning. Last (but not least) one finds an
exhaustive study of the integer square root in a
realistic arithmetic.\par
Due to the great significance of the matter, we must
call attention to this paper. \par
M. F. Aribaud, Paris, France \par
REFERENCES \par
[1] BROWN, W. S. A simple but realistic model of
floating-point computation, ACM Trans. Math. Softw. 7
(1981), 445 480. \par
[2] SANDERSON, J. G. A relational theory of computing,
Lecture Notes in Computer \ldots{}",
CRclass = "D.2.4 Program Verification; D.2.4 Program
Verification; D.2.4 Correctness proofs; F.3.1
Specifying and Verifying and Reasoning about Programs",
CRnumber = "39409",
descriptor = "Software, SOFTWARE ENGINEERING, Program Verification;
Software, SOFTWARE ENGINEERING, Program Verification,
Correctness proofs; Theory of Computation, LOGICS AND
MEANINGS OF PROGRAMS, Specifying and Verifying and
Reasoning about Programs",
fjournal = "Acta Informatica",
genterm = "LANGUAGES; RELIABILITY; THEORY; VERIFICATION",
journal-URL = "http://www.springerlink.com/content/0001-5903",
reviewer = "M. F. Aribaud",
subject = "D. Software; D.2 SOFTWARE ENGINEERING; D. Software;
D.2 SOFTWARE ENGINEERING; F. Theory of Computation; F.3
LOGICS AND MEANINGS OF PROGRAMS",
}
@TechReport{Brent:1981:MUG,
author = "Richard P. Brent",
title = "{MP} User's Guide",
number = "TR-CS-81-08",
institution = "Department of Computer Science, Australian National
University",
address = "Canberra, ACT, Australia",
edition = "Fourth",
pages = "73",
month = jun,
year = "1981",
bibdate = "Fri Nov 28 15:59:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "MP is a multiple-precision floating-point arithmetic
package. It is almost completely machine-independent,
and should run on any machine with an ANSI Standard
Fortran (ANS X3.9-1966) compiler, sufficient memory,
and a wordlength (for integer arithmetic) of at least
16 bits. A precompiler (Augment) which facilitates the
use of the MP package is available.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@InProceedings{Bridge:1981:AAA,
author = "Carol L. Bridge and P. David Fisher and Robert G.
Reynolds",
title = "Asynchronous Arithmetic Algorithms for Data-Driven
Machines",
crossref = "IEEE:1981:PSC",
pages = "56--62",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Bridge_Fisher_Reynolds.pdf",
abstract = "With data-driven machines a statement associated with
a given processing element fires the moment its input
operands become available. In order to take full
advantage of this computer structure and achieve
maximum throughput, the processing elements themselves
should also be asynchronous; i.e., instruction
execution times should be data dependent to minimize
overall delays. Five general procedures are described
that may be used to design self-timing processing
units: task completion prediction, task completion
detection, operand preprocessing, pre-estimation of
input operand values, and significance control.
Analysis and simulations suggest that the greatest
potential for speed improvement over synchronous
counterparts comes with self-timing algorithms for both
division and the evaluation of special functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Brown:1981:SRM,
author = "W. S. Brown",
title = "A Simple but Realistic Model of Floating-Point
Computation",
journal = j-TOMS,
volume = "7",
number = "4",
pages = "445--480",
month = dec,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355972.355975",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Aug 29 23:03:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "computer arithmetic; environment parameters; error
analysis; Euclidean norm; floating-point arithmetic;
software portability",
}
@MastersThesis{Cariker:1981:RFM,
author = "Earnest Allan Cariker",
title = "A rapid-approximation floating-point mathematics
package for the {INTEL} 8080 microprocessor",
type = "Computing Science Thesis ({M.S.})",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "viii + 152",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Mathematical analysis.; Microprocessors.; Programming
(Electronic computers); Programming languages
(Electronic computers)",
}
@MastersThesis{Cary:1981:BFP,
author = "David A. Cary",
title = "The {Berkeley} floating point project",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical and Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "107",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Noted as posthumous in \cite{Aspinwall:1985:RVM}.",
}
@Article{Ceruzzi:1981:ECK,
author = "Paul E. Ceruzzi",
title = "The Early Computers of {Konrad Zuse}, 1935 to 1945",
journal = j-ANN-HIST-COMPUT,
volume = "3",
number = "3",
pages = "241--262",
month = jul # "\slash " # sep,
year = "1981",
CODEN = "AHCOE5",
ISSN = "0164-1239",
bibdate = "Fri Nov 1 15:29:18 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1981/pdf/a3241.pdf;
http://www.computer.org/annals/an1981/a3241abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Manual{Cheng:1981:AAF,
author = "Steven Cheng",
title = "{Am9511A\slash Am9512} floating point processor
manual",
organization = "Advanced Micro Devices",
address = "Sunnyvale, CA, USA",
pages = "55",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Floating-point
arithmetic.",
}
@InProceedings{Chow:1981:PDA,
author = "P. Chow and Z. G. Vranesic and J. L. Yen",
title = "A Pipelined Distributed Arithmetic {PFFT} Processor",
crossref = "IEEE:1981:PSC",
pages = "198--206",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Chow_Vranesic_Yen.pdf",
abstract = "Previous experience i,n implementing the Prime Factor
Fourier Transform showed that it was much more
difficult to do than the FFT because of its complicated
structure. In most FFT implementations the
``butterfly'' structure is the basic arithmetic unit
implemented. It is much simpler than the equivalent
PFFT unit.\par
This paper describes a different architecture for
implementing PFFT machines using distributed arithmetic
and ROM's to perform the computations. It is found to
be much simpler and more modular than a design which
uses multipliers and adders. The implementation of a
PFFT processor with a throughput of 104 kHz for complex
data points is described.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; Prime Factor Fourier Transform (PFFT)",
}
@Article{Chroust:1981:MAD,
author = "G. Chroust",
title = "Method of Adding Decimal Numbers by Means of Binary
Arithmetic",
journal = j-IBM-TDB,
volume = "23",
number = "10",
pages = "4525--4526",
month = mar,
year = "1981",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Ciminiera:1981:AAF,
author = "L. Ciminiera and A. Serra",
title = "Arithmetic Array for Fast Inner Product Evaluation",
crossref = "IEEE:1981:PSC",
pages = "207--214",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ciminiera_Serra.pdf",
abstract = "The paper presents a new fast arithmetic array,
suitable for VLSI implementation, which computes the
inner product of two vectors. The operands and the
result are expressed using the 2's complement notation,
which is the most general and flexible one. Cells
performing the $ 2 \times 2 $ bit full multiplication
are used for obtaining a reduction of the operation
time.\par
A particular pipelining scheme, with different degrees
of latching, is used in order to implement parallel
computations with a moderate cost increase. Graphs
showing the characteristics and the advantage domain of
the proposed array are presented. An IC implementation
of the proposed array could have a speed from 5 to 10
times greater than the multiplier-accumulator circuits
currently available.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Ciminiera:1981:FAM,
author = "L. Ciminiera and A. Serra and A. Valenzano",
title = "{Fast and Accurate Matrix Triangularization Using an
Iterative Structure}",
crossref = "IEEE:1981:PSC",
pages = "215--221",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ciminiera_Serra_Valenzano.pdf",
abstract = "The paper presents a new iterative array, which
performs the triangularization of a dense matrix, using
the Givens rotation algorithm. Two slightly different
arrays are presented: the first one performs the
factorization of a single matrix; the second one
performs the recursive triangularization. The
implementation of the cell in the array is based on the
on-line arithmetic, which allows us to obtain high
performances. Furthermore, the cell implementation
requires only three types of arithmetic units
(multiplication\slash addition, square root, division)
and shift registers for data buffering and for
generating the timing signals.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Cody:1981:APF,
author = "William J. {Cody, Jr.}",
title = "Analysis of Proposals for the Floating-Point
Standard",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "63--68",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220379",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Sep 24 09:21:33 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Cohen:1981:CAU,
author = "M. Cohen and V. C. Hamacher and T. E. Hull",
title = "{CADAC}: An Arithmetic Unit for Clean Decimal
Arithmetic and Controlled Precision",
crossref = "IEEE:1981:PSC",
pages = "106--112",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Cohen_Hamacher_Bull.pdf",
abstract = "This paper describes the design of an arithmetic unit
called CADAC (Clean Arithmetic with Decimal base And
Controlled Precision). A brief indication of
programming language specifications for carrying out
``ideal'' floating-point arithmetic is given. These
specifications include detailed requirements for
precision control and exception handling at the level
of a programming language such as Fortran. CADAC is an
arithmetic unit which performs the four floating-point
operations add\slash subtract \slash multiply\slash
divide on decimal base numbers in accordance with the
language requirements. A three-level pipeline is used
to overlap 2-digit-at-a-time (``double digit'') serial
processing of the partial products\slash remainders.
Although the logic design is relatively complex, the
performance is efficient and the advantages gained by
implementing programmer-controlled precision directly
in the hardware are significant.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Coonen:1981:EIG,
author = "Jerome T. Coonen",
title = "Errata: {An Implementation Guide to a Proposed
Standard for Floating Point Arithmetic}",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "62--62",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220378",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Wed Sep 14 21:15:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Coonen:1980:IGP,IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Coonen:1981:UDN,
author = "Jerome T. Coonen",
title = "Underflow and the Denormalized Numbers",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "75--87",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220382",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Sep 2 23:38:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nj,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@MastersThesis{Curley:1981:PPN,
author = "A. Curley",
title = "{PNCL}: a Prototype Numerical Computation Language",
type = "{M.Sc.} thesis",
school = "Department of Computer Science, University of
Toronto",
address = "Toronto, ON, Canada",
year = "1981",
bibdate = "Sun Dec 30 15:41:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Davis:1981:EFA,
author = "Diane F. Davis",
title = "Elementary Functions on an Array Processor",
crossref = "IEEE:1981:PSC",
pages = "170--178",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Davis.pdf",
abstract = "The algorithms used for elementary functions on the
FPS-164 array processor are described. In each case,
the choice of the algorithm depends on the parallel
hardware, the capability of the instruction word, and
the precision desired. For some, the choice depends on
the version, either scalar or vector. Algorithms for
the divide, square root, cosine\slash sine,
exponential, and logarithm are discussed. Those for
arctangent, tangent, arc-cosine\slash sine, cosh, sinh,
and tanh are summarized.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; Floating-Point Systems FPS-164",
}
@Manual{DECESD:1981:VIS,
author = "{Digital Equipment Corporation.Educational Services
Dept}",
title = "{VAX-11} instruction set",
organization = "Digital Equipment Corporation",
address = "Maynard, MA, USA",
edition = "Revised",
pages = "various",
year = "1981",
bibdate = "Sun May 02 09:19:03 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "VAX-11 (Computer) --- Programming.",
remark = "In container. Student guide --- Programming examples
--- Character string instructions --- Instruction
formats and addressing modes --- Variable bit field
instructions --- Stack and address instructions ---
Integer, logical and branch instructions --- Floating
point instructions --- Decimal string instructions
--Procedure and subroutine instructions --- Special
instructions --- Module tests --- Evaluation sheets ---
Selected tables.",
}
@InProceedings{Demmel:1981:EUS,
author = "James Demmel",
title = "Effects of Underflow on Solving Linear Systems",
crossref = "IEEE:1981:PSC",
pages = "113--119",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Demmel.pdf",
abstract = "Software to solve systems of linear equations by
Gaussian elimination has in the past ignored the
effects of underflow. But when underflows are replaced
by zeroes, this software can give spurious though
plausible results much worse than would be blamed on
roundoff. When underflow is gradual, as in the proposed
IEEE standard for floating point arithmetic, the same
software gives provably more reliable results. To
achieve the same reliability without gradual underflow,
but with underflows set to zero, complicated tests must
be inserted into the software.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Efe:1981:MOA,
author = "Kemal Efe",
title = "Multi-Operand Addition with Conditional Sum Logic",
crossref = "IEEE:1981:PSC",
pages = "251--255",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Efe.pdf",
abstract = "Column-wise addition schemes involve counting the
number of 1's in a column and representing this number
in binary weighted form. In Conditional Sum Logic
(CSL), partial results are first generated for every
column, then one of these results is selected depending
on the incoming carry value. A compact scheme for
counting the number of 1's and generating partial
results for all possible distributions of incoming
carries is introduced. Application of such counters to
CSL yields a high speed in multi-operand addition.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@TechReport{Eide:1981:FPA,
author = "Vigleik Eide",
title = "Floating-point arithmetic on a micro-computer",
type = "Hovedoppgave i informatikk (cand. real)",
institution = "Universitetet i Oslo",
address = "Oslo, Norway",
pages = "71",
year = "1981",
bibdate = "Thu May 09 08:12:55 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Farmwald:1981:DHP,
author = "P. M. Farmwald",
title = "On the Design of High Performance Digital Arithmetic
Units",
type = "Thesis ({Ph.D.})",
school = "Stanford University",
address = "Stanford, CA, USA",
pages = "????",
month = aug,
year = "1981",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{Farmwald:1981:HBE,
author = "P. Michael Farmwald",
title = "High bandwidth evaluation of certain elementary
functions",
crossref = "IEEE:1981:PSC",
pages = "139--142",
year = "1981",
bibdate = "Mon May 20 05:27:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Farmwald.pdf",
abstract = "Among the requirements currently being imposed on
high-performance digital computers to an increasing
extent are the high-bandwidth computations of
elementary functions, which are relatively
time-consuming procedures when conducted in software.
In this paper, we elaborate on a technique for
computing piecewise quadratic approximations to many
elementary functions. This method permits the effective
use of large RAMs or ROMs and parallel multipliers for
rapidly generating single-precision floating-point
function values (e.g., 30-45 bits of fraction, with
current RAM and ROM technology). The technique, based
on the use of Taylor series, may be readily pipelined.
Its use for calculating values for floating-point
reciprocal, square root, sine, cosine, arctangent,
logarithm, exponential and error functions is
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Fredette:1981:RES,
author = "G. Fredette",
title = "68000 routine extracts square roots",
journal = j-EDN,
volume = "26",
number = "16",
pages = "185--194",
month = aug,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Ganesan:1981:GSC,
author = "K. Ganesan and A. Augustine",
title = "8086 generates sines and cosines",
journal = j-EDN,
volume = "26",
number = "6",
pages = "186--188",
month = mar,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Book{Glaser:1981:HBO,
author = "Anton Glaser",
title = "History of Binary and Other Nondecimal Numeration",
publisher = "Tomash",
address = "Los Angeles, CA, USA",
edition = "Revised",
pages = "xiii + 218",
year = "1981",
ISBN = "0-938228-00-5",
ISBN-13 = "978-0-938228-00-4",
LCCN = "QA141.2 .G55 1981",
bibdate = "Fri Mar 17 08:12:27 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "See also original edition \cite{Glaser:1971:HBO}.",
acknowledgement = ack-nhfb,
author-dates = "1924--",
remark = "Based on the author's thesis (Ph.D.--Temple
University), presented under the title: History of
modern numeration systems.",
subject = "Numeration; History; 31.14 number theory; 15.00
history: general; Numeration; Dualsystem; Geschichte;
Talstelsels; History; Num{\'e}ration; Histoire;
Dualsystem; Geschichte.",
}
@Book{Gorin:1981:IDA,
author = "Ralph E. Gorin",
title = "Introduction to {DECSYSTEM}-20 Assembly Language
Programming",
publisher = pub-DP,
address = pub-DP:adr,
pages = "xxx + 545",
year = "1981",
ISBN = "0-932376-12-6",
ISBN-13 = "978-0-932376-12-1",
LCCN = "QA76.8.D17 .G67",
bibdate = "Tue Dec 14 22:54:14 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$40.00",
acknowledgement = ack-nhfb,
}
@InProceedings{Gorji-Sinaki:1981:DDS,
author = "A. Gorji-Sinaki and M. D. Ercegovac",
title = "Design of a Digit-Slice On-Line Arithmetic Unit",
crossref = "IEEE:1981:PSC",
pages = "72--80",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_GorjiSinaki_Ercegovac.pdf",
abstract = "A gate level design of a digit-slice on-line
arithmetic unit is presented. This unit is designed as
a set of basic modules Processing Elements (PE), each
of which operates on a single digit of the operands and
the results. It is capable of executing four basic
operations of addition\slash subtraction,
multiplication and division in an on-line manner. The
results are generated during the digit-serial input of
the operands, beginning always with the most
significant digit. A general (with respect to radix)
analysis of the cost and speed of the proposed unit is
also given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Gosling:1981:CSH,
author = "J. B. Gosling and J. H. P. Zurawski and D. B. G.
Edwards",
title = "A Chip-Set for a High-Speed Low-cost Floating-Point
Unit",
crossref = "IEEE:1981:PSC",
pages = "50--55",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Gosling_Zurawski_Edwards.pdf",
abstract = "Although the advent of microprocessors has put
considerable computing power in the hands of large
numbers of users, there is still an important group who
have yet to benefit fully from large scale
integration., As a step in the direction of rectifying
this situation, a highly flexible chip set is being
designed, with a view to reducing the cost of a
powerful floating point processor by a factor of about
4. Processing speed will be up to twice that of an
equivalent unit built from MSI devices, before
allowance is made for savings on wiring delays. It will
be possible to construct a unit satisfying all
published standards, proposed and existing (de facto),
as well as permitting a number of extensions not
specifically in these standards. At a cost between 100
and 150 ICs, and with a floating-point add time of
around 120ns, the proposed unit is cost-effective
compared to currently available coprocessors.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Grappel:1981:RDB,
author = "R. D. Grappel",
title = "68000 routine divides 32-bit numbers",
journal = j-EDN,
volume = "26",
number = "5",
pages = "161--162",
month = mar,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Gregory:1981:RAR,
author = "R. T. Gregory",
title = "Residue Arithmetic with Rational Operands",
crossref = "IEEE:1981:PSC",
pages = "144--145",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Gregory.pdf",
abstract = "A method is described for doing residue arithmetic
when the operands are rational numbers. A rational
operand $ a / b $ is mapped onto the integer $ a
b^{-1}|_p $ and the arithmetic is performed in $
\mathrm {GF}(p) $. A method is given for taking an
integer result and finding its rational equivalent (the
one which corresponds to the correct rational
result).",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; residue number system",
}
@Article{Griffiths:1981:BDC,
author = "L. K. Griffiths",
title = "Binary-to-Decimal Conversion",
journal = j-IBM-TDB,
volume = "24",
number = "1A",
pages = "237--238",
month = jun,
year = "1981",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 17:04:53 2003",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Binary to decimal conversion can be achieved by
multiplying $ 1 / 10 $ as $ 51 / 512 \times 256 / 255 $
and using the fact that $ 256 / 255 = 1 + 1 / 256 + 1 /
256^2 + \cdots $, i.e., $ 256 / 255 = 257 - 256 $
rounded up.\par
This method can be performed efficiently on short word
computers with only adding and shifting operations,
i.e., first multiplying by $ 51 / 512 $ and then
correcting by multiplying by $ 256 / 255 $.",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "decimal floating-point arithmetic",
}
@Article{Grote:1981:CIS,
author = "H. Grote",
title = "Code improves on a square-root routine",
journal = j-EDN,
volume = "26",
number = "11",
pages = "198--200",
month = may,
year = "1981",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@MastersThesis{Hazlerig:1981:CES,
author = "Steven Jackson Hazlerig",
title = "Comparison and evaluation of several floating-point
schemes for the {Motorola} 68000 microprocessor",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical and Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "103",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Richard E. Zippel.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors ---
Programming.; Microprogramming.",
}
@TechReport{Hendra:1981:FPS,
author = "R. G. Hendra",
title = "A floating point software package for use on {LSI-11}
computers at {SLAC}",
type = "Technical note",
number = "SLAC TN 81-3",
institution = "SLAC",
address = "Stanford, CA, USA",
pages = "8",
month = jun,
year = "1981",
bibdate = "Fri May 25 05:50:26 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0046833",
acknowledgement = ack-nhfb,
}
@Article{Hough:1981:API,
author = "David Hough",
title = "Applications of the Proposed {IEEE-754} Standard for
Floating Point Arithmetic",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "70--74",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220381",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Sep 2 23:38:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nhfb # " and " # ack-nj,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Huang:1981:IFD,
author = "Chao Huang and D. Peterson and H. Rauch and J. Teague
and D. Fraser",
title = "Implementation of a fast digital processor using the
residue number system",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "28",
number = "1",
pages = "32--38",
month = jan,
year = "1981",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23509",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "This paper contains a description of a special purpose
digital processor which has been implemented using
residue arithmetic. The processor does two-dimensional
pulse matching by convolving a two-dimensional
five-by-five filter with the Incoming data \ldots{}",
}
@MastersThesis{Hwang:1981:CFF,
author = "Shu-Hwa Hwang",
title = "Computation in a finite field using rational
operands",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "v + 80",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Floating-point arithmetic.; Modular
arithmetic.; Programming (Electronic computers)",
}
@InProceedings{Hwang:1981:PAV,
author = "Kai Hwang and Yen-Heng Cheng",
title = "Partitioned Algorithms and {VLSI} Structures for
Large-Scale Matrix Computations",
crossref = "IEEE:1981:PSC",
pages = "222--232",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Hwang_Cheng.pdf",
abstract = "VLSI modular arithmetic structures and new partitioned
matrix algorithms are developed in this paper to
perform hardware matrix computations in solving
large-scale linear system of equations. Gaussian
elimination and inversion of triangular matrices are
shown systematically partitionable. All the partitioned
algorithms being developed can achieve linear
computation time $ O(n) $, where $n$ is the order of
the linear system. The partitioned matrix computations
are feasible for modular VLSI implementation with
constrained I/O terminals. Performance analysis and
design tradeoffs of the partitioned VLSI arithmetic
structures are also provided.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Irwin:1981:RAP,
author = "Mary Jane Irwin and Dwight R. Smith",
title = "A Rational Arithmetic Processor",
crossref = "IEEE:1981:PSC",
pages = "241--245",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Irwin_Smith.pdf",
abstract = "An arithmetic processor based upon a rational
representation scheme is examined. The key feature of
this rational processor is its ability to efficiently
reduce a result ratio to its irreducible form (the
greatest common divisor of the numerator and
denominator is unity). The reduction algorithm
presented generates the reduced ratio in parallel with
the evaluation of the ratio's greatest common divisor.
Hardware designs for the reduction algorithm and the
basic arithmetic operations are given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Jenkins:1981:CSP,
author = "W. K. Jenkins and M. H. Etzel",
title = "Correction to {``Special} properties of complement
codes for redundant residue number systems''",
journal = j-PROC-IEEE,
volume = "69",
number = "8",
pages = "1086--1086",
month = aug,
year = "1981",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Jenkins:1981:SPC}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31304",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "residue arithmetic; residue number system",
}
@Article{Jenkins:1981:SPC,
author = "W. K. Jenkins and M. H. Etzel",
title = "Special properties of complement codes for redundant
residue number systems",
journal = j-PROC-IEEE,
volume = "69",
number = "1",
pages = "132--133",
month = jan,
year = "1981",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See correction \cite{Jenkins:1981:CSP}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31297",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "residue arithmetic; residue number system",
summary = "Redundant residue number systems are of interest
because they have properties that are useful for error
control and failure recovery in digital processors.
This letter shows how complement coding interferes with
error detection in redundant residue \ldots{}",
}
@TechReport{Kahan:1981:WDW,
author = "W. Kahan",
title = "Why Do We Need a Floating-Point Arithmetic Standard?",
type = "Technical Report",
institution = inst-BERKELEY,
address = inst-BERKELEY:adr,
pages = "41",
day = "12",
month = feb,
year = "1981",
bibdate = "Fri Apr 7 12:22:17 GMT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Available in a retypeset version
\cite{Kahan:2001:WDW}.",
}
@Article{Karplus:1981:ASI,
author = "W. J. Karplus and D. Cohen",
title = "Architectural and Software Issues in the Design of
Peripheral Array Processors",
journal = j-COMPUTER,
volume = "??",
number = "??",
pages = "??--??",
month = sep,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Nov 09 19:01:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Kaushik:1981:SDS,
author = "Saroj Kaushik and R. K. Arora",
title = "Sign Detection in the Symmetric Residue Number
System",
crossref = "IEEE:1981:PSC",
pages = "146--150",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kaushik_Arora.pdf",
abstract = "This paper is concerned with the algebraic sign
detection of a number in the Symmetric Residue Number
System. A new approach has been suggested which
completely avoids the time consuming process of the
Symmetric Mixed Radix Conversion (SMRC). An algorithm
based on the above approach implementable in parallel
for sign detection is also presented. The hardware
representation of the above algorithm is shown. The
time and hardware complexity required for the process
have also been computed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Kielbasinski:1981:IRL,
author = "Andrzej Kie{\l}basi{\'n}ski",
title = "Iterative refinement for linear systems in
variable-precision arithmetic",
journal = j-BIT,
volume = "21",
number = "1",
pages = "97--103",
month = mar,
year = "1981",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934074",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05",
MRnumber = "83a:65042",
bibdate = "Wed Jan 4 18:52:17 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=1&spage=97",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; variable-precision
arithmetic",
}
@Book{Knuth:1981:SA,
author = "Donald E. Knuth",
title = "Semi\-nu\-mer\-i\-cal Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xi + 624",
year = "1981",
ISBN = "0-201-03822-6",
ISBN-13 = "978-0-201-03822-4",
LCCN = "QA76.6 .K64",
bibdate = "Wed Dec 15 15:47:38 1993",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$19.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nj,
}
@InProceedings{Kobayashi:1981:FMO,
author = "Hideaki Kobayashi",
title = "A Fast Multi-Operand Multiplication Scheme",
crossref = "IEEE:1981:PSC",
pages = "246--250",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kobayashi.pdf",
abstract = "Recent developments in integrated circuit technology
have made efficient schemes for computer arithmetic
possible. This paper discusses a generation-summation
scheme for fast multi-operand multiplication. Synthesis
of three-operand multipliers utilizing a single type of
standard LSI device is also discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Book{Kogge:1981:APC,
author = "Peter M. Kogge",
title = "The Architecture of Pipelined Computers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xii + 334",
year = "1981",
ISBN = "0-07-035237-2",
ISBN-13 = "978-0-07-035237-7",
LCCN = "QA76.5 .K587",
bibdate = "Wed Dec 15 10:37:46 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Koren:1981:CPN,
author = "I. Koren and Y. Maliniak",
title = "On Classes of Positive, Negative, and Imaginary Radix
Number Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "30",
number = "5",
pages = "212--317",
month = may,
year = "1981",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1981.1675788",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Aug 22 09:00:57 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A unified approach to a broad class of finite number
representation systems is proposed. This class contains
aDl positive and negative radix systems and other
well-known number systems. In addition, it can be
extended to include imaginary radix number systems. The
proposed approach enables us to develop a single set of
algorithms for arithmetic operations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kornerup:1981:IRA,
author = "Peter Kornerup and David W. Matula",
title = "An Integrated Rational Arithmetic Unit",
crossref = "IEEE:1981:PSC",
pages = "233--240",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kornerup_Matula.pdf",
abstract = "Based on the classical Euclidian Algorithm, we develop
the foundations of an arithmetic unit performing Add,
Subtract, Multiply and Divide on rational operands. The
unit uses one unified algorithm for all operations,
including rounding. A binary implementation, based on
techniques known from the SRT division, is described.
Finally, a hardware implementation using ripple-free,
carry-save addition is analyzed, and adapted to a
floating-slash representation of the rational
operands.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Book{Kulisch:1981:CAT,
author = "Ulrich W. Kulisch and Willard L. Miranker",
title = "Computer arithmetic in theory and practice",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiii + 249",
year = "1981",
ISBN = "0-12-428650-X",
ISBN-13 = "978-0-12-428650-4",
LCCN = "QA162 .K84",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Computer science and applied mathematics",
acknowledgement = ack-nhfb,
keywords = "Algebra, Abstract.; Computer arithmetic.;
Floating-point arithmetic.; Interval analysis
(Mathematics)",
remark = "See \cite[pp. 1.10--1.11]{Coonen:1984:CPS} for
negative comments about the floating-point model in
this book, and the impracticality of implementing it in
early-1980s technology. Coonen comments: ``their scheme
is {\em sufficient\/} to perform reliable computation,
aided by devious algorithms; there is no evidence that
their scheme is {\em necessary}. nor that the
deviousness of their algorithms is unavoidable.''",
}
@Article{Kunz:1981:QZ,
author = "W. Kunz",
title = "{Quadratwurzel mit dem $ \mu $P Z80} \toenglish
{Square Roots with the Z80 Microprocessor}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "7",
pages = "109--110",
year = "1981",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@InProceedings{Ligomenides:1981:CRF,
author = "P. Ligomenides and R. Newcomb",
title = "Complement Representations in the {Fibonacci}
Computer",
crossref = "IEEE:1981:PSC",
pages = "6--9",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ligomenides_Newcomb.pdf",
abstract = "Two complement representations and a sign-magnitude
one are introduced which allow for handling negative
numbers using only binary coefficients in Fibonacci
base expansions. These are developed for practical
implementation in Fibonacci computers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Ling:1981:HSB,
author = "Huey Ling",
title = "High-speed binary adder",
journal = j-IBM-JRD,
volume = "25",
number = "2/3",
pages = "156--166",
month = may # "\slash " # jun,
year = "1981",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C5120 (Logic and switching circuits)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "adders; fewer logic levels; high; neighbouring bit;
new carry propagation; new scheme; pairs; reduced
component count; speed binary adder; uniform fanin
loading; uniform fanout loading",
treatment = "N New Development",
}
@Article{Linnainmaa:1981:CEU,
author = "Seppo Linnainmaa",
title = "Combatting the effects of underflow and overflow in
determining real roots of polynomials",
journal = j-SIGNUM,
volume = "16",
number = "2",
pages = "11--16",
month = jun,
year = "1981",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:09 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Linnainmaa:1981:SDP,
author = "Seppo Linnainmaa",
title = "Software for Doubled-Precision Floating-Point
Computations",
journal = j-TOMS,
volume = "7",
number = "3",
pages = "272--283",
month = sep,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355958.355960",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "68B99 (65G99 68C05)",
MRnumber = "82h:68041",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/355958.355960",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accurate floating-point summation; exact
multiplication; floating-point arithmetic; rounding
errors; software portability",
}
@Article{Louie:1981:APS,
author = "T. Louie",
title = "Array Processors: a Selected Bibliography",
journal = j-COMPUTER,
volume = "??",
number = "??",
pages = "??--??",
month = sep,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Nov 09 19:04:04 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Markov:1981:IAA,
author = "Svetoslav Markov",
title = "On an Interval Arithmetic and Its Applications",
crossref = "IEEE:1981:PSC",
pages = "274--278",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Markov.pdf",
abstract = "It is our point of view that familiar interval
arithmetic defined by $ A*B = \{ a * b : a \in A, b \in
B \} $, $ * \in \{ +, -, \times, : \} $ is inefficient
in certain respects. For instance, it is not in a
position to produce exact representations of sets of
the form $ \{ f(x, y, \ldots {}, z) : x \in X. y \in Y,
\ldots {}, z \in Z \} $ even for simple functions $f$
of one variable. We make use of another interval
arithmetic which is very convenient for computer
computations and for construction of interval
algorithms. As an example we consider a method for the
construction of interval expressions for sets of the
form $ \{ f(x) : x \in [x_1, x_2] \} $, where $f$ is an
elementary function.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; interval arithmetic",
}
@Article{Maron:1981:IAP,
author = "N. Maron and T. A. Brengle",
key = "Maron \& Brengle",
title = "Integrating an Array Processor into a Scientific
Computing System",
journal = j-COMPUTER,
volume = "14",
number = "9",
pages = "41--44",
month = sep,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Wed Nov 14 19:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Parallel/Multi.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Matsui:1981:OUF,
author = "S. Matsui and M. Iri",
title = "An overflow\slash underflow-free floating-point
representation of numbers",
journal = j-J-INF-PROCESS,
volume = "4",
number = "3",
pages = "123--133",
year = "1981",
CODEN = "JIPRDE",
ISSN = "0387-6101",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0",
content = "The authors propose a floating-point number
representation whereby the allocation of digits between
exponent and mantissa would vary with the size of the
number. In extreme cases in which the entire word is
not long enough to contain the exponent, they move to a
different ``level'' and work with exponents of
exponents. They have implemented the scheme in
software, and they claim that a hardware implementation
is possible without loss of efficiency. Their examples
include Graeffe's method, which seems to survive better
in their environment than in a conventional
floating-point environment, and Racah symbols, which
are functions of factorials.\par
The examples are not totally convincing.
Polynomial-factoring is not a computational bottleneck.
The Racah symbols would indeed cause trouble if
computed in a direct manner in conventional floating
point; however, the use of a log-gamma function would
largely eliminate the problem.\par
By using certain bit-configurations to denote
``nonnumbers'' the authors make good their claim of
overflow-free arithmetic. The system clearly has the
merit of convenience. In the absence of a formal error
analysis it is not yet clear what price has to be paid
for the convenience. \par
A. C. R. Newbery, Lexington.",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
CRnumber = "40691",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
fjournal = "Journal of Information Processing",
genterm = "DESIGN; PERFORMANCE",
reviewer = "A. C. R. Newbery; Newbery, A. C. R",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Miller:1981:RGU,
author = "W. Miller",
title = "A Remark on Gradual Underflow",
journal = j-COMPUTING,
volume = "27",
number = "3",
pages = "217--225",
year = "1981",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Univ of Ariz, Tucson, USA",
classification = "723",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer metatheory;
floating-point arithmetic; IEEE 754 arithmetic",
}
@Article{Mitra:1981:CRA,
author = "D. Mitra and V. Lawrence",
title = "Controlled rounding arithmetics, for second-order
direct-form digital filters, that eliminate all
self-sustained oscillations",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "28",
number = "9",
pages = "894--905",
month = sep,
year = "1981",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Quantization often allows a recursive second-order
filter to oscillate even when the underlying linear
model is absolutely stable and there is no external
signal present to excite the filter. One of the
significant innovative ideas recently \ldots{}",
}
@Article{Munson:1981:FPR,
author = "David C. {Munson, Jr.} and Bede Liu",
title = "Floating point roundoff error in the prime factor
{FFT}",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "29",
number = "4",
pages = "877--882",
month = aug,
year = "1981",
CODEN = "IETABA",
ISSN = "0096-3518",
MRclass = "65R10 (94A05)",
MRnumber = "82f:65132",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The prime factor fast Fourier transform (PF FFT),
developed by Kolba and Parks, makes use of recent
computational complexity results by Winograd to compute
the DFT with a fewer number of multiplications than
that required by the FFT. Patterson and McClellan have
derived an expression for the mean squared error (MSE)
in the PF FFT, assuming finite precision fixed point
arithmetic. In this paper, we derive an expression for
the MSE in the PF FFT, assuming floating point
arithmetic. This expression is quite complicated, so an
upper bound on the MSE is also derived which is easier
to compute. Simulation results are presented comparing
the error in the PF FFT with both the derived bound and
the error observed in a radix-2 FFT.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
}
@InProceedings{Nguyen:1981:SAD,
author = "Diem Dinh Nguyen",
title = "A Systematic Approach to the Design of Structures for
Addition and Subtraction --- Case of Radix $ r = m^k
$",
crossref = "IEEE:1981:PSC",
pages = "42--49",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Nguyen.pdf",
abstract = "The results of Robertson concerning a systematic
approach to the design of Adder\slash Subtracter
structures of radix $ r = 2^k $, $ k \geq I $ are
generalised to cover all structures of radix $ r = m^k
$, $ k \geq I $ and $ m \geq 2 $. The use of
quasibinary representations help reduce the number of
types of fundamental structures required. In addition
to the types encountered in the earlier case, only one
new type of fundamental structure called Radix-$m$
Carry Generator is needed. Examples in the particular
case of Decimal Adder\slash Subtracter structures are
used to illustrate the results.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Ong:1981:TQC,
author = "S. Ong and D. E. Atkins",
title = "Towards Quantitative Comparison of Computer Number
Systems",
crossref = "IEEE:1981:PSC",
pages = "21--33",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ong_Atkins.pdf",
abstract = "This paper describes an evolving Arithmetic Design
System (ADS) to support the quantitative evaluation of
alternate number systems with respect to a given
application and realization technology. In computer
arithmetic we are concerned with establishing a
correspondence between abstract quantities (numbers)
and some physical representation (symbols), and with
simulating the operations on these symbols. The ADS is
intended to help study the cost and performance of
alternate simulations. A finite number system is a
triple consisting of a symbol set (elements are called
``digit-vectors''), an interpretation set, a mapping
between these two sets, and a set of operators
(digit-vector algorithms) defined on its symbol set. A
set of these digit vector algorithms are proposed for
conducting arithmetic design. A number system matrix
defines the digit vector algorithm for numerous number
systems and a method for computing time and space
complexity of compositions of these algorithms is
proposed. An example of how the system could be used to
compare addition, with and without overflow detection,
for three number systems is given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Owens:1981:CAD,
author = "Robert Michael Owens",
title = "Compound Algorithms for Digit On-Line Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "64--71",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Owens.pdf",
abstract = "This paper describes a systematic method which has
been. successfully used to create several digit online
algorithms. Basically, the method entails converting in
a systematic way a known continued sums\slash products
algorithm and combining the converted form of the
continued sums\slash product algorithm with a
generalized digitization algorithm. Not only does the
method seem to have wide applicability in the creation
of digit online algorithms for many elementary
functions but the algorithms which have resulted from
this method themselves have several desirable
properties.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Padegs:1981:SB,
author = "A. Padegs",
title = "{System\slash 360} and Beyond",
journal = j-IBM-JRD,
volume = "25",
number = "5",
pages = "377--390",
month = sep,
year = "1981",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Sat Jan 29 17:56:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Pan:1981:BCA,
author = "V. Pan",
title = "The bit-complexity of arithmetic algorithms",
journal = j-J-ALG,
volume = "2",
number = "2",
pages = "144--163",
month = jun,
year = "1981",
CODEN = "JOALDV",
DOI = "https://doi.org/10.1016/0196-6774(81)90016-X",
ISSN = "0196-6774 (print), 1090-2678 (electronic)",
ISSN-L = "0196-6774",
bibdate = "Tue Dec 11 09:13:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jalg.bib",
URL = "http://www.sciencedirect.com/science/article/pii/019667748190016X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms",
journal-URL = "http://www.sciencedirect.com/science/journal/01966774",
}
@InProceedings{Papachristou:1981:APA,
author = "C. A. Papachristou",
title = "Algorithms for Parallel Addition and Parallel
Polynomial Evaluation",
crossref = "IEEE:1981:PSC",
pages = "256--263",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Papachristou.pdf",
abstract = "This paper presents two related algorithms for
implementing parallel $n$-bit binary addition and
evaluating $n$-th degree polynomials, respectively. The
approach taken makes use of an iterative construction,
the computation tree. The algorithms are particularly
effective for moderate values of $n$ and are in accord
with well-known asymptotic bounds. In the case of
$n$-bit addition, the implementations constitute
lookahead tree circuits of $r$-input standard logic
elements. Extensions to modular tree structures for
lookahead adders are also considered. In the case of
parallel polynomial evaluation, the operations of
ordinary addition and multiplication are assumed with
the capability to employ $r$ arguments
simultaneously.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Peng:1981:AES,
author = "Hong Peng",
title = "Algorithms for extracting square roots and cube
roots",
crossref = "IEEE:1981:PSC",
pages = "121--126",
year = "1981",
bibdate = "Thu Sep 01 11:37:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf",
abstract = "This paper describes a kind of algorithms for fast
extracting square roots and cube roots, their
mathematical proofs, their revised algorithm formulae,
and hardware implementation of the square root
algorithm. These algorithms may be of no significance
for large scale computer with fast division. But I am
sure that it is effective and economical to apply these
algorithms to the circuit designs of some mini- and
microcomputers with general multiplication and
division, such as nonrestoring division.",
acknowledgement = ack-nj,
keywords = "ARITH-5",
}
@Article{Peters:1981:EFB,
author = "James V. Peters",
title = "An Equivalent Form of {Benford's Law}",
journal = j-FIB-QUART,
volume = "19",
number = "1",
pages = "74--75",
month = feb,
year = "1981",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:53 MDT 2011",
bibsource = "http://www.fq.math.ca/19-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@InProceedings{Raghavendra:1981:SLA,
author = "C. S. Raghavendra and M. D. Ercegovac",
title = "A Simulator for On-Line Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "92--98",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Raghavendra_Ercegovac.pdf",
abstract = "On-line arithmetic is a special class of serial
arithmetic where algorithms produce results with the
most significant digit first during the serial input of
the operands. Speedup of computations can be achieved
by overlapping or pipelining successive operations with
small delays. This paper describes the design and
implementation of a simulator for on-line arithmetic
algorithms. The simulator was designed primarily to
serve as\par
(1) an experimental tool for synthesis of on-line
algorithms;\par
(2) a performance evaluation tool of on-line
arithmetic;\par
(3) an on-line calculator in solving some problems
involving linear and non-linear recurrences.\par
The simulator evaluates arithmetic expressions given in
a highly functional form. Presently, the set of
operations supported include addition, subtraction,
multiplication, division, and square root. Several
examples are presented in this paper to illustrate the
usage of the simulator. The simulator package is
implemented in 'C' language on a VAX 11/780 system.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Rao:1981:AFF,
author = "T. R. N. Rao",
title = "Arithmetic of Finite Fields",
crossref = "IEEE:1981:PSC",
pages = "2--5",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rao.pdf",
abstract = "The arithmetic operations in finite fields and their
implementation are important to the construction of
error detecting and correcting codes. The addition,
multiplication and division in the field $ \mathrm
{GF}(2^m) $ are implemented as polynomial operations
using binary logic of flip-flops and EXOR's. For fields
of nonbinary characteristic, modular arithmetic (with
modulus $p$, a prime) becomes important. This paper
focuses on problems relating to the arithmetic of $
\mathrm {GF}(p) $, and some recent results and new
ideas on this topic are presented here.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Rao:1981:CHC,
author = "T. M. Rao and R. T. Gregory",
title = "The Conversion of {Hensel} Codes to Rational Numbers",
crossref = "IEEE:1981:PSC",
pages = "10--14",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rao_Gregory.pdf",
abstract = "In a finite-segment p-adic number system one of the
difficult problems is concerned with converting Hensel
codes back into rational numbers. An algorithm for this
conversion is proposed which is based on a
sophisticated table look-up procedure.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Redinbo:1981:SRN,
author = "G. Redinbo and W. Hunnebeck",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '81}",
title = "On the simulation of residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "339--342",
year = "1981",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19800468",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "It is sometimes difficult to simulate on general
purpose computers the performance of digital systems
that use residue number systems. This paper
demonstrates a new technique that makes effective use
of a Fast Fourier Transform (FFT) to simulate the
\ldots{}",
}
@InProceedings{Robertson:1981:SAD,
author = "J. E. Robertson",
title = "A Systematic Approach to the Design of Structures for
Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "35--41",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Robertson.pdf",
abstract = "A design tool for the decomposition of binary digital
structures for addition and subtraction has been
developed. A simplified theory reduces a complex
structure to a collection of basic structures of one
type, namely, a full adder. The simplified theory is
applicable to the design of parallel counters and array
multipliers. A general theory is used for decomposition
to three types of basic structures, whose complexity is
usually on the order of a half-adder. The general
theory is applicable to redundant array multipliers and
signed-digit adders.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Rodrigues:1981:HEM,
author = "M. R. D. Rodrigues and J. H. P. Zurawski and J. B.
Gosling",
title = "Hardware evaluation of mathematical functions",
journal = j-IEE-PROC-E,
volume = "128",
number = "4",
pages = "155--164",
month = jul,
year = "1981",
CODEN = "IPETD3",
ISSN = "0143-7062",
bibdate = "Thu Sep 1 10:15:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEE proceedings, E: Computers and digital techniques",
}
@InProceedings{Rutenbar:1981:CSV,
author = "R. A. Rutenbar and Y. E. Park",
title = "Case Study of a {VLSI} Design Project: a Simple Inner
Product Machine",
crossref = "IEEE:1981:PSC",
pages = "184--189",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rutenbar_Park.pdf",
abstract = "We present a case study of the application of recently
evolved structured VLSI design methodologies to the
design and implementation of a simple VLSI quasi-serial
inner product machine.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Schonfelder:1981:ECP,
author = "J. L. Schonfelder and M. Razaz",
title = "Error control with polynomial approximations",
journal = j-IMA-J-NUMER-ANAL,
volume = "1",
number = "1",
pages = "105--114",
year = "1981",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65D15",
MRnumber = "83d:65043, 607250",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@TechReport{Schryer:1981:TCF,
author = "N. L. Schryer",
title = "A Test of a Computer's Floating-Point Arithmetic
Unit",
number = "Computer Science Technical Report 89",
institution = "AT\&T Bell Laboratories",
pages = "66",
month = feb,
year = "1981",
bibdate = "Fri Nov 30 11:20:24 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://plan9.bell-labs.com/cm/cs/cstr/89.ps.gz;
http://www.bell-labs.com/topic/swdist/",
acknowledgement = ack-nj,
keywords = "floating-point testing",
}
@Article{Schwarz:1981:EYC,
author = "H. R. Schwarz",
title = "The Early Years of Computing in {Switzerland}",
journal = j-ANN-HIST-COMPUT,
volume = "3",
number = "2",
pages = "121--132",
month = apr # "\slash " # jun,
year = "1981",
CODEN = "AHCOE5",
DOI = "https://doi.org/10.1109/MAHC.1981.10013",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1981/pdf/a2121.pdf;
http://www.computer.org/annals/an1981/a2121abs.htm",
acknowledgement = ack-nhfb,
content = "Schwartz describes two early computers used at the
Swiss Federal Institute of Technology (whose German
acronym is ETH) during the 1950s. Despite the more
general title, he does not mention any non-ETH
computers in this article. According to Schwartz, the
first programmable computer in Switzerland was the Z4
developed by Konrad Zuse in Germany during World War II
and installed at the ETH in 1950. Except for the ERMETH
(also at the ETH), he does not mention any subsequent
Swiss installations during the period, leaving a weak
implication that there were none.\par
The Z4 was an electromechanical machine with a total
data memory of 64 32-bit words and no program memory.
Programs were executed while being read from punched
tape. Conditional test instructions permitted
instructions on the tape to be skipped; other control
instructions caused an alternate tape reader to begin
processing a program (a form of subroutine-call). The
arithmetic unit could perform true floating-point
operations. This arithmetic unit contained built-in
functions for computing squares, reciprocals, and
square roots. (Ten years later, mere integer division
was still optional at an extra cost on the IBM 1401.)
There were special representations for infinity and
``undefined'' so that operations such as division by
zero could continue without interruption but with a
meaningful result.",
CRclass = "K.2.7 ERMETH; K.2 Hardware; K.2 Software",
CRnumber = "39473",
descriptor = "Computing Milieux, HISTORY OF COMPUTING; Computing
Milieux, HISTORY OF COMPUTING, ERMETH; Computing
Milieux, HISTORY OF COMPUTING, Hardware; Computing
Milieux, HISTORY OF COMPUTING, Software",
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
reviewer = "D. Ross",
subject = "K. Computing Milieux; K.2 HISTORY OF COMPUTING",
subject-dates = "Ambros Speiser (13 November 1922--10 May 2003); Heinz
Rutishauser (30 January 1918--10 November 1970); Eduard
Stiefel (21 April 1909--25 November 1978)",
}
@Article{Smith:1981:ERA,
author = "J. M. Smith and F. W. J. Olver and D. W. Lozier",
title = "Extended-Range Arithmetic and Normalized {Legendre}
Polynomials",
journal = j-TOMS,
volume = "7",
number = "1",
pages = "93--105",
month = mar,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355934.355940",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65G05)",
MRnumber = "83a:65017",
bibdate = "Mon Aug 29 22:02:12 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/355934.355940",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "angular momentum; extended-range arithmetic; Legendre
polynomials; overflow; underflow",
}
@Book{Spaniol:1981:CAL,
author = "Otto Spaniol",
title = "Computer Arithmetic: Logic and Design",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "280",
year = "1981",
ISBN = "0-471-27926-9",
ISBN-13 = "978-0-471-27926-6",
LCCN = "QA76.6 .S6613, TK7888.3.S7",
bibdate = "Thu Sep 01 22:26:58 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation of \cite{Spaniol:1976:AR}.",
acknowledgement = ack-nhfb,
}
@Article{Stevenson:1981:ITP,
author = "David Stevenson",
title = "{IEEE Task 754}: a Proposed Standard for Binary
Floating-Point Arithmetic: Draft 8.0",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "51--62",
month = mar,
year = "1981",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Thu Sep 1 10:14:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
annote = "Offered here for public comment, this proposed
standard facilitates transportation of numerically
oriented programs and encourages development of
high-quality numerical software.",
country = "USA",
date = "30/10/88",
descriptors = "Standardization; computer arithmetic; IEEE 754;
floating point; computation structure; numerical
software",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Stevenson:1981:PSBa,
author = "David Stevenson",
title = "A Proposed Standard for Binary Floating-Point
Arithmetic",
journal = j-COMPUTER,
volume = "14",
number = "3",
pages = "51--62",
month = mar,
year = "1981",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/C-M.1981.220377",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sun May 2 09:21:54 1999",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1981.bib;
https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nhfb # " and " # ack-nj,
annote = "Offered here for public comment, this proposed
standard facilitates transportation of numerically
oriented programs and encourages development of
high-quality numerical software.",
country = "USA",
date = "30/10/88",
descriptors = "Standardization; computer arithmetic; IEEE 754;
floating point; computation structure; numerical
software",
enum = "2967",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
location = "PKI-OG: Li-Ord.Le; RWTH-AC-DFV: Bibl.",
references = "0",
revision = "21/04/91",
}
@Book{Stevenson:1981:PSBb,
author = "David Stevenson",
title = "A proposed standard for binary floating-point
arithmetic: draft 8.0 of {IEEE} Task {P754}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "36",
year = "1981",
bibdate = "Sun May 02 09:22:07 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
acknowledgement = ack-nhfb,
keywords = "Compiling (Electronic computers).; Floating-point
arithmetic.",
remark = "Reprinted from: Computer, v. 14, no. 3 (Mar. 1981):
51--87. Includes articles by W.J. Cody, David Hough,
and Jerome T. Coonen.",
}
@InProceedings{Stummel:1981:PAM,
author = "F. Stummel",
title = "Optimal error estimates for {Gaussian} elimination in
floating-point arithmetic",
crossref = "GAMM:1981:PAM",
journal = j-Z-ANGE-MATH-MECH,
volume = "62",
number = "5",
pages = "T355--T357",
year = "1981",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
MRclass = "65G05 (65F10)",
MRnumber = "84j:65039",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
}
@InProceedings{Tan:1981:ADC,
author = "C.-I. Tan and B. C. McInnis",
booktitle = "20th {IEEE} Conference on Decision and Control
including the Symposium on Adaptive Processes",
title = "Adaptive digital control implemented using residue
number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "808--812",
year = "1981",
CODEN = "????",
DOI = "https://doi.org/10.1109/CDC.1981.269326",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The application of residue number systems for the
implementation of adaptive digital controllers is
presented. Division operations are avoided through the
use of iteration to solve for the value of the control.
Decoding computations are simplified \ldots{}",
}
@InProceedings{Taylor:1981:CHD,
author = "George S. Taylor",
title = "Compatible hardware for division and square root",
crossref = "IEEE:1981:PSC",
pages = "127--134",
year = "1981",
bibdate = "Mon Sep 16 16:30:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf",
abstract = "Hardware for radix four division and radix two square
root is shared in a processor designed to implement the
proposed IEEE floating-point standard. The division
hardware looks ahead to find the next quotient digit in
parallel with the next partial remainder. An 8-bit ALU
estimates the next remainder's leading bits. The
quotient digit look-up table is addressed with a
truncation of the estimate rather than a truncation of
the full partial remainder. The estimation ALU and the
look-up table are asymmetric for positive and negative
remainders. This asymmetry reduces the width of the ALU
and the number of minterms in the logic equations for
the look-up table. The square root algorithm obtains
the correctly rounded result in about two division
times using small extensions to the division
hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; correct rounding; floating-point arithmetic",
}
@Article{Taylor:1981:FPR,
author = "Fred J. Taylor and Chao H. Huang",
title = "A floating-point residue arithmetic unit",
journal = j-J-FRANKLIN-INST,
volume = "311",
number = "1",
pages = "33--53",
month = jan,
year = "1981",
CODEN = "JFINAB",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "94A11 (68A05)",
MRnumber = "82a:94013",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "B.2; G.1.0",
content = "This paper describes the logical design of a floating
point arithmetic unit using a hybrid residue number
system. Mantissas of numbers are operated in a residue
system while the exponents are in binary. Some basic
operations, such as scaling and underflow/overflow
detection, are described, and circuit implementation
using ROMs indicated. ``For example, let m(z)` be a
2N-bit work in integer form and H_0 and H_1 represent
the two following hypotheses. If m(z`) e H_1, then
m(z`) W 1-2- 2^2N = 2^2N 1. If m(z)` e H_0, then m(z)`
< 1-2- 2^2N = 2^2N 1. The hypothesis testing is
accomplished by comparing each of the mixed-radix
digits of m(z)` to that of 2^2N 1 through L independent
binary comparators.'' Circuits for multiplication,
addition, and subtraction are derived. The procedures
seem reasonable and the proofs rigorous. Table look up
cycle times and memory requirements for different
implementation of the arithmetic units are estimated.
These are comparable with corresponding times and
memory needs for PDP/11. Use in algorithms such as FFT
is argued for.\par
The exposition is somewhat difficult. As with many
logical designs one is not sure whether the approach
given is optimum (for any sense of the word
``optimum''). In the absence of a working system one
can not be sure",
CRclass = "B.2.1 Design Styles; G.1.0 General; G.1.0 Computer
arithmetic",
CRnumber = "39211",
descriptor = "Hardware, ARITHMETIC AND LOGIC STRUCTURES, Design
Styles; Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic",
fjournal = "Journal of {The Franklin Institute}",
genterm = "DESIGN",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
reviewer = "B. Hazeltine; Hazeltine, B",
subject = "B. Hardware; B.2 ARITHMETIC AND LOGIC STRUCTURES; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Taylor:1981:VHP,
author = "George S. Taylor and David A. Patterson",
title = "{VAX} Hardware for the Proposed {IEEE} Floating-Point
Standard",
crossref = "IEEE:1981:PSC",
pages = "190--196",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor_Patterson.pdf",
abstract = "The proposed IEEE floating-point standard has been
implemented in a substitute floating-point accelerator
for the VAX-11/760. We explain how features of the
proposed standard influenced the design of the new
processor. By comparing it with the original VAX
accelerator, we illustrate the differences between
hardware for the proposed standard and hardware for a
more traditional floating-point architecture.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Todericiu:1981:AOBb,
author = "Doru Todericiu",
title = "Analyses d'ouvrages: {{\booktitle{Whilhelm Schickard
(1592--1635), Astronom, Geograph, Orientalist, Erfinder
der Rechenmaschine}} par Friedrich Seck}",
journal = j-REV-HIST-SCI,
volume = "34",
number = "3--4",
pages = "374--374",
month = "juillet--octobre",
year = "1981",
CODEN = "RHSAAM",
DOI = "https://doi.org/10.2307/23632469",
ISSN = "0151-4105 (print), 1969-6582 (electronic)",
ISSN-L = "0048-7996",
bibdate = "Tue Jun 16 11:06:47 MDT 2015",
bibsource = "http://www.jstor.org/stable/i23631674;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/revhistsci.bib",
URL = "http://www.jstor.org/stable/23632469",
acknowledgement = ack-nhfb,
ajournal = "Rev. hist. sci.",
fjournal = "Revue d'Histoire des Sciences",
journal-URL = "http://www.jstor.org/journals/00487996.html;
http://www.persee.fr/collection/rhs",
language = "French",
}
@Book{Tyner:1981:GDP,
author = "Paul Tyner",
title = "{iAPX} 432 General Data Processor Architecture
Reference Manual",
publisher = pub-INTEL,
address = pub-INTEL:adr,
pages = "various",
year = "1981",
LCCN = "TK7895.M5 T85 1981",
bibdate = "Fri Dec 08 13:03:20 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Manual{vonGudenberg:1981:GAP,
author = "J. Wolff von Gudenberg",
title = "{Gesamte Arithmetik des Pascal-SC Rechners.
Benutzerhandbuch}. ({German}) [{Complete} Arithmetic of
the {Pascal-SC} Computer: User Handbook]",
organization = "Institute for Applied Mathematics, University of
Karlsruhe",
address = "Karlsruhe, West Germany",
pages = "????",
year = "1981",
bibdate = "Wed Oct 13 22:27:27 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@InProceedings{Walker:1981:EMA,
author = "Gregory Walker",
title = "Extension of the {MC68000} Architecture to Include
Standard Floating-Point Arithmetic",
crossref = "IEEE:1981:PSC",
pages = "179--182",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Walker.pdf",
abstract = "The synthetic aspect of designing a computer
architecture is particularly evident when the design is
highly constrained from two independent directions.
Floating-point extensions of the MC68000 architecture
incorporate the IEEE Proposed Floating-point Standard
into the existing MC68000 architecture.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Washington:1981:BLF,
author = "Lawrence C. Washington",
title = "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
journal = j-FIB-QUART,
volume = "19",
number = "2",
pages = "175--176",
month = apr,
year = "1981",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 17:59:55 MDT 2011",
bibsource = "http://www.fq.math.ca/19-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@TechReport{Watanuki:1981:FOAa,
author = "Osaaki Watanuki",
title = "Floating-point on-line arithmetic for highly
concurrent digit-serial computation: application to
mesh problems",
institution = "Computer Science Dept. Research Laboratory",
address = "Los Angeles, CA, USA",
pages = "xvi + 149",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "UCLA-ENG; 8107 ReRport [sic] / UCLA Computer Science
Department; no. CSD 810529 Report (University of
California, Los Angeles. Computer Science Dept.); no.
CSD-810529",
acknowledgement = ack-nhfb,
keywords = "Differential equations, Partial.; Floating-point
arithmetic.",
remark = "Consists of the author's thesis ({Ph.D.})--UCLA, 1981.
Bibliography: p. 146-149.",
}
@PhdThesis{Watanuki:1981:FOAb,
author = "Osaaki Watanuki",
title = "Floating-point on-line arithmetic for highly
concurrent digit-serial computation: application to
mesh problems",
type = "Thesis ({Ph.D.})",
school = "UCLA",
address = "Los Angeles, CA, USA",
pages = "xvi + 149",
year = "1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Differential equations, Partial.; Floating-point
arithmetic.",
}
@InProceedings{Watanuki:1981:FPLa,
author = "O. Watanuki and M. D. Ercegovac",
title = "Floating-point On-Line Arithmetic: Algorithms",
crossref = "IEEE:1981:PSC",
pages = "81--86",
year = "1981",
bibdate = "Wed Nov 14 17:53:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Watanuki_Ercegovac_a.pdf",
abstract = "For effective application of on-line arithmetic to
practical numerical problems, floating-point algorithms
for on-line addition\slash subtraction and
multiplication have been implemented by introducing the
notion of quasi-normalization. Those proposed are
normalized fixed-precision FLPOL (floating-point
on-line) algorithms.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@InProceedings{Watanuki:1981:FPLb,
author = "O. Watanuki and M. D. Ercegovac",
title = "Floating-point On-Line Arithmetic: Error Analysis",
crossref = "IEEE:1981:PSC",
pages = "87--91",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Watanuki_Ercegovac_b.pdf",
abstract = "The properties of redundant number system in mantissa
representation are studied and the range of the
redundant mantissa is derived. From the range of the
mantissa and the absolute error of on-line operations,
the MRRE (maximum relative representation error) is
defined and analyzed for redundant floating-point
numbers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Wehringer:1981:FSA,
author = "A. Wehringer",
title = "{Flie{\ss}komma-Arithmetik} \toenglish {Floating-point
Arithmetic} \endtoenglish",
journal = "Elektronikschau",
volume = "5",
pages = "34--36",
year = "1981",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Wehringer:1981:SBM,
author = "A. Wehringer",
title = "{Schnelle 16-bit-Multiplikation und Division}
\toenglish {Fast 16-bit Multiplication and Division}
\endtoenglish",
journal = "Elektronikschau",
volume = "10",
pages = "36--37",
year = "1981",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Manual{Weinreb:1981:LMM,
author = "Daniel Weinreb and David Moon",
title = "{LISP} Machine Manual",
organization = "MIT Artificial Intelligence Laboratory",
address = "Cambridge, MA, USA",
edition = "Third",
month = mar,
year = "1981",
bibdate = "Wed Jan 29 17:08:51 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``The number of digits
printed is the `correct' number; no information present
in the flonum is lost, and no extra trailing digits are
printed that do not represent information in the
flonum. Feeding the [printed representation] of a
flonum back to the reader is always supposed to produce
an equal flonum.''",
}
@InProceedings{Willoner:1981:AME,
author = "Robert Willoner and I-Ngo Chen",
title = "An Algorithm for Modular Exponentiation",
crossref = "IEEE:1981:PSC",
pages = "135--138",
year = "1981",
bibdate = "Thu Nov 15 11:37:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Willoner_Chen.pdf",
abstract = "The best known algorithm for {\em modular
exponentiation}, $ M^e \bmod t $ for arbitrary $M$,
$e$, and $t$ is of $ O(n^3) $ where $n$ is the number
ot bits in the largest of $M$, $e$ and $t$. This paper
presents an $ O(n) $ algorithm for the problem where $
M^e \bmod t $ is required for many values of $M$ and
$e$ with constant $t$. Some preprocessing is done on
$t$, and the results are applied repeatedly to
different values of $M$ and $e$. The main algorithm
involves {\em on-line} arithmetic in a {\em redundant}
number system. An immediate application is in
encoding\slash decoding of messages in an RSA-based
{\em public-key cryptosystem}.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5",
}
@Article{Zurawski:1981:DHS,
author = "J. H. P. Zurawski and J. B. Gosling",
title = "Design of High-Speed Digital Divider Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-30",
number = "9",
pages = "691--699",
month = sep,
year = "1981",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1981.1675869",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 18:45:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675869",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InCollection{Aiken:1982:ASC,
author = "Howard H. Aiken and Grace M. Hopper",
title = "The Automatic Sequence Controlled Calculator (1946)",
crossref = "Randell:1982:ODC",
pages = "203--222",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Andrews:1982:MMS,
author = "M. Andrews",
title = "Mathematical Microprocessor Software: a $ \sqrt (x) $
Comparison",
journal = j-IEEE-MICRO,
volume = "2",
number = "3",
pages = "63--79",
month = jul # "\slash " # sep,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.290970",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Andrews:1982:SRX,
author = "M. Andrews",
title = "Square-Root-{X} Comparison --- New Results Discovered
--- Reply",
journal = j-IEEE-MICRO,
volume = "2",
number = "4",
pages = "5--6",
month = oct # "\slash " # dec,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.291010",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Anonymous:1982:ARBf,
author = "Anonymous",
title = "Article Review: {{\booktitle{Ada model arithmetic:
costs and benefits}}: Wallis, P. J. L. \booktitle{IEE
Proc.-E Comput. Dig. Tech.} Vol 129 No 2 (March 1982)
pp 75--80}",
journal = j-MICROPROC-MICROSYS,
volume = "6",
number = "9",
pages = "497--498",
month = nov,
year = "1982",
CODEN = "MIMID5",
DOI = "https://doi.org/10.1016/0141-9331(82)90515-4",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Mon Jan 14 21:50:13 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0141933182905154",
acknowledgement = ack-nhfb,
fjournal = "Microprocessors and Microsystems",
}
@TechReport{Anonymous:1982:MKF,
author = "Anonymous",
title = "{Materialiensammlung zum 5. Kolloquium (mit Floating
Point Systems) Neue Rechnerarchitekturen:
Anwendungsgebiete und Realisierungen: Hannover, (18.Mai
1982)}",
type = "{Bericht}",
number = "30",
institution = "Regionales Rechenzentrum f{\"u}r Niedersachsen bei der
Universit{\"a}t Hannover",
address = "Hannover, Germany",
pages = "58",
year = "1982",
bibdate = "Thu May 09 09:13:36 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1982:NPAa,
author = "Anonymous",
title = "New product applications: Array processor performs 5
million floating-point operations per second, has
200-ns operation time",
journal = j-IEEE-SPECTRUM,
volume = "19",
number = "1",
pages = "104--118",
month = jan,
year = "1982",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1982.6366777",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 16:51:45 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Algorithms; Arrays; Microcomputers; Microprocessors;
Process control; Speech; Standards",
}
@MastersThesis{Arnold:1982:EPS,
author = "Mark Gordon Arnold",
title = "Extending the Precision of the Sign Logarithm Number
System",
type = "{M.S.} Thesis",
school = "University of Wyoming",
address = "Laramie, WY, USA",
year = "1982",
bibdate = "Fri Jun 24 16:06:13 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Bairstow:1982:FPP,
author = "R. Bairstow and J. Barlow and M. Jires and M. Waters",
title = "A floating point processor for {Intel 8080A}
microprocessor systems",
type = "Technical report",
number = "RL 82-020",
institution = "Rutherford Appleton Lab.",
address = "Harwell, Oxon, UK",
pages = "44",
month = mar,
year = "1982",
bibdate = "Fri May 25 05:47:40 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0050018",
acknowledgement = ack-nhfb,
}
@InProceedings{Baraniecki:1982:QEL,
author = "A. Baraniecki and G. Jullien",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '82}",
title = "Quantization error and limit cycles analysis in
residue number system coded recursive filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "52--55",
year = "1982",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The paper discusses the Residue Number System (RNS)
implementation of second order recursive digital filter
sections. The RNS offers the advantage of using integer
based arithmetic operations and a simple hardware
realization involving arrays of \ldots{}",
}
@Article{Barnes:1982:RNI,
author = "C. Barnes and T. Miyawaki",
title = "Roundoff Noise Invariants in Normal Digital Filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "29",
number = "4",
pages = "251--256",
month = apr,
year = "1982",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The unit noise gains for optimal and parallel normal
realizations of digital filters can be expressed in
terms of a set of noise gain parameters that are simply
related to the pole locations and pole residues. These
noise gain parameters are shown \ldots{}",
}
@Article{Bernhard:1982:CCS,
author = "R. Bernhard",
title = "Computers: Computing at the speed limit: Computers
1000 times faster than today's supercomputers would
benefit vital scientific applications",
journal = j-IEEE-SPECTRUM,
volume = "19",
number = "7",
pages = "26--31",
month = jul,
year = "1982",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1982.6366940",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 16:51:45 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Computational modeling; Computer architecture;
computer industry; Computers; Educational institutions;
engineering applications; floating-point operations per
second; flops; Program processors; scientific
applications; Solid modeling; special purpose
computers; very large-scale integration; VLSI",
}
@Article{Bernhard:1982:GSP,
author = "R. Bernhard",
title = "Giants in small packages [array processors]",
journal = j-IEEE-SPECTRUM,
volume = "19",
number = "2",
pages = "39--44",
month = feb,
year = "1982",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1982.6366796",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 16:51:45 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "architecture; array processor; Arrays; arrays of
numbers; computer; computer architecture; digital
arithmetic; digital computers; Hardware; matrices;
Microcomputers; Pipelines; Program processors;
repetitive arithmetic operations; Vectors; vectors",
}
@Article{Bohannan:1982:MAP,
author = "J. W. Bohannan and D. J. Bradley and D. A. Kummer and
J. A. Saenz",
title = "Multiplication Algorithm for Packed {BCD} Numbers",
journal = j-IBM-TDB,
volume = "25",
number = "4",
pages = "2225",
month = sep,
year = "1982",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Bohlender:1982:ROA,
author = "G. Bohlender and K. Gr{\"u}ner and J. Wolff {von
Gudenberg}",
title = "{Realisierung einer optimalen Arithmetik} \toenglish
{Realization of Optimal Arithmetic} \endtoenglish",
journal = j-ELEK-RECHENANLAGEN,
volume = "24",
number = "2",
pages = "68--72",
month = apr,
year = "1982",
CODEN = "ELRAA4",
ISSN = "0013-5720",
bibdate = "Sat Feb 10 12:41:07 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronische Rechenanlagen",
}
@Article{Brent:1982:RLP,
author = "R. P. Brent and H. T. Kung",
title = "A regular layout for parallel adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "??",
pages = "260--264",
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675982",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Sep 16 16:06:24 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brooks:1982:OCL,
author = "R. A. Brooks and R. P. Gabriel and G. L. {Steele
Jr.}",
title = "An optimizing compiler for lexically scoped {LISP}",
journal = j-SIGPLAN,
volume = "17",
number = "6",
pages = "261--275",
month = jun,
year = "1982",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Apr 25 11:46:37 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages); C6150C (Compilers,
interpreters and other processors)",
conflocation = "Boston, MA, USA; 23--25 June 1982",
conftitle = "Proceedings of the SIGPLAN '82 Symposium on Compiler
Construction",
corpsource = "MIT, Cambridge, MA, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "BLISS-11; complex numbers; floating-point; FORTRAN;
lexically scoped LISP; LISP; list manipulation;
multiprocessing supercomputer; optimizing compiler;
PASCAL; PQCC compiler; program compilers; S-1 PASCAL;
stable-driven; symbolic processing; TNBIND technique;
vectors",
sponsororg = "ACM",
treatment = "P Practical",
}
@Article{Burr:1982:CCR,
author = "S. A. Burr",
title = "Computing cube roots when a fast square root is
available",
journal = j-COMPUT-MATH-APPL,
volume = "8",
number = "3",
pages = "181--183",
month = "????",
year = "1982",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(82)90041-4",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122182900414",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@Article{Cassola:1982:FPA,
author = "R. L. Cassola",
title = "Floating Point Algorithm Design",
journal = j-COMP-DESIGN,
volume = "21",
number = "6",
pages = "107--114",
month = jun,
year = "1982",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@Article{Cassola:1982:FPM,
author = "R. L. Cassola",
title = "A Floating Point Module for Military Computers",
journal = j-COMP-DESIGN,
volume = "21",
number = "2",
pages = "67--76",
month = feb,
year = "1982",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@MastersThesis{Cavanagh:1982:DCA,
author = "Joseph J. F. Cavanagh",
title = "Digital computer arithmetic: design and
implementation",
type = "Thesis ({M.S.})",
school = "University of Santa Clara",
address = "Santa Clara, CA, USA",
pages = "vii + 503",
year = "1982",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Floating-point
arithmetic.",
}
@InProceedings{Cody:1982:BCC,
author = "W. J. Cody",
title = "Basic concepts for computational software",
crossref = "Messina:1982:PMM",
pages = "1--23",
year = "1982",
DOI = "https://doi.org/10.1007/3-540-11603-6_1",
bibdate = "Fri Sep 23 23:12:32 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cody:1982:FPM,
author = "W. J. Cody",
title = "Floating-point parameters, models, and standards",
crossref = "Reid:1982:RBN",
pages = "51--69",
year = "1982",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; D.3.0",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic; D.3.0
General; D.3.0 Standards",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic; Software, PROGRAMMING LANGUAGES,
General, Standards",
genterm = "THEORY; STANDARDIZATION",
guideno = "10367",
keywords = "languages; standardization",
review = "ACM CR 8402-0092",
reviewer = "Hansen, E",
subject = "D.3.0 Software, PROGRAMMING LANGUAGES, General,
Standards \\ G.1.0 Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic; G. Mathematics
of Computing; G.1 NUMERICAL ANALYSIS; D. Software; D.3
PROGRAMMING LANGUAGES",
}
@TechReport{Cody:1982:GPI,
author = "W. J. Cody",
title = "A Generalization of the Proposed {IEEE} Standard for
Floating-Point Arithmetic",
type = "Technical Report",
number = "??",
institution = inst-ANL,
address = inst-ANL:adr,
pages = "20",
year = "1982",
bibdate = "Thu Nov 17 10:40:11 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Republished in \cite{Cody:1983:GPI}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cody:1982:ITF,
author = "W. J. Cody",
title = "Implementation and Testing of Function Software",
crossref = "Messina:1982:PMM",
pages = "24--47",
year = "1982",
DOI = "https://doi.org/10.1007/3-540-11603-6_1",
bibdate = "Sat Sep 24 01:18:12 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "range reduction",
}
@Article{Corbett:1982:EAF,
author = "R. P. Corbett",
title = "Enhanced arithmetic for {Fortran}",
journal = j-SIGPLAN,
volume = "17",
number = "12",
pages = "41--48",
month = dec,
year = "1982",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Apr 25 11:46:37 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages)",
corpsource = "Department of Computer Sci., University of California,
Berkeley, CA, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "accuracy; arithmetic; digital arithmetic; efficiency;
FORTRAN; Fortran; programmers; speed; widest need
evaluation",
treatment = "P Practical",
}
@InProceedings{Dao:1982:KCA,
author = "T. T. Dao",
editor = "{IEEE}",
booktitle = "Proceedings of the 12th International Symposium on
Multiple-Valued Logic, May 1982",
title = "{Knuth}'s Complex Arithmetic with Quaternary
Hardware",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "94--98",
month = may,
year = "1982",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Aug 22 09:14:13 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dekker:1982:PCM,
author = "T. J. Dekker",
editor = "Paul C. Messina and Almerico Murli",
booktitle = "Problems and Methodologies in Mathematical Software
Production",
title = "Program Correctness and Machine Arithmetic",
volume = "142",
publisher = pub-SV,
address = pub-SV:adr,
pages = "48--80",
year = "1982",
bibdate = "Sat May 1 15:24:45 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Book{DeSautels:1982:ALP,
author = "Edouard J. DeSautels",
title = "Assembly language programming for {PDP-11} and
{LSI-11} computers: an introduction to computer
organization",
publisher = "William C. Brown Co. Publ.",
address = "Dubuque, IA",
pages = "574",
year = "1982",
ISBN = "0-697-08164-8",
ISBN-13 = "978-0-697-08164-3",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$21.95",
acknowledgement = ack-nhfb,
catcode = "A; C.1.1; D.3; D.3.2; D.3.2",
content = "The author has provided material on the Assembler
language for the PDP-11 or LSI-11 computers in an
original and comprehensive manner. Users of this
Assembler or even of this computer should find this
text especially valuable as a student text or as a
permanent reference. Much of the material in the
PDP-11, MACRO-11 Reference Manual, Processor Handbook,
Peripheral Handbook, and Terminals and Communications
Handbook is organized in this book in a readable,
step-by-step manner. Required is access to a PDP-11 (or
LSI-11) and some knowledge of programming in a
high-level language.\par
Topics include the following: \par
* Very accessible and detailed material on introduction
to computers and programming. It is unlikely that a
reader would require much if any prior knowledge of
computers.\par
* An early introduction to machine language to explain
the functioning of a computer, and then a lead-in into
Assembler language.\par
* Development of the use of registers, Assembler
Directives, indexing, immediate operands, arithmetic
for signed and unsigned data, subroutines, stacks,
passing parameters, input/output, floating-point
arithmetic, and more.\par
* An interesting chapter, ``Selected Topics,'' covering
such subjects as tables, lists, queues, trees, threaded
code, and reentrant co",
CRclass = "C.1.1 Single Data Stream Architectures; C.1.1 PDP-11;
D.3.2 Language Classifications; D.3.2 Language
Classifications; D.3.2 Macro and assembly languages;
D.3.2 Language Classifications; D.3.2 PDP-11 assembly
language",
CRnumber = "40452",
descriptor = "General Literature, INTRODUCTORY AND SURVEY; Computer
Systems Organization, PROCESSOR ARCHITECTURES, Single
Data Stream Architectures, PDP-11; Software,
PROGRAMMING LANGUAGES, Language Classifications;
Software, PROGRAMMING LANGUAGES, Language
Classifications, Macro and assembly languages;
Software, PROGRAMMING LANGUAGES, Language
Classifications, PDP-11 assembly language",
genterm = "LANGUAGES",
pubname = "William C. Brown Co. Publ., Dubuque, IA",
reviewer = "P. Abel; Abel, P",
subject = "A. General Literature; A.1 INTRODUCTORY AND SURVEY; C.
Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; D. Software; D.3 PROGRAMMING LANGUAGES;
D. Software; D.3 PROGRAMMING LANGUAGES; D. Software;
D.3 PROGRAMMING LANGUAGES",
}
@InCollection{Dreyer:1982:ACI,
author = "H.-J. Dreyer and A. Walther",
title = "The Automatic Calculator {IPM} (1946)",
crossref = "Randell:1982:ODC",
pages = "155--161",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Epstein:1982:UAF,
author = "C. Epstein and W. L. Miranker and T. J. Rivlin",
title = "Ultra-arithmetic {I}: function data types",
journal = j-MATH-COMP-SIM,
volume = "24",
number = "1",
pages = "1--18",
month = feb,
year = "1982",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1; G.1.2; G.1.2",
CRclass = "G.1.5 Roots of Nonlinear Equations; G.1.2
Approximation; G.1.2 Chebyshev approximation and
theory; G.1.2 Approximation; G.1.2 Elementary function
approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
Nonlinear Equations; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Chebyshev
approximation and theory; Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation, Elementary function
approximation",
fjournal = "Mathematics and Computers in Simulation",
genterm = "algorithms",
guideno = "09324",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Epstein:1982:UAI,
author = "C. Epstein and W. L. Miranker and T. J. Rivlin",
title = "Ultra-arithmetic {II}: intervals of polynomials",
journal = j-MATH-COMP-SIM,
volume = "24",
number = "1",
pages = "19--29",
month = feb,
year = "1982",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.2; G.1.1; G.1.0",
CRclass = "G.1.2 Approximation; G.1.2 Elementary function
approximation; G.1.1 Interpolation; G.1.1 Spline and
piecewise polynomial interpolation; G.1.0 General;
G.1.0 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation;
Mathematics of Computing, NUMERICAL ANALYSIS,
Interpolation, Spline and piecewise polynomial
interpolation; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Error analysis",
fjournal = "Mathematics and Computers in Simulation",
genterm = "algorithms",
guideno = "09325",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
jrldate = "Feb. 1982",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{Fateman:1982:HLL,
author = "Richard J. Fateman",
title = "High-Level Language Implications of the Proposed
{IEEE} Floating-Point Standard",
journal = j-TOPLAS,
volume = "4",
number = "2",
pages = "239--257",
month = apr,
year = "1982",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/357162.357168",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Thu Nov 8 14:50:28 2007",
bibsource = "Compiler/bevan.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An IEEE Computer Society working group on
floating-point arithmetic has recommended a standard
for binary floating-point number formats, operations,
and semantics. This paper, which has evolved in part
during the deliberations of that committee, describes
the significance to languages and, in particular, to
FORTRAN and its variants, of various novel features of
the recommended standard.",
acknowledgement = ack-pb,
checked = "19940302",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
keywords = "computer arithmetic; control structures; data types
and structures; error handling and recovery;
floating-point arithmetic; FORTRAN; run-time
environments",
source = "Dept. Library",
}
@TechReport{Feldstein:1982:EPI,
author = "A. Feldstein and R. Goodman",
title = "The evaluation of probability integrals for the loss
of significance in floating point subtraction and
addition",
type = "Technical report",
institution = "Department of Mathematics, Arizona State University",
address = "Tempe, AZ, USA",
year = "1982",
bibdate = "Tue Oct 09 09:50:41 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Feldstein:1982:LSF,
author = "A. Feldstein and R. Goodman",
title = "Loss of Significance in Floating Point Subtraction and
Addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "4",
pages = "328--335",
month = apr,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676002",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We study the loss of significant $ \beta $ its (base $
\beta $ digits) in floating point addition or
subtraction. To do this, we calculate the conditional
probability of a post-arithmetic normalization shift of
$m$ $ \beta $ its, given an exponent difference of $k$
$ \beta $ its. The study is done for various bases $
\beta $, under two different assumptions---that the
operands are selected at random from the logarithmic
distribution or from the uniform distribution.",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fulton:1982:BJB,
author = "T. A. Fulton and L. N. Dunkleberger",
title = "{B.S.T.J.} Briefs: a {Josephson} Parallel Multiplier",
journal = j-BELL-SYST-TECH-J,
volume = "61",
number = "5",
pages = "931--933",
month = may # "--" # jun,
year = "1982",
CODEN = "BSTJAN",
ISSN = "0005-8580",
bibdate = "Tue Nov 9 11:15:56 MST 2010",
bibsource = "http://bstj.bell-labs.com/oldfiles/year.1982/BSTJ.1982.6105.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bstj.bell-labs.com/BSTJ/images/Vol61/bstj61-5-931.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Bell System Technical Journal",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}
@Article{Gerrity:1982:CRR,
author = "G. W. Gerrity",
title = "Computer Representation of Real Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "8",
pages = "709--714",
month = aug,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676076",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676076",
abstract = "Hwang's model for the computer representation of real
numbers is extended to explicitly distinguish between
the representational system used to denote real numbers
and the internal encoding of the digits of the
representation in the computer memory. The encoding
function can then be chosen to preserve certain
properties of the real number system and to optimize
the computer arithmetic in a sense to be described
herein. Two examples of optimal computer arithmetics
are discussed.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Goodrich:1982:VEP,
author = "J. L. Goodrich",
title = "Very efficient 8080 program multiplies and divides",
journal = j-ELECTRONICS,
volume = "55",
number = "4",
pages = "144--145",
month = feb,
year = "1982",
ISSN = "0883-4989",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@InProceedings{Gordon:1982:BFS,
author = "E. Gordon and C. Hastings",
booktitle = "Conference Record, {SOUTHCON, 1982}",
title = "Big, Fast and Simple Algorithms, Architecture and
Components for High-end Minis",
publisher = "????",
address = "????",
pages = "????",
year = "1982",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Nov 09 18:54:03 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Paper 21/3.",
acknowledgement = ack-nhfb,
}
@Article{Hantler:1982:ESS,
author = "S. L. Hantler and A. H. Karp",
title = "Exponential by Sequential Squaring",
journal = j-IBM-TDB,
volume = "25",
number = "1",
pages = "171--173",
month = jun,
year = "1982",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InProceedings{Hull:1982:PCE,
author = "T. E. Hull",
title = "Precision Control, Exception Handling and a Choice of
Numerical Algorithms",
crossref = "Watson:1982:NAP",
pages = "169--178",
year = "1982",
DOI = "https://doi.org/10.1007/BFb0093156",
bibdate = "Sat Feb 8 10:29:52 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "Proposes precision control as later provided in
Numerical Turing.",
}
@InProceedings{Hull:1982:UCP,
author = "T. E. Hull",
title = "The uses of controlled precision",
crossref = "Reid:1982:RBN",
pages = "71--82",
year = "1982",
bibdate = "Fri Jan 04 12:57:37 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
xxpages = "71--84",
}
@Article{Hwang:1982:PMA,
author = "Kai Hwang and Yeng-Heng Cheng",
title = "Partitioned Matrix Algorithms for {VLSI} Arithmetic
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "12",
pages = "1215--1224",
month = dec,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675945",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675945",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Jenkins:1982:FRD,
author = "W. Jenkins",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '82}",
title = "Failure resistant digital filters based on residue
number system product codes",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "60--63",
year = "1982",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue number system product codes are proposed for
the design of self-checking digital filters. It is
shown that product codes require redundancy that is
similar to, but slightly less than that of systematic
codes for simultaneous overflow \ldots{}",
}
@Article{Jenkins:1982:RNS,
author = "W. K. Jenkins",
title = "Residue number system error checking using expanded
projection",
journal = j-ELECT-LETTERS,
volume = "18",
number = "21",
pages = "927--928",
day = "14",
month = oct,
year = "1982",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4246948",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A new concept called expanded projection is presented
that simplifies the process of error detection and
location in redundant residue number codes. Expanded
projection simplifies the circuit complexity of the
error checker, resulting in a structure \ldots{}",
}
@InProceedings{Kahan:1982:NOS,
author = "W. Kahan and Jerome T. Coonen",
title = "The Near Orthogonality of Syntax, Semantics, and
Diagnostics in Numerical Programming Environments",
crossref = "Reid:1982:RBN",
pages = "103--115",
year = "1982",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "D.3; G.1.0; F.3.2; D.2.5; D.2; D.3",
content = "Programmers of early computers had to content
themselves with what the machine designers offered and
be glad that the hardware worked at all. Later, with
the introduction of higher-level languages, the
computing environment was modified by the language
designers who attempted to resolve a three-cornered
tug-of-war among implementation efficiency, program
portability, and usefulness to the programmer. The
conflict between the first two resulted in languages
that reflected the least common denominator of
available hardware, since language designers were
disinclined to mention any capability not available on
all computers. A case in point is floating-point
arithmetic, where the subtleties of overflow,
underflow, and rounding are generally well beyond the
control of the programmer in a high-level language. The
new standard for binary floating-point arithmetic that
has been proposed by IEEE Computer Society's
Floating-Point Committee, Task P754 [1], makes an
attempt to escape from this situation. It represents
the Committee's view of the floating-point requirements
of the \ldots{}",
CRclass = "D.3.1 Formal Definitions and Theory; G.1.0 General;
G.1.0 Computer arithmetic; F.3.2 Semantics of
Programming Languages; F.3.2 Algebraic approaches to
semantics; D.2.5 Testing and Debugging; D.2.5
Diagnostics; D.2.6 Programming Environments; D.3.3
Language Constructs",
CRnumber = "8401-0021",
descriptor = "Software, PROGRAMMING LANGUAGES, Formal Definitions
and Theory; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic; Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics
of Programming Languages, Algebraic approaches to
semantics; Software, SOFTWARE ENGINEERING, Testing and
Debugging, Diagnostics; Software, SOFTWARE ENGINEERING,
Programming Environments; Software, PROGRAMMING
LANGUAGES, Language Constructs",
genterm = "LANGUAGES; STANDARDIZATION",
keywords = "floating-point arithmetic; rounding errors",
remark = "This article forms the body of \cite[Chapter
3]{Coonen:1984:CPS}.",
reviewer = "M. Marcotty; Marcotty, M",
source = "in the relationship between numerical computation and
programming languages. Proc. IFIP TC2 working
conference (Boulder, CO, Aug. 3--7, 1981) J. K. Reid
(Ed.) Elsevier North-Holland, Inc., New York, 1982",
subject = "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of
Computation; F.3 LOGICS AND MEANINGS OF PROGRAMS; D.
Software; D.2 SOFTWARE ENGINEERING; D. Software; D.2
SOFTWARE ENGINEERING; D. Software; D.3 PROGRAMMING
LANGUAGES",
}
@Book{Katzan:1982:IAA,
author = "Harry Katzan",
title = "Invitation to {Ada} and {Ada} reference manual ({July
1980})",
publisher = "PBI",
address = "New York, NY, USA",
pages = "xi + 429",
year = "1982",
ISBN = "0-89433-132-9",
ISBN-13 = "978-0-89433-132-9",
LCCN = "QA76.73.A35 K37 1982",
bibdate = "Wed Oct 13 06:37:40 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "See \cite[p. 1.10]{Coonen:1984:CPS} for negative
comments about the floating-point model for Ada in this
book.",
subject = "Ada (computer program language)",
}
@InProceedings{Kerkhoff:1982:LDM,
author = "H. G. Kerkhoff and H. A. J. Robroek",
editor = "{IEEE}",
booktitle = "Proceedings of the 12th International Symposium on
Multiple-Valued Logic, May 1982",
title = "The Logic Design of Multiple-valued Logic Functions
Using {CCD}'s",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "35--44",
year = "1982",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Aug 22 09:16:45 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Korn:1982:EDF,
author = "G. A. Korn",
title = "{EARLY DESIRE}: a floating-point equation language
simulation system for minicomputers and
microcomputers",
journal = j-SIMULATION,
volume = "38",
number = "5",
pages = "151--159",
month = may,
year = "1982",
CODEN = "SIMUA2",
ISSN = "0037-5497 (print), 1741-3133 (electronic)",
ISSN-L = "0037-5497",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "I.6; G; D.4.7",
CRclass = "I.6.2 Simulation Languages; D.4.7 Organization and
Design; D.4.7 Interactive systems",
descriptor = "Computing Methodologies, SIMULATION AND MODELING,
Simulation Languages; Mathematics of Computing,
MISCELLANEOUS; Software, OPERATING SYSTEMS,
Organization and Design, Interactive systems",
fjournal = "Simulation",
genterm = "DESIGN; LANGUAGES",
guideno = "08785",
journal-URL = "http://sim.sagepub.com/content/by/year",
subject = "I. Computing Methodologies; I.6 SIMULATION AND
MODELING; G. Mathematics of Computing; G.m
MISCELLANEOUS; D. Software; D.4 OPERATING SYSTEMS",
}
@Article{Leuprecht:1982:PAR,
author = "H. Leuprecht and W. Oberaigner",
title = "Parallel Algorithms for the Rounding-Exact Summation
of Floating-Point Numbers",
journal = j-COMPUTING,
volume = "28",
number = "2",
pages = "89--104",
month = "????",
year = "1982",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68A05 (65G05)",
MRnumber = "83c:68009",
bibdate = "Fri Dec 08 11:53:42 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "accurate floating-point summation",
}
@Article{McCormick:1982:EFM,
author = "S. F. McCormick and G. D. Taylor and D. V. Pryor",
title = "Evaluation of Functions on Microcomputers: $ \ln (x)
$",
journal = j-COMPUT-MATH-APPL,
volume = "8",
number = "5",
pages = "389--392",
year = "1982",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:41:01 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@Article{McPherson:1982:LSG,
author = "John C. McPherson and Frank E. Hamilton and Robert R.
{Seeber, Jr.}",
title = "A Large-Scale, general-Purpose Electronic Digital
calculator: The {SSEC}",
journal = j-ANN-HIST-COMPUT,
volume = "4",
number = "4",
pages = "313--326",
month = oct # "\slash " # dec,
year = "1982",
CODEN = "AHCOE5",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:19 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1982/pdf/a4313.pdf;
http://www.computer.org/annals/an1982/a4313abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Article{Monroe:1982:FFP,
author = "Alfred J. Monroe",
title = "{Forth} Floating Point Package",
journal = j-DDJ,
volume = "7",
number = "9",
pages = "16--??",
month = sep,
year = "1982",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Oklobdzija:1982:LSR,
author = "V. G. Oklobdzija and M. D. Ercegovac",
title = "An On-Line Square Root Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "1",
pages = "70--75",
month = jan,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675887",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Palmer:1982:VRN,
author = "J. F. Palmer",
title = "{VLSI} and the Revolution in Numeric Computation",
crossref = "Ruschitzka:1982:IWC",
pages = "339--341",
year = "1982",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{Phillips:1982:BC,
author = "E. William Phillips",
title = "Binary Calculation",
crossref = "Randell:1982:ODC",
pages = "303--314",
year = "1982",
bibdate = "Wed Oct 13 09:51:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "The 1936 epigraph credited to this author in
\cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
aim is to persuade all of the civilized world to
abandon the decimal numeration and to use octonal in
its place; to discontinue counting in tens and to count
in eights instead. However, it seems unlikely that the
whole civilized world will be persuaded to complete
this change during the next twelve months, having
previously declined similar invitations.''",
}
@InProceedings{Rall:1982:ACA,
author = "L. B. Rall",
editor = "Anonymous",
booktitle = "{Proceedings of the 1982 Army Numerical Analysis and
Computers Conference}",
title = "Accurate computer arithmetic for scientific
computation",
volume = "82--83",
publisher = "US Army Research Office",
address = "Research Triangle Park, NC, USA",
bookpages = "xiv + 606",
pages = "343--356",
month = aug,
year = "1982",
bibdate = "Wed Oct 13 21:52:01 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
URL = "http://books.google.com/books?id=pFb-QQAACAAJ",
abstract = "The operations of accurate arithmetic can be
implemented easily on a microcomputer or a computer
with microprogrammable arithmetic operations. In
addition, for accurate final results, a compiler is
necessary which will select the appropriate operations.
A language of this type (PASCAL-SC) was developed.
Along with accurate real arithmetic, this compiler
provides accurate complex arithmetic, real and complex
interval arithmetic, and vector and matrix arithmetic
over these data types. Some features of PASCAL-SC
related to scientific and engineering computation are
described. In most cases, the operations of accurate
arithmetic are performed at the same speed as ordinary
(uncontrolled) floating-point arithmetic.",
acknowledgement = ack-nhfb,
keywords = "analysis (mathematics); arithmetic; computation;
microcomputers; microprogramming; Pascal (programming
language)",
meetingname = "Army Numerical Analysis and Computers Conference (1982
: Vicksburg, Miss.)",
remark = "The theme of the 1982 Conference was Grid Techniques
for Partial Differential Equations.",
subject = "Numerical analysis; Computer programs; Congresses;
Numerical Mathematics. Computer Hardware. Computers.
Partial differential equations. Symposia. Numerical
analysis. Grids. Computations. Methodology.
Mathematical programming. Finite difference theory.
Finite element analysis. Boundaries. Hydrodynamics. Gas
dynamics. Interior ballistics. Autofrettage. Land
mines. Blast loads. Conduction(heat transfer) Magnet
coils. Water waves. Currents",
xxtitle = "Accurate arithmetic for scientific computation",
xxvolume = "82-3",
}
@InProceedings{Ramnarayan:1982:AER,
author = "R. Ramnarayan and F. Taylor",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '82}",
title = "Analysis of errors in residue number system ({RNS})
based {IIR} digital filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "56--59",
year = "1982",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The problem of analyzing errors in Residue Number
System (RNS) based IIR Digital filters is considered in
this paper. There are basically three types of errors
in RNS based digital filters, They are coefficient
quantization errors(1), scaling errors \ldots{}",
}
@Article{Rix:1982:UQA,
author = "P. Rix",
title = "{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus}
\toenglish {Universal Square Root Algorithms}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "23",
pages = "81--82",
year = "1982",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{Rump:1982:CR,
author = "Siegfried M. Rump",
title = "{Computer und Rechengenauigkeit} \toenglish {Computer
and Computational Precision} \endtoenglish",
journal = j-ELEK-RECHENANLAGEN,
volume = "24",
number = "6",
pages = "268--277",
month = dec,
year = "1982",
CODEN = "ELRAA4",
ISSN = "0013-5720",
bibdate = "Sat Feb 10 12:41:06 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronische Rechenanlagen",
}
@Article{Sacks-Davis:1982:ARN,
author = "R. Sacks-Davis",
title = "Applications of Redundant Number Representations to
Decimal Arithmetic",
journal = j-COMP-J,
volume = "25",
number = "4",
pages = "471--477",
month = nov,
year = "1982",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/471.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/472.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/473.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/474.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/475.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/476.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/477.tif",
abstract = "A decimal arithmetic unit is proposed for both integer
and floating-point computations. To achieve comparable
speed to a binary arithmetic unit, the decimal unit is
based on a redundant number representation. With this
representation no loss of compactness is made relative
to binary coded decimal (BCD) form. In this paper the
hardware required for the implementation of the basic
operations of addition, subtraction, multiplication and
division are described and the properties of
floating-point arithmetic based on a redundant number
representation are investigated.",
acknowledgement = ack-nhfb,
classcodes = "C5260 (Digital signal processing)",
classification = "721; 723",
corpsource = "Department of Computer Sci., Monash University,
Clayton, Vic., Australia",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "addition; binary; binary arithmetic unit; coded
decimal; computers, digital; decimal floating-point
arithmetic; digital arithmetic; division; floating
point arithmetic; floating-point; integer;
multiplication; redundant number representations;
subtraction",
remark = "The redundant number representation postpones the need
to carry during add, subtract, multiply, and divide,
delaying it until the final rounding step in a store
instruction. See
\cite{Fahmy:2003:CRF,Fahmy:2003:RDF}.",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Samsen:1982:AFP,
author = "G. R. Samsen",
title = "An Advanced Floating Point Processor to Enhance Speed
of Mathematical Processing",
crossref = "Southcon:1982:SCR",
pages = "16/1/1--3",
year = "1982",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sasaki:1982:EGE,
author = "T. Sasaki and H. Murao",
key = "Symbolic_determinant; Symbolic_linear_systems;
Gaussian_elimination",
title = "Efficient {Gaussian} elimination method for symbolic
determinants and linear systems",
journal = j-TOMS,
volume = "8",
number = "3",
pages = "277--289",
month = sep,
year = "1982",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356004.356007",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "F.2; G.1.3; I.1.2",
content = "The computation of the solution of a linear system
whose entries are indeterminates or polynomials is of
interest both for theoretic and practical reasons. The
similar problem of computing the determinant is
important because of the relationship of the
determinant and resultant to factorization, polynomial
greatest-common-divisor calculations, and computation
with algebraic functions. Engineering application areas
of this material include the analysis of electrical or
other networks.\par
These computation problems are quite distinct from
others which would appear to be superficially similar,
namely numerical linear algebra problems. The result of
computing a numerical determinant is a floating point
number with an associated error. The result of
computing an exact algebraic determinant is, typically,
a large expression whose terms may be rearranged into
various ``factored'' forms for savings in computation
time and space. This answer has no error
whatsoever.\par
Clever and efficient programs in each domain have been
shown to be disastrous in the other. Thus one of the
best algebraic techniques for determinant calculations
for ``sparse polynomial'' matrices is expansion by
minors [1]; whereas Gaussian elimination is far
superior \ldots{}",
CRclass = "F.2.1 Numerical Algorithms and Problems; G.1.3
Numerical Linear Algebra; G.1.3 Linear systems (direct
and iterative methods); I.1.2 Algorithms; I.1.2
Algebraic algorithms",
CRnumber = "40106",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Linear systems (direct and iterative
methods); Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms, Algebraic algorithms",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
genterm = "ALGORITHMS; PERFORMANCE",
journal-URL = "https://dl.acm.org/loi/toms",
reviewer = "R. J. Fateman; Fateman, R. J",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
ALGEBRAIC MANIPULATION",
}
@Article{Sasaki:1982:PFM,
author = "T. Sasaki and Y. Kanada",
title = "Practically Fast Multiple Precision Evaluation of
{LOG} ($ {X} $)",
journal = j-INFO-PROC,
volume = "5",
number = "4",
pages = "247--250",
month = "????",
year = "1982",
bibdate = "Thu Sep 8 08:20:54 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Schatte:1982:FPF,
author = "P. Schatte",
title = "The Frequency of Postshifts in Floating-Point
Multiplication",
journal = "Elektronische Informationsverarbeitung und
Kybernetik",
volume = "18",
number = "9",
pages = "523--526",
month = "????",
year = "1982",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sewell:1982:RLT,
author = "B. T. Sewell",
title = "A Rapid Lookup Table Method for Trigonometric
Functions",
journal = j-SPE,
volume = "12",
number = "10",
pages = "885--887",
month = oct,
year = "1982",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "algorithms",
subject = "G Mathematics of Computing, MISCELLANEOUS \\ J.2
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Chemistry",
}
@InCollection{Sheldon:1982:ICP,
author = "John W. Sheldon and Liston Tatum",
title = "The {IBM} Card-Programmed Electronic Calculator
(1951)",
crossref = "Randell:1982:ODC",
pages = "233--239",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Sippel:1982:FRI,
author = "Timothy N. Sippel",
title = "Floating {RISCS}: implementation and analysis of
floating point on {RISC} {I}",
type = "Electrical Engineering and Computer Sciences Master of
Science Report",
school = "University of California, Department of Electrical
Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "various",
year = "1982",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sips:1982:CPM,
author = "H. J. Sips",
title = "Comments on {``An $ O(n) $ Parallel Multiplier with
Bit-Sequential Input and Output''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "4",
pages = "325--327",
month = apr,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676000",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676000",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Strader:1982:CBS,
author = "N. R. Strader and V. T. Rhyne",
title = "A Canonical Bit-Sequential Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "8",
pages = "791--795",
month = aug,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676085",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676085",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Tan:1982:ADC,
author = "Chung-I Tan and B. McInnis",
title = "Adaptive digital control implemented using residue
number systems",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "27",
number = "2",
pages = "499--502",
month = apr,
year = "1982",
CODEN = "IETAA9",
DOI = "https://doi.org/10.1109/CDC.1981.269326",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Pei:1984:CAD}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24189",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
keywords = "residue arithmetic; residue number system",
summary = "The application of residue number systems for the
implementation of adaptive digital controllers is
presented. Division operations are avoided through the
use of iteration to solve for the value of the control.
Decoding computations are simplified \ldots{}",
}
@Article{Taylor:1982:ARM,
author = "F. J. Taylor and C. H. Huang",
title = "An Autoscale Residue Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "4",
pages = "321--325",
month = apr,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1675999",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 09 19:30:01 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Taylor:1982:VRA,
author = "F. J. Taylor",
title = "A {VLSI} Residue Arithmetic Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-31",
number = "6",
pages = "540--546",
month = jun,
year = "1982",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1982.1676036",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:33:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676036",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Teachey:1982:SRX,
author = "R. D. Teachey",
title = "Square-Root-{X} Comparison --- New Results
Discovered",
journal = j-IEEE-MICRO,
volume = "2",
number = "4",
pages = "5--5",
month = oct # "\slash " # dec,
year = "1982",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1982.290929",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@InCollection{TorresyQuevedo:1982:EAD,
author = "Leonardo {Torres y Quevedo}",
title = "Essays on Automatics --- Its Definitions ---
Theoretical Extent of its Applications (1914)",
crossref = "Randell:1982:ODC",
pages = "89--107",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "This translation and reprint contains a description of
what is believed to be the first design, albeit purely
theoretical, and for an electromechanical device, of
floating-point arithmetic. See, however, the
independent work, and first practical implementation of
floating-point arithmetic of Zuse
\cite{Zuse:1982:MAE,Zuse:1982:OCD}.",
}
@Article{Turner:1982:DLS,
author = "Peter R. Turner",
title = "The distribution of leading significant digits",
journal = j-IMA-J-NUMER-ANAL,
volume = "2",
number = "4",
pages = "407--412",
year = "1982",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G99 (60E05)",
MRnumber = "84f:65038",
MRreviewer = "Seppo Linnainmaa",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Velasevic:1982:RLC,
author = "Dusan M. Velasevi{\'c}",
title = "Right-to-Left Code Generation for Arithmetic
Expressions",
journal = j-COMP-J,
volume = "25",
number = "3",
pages = "316--326",
month = aug,
year = "1982",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/25.3.316",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:13 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/25/3.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/25/3/316.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/316.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/317.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/318.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/319.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/320.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/321.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/322.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/323.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/324.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/325.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/326.tif",
acknowledgement = ack-nhfb,
classcodes = "C6110 (Systems analysis and programming); C6120 (File
organisation)",
classification = "723",
corpsource = "Faculty of Electrical Engng., University of Belgrade,
Belgrade, Yugoslavia",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic; automatic programming; binary tree
structure; code generator; codes, symbolic; data
structures; expressions; FORTRAN; notation; postfix;
right-to-left code generation; translation grammar;
vector-generatrice",
treatment = "P Practical",
}
@Article{Ware:1982:BMF,
author = "F. A. Ware and W. H. McAllister and J. R. Carlson and
D. K. Sun and R. J. Vlach",
title = "64 Bit Monolithic Floating Point Processors",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-17",
number = "5",
pages = "898--907",
month = oct,
year = "1982",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "Describes a set of three processor chips capable of
performing 32 and 64 bit floating point add/subtract,
multiply, and divide operations. The chips can perform
over one million scalar floating point operations per
second, and over four million vector \ldots{}",
}
@Book{Waser:1982:IAD,
author = "Shlomo Waser and Michael J. Flynn",
title = "Introduction to Arithmetic for Digital Systems
Designers",
publisher = pub-HRW,
address = pub-HRW:adr,
pages = "xvii + 308",
year = "1982",
ISBN = "0-03-060571-7",
ISBN-13 = "978-0-03-060571-0",
LCCN = "TK7895 A65 W37 1982",
bibdate = "Sat Sep 03 09:25:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Master copy output on Alphatype CRS high-resolution
phototypesetter. This book went to press while the IEEE
754 Floating-Point Standard was still in development;
consequently, some of the material on that system was
invalidated by the final Standard (1985)
\cite{IEEE:1985:AIS}.",
acknowledgement = ack-nj # " and " # ack-nhfb,
tableofcontents = "Preface\\
Acknowledgments\\
Abbreviations and Symbols\\
1. Numeric Data Representation\\
2. Residue Numbers and the Limits of Fast Arithmetic\\
3. Addition and Subtraction\\
4. Multiplication\\
5. Division\\
6. Pipelining of Arithmetic Operations\\
Appendix.\\
References.\\
Index.",
}
@Book{Wilkes:1982:PPE,
author = "M. V. (Maurice Vincent) Wilkes and David J. Wheeler
and Stanley Gill",
title = "The Preparation of Programs for an Electronic Digital
Computer: with Special Reference to the {EDSAC} and the
Use of a Library of Subroutines",
volume = "1",
publisher = pub-TOMASH,
address = pub-TOMASH:adr,
pages = "xxxi + 167",
year = "1982",
ISBN = "0-262-23118-2 (MIT Press 1984), 0-938228-03-X",
ISBN-13 = "978-0-262-23118-3 (MIT Press 1984),
978-0-938228-03-5",
LCCN = "QA76.6 .W545 1982",
bibdate = "Mon Feb 10 11:33:59 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With a new introduction by Martin Campbell-Kelly.",
series = "Charles Babbage Institute reprint series for the
history of computing",
acknowledgement = ack-nhfb,
}
@InCollection{Wilson:1982:PC,
author = "Kenneth G. Wilson",
title = "Experiences with a floating point systems array
processor",
crossref = "Rodrigue:1982:AC",
pages = "279--314",
year = "1982",
MRclass = "65W05",
MRnumber = "759 559",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Wu:1982:DFA,
author = "Market Wen-Han Wu",
title = "Design of a fast addressable hardware floating-point
arithmetic package for small computer",
type = "Thesis ({M.S.})",
school = "Tufts University. Department of Engineering",
address = "Boston, MA, USA",
pages = "iii + 102",
year = "1982",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microcomputers ---
Programming.",
}
@InCollection{Zuse:1982:MAE,
author = "Konrad Zuse",
title = "Method for Automatic Execution of Calculations with
the aid of Computers (1936)",
crossref = "Randell:1982:ODC",
pages = "163--170",
year = "1982",
bibdate = "Sun Nov 03 08:36:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "This translation and reprint of a German patent
application of 11 April 1936 briefly describes the
floating-point system that was first successfully
implemented in a digital computer, the Zuse Z3, in
1941.",
}
@InProceedings{Agrawal:1983:DPV,
author = "Dharma P. Agrawal and Girish C. Pathak and Nikunja K.
Swain and Shuwan K. Agrawal",
title = "On Design and Performance of {VLSI} Based Parallel
Multiplier",
crossref = "IEEE:1983:PSC",
pages = "17--21",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Agrawal_Pathak_Swain_Agrawal.pdf",
abstract = "This paper introduces the VLSI design and layout of a
$ (\log^2 n) $ time $n$-bit binary parallel multiplier
for two unsigned operands. Proposed design consists of
partitioning the multiplier and multiplicand bits into
four groups of $ n / 4 $ bits each and then reducing
the matrix of sixteen product terms using three to two
parallel counters and Brent-Kung $ (\log n) $ time
parallel adder. Area-time performance of the present
scheme has been compared with the existing schemes for
parallel multipliers. Regular and recursive design of
the multiplier is shown to be suitable for VLSI
implementation and an improved table look up multiplier
has been used to form the basis of the recursive design
scheme.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Agrawal:1983:ICA,
author = "D. P. Agrawal and T. R. N. Rao",
title = "Introduction: Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "329--330",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676232",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Akamine:1983:SMQ,
author = "Masami Akamine and Tatsuo Higuchi",
title = "Synthesis of minimum quantization error digital
filters using floating-point arithmetic",
journal = j-ELECTRON-COMMUN-JPN,
volume = "66",
number = "10",
pages = "29--38",
year = "1983",
CODEN = "ECOJAL",
ISSN = "0424-8368",
MRclass = "94A12",
MRnumber = "85k:94010",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan",
}
@InProceedings{Annaratone:1983:MME,
author = "M. Annaratone and R. Stefanelli",
title = "A Multiplier with Multiple Error Correction
Capability",
crossref = "IEEE:1983:PSC",
pages = "44--51",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Annaratone_Stefanelli.pdf",
abstract = "This paper presents a technique for increasing the
reliability of arithmetic units. An error model is then
presented: this model well represents the faulty
behavior of many arithmetic units. The Residue Number
System and its related properties are used in order to
obtain a simple architecture (called Reliability
Network, R-Net). The main characteristics of the
presented technique are a significant reduction in the
number of gates and a limited increase of global
execution times. The extensive use of combinational
logic makes it possible to implement the R-Net almost
completely by means of Programmable Logic Arrays
(PLA's). Finally, both the intrinsic regularity of the
R-Net and its simple internal interconnection scheme
make this approach suitable for a practical VLSI
implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Armer:1983:DCR,
author = "Paul Armer",
title = "11. The {Defense Calculator} at the {Rand
Corporation}",
journal = j-ANN-HIST-COMPUT,
volume = "5",
number = "2",
pages = "202--202",
month = apr # "\slash " # jun,
year = "1983",
CODEN = "AHCOE5",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:20 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1983/pdf/a2202a.pdf;
http://www.computer.org/annals/an1983/a2202aabs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Article{Asai:1983:CPI,
author = "H. Asai",
title = "A Consideration of a Practical Implementation For a
New Convergence Division",
journal = j-INFO-PROC-LETT,
volume = "17",
number = "5",
pages = "273--281",
month = dec,
year = "1983",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Asai:1983:SOM,
author = "Hitohisa Asai and C. K. Cheng",
title = "Speeding Up an Overrelaxation Method of Division in
Radix-$ 2^n $ Machine",
journal = j-CACM,
volume = "26",
number = "3",
pages = "216--220",
year = "1983",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:22:06 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#AsaiC83;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "arithmetic",
oldlabel = "AsaiC83",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/AsaiC83",
}
@MastersThesis{Aspinwall:1983:IIF,
author = "David Brian Masters Aspinwall",
title = "An implementation of the {IEEE} floating point
standard on a {VAX-11\slash 780}",
type = "Thesis ({M.S.})",
school = "San Francisco State University",
address = "San Francisco, CA, USA",
pages = "ix + 138",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Microprogramming.; VAX-11 (Computer) --- Programming.",
}
@Article{Aspinwall:1983:MVM,
author = "David B. Aspinwall and Yale N. Patt",
title = "Modifications to the {VAX-11\slash 780}
microarchitecture to support {IEEE} floating point
arithmetic",
journal = j-SIGMICRO,
volume = "14",
number = "4",
pages = "61--69",
month = dec,
year = "1983",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/1096419.1096429",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:31 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/1096419.1096429",
abstract = "The VAX-11/780 was designed specifically to implement
the VAX architecture. As such, it does not support the
IEEE standard for floating point arithmetic. A project
was undertaken to provide this support by modifying the
11/780 microarchitecture. Our objective was to produce
a microengine that would efficiently execute a modified
VAX instruction set, in particular, one that executes
VAX floating point instructions consistent with the
IEEE standard. We made minimal changes to the 11/780
hardware, relying primarily on changes to the
microcode. This paper describes the work of this
project.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@InProceedings{Avizienis:1983:AAE,
author = "Algirdas Avizienis and C. S. Raghavendra",
title = "Applications for Arithmetic Error Codes in Large,
High-Performance Computers",
crossref = "IEEE:1983:PSC",
pages = "169--173",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Avizienis_Raghavendra.pdf",
abstract = "Large, high-performance computers are too costly to
allow full replication for fault detection and error
correction in the communication and processing of
numerical information. For this reason more
cost-effective arithmetic error code applications offer
an attractive alternative.\par
Part I of this paper presents a generalization of
low-cost inverse residue codes into two-dimensional
encodings. Error detecting and error correcting
properties of two-dimensional inverse residue codes are
discussed.\par
Part II discusses a multi-phase application of inverse
residue codes in which the form of encoding is altered
and additional time is allocated after faults occur.
The goal is to defer repair and to continue operation
at a slower speed until scheduled maintenance can take
place.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Bandeira:1983:TCA,
author = "N. Bandeira and K. Vaccaro and J. A. Howard",
title = "A Two's Complement Array Multiplier Using True Values
of the Operands",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "8",
pages = "745--747",
month = aug,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676312",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676312",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Banerji:1983:RPF,
author = "D. K. Banerji and S. Kaushik",
title = "Representation and Processing of Fractions in a
Residue System",
crossref = "IEEE:1983:PSC",
pages = "29--36",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Banerji_Kaushik.pdf",
abstract = "This paper proposes a scheme for the representation
and processing of fractions in a residue system. The
scheme is based on a mixed radix representation of a
fraction in a residue system. The algorithms for basic
arithmetic operations of addition, subtraction, and
multiplication involving fractions are developed and
are shown to provide some improvement over an existing
method. Application of these algorithms to division of
two integers in the residue system has been shown.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; residue number systems",
}
@Article{Baxter:1983:CRS,
author = "I. Baxter",
title = "Code replication speeds multiplication",
journal = j-EDN,
volume = "28",
number = "4",
pages = "261--262",
month = feb,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Bayoumi:1983:MVI,
author = "M. A. Bayoumi and G. A. Jullien and W. C. Miller",
title = "Models for {VLSI} Implementation of Residue Number
System Arithmetic Modules",
crossref = "IEEE:1983:PSC",
pages = "174--183",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Bayoumi_Jullien_Miller.pdf",
abstract = "This paper discusses the implementation of RNS
arithmetic modules using VLSI technology. The modules
are based on the interconnection of readonly memory
look-up tables. The paper first outlines a memory model
for a single look-up table which allows the selection
of the most efficient layout for memories which do not
have power of $2$ dimensions. The paper then discusses
various examples of interconnected memory modules with
associated optimizing layout algorithms. Finally, an
example is given of the application of one of the
modules to a large prime modulus multiplier.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; residue number systems",
}
@InProceedings{Bhat:1983:HPF,
author = "J. Bhat",
title = "High Performance Floating Point Co-Processor for
Protected Multi-User Systems",
crossref = "Mini-Micro:1983:MMN",
pages = "7/2/1--5",
year = "1983",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Blakley:1983:MAI,
author = "G. R. Blakley and I. Borosh",
title = "Modular arithmetic of iterated powers",
journal = j-COMPUT-MATH-APPL,
volume = "9",
number = "4",
pages = "567--581",
month = "????",
year = "1983",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:24 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122183901141",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221/",
}
@InProceedings{Boney:1983:FPPa,
author = "J. Boney and V. Shahan",
title = "Floating-point Power for the {M68000} Family",
crossref = "Mini-Micro:1983:MMN",
pages = "7/3/1--9",
year = "1983",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Boney:1983:FPPb,
author = "J. Boney and V. Shahan",
title = "Floating-point Power for the {M68000} Family",
crossref = "Mini-Micro:1983:MMW",
pages = "16/5/1--10",
year = "1983",
bibdate = "Mon Sep 12 22:01:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Brown:1983:NEA,
author = "W. S. Brown and C. S. Wetherell",
title = "A Numeric Error Algebra",
crossref = "IEEE:1983:PSC",
pages = "86--93",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Brown_Wetherell.pdf",
abstract = "Wetherell recently described an algebra of error
values that could be added to the ordinary arithmetic
of a programming language. Along with ordinary
arithmetic values, error values were included in the
set of computational quantities. The error values could
participate in all arithmetic operations and return
meaningful results. Unfortunately, the definitions of
the error values were not precise enough. Using Brown's
model of computer arithmetic, we supply precise
definitions for the error values, define the
fundamental arithmetic operations on the new values,
comment on their properties, and discuss briefly how
they might be used and implemented. We also compare our
model to the error handling features of the proposed
IEEE floating point standard",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Bushard:1983:MTS,
author = "L. B. Bushard",
title = "A Minimum Table Size Result for Higher Radix
Nonrestoring Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "6",
pages = "521--526",
month = jun,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676273",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676273",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Caraiscos:1983:REA,
author = "C. Caraiscos and Bede Liu",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '83}",
title = "A round-off error analysis of the {LMS} adaptive
algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "29--32",
year = "1983",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The steady state output error of the Least Mean Square
(LMS) Adaptive Algorithm due to the finite precision
arithmetic of a digital processor is analyzed. It is
found to consist of three terms: (1) the error due to
the input data quantization, (2) \ldots{}",
}
@Article{Chamrad:1983:FFP,
author = "V. Chamrad",
title = "A Fast Floating-Point Square-Rooting Routine for the
8080\slash 8085 Microprocessors",
journal = j-KYBERNETIKA,
volume = "19",
number = "4",
pages = "335--344",
month = "????",
year = "1983",
CODEN = "KYBNAI",
ISSN = "0023-5954",
bibdate = "Wed Sep 14 20:24:32 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Kybernetika",
}
@Article{Chan:1983:ACS,
author = "Tony F. Chan and Gene H. Golub and Randall J.
LeVeque",
title = "Algorithms for computing the sample variance: Analysis
and recommendations",
journal = j-AMER-STAT,
volume = "37",
number = "3",
pages = "242--247",
month = aug,
year = "1983",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.2307/2683386",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRclass = "62-04",
MRnumber = "84k:62003",
bibdate = "Mon May 5 09:19:29 MDT 1997",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1983.bib;
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2683386",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
country = "USA",
date = "13/05/93",
descriptors = "Simulation; statistics; numeric calculation",
enum = "7109",
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
}
@Article{Chang:1983:HSN,
author = "Tung-Liang Chang and P. Fisher",
title = "High-speed normalization and rounding circuits for
pipelined floating-point processors",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "31",
number = "6",
pages = "1403--1408",
month = dec,
year = "1983",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A fast leading/trailing-zero detection circuit
(LZDC/TZDC) is described, and then applied to the
design of a pipelined floating-point (FLP) processor.
This circuit has a total delay of 5{\Delta} and a
hardware complexity of(m + 1)(3 log_{2}(p) + 4
\ldots{}).",
}
@Article{Chow:1983:PDA,
author = "P. Chow and Z. Vranesic and Jui Lin Yen",
title = "A Pipelined Distributed Arithmetic {PFFT} Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "12",
pages = "1128--1136",
month = dec,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676173",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:13 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See correction \cite{Anonymous:1984:CPD}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676173",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ciminiera:1983:FIM,
author = "L. Ciminiera and A. Serra",
title = "Fast Iterative Multiplying Array",
crossref = "IEEE:1983:PSC",
pages = "60--66",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ciminiera_Serra.pdf",
abstract = "A high speed multiplying array is presented. It is
based on a new cell, which is able to generate and add
a rectangular block of elementary products. A careful
design of the cell allows us to obtain a small delay
for the signals which should be propagated through the
whole array. This feature leads to a remarkable
improvement in the array speed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Cloutier:1983:PAR,
author = "Mark J. Cloutier and Matthew J. Friedman",
title = "Precision Averaging for Real-Time Analysis",
journal = j-CACM,
volume = "26",
number = "7",
pages = "525--529",
year = "1983",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Jan 22 06:31:47 MST 2001",
bibsource = "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#CloutierF83;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
oldlabel = "CloutierF83",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/CloutierF83",
}
@InProceedings{Cody:1983:GPI,
author = "W. J. Cody",
title = "A generalization of the proposed {IEEE} standard for
floating-point arithmetic",
crossref = "Gentle:1983:CSS",
pages = "133--139",
year = "1983",
bibdate = "Thu Nov 17 10:41:05 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Republication of \cite{Cody:1982:GPI}.",
acknowledgement = ack-nhfb,
keywords = "standardization",
subject = "G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic \\ K.7 Computing Milieux,
THE COMPUTING PROFESSION, Miscellaneous \\ K.1
Computing Milieux, THE COMPUTER INDUSTRY, Standards",
}
@Article{Cohen:1983:CCP,
author = "Marty S. Cohen and T. E. Hull and V. Carl Hamacher",
title = "{CADAC}: a Controlled-Precision Decimal Arithmetic
Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "370--377",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676238",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676238",
abstract = "This paper describes the design of an arithmetic unit
called CADAC (clean arithmetic with decimal base and
controlled precision). Programming language
specifications for carrying out `ideal' floating-point
arithmetic are described first. These specifications
include detailed requirements for dynamic precision
control and exception handling, along with both complex
and interval arithmetic at the level of a programming
language such as Fortran or PL/I.\par
CADAC is an arithmetic unit which performs the four
floating-point operations add\slash subtract\slash
multiply\slash divide on decimal numbers in such a way
as to support all the language requirements
efficiently. A three-level pipeline is used to overlap
two-digit-at-a-time serial processing of the partial
products\slash remainders. Although the logic design is
relatively complex, the performance is efficient, and
the advantages gained by implementing
programmer-controlled precision directly in the
hardware are significant.",
acknowledgement = ack-nhfb # "\slash " # ack-jr,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
remark = "From MFC: Normalized decimal floating-point. Need for
variable precision (intermediate > final, increasing
precision, etc.). Base representation is BCD (2-32
digits). Hardware prototype built",
}
@Article{Collis:1983:MSZ,
author = "B. Collis",
title = "Macros speed 8080, {Z80} multiplication",
journal = j-EDN,
volume = "28",
number = "24",
pages = "225",
month = nov,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Corbett:1983:EAF,
author = "Robert Paul Corbett",
title = "Enhanced arithmetic for {Fortran}",
journal = j-SIGNUM,
volume = "18",
number = "1",
pages = "24--28",
month = jan,
year = "1983",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:11 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Coupe:1983:SPZ,
author = "B. Coupe",
title = "Superefficient programs for 8080 and {Z80} multiply",
journal = j-ELECTRONICS,
volume = "56",
number = "6",
pages = "142--143",
month = mar,
year = "1983",
ISSN = "0883-4989",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@InProceedings{Dadda:1983:SSF,
author = "Luigi Dadda",
title = "Some Schemes for Fast Serial Input Multipliers",
crossref = "IEEE:1983:PSC",
pages = "52--59",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Dadda.pdf",
abstract = "The design of fast multipliers for binary numbers
represented in serial form is considered according to a
general scheme composed by an array generator and a
summator. The bits of the product are generated with
the least delay with respect to the operators bits. The
array generator computes the elements of the multiplier
array. The summator computes the sum of the array
elements in order to generate the product bits. The
array elements can be generated according to two
different general schemes: the first computes all the
new array elements at each step (arranged on a diagonal
and on a row of the multiplier array), the second
computes the multiplier array elements column by
column. Several schemes of array generators are given
and compared, and for each of them a suitable summator
using parallel counters is illustrated.",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-6",
}
@InProceedings{Dao:1983:QCA,
author = "T. T. Dao",
editor = "{IEEE}",
booktitle = "Proceedings of the 13th International Symposium on
Multiple-valued Logic, May 1983",
title = "A Quaternary Cellular Array Complex Number
Multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "255--262",
year = "1983",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Aug 22 09:15:45 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Davis:1983:HSD,
author = "George R. Davis and Thomas M. King",
title = "A High-Speed Digital Divider",
journal = j-IEEE-TRANS-INSTRUM-MEAS,
volume = "IM-32",
number = "2",
pages = "309--312",
month = jun,
year = "1983",
CODEN = "IEIMAO",
DOI = "https://doi.org/10.1109/TIM.1983.4315069",
ISSN = "0018-9456 (print), 1557-9662 (electronic)",
ISSN-L = "0018-9456",
bibdate = "Tue Jan 08 22:43:51 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes an efficient method for
generating the quotient of two binary numbers at speeds
comparable to existing multiplier chips. A digital
divider is designed using the BEST LINE segmentation
approximation. The reciprocal curve is subdivided into
small sections, and a least squares straight line
approximation is used to recreate each section. An
analysis is presented to determine the segmentation
granularity and the binary word length of constants
needed to closely approximate the curve. A compromise
design based on statistical performance as well as the
complexity of the hardware requirements are
evaluated.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Instrument \& Measurement",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19",
}
@Article{Demsky:1983:MMC,
author = "J. Demsky and M. Schlesinger and R. D. Kent",
title = "Micro/mini computer program for calculating the square
root of rationals at arbitrary precision",
journal = j-COMP-PHYS-COMM,
volume = "29",
number = "3",
pages = "237--244",
month = may,
year = "1983",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(83)90004-8",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:04 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465583900048",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Dietrich:1983:VQF,
author = "D. Dietrich",
title = "{Verfahren zur L{\"o}sung von Quadratwurzeln f{\"u}r
Mikrorechnerprozeduren} \toenglish {Methods for the
Solution of Square Roots for Microprocessor
Subroutines} \endtoenglish",
journal = j-ELEKTRONIKER,
volume = "8",
pages = "EL-1--EL-6",
year = "1983",
CODEN = "ELKRBL",
ISSN = "0531-9218",
bibdate = "Fri Dec 08 13:05:49 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektroniker (Switzerland)",
}
@InProceedings{Donthi:1983:BSM,
author = "Ravindra V. Donthi and Mohammed Saleem and Harpreet
Singh",
title = "On Bit Sequential Multipliers",
crossref = "IEEE:1983:PSC",
pages = "104--108",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Donthi_Saleem_Singh.pdf",
abstract = "Recently bit sequential multiplier algorithms have
been found more useful in the area of interconnection
of multiple processors within a VLSI structure [1],
[2]. The object of the present paper is to suggest
modified bit sequential algorithms to achieve more
speed and to attain its conformity with other
algorithms such as division, square-rooting, etc. with
a view to utilize them in future arithmetic arrays. In
the present paper the following has been taken up: (a)
Bit sequential multiplier using carry look-ahead
technique, (b) Bit sequential multiplier using most
significant bit first,and (c) Negabinary bit sequential
multiplier.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Dubrulle:1983:CNM,
author = "Augustin A. Dubrulle",
title = "Class of Numerical Methods for the Computation of
{Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "582--589",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moler:1983:RSR} and generalization
\cite{Jamieson:1989:SNR}.",
abstract = "Moler and Morrison have described an iterative
algorithm for the computation of the Pythagorean sum
(a**2 plus b**2)** one-half of two real numbers a and
b. This algorithm is immune to unwarranted
floating-point overflows, has a cubic rate of
convergence, and is easily transportable. This paper,
which shows that the algorithm is essentially Halley's
method applied to the computation of square roots,
provides a generalization to any order of convergence.
Formulas of orders 2 through 9 are illustrated with
numerical examples. The generalization keeps the number
of floating-point divisions constant and should be
particularly useful for computation in high-precision
floating-point arithmetic.",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C5230 (Digital
arithmetic methods)",
classification = "723; 921",
corpsource = "IBM Sci. Centre, Palo Alto, CA, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
journalabr = "IBM J Res Dev",
keywords = "computer programming; digital arithmetic;
floating-point divisions; Halley's method;
high-precision floating-point arithmetic; iterative
algorithm; iterative methods; mathematical techniques
--- Numerical Methods; Pythagorean sums; rate of
convergence; square roots",
treatment = "T Theoretical or Mathematical",
}
@Article{Dyer:1983:ZRP,
author = "D. C. Dyer",
title = "{Z80} routine performs 16-bit multiply",
journal = j-EDN,
volume = "28",
number = "5",
pages = "144",
month = mar,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Ercegovac:1983:HRD,
author = "Milo{\v{s}} D. Ercegovac",
title = "A Higher-Radix Division with Simple Selection of
Quotient Digits",
crossref = "IEEE:1983:PSC",
pages = "94--98",
month = jun,
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ercegovac.pdf",
abstract = "A higher-radix division algorithm with simple
selection of quotient digits is described. The proposed
scheme is a combination of the multiplicative
normalization used in the continued-product algorithms
and the recursive division algorithm. The scheme
consists of two parts: in the first part, the divisor
and the dividend are transformed into the range which
allows the quotient digits to be selected by rounding
partial remainders to the most significant radix-$r$
digit in the second part. Since the selection requires
only the most significant part of the partial
remainder, limited carry-propagation adders can be used
to form the partial remainders. The divisor and
dividend transformations are performed in three steps
using multipliers of the form $ 1 + s_k r^{-k} $ as in
the continued product algorithm. The higher radix of
the form $ r = 2^k, k = 2, 4, 8, \ldots {} $ can be
used to reduce the number of steps while retaining the
simple quotient selection rules.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; division",
}
@InProceedings{Ferguson:1983:DTE,
author = "Joel Ferguson and John Paul Shen",
title = "The Design of Two Easily-Testable {VLSI} Array
Multipliers",
crossref = "IEEE:1983:PSC",
pages = "2--9",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ferguson_Shen.pdf",
abstract = "Array multipliers are well-suited for VLSI
implementation because of the regularity in their
iterative structure. However, most VLSI circuits are
very difficult to test. This paper shows that, with
appropriate cell design, array multipliers can be
designed to be very easily-testable. An array
multiplier is called C-testable if all its adder cells
can be exhaustively tested while requiring only a
constant number of test patterns. The testability of
two well-known array multiplier structures are [sic]
studied. The conventional design of the carry-save
array multiplier is shown to be not C-testable.
However, a modified design, using a modified adder
cell, is generated and shown to be C-testable and
requires only 16 test patterns. Similar results are
obtained for the Baugh--Wooley two's complement array
multiplier. A modified design of the Baugh--Wooley
array multiplier is shown to be C-testable and requires
55 test patterns. The implementation of a practical
C-testable $ 16 \times 16 $ array multiplier is also
presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@InProceedings{Fraenkel:1983:SN,
author = "A. S. Fraenkel",
title = "Systems of Numeration",
crossref = "IEEE:1983:PSC",
pages = "37--42",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Fraenkel.pdf",
abstract = "A numeration system is a set of integers (basis
elements) such that every integer can be represented
uniquely over the set using integer digits of bounded
size. Such systems are scattered in many fields in
mathematics and computer science. Many of the known
ones and new ones are unified and derived from a basic
result on recursively defined basis elements.
Applications are indicated.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; number systems",
}
@Article{Gaitanis:1983:NPC,
author = "N. Gaitanis and C. Halatsis",
title = "Near-Perfect Codes for Binary-Coded Radix-$r$
Arithmetic Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "5",
pages = "494--497",
month = may,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676261",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676261",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Galand:1983:FD,
author = "C. Galand",
title = "Fast Division",
journal = j-IBM-TDB,
volume = "26",
number = "3B",
pages = "1537--1539",
month = aug,
year = "1983",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Gavrielov:1983:CSF,
author = "M. Gavrielov and A. Kaminker and Y.-T. Sidi",
title = "Coprocessors Speed Floating Point Calculations",
journal = j-COMP-DESIGN,
volume = "22",
number = "11",
pages = "197--204",
month = oct,
year = "1983",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sun Sep 11 11:55:54 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Design",
}
@Article{Gnanasekaran:1983:BSI,
author = "R. Gnanasekaran",
title = "On a Bit-Serial Input and Bit-Serial Output
Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "9",
pages = "878--880",
month = sep,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676341",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676341",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Gosling:1983:STF,
author = "J. B. Gosling",
title = "Some Tricks of the (Floating-Point) Trade",
crossref = "IEEE:1983:PSC",
pages = "218--220",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Gosling.pdf",
abstract = "In designing a floating-point arithmetic unit there
are a number of places where the characteristics of the
operations and the operands permit simplifications in
the logical design. These have not been well
documented, with the result that each new generation of
designers has made the same mistakes as their
predecessors. This paper describes some of these
simplifications as they affect the mantissa section of
a floating-point addition and subtraction unit. The
areas covered include normalisation and rounding.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Grappel:1983:FPP,
author = "R. D. Grappel",
title = "Floating-point-processing unit improves 16-bit-$ \mu
{P} $ performance",
journal = j-EDN,
volume = "28",
number = "19",
pages = "181--188",
month = sep,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Grnarov:1983:LMN,
author = "A. L. Grnarov and M. D. Ercegovac",
title = "On-line multiplicative normalization",
crossref = "IEEE:1983:PSC",
pages = "151--155",
year = "1983",
bibdate = "Tue Nov 13 15:44:54 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Grnarov_Ercegovac.pdf",
abstract = "In this article we describe a derivation and an
algorithm for on-line multiplicative normalization of
fractions. The algorithm is a variation of the
continued product normalization algorithm and it is
used for on-line evaluation of elementary functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; elementary functions; on-line arithmetic",
}
@InProceedings{Guibas:1983:FBA,
author = "L. Guibas and J. E. Vuillemin",
title = "On Fast Binary Addition in {MOS} Technologies",
crossref = "IEEE:1983:PSC",
pages = "22--23",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Guibas_Vuillemin.pdf",
acknowledgement = ack-nhfb,
keywords = "addition; ARITH-6",
remark = "Paper did not arrive in time for the proceedings.",
}
@Article{Halatsis:1983:ECC,
author = "C. Halatsis and N. Gaitanis and M. Sigala",
title = "Error-Correcting Codes in Binary-Coded Radix-$r$
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "3",
pages = "326--328",
month = mar,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676227",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676227",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hamada:1983:UUR,
author = "H. Hamada",
title = "{URR}: Universal representation of real numbers",
journal = j-NEW-GEN-COMP,
volume = "1",
number = "2",
pages = "205--209",
month = jun,
year = "1983",
CODEN = "NGCOE5",
DOI = "https://doi.org/10.1007/BF03037427",
ISSN = "0288-3635 (print), 1882-7055 (electronic)",
ISSN-L = "0288-3635",
bibdate = "Thu Dec 14 16:45:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "New Generation Computing",
journal-URL = "https://dl.acm.org/loi/newg",
}
@Article{Heninger:1983:ZZF,
author = "A. Heninger",
title = "{Zilog}'s {Z8070} Floating Point Processor",
crossref = "Mini-Micro:1983:MMN",
pages = "16/2/1--7",
year = "1983",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{HP:1983:CDR,
author = "{Hewlett Packard}",
booktitle = "Software Internal Design Specification for the
{HP-71}, Vol. 1",
title = "Chapter 13: Data Representations",
publisher = "Hewlett Packard Company",
address = "Palo Alto, CA, USA",
pages = "13.1--13.17",
month = dec,
year = "1983",
bibdate = "Fri Nov 28 17:17:29 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Part \#00071-90068. Manual available from {\em The
Museum of HP Calculators}.",
URL = "http://www.hpmuseum.org/",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Huang:1983:FPM,
author = "C. H. Huang",
title = "A Fully Parallel Mixed-Radix Conversion Algorithm for
Residue Number Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "398--402",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676242",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676242;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A new, fully parallel mixed-radix conversion (MRC)
algorithm which utilizes the maximum parallelism that
exists in the residues (RNS) to mixed-radix (MR) digits
conversion to achieve high throughput rate and very
short conversion time is presented. \ldots{}",
}
@Article{Huntsman:1983:MFP,
author = "Clayton Huntsman and Duane Cawthron",
title = "The {MC68881} Floating-Point Coprocessor",
journal = j-IEEE-MICRO,
volume = "3",
number = "6",
pages = "44--54",
month = nov # "\slash " # dec,
year = "1983",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1983.291185",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
classification = "714; 723; 902",
corpsource = "Motorola Inc., Austin, TX, USA",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "arithmetic; computer architecture; computers;
coprocessor; digital arithmetic; floating-point;
floating-point arithmetic; IEEE arithmetic; IEEE
standard; integrated circuits, VLSI --- Applications;
M68000 family; M68000 microprocessor; MC68881
floating-point processor; microprocessor chips;
real-number computations; satellite; standards",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Iffrig:1983:ULC,
author = "L. D. Iffrig",
title = "Use less code for fast 8080 multiply",
journal = j-EDN,
volume = "28",
number = "13",
pages = "293",
month = jun,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@TechReport{Ingram:1983:ACW,
author = "Windell F. Ingram and Radhakrishnan, N. (Narayanswamy)
and Deborah F. Dent",
title = "Accuracy considerations when using some minicomputers
for scientific and engineering problems",
institution = "U.S. Army Engineer Waterways Experiment Station;
available from National Technical Information Service",
address = "Vicksburg, MS, USA",
pages = "76 + 6 + 3",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Technical report; K-83-2 Technical report (U.S. Army
Engineer Waterways Experiment Station); K-83-2.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Minicomputers.;
Programming (Electronic computers).",
remark = "Cover title. ``September 1983.'' ``Prepared for
Office, Chief of Engineers, U.S. Army.'' Funded by
Office, Chief of Engineers.",
}
@Book{Intel:1983:HRM,
author = "Intel",
title = "The {iAPX} 286 Hardware Reference Manual",
publisher = pub-INTEL,
address = pub-INTEL:adr,
year = "1983",
LCCN = "QA76.8.I264 I14 1983",
bibdate = "Wed Feb 9 09:02:53 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The definitive statement of the 80286 and 80287
hardware at a strongly technical level. Not an
instruction set reference, but does contain instruction
timing tables. See also \cite{Intel:1985:PRM}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Irwin:1983:NLD,
author = "Mary Jane Irwin and Robert Michael Owens",
title = "Numerical Limitation on the Design of Digit On-Line
Networks",
crossref = "IEEE:1983:PSC",
pages = "156--161",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Owens_Irwin.pdf",
abstract = "A fully digit online arithmetic unit generates at
least the $i$ most (least) significant digits of the
result after having been supplied no more than the $ (i
+ k) $ most (least) significant digits of each operand,
where $k$ is a small constant. This digit serial
property can be used to reduce the aggregate fill and
flush times of a chained array of digit online
arithmetic units and to reduce their VLSI
interconnection complexity. However, because of this
digit serial property, unique and inherent limitations
may have to be imposed on any arithmetic unit which
performs digit online operations. For some
calculations, these limitations may be so severe as to
make digit online evaluation virtually impossible. We
show several important signal processing problems where
these limitations have either been avoided or their
effect greatly reduced.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; on-line arithmetic",
}
@Article{James:1983:RDB,
author = "F. V. James",
title = "An 8085 routine divides 32-bit unsigned numbers",
journal = j-ELECTRONICS,
volume = "56",
number = "22",
pages = "163--165",
month = nov,
year = "1983",
ISSN = "0883-4989",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@Article{Jankowski:1983:NFS,
author = "M. Jankowski and A. Smoktunowicz and H.
Wo{\'z}niakowski",
title = "A note on floating-point summation of very many
terms",
journal = "Elektron. Informationsverarb. Kybernet.",
volume = "19",
number = "9",
pages = "435--440",
year = "1983",
MRclass = "65V05",
MRnumber = "85c:65161",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
altjournal = "Journal of Information Processing and Cybernetics ---
EIK",
keywords = "accurate floating-point summation",
}
@Article{Jenkins:1983:DEC,
author = "W. K. Jenkins",
title = "The Design of Error Checkers for Self-Checking Residue
Number Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "388--396",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676240",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676240;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "During the last few years residue number (RNS)
arithmetic has gained increasing importance for
providing high speed fault tolerant performance in
dedicated digital signal processors. One factor that
has limited the use of redundant RNS theory in
\ldots{}",
}
@InProceedings{Johnsen:1983:IFP,
author = "K. Johnsen",
title = "An {IEEE} Floating Point Arithmetic Implementation",
crossref = "IEEE:1983:PSC",
pages = "130--135",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Johnsen.pdf",
abstract = "This article describes some of the methods and
algorithms used in an implementation of floating point
arithmetic following (almost) the IEEE standard defined
in (1). The description is more directly
algorithm-oriented than the `Implementation Guide' for
this standard (2), since the latter does not treat an
actual implementation. The article consists of two
parts. One concerns the problem of getting the
preliminary result from each of the arithmetic
operations, this result is the basis for a correct
rounding. The other part treats the multiword
arithmetic, i.e., the routines to perform an $ m \times
n $ bit operation, using the corresponding $n$ bit
operation supplied by the hardware. Only multiplication
and division are described, since the add\slash
subtract routines are trivial. For division also a
method for getting an $n$ bit inverse is included,
since the hardware in the case had no division
operation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; correct rounding; floating-point arithmetic;
IEEE 754",
}
@MastersThesis{Jung:1983:BRR,
author = "C. Jung",
title = "{Berechnung der reellen und reellintervallwertigen
Standard- funktionen mit maximaler Genauigkeit in einem
hexadezimalen Gleitkommaformat} \toenglish {Computation
of the Real and Real Interval Valued Standard Functions
with Maximal Accuracy in a Hexadecimal Floating-Point
Format} \endtoenglish",
type = "{Diplomarbeit}",
school = "Institut f{\"u}r Angewandte Mathematik,
Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
month = sep,
year = "1983",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Kahan:1983:M,
author = "W. Kahan",
title = "Minimizing $ q {\rm *} m - n $",
institution = "Department of Mathematics and Department of Electrical
Engineering and Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
month = mar,
year = "1983",
bibdate = "Fri May 03 12:26:29 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/testpi/nearpi.c",
acknowledgement = ack-nhfb,
remark = "Nearpi, a C program to exhibit large floating-point
numbers $ Z = m * 2^L $ very close to integer multiples
of $ \pi / 2 $.",
}
@InProceedings{Kahan:1983:MWS,
author = "W. Kahan",
title = "Mathematics Written in Sand --- The {HP-15C}, {Intel
8087}, etc.",
crossref = "Anonymous:1983:PSC",
bookpages = "vi + 344",
pages = "12--26",
year = "1983",
bibdate = "Fri May 03 12:02:15 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/MathSand.pdf",
acknowledgement = ack-nhfb,
remark = "The original published version was a photoreduction of
dot-matrix printer output; the URL points to a cleaner
version.",
}
@TechReport{Kanada:1983:CDP,
author = "Y. Kanada and Y. Tamura and S. Yoshino and Y. Ushiro",
title = "Calculation of $ \pi $ to 10,013,395 Decimal Places
Based on the {Gauss--Legendre} Algorithm and {Gauss}
Arctangent Relation",
type = "Technical report",
number = "CCUT-TR-84-01",
institution = "Computer Centre, University of Tokyo",
address = "Bunkyo-ky, Yayoi 2-11-16, Tokyo 113, Japan",
month = dec,
year = "1983",
bibdate = "Mon Jul 18 17:50:42 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaushik:1983:SDN,
author = "S. Kaushik",
title = "Sign Detection in Non-Redundant Residue Number System
with Reduced Information",
crossref = "IEEE:1983:PSC",
pages = "24--28",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kaushik.pdf",
abstract = "A necessary and sufficient condition for sign
detection in Non-Redundant Residue Number System by
reducing the information of a residue digit has been
obtained. The function to reduce the information of a
residue digit $ x_p $ corresponding to a modulus $ m_p
$ has been assumed to be periodic with the period
length $ \hat {m}_p $, where $ \hat {m}_p = M / m_p $
and $ M = \prod_{i = 1}^n m_i $. A sequential method
for determining the sign of a number is shown to
demonstrate the applicability of the results thus
proved.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; residue number systems",
}
@MastersThesis{Kirk:1983:MFP,
author = "Patrick Donald Kirk",
title = "Microcomputer and floating point firmware design",
type = "Thesis ({M.S.})",
school = "California State University, Long Beach",
address = "Long Beach, CA, USA",
pages = "2 + xi + 237",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microcomputers ---
Programming.",
}
@InProceedings{Kobayashi:1983:AHS,
author = "Hideaki Kobayashi and Ronald D. Bonnell",
title = "Arithmetic for a High-Speed Adaptive Learning Network
Element",
crossref = "IEEE:1983:PSC",
pages = "164--168",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kobayashi_Bonnel.pdf",
abstract = "This paper presents a novel arithmetic scheme for a
high-speed adaptive learning network (ALN) element. An
ALN is a self-organizing scheme for implementing the
Kolmogorov--Gabor (K-G) polynomial which maps an input
vector $X$ into an output scalar $Y$. In the first
layer of an ALN there are $ n(n - 1) / 2 $ elements. In
the next layer the number of elements needed depends
upon the number of outputs that are propagated from the
first layer. In this paper only the design of a single
element is considered. An array of memories (RAMs) and
a parallel adder are used to perform multinomial
arithmetic for the element. The memory array contains
subfunction values which are calculated by an external
host computer and downloaded to the memory array. All
the memories operate on the input variables
concurrently via a common address bus. The subfunction
values from the memory array are then summed by a
parallel adder to obtain the output of the element.
complete ALN implemented with the proposed ALN elements
has advantages in operation speed and less hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Kornerup:1983:FPR,
author = "Peter Kornerup and David W. Matula",
title = "Finite precision rational arithmetic: An arithmetic
unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "378--388",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676239",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676239",
abstract = "The foundations of an arithmetic unit performing the
add, subtract, multiply, and divide operations on
rational operands are developed. The unit uses the
classical Euclidean algorithm as one unified algorithm
for all the arithmetic operations, including rounding.
Binary implementations are discussed, based on
techniques known from SRT division, and utilizing
ripple-free borrow-save and carry-save addition.
Average time behavior is investigated.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Krishnamurthy:1983:FID,
author = "E. V. Krishnamurthy and V. K. Murthy",
title = "Fast Iterative Division of $p$-adic Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "396--398",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676241",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676241",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lastman:1983:DFP,
author = "G. J. Lastman",
title = "Determination of Floating Point Characteristics for a
Personal Computer",
crossref = "IEEE:1983:IEE",
pages = "424--427",
year = "1983",
bibdate = "Thu Sep 01 12:11:33 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Linnainmaa:1983:ELE,
author = "Seppo Linnainmaa",
title = "Error linearization as an effective tool for
experimental analysis of the numerical stability of
algorithms",
journal = j-BIT,
volume = "23",
number = "3",
pages = "346--359",
month = sep,
year = "1983",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934463",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05 (65J05)",
MRnumber = "85e:65020",
bibdate = "Wed Jan 4 18:52:18 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=23&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=23&issue=3&spage=346",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Lozier:1983:UFP,
author = "Daniel W. Lozier",
title = "The use of floating-point and interval arithmetic in
the computation of error bounds",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "411--417",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676245",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65G05",
MRnumber = "85f:65042",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676245",
abstract = "Three forms of interval floating-point arithmetic are
defined in terms of absolute precision, relative
precision, and combined absolute and relative
precision. The absolute-precision form corresponds to
the centered form of conventional rounded-interval
arithmetic. The three forms are compared on the basis
of the number of floating-point operations needed to
generate error bounds for inner-product accumulation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
catcode = "G.1.0",
CRclass = "G.1.0 General; G.1.0 Error analysis",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
genterm = "ALGORITHMS; PERFORMANCE",
guideno = "06575",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
reviewer = "N. N. Abdelmalek",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Majerski:1983:SRA,
author = "Stanislaw Majerski",
title = "Square-Root Algorithms for High-Speed Digital
Circuits",
crossref = "IEEE:1983:PSC",
pages = "99--102",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Majerski.pdf",
abstract = "Two binary algorithms for the square rooting of a sum
of two numbers are presented. They are designed for
high-speed digital circuits and are based on the
classical nonrestoring method. The main difference lies
in the replacement of subtractions and additions by the
parallel reduction of three summands to two, their sum
being unchanged to eliminate a carry propagation. The
term ``parallel reduction'' is introduced here for the
carry-save addition of three summands, positive and
negative as well. The two result summands form a
successive partial remainder. Their most significant
three-bit groups are used to determine the ``digits''
$1$, $0$, $ + 1 $ of the square root in a redundant
notation. These digits are transformed into the
conventional-notation bits, which are used in the
further steps of the square-rooting process",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; square root",
}
@Article{Maric:1983:PBC,
author = "I. Maric and L. Cucancic",
title = "On the Possibilities of the {BCD} Code Application in
the Floating-Point Arithmetic Algorithms",
journal = j-INT-J-MINI-MICROCOMPUTERS,
volume = "5",
number = "2",
pages = "19--22",
month = "????",
year = "1983",
CODEN = "IJMMDE",
ISSN = "0702-0481",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "International Journal of Mini and Microcomputers",
}
@InProceedings{Markov:1983:NAF,
author = "Svetoslav Markov",
title = "On the Numerical Algorithms Formulated in Computer
Arithmetic",
crossref = "IEEE:1983:PSC",
pages = "82--85",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Markov.pdf",
abstract = "We discuss some mathematical tools and techniques
supporting the construction of rigorous bounds
producing, numerically convergent algorithms, which are
formulated in terms of computer arithmetic operations.
Two important computer-arithmetic effects are
considered and their application as stopping criteria
is illustrated.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@InProceedings{Martin:1983:FPS,
author = "G. R. Martin",
title = "Floating Point Support for the {NS16000} Family -- The
{NS16081}",
crossref = "Mini-Micro:1983:MMW",
pages = "16/3/1--3",
year = "1983",
bibdate = "Wed Sep 07 22:33:22 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Matula:1983:OPF,
author = "David W. Matula and Peter Kornerup",
title = "An Order Preserving Finite Binary Encoding of the
Rationals",
crossref = "IEEE:1983:PSC",
pages = "201--209",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Matula_Kornerup.pdf",
abstract = "We describe a new binary encoding for numbers termed
lexicographic continued fraction (LCF) representation
that provides a one-to-one order preserving finite bit
string representation for every rational. Conversion
either way between binary integer numerator-denominator
pair representation and LCF representation is shown
feasible in time linear with bit string length, given
registers of length sufficient to hold the numerator
and denominator. LCF bit string length is about $ 2
\max \{ \log_2 P, \log_2 q \} $ for the irreducible
fraction $ p / q $. Realization of arithmetic $ ( +, -,
\times, \divide) $ on LCF bit string encoded operands
is shown feasible. Some relations between the theory of
best rational approximation and the values represented
by truncated LCF bit strings are noted to assess the
feasibility of a finite precision arithmetic based on
LCF representation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; lexicographic continued fraction (LCF);
rational arithmetic",
}
@Article{McCool:1983:NDC,
author = "Thomas E. McCool",
title = "4. {NSA}'s {Defense Calculator}, 1952--1953",
journal = j-ANN-HIST-COMPUT,
volume = "5",
number = "2",
pages = "186--187",
month = apr # "\slash " # jun,
year = "1983",
CODEN = "AHCOE5",
ISSN = "0164-1239",
ISSN-L = "0164-1239",
bibdate = "Fri Nov 1 15:29:20 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/an/books/an1983/pdf/a2186.pdf;
http://www.computer.org/annals/an1983/a2186abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}
@Article{McGuire:1983:PCB,
author = "D. W. McGuire",
title = "8048 program computes 16-by-8-bit quotient",
journal = j-ELECTRONICS,
volume = "56",
number = "10",
pages = "152--153",
month = may,
year = "1983",
ISSN = "0883-4989",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@TechReport{Midttun:1983:FMP,
author = "G. Midttun",
title = "A fast micro-programmable floating point processor",
type = "Technical report",
number = "CERN DD 83-16",
institution = "CERT",
address = "Geneva, Switzerland",
pages = "31",
month = sep,
year = "1983",
bibdate = "Fri May 25 05:43:42 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0058382",
acknowledgement = ack-nhfb,
keywords = "emulation; MICE; microcode; PDP11",
}
@Article{Mikov:1983:PAFa,
author = "A. I. Mikov",
title = "Probabilistic analysis of floating-point addition
({Russian})",
journal = "Kibernetika (Kiev)",
volume = "3",
pages = "87--93",
year = "1983",
MRclass = "60K99 (65G05)",
MRnumber = "85h:60154",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation in \cite{Mikov:1983:PAFb}.",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Mikov:1983:PAFb,
author = "A. I. Mikov",
title = "Probabilistic analysis of floating-point addition",
journal = j-CYBER,
volume = "19",
number = "3",
pages = "401--410",
month = may,
year = "1983",
CODEN = "CYBNAW",
DOI = "https://doi.org/10.1007/BF01072156",
ISSN = "0011-4235 (print), 2375-0189 (electronic)",
MRclass = "60K99 (65G05)",
MRnumber = "85h:60154",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from \cite{Mikov:1983:PAFa}.",
URL = "http://link.springer.com/article/10.1007/BF01072156",
acknowledgement = ack-nhfb,
fjournal = "Cybernetics",
journal-URL = "http://link.springer.com/journal/10559",
}
@Article{Miller:1983:RNS,
author = "D. D. Miller and J. N. Polky",
title = "A Residue Number System Implementation of the {LMS}
Algorithm Using Optical Waveguide Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "11",
pages = "1013--1028",
month = nov,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676152",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676152;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35222",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A detailed design of a real-time data processor based
on the residue number system is presented which uses
near-term optical waveguide devices and concepts. The
optical computational units consist of cascaded,
mask-programmable arrays of total \ldots{}",
}
@InProceedings{Miola:1983:UVA,
author = "A. Miola",
title = "A Unified View of Approximate Rational Arithmetic and
Rational Interpolation",
crossref = "IEEE:1983:PSC",
pages = "210--215",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Miola.pdf",
abstract = "In this paper we cover the problem of approximation of
numbers and of functions by presenting some well known
results in a unified view that could help in better
understanding the algebraic bases of the problem. In
fact, the Extended Euclid's algorithm happens to be the
unique and common tool solving the approximation
problems both for numbers and for functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; rational arithmetic; rational interpolation",
}
@Article{Moler:1983:RSR,
author = "Cleve B. Moler and Donald Morrison",
title = "Replacing Square Roots by {Pythagorean} Sums",
journal = j-IBM-JRD,
volume = "27",
number = "6",
pages = "577--581",
month = nov,
year = "1983",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Dubrulle:1983:CNM} and generalization
\cite{Jamieson:1989:SNR}.",
URL = "http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf",
abstract = "An algorithm is presented for computing a 'Pythagorean
sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from
a and b without computing their squares or taking a
square root. No destructive floating point overflows or
underflows are possible. The algorithm can be extended
to compute the Euclidean norm of a vector. The
resulting subroutine is short, portable, robust, and
accurate, but not as efficient as some other
possibilities. The algorithm is particularly attractive
for computers where space and reliability are more
important than speed",
acknowledgement = ack-nj # " and " # ack-nhfb,
classcodes = "C4190 (Other numerical methods); C5230 (Digital
arithmetic methods)",
corpsource = "Department of Computer Sci., University of New Mexico,
Albuquerque, NM, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "algorithms; digital arithmetic; Euclidean norm;
floating-point arithmetic; iterative methods;
performance; Pythagorean sums; subroutine; vector",
review = "ACM CR 8406-0463",
subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
Roots of Nonlinear Equations \\ F.2.1 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on polynomials \\ F.2.2 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Geometrical problems and computations",
treatment = "T Theoretical or Mathematical",
}
@Article{Moran:1983:BRB,
author = "Bruce T. Moran",
title = "Book Review: {{\booktitle{Wissenschaftsgeschichte um
Wilhelm Schickard: Vortr{\"a}ge bei dem Symposion der
Universitat T{\"u}bingen im 500 Jahr ihres Bestehens am
24. und 25. Juni 1977}} by Friedrich Seck}",
journal = j-ISIS,
volume = "74",
number = "3",
pages = "448--449",
month = sep,
year = "1983",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:22:47 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211164;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1980.bib",
URL = "http://www.jstor.org/stable/232640",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@InProceedings{Morrison:1983:EHL,
author = "R. Morrison and A. J. Cole and P. J. Bailey and M. A.
Wolfe and M. Shearer",
title = "Experience with a High Level Language that Supports
Interval Arithmetic",
crossref = "IEEE:1983:PSC",
pages = "74--78",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Morrison_Cole_Bailey_Wolfe_Shearer.pdf",
abstract = "An extension of the language S-algol called Triplex
which facilitates the use of interval arithmetic and
which is similar to triplex algol 60 is described.
Experience in the use of Triplex is reported. In
particular, a Triplex program corresponding to a
triplex algol 60 program of Nickel is given, together
with numerical results.",
acknowledgement = ack-nhfb,
keywords = "Algol 60; ARITH-6; interval arithmetic; S-Algol;
Triplex (Algol)",
}
@Article{Murugesan:1983:ACF,
author = "S. Murugesan and V. K. Agrawal",
title = "Algorithm converts fractions to {BCD}",
journal = j-EDN,
volume = "28",
number = "19",
pages = "245--246",
month = sep,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Nagpal:1983:PAT,
author = "H. K. Nagpal and G. A. Jullien and W. C. Miller",
title = "Processor Architectures for Two-Dimensional Convolvers
Using a Single Multiplexed Computational Element with
Finite Field Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "11",
pages = "989--1001",
month = nov,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676150",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676150",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Nave:1983:ITF,
author = "R. Nave",
title = "Implementation of Transcendental Functions on a
Numerics Processor",
journal = j-MICROPROC-MICROPROG,
volume = "11",
number = "3--4",
pages = "221--225",
month = mar # "--" # apr,
year = "1983",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Fri Dec 08 13:05:28 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessing and Microprogramming",
}
@InProceedings{Ni:1983:VRM,
author = "Lionel M. Ni and Kai Hwang",
title = "Vector Reduction Methods for Arithmetic Pipelines",
crossref = "IEEE:1983:PSC",
pages = "144--150",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ni_Hwang.pdf",
abstract = "Vector reduction arithmetic accepts a vector as input
and produces a scalar output. This class of vector
operations forms the basis of many scientific
computations. In a pipelined processor, a feedback loop
is required to reduce vectors. Since the output of the
pipeline depends on previous outputs, improper control
of the feedback loop will destroy the benefit from
pipelining. A generalized computing model is proposed
to schedule the activities in a vector reduction
pipeline. Two new vector reduction methods, symmetric
and asymmetric, are proposed and analyzed for pipelined
processing. These two methods compare favorably with
the known recursive reduction method in achieving
higher pipeline utilization and in eliminating large
memory for intermediate results. An interleaving method
is proposed to reduce multiple vectors to multiple
scalars in a single arithmetic pipeline. The pipeline
can be fully utilized by interleaved multiple vector
processing.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@InProceedings{Ohlsson:1983:MML,
author = "Lennart Ohlsson and Bertil Svensson",
title = "Matrix Multiplication on {LUCAS}",
crossref = "IEEE:1983:PSC",
pages = "116--122",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ohlsson_Svensson.pdf",
abstract = "Multiplication of two $N$ by $N$ matrices involves $
N^3 $ multiplications of elements. The task allows a
large amount of parallelism to be utilized, indicating
that it can be efficiently executed on a parallel
computer. This paper describes how matrix
multiplication is performed on LUCAS, an SIMD type
parallel processor with bit-serial processing elements.
The interconnection network is of Perfect Shuffle\slash
Exchange type. The case of study is when the number of
processing elements is between $ N^2 $ and $ N^3 $. The
algorithm presented can be applied to any computer with
the same interconnection structure. Formulas showing
how the execution time depends on data length and
matrix size are presented together with measured values
from execution on LUCAS.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; LUCAS (Lund University Content Addressable
System)",
}
@InProceedings{Ong:1983:CAS,
author = "Shauchi Ong and D. E. Atkins",
title = "A Comparison of {ALU} Structures for {VLSI}
Technology",
crossref = "IEEE:1983:PSC",
pages = "10--16",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ong_Atkins.pdf",
abstract = "Although many of the basic techniques of computer
arithmetic have been known since the earliest days of
electronic computing, there is a continuing need to
re-evaluate them in the context of developments in VLSI
circuit technology. Furthermore, recent work in
complexity of algorithms, particularly the solution of
recurrence relations, suggests new candidate structures
for generating the carry vector and raises the
questions as to their practicality in modern logic
design practice.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Owens:1983:TRI,
author = "R. M. Owens",
title = "Techniques to Reduce the Inherent Limitations of Fully
Digit On-Line Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "406--411",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676244",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676244",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ozawa:1983:AIK,
author = "K. Ozawa",
title = "Analysis and Improvement of {Kahan}'s Summation
Algorithm",
journal = j-INFO-PROC,
volume = "6",
number = "4",
pages = "226--230",
year = "1983",
bibdate = "Mon Sep 12 08:06:17 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "accurate floating-point summation",
}
@InProceedings{Palmer:1983:VSN,
author = "J. F. Palmer",
title = "{VLSI} starts a numeric revolution",
crossref = "IEEE:1983:PII",
pages = "186--189",
year = "1983",
bibdate = "Wed Sep 7 22:31:27 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Pan:1983:ALC,
author = "V. Ya Pan",
title = "The additive and logical complexities of linear and
bilinear arithmetic algorithms",
journal = j-J-ALG,
volume = "4",
number = "1",
pages = "1--34",
month = mar,
year = "1983",
CODEN = "JOALDV",
DOI = "https://doi.org/10.1016/0196-6774(83)90031-7",
ISSN = "0196-6774 (print), 1090-2678 (electronic)",
ISSN-L = "0196-6774",
bibdate = "Tue Dec 11 09:14:02 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jalg.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0196677483900317",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms",
journal-URL = "http://www.sciencedirect.com/science/journal/01966774",
}
@Article{Patel:1983:CED,
author = "J. H. Patel and L. Y. Fung",
title = "Concurrent Error Detection in Multiply and Divide
Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "417--422",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676246",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676246",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Payne:1983:DRT,
author = "M. H. Payne and R. N. Hanek",
title = "Degree Reduction for Trigonometric Functions",
journal = j-SIGNUM,
volume = "18",
number = "2",
pages = "18--19",
month = apr,
year = "1983",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057605.1057606",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This report is a companion to Reference 1 on radian
reduction. As in Reference 1 \cite{Payne:1983:RRT}, the
motivation arises from a desire to eliminate messages
like ``argument too large'' in trigonometric function
routines. The presence of very large arguments in the
VAX H format, on the Cray 1, and on an IEEE machine
with extended registers, make this a real problem. As
for the radian reduction algorithm, the degree
algorithm will reduce any argument, however large, so
long as it is representable; its speed is nearly
independent of the size of the argument to be reduced;
and full accuracy is maintained in the neighborhoods of
the zeros of the desired function. We believe that the
approach is new and represents a significant
improvement over procedures currently in use. A variant
of the procedure is used in Version 3 of the VAX Math
Library.",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "range reduction",
}
@Article{Payne:1983:RRT,
author = "M. H. Payne and R. N. Hanek",
title = "Radian Reduction for Trigonometric Functions",
journal = j-SIGNUM,
volume = "18",
number = "1",
pages = "19--24",
month = jan,
year = "1983",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057600.1057602",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An accurate reduction poses little difficulty for
arguments of a few radians. However for, say, a CRAY 1,
H format on the VAX, or double extended in the proposed
IEEE standard, the maximum argument which might be
presented for reduction is of the order of $ 2^{16000}
$ radians. Accurate reduction of such an argument would
require storage of $ \pi $ (or its reciprocal) to over
16,000 bits. Direct reduction by division (or
multiplication) then requires generation of a somewhat
larger number of bits in the result in order to
guarantee the accuracy of the reduction. Of these bits
only the low few bits of the integer part of the
quotient (product) and enough bits to correctly round
the remainder are relevant; the rest will be
discarded.",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "correct rounding; floating-point arithmetic; range
reduction",
}
@Article{Preparata:1983:MCA,
author = "F. P. Preparata",
title = "A Mesh-Connected Area-Time Optimal {VLSI} Multiplier
of Large Integers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "2",
pages = "194--198",
month = feb,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676203",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:07 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676203",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Prosser:1983:NCS,
author = "C. J. Prosser",
title = "A note on computing the square root of an integer",
journal = j-COMP-J,
volume = "26",
number = "2",
pages = "187--188",
month = may,
year = "1983",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C7310 (Mathematics
computing)",
corpsource = "Rutherford and Appleton Lab., Chilton, Didcot, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary; computer; fixed-point number; integer;
interactive methods; iterative methods; PASCAL; Pascal
implementation; square root; subroutines; successive
subtraction",
treatment = "P Practical",
}
@Article{Prosser:1983:SNN,
author = "C. J. Prosser",
title = "Short Notes: a Note on Computing the Square Root of an
Integer",
journal = j-COMP-J,
volume = "26",
number = "2",
pages = "187--188",
month = may,
year = "1983",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/26.2.187",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:14 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/26/2.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/26/2/187.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
acknowledgement = ack-nhfb,
classcodes = "C4190 (Other numerical methods); C7310 (Mathematics
computing)",
corpsource = "Rutherford and Appleton Lab., Chilton, Didcot, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "binary; computer; fixed-point number; integer;
iterative methods; PASCAL; Pascal implementation;
square root; subroutines; successive subtraction",
treatment = "P Practical",
}
@Article{Quinn:1983:EPR,
author = "Kevin Quinn",
title = "Ever Had Problems Rounding Off Figures? {This} Stock
Exchange Has",
journal = j-WALL-ST-J,
volume = "??",
number = "??",
pages = "37--37",
day = "8",
month = nov,
year = "1983",
CODEN = "WSJOAF",
ISSN = "0099-9660",
bibdate = "Thu Oct 17 06:28:35 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Wall Street Journal",
}
@Article{Rall:1983:BRB,
author = "L. B. Rall",
title = "Book Review: {{\booktitle{Computer Arithmetic in
Theory and Practice}} (Ulrich W. Kulisch and Willard L.
Miranker)}",
journal = j-SIAM-REVIEW,
volume = "25",
number = "4",
pages = "585--588",
month = "????",
year = "1983",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1025138",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:53:41 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/25/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1983",
}
@Article{Rall:1983:CAT,
author = "L. B. Rall",
title = "Computer Arithmetic in Theory and Practice ---
{Kulisch, U. W., Miranker, W. L.}",
journal = j-SIAM-REVIEW,
volume = "25",
number = "4",
pages = "585--588",
month = "????",
year = "1983",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1025138",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Ramachandran:1983:SRE,
author = "V. Ramachandran",
title = "Single Residue Error Correction in Residue Number
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "5",
pages = "504--507",
month = may,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676264",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676264;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35227",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "We present a new method to correct single errors in an
n-residue number system through the use of r redundant
moduli. The method requires {\lceil}2n/r{\rceil} + 2
recombinations of n residues in the worst case. This is
of lower complexity than any \ldots{}",
}
@InProceedings{Rao:1983:ICS,
author = "T. R. N. Rao and P. Kornerup",
title = "{IEEE Computer Society Sixth Symposium on Computer
Arithmetic}",
crossref = "IEEE:1983:PSC",
pages = "1--1",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Rao_Kornerup.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@InProceedings{Robertson:1983:CDM,
author = "James E. Robertson",
title = "Conditions for the Distributivity of Multiplication
with Respect to Set Addition and Their Effect on the
Design of Array Multipliers",
crossref = "IEEE:1983:PSC",
pages = "67--71",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Robertson.pdf",
abstract = "Some conditions for distributivity of multiplication
with respect to set addition are determined. In
particular, distributivity holds if positive numbers
are used, but does not hold for negative numbers in
radix complement form. Use of simple recoding methods
to achieve distributivity is not helpful, since costs
of elementary multipliers and summing networks are
increased. Distributivity does hold for the digit sets
used for signed-digit arithmetic, and the requirement
for distributivity provides guidance for the design of
elementary multipliers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Article{Robison:1983:USF,
author = "A. D. Robison",
title = "Use Squares for Fast Multiplication",
journal = j-EDN,
volume = "28",
number = "21",
pages = "263, 267",
month = oct,
year = "1983",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@MastersThesis{Rosenblum:1983:IIS,
author = "David Samuel Rosenblum",
title = "An implementation of the {IEEE} standard for binary
floating-point arithmetic for the {Motorola} 6809
microprocessor",
type = "Thesis ({M.S.})",
school = "North Texas State University",
address = "Denton, TX, USA",
pages = "vi + 83",
month = aug,
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Microprocessors ---
Programming.",
}
@InProceedings{Rump:1983:SAP,
author = "Siegfried M. Rump",
title = "Solving algebraic problems with high accuracy",
crossref = "Kulisch:1983:NAS",
pages = "51--120",
year = "1983",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1; G.1.3; G.1.0; G.1.0",
content = "Numerical methods for the following applications are
surveyed in this paper: solving systems of linear
algebraic equations; obtaining the inverse of a given
matrix; finding zeros of functions and polynomials;
computing eigenvalues and eigenvectors of a matrix;
treating linear, quadratic and convex programming
problems; and calculating the values of arithmetic
expressions. Both the case where the coefficient matrix
is square and the case where the coefficient matrix is
rectangular are handled in connection with the solution
of systems of linear algebraic equations. Moreover,
methods for the special, but important, cases where the
coefficient matrix of a system of linear algebraic
equations is band or sparse are given. (In the latter
case, it is assumed that the system is solved by
iterative processes.) The common feature of all these
methods is that by studying carefully the basic
properties of the computer arithmetic (sketched in the
beginning of the paper), one can avoid the round-off
errors and, thus, achieve a high degree of accuracy. If
the data are exactly representable on the computer
under consideration, \ldots{}",
CRclass = "G.1.3 Numerical Linear Algebra; G.1.3 Numerical Linear
Algebra; G.1.3 Sparse and very large systems; G.1.0
General; G.1.0 Computer arithmetic; G.1.0 General;
G.1.0 Error analysis",
CRnumber = "8503-0216",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra; Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse
and very large systems; Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic;
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis",
genterm = "ALGORITHMS; PERFORMANCE",
reviewer = "Z. Zlatev; Zlatev, Z",
source = "in A new approach to scientific computation. Proc. of
the symposium on a new approach to scientific
computation (Yorktown Heights, NY, August 3, 1982), U.
Kulisch and W. Miranker (Eds.), Academic Press, Inc.,
New York, NY, 1983",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Sand:1983:DIP,
author = "J. R. Sand and J. O. Bumgarner",
title = "{Dysan IEEE P-754} Binary Floating Point
Architecture",
crossref = "Ranocchia:1983:RFA",
pages = "185--194",
year = "1983",
bibdate = "Sat Nov 12 21:59:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Sandesara:1983:ZZF,
author = "S. Sandesara",
title = "{Zilog}'s {Z8070} Floating-Point Processor",
crossref = "Mini-Micro:1983:MMN",
pages = "7/4/1--3",
year = "1983",
bibdate = "Mon Sep 12 08:05:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Schelin:1983:CFA,
author = "Charles W. Schelin",
title = "Calculator function approximation",
journal = j-AMER-MATH-MONTHLY,
volume = "90",
number = "5",
pages = "317--325",
month = may,
year = "1983",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2975781",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "65D15 (65-03 65-04)",
MRnumber = "84h:65021",
MRreviewer = "J. Albrycht",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "http://www.jstor.org/journals/00029890.htm;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.jstor.org/stable/2975781",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
keywords = "Computer Function Evaluation; CORDIC Scheme; tabular
function values",
}
@InProceedings{Scherson:1983:MOA,
author = "Isaac Scherson and Smil Ruhman",
title = "Multi-operand Associative Arithmetic",
crossref = "IEEE:1983:PSC",
pages = "123--129",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Scherson_Ruhman.pdf",
abstract = "Multi-operand associative techniques attain their full
power in algorithms where the data may be recast into
disjoint data sets, all acted upon concurrently, each
by a different operand common to the set. But the
multi-operand approach can also serve to enhance
arithmetic operations significantly. The speed-up of
associative multiplication by handling a number of
multiplier bits at a time is described and analyzed,
including an effective algorithm for a limited sum of
products. The most complex process treated is
convolution, which serves to illustrate the enhancement
of an extended sum of products. Any number of vectors
stored in memory can be convolved simultaneously by a
common filter vector. Execution time is 45 milliseconds
for 1024 element data and filter vectors, 2048 element
results, and 16-bit precision.",
acknowledgement = ack-nhfb,
}
@Book{Schmid:1983:DC,
author = "Hermann Schmid",
title = "Decimal Computation",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "xi + 266",
year = "1983",
ISBN = "0-89874-318-4",
ISBN-13 = "978-0-89874-318-0",
LCCN = "QA75 .S34 1983",
bibdate = "Thu Sep 1 10:14:05 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprint of \cite{Schmid:1974:DC}.",
acknowledgement = ack-nhfb,
keywords = "binary-coded decimal system; calculators--circuits;
decimal floating-point arithmetic",
}
@InProceedings{Seidensticker:1983:CFH,
author = "R. B. Seidensticker",
title = "Continued Fractions For High-Speed and High-Accuracy
Computer Arithmetic",
crossref = "IEEE:1983:PSC",
pages = "184--193",
year = "1983",
bibdate = "Tue Nov 13 15:50:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Seidensticker.pdf",
abstract = "Continued fraction representation has many advantages
for fast and high-accuracy computation when compared
with positional notation. A continued fraction is a
number of the form\par
$$ p_1 + q_1 / (p_2 + q_2 / (p_3 + \cdots {}))
$$,\par
\noindent where $p$ and $q$ are integers. Some of the
benefits of continued fraction representation for
computer arithmetic are: faster multiply and divide
than with positional notation, fast evaluation of
trigonometric, logarithmic, and other unary functions,
easy extension to infinite-precision arithmetic,
infinite-precision representation of many
transcendental numbers, no roundoff or truncation
errors, and improved software transportability because
accuracy is not hardware dependent. A unified system
for continued fraction arithmetic is given along with
an outline of a hardware architecture for evaluating
these functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; continued fractions",
}
@MastersThesis{Shah:1983:FPP,
author = "Kamalesh Ramanlal Shah",
title = "Floating point processor for {STOIC} instrumentation",
type = "Thesis ({M.S. in Engineering})",
school = "University of Texas at Austin",
address = "Austin, TX, USA",
pages = "xi + 188",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Medical electronics.; Medical instruments and
apparatus --- Design and construction.;
Microprocessors.",
}
@Article{Smith:1983:FPA,
author = "Burks Smith",
title = "Floating Point Arithmetic and Numeric Representation
in Computers [letter] in {DDC}",
journal = j-DDJ,
volume = "8",
number = "2",
pages = "55--??",
month = feb,
year = "1983",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Soderstrand:1983:IRN,
author = "M. Soderstrand and C. Vernia and Jui-Hua Chang",
title = "An improved residue number system digital-to-analog
converter",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "30",
number = "12",
pages = "903--907",
month = dec,
year = "1983",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19820632",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23540",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "A new technique for Residue Number System (RNS)
Digital-to-Binary or Digital-to-Analog conversion based
on the Chinese Remainder Theorem allows conversion with
only one level of ROM and one level of Adders. The
ROM's are small (e.g., 256 x 8) and \ldots{}",
}
@TechReport{Spafford:1983:RAP,
author = "Eugene Howard Spafford",
title = "A report on the accuracy of {PRIME} computers'
floating point software and hardware and the {SWT} math
library user's guide",
type = "{GIT-ICS}",
number = "83/09",
institution = "School of Information and Computer Science, Georgia
Institute of Technology",
address = "Atlanta, GA, USA",
pages = "v + 57",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computers.",
}
@Article{Speiser:1983:SFP,
author = "Jeffrey Speiser",
title = "{Savage} Floating Point Benchmark in {PASCAL} in
{16BST}",
journal = j-DDJ,
volume = "8",
number = "11",
pages = "112--??",
month = nov,
year = "1983",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@TechReport{Springer:1983:FP,
author = "Charles Towne Springer",
title = "Floating point",
institution = "Mountain View Pr.",
address = "Mountain View, CA, USA",
pages = "22",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "MVP-FORTH series; v. 3",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; FORTH (Computer program
language)",
remark = "Title on cover: FORTH floating point.
``Pre-publication.''",
}
@Article{Swartzlander:1983:SLA,
author = "E. E. {Swartzlander, Jr.} and D. V. Satish Chandra and
H. T. {Nagle, Jr.} and S. A. Starks",
title = "Sign\slash Logarithm Arithmetic for {FFT}
Implementation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "6",
pages = "526--534",
month = jun,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676274",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See comments \cite{Hongyuan:1986:CSL}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676274",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Takefuji:1983:FMS,
author = "Yoshiyasu Takefuji and Takakazu Kurokawa and Hideo
Aiso",
title = "Fast Matrix Solver in {$ \mathrm {GF}(2) $}",
crossref = "IEEE:1983:PSC",
pages = "138--143",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Takefuji_Kurokawa_Aiso.pdf",
abstract = "In this paper a parallel and pipelined fast matrix
equation solver in $ \mathrm {GF}(2) $ is proposed
where the elements are 0s or 1s. The solver employing
the iterative logic circuits which are suitable for
VLSI implementation can be realized by the conventional
Gauss--Jordan Elimination Method. $ O(n) $ gate stages
in the pipeline and $ O(n^2) $ total gates are required
for solving $ A X = b $ where $A$ is a matrix of $ n
\times n $, $X$ and $b$ are vectors respectively. The
organization of the solver is discussed in this
paper.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@TechReport{Tamura:1983:CDB,
author = "Y. Tamura and Y. Kanada",
title = "Calculation of $ \pi $ to 4,194,293 Decimals Based on
the {Gauss--Legendre} Algorithm",
type = "Technical report",
number = "CCUT-TR-83-01",
institution = "Computer Centre, University of Tokyo",
address = "Tokyo, Japan",
month = may,
year = "1983",
bibdate = "Mon Jul 18 17:46:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Taylor:1983:AE,
author = "George S. Taylor",
title = "Arithmetic on the {ELXSI 6400}",
crossref = "IEEE:1983:PSC",
pages = "110--115",
year = "1983",
bibdate = "Tue Nov 13 15:50:05 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Taylor.pdf",
abstract = "The ELXSI System 6400 is a new 64-bit general-purpose
mainframe computer [1]. This paper describes its
arithmetic instruction set architecture and the
organization of the arithmetic processor. The ELXSI
instruction set supports a complete implementation of
the proposed IEEE floating point standard [2], plus
integer and decimal arithmetic. The System 6400
arithmetic processor uses ECL gate arrays to execute
these instructions at high speed using a single board
of hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; ELXSI 6400",
}
@Article{Taylor:1983:OFR,
author = "F. J. Taylor",
title = "An Overflow-Free Residue Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "5",
pages = "501--504",
month = may,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676263",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676263",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Thomas:1983:HLM,
author = "James W. Thomas",
title = "High-level language management of the {IEEE}
floating-point environment: research project",
type = "Thesis ({M.S. in Electrical Engineering})",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "27",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Tseng:1983:FIP,
author = "Yeong-Jeng Tseng",
title = "A floating-point inner product step processor for use
in a {VLSI} Systolic array",
type = "Thesis ({M.S.})",
school = "Michigan State University",
address = "East Lansing, MI 48824, USA",
pages = "ix + 63",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units; Electronic
digital computers --- Circuits; Floating-point
arithmetic; Integrated circuits --- Very large scale
integration.",
}
@Article{Ulman:1983:SDI,
author = "Z. D. Ulman",
title = "Sign Detection and Implicit-Explicit Conversion of
Numbers in Residue Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "6",
pages = "590--594",
month = jun,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676282",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 10:01:10 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676282",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Voelz:1983:CAE,
author = "H. V{\"o}lz",
title = "{CORDIC und {\"a}hnliche Algorithmen der elementaren
Funktionen mit besonderer Eignung f{\"u}r Mikrorechner}
\toenglish {CORDIC and Similar Algorithms for
Elementary Functions with Particular Aptitude for
Microcomputers} \endtoenglish",
journal = j-NACH-ELEK,
volume = "33",
number = "12",
pages = "506--510",
month = "????",
year = "1983",
CODEN = "NTELAP",
ISSN = "0323-4657",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Nachrichtentechnik Elektronik",
}
@Article{Vogt:1983:AFM,
author = "R. Vogt and R. Waser",
title = "{Arithmetikroutinen f{\"u}r die
Me{\ss}\-dat\-en\-ver\-ar\-beit\-ung} \toenglish
{Arithmetic Routines for Measurement Applications}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "20",
pages = "85--92",
year = "1983",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@InProceedings{Wallis:1983:AFP,
author = "Peter J. L. Wallis",
title = "{Ada} Floating-Point Arithmetic as a Basis for
Portable Numerical Software",
crossref = "IEEE:1983:PSC",
pages = "79--81",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Wallis.pdf",
abstract = "Ada supports two different schemes for floating-point
arithmetic portability -- one based on the use of the
underlying machine arithmetic and the other based on
the `model arithmetic' that the underlying machine
supports, Features of both schemes are explained in the
context of their suitability as bases for the
production of portable numerical software.",
acknowledgement = ack-nhfb,
keywords = "Ada; ARITH-6",
}
@MastersThesis{Walsh:1983:FGE,
author = "Edmund John Walsh",
title = "Floating gatefield effect transistor operating point
changes: causes, characterization, and effect on
electric field measurement by the device",
type = "Thesis ({M.S.})",
school = "Boston University",
address = "Boston, MA, USA",
pages = "v + 121",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Boston University. --- College of Engineering ---
Theses.",
}
@Article{Watanuki:1983:EAC,
author = "Osaaki Watanuki and Milo{\v{s}} D. Ercegovac",
title = "Error analysis of certain floating-point on-line
algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-32",
number = "4",
pages = "352--358",
month = apr,
year = "1983",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1983.1676236",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65G05",
MRnumber = "85h:65099",
bibdate = "Sun Jul 10 10:01:08 MDT 2011",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676236",
abstract = "he properties of redundant number system in
significand (mantissa) representation are studied and
the range of redundant significand is derived. From the
range of the redundant significand and the absolute
error of on-line operations, the MRRE (maximum relative
representation error) is defined and analyzed for
floating-point on-line addition and multiplication.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
catcode = "G.1.0; G.1.0",
CRclass = "G.1.0 General; G.1.0 Error analysis; G.1.0 General;
G.1.0 Parallel algorithms",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis; Mathematics of Computing, NUMERICAL
ANALYSIS, General, Parallel algorithms",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
guideno = "06565",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
reviewer = "Oliver, J",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@MastersThesis{Williams:1983:BFP,
author = "Bertrand Jeffery Williams",
title = "A bit-serial floating point multiply\slash add
architecture for signal processing applications",
type = "Electrical Engineering Thesis ({M.S.})",
school = "Texas A\&M University",
address = "College Station, TX, USA",
pages = "x + 97",
year = "1983",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Signal processing.",
}
@Article{Wingert:1983:ITA,
author = "J. A. Wingert",
title = "Improved Table-assisted Addition and Multiplication
Methods",
journal = j-IBM-TDB,
volume = "25",
number = "9",
pages = "4742--4743",
month = feb,
year = "1983",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@InProceedings{Yoshida:1983:FPR,
author = "Kaoru Yoshida",
title = "Floating-Point Recurring Rational Arithmetic System",
crossref = "IEEE:1983:PSC",
pages = "194--200",
year = "1983",
bibdate = "Tue Nov 13 15:58:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Yoshida.pdf",
abstract = "Major computer arithmetic systems are based on the
concept of realizing only terminate rationals in
positional notation. This paper proposes a new
arithmetic scheme of indicating periodicity in the
radix representation of a mantissa to realize recurring
rationals as well as terminate rationals. A new
arithmetic system adopting the scheme, called the
``FLP/R* arithmetic system'', is proposed. Properties
of the FLP/R* numbers and the procedure of the FLP/R*
arithmetic are described.",
acknowledgement = ack-nhfb,
keywords = "ARITH-6; rational arithmetic",
}
@Article{Ypma:1983:ERE,
author = "T. J. Ypma",
title = "The effect of rounding errors on {Newtonlike}
methods",
journal = j-IMA-J-NUMER-ANAL,
volume = "3",
number = "1",
pages = "109--118",
year = "1983",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G05 (65H05)",
MRnumber = "84h:65047",
MRreviewer = "Ren{\'e} Alt",
bibdate = "Sat Dec 23 17:06:35 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@InProceedings{Abruzzo:1984:ACA,
author = "J. Abruzzo",
title = "Applicability of {CORDIC} Algorithm to Arithmetic
Processing",
crossref = "Kirk:1984:CRE",
pages = "79--86",
year = "1984",
bibdate = "Thu Sep 01 11:21:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Agrawal:1984:ACB,
author = "V. K. Agrawal and S. Murugesan",
title = "Algorithm converts {BCD} fractions to binary",
journal = j-EDN,
volume = "29",
number = "13",
pages = "278--280",
month = jun,
year = "1984",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:16:10 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Alia:1984:VAD,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} algorithm for direct and reverse conversion
from weighted binary number system to residue number
system",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "12",
pages = "1033--1039",
month = dec,
year = "1984",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/TC.1984.1676355",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23552",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "Residue Number Systems (RNS) are proved to be useful
in many applications, as for example in signal
processing. In this paper, a VLSI computing
architecture is proposed for converting an integer
number N from the weighted binary representation into
\ldots{}",
}
@InProceedings{Ancona:1984:PET,
author = "M. Ancona and G. Dodero and F. Ricci",
title = "A portable environment for teaching mathematical
software development",
crossref = "Ford:1984:TML",
pages = "135--145",
year = "1984",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See main entry CR, Rev. 8508--0689.",
acknowledgement = ack-nhfb,
content = "ALGORITHMS; DESIGN; LANGUAGES; STANDARDIZATION",
procloc = "Proceedings paper",
subject = "G. Mathematics of Computing; G.4 MATHEMATICAL
SOFTWARE; K. Computing Milieux; K.6 MANAGEMENT OF
COMPUTING AND INFORMATION SYSTEMS; D. Software; D.2
SOFTWARE ENGINEERING; K. Computing Milieux; K.3
COMPUTERS AND EDUCATION",
subjects = "mathematics of computing, mathematical software,
portability; computing milieux, management of computing
and information systems, software management, software
development; software, software engineering,
distribution and maintenance, portability; computing
milieux, computers and education, computer and
information science education, computer science
education",
wsub = "A. C. R. Newbery",
}
@Article{Anonymous:1984:CPD,
author = "Anonymous",
title = "Correction to {``A Pipelined Distributed Arithmetic
PFFT Processor''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "3",
pages = "288--288",
month = mar,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676429",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See \cite{Chow:1983:PDA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676429",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Bell:1984:RMR,
author = "M. {Bell, Jr.} and W. Jenkins",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '84}",
title = "A residue to mixed radix converter and error checker
for a five-moduli residue number system",
volume = "??",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "242--245",
year = "1984",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A design is presented for an experimental device which
converts data from residue representation to mixed
radix representation while simultaneously checking for
single digit errors. The experimental system has a high
speed pipelined architecture and \ldots{}",
}
@Article{Black:1984:NIS,
author = "Cheryl M. Black and Robert P. Burton and Thomas M.
Miller",
title = "The Need for an Industry Standard of Accuracy for
Elementary-Function Programs",
journal = j-TOMS,
volume = "10",
number = "4",
pages = "361--366",
month = dec,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2701.356101",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 20:32:29 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Bollen:1984:NSD,
author = "J. A. M. Bollen",
title = "Numerical Stability of Descent Methods for Solving
Linear Equations",
journal = j-NUM-MATH,
volume = "43",
number = "3",
pages = "361--377",
year = "1984",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65G05 (65F10)",
MRnumber = "85f:65041",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Department of Appl. Maths., Twente University of
Technol., Enschede, Netherlands",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "descent methods; digital arithmetic; error analysis;
floating point arithmetic; Gauss-Southwell method;
gradient method; linear differential equations; linear
equations; linear systems; numerical stability;
roundoff error analysis; stability",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Boney:1984:GTD,
author = "J. Boney",
title = "Goals and tradeoffs in the design of the {MC68881}
floating point coprocessor",
crossref = "NCC:1984:ACP",
pages = "107--113",
year = "1984",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Borwein:1984:AGM,
author = "J. M. Borwein and P. B. Borwein",
title = "The Arithmetic-Geometric Mean and Fast Computation of
Elementary Functions",
journal = j-SIAM-REVIEW,
volume = "26",
number = "3",
pages = "351--366",
month = jul,
year = "1984",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1026073",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65D20 (26A09)",
MRnumber = "86d:65029",
MRreviewer = "S. Conde",
bibdate = "Sat Mar 29 09:53:48 MDT 2014",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
http://epubs.siam.org/toc/siread/26/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
abstract = "We produce a self contained account of the
relationship between the Gaussian arithmetic-geometric
mean iteration and the fast computation of elementary
functions. A particularly pleasant algorithm for pi is
one of the by-products.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
classification = "723; 921",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "AGM (Arithmetic-Geometric Mean); arithmetic-geometric
mean; calculation of pi; computational methods;
elliptic functions; Iterative Methods; mathematical
techniques; numerical mathematics",
onlinedate = "July 1984",
}
@InProceedings{Braddock:1984:ASP,
author = "M. Braddock and V. Shahan",
title = "Amplifying System Performance in Floating-point
Intensive Applications with the {MC68881}",
crossref = "Mini-Micro:1984:MMS",
pages = "6/2/1--7",
year = "1984",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Butterfield:1984:MT,
author = "J. Butterfield",
title = "Math and Tables",
journal = j-COMPUTE,
volume = "6",
number = "9",
pages = "134--135",
month = sep,
year = "1984",
CODEN = "COMPER",
ISSN = "0194-357X",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Compute",
}
@Article{Caraiscos:1984:REA,
author = "C. Caraiscos and Bede Liu",
title = "A roundoff error analysis of the {LMS} adaptive
algorithm",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "32",
number = "1",
pages = "34--41",
month = feb,
year = "1984",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The steady state output error of the least mean square
(LMS) adaptive algorithm due to the finite precision
arithmetic of a digital processor is analyzed. It is
found to consist of three terms: (1) the error due to
the input data quantization, (2) the \ldots{}",
}
@Book{Cavanagh:1984:DCA,
author = "Joseph J. F. Cavanagh",
title = "Digital Computer Arithmetic: Design and
Implementation",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xi + 468",
year = "1984",
ISBN = "0-07-010282-1",
ISBN-13 = "978-0-07-010282-8",
LCCN = "QA76.9.C62 C38 1984",
bibdate = "Sat May 18 14:16:35 2002",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$21.95",
acknowledgement = ack-nj,
}
@MastersThesis{Cheng:1984:FPC,
author = "Doreen Y. Cheng",
title = "A floating point coprocessor for the {Butterfly}
multiprocessor system: research project",
type = "Thesis ({M.S. in Electrical Engineering})",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "51 + 38",
month = may,
year = "1984",
bibdate = "Wed Nov 25 08:35:11 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Clarke:1984:AAR,
author = "M. R. Clarke",
title = "An Analytical Approach to Rounding",
journal = j-J-APPL-STAT,
volume = "11",
number = "1",
pages = "12--20",
year = "1984",
CODEN = "????",
DOI = "https://doi.org/10.1080/02664768400000003",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:15:48 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "28 Jul 2006",
}
@Article{Clenshaw:1984:BFP,
author = "C. W. Clenshaw and F. W. J. Olver",
title = "Beyond Floating Point",
journal = j-J-ACM,
volume = "31",
number = "2",
pages = "319--328",
month = apr,
year = "1984",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/62.322429",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65G05",
MRnumber = "819 141",
bibdate = "Wed Jan 15 18:12:53 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
abstract = "A new number system is proposed for computer
arithmetic based on iterated exponential functions. The
main advantage is to eradicate overflow and underflow,
but there are several other advantages and these are
described and discussed.",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Lancaster, Dep of Mathematics,
Lancaster, Engl",
classification = "723",
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
journalabr = "J Assoc Comput Mach",
keywords = "computer arithmetic; computer metatheory; error
analysis; mathematical techniques --- Digital
Arithmetic; overflow; rounding error; underflow",
}
@Article{Cody:1984:PRW,
author = "William J. {Cody, Jr.} and Jerome T. Coonen and David
M. Gay and K. Hanson and David Hough and W. Kahan and
R. Karpinski and John F. Palmer and F. N. Ris and D.
Stevenson",
title = "A Proposed Radix- and Word-length-independent Standard
for Floating-Point Arithmetic",
journal = j-IEEE-MICRO,
volume = "4",
number = "4",
pages = "86--100",
month = jul # "\slash " # aug,
year = "1984",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1984.291224",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Nov 8 14:50:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@PhdThesis{Coonen:1984:CPS,
author = "Jerome Toby Coonen",
title = "Contributions to a Proposed Standard for Binary
Floating-Point Arithmetic",
type = "Thesis ({Ph.D.} in Mathematics)",
school = "Department of Mathematics, University of California at
Berkeley",
address = "Berkeley, CA, USA",
pages = "320",
day = "18",
month = dec,
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the fall of 1977 the Institute of Electrical and
Electronics Engineers commissioned working group 754 to
draft a standard for binary floating-point arithmetic.
It was intended to prevent the proliferation of
disparate arithmetics in the new microprocessor
industry. At that time there were so many different
flavors of arithmetic available on mainframes and
minicomputers that the cost of reconciling their
differences in numerical software had become, and
remains, staggering. Now, more than five years later,
draft 10.0 of the proposed standard has been voted out
of the working group for IEEE approval.\par
This thesis consists of a set of ``footnotes'' to the
proposed standard. The first of them, an implementation
guide published in January 1980, served as a working
draft of the standard for over a year. The remaining
chapters unfolded as the proposed standard did. They
include an analysis of gradual underflow, the most
controversial feature of the standard; an exhaustive
discussion of radix conversion, which has been
specified in the proposed standard only up to a
worst-case error bound; and a revised version of the
arithmetic test suite which has been available in
machine-readable form from the working group.",
acknowledgement = ack-nj # " and " # ack-nhfb,
advisor = "William M. Kahan",
remark = "Doctoral degree conferred December 18, 1984.",
}
@InCollection{Corliss:1984:AGT,
author = "George F. Corliss and Louis B. Rall",
title = "Automatic generation of {Taylor} series in
{Pascal-SC}: {Basic} operations and applications to
differential equations",
crossref = "Anonymous:1984:TFA",
pages = "177--209",
year = "1984",
bibdate = "Fri Dec 8 13:09:09 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Pascal-SC supports user-defined data types,
user-defined operators, and accurate floating point and
interval arithmetic for numerical computations. The
authors implement data types TAYLOR and ITAYLOR
(Interval Taylor) with operators $+$, $-$, $*$, $/$, $
** $, and the functions SQR, SQRT, EXP, SIN, COS,
ARCTAN, and LN. An initial value problem $ y' = y^2 $,
$ y(0) = 1 $, is solved with TAYLOR and with ITAYLOR
types to show that the series generation exhibits a
mild instability which has no significant effect on the
values of the solution computed by analytic
continuation.",
acknowledgement = ack-nj,
comment = "Also appeared as {\sl MRC Technical Summary Report No.
2497}, Mathematics Research Center, University of
Wisconsin-Madison, 1983.",
keywords = "automatic differentiation; stability.; Taylor series",
}
@Article{Cowlishaw:1984:DRL,
author = "M. F. Cowlishaw",
title = "The Design of the {REXX} Language",
journal = j-IBM-SYS-J,
volume = "23",
number = "4",
pages = "326--335",
year = "1984",
CODEN = "IBMSA7",
ISSN = "0018-8670",
bibdate = "Wed Jan 08 16:35:07 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "First published as IBM Hursley Technical Report
TR12.223, October 1983.",
abstract = "One way of classifying computer languages is by two
classes: languages needing skilled programmers, and
personal languages used by an expanding population of
general users. REstructured eXtended eXecutor (REXX) is
a flexible personal language designed with particular
attention to feedback from its users. It has proved to
be effective and easy to use, yet it is sufficiently
general and powerful to fulfill the needs of many
demanding professional applications. REXX is system and
hardware independent, so that it has been possible to
integrate it experimentally into several operating
systems. Here REXX is used for such purposes as command
and macro programming, prototyping, education, and
personal programming. This study introduces REXX and
describes the basic design principles that were
followed in developing it.",
acknowledgement = ack-nhfb,
affiliation = "IBM UK Ltd, Scientific Cent, Winchester, Engl",
affiliationaddress = "IBM UK Ltd, Scientific Cent, Winchester, Engl",
classification = "723",
fjournal = "IBM Systems Journal",
journalabr = "IBM Syst J",
keywords = "command program interpreters; computer operating
systems; computer programming languages; decimal
floating-point arithmetic; language concepts; personal
language; REXX language",
remark = "REXX supports arbitrary precision arithmetic with up
to $ 10^9 $ digits, and an exponent range of $ \pm 10^9
$. This capability was added to REXX in 1981.",
}
@Article{Demmel:1984:URN,
author = "James Demmel",
title = "Underflow and the reliability of numerical software",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "5",
number = "4",
pages = "887--919",
month = dec,
year = "1984",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65G05",
MRnumber = "85m:65035",
MRreviewer = "G. Alefeld",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Div. of Computer Science, California University,
Berkeley, CA, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "codes; digital arithmetic; eigenvalue calculation;
Gaussian elimination; gradual underflow; numerical
software; polynomial evaluation; reliability; roundoff;
roundoff errors; store zero; uncertainty; underflow
mechanisms",
treatment = "T Theoretical or Mathematical",
}
@Article{Demsky:1984:MMC,
author = "J. Demsky and M. Schlesinger and R. D. Kent",
title = "Micro/mini computer program for calculating the square
root of rationals at arbitrary precision",
journal = j-COMP-PHYS-COMM,
volume = "35",
number = "1--3",
pages = "C-877",
month = "????",
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(84)82981-1",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 25 10:56:58 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465584829811",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Dietrich:1984:FPR,
author = "D. Dietrich and R. Fischer",
title = "{Floating-Point-Routinen, entwickelt f{\"u}r
Mikrorechner} \toenglish {Floating-point Routines
Developed for Microcomputers} \endtoenglish",
journal = j-ELEKTRONIKER,
volume = "8",
pages = "49--54",
year = "1984",
CODEN = "ELKRBL",
ISSN = "0531-9218",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektroniker (Switzerland)",
}
@Article{Duncan:1984:FSF,
author = "Ray Duncan and Martin Tracy",
title = "The {FVG} Standard Floating-Point Extension",
journal = j-DDJ,
volume = "9",
number = "9",
pages = "110--??",
month = sep,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
xxnote = "??Check author order??",
}
@Article{Dunford:1984:SFPa,
author = "Christopher J. Dunford",
title = "{Savage} floating-point benchmark in 8088\slash 8087
assembly language in {16BST}",
journal = j-DDJ,
volume = "9",
number = "7",
pages = "116--??",
month = jul,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Dunford:1984:SFPb,
author = "Christopher J. Dunford",
title = "{Savage} floating-point benchmark in {Modula-2} in
{16BST}",
journal = j-DDJ,
volume = "9",
number = "8",
pages = "106--??",
month = aug,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Ercegovac:1984:LAO,
author = "Milo{\v{s}} D. Ercegovac",
title = "On-line arithmetic: An overview",
journal = j-SPIE,
volume = "495",
pages = "86--93",
year = "1984",
bibdate = "Fri Nov 30 06:32:39 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Real Time Signal Processing VII.",
acknowledgement = ack-nhfb,
}
@Article{Ferguson:1984:SFP,
author = "Kenneth M. Ferguson",
title = "{Savage} floating-point benchmark deficiencies of in
{16BST}",
journal = j-DDJ,
volume = "9",
number = "8",
pages = "107--??",
month = aug,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Fisher:1984:UAP,
author = "Gerry Fisher",
title = "Universal Arithmetic Packages",
journal = j-SIGADA-LETTERS,
volume = "3",
number = "6",
pages = "30--47",
month = may # "\slash " # jun,
year = "1984",
CODEN = "AALEE5",
DOI = "https://doi.org/10.1145/998388.998389",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Sep 28 07:33:23 MDT 2000",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://www.adahome.com/Resources/Bibliography/articles.ref;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
note = "See erratum \cite{Froggatt:2015:EAU}.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "universal integer, universal real, rational
arithmetic",
}
@InCollection{Gautschi:1984:QNC,
author = "Walter Gautschi",
title = "Questions of numerical condition related to
polynomials",
crossref = "Golub:1984:SNA",
volume = "24",
pages = "140--177",
year = "1984",
MRclass = "65F35 (65H05)",
MRnumber = "925213",
bibdate = "Fri Feb 9 15:28:14 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Gleditsch:1984:FTR,
author = "Torstein Gleditsch",
title = "Forslag til rask prosessor for flerformat
floating-point aritmetikk. ({Norwegian}) [{Proposal}
for a fast processor for multiformat floating-point
arithmetic]",
type = "Hovedoppgave i informatikk (cand.scient)",
school = "Universitetet i Oslo",
address = "Oslo, Norway",
year = "1984",
bibdate = "Thu May 09 08:19:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Norwegian",
}
@Article{Goldberg:1984:LVS,
author = "Morton Goldberg",
title = "{LISP} Version of the {Savage} Floating Point
Benchmark in {16BST}",
journal = j-DDJ,
volume = "9",
number = "6",
pages = "82--??",
month = jun,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Book{Gregory:1984:MAE,
author = "Robert Todd Gregory and E. V. Krishnamurthy",
title = "Methods and Applications of Error-Free Computation",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 194",
year = "1984",
ISBN = "0-387-90967-2",
ISBN-13 = "978-0-387-90967-7",
LCCN = "QA297.5 .G735 1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Texts and monographs in computer science",
acknowledgement = ack-nhfb,
keywords = "Approximation theory --- Data processing.;
Floating-point arithmetic.",
shorttableofcontents = "Glossary of Notation / xi \\
I: Residue or Modular Arithmetic / 1 \\
II: Finite-Segment p-adic Arithmetic / 63 \\
III: Exact Computation of Generalized Inverses / 109
IV: Integer Solutions to Linear Equations / 134 \\
V: Iterative Matrix Inversion and the Iterative
Solution of Linear Equations / 162 \\
VI: The Exact Computation of the Characteristic
Bibliography / 186 \\
Index / 191",
tableofcontents = "Glossary of Notation / xi \\
I: Residue or Modular Arithmetic / 1 \\
1. Introduction / 1 \\
2. Single-Modulus Residue Arithmetic / 3 \\
3. Multiple-Modulus Residue Arithmetic / 11 \\
4. Mapping Standard Residue Representations onto
Integers / 17 \\
5. Single-Modulus Residue Arithmetic with Rational
Numbers / 23 \\
6. The Forward Mapping and the Inverse Mapping / 31 \\
7. Multiple-Modulus Residue Arithmetic with Rational
Numbers / 49 \\
II: Finite-Segment p-adic Arithmetic / 63 \\
1. Introduction / 63 \\
2. The Field of p-adic Numbers / 63 \\
3. Arithmetic in QP / 73 \\
4. A Finite-Segment p-adic Number System / 79 \\
5. Arithmetic Operations on Hensel Codes / 90 \\
6. Removing a Leading Zero from a Hensel Code / 99 \\
7. Mapping a Hensel Code onto a Unique Order-N Farey
Fraction / 100 \\
III: Exact Computation of Generalized Inverses / 109
\\
1. Introduction / 109 \\
2. Properties of g-inverses / 110 \\
3. Applications of g-inverses / 116 \\
4. Exact Computation of A+ if A Is a Rational Matrix /
118 \\
5. Failures of Residue Arithmetic and Precautionary
Measures / 131 \\
IV: Integer Solutions to Linear Equations / 134 \\
1. Introduction / 134 \\
2. Theoretical Background / 135 \\
3. The Matrix Formulation of Chemical Equations / 138
\\
4. Solving the Homogeneous System / 140 \\
5. Solving a Non-Homogeneous System / 148 \\
6. Solving Interval Linear Programming Problems / 150
\\
7. The Solution of Systems of Mixed-Integer Linear
Equations / 155 \\
V: Iterative Matrix Inversion and the Iterative
Solution of Linear Equations / 162 \\
1. Introduction / 162 \\
2. The Newton--Schultz Method for the Matrix Inverse /
163 \\
3. Iterative Solution of a Linear System / 169 \\
4. Iterative Computation of g-inverses / 174 \\
VI: The Exact Computation of the Characteristic
Polynomial of a Matrix / 180 \\
1. Introduction / 180 \\
2. The Algorithm Applied to Lower Hessenberg Matrices /
181 \\
Bibliography / 186 \\
Index / 191",
}
@Article{Guest:1984:RNS,
author = "C. C. Guest and M. M. Mirsalehi and T. K. Gaylord",
title = "Residue Number System Truth-Table Look-Up Processing
--- Moduli Selection and Logical Minimization",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "10",
pages = "927--931",
month = oct,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676355",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676355;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35232",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Truth table look-up processing using binary coded
residue numbers is investigated for full-precision
addition and multiplication for implementations using
either electronic or optical technologies. The
logically minimized numbers of input \ldots{}",
}
@Book{Hamacher:1984:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Second",
pages = "xvi + 590",
year = "1984",
ISBN = "0-07-025683-7",
ISBN-13 = "978-0-07-025683-5",
LCCN = "QA76.9.A73 H351 1984",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$34.95",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
catcode = "C; B",
content = "The reviewer recommends this book to those who are
interested in learning the basics of computer
organization, particularly at the hardware and device
level. This book does not deal with the concepts
related to computer organization from an abstract,
mathematical level. It also does not attempt to
describe the computer organization using a high-level
language. Instead, the authors concentrate on
uniprocessing systems, with a large number of examples
drawn from VAX-11, IBM 370, and HP 3000. The book does
not cover multiprocessors.\par
The organization of the book is summarized here.
Chapter 1 introduces a number of terms. Chapters 2 and
3 concentrate in detail (a total of 101 pages) on the
addressing methods and instruction sets, with examples
taken primarily from the above mentioned machines.
Chapters 4 and 5 (a total of 50 pages) deal with the
control unit for the instruction fetch and execute,
with Chapter 5 being devoted to microprogrammed control
and bit slice designs. In Chapter 6 (a total of 64
pages) the authors cover Input/Output organization,
which includes a good deal about the
synchronous/asynchronous I/O operations, I/O
interfaces, etc. Chapter 7 presents the usual material
on the fixed- and floating-point arithmetic. \ldots{}",
CRnumber = "8509-0786",
descriptor = "Computer Systems Organization, GENERAL; Hardware,
GENERAL",
genterm = "DESIGN",
reviewer = "A. Deb",
subject = "C. Computer Systems Organization; C.0 GENERAL; B.
Hardware; B.0 GENERAL",
}
@Article{Honma:1984:IAE,
author = "Hitoshi Honma and Masahiko Sagawa",
title = "Improving the accuracy and error analysis in
floating-point {FFT} computation",
journal = j-ELECTRON-COMMUN-JPN,
volume = "67",
number = "11",
pages = "9--18",
year = "1984",
CODEN = "ECOJAL",
ISSN = "0424-8368",
MRclass = "65T05 (65G05 94A11)",
MRnumber = "86g:65238",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan",
}
@TechReport{IBM:1984:ISR,
author = "{IBM Corporation}",
title = "{IBM System\slash 370 RPQ}. High Accuracy Arithmetic",
type = "Technical report",
number = "SA22-7093-0",
institution = pub-IBM,
address = pub-IBM:adr,
month = jan,
year = "1984",
bibdate = "Wed Oct 04 09:39:49 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bitsavers.trailing-edge.com/pdf/ibm/370/princOps/SA22-7093-0_High_Accuracy_Arithmetic_Jan84.pdf",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point dot product; accurate
floating-point summation; ACRITH",
remark = "According to IBM Web pages, ACRITH was withdrawn in
1991, and replaced by ACRITH XSC; however, I have yet
to be able to find online documentation for that
system.",
tableofcontents = "HIGH-ACCURACY-ARITHMETIC FACILITY / 1 \\
Floating-Point Instructions With Rounding Options / 1
\\
Normalization / 2 \\
Rounding / 2 \\
Rounding Modes / 2 \\
Guard Digit, Rounding Digit, and Sticky Bit / 3 \\
Arithmetic Exceptions / 4 \\
Default Result for Exponent Underflow / 5 \\
Floating-Point Accumulator / 5 \\
Vectors / 5 \\
Accumulator Layout / 6 \\
Accumulator Status Area / 8 \\
Accumulator Overflow / 9 \\
Storage-Operand Consistency / 9 \\
Instructions / 10 \\
ADD ACCUMULATOR TO ACCUMULATOR / 11 \\
ADD TO ACCUMULATOR / 12 \\
ADD WITH ROUNDING / 12 \\
CLEAR ACCUMULATOR / 13 \\
DIVIDE WITH ROUNDING / 13 \\
LOAD WITH ROUNDING / 14 \\
MULTIPLY AND ACCUMULATE / 15 \\
MULTIPLY WITH ROUNDING / 17 \\
ROUND FROM ACCUMULATOR / 17 \\
SUBTRACT ACCUMULATOR FROM ACCUMULATOR / 18 \\
SUBTRACT FROM ACCUMULATOR / 18 \\
SUBTRACT WITH ROUNDING / 19 \\
INDEX / 21",
}
@Book{ISO:1984:IID,
author = "{International Organization for Standardization}",
key = "ISO",
title = "{ISO\slash IEC DIS 10858}: {Information} technology
--- {Radix-independent} floating-point arithmetic",
publisher = pub-ISO,
address = pub-ISO:adr,
pages = "????",
year = "1984",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri May 28 21:52:25 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.iso.ch/cate/d18890.html",
acknowledgement = ack-nhfb,
}
@Article{Jones:1984:SRM,
author = "Christopher B. Jones",
title = "A Significance Rule for Multiple-Precision
Arithmetic",
journal = j-TOMS,
volume = "10",
number = "1",
pages = "97--107",
month = mar,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/356068.356076",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G05 (65G10)",
MRnumber = "86e:65063",
bibdate = "Sun Sep 04 20:02:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Multiple-precision arithmetic overcomes the round-off
error incurred in conventional floating-point
arithmetic, at the cost of increased processing
overhead. Significance arithmetic takes into account
the inexactness of the operands of a calculation, but
can lead to loss of significant digits after a long
series of operations. A new technique is described
which alleviates the overhead of multiple-precision
arithmetic by allowing nonsignificant digits to be
discarded, while limiting the significance loss per
operation to a controllable and acceptable rate. The
technique is based on storing an inexact number
interval, using a criterion of significance to
determine the precision with which the limits of
interval should be stored. A procedure referred to as a
significance rule uses this criterion to remove some of
the nonsignificant digits from the limits of an
interval prior to storage. A certain number of
nonsignificant digits are retained as guard digits.
Calculations are performed using exact interval
arithmetic and the significance-rule procedure is
invoked after each operation to remove superfluous
digits. Round-off in the procedure causes a slight
increase in the interval width on each operation. This
results in a cumulative loss of significance at a rate
related to the number of guard digits.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Karp:1984:ELS,
author = "A. H. Karp",
title = "Exponential and Logarithm by Sequential Squaring",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "5",
pages = "462--464",
month = may,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676464",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Katzan:1984:IA,
author = "Harry Katzan",
title = "Invitation to {Ada}",
publisher = "PBI",
address = "New York, NY, USA",
pages = "x + 173",
year = "1984",
ISBN = "0-89433-239-2 (paperback)",
ISBN-13 = "978-0-89433-239-5 (paperback)",
LCCN = "QA76.73.A35 K36 1984",
bibdate = "Wed Oct 13 06:37:40 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$14.95",
series = "Petrocelli invitation to series",
acknowledgement = ack-nhfb,
remark = "See \cite[p. 1.10]{Coonen:1984:CPS} for negative
comments about the floating-point model for Ada in the
predecessor of this book \cite{Katzan:1982:IAA}.",
subject = "Ada (Computer program language)",
}
@Article{Kawabata:1984:SFP,
author = "Hugh M. Kawabata",
title = "{Savage} Floating Point Benchmark in {Fortran} in
{16BST}",
journal = j-DDJ,
volume = "9",
number = "1",
pages = "83--??",
month = jan,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Book{Koopman:1984:FFP,
author = "Philip J. Koopman",
title = "{FORTH} floating point",
publisher = "Mountain View Pr.",
address = "Mountain View, CA, USA",
edition = "Second",
pages = "346",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "MVP-FORTH series; v. 3",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; FORTH (Computer program
language)",
}
@Article{Korn:1984:ISD,
author = "G. A. Korn",
title = "Interactive simulation with a direct-executing,
floating-point equation language",
journal = j-SYS-ANA-MODEL-SIM,
volume = "1",
number = "1",
pages = "45--54",
year = "1984",
CODEN = "SAMSEC",
ISSN = "0232-9298",
ISSN-L = "0232-9298",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "The University of Arizona, Tucson",
bibno = "43792",
catcode = "I.6.2; I.6.3",
CRclass = "I.6.2 Simulation Languages; I.6.3 Applications",
descriptor = "Computing Methodologies, SIMULATION AND MODELING,
Simulation Languages; Computing Methodologies,
SIMULATION AND MODELING, Applications",
fjournal = "Systems analysis, modelling, simulation",
genterm = "THEORY; DESIGN; LANGUAGES",
guideno = "1988-14427",
journalabbrev = "Syst. Anal. Model. Simul.",
subject = "I. Computing Methodologies; I.6 SIMULATION AND
MODELING; I. Computing Methodologies; I.6 SIMULATION
AND MODELING",
}
@Article{Kornerup:1984:CFP,
author = "Peter Kornerup and David W. Matula",
title = "Correction to `{`Finite Precision Rational Arithmetic:
An Arithmetic Unit''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "7",
pages = "682--682",
month = jul,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.5009346",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009346",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lin:1984:DSD,
author = "Ming-Liang Lin and Ernst Leiss and Bayliss McInnis",
title = "Division and sign detection algorithms for residue
number systems",
journal = j-COMPUT-MATH-APPL,
volume = "10",
number = "4--5",
pages = "331--342",
month = "????",
year = "1984",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:00:50 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122184900610",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Ling:1984:NAS,
author = "Fuyun Ling and J. Proakis",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '84}",
title = "Numerical accuracy and stability: Two problems of
adaptive estimation algorithms caused by round-off
error",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "571--574",
year = "1984",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper investigates the numerical accuracy and the
numerical stability of adaptive estimation algorithms.
A feedback system model is provided to investigate the
numerical stability of the algorithms. Simulation
results on the comparison of \ldots{}",
}
@Article{Longo:1984:CFU,
author = "S. A. Longo",
title = "Calculating Functions using {Ada}",
journal = j-J-PAS-ADA,
volume = "3",
number = "4",
pages = "34--36",
month = jul # "--" # aug,
year = "1984",
ISSN = "0735-1232",
bibdate = "Fri Dec 08 13:05:34 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of Pascal and Ada",
}
@InProceedings{Look:1984:CSH,
author = "H. W. Look",
title = "Compatible software and hardware implementations
permitted by {IEEE} standards for binary floating-point
arithmetic",
crossref = "NCC:1984:ACP",
pages = "101--105",
year = "1984",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Lorenz:1984:MIL,
author = "E. Lorenz and R. Sandau",
title = "{M{\"o}glichkeiten der Implementierung
leistungsf{\"a}higer Multiplikationsprogramme in
Mikrorechnersystemen} \toenglish {Possibilities of the
Implementation of Efficient Multiplication Instructions
in Microcomputer Systems} \endtoenglish",
journal = j-NACH-ELEK,
volume = "34",
number = "8",
pages = "288--290",
month = "????",
year = "1984",
CODEN = "NTELAP",
ISSN = "0323-4657",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Nachrichtentechnik Elektronik",
}
@TechReport{Mackin:1984:FFG,
author = "Michael A. Mackin and James F. Soeder",
title = "Floating-point function generation routines for 16-bit
microcomputers",
institution = "National Aeronautics and Space Administration",
address = "Washington DC, USA",
pages = "????",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "NASA technical memorandum; 83783",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.15:83783 830-D (MF)",
keywords = "Microcomputers --- Programming.",
remark = "Distributed to depository libraries in microfiche.
Microfiche. [Washington, D.C.?: National Aeronautics
and Space Administration], 1984. 1 microfiche.",
}
@Article{Mactaggart:1984:SCR,
author = "I. Ross Mactaggart and Mervyn A. Jack",
title = "A single chip radix-$2$ {FFT} butterfly architecture
using parallel data distributed arithmetic",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-19",
number = "3",
pages = "368--373",
month = jun,
year = "1984",
CODEN = "IJSCBC",
DOI = "https://doi.org/10.1109/JSSC.1984.1052151",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Jul 07 10:57:50 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Mansfield:1984:CAC,
author = "Richard Mansfield",
title = "A Complete Axiomatization of Computer Arithmetic",
journal = j-MATH-COMPUT,
volume = "42",
number = "166",
pages = "623--635",
month = apr,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G99 (03B70 03C70 68Q40)",
MRnumber = "85k:65040",
MRreviewer = "R. P. Brent",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C5230 (Digital arithmetic methods)",
corpsource = "Department of Math., Pennsylvania State University,
University Park, PA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "axiom system; complete axiomatization; computer
arithmetic; digital arithmetic; multiplication; rounded
addition; rounded arithmetic",
treatment = "T Theoretical or Mathematical",
}
@Article{Miller:1984:ILA,
author = "D. Miller and J. Polky",
title = "An implementation of the {LMS} algorithm in the
residue number system",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "5",
pages = "452--461",
month = may,
year = "1984",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/TC.1984.1676355",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23556",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "The Residue Arithmetic Adaptive Filter (RAAF)
processor performs the least mean square (LMS)
algorithm using 60 ns discrete PROM-latch combinations
for the residue operations. Parallel and pipeline
techniques are used throughout. Since the LMS
\ldots{}",
}
@Article{Moran:1984:SST,
author = "Thomas W. Moran",
title = "Some Spreadsheet Tests of the {Savage} Floating-Point
Benchmark in {16BST}",
journal = j-DDJ,
volume = "9",
number = "8",
pages = "106--??",
month = aug,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InCollection{Munzel:1984:RAE,
author = "Georg M{\"u}nzel",
booktitle = "Parallel computing 83 (Berlin, 1983)",
title = "Residue arithmetic for exact calculations on the
{DAP}",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "199--204",
year = "1984",
MRclass = "65W05",
MRnumber = "MR809397 (86k:65141)",
bibdate = "Thu Nov 8 14:50:29 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Murray:1984:SFA,
author = "J. T. Murray",
title = "Sin\slash Cos Functions via Approximations Plus Error
Compensation",
journal = j-IBM-TDB,
volume = "26",
number = "10A",
pages = "4967--4968",
month = mar,
year = "1984",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Misc{OliverWhiteheadQuintet:1984:FN,
author = "Oliver Whitehead Quintet",
title = "Free for now",
publisher = "Justin Time Records",
address = "????",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 sound disc",
acknowledgement = ack-nhfb,
keywords = "Jazz --- 1981-1990.",
remark = "Brief record. Free for now --- Six-string waltz ---
Old friend --- Invention; Excuses, excuses --- Getting
away --- Woman in blue --- Floating point --- Crazy
season --- Do it with your socks on. Performed by the
Oliver Whitehead Quintet. JUST 4; Justin Time Records",
}
@Book{Palmer:1984:P,
author = "John F. Palmer and Stephen P. Morse",
title = "The 8087 Primer",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "viii + 182",
year = "1984",
ISBN = "0-471-87569-4",
ISBN-13 = "978-0-471-87569-7",
LCCN = "QA76.8.I2923 P34 1984",
bibdate = "Wed Dec 15 10:40:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Excellent coverage of the 8087 numeric coprocessor by
the chief architects of the Intel 8087 (Palmer) and
8086 (Morse). Contains many candid statements about
design decisions in these processors. A must for
serious assembly language coding of the 8087 and 80287
chips. See also \cite{Intel:1985:PRM}.",
acknowledgement = ack-nhfb,
}
@Article{Parker:1984:CCS,
author = "J. R. Parker",
title = "On Converting Character Strings to Integers",
journal = j-INFO-PROC-LETT,
volume = "19",
number = "1",
pages = "17--19",
day = "26",
month = jul,
year = "1984",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/0020-0190(84)90122-4",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0020019084901224",
acknowledgement = ack-nhfb,
classification = "723; C4240 (Programming and algorithm theory)",
corpsource = "Department of Computer Sci., University of Calgary,
Calgary, Alta., Canada",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
journalabr = "Inf Process Lett",
keywords = "character strings; character to integer conversion;
computer programming; integer overflow; programming
theory",
treatment = "T Theoretical or Mathematical",
}
@Article{Pei:1984:CAD,
author = "Soo-Chang Pei and Kuo-Chih Ho",
title = "Comments on {``Adaptive digital control implemented
using residue number systems''}",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "29",
number = "9",
pages = "863--863",
month = sep,
year = "1984",
CODEN = "IETAA9",
DOI = "https://doi.org/10.1109/TC.1984.1676355",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Tan:1982:ADC}.",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24217",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
keywords = "residue arithmetic; residue number system",
summary = "The aim of this correspondence is to correct some
errors and modify Tan and McInnis residue number
decoding scheme into a simplified \ldots{}",
}
@Article{Pfenninger:1984:DES,
author = "E. Pfenninger",
title = "{Divisionsalgorithmus -- einfach und schnell}
\toenglish {Division Algorithms -- Simple and Fast}
\endtoenglish",
journal = j-ELEKTRONIKER,
volume = "15",
pages = "62--64",
year = "1984",
CODEN = "ELKRBL",
ISSN = "0531-9218",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektroniker (Switzerland)",
}
@Article{Pountain:1984:PM,
author = "D. Pountain",
title = "{PROLOG} on Microcomputers",
journal = j-BYTE,
volume = "9",
number = "13",
pages = "355--62",
month = dec,
year = "1984",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
LCCN = "QA 76.5 B98",
bibdate = "Thu Nov 8 14:50:29 2007",
bibsource = "/usr/local/src/bib/bibliography/Ai/log.prog.85.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Discusses micro-PROLOG, a dialect of PROLOG originally
written for the z80 microprocessor, which was the first
microcomputer implementation of the language. The
micro-PROLOG language is an interpreted language. A
program consists of a database of facts and rules that
you can query to solve problems. Logical propositions
replace computer-oriented instructions. Micro-PROLOG
has floating point arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
keywords = "PROLOG",
}
@Article{Prince:1984:SFP,
author = "Thomas Prince",
title = "{Savage} Floating Point Benchmark in Logo in {16BST}",
journal = j-DDJ,
volume = "9",
number = "6",
pages = "82--??",
month = jun,
year = "1984",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Rauchwerk:1984:MBF,
author = "M. D. Rauchwerk",
title = "A micro\-pro\-cess\-or-based fast floating point
library",
crossref = "IEEE:1984:CPI",
pages = "488--490",
year = "1984",
bibdate = "Thu Sep 01 12:03:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Regener:1984:MID,
author = "Eric Regener",
title = "Multiprecision Integer Division Examples Using
Arbitrary Radix",
journal = j-TOMS,
volume = "10",
number = "3",
pages = "325--328",
month = sep,
year = "1984",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1271.2738",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65V05",
MRnumber = "86g:65241",
bibdate = "Sun Sep 04 20:18:56 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See also \cite{BrinchHansen:1994:MLD}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InCollection{Schryer:1984:DCF,
author = "N. L. Schryer",
title = "Determination of Correct Floating-Point Model
Parameters",
crossref = "Cowell:1984:SDM",
pages = "360--366",
year = "1984",
bibdate = "Thu Sep 08 17:23:39 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Shahan:1984:MIF,
author = "V. Shahan",
title = "The {MC68881}: The {IEEE} Floating Point Standard
Reduced to One {VLSI} Chip",
crossref = "IEEE:1984:ILD",
pages = "172--176",
year = "1984",
bibdate = "Wed Sep 7 22:31:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Shen:1984:DET,
author = "J. P. Shen and F. J. Ferguson",
title = "The Design of Easily Testable {VLSI} Array
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "6",
pages = "554--560",
month = jun,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.1676480",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676480",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Shively:1984:CTG,
author = "R. R. Shively and W. V. Robinson and D. E. Orton",
title = "Cascading Transmission Gates to Enhance Multiplier
Performance",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "7",
pages = "677--679",
month = jul,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.5009343",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009343",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Sips:1984:BSA,
author = "Henk J. Sips",
title = "Bit-Sequential Arithmetic for Parallel Processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-33",
number = "1",
pages = "7--20",
month = jan,
year = "1984",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1984.5009311",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 09:22:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009311",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Smoktunowicz:1984:BCI,
author = "Alicja Smoktunowicz and Jolanta Sokolnicka",
title = "Binary cascades iterative refinement in
doubled-mantissa arithmetics",
journal = j-BIT,
volume = "24",
number = "1",
pages = "123--127",
month = mar,
year = "1984",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934524",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F05 (65G05)",
MRnumber = "85i:65039",
MRreviewer = "A. Bultheel",
bibdate = "Wed Jan 4 18:52:18 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=24&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=24&issue=1&spage=123",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Soderstrand:1984:AQL,
author = "M. Soderstrand and G. Poe",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '84}",
title = "Application of quadratic-like complex residue number
system arithmetic to ultrasonics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "484--487",
year = "1984",
CODEN = "ITCOB4",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The concept of a ``Quadratic-Like'' Complex Residue
Number System is introduced in which certain purely
imaginary numbers exist as reals within the system. It
is shown that the desirable properties of a Quadratic
Complex Residue Number System with \ldots{}",
}
@Article{Soderstrand:1984:PRR,
author = "M. Soderstrand and B. Sinha",
title = "A pipelined recursive residue number system digital
filter",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "4",
pages = "415--417",
month = apr,
year = "1984",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/TC.1983.1676240",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23555",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "The well-known advantages of pipelining as applied to
Finite Impulse Response (FIR) Residue Number System
(RNS) arithmetic digital filters is extended to the
important area of Infinite Impulse Response (IIR)
digital filters through a new technique \ldots{}",
}
@Book{Steele:1984:CLL,
author = "Guy L. Steele",
title = "{COMMON LISP}: the language",
publisher = pub-DP,
address = pub-DP:adr,
pages = "xii + 465",
year = "1984",
ISBN = "0-932376-41-X (paperback)",
ISBN-13 = "978-0-932376-41-1 (paperback)",
LCCN = "QA76.73.L23S73 1984",
bibdate = "Wed Jan 29 17:05:18 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With contributions by Scott E. Fahlman and Richard P.
Gabriel and David A. Moon and Daniel L. Weinreb.",
acknowledgement = ack-nhfb,
keywords = "COMMON LISP (Computer program language)",
remark = "From \cite{Steele:2004:RHP}: ``In general,
computations with floating-point numbers are only
approximate.''",
}
@InProceedings{Stetter:1984:SDC,
author = "Hans J. Stetter",
title = "Sequential defect correction for high-accuracy
floating-point algorithms",
crossref = "Griffiths:1984:NAP",
pages = "186--202",
year = "1984",
DOI = "https://doi.org/10.1007/BFb0099525",
MRclass = "65V05 (65B05 65G05)",
MRnumber = "86j:65188",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Stewart:1984:PWG,
author = "R. G. Stewart",
title = "{P854} Working Group Completes Radix-Independent
Floating-Point Draft",
journal = j-IEEE-MICRO,
volume = "4",
number = "1",
pages = "82--83",
month = jan # "\slash " # feb,
year = "1984",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1984.291326",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Takla:1984:MBF,
author = "N. Takla and M. Hecker",
title = "A Monolithic 64 Bit Floating-Point Coprocessor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-19",
number = "4",
pages = "538--539",
month = aug,
year = "1984",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A double/single-precision floating-point processor
using a titanium disilicide 3.5-$\mu$m NMOS process
achieves double-precision add/subtract, multiply, and
divide in 2, 8, and 16 $\mu$s respectively. The chip
has about 35K devices and is about \ldots{}",
}
@Article{Taylor:1984:BFP,
author = "F. Taylor",
title = "Block floating-point distributed filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "31",
number = "3",
pages = "300--304",
month = mar,
year = "1984",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Distributed filters have been shown to offer an
impressive complexity-throughput tradeoff. In this
correspondence, a precision improvement is made in
distributed filtering using block floating-point
arithmetic. Performance improvement is predicted
\ldots{}",
}
@InProceedings{Teufel:1984:HAO,
author = "Thomas Teufel",
title = "A hardware architecture of an optimal
{BCD}-floating-point processor",
crossref = "Feilmeier:1984:PCP",
pages = "553--560",
year = "1984",
MRclass = "65G05",
MRnumber = "86j:65055",
bibdate = "Mon Apr 14 17:57:50 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Teufel:1984:OG,
author = "T. Teufel",
title = "{Ein optimaler Gleitkommaprozessor} \toenglish {An
Optimal Floating-Point Processor} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1984",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Tricker:1984:ERM,
author = "A. R. Tricker",
title = "Effects of Rounding on the Moments of a Probability
Distribution",
journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN,
volume = "33",
number = "4",
pages = "381--390",
month = dec,
year = "1984",
CODEN = "????",
DOI = "https://doi.org/10.2307/2987741",
ISSN = "0039-0526 (print), 1467-9884 (electronic)",
ISSN-L = "0039-0526",
bibdate = "Thu Jan 22 18:10:22 MST 2015",
bibsource = "http://www.jstor.org/stable/i349978;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jrss-d-1980.bib",
URL = "http://www.jstor.org/stable/2987741",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Royal Statistical Society. Series D
(The Statistician)",
journal-URL = "http://www.jstor.org/journals/00390526.html",
}
@MastersThesis{Trivedi:1984:DVF,
author = "Mrugesh Popatlal Trivedi",
title = "Dianostics of {VLSI} floating-point processors",
type = "Thesis ({M.S.})",
school = "The University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "viii + 98",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@MastersThesis{Truong:1984:FPP,
author = "Hung Si Truong",
title = "A floating point processor",
type = "Project ({M.S., Electrical and Electronic
Engineering})",
school = "California State University",
address = "Sacramento, CA, USA",
pages = "viii + 81",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Charles Lytle, Chairperson",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
}
@Article{Uya:1984:CFP,
author = "M. Uya and K. Kaneko and J. Yasui",
title = "A {CMOS} floating point multiplier",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "19",
number = "5",
pages = "697--702",
month = oct,
year = "1984",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A 32-bit CMOS floating-point multiplier is described.
The chip can perform 32-bit floating-point
multiplication (based on the proposed IEEE Standard
format) and 24-bit fixed-point multiplication (two's
complement format) in less than 78.7 and 71.1 ns
\ldots{}",
}
@Article{vonGudenberg:1984:BMG,
author = "J. Wolff von Gudenberg",
title = "{Berechnung maximal genauer Standardfunktionen mit
einfacher Mantissenl{\"a}nge} \toenglish {Computation
of Maximally Accurate Elementary Functions Using Simple
Mantissa Length} \endtoenglish",
journal = j-ELEK-RECHENANLAGEN,
volume = "26",
number = "5",
pages = "230--238",
month = oct,
year = "1984",
CODEN = "ELRAA4",
ISSN = "0013-5720",
bibdate = "Sat Feb 10 12:41:08 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronische Rechenanlagen",
}
@InCollection{Ware:1984:CMC,
author = "F. Ware and W. McAllister",
title = "{C-MOS} chip set streamlines floating-point
processing",
crossref = "Evanczuk:1984:MSS",
pages = "374--377",
year = "1984",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0; C.5; C.5",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic; C.5.3
Microcomputers; C.5.4 VLSI Systems",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic; Computer Systems Organization,
COMPUTER SYSTEM IMPLEMENTATION, Microcomputers;
Computer Systems Organization, COMPUTER SYSTEM
IMPLEMENTATION, VLSI Systems",
genterm = "DESIGN",
guideno = "00769",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
C. Computer Systems Organization; C.5 COMPUTER SYSTEM
IMPLEMENTATION; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION",
}
@MastersThesis{Wehmeyer:1984:EFF,
author = "Keith R. Wehmeyer",
title = "Effects of fixed and floating point mathematics on
digital filters",
type = "Thesis ({M.S.})",
school = "University of Cincinnati",
address = "Cincinnati, OH, USA",
pages = "vi + 92",
year = "1984",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "University of Cincinnati --- Theses. M.S. (Electrical
and Computer Engineering (1984))",
}
@Article{Wolrich:1984:HPF,
author = "G. Wolrich and E. McLellan and L. Harada and J.
Montanaro and R. A. J. Yodlowski",
title = "A High Performance Floating Point Coprocessor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-19",
number = "5",
pages = "690--696",
month = oct,
year = "1984",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A 34000-transistor single-chip floating-point
coprocessor fabricated in 3-$\mu$m double metal NMOS
technology is described. The fraction data path,
including a shifter and 60-bit carry propagate ALU, is
cycled in 100 ns for all operations requiring
\ldots{}",
}
@InCollection{Woo:1984:AMC,
author = "B. Woo and L. Lin and R. E. Owen",
title = "{ALU}, multiplier chips zip through {IEEE}
floating-point operations",
crossref = "Evanczuk:1984:MSS",
pages = "354--359",
year = "1984",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "C.1.2; G.1.0",
CRclass = "C.1.2 Multiple Data Stream Architectures
(Multiprocessors); C.1.2 Pipeline processors; G.1.0
General; G.1.0 Computer arithmetic",
descriptor = "Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Pipeline processors; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic",
genterm = "DESIGN",
guideno = "00766",
subject = "C. Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Book{Zuse:1984:CML,
author = "Konrad Zuse",
title = "{Der Computer, mein Lebenswerk}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 218",
year = "1984",
ISBN = "0-387-13814-5 (U.S.)",
ISBN-13 = "978-0-387-13814-5 (U.S.)",
LCCN = "TK7885.22.Z87 A33 1984",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Based on the author's autobiography with the same
title published in 1970.",
acknowledgement = ack-nhfb,
keywords = "computer engineers --- Germany --- biography;
computers --- Germany --- history; Zuse, Konrad",
}
@Article{Aridgides:1985:EIQ,
author = "A. Aridgides and D. Morgan",
title = "Effects of input quantization in floating-point
digital pulse compression",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "33",
number = "2",
pages = "434--435",
month = apr,
year = "1985",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A computer simulation of an FFT-based digital LFM
pulse compressor using vector floating point arithmetic
is presented, showing the effects of retaining various
number of mantissa bits at the input quantizer. Plots
of the compressed pulse waveforms \ldots{}",
}
@TechReport{Armstrong:1985:PLHa,
author = "Robert Clyde Armstrong",
title = "Procedural layout of a high-speed floating-point
arithmetic unit",
institution = "Massachusetts Institute of Technology, Research
Laboratory of Electronics",
address = "Cambridge, MA, USA",
pages = "116",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Technical report; no 508 Technical report
(Massachusetts Institute of Technology. Research
Laboratory of Electronics); no. 508.",
acknowledgement = ack-nhfb,
remark = "Originally presented as author's thesis (Electrical
Engineer --- Massachusetts Institute of Technology)
1985. Bibliography: leaf 116. Supported in part by the
U.S. Air Force Office of Scientific Research contract",
}
@PhdThesis{Armstrong:1985:PLHb,
author = "Robert Clyde Armstrong",
title = "Procedural layout of a high-speed floating-point
arithmetic unit",
type = "Thesis ({Elect. E.})",
school = "Massachusetts Institute of Technology. Dept. of
Electrical Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "116",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Jonathan Allen.",
acknowledgement = ack-nhfb,
}
@Article{Aspinwall:1985:RVM,
author = "D. B. Aspinwall and Y. N. Patt",
title = "Retrofitting the {VAX-11\slash 780} Microarchitecture
for {IEEE} Floating Point Arithmetic --- Implementation
Issues, Measurements, and Analysis",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "692--708",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676615",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676615",
abstract = "The VAX-11/7801 was designed specifically to implement
the VAX architecture. As such, it does not support the
IEEE standard for floating point arithmetic. A project
was undertaken to provide this support by modifying the
11/780 microarchitecture. Our objective was to produce
a microengine that would efficiently execute the VAX
instruction set, modified to handle VAX floating point
instructions in accordance with the IEEE standard. Our
methodology was to make minimal changes to the 11/780
hardware, relying primarily on changes to the
microcode. This paper describes the modifications
required to implement the IEEE standard, examines the
various design alternatives available to us, presents
measurements of our implementation, and analyzes our
results. We also offer some comments on the matter of
retrofitting an existing architecture to a new
unintended use.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Auzinger:1985:AAR,
author = "W. Auzinger and H. J. Stetter",
title = "Accurate arithmetic results for decimal data on
non-decimal computers",
journal = "Computing (New York)",
volume = "35",
number = "2",
pages = "141--151",
year = "1985",
CODEN = "????",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G.1.0",
content = "One potentially useful feature absent from the High
Accuracy Arithmetic Subroutine Library (ACRITH) is the
generation of tight and guaranteed bounds on the
computed solution of numerical problems in cases where
some of the original data values are not representable
exactly as machine numbers. At present, such data
values must be replaced by enclosing machine intervals;
for ill-conditioned problems, the final interval
defining the solution may be relatively wide.\par
The authors here discuss the implementation of some
earlier ideas of Stetter's [1], relating to the
coupling of a conversion procedure for decimal data to
the evaluation algorithm proper, with the objective of
generating much narrower inclusions. A clear indication
of how this might be done is presented by means of an
illustrative example. A detailed specification is given
for a linear equation solver which should compute last
bit accurate inclusions of the solution for decimal
data using a hexadecimal machine. Also included are
four varied numerical examples, for which the results
are most impressive, and which appear to justify the
authors' claim. \par
-J. Oliver, Essex, UK \par
REFERENCES \par
[1] STETTER, H. J. Sequential defect correction for
high-accuracy floating-point algorithms, in Numerical
analysis, Proc. of the conference (Dundee, 1983),
Springer-Verlag",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
CRnumber = "8607-0617",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
genterm = "THEORY; ALGORITHMS",
guideno = "04640",
keywords = "decimal floating-point arithmetic",
reviewer = "J. Oliver",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Avizienis:1985:AAO,
author = "Algirdas Avi{\v{z}}ienis",
title = "Arithmetic Algorithms for Operands Encoded in
Two-Dimensional Low-Cost Arithmetic Error Code",
crossref = "Hwang:1985:PSC",
pages = "285--292",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Avizienis.pdf",
abstract = "A generalization of low-cost residue codes into
two-dimensional encodings was presented and error
detecting and error correcting properties of two
dimensional inverse residue codes were discussed
previously. This paper presents byte-serial checking,
additive inverse (complementation), and addition
algorithms for operands encoded in two-dimensional
residue and inverse residue codes.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Bannur:1985:VIS,
author = "J. Bannur and A. Varma",
title = "The {VLSI} Implementation of a Square Root Algorithm",
crossref = "Hwang:1985:PSC",
pages = "159--165",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bannur_Varma.pdf",
abstract = "VLSI implementation of a square root algorithm is
studied. Two possible implementations of the basic
nonrestoring algorithm are presented --- the second is
more area-efficient and modular than the first. The
implementations are simple and easy to control, but, at
the same time, are more area-time efficient than many
existing designs. A hardware algorithm suited to
microprogram implementation is also given. Extension of
the algorithms to achieve $ 1 / 2 $-bit precision is
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Barlow:1985:PEA,
author = "J. L. Barlow and E. H. Bareiss",
title = "Probabilistic error analysis of {Gaussian} elimination
in floating point and logarithmic arithmetic",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "349--364",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87c:65046",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "N. N. Abdelmalek",
}
@Article{Barlow:1985:RED,
author = "J. L. Barlow and E. H. Bareiss",
title = "On Roundoff Error Distributions in Floating Point and
Logarithmic Arithmetic",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "325--347",
month = dec,
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87c:65045",
MRreviewer = "N. N. Abdelmalek",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Pennsylvania State Univ, Computer Science Dep,
University Park, PA, USA",
affiliationaddress = "USA",
classification = "723",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer arithmetic; computer metatheory; floating
point arithmetic; logarithmic arithmetic; roundoff
error distributions",
}
@Article{Barnes:1985:SFP,
author = "C. Barnes and Boi Tran and Shu Leung",
title = "On the statistics of fixed-point roundoff error",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "33",
number = "3",
pages = "595--606",
month = jun,
year = "1985",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "Roundoff error after fixed-point multiplication is
commonly modeled as uniformly distributed white noise
that is uncorrelated with the signal. This paper
presents a statistical analysis of fixed-point roundoff
error that identifies the conditions \ldots{}",
}
@Article{Bayoumi:1985:HVA,
author = "M. A. Bayoumi and G. A. Jullien and W. C. Miller",
title = "Hybrid {VLSI} architecture of {FIR} filters using
residue number systems",
journal = j-ELECT-LETTERS,
volume = "21",
number = "8",
pages = "358--359",
day = "11",
month = apr,
year = "1985",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4251043",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "An efficient VLSI architecture of FIR filters based on
large moduli set is described. The structure is hybrid,
combining both binary-based elements and look-up
tables. The binary-based section is arranged as a
two-dimensional systolic array using \ldots{}",
}
@Article{Bittner:1985:WPD,
author = "L. Bittner",
title = "{Weiteres {\"u}ber Pseudo-Divisionsverfahren zur
Berechnung der Standardfunktionen und gewisser
Nicht-Stan\-dard\-funk\-tion\-en} \toenglish {Further
Details on Pseudo-Division Procedures for Computation
of Standard Functions and Certain Nonstandard
Functions} \endtoenglish",
journal = j-Z-ANGE-MATH-MECH,
volume = "65",
number = "12",
pages = "605--612",
year = "1985",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
xxmonth = "(none)",
}
@InProceedings{Bleher:1985:AHA,
author = "J. H. Bleher and A. E. Roeder and Siegfried M. Rump",
title = "{ACRITH}: High-accuracy arithmetic, an advanced tool
for numerical computation",
crossref = "Hwang:1985:PSC",
pages = "318--321",
year = "1985",
bibdate = "Sun May 28 18:31:07 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bleher_Roeder_Rump.pdf",
abstract = "The High-Accuracy Arithmetic Subroutine Library
(ACRITH) is a program product for engineering /
scientific application. It consists of a subroutine
library for solving problems in numerical computation.
All results obtained have algorithmically verified
accuracy.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Bohte:1985:GEF,
author = "Zvonimir Bohte and Marko Petkov{\v{s}}ek",
title = "{Gaussian} elimination in floating-point arithmetic",
crossref = "Vrdoljak:1985:ICA",
pages = "85--91",
year = "1985",
MRclass = "65F05 (65G05)",
MRnumber = "86m:65028",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brent:1985:SAI,
author = "R. P. Brent and H. T. Kung",
title = "A Systolic Algorithm for Integer {GCD} Computation",
crossref = "Hwang:1985:PSC",
pages = "118--125",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Brent_Kung.pdf",
abstract = "It is shown that the greatest common divisor of two
$n$-bit integers (given in the usual binary
representation) can be computed in time $ O(n) $ on a
linear systolic array of $ O(n) $ identical cells.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Burton:1985:SFE,
author = "C. G. Burton",
title = "The solution of finite element equations on the
floating point systems {FPS-164} attached processor",
journal = j-COMP-PHYS-COMM,
volume = "37",
number = "1-3",
pages = "171--180",
year = "1985",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
MRclass = "65N20 (65W05)",
MRnumber = "817 063",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Cantoni:1985:PPA,
author = "V. Cantoni and M. Ferretti and S. Levialdi and R.
Stefanelli",
title = "{PAPIA}: {Pyramidal Architecture for Parallel Image
Analysis}",
crossref = "Hwang:1985:PSC",
pages = "237--242",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Cantoni_Ferretti_Levialdi_Stefanelli.pdf",
abstract = "In 1981 a national research program for the design,
simulation and construction of a multiprocessor image
processing system was started. After a first phase
devoted to the comparison of suggested and existing
systems and to the definition of a set of benchmarks
and to the evaluation of the performances of the major
classes of machines, a new system has been defined. The
structure of the new system is based on a pyramid of
processors and many applications in which this machine
may be exploited are highlighted. The multiprocessor
architecture has been fully designed and the chip will
be built by an Italian silicon foundry, the SGS
company, within the framework of the multichip national
project.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Cathey:1985:ISR,
author = "James Cathey",
title = "68000 Integer square root routine in {16BST}",
journal = j-DDJ,
volume = "10",
number = "5",
pages = "118--??",
month = may,
year = "1985",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@MastersThesis{Chen:1985:FPP,
author = "Jen-Chyun Chen",
title = "8087 floating point processor software utilities
development and evaluation",
type = "Thesis ({M.S.E.E.})",
school = "University of Alabama. Graduate School. Dept. of
Electrical and Engineering",
address = "Tuscaloosa, AL, USA",
pages = "x + 128",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Programming (Electronic computers); Software
compatibility.",
}
@InProceedings{Chen:1985:MRS,
author = "Tien Chi Chen",
title = "Maximal Redundancy Signed-Digit Systems",
crossref = "Hwang:1985:PSC",
pages = "296--300",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chen.pdf",
abstract = "The maximal redundancy signed-digit (MAXSD) number
system has the highest redundancy within the
carry-absorbing signed-digit number system proposed by
Avizienis in 1961. The digital values for radix R lie
in $ [1 - R, R - 1] $.\par
Its compatibility with both standard nonredundant
systems and binary arithmetic makes it an excellent
choice for multiprecision arithmetic on binary
machines. The representations for finite numbers are
however nonunique and can even be unbounded in
wordlength; this is resolved by algorithms for partial
or complete conversion to standard nonredundant
notation without explicit carry propagation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Cheng:1985:APF,
author = "H. D. Cheng and K. S. Fu",
title = "Algorithm Partition for a Fixed-Size {VLSI}
Architecture Using Space-Time Domain Expansion",
crossref = "Hwang:1985:PSC",
pages = "126--132",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Cheng_Fu.pdf",
abstract = "The space-time domain expansion method has recently
been used to transform a computational task with a
recursive formula into a VLSI architecture. In addition
to its simplicity and completeness, an important
advantage of this method is that it can easily solve
the problem of partitioning an algorithm to fit a fixed
size VLSI architecture. We propose a computational
model and a partition rule which can be easily used to
partition any recursive computation problem suited to
the space-time domain expansion method so it can be
solved on fixed-size VLSI architectures. Several
examples, such as partitioned vector inner product,
partitioned comparators in relational database
management, partitioned matrix multiplications. and
partitioned transitive closure computation, parallel
recognition of general context-free languages, string
matching and dynamic time-warp pattern-matching are
used to illustrate the proposed method.",
acknowledgement = ack-nhfb,
keywords = "algorithm partition; ARITH-7; multiprocessing;
pipelining; recursive task; space-time domain
expansion; very large scale integration (VLSI)",
}
@InProceedings{Chiarulli:1985:DDR,
author = "Donald M. Chiarulli and W. G. Rudd and Duncan A.
Buell",
title = "{DRAFT}: a Dynamically Reconfigurable Processor for
Integer Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "309--317",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chiarulli_Rudd_Buell.pdf",
abstract = "A special computer for high-precision arithmetic
features an ALU that is dynamically reconfigurable
under program control. The 256-bit ALU consists of 8
32-bit slices each of which has its own ALU operation
code in each microinstruction. The slices can remain
logically separated from each other, or be dynamically
connected to either or both of their neighbors under
control of a segment control code that is part of each
microinstruction. The micro-assembly language designed
for the machine includes special features to assist in
the control of the segmentation, data addressing, and
control sequencing. Estimations of the times required
to execute arithmetic operations on the machine show
that it will be exceptionally fast for problems in
computational number theory and factoring of
integers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Chow:1985:PFD,
author = "Edward T. Chow and Dan I. Moldovan",
title = "Prime Factor {DFT} Parallel Processor Using Wafer
Scale Integration",
crossref = "Hwang:1985:PSC",
pages = "133--139",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chow_Moldovan.pdf",
abstract = "A high speed, flexible, simple and regular Discrete
Fourier Transform (DFT) Array Processor architecture
based on the Prime Factor Algorithm (PFA) is presented
in this paper. The array processor is based only on one
type of VLSI cell and can compute an $N$ point DFT in
$N$ clock cycles throughput when $N$ is a composite
number of prime numbers. The high throughput rate is
achieved with only a small number of cells. With a
special indexing scheme presented in this paper, this
processor can use shift registers as the system memory
so that minimum global control and addressing is
achieved. This array processor architecture is also
highly tolerant to both semiconductor processing yield
and processor defects during run time. Thus, it can be
manufactured in large quantity with VLSI technology on
a single wafer and used in hazardous environments. With
these advantages, it is very attractive to satellite,
military and commercial applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Ciminiera:1985:ESP,
author = "L. Ciminiera and A. Serra",
title = "Efficient Serial-Parallel Arrays for Multiplikation
and Addition",
crossref = "Hwang:1985:PSC",
pages = "28--35",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ciminiera_Serra.pdf",
abstract = "Three new arrays for unsigned and signed
multiplication, and for multiplication\slash addition
are presented. It is assumed that the factors are
expressed in 2's complement, while the addend (in the
latter array only) and the result are expressed in a
redundant notation. The arrays operate in
serial-parallel way since one factor is input in
parallel, while the second factor and the addend (in
the case of multiplication\slash addition) are entered
digit by digit starting from the most significant one;
the result is also produced serially with the most
significant digit first. Hence, the arithmetic unit
presented is suitable to be used as basic block of
special purpose processors performing functions such as
non-recursive digital filtering, signal correlation and
matrix multiplication. Indeed, they have the same speed
improvements as other similar units using redundant
representations for the result, with a cost: equivalent
to their counterparts based on full 2's complement
representation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Cody:1985:PRW,
author = "W. J. Cody and J. T. Coonen and D. M. Gay and K.
Hanson and D. Hough and W. Kahan and R. Karpinski and
J. Palmer and F. N. Ris and D. Stevenson",
title = "A Proposed Radix- and Word-length-independent Standard
for Floating-point Arithmetic",
journal = j-SIGNUM,
volume = "20",
number = "1",
pages = "37--51",
month = jan,
year = "1985",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:14:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Conover:1985:AHS,
author = "B. Conover and D. L. Gustafson",
title = "An Algorithm for High Speed Square Roots",
crossref = "IEEE:1985:ERC",
pages = "19--21",
year = "1985",
bibdate = "Fri Jun 11 18:04:41 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Cozzens:1985:CDF,
author = "J. Cozzens and L. Finkelstein",
title = "Computing the discrete {Fourier} transform using
residue number systems in a ring of algebraic
integers",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "31",
number = "5",
pages = "580--588",
month = sep,
year = "1985",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/TIT.1985.1057081",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=22750",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
keywords = "residue arithmetic; residue number system",
summary = "A new method is described for computing an $N = R^{m}
= 2^{upsilon m}$-point complex discrete Fourier
transform that uses quantization within a dense ring of
algebraic integers in conjunction with a residue number
system over this ring. The \ldots{}",
}
@Article{Cuyt:1985:REA,
author = "Annie Cuyt and Paul Van der Cruyssen",
title = "Rounding error analysis for forward continued fraction
algorithms",
journal = j-COMPUT-MATH-APPL,
volume = "11",
number = "6",
pages = "541--564",
month = jun,
year = "1985",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:00:53 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122185900379",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Dadda:1985:FMT,
author = "Luigi Dadda",
title = "Fast Multipliers for Two's-Complement Numbers in
Serial Form",
crossref = "Hwang:1985:PSC",
pages = "57--63",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dadda.pdf",
abstract = "Schemes for designing multipliers of binary
two's-complement numbers in serial form are considered
with the condition of the least possible delay between
inputs and output.\par
Such schemes are composed by two parts: the first, the
array generator, produces the terms of the multiplier
array; the second, the summer, is fed by the array
generator and produces the product. Two classes of
multipliers are illustrated: the first generating the
multiplier array by diagonals and rows, the second by
columns.\par
The array generators are composed by and\slash or stack
registers and linear arrays of gates; the summer is
shown to be conveniently using parallel counters.",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-7",
}
@InProceedings{Dadda:1985:SBN,
author = "Luigi Dadda",
title = "Squares for Binary Numbers in Serial Form",
crossref = "Hwang:1985:PSC",
pages = "173--180",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dadda1.pdf",
abstract = "The problem of designing squarers for binary number[s]
in serial form (with the condition of the least
possible delay between input and output) is
treated.\par
Several schemes are illustrated, derived from fast
multipliers for binary numbers in serial form,
described in a previous paper.\par
It is shown that some of such multipliers offer a
considerable saving in components when they are reduced
to squarers. Some schemes are illustrated, both for
positive and for two's-complement numbers.",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-7",
}
@InProceedings{DeMori:1985:DRP,
author = "R. {De Mori} and R. Cardin",
title = "Design for a Recursive Parallel Multiplier",
crossref = "Hwang:1985:PSC",
pages = "44--50",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Demori_Cardin.pdf",
abstract = "A network for performing multiplications of two two's
complement number's is proposed. The network can be
implemented in a synchronous or an asynchronous way. If
the factors to be multiplied have $N$ bits, the area
complexity of the network is $ O(N^2) $ for practical
values of $N$ as in the case of cellular multipliers.
Due to the design approach based on a recursive
algorithm, a time complexity $ O(\log N) $ is
achieved.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Dongarra:1985:FAS,
author = "J. J. Dongarra and D. C. Sorensen",
title = "A Fast Algorithm for the Symmetric Eigenvalue
Problem",
crossref = "Hwang:1985:PSC",
pages = "338--342",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dongarra_Sorensen.pdf",
abstract = "The symmetric eigenvalue problem is one of the most
fundamental problems of computational mathematics. It
arises in many applications, and therefore represents
an important area for algorithmic research. It is also
one of the first eigenvalue problems for which reliable
methods have been obtained. It would be surprising
therefore, if a new method were to be found that would
offer a significant improvement in execution time over
the fundamental algorithms available in standard
software packages such as EISPACK [7]. However, it is
reasonable to expect that eigenvalue calculations might
be accelerated through the use of parallel algorithms
for parallel computers that are emerging. We shall
present such an algorithm in this paper. The algorithm
is able to exploit parallelism at all levels of the
computation and is well suited to a variety of
architectures. However, a pleasant bonus of this
research is that the parallel algorithm, even when run
in serial mode, is significantly faster than the best
sequential algorithm on large problems, and is
effective on moderate size (order $ \geq 30 $) problems
when run in serial mode.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
remark = "Listed in table of contents as 276--277.",
}
@InProceedings{Dunham:1985:PFM,
author = "C. B. Dunham",
title = "Floating point with rounding before normalization",
crossref = "Meek:1985:PFM",
pages = "91--102",
year = "1985",
MRclass = "65G05",
MRnumber = "86f:65089",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Eldon:1985:FCF,
author = "John A. Eldon",
title = "A Family of {CMOS} Floating Point Arithmetic Chips",
crossref = "Hwang:1985:PSC",
pages = "101--109",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Eldon.pdf",
abstract = "Although the advantages of floating point arithmetic
have long been recognized, hardware complexity and
expense have impeded its use in high speed digital
signal processing (DSP). Now, however, the availability
of a growing number of fast dedicated floating point
adder and multiplier chips is spurring renewed interest
in floating point for real time filtering and spectral
analysis.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Enzmann:1985:WDS,
author = "K. Enzmann",
title = "{Wurzelziehen durch sukzessive Approximation}
\toenglish {Root-Finding by Successive Approximation}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "18",
pages = "92",
year = "1985",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@InProceedings{Ercegovac:1985:DAP,
author = "M. D. Ercegovac and T. Lang",
title = "A Division Algorithm with Prediction of Quotient
Digits",
crossref = "Hwang:1985:PSC",
pages = "51--56",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ercegovac_Lang.pdf",
abstract = "A division algorithm with a simple selection of
quotient digits including prediction is possible if the
divisor is restricted to a suitable range. The
condition that the divisor must satisfy to have the
quotient digit $ q_{i + 1} $ predicted while computing
$ R_{i + 1} $ are determined. Some implementation
considerations are also given.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Book{Ercegovac:1985:DSH,
author = "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang",
title = "Digital systems and hardware\slash firmware
algorithms",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 838",
year = "1985",
ISBN = "0-471-88393-X",
ISBN-13 = "978-0-471-88393-7",
LCCN = "TK7868.D5 E73 1985",
bibdate = "Wed Nov 14 14:42:00 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$32.95",
URL = "http://www.loc.gov/catdir/bios/wiley043/84021983.html;
http://www.loc.gov/catdir/description/wiley035/84021983.html;
http://www.loc.gov/catdir/toc/onix06/84021983.html",
acknowledgement = ack-nhfb,
subject = "computer firmware; digital electronics",
}
@InProceedings{Fandrianto:1985:VFP,
author = "Jan Fandrianto and B. Y. Woo",
title = "{VLSI} Floating-Point Processors",
crossref = "Hwang:1985:PSC",
pages = "93--100",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Fandrianto_Woo.pdf",
abstract = "The advance of VLSI technology has been the enabling
factor in the appearance of VLSI circuits handling
floating-point arithmetics. These circuits have found
their way into many number-crunching applications such
as telecommunications, seismic energy exploration,
radar, medical imaging, graphics and simulation.
Because of the different requirements for different
applications, some processors have a rich repertoire of
functions but rather low performance, while some
processors aim at haying the highest throughput for the
most frequent operations such as multiply and add. This
paper will review the architecture, the technology, and
the design techniques for the current VLSI
floating-point processors; and it will also report a
high performance chipset (Weitek WTL1164\slash 1165)
implementing complete basic arithmetic functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Ferguson:1985:RBA,
author = "Warren E. Ferguson and David W. Matula",
title = "Rationally Biased Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "194--202",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ferguson_Matula.pdf",
abstract = "One can naively view a computer number system as a
pair $ (F, P) $ consisting of a finite set $F$ of real
numbers and a rounding rule $P$. One such number system
is a hyperbolic rational number system which has as $F$
a finite set of rational numbers and as $P$ the
so-called mediant rounding rule. In this paper we
demonstrate how one can simulate a hyperbolic rational
number system in any high level language that supports
floating point computation. From this simulation we
infer that hyperbolic rational number systems form
viable alternatives to traditional binary floating
point number systems. Many properties of hyperbolic
rational number systems are derived fran the
relationship of their rounding rule to the
well-developed theory of best rational approximation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Book{Froberg:1985:NMT,
author = "Carl Erik Fr{\"o}berg",
title = "Numerical mathematics: theory and computer
applications",
publisher = pub-BENCUM,
address = pub-BENCUM:adr,
pages = "xi + 436",
year = "1985",
ISBN = "0-8053-2530-1",
ISBN-13 = "978-0-8053-2530-0",
LCCN = "QA297 .F6813 1985",
bibdate = "Fri Aug 20 09:03:54 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Revised edition of {\em Introduction to numerical
analysis, second edition, 1969}
\cite{Froberg:1969:INA}",
subject = "Numerical analysis; Data processing",
}
@InProceedings{Gal:1985:CEF,
author = "Shmuel Gal",
title = "Computing Elementary Functions: a New Approach for
Achieving High Accuracy and Good Performance",
crossref = "Miranker:1985:ASC",
pages = "1--16",
year = "1985",
DOI = "https://doi.org/10.1007/3-540-16798-6_1",
bibdate = "Thu Sep 01 12:27:23 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Gannon:1985:SPH,
author = "Dennis Gannon",
title = "{On} the Structure of Parallelism in a Highly
Concurrent {PDE} Solver",
crossref = "Hwang:1985:PSC",
pages = "252--259",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Gannon.pdf",
abstract = "This paper studies a variation of a parallel multigrid
PDE solver originally due to John Van Rosendale. This
paper gives a detailed analysis of the method and
discusses the large scale parallel structure. It will
show that the method can be viewed as a data driven
``large grain'' systolic structure. At a lower level
the algorithm is seen to be built from grid operators
that are, in turn, defined by expressions involving
vector functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Gnanasekaran:1985:FSP,
author = "R. Gnanasekaran",
title = "A Fast Serial-Parallel Binary Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "741--744",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676620",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676620",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gomez:1985:PFA,
author = "Gustavo Rodr{\'\i}guez G{\'o}mez and David {Carrasco
Villareal}",
title = "Problems in floating-point arithmetic, and a method
for obtaining internal characteristics of digital
computers. ({Spanish})",
journal = "Miscel{\'a}nea Mat.",
volume = "15",
pages = "15--25",
year = "1985",
MRclass = "65G05",
MRnumber = "86h:65060",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Spanish",
}
@Article{Goodman:1985:REF,
author = "R. H. Goodman and A. Feldstein and J. Bustoz",
title = "Relative error in floating-point multiplication",
journal = j-COMPUTING,
volume = "35",
number = "2",
pages = "127--139",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "87d:65052",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "Luciano Biasini",
}
@MastersThesis{Gooley:1985:DFM,
author = "Markian Myron Gooley",
title = "Design of a floating-point multiplier with a recursive
fraction-unit",
type = "Thesis ({M.S.})",
school = "University of Illinois at Urbana-Champaign",
address = "Urbana-Champaign, IL 61801, USA",
pages = "vi + 54",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Graham:1985:IFF,
author = "Douglas R. Graham",
title = "Implementation of {FORTH} with floating point
capabilities of an 8085 system",
type = "Thesis ({M.S.})",
school = "Ohio University",
address = "Athens, OH, USA",
pages = "v + 122",
month = mar,
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "FORTH (Computer program language)",
}
@Article{Grappel:1985:FSC,
author = "R. D. Grappel",
title = "Fast subroutine calculates exponentials",
journal = j-EDN,
volume = "30",
number = "10",
pages = "231",
month = may,
year = "1985",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@InProceedings{Gridley:1985:IPS,
author = "Curt Gridley",
title = "Improving the Performance of Scientific Applications
on a Supermicro Using a Custom Floating Point Processor
and An Optimizing Compiler",
crossref = "USENIX:1985:SCP",
pages = "597--610",
year = "1985",
bibdate = "Tue Feb 20 15:42:13 MST 1996",
bibsource = "ftp://ftp.uu.net/library/bibliography;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Massachusetts Computer Corp.",
}
@InProceedings{Gross:1985:FPA,
author = "Thomas Gross",
title = "Floating-Point Arithmetic on a Reduced-Instruction-Set
Processor",
crossref = "Hwang:1985:PSC",
pages = "86--92",
year = "1985",
bibdate = "Thu Sep 01 12:02:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Gross.pdf",
abstract = "Current single chip implementations of
reduced-instruction-set processors do not support
hardware floating-point operations. Instead, floating
point operations have to be provided either by a
co-processor or by software. This paper discusses
issues arising from a software implementation of
floating point arithmetic for the MIPS processor, an
experimental VLSI architecture. Measurements indicate
that an acceptable level of performance is achieved.
but this approach is no substitute for a hardware
accelerator if higher precision results are required,
This paper includes instruction profiles for the basic
floating point operations and evaluates the usefulness
of some aspects of the instruction set.",
acknowledgement = ack-nj,
keywords = "ARITH-7",
}
@Article{Gross:1985:SIF,
author = "Thomas Gross",
title = "Software implementation of floating-point arithmetic
on a reduced-instruction-set processor",
journal = j-J-PAR-DIST-COMP,
volume = "2",
number = "4",
pages = "362--375",
month = nov,
year = "1985",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Carnegie-Mellon Univ, Pittsburgh, PA, USA",
classification = "723; C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6140B (Machine-oriented
languages)",
corpsource = "Department of Computer Science, Carnegie-Mellon
University, Pittsburgh, PA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "computer metatheory; computer software; data handling;
digital arithmetic; floating-point arithmetic;
instruction profiles; instruction sets; integrated
circuits, VLSI; million instructions per minute; MIPS
processor; processors; reduced-instruction-set;
reduced-instruction-set processor; RISC; single chip
implementations; single-chip processors; software
implementation; Stanford MIPS processor; VLSI
architecture",
treatment = "P Practical",
}
@InProceedings{Gudenberg:1985:CID,
author = "R. Lohner and J. Wolff V. Gudenberg",
title = "Complex Interval Division with Maximum Accuracy",
crossref = "Hwang:1985:PSC",
pages = "332--336",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Lohner_Gudenberg.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
xxabstract = "n/a",
}
@TechReport{Hack:1985:RPS,
author = "James J. Hack",
title = "The relationship of peak to sustained performance in
highly concurrent vector machine organizations",
type = "Research report",
number = "RC 11094 (\#49829)",
institution = "IBM T.J. Watson Research Center",
address = "Yorktown Heights, NY, USA",
pages = "22",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Performance.;
Supercomputers.",
}
@Article{Helyer:1985:SCC,
author = "R. Helyer",
title = "Sine and cosine calculations",
journal = j-MICROPROC-MICROSYS,
volume = "2",
number = "5",
pages = "284",
month = oct,
year = "1985",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Hull:1985:NT,
author = "T. E. Hull and A. Abraham and M. S. Cohen and A. F. X.
Curley and C. B. Hall and D. A. Penny and J. T. M.
Sawchuk",
title = "{Numerical Turing}",
journal = j-SIGNUM,
volume = "20",
number = "3",
pages = "26--34",
month = jul,
year = "1985",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Sat Aug 13 17:16:02 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Numerical Turing is an extension of the Turing
programming language. Turing is a Pascal-like language
(with convenient string handling, dynamic arrays,
modules, and more general parameter lists) developed at
the University of Toronto. Turing has been in use since
May, 1983, and is now available on several
machines.\par
The Numerical Turing extension is especially designed
for numerical calculations. The important new features
are: (a) clean decimal arithmetic, along with
convenient functions for directed roundings and
exponent manipulation; (b) complete precision control
of variables and operations.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "decimal floating-point arithmetic; documentation;
languages",
subject = "D.3.3 Software, PROGRAMMING LANGUAGES, Language
Constructs, Procedures, functions, and subroutines \\
D.3.2 Software, PROGRAMMING LANGUAGES, Language
Classifications, SUPERPILOT \\ G.1.0 Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic",
}
@Article{Hull:1985:PRV,
author = "T. E. Hull and A. Abrham",
title = "Properly Rounded Variable Precision Square Root",
journal = j-TOMS,
volume = "11",
number = "3",
pages = "229--237",
month = sep,
year = "1985",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/214408.214413",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15 (65G05)",
MRnumber = "87a:65041",
bibdate = "Mon Dec 08 12:36:56 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/",
abstract = "The square root function presented here returns a
properly rounded approximation to the square root of
its argument, or it raises an error condition if the
argument is negative. {\em Properly rounded} means
rounded to the nearest, or to nearest even in case of a
tie. It is {\em variable precision} in that it is
designed to return a $p$-digit approximation to a
$p$-digit argument, for any $ p > 0 $. (Precision $p$
means $p$ decimal digits.) The program and the analysis
are valid for all $ p > 0 $, but current
implementations place some restrictions on $p$.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; decimal floating-point arithmetic;
verification",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
General, Error analysis. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
}
@Book{Hunter:1985:III,
author = "Colin B. Hunter and James F. Ready and Erin Farquhar",
title = "Introduction to the {Intel iAPX 432} Architecture",
publisher = pub-RESTON,
address = pub-RESTON:adr,
pages = "vii + 181",
year = "1985",
ISBN = "0-8359-3222-2",
ISBN-13 = "978-0-8359-3222-6",
LCCN = "QA76.8.I267 H86 1984",
bibdate = "Mon Feb 7 19:14:11 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$16.95",
acknowledgement = ack-nhfb,
}
@Article{Hurson:1985:SMU,
author = "A. R. Hurson and B. Shirazi",
title = "A systolic multiplier unit and its {VLSI} design",
journal = j-COMP-ARCH-NEWS,
volume = "13",
number = "3",
pages = "302--309",
month = jun,
year = "1985",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:54 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@InProceedings{Hwang:1985:MEC,
author = "Kai Hwang and Zhiwei Xu",
title = "Multiprocessors for Evaluating Compound Arithmetic
Functions",
crossref = "Hwang:1985:PSC",
pages = "266--275",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Hwang_Xu.pdf",
abstract = "A dynamic network approach is proposed for designing
multifunctional arithmetic processors to support {\em
complex}, {\em interval}, {\em vector}, {\em matrix},
{\em polynomial}, and other {\em compound arithmetic}
operations. This arithmetic-network approach is
extended from the multipipeline chaining concept
implemented in Cray Research supercomputers. The
proposed design methodology offers a viable way of
developing very powerful and flexible arithmetic
multiprocessors for scientific supercomputing.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Hwang:1985:SIS,
author = "Kai Hwang and Daniel D. Gajski and Ahmed Sameh",
title = "The {Seventh IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "Hwang:1985:PSC",
pages = "iii--iii",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Hwang_Gajski_Sameh.pdf;
http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
xxabstract = "n/a",
}
@Book{IEEE:1985:AIS,
author = "{IEEE Task P754}",
title = "{ANSI\slash IEEE 754-1985, Standard for Binary
Floating-Point Arithmetic}",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "20",
day = "12",
month = aug,
year = "1985",
ISBN = "1-55937-653-8",
ISBN-13 = "978-1-55937-653-2",
bibdate = "Thu Mar 02 09:57:22 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised 1990. A preliminary draft was published in the
January 1980 issue of IEEE Computer, together with
several companion articles
\cite{Cody:1981:APF,Coonen:1981:UDN,Coonen:1980:IGP,Coonen:1981:EIG,Hough:1981:API,Stevenson:1981:PSBa,Stevenson:1981:PSBb}.
The final version was republished in
\cite{IEEE:1985:ISBa,IEEE:1985:ISBb}. See also
\cite{Waser:1982:IAD}. Also standardized as {{\em IEC
60559 (1989-01) Binary floating-point arithmetic for
microprocessor systems}}.",
price = "US\$35.00",
URL = "http://ieeexplore.ieee.org/iel1/2355/1316/00030711.pdf;
http://standards.ieee.org/reading/ieee/std/busarch/754-1985.pdf;
http://standards.ieee.org/reading/ieee/std_public/description/busarch/754-1985_desc.html;
http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=019113",
acknowledgement = ack-nhfb,
}
@Manual{IEEE:1985:ASI,
author = "{IEEE Task P754}",
title = "{ANSI}\slash {IEEE 754}-1985, Standard for Binary
Floating-Point Arithmetic",
organization = "IEEE, New York",
month = aug # " 12",
year = "1985",
bibdate = "Thu Nov 8 14:50:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A preliminary draft was published in the January 1980
issue of IEEE Computer, together with several companion
articles
\cite{Cody:1981:APF,Coonen:1981:UDN,Coonen:1980:IGP,Coonen:1981:EIG,Hough:1981:API,Stevenson:1981:PSBa,Stevenson:1981:PSBb}.
Available from the IEEE Service Center, Piscataway, NJ,
USA.",
acknowledgement = ack-nj,
}
@Article{IEEE:1985:ISBa,
author = "IEEE",
title = "{IEEE} Standard for Binary Floating-Point Arithmetic",
journal = j-SIGPLAN,
volume = "22",
number = "2",
pages = "9--25",
month = feb,
year = "1985",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun May 02 09:20:35 1999",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS}.",
acknowledgement = ack-nj,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
xxnote = "This reference is wrong; the volume 22 is from 1987,
and neither volume 20 (1985) nor 22 have this
article??",
}
@Book{IEEE:1985:ISBb,
author = "{IEEE Computer Society Standards Committee.Working
group of the Microprocessor Standards Subcommittee} and
{American National Standards Institute}",
title = "{IEEE} standard for binary floating-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "18",
year = "1985",
bibdate = "Sun May 02 09:20:47 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{IEEE:1985:AIS}.",
series = "ANSI/IEEE Std 754-1985.",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units --- Standards.;
Floating-point arithmetic --- Standards.",
}
@Book{Intel:1985:FPL,
author = "{Intel Staff}",
title = "Floating Point Library for {DOS} 8096 Systems Manual",
publisher = "Intel Corporation",
address = "Santa Clara",
pages = "60",
month = dec,
year = "1985",
ISBN = "0-917017-75-7",
ISBN-13 = "978-0-917017-75-9",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$10.00",
acknowledgement = ack-nhfb,
keywords = "(COMPUTER OPERATING SYSTEM); PC-DOS; TECHNOLOGY ---
COMPUTERS AND COMPUTER TECHNOLOGY",
language = "eng",
}
@Book{Intel:1985:PRM,
author = "Intel",
title = "The {iAPX} 286 Programmer's Reference Manual",
publisher = pub-INTEL,
address = pub-INTEL:adr,
year = "1985",
bibdate = "Sun May 2 09:20:57 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The definitive statement of what the 80286 and 80287
are. A valuable reference for instruction definitions.
See also \cite{Intel:1983:HRM,Palmer:1984:P}.",
acknowledgement = ack-nhfb,
}
@Manual{IntelCorporation:1985:FAL,
author = "{Intel Corporation}",
title = "The 8096 floating-point arithmetic library user's
guide for {DOS} systems",
organization = "Intel Corporation",
address = "Santa Clara, CA.",
pages = "various",
year = "1985",
ISBN = "0-917017-75-7",
ISBN-13 = "978-0-917017-75-9",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer programs.; Floating-point arithmetic.;
Operating systems (Computers)",
remark = "``Order number: 122366-001.'' On cover: Software
development tools. Cover title: 8096 floating point
library for DOS systems.",
}
@Article{Jankowski:1985:ASC,
author = "M. Jankowski and H. Wo{\'z}niakowski",
title = "The accurate solution of certain continuous problems
using only single precision arithmetic",
journal = j-BIT,
volume = "25",
number = "4",
pages = "635--651",
year = "1985",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65G05 (65L05)",
MRnumber = "87d:65053",
MRreviewer = "E. R. Hansen",
bibdate = "Thu Nov 12 18:12:56 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation",
}
@InProceedings{Jenkins:1985:CDI,
author = "W. Jenkins and E. Davidson and D. Paul",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '85}",
title = "A custom-designed integrated circuit for the
realization of residue number digital filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "220--223",
year = "1985",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Results are presented on the design, layout, and
fabrication of a custom-designed integrated circuit for
a residue number system digital filter module. The
architecture is based on a ROM-ACCUMULATOR FIR
structure in which the modular arithmetic for
\ldots{}",
}
@InProceedings{Kahan:1985:AIA,
author = "W. Kahan and E. LeBlanc",
title = "Anomalies in the {IBM ACRITH} Package",
crossref = "Hwang:1985:PSC",
pages = "322--331",
year = "1985",
bibdate = "Thu Sep 08 00:10:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kahan_LeBlanc.pdf",
abstract = "The IBM ACRITH package of numerical software is
advertised as reliable and easy to use; but sometimes
its results must astonish or confuse a naive user. This
report exhibits a few of the surprises. For instance, a
finite continued fraction, easy to evaluate in two
dozen keystrokes on a handheld calculator, causes
ACRITH to overflow either exponent range or 15
Megabytes of virtual memory. Lacking access to source
code, we must speculate to explain the anomalies. Some
seem attributable to small bugs in the code; some to
optimistic claims or oversimplifications in the code's
documentation; some to flaws in the doctrine underlying
the code. We conclude that different techniques than
used by ACRITH might have been about as accurate and
yet more economical, robust and perspicuous.",
acknowledgement = ack-nj,
keywords = "ARITH-7",
}
@Article{Karpinski:1985:PFP,
author = "R. Karpinski",
title = "Paranoia: a Floating-Point Benchmark",
journal = j-BYTE,
volume = "10",
number = "2",
pages = "223--235",
month = feb,
year = "1985",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@InProceedings{Kaushik:1985:MEC,
author = "Saroj Kaushik",
title = "Multiple Error Correction and Addictive Overflow
Detection with Magnitude Indices in Residue Code",
crossref = "Hwang:1985:PSC",
pages = "278--284",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kaushik.pdf",
abstract = "A new approach for correcting multiple errors and
detecting an additive overflow in the Residue Number
System (RNS) is suggested. It works with the code whose
redundancy is in the form of magnitude indices. The
residue representation of a number with magnitude index
is reconsidered. The RNS with magnitude index were
first studied by Sasaki [16] and Rao [15] and then by
Barsi and Maestrini [5,6]. The range of a given RNS is
divided into intervals of equal width and the magnitude
of a number X is defined as a integer locating X into
one of such intervals. We have proposed algorithm which
detects and corrects multiple errors in residue number.
The algorithms for special cases viz., single burst
residue error and single residue error are also
suggested. Some of the advantages are pointed out over
the existing approaches.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Klatte:1985:ASS,
author = "R. Klatte and C. P. Ullrich and J. W. {Von
Gudenberg}",
title = "Arithmetic Specification for Scientific Computation in
{ADA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "11",
pages = "996--1005",
month = nov,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676532",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676532",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kobayashi:1985:MTC,
author = "Hideaki Kobayashi",
title = "A Multioperand Two's Complement Addition Algorithm",
crossref = "Hwang:1985:PSC",
pages = "16--19",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kobayashi.pdf",
abstract = "This paper presents a novel algorithm for summing a
set of 2's complement numbers in parallel. The 2's
complement addition is converted to an equivalent
parallel summation of unsigned numbers. The conversion
is performed by simply complementing all the sign bits.
Only a few constant bits are required for sign
correction. This algorithm is suitable for
computer-aided design (CAD) of custom VLSI.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Manual{Koopman:1985:FFP,
author = "Philip J. Koopman",
title = "{FORTH} floating point",
volume = "3",
organization = "Mountain View Press",
address = "Mountain View, CA, USA",
edition = "Revised",
pages = "346",
year = "1985",
ISBN = "0-914699-28-8",
ISBN-13 = "978-0-914699-28-6",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "MVP-FORTH books",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming;
Floating-point arithmetic; FORTH (Computer program
language)",
remark = "Running title: MVP-FORTH integer and floating point
math. A complete glossary of MVP-FORTH math
extensions.",
}
@InProceedings{Kornerup:1985:FPL,
author = "Peter Kornerup and David W. Matula",
title = "Finite Precision Lexicographic Continued Fraction
Number Systems",
crossref = "Hwang:1985:PSC",
pages = "207--214",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kornerup_Matula.pdf",
abstract = "Lexicographic continued fraction binary (LCF)
representation provides an order preserving bitstring
representation of the non negative real numbers where
every rational number has a finite length bitstring
representation. We investigate the precision of $k$-bit
LCF approximation. The maximum gap size over $ [0, 1) $
for $ (k + 1) $-bit LCF representation is shown to be
less than $ 2^{0.81k} $, comparable to binary coded
decimal in worst case representation efficiency. The
distribution of gap sizes for $ (k + 1) $-bit LCF
representation over $ [0, 1] $ is shown on a
logarithmic scale to be bell shaped between $ 2^{0.81k}
$ and $ 2^{-1.39k} $, becoming more peaked near the
value corresponding to uniform spacing, $ 2^{-k} $,
with increasing $k$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Krishnan:1985:CDS,
author = "R. Krishnan and G. Jullien and W. Miller",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '85}",
title = "Complex digital signal processing using quadratic
residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "764--767",
year = "1985",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Recently, the Quadratic Residue Number System (QRNS)
has been introduced [4,5,6], which allows the
multiplication of complex integers with two real
multiplications. Restrictions on the form of the moduli
can be removed if an increase in real \ldots{}",
}
@InProceedings{Kurokawa:1985:PT,
author = "Takakazu Kurokawa and Hideo Aiso",
title = "Polynomial Transformer",
crossref = "Hwang:1985:PSC",
pages = "153--158",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kurokawa_Aiso.pdf",
abstract = "Any relations among finite fields can be transformed
to a unique polynomial of one variable using Galois
Fields. In this paper, we explain the design of a
``Polynomial Transformer'' which executes the
transformation.\par
Polynomial Transformer consists of very simple and
iterative logic, and it is very suitable for parallel
and pipelined VLSI algorithm. Moreover, three
dimensional construction of a Polynomial Transformer is
possible. Thus, it serves as an example of a typical
three dimensional VLSI.\par
Its application can be found in Polynomial
Transformation, disturbance of data and so on.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Kwan:1985:MOW,
author = "Hon Kwan",
title = "A multi-output wave --- digital biquad using magnitude
truncation instead of controlled rounding",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "11",
pages = "1185--1187",
month = nov,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The use of magnitude truncation instead of controlled
rounding for the elimination of zero-input and
constant-input oscillations in the wave digital biquad
derived from the feedforwardRC-active configuration is
described. We also describe \ldots{}",
}
@Article{Lang:1985:ICL,
author = "J. H. Lang and C. A. Zukowski and R. O. Lamaire and
Chae Han",
title = "Integrated-Circuit Logarithmic Arithmetic Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "5",
pages = "475--483",
month = may,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676588",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676588",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Li:1985:FCD,
author = "S.-Y. R. Li",
title = "Fast Constant Division Routines",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "9",
pages = "866--869",
month = sep,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676646",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676646",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Li:1985:PAC,
author = "Xiaobo Li and Lionel M. Ni",
title = "A Pipeline Architecture for Computing Cumulative
Hypergeometric Distributions",
crossref = "Hwang:1985:PSC",
pages = "166--172",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Li_Ni.pdf",
abstract = "The hypergeometric distribution is a widely used
arithmetic function and is fundamental to many
statistical sampling and statistical pattern
recognition problems. Computation of the cumulative
hypergeometric distribution function, $ H(a) $, is
extremely time-consuming. As a result, many
approximation algorithms have been proposed to evaluate
the cumulative hypergeometric distribution. This paper
describes a two-level pipeline architecture for
computing $ H(a) $ with computation complexity reduced
to $ c + a $, where $c$ is a constant. The main part of
the design is a type of recurrence computation. A
modular and systematic approach is suggested to
implement the recurrence formula. The computation
complexity of the proposed architecture is also
compared with various other known methods. The highly
regular structure of the design can lead to efficient
VLSI implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Ling:1985:NFL,
author = "Fuyun Ling and D. Manolakis and J. Proakis",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '85}",
title = "New forms of {LS} lattice algorithms and an analysis
of their round-off error characteristics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1739--1742",
year = "1985",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "New formulas are presented for direct updating of the
reflection coefficients in the a priori and a
posteriori forms of the least squares (LS) lattice
algorithms. An analysis of the numerical
characteristics of the new LS lattice forms is given
and \ldots{}",
}
@InProceedings{Liu:1985:DVR,
author = "Wentai Liu and J. C. Duh and Daniel E. Atkins",
title = "The Design of a Vector-Radix {2DFFT} Chip",
crossref = "Hwang:1985:PSC",
pages = "231--236",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Liu_Duh_Atkins.pdf",
abstract = "Architectures based on the vector-radix 2DFFT
algorithm and hence can avoid the matrix transpose
problem have been proposed. The unique feature of the
proposed architectures is that the data can be driven
into the arithmetic processors in a pipeline fashion.
This paper presents a prototype chip, which has been
designed in $ 2 \mu $ m NMOS technology, for the
generalized butterfly unit. The chip is a two-stage
pipelined processor. The design experience, timing
information, and the chip features including four
multipliers, one adder\slash subtracter and PLA
controllers are presented.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Lohninger:1985:GF,
author = "H. Lohninger",
title = "{Gleitkommaarithmetik f{\"u}r den 68000} \toenglish
{Floating-point Arithmetic for the 68000}
\endtoenglish",
journal = j-MC,
volume = "2",
pages = "58--64",
year = "1985",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Lorenz:1985:AIP,
author = "E. Lorenz",
title = "{Aspekte der Implementierung eines Programmpaketes zur
schnellen und flexiblen Ausf{\"u}hrung von
arithmetischen Operationen mit dem U880} \toenglish
{Aspects of the Implementation of a Software Package
for Fast and Flexible Execution of Arithmetic
Operations on the U880} \endtoenglish",
journal = j-NACH-ELEK,
volume = "35",
number = "5",
pages = "179--181",
month = "????",
year = "1985",
CODEN = "NTELAP",
ISSN = "0323-4657",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The U880 is a Z80 clone microprocessor that was built
in the GDR (East Germany).",
acknowledgement = ack-nj,
fjournal = "Nachrichtentechnik Elektronik",
}
@InProceedings{Luk:1985:PMC,
author = "Franklin T. Luk",
title = "A Parallel Method for Computing the Generalized
Singular Value Decomposition",
crossref = "Hwang:1985:PSC",
pages = "260--265",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Luk.pdf",
abstract = "We describe a new parallel algorithm for computing the
generalized singular value decomposition of two $ n
\times n $ matrices, one of which is nonsingular. Our
procedure requires $ O(n) $ e time and one triangular
array of $ O(n^2) $ processors.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Majerski:1985:SRA,
author = "S. Majerski",
title = "Square-Rooting Algorithms for High-Speed Digital
Circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "8",
pages = "724--733",
month = aug,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676618",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:17 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Matula:1985:FPR,
author = "David W. Matula and Peter Kornerup",
title = "Finite Precision Rational Arithmetic: Slash Number
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "1",
pages = "3--18",
month = jan,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676511",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 30 06:21:13 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Fraction number systems characterized by fixed-slash
and floating-slash formats are specified. The structure
of arithmetic over such systems is prescribed by the
rounding obtained from ``best rational approximation.''
Multitiered precision hierarchies of both the
fixed-slash and floating-slash type are described and
analyzed with regards to their support of both exact
rational and approximate real computation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Manual{ME:1985:FPS,
title = "Floating point and string listing",
organization = "Microprocessor Engineering",
address = "Southampton, UK",
edition = "Second",
pages = "36",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@Article{Mithani:1985:ASN,
author = "D. Mithani and S. Iyer",
title = "Algorithm speeds nonrestoring division in
microprogrammed systems",
journal = j-EDN,
volume = "30",
number = "4",
pages = "199--208",
month = feb,
year = "1985",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 15 18:42:21 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Modi:1985:AIS,
author = "J. J. Modi and J. S. Rollett",
title = "An algorithm for inverse square-roots",
journal = j-PARALLEL-COMPUTING,
volume = "2",
number = "1",
pages = "69--71",
month = mar,
year = "1985",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/0167-8191(85)90018-3",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
MRclass = "65W05 (65D15)",
MRnumber = "86j:65195",
bibdate = "Mon Apr 14 12:07:40 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An algorithm is presented for finding $ x^{ 1 / 2} $,
given $x$. The algorithm is designed to be particularly
suited for parallel computation, in which
floating-point multiplication, floating-point addition
and fixed-point arithmetic can be performed
simultaneously.",
acknowledgement = ack-nhfb,
classification = "C4290 (Other computer theory)",
corpsource = "Department of Eng., Cambridge University, UK",
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
keywords = "fixed-point arithmetic; floating-point addition;
floating-point multiplication; inverse square roots
algorithm; parallel computation; parallel processing",
treatment = "T Theoretical or Mathematical",
}
@Article{Moharir:1985:ESG,
author = "P. S. Moharir",
title = "Extending the Scope of {Golub}'s Method Beyond Complex
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "5",
pages = "484--487",
month = may,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676590",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676590",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Montgomery:1985:MMT,
author = "Peter L. Montgomery",
title = "Modular Multiplication Without Trial Division",
journal = j-MATH-COMPUT,
volume = "44",
number = "170",
pages = "519--521",
month = apr,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y16",
MRnumber = "86e:11121",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2007970",
abstract = "Let $ N > 1 $. We present a method for multiplying two
integers (called $N$-residues) modulo $N$ while
avoiding division by $ N. N $-residues are represented
in a nonstandard way, so this method is useful only if
several computations are done modulo one $N$. The
addition and subtraction algorithms are unchanged.",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods); C6130 (Data handling techniques)",
corpsource = "Syst. Dev. Corp., Santa Monica, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "digital arithmetic; integer; integer arithmetic;
modular arithmetic; modular multiplication;
multiplication; N-residue; N-residue arithmetic; number
theory",
treatment = "T Theoretical or Mathematical",
}
@Manual{Motorola:1985:MFC,
title = "{MC68881} floating-point coprocessor user's manual",
organization = "Motorola, Inc.",
address = "Phoenix, AZ, USA",
pages = "various",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors --- Handbooks, manuals, etc.",
remark = "Spine title: MC68881 user's manual. ``MC68881
UM/AD''--Cover.",
}
@Book{Motorola:1985:MFP,
author = "Motorola",
title = "{MC68881} Floating-Point Coprocessor User's Manual",
publisher = pub-MOTOROLA,
address = pub-MOTOROLA:adr,
edition = "Second",
year = "1985",
bibdate = "Fri Sep 02 23:38:03 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Muller:1985:DBC,
author = "Jean-Michel Muller",
title = "Discrete basis and computation of elementary
functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "9",
pages = "857--862",
month = sep,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676643",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65D20 (65V05)",
MRnumber = "87e:65016",
MRreviewer = "D. Zwick",
bibdate = "Sun Jul 10 08:33:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643",
abstract = "We give necessary and sufficient conditions in order
that the infinite product or sum of the terms of a
positive decreasing sequence generates the reals in a
given interval.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Naseem:1985:MCA,
author = "Asif Naseem and P. David Fisher",
title = "The Modified {CORDIC} Algorithm",
crossref = "Hwang:1985:PSC",
pages = "144--152",
year = "1985",
bibdate = "Wed Sep 14 20:50:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Naseem_Fisher.pdf",
abstract = "A Modified CORDIC Algorithm (MCA) has been developed
for the evaluation of elementary arithmetic functions.
MCA incorporates increased parallelism over the
original CORDIC algorithm, thus, resulting in an
enhanced speed of computation. This has been
accomplished by decoupling the CORDIC iteration
equations, and transforming the sequential nature of
these equations. $n$-bit fixed point data operands are
assumed and the parameter $k$ relates to the level of
parallelism in the algorithm. The modified algorithm
employs a $ [k + 1]n^2 $-bit ROM for lookup tables that
enable elementary arithmetic functions to be evaluated
in no more than $ [3 n + 2] $ and no less than $2$ time
steps. The two bounds correspond to a pipelined and a
parallel implementation, respectively. The formulation
of the MCA can be manipulated to obtain implementations
with various speed\slash cost characteristics. This
compares to $ n(3 n + 1) / 2 $ time steps for the
original CORDIC algorithm. For example, 32-bit ALU has
$ k = 12 $ and $ n = 32 $; so, a 13,312-bit ROM is
required to store the lookup tables, and the
computation requires 98 time steps for a pipelined
implementation.",
acknowledgement = ack-nj,
keywords = "ARITH-7",
}
@Article{Neumaier:1985:IPR,
author = "A. Neumaier",
title = "Inner Product Rounding Error Analysis in the Presence
of Underflow",
journal = j-COMPUTING,
volume = "34",
number = "4",
pages = "365--373",
year = "1985",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05",
MRnumber = "86j:65054",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Univ Freiburg, Inst f{\"u}r Angewandte Mathematik,
Freiburg, West Germany",
classification = "723; 921",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Computing (Vienna/New York)",
keywords = "computer metatheory; inner product rounding error
analysis; inner products; mathematical techniques ---
error analysis; underflow",
}
@InProceedings{Ngai:1985:RAT,
author = "Tin-Fook Ngai and Mary Jane Irwin",
title = "Regular, area-time efficient carry-lookahead adders",
crossref = "Hwang:1985:PSC",
pages = "9--15",
year = "1985",
bibdate = "Fri Nov 16 10:05:44 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ngai_Irwin.pdf",
abstract = "For fast binary addition, a carrylookahead (CLA)
design is the obvious choice [OnAt83, BaJM83]. However,
the direct implementation of a CLA adder in VLSI faces
some undesirable limitations. Either the design lacks
regularity, thus increasing the design and
implementation costs, or the interconnection wires are
too long, thus causing area-time inefficiency and
limits on the size of addition. Brent and Kung solved
the regularity problem by reformulating the carry chain
computation [BrKu82]. They showed that an $n$-bit
addition can be performed in time $ O(\log n) $, using
area $ O(n \log n) $ with maximum interconnection wire
length $ O(n) $. In this paper, we give an alternative
$ \log n $ stage design which is nearly optimum with
respect to regularity, area-time efficiency, and
maximum interconnection wire length.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Ni:1985:VRT,
author = "L. M. Ni and Kai Hwang",
title = "Vector-Reduction Techniques for Arithmetic Pipelines",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "5",
pages = "404--411",
month = may,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676580",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:26 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676580",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ohhashi:1985:HSC,
author = "M. Ohhashi and R. E. Schneider",
title = "High-Speed Computation of Unary Functions",
crossref = "Hwang:1985:PSC",
pages = "82--85",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ohhashi_Schneider.pdf",
abstract = "This paper presents an architecture for fast
evaluation of unary functions such as reciprocal,
square root and reciprocal square root. The theory
behind the architecture has been presented in [1]. The
paper shows the results of extensive simulation that
have allowed us to implement the architecture with
minimum chip count and maximum accuracy. The accuracy
is about 8\% error rate in the LSB of the chosen
representation (IEEE 32-bit floating point format).
This architecture allows the computation of unary
functions in less than 200 nsec.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Oklobdzija:1985:SOS,
author = "Vojin G. Oklobdzija and Earl R. Barnes",
title = "Some Optimal Schemes for {ALU} Implementations in
{VLSI} Technology",
crossref = "Hwang:1985:PSC",
pages = "2--8",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Oklobdzija_Barnes.pdf",
abstract = "An efficient scheme for carry propagation in an ALU
implemented in n-MOS technology is presented. An
algorithm that determines the optimum division of the
carry chain of a parallel adder for various data path
sizes is developed. This yields an implementation of a
fast ALU which due to its regular structure occupies a
modest amount of silicon. The speed of the
implementation described is comparable to the carry
look-ahead scheme. Our method is based on the
optimization of the carry path implemented in n-MOS
technology but the results can be applied to other
technologies.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Book{Palmer:1985:MGN,
author = "John F. Palmer and Stephen P. Morse",
title = "{Die mathematischen Grundlagen der Numerik-Prozessoren
8087\slash 80287}",
publisher = pub-TEWI,
address = pub-TEWI:adr,
pages = "240",
year = "1985",
ISBN = "3-921803-33-0",
ISBN-13 = "978-3-921803-33-2",
LCCN = "????",
bibdate = "Wed Sep 07 21:14:32 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "German translation of {\em The 8087 Primer}
\cite{Palmer:1984:P}.",
acknowledgement = ack-nj,
}
@InProceedings{Papachristou:1985:MIR,
author = "Christos A. Papachristou",
title = "Multi-Input Residue Arithmetic Utilizing Read-Only
Associate Memory",
crossref = "Hwang:1985:PSC",
pages = "182--188",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Papachristou.pdf",
abstract = "In this paper an approach to residue arithmetic is
presented using Read-Only-Associative Memories (ROAMs),
such as PLAs. These memories have considerable
advantages for table lookup arithmetic processing over
the conventional ROMs in terms of their storage and
time efficiency. In residue arithmetic, the ROAM
storage required largely depends on the residue
recurrences in arithmetic tables modulo $M$. After
reviewing recent results on the computation of
recurrences, a scheme is proposed for implementing
residue arithmetic based on ROAMs. The efficiency of
the scheme is established by comparison to conventional
ROM-based table lookup techniques. Applications to
residue-to-binary number system conversion are also
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Parker:1985:GCI,
author = "J. R. Parker",
title = "A General Character to Integer Conversion Method",
journal = j-SPE,
volume = "15",
number = "8",
pages = "761--766",
month = aug,
year = "1985",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380150804",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "algorithms; integer overflow detection; languages;
programming techniques; type conversion",
review = "ACM CR 8603-0209",
subject = "D.1.m Software, PROGRAMMING TECHNIQUES,
Miscellaneous",
}
@InProceedings{Pellegrino:1985:RNS,
author = "J. M. Pellegrino and B. M. Sadler and S. D. Casey",
editor = "Bruce Ronald McAvoy",
booktitle = "{IEEE 1985 Ultrasonics Symposium: proceedings, October
16--18, 1985, Cathedral Hill Hotel, Van Ness at Geary,
San Francisco, CA}",
title = "A Residue Number System for Wideband Acousto-Optic
Spectrum Analysis",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "385--390",
year = "1985",
CODEN = "????",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "????",
LCCN = "A367 .U46 1985eb",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 85CH2209-5.",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@PhdThesis{Peralta:1985:TRN,
author = "Rene Caupolican Peralta",
title = "Three results in number theory and cryptography: a new
algorithm to compute square roots modulo a prime
number; On the bit complexity of the discrete
logarithm; {A} framework for the study of
cryptoprotocols",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "52",
month = dec,
year = "1985",
LCCN = "????",
bibdate = "Sat Oct 17 16:25:07 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "dissertations; dissertations, academic --- UCB ---
computer science --- 1981--1990; University of
California, Berkeley. computer science division --",
}
@Article{Raimi:1985:FDP,
author = "Ralph A. Raimi",
title = "The First Digit Phenomenon Again",
journal = j-PROC-AMER-PHIL-SOC,
volume = "129",
number = "2",
pages = "211--219",
month = jun,
year = "1985",
CODEN = "PAPCAA",
ISSN = "0003-049X (print), 2326-9243 (electronic)",
ISSN-L = "0003-049X",
bibdate = "Sat Nov 12 16:56:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This paper contains strong criticism of a derivation
of Benford's Law \cite{Logan:1978:FDP}.",
URL = "http://www.jstor.org/stable/986989",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the {American Philosophical Society}
held at {Philadelphia} for promoting useful knowledge",
journal-URL = "http://www.jstor.org/journal/procamerphilsoci",
remark = "This paper contains mathematical derivations of both
Stigler's Law and Benford's Law. Raimi comments on p.
217: ``the Benford law itself as a conclusion to be
derived is by no means as firm as Kepler's planetary
curves. Indeed, it has been pointed out by Diaconis and
Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
statistical analysis of Benford's announced data gives
a high probability to the conjecture that he did a bit
of rounding-off here and there, always in the direction
of his law. The license that a physicist often takes on
the path from his hypotheses to verified, observable,
and repeatable conclusion is not justified here.''.",
}
@Article{Ramnarayan:1985:LMR,
author = "R. Ramnarayan and F. Taylor",
title = "On large moduli residue number system recursive
digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "4",
pages = "349--359",
month = apr,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23567",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "The three moduli set{2^{n} - 1, 2^{n},2^{n} +
1}residue number system, or RNS, has recently been
shown to possess several attractive properties. In
particular, the problem of scaling is much simplified
through the use of an autoscale \ldots{}",
}
@InProceedings{Rao:1985:CCC,
author = "T. R. N. Rao and Kasem Vathanvit",
title = "A Class of {$ A(N + C) $} Codes and Its Properties",
crossref = "Hwang:1985:PSC",
pages = "293--295",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rao_Vathanvit.pdf",
abstract = "We discuss here a new class of arithmetic codes,
called $ A(N + C) $ codes where $A$ and $C$ are
constant positive integers, $N$ is information to be
coded. $ A(N + C) $ codes are a special case of $ A N +
B $ arithmetic codes which were first studied by Brown.
$ A N $ codes are linear and cannot be used to detect
unidirectional multiple errors. $ A(N + C) $ codes are
non-linear and are useful for detecting and\slash or
correcting symmetric errors, arithmetic errors and
unidirectional errors. Furthermore, $ A(N + C) $ codes
can be constructed to provide constant-weight,
self-complementing and cyclic-code properties. It is
apparent that the codes with these properties have, in
some sense, broader capabilities of error detection and
error correction.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Reed:1985:VRM,
author = "I. S. Reed and T. K. Truong and J. J. Chang and H. M.
Shao and I. S. Hsu",
title = "{VLSI} Residue Multiplier Modulo a {Fermat} Number",
crossref = "Hwang:1985:PSC",
pages = "203--206",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Reed_Truong_Chang_Shao_Hsu.pdf",
abstract = "Multiplication is central in the implementation of
Fermat number transforms (FNT) and other residue number
algorithms. There is need for a good multiplication
algorithm which can be realized easily on a VLSI chip.
In this paper, the Leibowitz multiplier [1] is modified
to realize multiplication in the ring of integers
modulo a Fermat number. The advantage of this new
algorithm over Leibowitz's algorithm is that
Leibowitz's algorithm takes modulo after the product of
multiplication is obtained. Hence time is wasted. In
this new algorithm, modulo is taken in every bit
operation when performing multiplication. Therefore no
time is wasted in this respect. Furthermore, this
algorithm requires only a sequence of cyclic shifts and
additions. The design[s] for this new multiplier are
regular, simple, expandable and therefore, suitable far
VLSI implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Rump:1985:HOC,
author = "Siegfried M. Rump",
title = "Higher Order Computer Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "302--308",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rump.pdf",
abstract = "The floating-point arithmetic on computers is designed
to approximate the corresponding operations over the
real numbers as close as possible. In this paper it is
shown by means of counterexamples that this need not be
true for existing machines. For achieving good
numerical results a floating-point arithmetic
approximating the real operations as close as possible
is probably best. For achieving verifications on
computers, at least a precisely defined computer
arithmetic is indispensable.\par
In this paper we first introduce the Kulisch\slash
Miranker theory, which represents a sound basis for
computer arithmetic. Each operation is precisely
defined and, moreover, is of maximum accuracy. That
means, the computed result is the floating-point number
of the working precision closest to the infinite
precise result. The theory also covers directed
roundings allowing computations with intervals. These
properties hold true for the floating-point numbers of
single and double precision as well as for the vectors,
matrices and complex extensions over those.\par
In the second part of the paper we demonstrate the
theoretical basis for what we call 'Higher Order
Computer Arithmetic'. This is an inclusion theory
allowing the development of algorithms to compute
bounds for the solution of various problems in
numerical analysis. These bounds are automatically
verified to be correct and they are of high accuracy.
Very often they are of maximum accuracy, that means the
left and right bounds of all components of the solution
are adjacent in the floating-point screen. Moreover
existence and uniqueness of a solution within the
computed bounds is automatically verified by the
algorithm. If this verification is not possible, a
respective message is given. We develop the theory and
give algorithms for the solution of systems of linear
and nonlinear equations. As demonstrated by examples
even for extremely ill-conditioned problems existence
and uniqueness of the solution is verified within
bounds of least significant bit accuracy.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Salomon:1985:TGF,
author = "D. Salomon",
title = "Two generalized floating-point representations",
journal = j-BYTE,
volume = "10",
number = "9",
pages = "154--158",
month = sep,
year = "1985",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
genterm = "ALGORITHMS; DESIGN",
guideno = "03372",
}
@InProceedings{Schaeffer:1985:SPE,
author = "Jonathan Schaeffer and Darrell Makarenko",
title = "Systolic Polynomial Evaluation and Matrix
Multiplication with Multiple Precision",
crossref = "Hwang:1985:PSC",
pages = "110--117",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Schaeffer_Makarenko.pdf",
abstract = "The design and implementation of a systolic VLSI
multi-precision polynomial evaluator and matrix
multiplier is described. The use of bit-serial
arithmetic allows for a very simple cell design (two
registers and an accumulator) enabling a substantial
number of cells to be placed on a chip. A configuration
of $ N^2 $ cells can evaluate $N$ polynomials of $N$
coefficients at $N$ points and perform $N$-width band
matrix multiplication and $ N \times N $ full matrix
multiplication, each in linear time. Using current
technology, 100 polynomials of 100 coefficients can be
evaluated at 100 data points with 32 bit precision in
an estimated one millisecond.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Schoof:1985:ECF,
author = "Ren{\'e} Schoof",
title = "Elliptic Curves Over Finite Fields and the Computation
of Square Roots $ \operatorname {mod} p $",
journal = j-MATH-COMPUT,
volume = "44",
number = "170",
pages = "483--494",
month = apr,
year = "1985",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y16 (11G20 14G15)",
MRnumber = "86e:11122",
MRreviewer = "Karl Rubin",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0250 (Combinatorial mathematics); B0290D (Functional
analysis); C1160 (Combinatorial mathematics); C4120
(Functional analysis); C4240 (Programming and algorithm
theory)",
corpsource = "Amsterdam University, Netherlands",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computational complexity; deterministic algorithm;
elliptic curve; F/sub q/-points; finite fields;
function evaluation; number theory; square roots mod p;
Weierstrass equation",
treatment = "T Theoretical or Mathematical",
}
@Book{Scott:1985:CNS,
author = "Norman R. Scott",
title = "Computer Number Systems and Arithmetic",
publisher = pub-PH,
address = pub-PH:adr,
pages = "x + 254",
year = "1985",
ISBN = "0-13-164211-1",
ISBN-13 = "978-0-13-164211-9",
LCCN = "QA76.9.C62 S38 1985",
bibdate = "Thu Sep 1 10:14:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Shah:1985:PHS,
author = "A. Shah and M. Sid-Ahmed and G. Jullien",
title = "A proposed hardware structure for two-dimensional
recursive digital filters using the residue number
system",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "3",
pages = "285--288",
month = mar,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23566",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "A hardware structure is proposed for implementing
two-dimensional ($2$-D) recursive digital filters based
on the residue number system (RNS). The parallel
pipelined structure arising from the use of RNS
arithmetic facilitates video bandwidth filtering.
\ldots{}",
}
@Article{Shimada:1985:NAC,
author = "R. Shimada and Y. Ohkura and J. Aoe",
title = "Nonbinary Arithmetic {AN} Codes Using Odd Radix
Expressions",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "11",
pages = "1050--1056",
month = nov,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676538",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:33:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676538",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Smith:1985:DFI,
author = "S. P. Smith and H. C. Torng",
title = "Design of a Faster Inner Product Processor",
crossref = "Hwang:1985:PSC",
pages = "38--43",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Smith_Torng.pdf",
abstract = "This paper presents the design of a fast inner product
processor, with appreciably reduced latency and cost.
The inner product processor is implemented with a tree
of carry propagate or carry save adders; this tree is
obtained with the incorporation of three innovations in
the conventional multiply/add tree:\par
(1) The leaf-multipliers are expanded into adder
subtrees, thus achieving an $ O(\log N b) $ latency,
where $N$ denotes the number of elements in a vector
and $b$ the number of bits in each element.\par
(2) The partial products, to be summed in producing an
inner product, are reordered according to their
``minimum alignments'' bringing approximately a 20\%
saving in hardware.\par
(3) The reordering also truncates the carry propagation
chain in the final propagation stage by $ 2 \log b - 1
$ positions, significantly reducing the latency
further. A form of the Baugh and Wooley algorithm is
adopted to implement two's complement notation with
changes only in peripheral hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Smith:1985:FIP,
author = "S. P. Smith and H. C. Torng",
title = "A fast inner product processor based on equal
alignments",
journal = j-J-PAR-DIST-COMP,
volume = "2",
number = "4",
pages = "376--390",
month = nov,
year = "1985",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
classification = "713; 723; 921; B0290H (Linear algebra); B1265F
(Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); C4140 (Linear
algebra); C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
corpsource = "Sch. of Electr. Eng., Cornell University, Ithaca, NY,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "adder subtrees; Algorithms; alignments; Baugh and
Wooley algorithm; carry-; carry-propagate adder tree;
computer metatheory --- Boolean Algebra; computer
programming; computers --- Multiplying Circuits;
digital arithmetic; equal alignments; fast inner
product processor; free of carry-propagate or
carry-save adders; inner product processor; integrated
circuits, VLSI; leaf-multipliers; matrix algebra;
matrix multiplications; microprocessor chips; minimum;
satellite computers; save adders; special purpose
computers; two's complement notation; VLSI",
treatment = "P Practical",
}
@TechReport{Spafford:1985:RAS,
author = "Eugene Howard Spafford",
title = "A report on the accuracy of some floating point math
functions on selected computers",
institution = "School of Information and Computer Science, Georgia
Institute of Technology",
address = "Atlanta, GA, USA",
pages = "26",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "GIT-ICS; 85/06",
acknowledgement = ack-nhfb,
keywords = "Operating systems (Computers)",
}
@Article{Sreedharan:1985:ASS,
author = "J. Sreedharan and A. Dhurkadas",
title = "8086 algorithm solves square roots",
journal = j-EDN,
volume = "30",
number = "7",
pages = "272",
month = apr,
year = "1985",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Stewart:1985:NCD,
author = "G. W. Stewart",
title = "A Note on Complex Division",
journal = j-TOMS,
volume = "11",
number = "3",
pages = "238--241",
month = sep,
year = "1985",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/214408.214414",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Aug 26 23:38:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Stewart:1986:CNC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/",
abstract = "An algorithm for computing the quotient of two complex
numbers is modified to make it more robust in the
presence of underflows.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; complex arithmetic; computer arithmetic;
na",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness.",
}
@Article{Stummel:1985:FEA,
author = "Friedrich Stummel",
title = "Forward error analysis of {Gaussian} elimination. {I}.
Error and residual estimates",
journal = j-NUM-MATH,
volume = "46",
number = "3",
pages = "365--395",
year = "1985",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65G05 (65F10)",
MRnumber = "87d:65054a",
MRreviewer = "Karl-Heinz Bachmann",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290B (Error analysis in numerical methods); C4110
(Error analysis in numerical methods)",
corpsource = "Fachbereich Math., Johann Wolfgang Goethe-University,
Frankfurt, West Germany",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "absolute errors; arithmetic floating-point operations;
associated optimal component-wise error; coefficient
matrices; condition numbers; data perturbations; error
analysis; error estimates; first order approximations;
forward error analysis; Gaussian elimination; general
linear algebraic systems; linearization method; matrix
norms; perturbation theory; residual estimates;
rounding errors; superposition; vector norms",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Swartzlander:1985:AHS,
author = "Earl {Swartzlander, Jr.} and John Eldon",
title = "Arithmetic for High Speed {FFT} Implementation",
crossref = "Hwang:1985:PSC",
pages = "223--230",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Swartzlander_Eldon.pdf",
abstract = "This paper describes recent progress in the
implementation of high speed spectrum analysis systems
with state-of-the-art commercial and semi-custom VLSI
circuits. Initial efforts are producing Fast Fourier
Transform (FFT) and inverse FFT processors that operate
at data rates of up to 40 MHz (complex). The current
implementation computes transforms of up to 16,384
points in length by means of the radix 4 pipeline FFT
algorithm. The interstage reordering is performed by
delay commutators implemented with semi-custom VLSI,
while the arithmetic is performed by commercial single
chip 22 bit floating point adders and multipliers. This
paper explains the pipeline FFT implementation and
focuses attention on the arithmetic used to realize the
design.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Manual{Symbolics:1985:RGS,
title = "Reference Guide to {Symbolics-Lisp}",
organization = "Symbolics, Inc.",
address = "Cambridge, MA, USA",
month = mar,
year = "1985",
bibdate = "Wed Jan 29 17:06:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``The number of digits
printed is the `correct' number\ldots{}''",
}
@Article{Takagi:1985:HSV,
author = "N. Takagi and H. Yasuura and S. Yajima",
title = "High-speed {VLSI} multiplication algorithm with a
redundant binary addition tree",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "9",
pages = "789--796",
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676634",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Sep 16 16:29:25 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Takeda:1985:SCB,
author = "K. Takeda and F. Ishino and Y. Ito and T. Nakashima",
title = "A single-chip 80-bit floating point processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "20",
number = "5",
pages = "986--992",
month = oct,
year = "1985",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A single-chip 80-bit floating point VLSI processor
capable of performing 5.6 million floating point
operations per second has been realized using
1.2-$\mu$m n-well CMOS technology. The processor
handles 80-bit double-extended floating point data
\ldots{}",
}
@InProceedings{Taniguchi:1985:TDI,
author = "Kenji Taniguchi",
title = "Three Dimensional {IC}'s and Application to High Speed
Image Processor",
crossref = "Hwang:1985:PSC",
pages = "216--222",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taniguchi.pdf",
abstract = "Present state-of-the-art 3-D IC fabrication
technologies are reviewed. Both short interconnection
wiring inherent to 3-D structure and parallel
processing architecture offer high performance for 3-D
integrated circuit. An idea of a high speed image
sensor composed of six layers is proposed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Taylor:1985:HFP,
author = "F. Taylor",
title = "A hybrid floating-point logarithmic number system
processor",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "1",
pages = "92--95",
month = jan,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The attributes of the traditional floating-point
processor and the logarithmic number system are
combined. The result is a hybrid system which offers
some advantages over the familiar floating-point
system. The new system, called the(FU)^{2}",
}
@InProceedings{Taylor:1985:MER,
author = "Fred J. Taylor",
title = "A More Efficient Residue Arithmetic Implementation of
the {FFT}",
crossref = "Hwang:1985:PSC",
pages = "243--250",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor1.pdf",
abstract = "After 20 years, the FFT remains restricted in its real
time capabilities. To overcome this throughput
obstacle, fast residue arithmetic units are studied
based on several recent innovations in the field of
complex finite rings. A dedicated machine is designed
which makes use of these new results and is compared to
conventional FFT designs. Using high speed
semiconductor memory to implement the required residue
arithmetic mappings, speed and complexity metrics of a
basic FFT unit are shown to be improved. However, the
derived architecture and arithmetic introduce a new and
challenging set of magnitude scaling problems. They are
resolved with the result being an integrated residue
arithmetic FFT system capable of supporting very high
real time data rates.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Taylor:1985:RFU,
author = "F. J. Taylor and G. Papadourakis and A. Skavantzos and
A. Stouraitis",
title = "A Radix-$4$ {FFT} Using Complex {RNS} Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "6",
pages = "573--576",
month = jun,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.5009414",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009414",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Taylor:1985:RSD,
author = "George S. Taylor",
title = "Radix 16 {SRT} dividers with overlapped quotient
selection stages: a 225 Nanosecond Double Precision
Divider for the {S-1 Mark IIB}",
crossref = "Hwang:1985:PSC",
pages = "64--71",
year = "1985",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor.pdf",
abstract = "This paper compares the three simplest SRT division
methods by using them to design a divider that produces
four quotient bits per cycle (radix 16). The three
methods are distinguished by the number of bits found
per stage of quotient selection logic:\par
(a) one bit per stage (radix 2) with quotient digits
chosen from the set $ \{ - 1, 0, 1 \} $,\par
(b) two bits per stage (radix 4) with quotient digits $
\{ - 2, - 1, 0, 1, 2 \} $, or\par
(c) two bits per stage (radix 4) with quotient digits $
\{ - 3, - 2, - 1, 0, 1, 2, 3 \} $.\par
For each method, we compare several ways to overlap
multiple stages of quotient selection logic and we
consider both irredundant and redundant (carry-save)
representations for the remainder.\par
The cost and performance of each alternative is
evaluated in terms a specific ECL gate array
technology. We find that we can build a 15\% faster
divider with radix four stages than with radix two
stages, for about the same amount of hardware. Between
the two radix 4 alternatives, method (c) offers more
speed than method (b) at the cost of 20\% more
hardware.\par
A radix 16 divider using method (b) has been built for
the S-1 Mark IIB computer under development at Lawrence
Livermore Laboratory. This divider consists of eight
ECL gate arrays and has a 12.5 nanosecond cycle time.
It performs IEEE single and double precision floating
point division in 150 and 225 nanoseconds,
respectively, the shortest times reported for any
general purpose computer.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-7",
}
@MastersThesis{Tesnow:1985:IDS,
author = "Kurt Alan Tesnow",
title = "Implementation of the digital simulation of a
synchronous machine using a floating-point processor",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering and Applied
Physics, Case Western Reserve University",
address = "Cleveland, OH 44106, USA",
pages = "vii + 255",
year = "1985",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Thies:1985:NPE,
author = "Klaus-Dieter Thies",
title = "{Die 8087\slash 80287 numerischen Prozessor
Erweiterungen f{\"u}r 8086\slash 80286 Systeme}
\toenglish {The 8087\slash 80287 Numeric Processor
Extension for 8086\slash 80286 Systems} \endtoenglish",
publisher = pub-TEWI,
address = pub-TEWI:adr,
pages = "355",
year = "1985",
ISBN = "3-921803-53-5",
ISBN-13 = "978-3-921803-53-0",
LCCN = "????",
bibdate = "Sat Nov 09 10:08:28 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Tsuji:1985:REF,
author = "Kumiko Tsuji",
title = "Round-off errors in floating-point additions",
journal = j-MEM-FAC-SCI-KYUSHU-UNIV-A,
volume = "39",
number = "2",
pages = "209--225",
year = "1985",
CODEN = "MFKAAF",
ISSN = "0373-6385 (print), 1883-2172 (electronic)",
ISSN-L = "0373-6385",
MRclass = "65G05 (65-04)",
MRnumber = "86j:65056",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Memoirs of the Faculty of Science, Kyushu Imperial
University. Series A, Mathematics = Kyushu Teikoku
Daigaku Rigakubu kiyo",
reviewer = "Aur{\'e}l Gal{\'a}ntai",
}
@InProceedings{vonGudenberg:1985:FPC,
author = "J. W. von Gudenberg",
title = "Floating-point computation in {PASCAL-SC} with
verified results",
crossref = "Buchberger:1985:PEE",
pages = "322--324",
year = "1985",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
catcode = "G; G.1.0",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
descriptor = "Mathematics of Computing, MATHEMATICAL SOFTWARE;
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
genterm = "THEORY; VERIFICATION; ALGORITHMS",
guideno = "12475",
subject = "G. Mathematics of Computing; G.4 MATHEMATICAL
SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
ANALYSIS",
}
@Article{Williamson:1985:NAB,
author = "D. Williamson and S. Sridharan and P. McCrea",
title = "A new approach for block floating-point arithmetic in
recursive filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "32",
number = "7",
pages = "719--722",
month = jul,
year = "1985",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "An approach to block floating-point arithmetic in
recursive second-order direct form digital filters is
proposed. Used in conjunction with residue (or error)
feedback, the method gives improved scaling and
roundoff noise properties compared to an \ldots{}",
}
@InProceedings{Yun:1985:BPS,
author = "David Y. Y. Yun and Chang N. Zhang",
title = "Binary Paradigm and Systolic Array Implementation for
Residue Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "189--193",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Yun_Zhang.pdf",
abstract = "The problem of residue, or modular, arithmetic is
fundamental to symbolic and algebraic computation,
coding theory and applications, as well as to
error-free arithmetic computations. This paper
describes novel algorithms that can lead to efficient
hardware for arithmetic operations in residue domains.
One of the main achievements is in allowing the
flexibility of changing moduli. The technology of
systolic array has been used to implement one of the
most representative operations, the modular multiplier.
It is shown that a linear systolic array can compute
$N$ modular products in time $ O(N) $ with constant
number of cells.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Zaccone:1985:INR,
author = "Richar J. Zaccone and Jesse L. Barlow",
title = "Improved Normalization Results for Digit On-Line
Arithmetic",
crossref = "Hwang:1985:PSC",
pages = "20--27",
year = "1985",
bibdate = "Wed Nov 14 18:06:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zaccone_Barlow.pdf",
abstract = "In digit on-line arithmetic, operands are introduced 1
digit at a time. After the first few operand digits
have been introduced. the result begins to appear a
digit at a time. This feature of digit on-line
arithmetic allows a significant amount of overlapping
of arithmetic operations.\par
Digit on-line arithmetic can sometimes produce
unnormalized results. This can present a problem for
the divide and square root algorithms. If the divisor
and radicand are highly unnormalized, these algorithms
will not produce the correct results. Two advances in
overcoming this problem are presented. First, several
techniques for producing results that are closer to
being normalized are developed. Second, it is shown
that normalized results are not necessary for divide
and square root to work properly. Combining these
results yields algorithms that will always give the
correct results.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@InProceedings{Zadrozny:1985:AFP,
author = "W{\l}odzimierz Zadro{\'z}ny",
title = "Axiomatizations of Floating Point Arithmetics",
crossref = "Hwang:1985:PSC",
pages = "74--81",
year = "1985",
bibdate = "Fri Nov 16 08:47:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zadrozny.pdf",
abstract = "We present a universal scheme for axiomatizing
floating point arithmetic. The schema can be used to
axiomatize any floating point arithmetic. It consists
of a labeled graph with vertices describing some
arithmetical properties and edges containing
appropriate axioms. The language of floating point
arithmetic is developed gradually in this scheme. The
scheme can provide a vehicle for studying and
implementing various versions of floating point
arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-7",
}
@Article{Zorpette:1985:BBN,
author = "Glenn Zorpette",
title = "The beauty of 32 bits: This near-optimum bit width has
unprecedented potential for the well-informed designer
of microprocessor-based systems",
journal = j-IEEE-SPECTRUM,
volume = "22",
number = "9",
pages = "65--71",
month = sep,
year = "1985",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1985.6370815",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Mon Jan 20 06:41:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "32 bit microprocessor chip; Companies; Computers;
dynamic RAM; floating-point arithmetic; mainframes;
memory management; microprocessor chips;
Microprocessors; Pipeline processing; pipelining;
processing rates; Random access memory; Registers; Sun;
very large scale integration; VLSI",
}
@TechReport{Adams:1986:FSSa,
author = "Glenn D. Adams",
title = "Functional specification and simulation of a floating
point co-processor for {SPUR} [1]",
type = "Report",
number = "UCB/CSD 87/311",
institution = "University of California. Computer Science Division",
address = "Berkeley, CA.",
pages = "52",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
Integrated circuits --- Design and construction.",
remark = "Sponsored by DARPA. Monitored by Naval Electronic
Systems Command.",
}
@MastersThesis{Adams:1986:FSSb,
author = "Glenn D. Adams",
title = "Functional specification and simulation of a floating
point co-processor for {SPUR}: research project",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical and Engineering and Computer Sciences",
address = "Berkeley, CA.",
pages = "various",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Agarwal:1986:NSV,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "New Scalar and Vector Elementary Functions for the
{IBM System\slash 370}",
journal = j-IBM-JRD,
volume = "30",
number = "2",
pages = "126--144",
month = mar,
year = "1986",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.302.0126",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "76W05",
MRnumber = "840 341",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
note = "See clarification \cite{Agarwal:1987:CNS}.",
abstract = "Algorithms have been developed to compute short-and
long-precision elementary functions: SIN, COS, TAN,
COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
ATAN2, and CABS, in scalar (28 functions) and vector
(22 functions) mode. They have been implemented as part
of the new VS FORTRAN library recently announced along
with the IBM 3090 Vector Facility. These algorithms are
essentially table-based algorithms. An important
feature of these algorithms is that they produce
bitwise-identical results on scalar and vector
System\slash 370 machines. Of these, for five functions
the computed value result is always the correctly
rounded value of the infinite-precision result. For the
rest of the functions, the value returned is one of the
two floating-point neighbors bordering the
infinite-precision result, which implies exact results
if they are machine-representable. For the five
correctly rounded elementary functions, scalar and
vector algorithms are designed independently to
optimize performance in each case.",
accepted = "2 December 1985",
acknowledgement = ack-nhfb,
ajournal = "IBM J. Res. Develop.",
classcodes = "C6140D (High level languages); C7310 (Mathematics
computing)",
classification = "723",
corpsource = "IBM Res. Div., Yorktown Heights, NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
journalabr = "IBM J Res Dev",
keywords = "ACOS; Algorithms; algorithms; ASIN; ATAN; ATAN2;
bitwise-identical results; CABS; computer metatheory;
computer programming; computer programming languages
--- fortran; COS; COTAN; design; elementary functions;
EXP; FORTRAN; fortran library; functions; IBM
computers; IBM System/370; infinite-precision result;
LOG; LOG10; mainframes; measurement; performance;
POWER; scalar elementary functions; SIN; SQRT;
subroutines; table-based algorithms; TAN; vector
elementary; VS FORTRAN library",
received = "5 November 1985",
remark-1 = "Numerous figures show errors in ulps, in either linear
or logarithmic scales, as dot plots over a range of
arguments, an idea that the authors credit to a
suggestion by Cleve Moler, then consulting with IBM
Palo Alto labs; such plots are used extensively in
\cite{Beebe:2017:MFC}.",
remark-2 = "From pages 128--129: ``A great deal of satisfaction
was obtained from the fact that five of the intrinsic
functions reported here always deliver correctly
rounded results; these are SQRT, DSQRT, CABS, CDABS,
and EXP. One important aspect of this is that correctly
rounded results were obtained with surprisingly little
sacrifice in performance.''",
remark-3 = "From page 132: ``Our CABS and CDABS functions satisfy
$\e/u < 0.5$ (this can also be called a half-ulp
criterion). They have best-possible rounding, except
that unavoidably there are cases when $| e/u | = 0.5$,
in which case it would be equally correct to round
downward or upward; we choose to round upward. This is
consistent with the System/370 definition of
rounding.''",
remark-4 = "From pages 134--135: ``Tuckerman's condition is of
historic significance, as its use allowed us to produce
IBM's first elementary function that delivered
correctly rounded results for all arguments.''",
remark-5 = "From page 137: ``X**2.0 usually produces a correctly
rounded value, while X*X always produces the truncated
value of $X^2$ .''",
remark-6 = "From page 139: ``Generating precise times is
difficult, since seemingly inconsequential changes in
the timing procedure may have a noticeable effect on
the measured times. For example, on the 3081KX the
performance of the STM [store multiple] and LM [load
multiple] instructions is severely degraded near page
boundaries. This means that in the rare event that the
save area of a subroutine is near a page boundary, the
speed of execution of the subroutine will be
substantially decreased.''",
subject = "C.4 Computer Systems Organization, PERFORMANCE OF
SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
MANIPULATION, Algorithms \\ F.3.3 Theory of
Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
of Program Constructs, Functional constructs \\ C.1.2
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Array and vector processors",
treatment = "N New Development; P Practical",
}
@Book{Apple:1986:ANM,
author = "{Apple Computer, Inc.} and Don Reed",
title = "{Apple} Numerics Manual",
publisher = pub-AW,
address = pub-AW:adr,
pages = "vii + 295",
year = "1986",
ISBN = "0-201-17741-2",
ISBN-13 = "978-0-201-17741-1",
LCCN = "QA297 .A66; QA76.8.A662 A59 1986",
bibdate = "Thu Nov 29 23:38:40 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "See also \cite{Apple:1988:ANM,Apple:1994:IMP}.",
acknowledgement = ack-nhfb,
keywords = "SANE (Standard Apple Numeric Environment)",
remark = "Standard Apple Numeric Environment for all Macintosh
and Apple II computers.",
subject = "Numerical calculations; Computer programs; Apple
computer",
}
@Article{Ardalan:1986:FPE,
author = "S. Ardalan",
title = "Floating-point error analysis of recursive
least-squares and least-mean-squares adaptive filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "12",
pages = "1192--1208",
month = dec,
year = "1986",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "A floating-point error analysis of the Recursive Least
Squares (RLS) and Least-Mean-Squares (LMS) algorithms
is presented. Both the prewindowed growing memory RLS
algorithm (lambda = 1) for stationary systems and the
exponentially windowed RLS \ldots{}",
}
@Article{Bayoumi:1986:LBV,
author = "Magdy A. Bayoumi",
title = "Lower bounds for {VLSI} implementation of residue
number system architectures",
journal = j-INTEGRATION-VLSI-J,
volume = "4",
number = "3",
pages = "263--269",
month = sep,
year = "1986",
CODEN = "IVJODL",
DOI = "https://doi.org/10.1016/0167-9260(86)90004-0",
ISSN = "0167-9260 (print), 1872-7522 (electronic)",
ISSN-L = "0167-9260",
bibdate = "Thu Nov 18 09:57:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since the number of components that can fit on a
single chip is large and rapidly growing, the
asymptotic analysis and computational complexity have
become applicable to the VLSI systems. We propose a
model of computation devoted to VLSI structures based
on Residue Number System (RNS). The developed model
employs the `cut theorem' which has been used by most
of the abstract VLSI models. It is not as general as
other reported models, but it gives tighter lower
bounds and more accurate measures of performance for
RNS structures. This computational model relates the
area and time complexities with the inherent properties
of RNS, the moduli size and the dynamic range. The
model supports the look-up table implementation
approach and it is technology-independent.",
acknowledgement = ack-nhfb,
fjournal = "Integration, the VLSI journal",
keywords = "area-time complexity; lower bounds; RNS; VLSI",
}
@InProceedings{Beims:1986:FPP,
author = "B. Beims",
title = "The Floating-Point Performance Standard Gets Even
Faster!",
crossref = "Wescon:1986:WCR",
pages = "35/1/1--13",
year = "1986",
bibdate = "Wed Sep 14 19:13:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Berger:1986:NNF,
author = "P. A. Berger",
title = "The {National NS32381} Floating Point Slave
Processor",
crossref = "Wescon:1986:WCR",
pages = "35/2/1--6",
year = "1986",
bibdate = "Mon Sep 12 08:32:02 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Bernstein:1986:MIC,
author = "Robert L. Bernstein",
title = "Multiplication by Integer Constants",
journal = j-SPE,
volume = "16",
number = "7",
pages = "641--652",
month = jul,
year = "1986",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380160704",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Methods are given for finding a sequence of `add',
`subtract' and `shift' instructions to multiply the
contents of a register by an integer constant. Each
method generalizes the previous one and requires only a
few intermediate or scratch registers. A variation of
the last method is used in the PL.8 compiler and uses
an unnoticeable amount of the overall compile time.
Some statistics roughly indicating the effectiveness of
the methods are presented.",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Campbell:1986:NSR,
author = "R. A. Campbell",
title = "{NS32000} Square Roots",
journal = j-DDJ,
volume = "11",
number = "3",
pages = "122--123, 106",
month = mar,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Fri Dec 08 13:05:56 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Campbell:1986:SS,
author = "R. A. Campbell",
title = "In Search of a Sine",
journal = j-DDJ,
volume = "11",
number = "12",
pages = "30--32",
month = dec,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 1 10:15:57 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@MastersThesis{Cao:1986:BFP,
author = "Hai Cao",
title = "A bit-slice floating point processor",
type = "Project ({M.S., Electrical and Electronic
Engineering})",
school = "California State University",
address = "Sacramento, CA, USA",
pages = "vii + 104",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Karl E. Stoffers, Chairperson.",
acknowledgement = ack-nhfb,
keywords = "Bit slice microprocessors.",
}
@Article{Cathey:1986:LEI,
author = "J. Cathey",
title = "Letter to the editor [Integer Square Root]",
journal = j-DDJ,
volume = "11",
number = "8",
pages = "14, 82--85",
month = aug,
year = "1986",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 08 07:59:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Chadha:1986:IHP,
author = "K. Chadha",
title = "{Intel} 80387: high performance, single chip numerics
coprocessor for the 80386",
crossref = "Wescon:1986:WCR",
pages = "35/4/1--5",
year = "1986",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Chakraborti:1986:IMR,
author = "N. B. Chakraborti and J. S. Soundararajan and A. L. N.
Reddy",
title = "An Implementation of Mixed-Radix Conversion for
Residue Number Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-35",
number = "8",
pages = "762--764",
month = aug,
year = "1986",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1986.1676829",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 14:09:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676829;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35258",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A method of residue number system (RNS) conversion to
mixed-radix (MR) representation is presented. This
method is found to be cost-effective and efficient,
particularly for moduli size 4/5 bits. A comparison of
conversion times and hardware \ldots{}",
}
@Article{Chowdary:1986:APR,
author = "N. Chowdary and W. Steenaart",
title = "Accumulation of product roundoff errors in modified
{FFT}'s",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "1",
pages = "103--107",
month = jan,
year = "1986",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "In this paper, expressions are derived for the mean
square error in modified radix-2 FFT algorithms. To
reduce the mean square error at the output of a special
purpose, high-speed low-order(n {leq} 32)FFT processor
implemented in fixed- \ldots{}",
}
@Article{Clenshaw:1986:GEL,
author = "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
and P. R. Turner",
title = "Generalized Exponential and Logarithmic Functions",
journal = j-COMPUT-MATH-APPL,
volume = "12",
number = "5--6",
pages = "1091--1101",
month = sep # "\slash " # dec,
year = "1986",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(86)90233-6",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "33A70 (39B10 65G05)",
MRnumber = "MR0871348 (88a:33027)",
bibdate = "Fri Jul 09 06:27:26 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Generalizations of the exponential and logarithmic
functions are defined and an investigation is made of
two possible versions of these functions. Some
applications are described, including computer
arithmetic, properties of very large and very small
numbers, and the determination of functional roots.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Clenshaw:1986:UAR,
author = "C. W. Clenshaw and F. W. J. Olver",
title = "Unrestricted algorithms for reciprocals and square
roots",
journal = j-BIT,
volume = "26",
number = "4",
pages = "475--492",
month = dec,
year = "1986",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01935054",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D20",
MRnumber = "87k:65019",
MRreviewer = "Luciano Biasini",
bibdate = "Wed Jan 4 18:52:19 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
xxpages = "476--492??",
}
@PhdThesis{Coonen:1986:CPS,
author = "Jerome Toby Coonen",
title = "Contributions to a proposed standard for binary
floating-point arithmetic",
type = "Thesis ({Ph.D.})",
school = "University of California, Berkeley",
address = "Berkeley, CA, USA",
pages = "various",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Binary system (Mathematics)",
}
@MastersThesis{Crowell:1986:ECU,
author = "Deborah Susan Crowell",
title = "Error-free computation using multiple-modulus residue
arithmetic",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vi + 106",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Approximation theory --- Data
processing.; Floating-point arithmetic.; Modular
arithmetic.",
}
@Article{Curtis:1986:CPL,
author = "T. W. Curtis and P. Allison",
title = "A {CORDIC} Processor for Laser Trimming",
journal = j-IEEE-MICRO,
volume = "6",
number = "3",
pages = "61--71",
month = may # "\slash " # jun,
year = "1986",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1986.304680",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 08 00:48:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@InProceedings{Desrosiers:1986:CFP,
author = "B. Desrosiers and J.-L. Peter and C. Sitbon",
title = "Custom Floating Point Chip Designed with a Cohesive
Structured Method",
crossref = "IEEE:1986:PII",
pages = "402--405",
year = "1986",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{DuCroz:1986:FFP,
author = "J. Du Croz",
title = "{FPV} -- a Floating-Point Validation Package",
crossref = "Unicom:1986:SQA",
pages = "47--55",
year = "1986",
bibdate = "Thu Sep 01 11:58:18 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dutka:1986:SRT,
author = "Jacques Dutka",
title = "On square roots and their representations",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "36",
number = "1",
pages = "21--39",
month = mar,
year = "1986",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/BF00357439",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A05 (11-03 11A63)",
MRnumber = "863340 (87m:01003)",
MRreviewer = "Donald Cook",
bibdate = "Fri Feb 4 21:50:24 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
MRtitle = "On square roots and their representations",
}
@Article{Dutta:1986:IMF,
author = "U. Dutta and D. Bhattacharya and A. D. Sarma",
title = "Implementation of Multibyte Floating Point Arithmetic
in 8-bit Microprocessor",
journal = j-MECH-ENG-BULL,
volume = "17",
number = "3",
pages = "104--113",
month = sep,
year = "1986",
CODEN = "MEGBBQ",
ISSN = "0379-5527",
bibdate = "Thu Sep 1 10:15:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mechanical Engineering Bulletin",
}
@Article{Feldstein:1986:OUS,
author = "Alan Feldstein and Peter Turner",
title = "Overflow, underflow, and severe loss of significance
in floating-point addition and subtraction",
journal = j-IMA-J-NUMER-ANAL,
volume = "6",
number = "2",
pages = "241--251",
month = apr,
year = "1986",
CODEN = "IJNADH",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65G05",
MRnumber = "89h:65065",
bibdate = "Sat Dec 23 14:52:49 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper it is shown that, under the assumption
of the logarithmic distribution of numbers,
floating-point addition and subtraction can result in
overflow or underflow with alarming frequency?--a
frequency that increases rapidly with machine speed
unless the range of the exponent is also increased. If
numbers are assumed to be distributed in accordance
with Sweeney's (1965) experiments, then severe loss of
significance occurs with large probability in floating
point subtraction. These results have implications for
computer design and lead to the suggestion of a long
word format which will reduce the risks to acceptable
levels.",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic
distribution; overflow; underflow; Zipf's Law",
}
@Article{Ferro:1986:DTF,
author = "F. Ferro",
title = "{DSP} tackles floating-point arithmetic",
journal = j-COMP-DESIGN,
volume = "25",
number = "15",
pages = "53--56",
day = "15",
month = aug,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "16915",
catcode = "B.7.1",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Advanced
technologies",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Advanced technologies",
fjournal = "Computer Design",
genterm = "DESIGN",
guideno = "1986-04012",
journalabbrev = "Comput. Des.",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS",
}
@Article{Gavrielov:1986:NFP,
author = "Moshe Gavrielov and Lev Epstein",
title = "The {NS32081} Floating-Point Unit --- Architecture and
Implementation",
journal = j-IEEE-MICRO,
volume = "6",
number = "2",
pages = "6--12",
month = mar # "\slash " # apr,
year = "1986",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1986.304737",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliationaddress = "Digital Equipment Corp, Hudson, MA, USA",
classcodes = "B1265F (Microprocessors and microcomputers); B2570F
(Other MOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
classification = "713; 714; 721; 722; 723; 902",
corpsource = "Digital Equipment Corp., Hudson, MA, USA",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "binary floating point arithmetic; binary floating-;
brand; carry propagation circuit; chip design; computer
architecture; computers, microcomputer; Construction;
data storage, semiconductor; digital arithmetic;
digital devices; field effect; floating-point
operations; high-speed; IEEE standard; integrated
circuits; internal structure; logic circuit
implementations; microcode; microprocessor chips; NMOS
processor; ns32081 floating-point processor; NS32081
floating-point unit; parallel multiway-; point
arithmetic; processor concept; semiconductor devices,
MOS; slave; slave processor; software package;
standards",
treatment = "P Practical; R Product Review",
xxtitle = "The {NS32081} Floating-point Unit",
}
@Article{Grappel:1986:SRA,
author = "R. D. Grappel",
title = "Square-root algorithm is fast and simple",
journal = j-EDN,
volume = "31",
number = "8",
pages = "248--248",
month = apr,
year = "1986",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Gustafson:1986:AHV,
author = "John L. Gustafson and Stuart Hawkinson and Ken Scott",
title = "The architecture of a homogeneous vector
supercomputer",
journal = j-J-PAR-DIST-COMP,
volume = "3",
number = "3",
pages = "297--304",
month = sep,
year = "1986",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Floating Point Systems Inc, Beaverton, OR, USA",
classification = "722; 723; C5220 (Computer architecture); C5440
(Multiprocessor systems and techniques); C6110 (Systems
analysis and programming)",
corpsource = "Floating Point Syst. Inc., Beaverton, OR, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "12 MFLOPS; 64-bit floating-point; 96 MFLOPS;
arithmetic; binary n-cube; computer architecture;
computer systems, digital; dual-ported memory design;
Floating Point; homogeneous vector supercomputer;
interconnection scheme; multiprocessing; parallel;
parallel architecture; parallel architectures; parallel
machines; Parallel Processing; pipeline processing;
pipeline vector arithmetic; pipelined vector
arithmetic; programming; software development;
supercomputer; Systems; technology; vector processing;
VLSI",
treatment = "P Practical",
}
@Book{Hamming:1986:NMS,
author = "R. W. (Richard Wesley) Hamming",
title = "Numerical methods for scientists and engineers",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "Second",
pages = "ix + 721",
year = "1986",
ISBN = "0-486-65241-6 (paperback)",
ISBN-13 = "978-0-486-65241-2 (paperback)",
LCCN = "QA297 .H28 1986",
bibdate = "Fri Aug 20 09:12:08 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$14.95",
URL = "http://www.loc.gov/catdir/description/dover032/86016226.html",
acknowledgement = ack-nhfb,
remark = "Reprint of \cite{Hamming:1973:NMS}.",
subject = "numerical analysis; data processing",
}
@Article{Heath:1986:NRD,
author = "J. Heath",
title = "A note on {``Realization of digital filters using
input-scaled floating-point arithmetic''}",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "34",
number = "4",
pages = "995--995",
month = aug,
year = "1986",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Heath:1979:RDF}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "In [1] and [2], a theoretical Bode plot with
experimental data points is shown. The experimental
data points on the Bode plot are not correct \ldots{}",
}
@Article{Henning:1986:KBD,
author = "D. Henning",
title = "{Konvertierung bin{\"a}rer in dezimale
Gleitkommazahlen f{\"u}r me{\ss}technische Anwendungen}
\toenglish {Conversion of Binary [Numbers] to Decimal
Floating-Point Numbers for Measurement Applications}
\endtoenglish",
journal = "Radio Fernsehen Elektronik",
volume = "35",
number = "11",
pages = "731--733",
month = "????",
year = "1986",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "decimal floating-point arithmetic",
}
@Article{Higginbotham:1986:AF,
author = "T. F. Higginbotham",
title = "Another factor of $ (10^{31} - 1) / 9 $",
journal = j-SIGNUM,
volume = "21",
number = "3",
pages = "12--12",
month = jul,
year = "1986",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/1057958.1057960",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Aug 07 18:41:01 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A second factor of $ (10^{31} - 1) / 9 $ was found to
be 6943319 with the use of an eight spoke wheel [1].
The spokes D(i) were 1, 7, 11, 13, 17, 19, 23, and 29.
The possible factors 2, 3, and 5 were tested prior to
starting the wheel. The constant multiplier was 30. The
possible divisors were of the form $ 30 \times K +
D(i), K = 0, 1, 2, 3, \ldots {} $. The program was
written in COBOL for the Honeywell DPS 8, running under
CP-6. The picture clauses were selected such that
31-digit decimal arithmetic was used. Execution time
was about forty-five minutes.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "decimal arithmetic",
remark = "Maple 8 reports in 2 sec on a 1400 MHz Itanium IA-64:
ifactor((10^31 - 1)/9) = (57336415063790604359)
(6943319) (2791).",
}
@Article{Hill:1986:DDS,
author = "Mark Hill and Susan Eggers and Jim Larus and George
Taylor and Glenn Adams and B. K. Bose and Garth Gibson
and Paul Hansen and Jon Keller and Shing Kong and
Corinna Lee and Daebum Lee and Joan Pendleton and Scott
Ritchie and David Wood and Ben Zorn and Paul Hilfinger
and Dave Hodges and Randy Katz and John Ousterhout and
Dave Patterson",
key = "C.0.B RISC",
title = "Design decisions in {SPUR}",
journal = j-COMPUTER,
volume = "19",
number = "11",
pages = "8--22",
month = nov,
year = "1986",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "University of California, Berkeley",
bibno = "9486",
catcode = "C.1.2; C.2.4; D.4.3; C.0; D.3.0; B.3.2; D.3.2",
content = "SPUR (Symbolic Processing Using RISCs) is a
multiprocessor workstation under development at the
University of California at Berkeley for parallel
processing research. Its development is part of a
long-term effort to study hardware and software issues
in multiprocessing, in general, and parallel processing
in LISP, in particular. This paper concentrates on the
initial architectural research and development of SPUR.
A SPUR processor is a general-purpose RISC processor
that provides support for Common LISP and IEEE
floating-point. A processor is implemented on a single
board with about 200 standard chips and three custom
two-micron CMOS chips: the cache controller, the CPU,
and the floating-point coprocessor. The chip that
manages the cache handles cache access by the CPU,
performing address translation, accessing shared memory
over the SPUR bus, and maintaining cache consistency.
Operating systems researchers are investigating network
file systems, network page servers, the effects of
large physical memories on virtual memory
implementations, and workload distribution. Programming
languages researchers ar",
CRclass = "C.1.2 Multiple Data Stream Architectures
(Multiprocessors); C.1.2 Parallel processors; C.2.4
Distributed Systems; D.4.3 File Systems Management; C.0
Instruction set design; D.3.0 General; B.3.2 Design
Styles; B.3.2 Cache memories; D.3.2 Language
Classifications; D.3.2 LIS-11",
CRnumber = "8710-0848",
descriptor = "Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Parallel processors; Computer
Systems Organization, COMPUTER-COMMUNICATION NETWORKS,
Distributed Systems; Software, OPERATING SYSTEMS, File
Systems Management; Computer Systems Organization,
GENERAL, Instruction set design; Software, PROGRAMMING
LANGUAGES, General; Hardware, MEMORY STRUCTURES, Design
Styles, Cache memories; Software, PROGRAMMING
LANGUAGES, Language Classifications, LIS-11",
fjournal = "Computer",
genterm = "DESIGN; HUMAN FACTORS; PERFORMANCE; EXPERIMENTATION",
guideno = "1986-03762",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabbrev = "Computer",
reviewer = "P. C. Patton",
subject = "C. Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; C. Computer Systems Organization; C.2
COMPUTER-COMMUNICATION NETWORKS; D. Software; D.4
OPERATING SYSTEMS; C. Computer Systems Organization;
C.0 GENERAL; D. Software; D.3 PROGRAMMING LANGUAGES; B.
Hardware; B.3 MEMORY STRUCTURES; D. Software; D.3
PROGRAMMING LANGUAGES",
}
@Article{Hongyuan:1986:CSL,
author = "Wang Hongyuan and S. C. Lee",
title = "Comments on {``Sign\slash Logarithm Arithmetic for FFT
Implementation''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-35",
number = "5",
pages = "482--484",
month = may,
year = "1986",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1986.1676792",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 14:09:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See \cite{Swartzlander:1983:SLA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676792",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hull:1986:VPE,
author = "T. E. Hull and A. Abrham",
title = "Variable Precision Exponential Function",
journal = j-TOMS,
volume = "12",
number = "2",
pages = "79--91",
month = jun,
year = "1986",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/6497.6498",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15 (65D20)",
MRnumber = "863 786",
bibdate = "Sun Sep 04 21:17:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/",
abstract = "The exponential function presented here returns a
result which differs from $ e^x $ by less than one unit
in the last place, for any representable value of $x$
which is not too close to values for which $ e^x $
would overflow or underflow. (For values of $x$ which
are not within this range, an error condition is
raised.) It is a ``variable precision'' function in
that it returns a $p$-digit approximation for a
$p$-digit argument, for any $ p > 0 $ ($p$-digit means
$p$-decimal-digit). The program and analysis are valid
for all $ p > 0 $, but current implementations place a
restriction on $p$. The program is presented in a
Pascal-like programming language called Numerical
Turing which has special facilities for scientific
computing, including precision control, directed
roundings, and built-in functions for getting and
setting exponents.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; decimal floating-point arithmetic; theory;
verification",
review = "ACM CR 8702-0091",
subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Verification.",
}
@TechReport{IBM:1986:IHA,
author = "{IBM Corporation}",
title = "{IBM High-Accuracy Arithmetic Subroutine Library
(ACRITH)}",
type = "Technical Report",
number = "GC 33-6163-02, SC 33-6164-02, GX 33-9009-02",
institution = pub-IBM,
address = pub-IBM:adr,
edition = "Third",
year = "1986",
bibdate = "Thu Jan 21 17:27:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1. General Information Manual \\
2. Program Description and User's Guide \\
3. Reference Summary",
}
@Book{IBM:1986:IRP,
author = "{IBM}",
title = "{IBM RT} Personal Computer Technology, publication
{SA23-1057}",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1986",
bibdate = "Sat Oct 28 08:16:44 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Iiguni:1986:REA,
author = "Y. Iiguni and H. Sakai and H. Tokumaru",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '86}",
title = "Rounding error analysis of the triangular lattice and
escalator algorithms",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2119--2122",
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "In this paper, first, the normalized Triangular
Lattice and Escalator algorithms for recursive least
squares estimation are presented. Next, roundoff errors
of both algorithms in fixed point arithmetic are
analyzed and compared. Expressions are \ldots{}",
}
@Article{Jansen:1986:HAA,
author = "Paul Jansen and Peter Weidner",
title = "High-Accuracy Arithmetic Software --- Some Tests of
the {ACRITH} Problem-Solving Routines",
journal = j-TOMS,
volume = "12",
number = "1",
pages = "62--70",
month = mar,
year = "1986",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/5960.5962",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65Dxx",
MRnumber = "868 096",
bibdate = "Sat Aug 13 17:26:53 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/5960.5962;
http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p62-jansen/",
abstract = "The program package ACRITH (High-Accuracy Arithmetic
Subroutine Library) provides FORTRAN subroutines for
the solution of several standard mathematical problems.
The routines use floating point operations with
extended precision and interval arithmetic and are
designated especially for the solution of
ill-conditioned problems. Test results for most of the
routines are presented with emphasis on the practical
usability of the package. It turns out that not all
routines are of equal high quality and reliability; in
the documentation, hints to the implemented numerical
algorithms are completely missing, and the error
messages are not always concise. Some possible
alternatives like symbolic algebra systems or multiple
precision packages are mentioned.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; floating-point testing",
review = "ACM CR 8612-1110",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, ACRITH. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms. {\bf I.1.3}: Computing Methodologies,
ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN. {\bf G.4}: Mathematics of
Computing, MATHEMATICAL SOFTWARE, Reliability and
robustness.",
}
@InProceedings{Johnson:1986:TRH,
author = "T. Johnson and G. Clark",
title = "Techniques for realization of high-speed recursive
digital filters using residue number system
arithmetic",
crossref = "IEEE:1986:III",
volume = "11",
pages = "2623--2626",
month = apr,
year = "1986",
CODEN = "ITCOB4",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue-number-arithmetic digital filters offer major
cost and speed advantages over binary-arithmetic
digital filters but suffer one major drawback. The
filter coefficients must remain constant because
efficient means of updating by fractional arithmetic in
residue number systems involves time consuming
overhead. To maintain high speed in the system the
choices are to use RNS in the adders and multipliers
with scaling done in ROM, to do RNS multiplies and
additions and scale as part of CRT conversion at the
output, or to apply a new fractional NTT interpretation
of multiplier output and use RNS throughout. These
methods are discussed in this paper.",
}
@InProceedings{Kabal:1986:PFP,
author = "P. Kabal and B. Sayar",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '86}",
title = "Performance of fixed-point {FFT}'s: Rounding and
scaling considerations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "221--224",
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The calculation of the discrete Fourier transform
using a fast Fourier transform (FFT) algorithm with
fixed-point arithmetic is considered. The input data is
scaled to prevent overflow and to maintain accuracy.
The implementation uses 16-bit fixed- \ldots{}",
}
@TechReport{Kahan:1986:RAF,
author = "W. Kahan",
title = "Rational Arithmetic in Floating-Point",
type = "Technical Report",
number = "PAM-343",
institution = inst-BERKELEY-CPAM,
address = inst-BERKELEY-CPAM:adr,
pages = "8",
month = sep,
year = "1986",
bibdate = "Sun Dec 18 15:33:08 GMT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Kreithen:1986:FPC,
author = "Daniel E. Kreithen",
title = "Floating point calculation speeds for the image
processing workstation",
institution = "Brown University, Division of Engineering",
address = "Providence, RI, USA",
pages = "23",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Krishnan:1986:CCN,
author = "R. Krishnan and G. Jullien and W. Miller",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '86}",
title = "Computation of complex number theoretic transforms
using quadratic residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "233--236",
year = "1986",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Very recently, the Quadratic Residue Number System
(QRNS) has been introduced [4,5]. The QRNS is obtained
from a mapping of Gaussian integers over a finite ring
to a ring of conjugate elements. The conjugate ring has
the remarkable property that \ldots{}",
}
@Article{Krishnan:1986:CDS,
author = "R. Krishnan and G. Jullien and W. Miller",
title = "Complex digital signal processing using quadratic
residue number systems",
journal = "Acoustics, Speech, and Signal Processing [see also
IEEE Transactions on Signal Processing], IEEE
Transactions on",
volume = "34",
number = "1",
pages = "166--177",
month = feb,
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26196",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Recently, the quadratic residue number system (QRNS)
has been introduced [6], [7] which allows the
multiplication of complex integers with two real
multiplications. The restriction is that the number
system has either all prime moduli of the form 4K
\ldots{}",
}
@Article{Krishnan:1986:ICN,
author = "R. Krishnan and G. Jullien and W. Miller",
title = "Implementation of complex number theoretic transforms
using quadratic residue number systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "8",
pages = "759--766",
month = aug,
year = "1986",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23583",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "Very recently, the Quadratic Residue Number System
(QRNS) has been introduced [6], [7]. The QRNS is
obtained from a mapping of Gaussian integers over a
finite ring to a ring of conjugate elements. The
conjugate ring has the remarkable property that
\ldots{}",
}
@Article{Krishnan:1986:MQR,
author = "R. Krishnan and G. Jullien and W. Miller",
title = "The modified quadratic residue number system ({MQRNS})
for complex high-speed signal processing",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "3",
pages = "325--327",
month = mar,
year = "1986",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23578",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "Recently, the Quadratic Residue Number System,(QRNS)
has been introduced [5], [6], which allows the
multiplication of complex integers with two real
multiplications. The restriction is that this special
residue number system has all moduli with \ldots{}",
}
@Article{Kulisch:1986:ADC,
author = "Ulrich W. Kulisch and Willard L. Miranker",
title = "The Arithmetic of the Digital Computer: a New
Approach",
journal = j-SIAM-REVIEW,
volume = "28",
number = "1",
pages = "1--40",
month = mar,
year = "1986",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1028001",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65G10 (68M15)",
MRnumber = "87e:65030",
MRreviewer = "G. Blanch",
bibdate = "Sat Mar 29 09:54:03 MDT 2014",
bibsource = "Compendex database;
http://epubs.siam.org/toc/siread/28/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
abstract = "A new approach to the arithmetic of the digital
computer is surveyed. The methodology for defining and
implementing floating-point arithmetic is described.
Shortcomings of elementary floating-point arithmetic
are revealed through sample problems. The development
of automatic computation with emphasis on the user
control of errors is reviewed. The limitations of
conventional rule-of-thumb procedures for error control
in scientific computation are demonstrated by means of
examples. Computer arithmetic is extended so that the
arithmetic operations in the linear spaces and their
interval correspondents which are most commonly used in
computation can be performed with maximum accuracy on
digital computers. A new fundamental computer
operation, the scalar product, is introduced to develop
this advanced computer arithmetic.",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of California, Computer Science Dep, Santa
Barbara, CA, USA",
classification = "723",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "accurate floating-point summation; computer
arithmetic; computer metatheory; computer programming
languages; computers, digital; floating-point
arithmetic",
onlinedate = "March 1986",
referred = "[Layn91a].",
}
@Misc{Kulisch:1986:CGS,
author = "Ulrich Kulisch",
title = "Circuitry for generating scalar products and sums of
floating point numbers with maximum accuracy",
howpublished = "US Patent 4622650",
day = "11",
month = nov,
year = "1986",
bibdate = "Mon Dec 29 16:20:01 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/4622650/fulltext.html",
abstract = "Circuitry for generating scalar products and sums of
floating point numbers with maximum accuracy and
circuitry and a method for electronic computers by
which scalar products of floating point numbers of the
type pi, qi, ES(b,l,e1,e2) are summed with full
precision in a fixed point representation by means of a
summing unit (ALU) and one or more accumulator
registers (ARC1, ARC2) with cells (Ai, j) for storing
of codes of a base b having a length (2l + 2 e1 + 2e2)
for fixed point representation and certain overflow
positions. By control means (SHR, E, Contr) the
mantissas of products are delivered depending on the
value of the respective exponents into the summing unit
(ALU). By control means (RD, Contro), rounding
operations demanded by the higher level computer are
performed, and a rounded floating point number and
overflow (OF) and underflow (UF) criteria are
delivered. Parallel, serial and word organized summing
units (ALU) and accumulator registers (ACR) are usable
and in another embodiment, the multiplication of the
factors (pi, qi) is performed using a table of
multiples store.",
acknowledgement = ack-nhfb,
}
@Article{Lorang:1986:SD,
author = "O. Lorang",
title = "{Schnelle Division} \toenglish {Fast Division}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "22",
pages = "167--168",
year = "1986",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{MacIntyre:1986:UOS,
author = "Ferren MacIntyre and Thomas Dowling",
title = "User-oriented suggestions for floating-point and
complex-arithmetic {Forth} standard extensions",
journal = j-J-FORTH-APPL-RES,
volume = "3",
number = "4",
pages = "65--84",
year = "1986",
CODEN = "JFAREL",
ISSN = "0738-2022",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "11736",
catcode = "D.3.2; D.3.0; H.1.2; G.1.0",
CRclass = "D.3.2 Language Classifications; D.3.2 FORTH; D.3.0
General; D.3.0 Standards; H.1.2 User/Machine Systems;
H.1.2 Human factors; G.1.0 General; G.1.0 Computer
arithmetic",
descriptor = "Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTH; Software, PROGRAMMING
LANGUAGES, General, Standards; Information Systems,
MODELS AND PRINCIPLES, User/Machine Systems, Human
factors; Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic",
fjournal = "Journal of FORTH Application and Research",
genterm = "LANGUAGES; THEORY; HUMAN FACTORS; STANDARDIZATION",
guideno = "1986-08466",
journalabbrev = "J. FORTH Appl. Res.",
subject = "D. Software; D.3 PROGRAMMING LANGUAGES; D. Software;
D.3 PROGRAMMING LANGUAGES; H. Information Systems; H.1
MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS",
}
@Article{Marrin:1986:MBF,
author = "K. Marrin",
title = "Microprocessor brings floating-point capability to
32-bit market",
journal = j-COMP-DESIGN,
volume = "25",
number = "9",
pages = "31--38",
day = "1",
month = may,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "20530",
catcode = "B.7.1",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Advanced
technologies",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Advanced technologies",
fjournal = "Computer Design",
genterm = "DESIGN",
guideno = "1986-03960",
journalabbrev = "Comput. Des.",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS",
}
@Article{Marrin:1986:PBT,
author = "K. Marrin",
title = "Plug-in boards transform {PCs} into floating-point
workstations",
journal = j-COMP-DESIGN,
volume = "25",
number = "4",
pages = "31--34",
day = "15",
month = feb,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "19192",
catcode = "K.8; C.1.2; C.4",
CRclass = "C.1.2 Multiple Data Stream Architectures
(Multiprocessors); C.1.2 Array and vector processors",
descriptor = "Computing Milieux, PERSONAL COMPUTING; Computer
Systems Organization, PROCESSOR ARCHITECTURES, Multiple
Data Stream Architectures (Multiprocessors), Array and
vector processors; Computer Systems Organization,
PERFORMANCE OF SYSTEMS",
fjournal = "Computer Design",
genterm = "DESIGN; PERFORMANCE; MEASUREMENT",
guideno = "1986-03913",
journalabbrev = "Comput. Des.",
subject = "K. Computing Milieux; K.8 PERSONAL COMPUTING; C.
Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES; C. Computer Systems Organization; C.4
PERFORMANCE OF SYSTEMS",
}
@InProceedings{Melear:1986:HSM,
author = "C. Melear and D. Tietjen",
title = "High Speed Math Using a Floating Point Coprocessor",
crossref = "Mini-Micro:1986:EMM",
pages = "14/3/1--8",
year = "1986",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Moore:1986:PFS,
author = "Brian A. Moore",
title = "A pipelined floating-point systolic array arithmetic
processor",
type = "Thesis ({M.S.})",
school = "Brigham Young University. Department of Electrical
Engineering",
address = "Provo, UT, USA",
pages = "vi + 58",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Computer arithmetic and logic
units.; Computers, Pipeline.",
}
@Article{Moshier:1986:CA,
author = "S. L. Moshier",
title = "Computer Approximations",
journal = j-BYTE,
volume = "11",
number = "4",
pages = "161--178",
month = apr,
year = "1986",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Ngai:1986:RAT,
author = "Tin-Fook Ngai and Mary Jane Irwin and Shishpal Rawat",
title = "Regular, Area-Time Efficient Carry-Lookahead Adders",
journal = j-J-PAR-DIST-COMP,
volume = "3",
number = "1",
pages = "92--105",
month = mar,
year = "1986",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Mon Apr 14 07:47:57 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Stanford Univ, Stanford, CA, USA",
classification = "723; 921; C5230 (Digital arithmetic methods)",
corpsource = "Department of Electr. Eng., Stanford University, CA,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "adders; Adders; area-time efficiency; carry chain
computation; carry logic; carry-lookahead adders;
carry-lookahead adders (cla); computers; digital
arithmetic; fast binary addition; integrated circuits,
VLSI --- Electric Wiring; interconnection wire length;
log n; log N stage design; maximum; regularity; stage
design; VLSI",
treatment = "P Practical",
}
@Article{Nowak:1986:HBU,
author = "M. Nowak",
title = "{Hex-BCD-Um\-wand\-lung} \toenglish {Hexadecimal-BCD
Conversion} \endtoenglish",
journal = j-MC,
volume = "10",
pages = "68",
year = "1986",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@PhdThesis{Paez-Monzon:1986:ERC,
author = "Gerard Paez-Monzon",
title = "{{\'E}}tude et {R}{\'e}alisation d'un Co-processeur
Arithm{\'e}tique en Virgule Flottante. ({French})
[{Study} and Implementation of a Floating-Point
Coprocessor]",
type = "Doctorat d'{\'E}tat",
school = "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
address = "Paris, France",
pages = "229",
year = "1986",
bibdate = "Thu May 09 09:55:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Sous la direction de Gerard Noguez.",
abstract = "Le premier chapitre d'introduction d{\'e}crit
l'{\'e}tat de l'art dans le domaine des
algorithmes-cabl{\'e}s {\'e}l{\'e}mentaires
utilis{\'e}s dans l'arithm{\'e}tique flottante. Nous y
pr{\'e}sentons une classification architecturale des
coprocesseurs arithm{\'e}tiques en virgule flottante.
{\`A} partir d'une comparaison de trois standards de
virgule flottante orient{\'e}s vers les syst{\`e}mes
bases sur microprocesseurs: IEEE-P754, VAX-DEC, et
Hewlett--Packard, le deuxi{\`e}me chapitre explique le
choix de l'architecture externe de coprocesseur. Le
troisi{\`e}me chapitre pr{\'e}sente l'architecture
interne microprogramm{\'e}e et l'organisation du
coprocesseur d{\'e}velopp{\'e} dans l'{\'e}tude,
nomm{\'e}e FPU-IP6. Dans le quatri{\`e}me chapitre,
nous proposons une nouvelle m{\'e}thode pour le
d{\'e}veloppement des microprogrammes. La cle de la
m{\'e}thode est la visualisation de la s{\'e}paration
des phases de planification et d'implantation. Le
cinqui{\`e}me chapitre pr{\'e}sente les microprogrammes
d{\'e}velopp{\'e}s pour notre coprocesseur. Nous
analysons les diff{\'e}rents micro-algorithmes selon le
type d'instruction (E/S, arith, etc) et la
pr{\'e}cision (simple, double). L'organisation de
l'espace de la microm{\'e}moire est present{\'e}e. Le
sixi{\`e}me chapitre d{\'e}crit l'{\'e}tude
realis{\'e}e pour l'int{\'e}gration du coprocesseur
dans le compilateur C et le syst{\`e}me UNIX de la
machine SM90.",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Payne:1986:PTF,
author = "Mary H. Payne",
title = "Proposal for the transfer of floating point data",
journal = j-SIGNUM,
volume = "21",
number = "3",
pages = "25--26",
month = jul,
year = "1986",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Mon Apr 25 11:24:15 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Petkovic:1986:SIS,
author = "M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}",
title = "On some improvements of square root iteration for
polynomial complex zeros",
journal = j-J-COMPUT-APPL-MATH,
volume = "15",
number = "1",
pages = "13--25",
month = may,
year = "1986",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(86)90235-9",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 11:59:55 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786902359",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "polynomial root finding",
}
@Article{Pfenninger:1986:SQA,
author = "E. Pfenninger",
title = "{Schneller Quadratwurzel-Algorithmus} \toenglish {Fast
Square-Root Algorithms} \endtoenglish",
journal = j-ELECTRONIK,
volume = "22",
pages = "179--180",
year = "1986",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{Porter:1986:FPM,
author = "K. Porter and J. Kath",
title = "Floating-point methods combine to boost performance",
journal = j-COMP-DESIGN,
volume = "25",
number = "3",
pages = "75--80",
month = feb,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "18468",
catcode = "G.1.0; K.1",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic; K.1
Standards",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic; Computing Milieux, THE COMPUTER
INDUSTRY, Standards",
fjournal = "Computer Design",
genterm = "DESIGN; THEORY; ALGORITHMS; PERFORMANCE;
STANDARDIZATION",
guideno = "1986-03910",
journalabbrev = "Comput. Des.",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
K. Computing Milieux; K.1 THE COMPUTER INDUSTRY",
}
@Article{Quong:1986:FPI,
author = "D. Quong",
title = "Floating-point $ \mu {P} $ implements high-speed math
functions",
journal = j-EDN,
volume = "31",
number = "3",
pages = "143--150",
month = feb,
year = "1986",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Wed Sep 7 22:31:45 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "EDN",
}
@Article{Ramnarayan:1986:LCL,
author = "R. Ramnarayan and F. Taylor",
title = "Limit cycles in large moduli residue number system
digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "9",
pages = "912--915",
month = sep,
year = "1986",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23584",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
}
@Article{Rhyne:1986:SBS,
author = "T. Rhyne and N. R. {Strader II}",
title = "A Signed Bit-Sequential Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-35",
number = "10",
pages = "896--901",
month = oct,
year = "1986",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1986.1676680",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 14:09:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See comments \cite{Smith:1989:CSB}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676680",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Robertson:1986:NQD,
author = "James Evans Robertson",
title = "Normalization and quotient digit selection for a
variable precision arithmetic unit",
type = "Report",
number = "UIUCDCS-R-86-1229",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "14",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "``April 1986.''--Cover. ``UILU-ENG-86-1723.''--Cover.
Bibliography: p. 13.",
}
@Article{Rump:1986:SER,
author = "Siegfried M. Rump",
title = "{Sichere Ergebnisse auf Rechenanlagen} \toenglish
{Safe Results from Computers} \endtoenglish",
journal = j-INFORMATIK-SPEKTRUM,
volume = "9",
number = "3",
pages = "174--183",
month = jun,
year = "1986",
CODEN = "INSKDW",
ISSN = "0170-6012 (print), 1432-122X (electronic)",
ISSN-L = "0170-6012",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Informatik Spektrum",
journal-URL = "http://link.springer.com/journal/287",
}
@Article{Schatte:1986:ALD,
author = "Peter Schatte",
title = "On the asymptotic logarithmic distribution of the
floating-point mantissas of sums",
journal = j-MATH-NACHR,
volume = "127",
pages = "7--20",
year = "1986",
CODEN = "MTMNAQ",
ISSN = "0025-584X",
MRclass = "60F05",
MRnumber = "87m:60059",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
reviewer = "A. Fuchs",
}
@TechReport{Schmickley:1986:CCP,
author = "Ronald D. Schmickley and David H. Bailey",
title = "A comparison of the {Cray-2} performance before and
after the installation of memory psudo-banking",
type = "{NASA} contractor report",
number = "NASA CR-177462",
institution = "National Aeronautics and Space Administration, Ames
Research Center; National Technical Information
Service, distributor",
address = "Moffett Field, CA, USA",
pages = "????",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.26:177462 0830-H-14 (MF)",
keywords = "Accounting.; Computer systems performance.; Cray
computers.; Floating point arithmetic.; Memory
(Computers); Response time (Computers)",
remark = "Distributed to depository libraries in microfiche.
Microfiche. [Washington, D.C.: National Aeronautics and
Space Administration, 1988] 1 microfiche.",
}
@Article{Semba:1986:ADL,
author = "I. Semba",
title = "An Algorithm for Division of Large Integers",
journal = j-INFO-PROC,
volume = "9",
number = "3",
pages = "145--147",
month = "????",
year = "1986",
bibdate = "Thu Sep 1 10:15:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Shukla:1986:IMN,
author = "Pankaj N. Shukla",
title = "An implementation on a {MC68000\slash NS32081}
microcomputer of binary floating-point arithmetic based
on the {IEEE 754} standard",
type = "Thesis ({M.S.})",
school = "Michigan Technological University",
address = "1400 Townsend Drive, Houghton, MI 49931-1295, USA",
pages = "vii + 166",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Michigan Technological University. --- Theses
({M.S.}).; MTU Electrical Engineering. --- Thesis
({M.S.}).",
}
@InProceedings{Simcoe:1986:MFP,
author = "R. J. Simcoe and A. Fisher and B. M. Leary and W. R.
Bidermann and W. R. Wheeler",
title = "The {MicroVAX} 78132 Floating Point Chip",
crossref = "IEEE:1986:PII",
pages = "420--425",
year = "1986",
bibdate = "Wed Sep 07 23:14:42 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Soderstrand:1986:RNS,
editor = "Michael A. Soderstrand and W. K. Jenkins and G. A.
Graham and F. J. Taylor",
title = "Residue number system arithmetic: modern applications
in digital signal processing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "vii + 418",
year = "1986",
ISBN = "0-87942-205-X",
ISBN-13 = "978-0-87942-205-9",
LCCN = "QA247.35 .R45 1986",
bibdate = "Wed Nov 14 14:28:02 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "IEEE Press selected reprint series",
acknowledgement = ack-nhfb,
subject = "modular arithmetic; signal processing; digital
techniques; computer programming",
}
@Article{Soderstrand:1986:VIM,
author = "M. Soderstrand and R. Escott",
title = "{VLSI} implementation in multiple-valued logic of an
{FIR} digital filter using residue number system
arithmetic",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "33",
number = "1",
pages = "5--25",
month = jan,
year = "1986",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1049/el:19850252",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23573",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "Computer simulations using SPICE establish the
feasibility of implementing a highly pipelined
high-speed FIR digital filter using Multiple-Valued
Logic (MVL) Read-Only Memories (ROM's) to implement
Residue Number System (RNS) Arithmetic in VLSI
\ldots{}",
}
@TechReport{Spafford:1986:RASa,
author = "E. H. Spafford and J. C. Flaspohler",
title = "A Report on the Accuracy of Some Floating-Point Math
Functions on Selected Computers",
type = "Technical Report",
number = "GIT-SERC-86/02, GIT-ICS-85/06",
institution = "Georgia Institute of Technology",
pages = "??",
year = "1986",
bibdate = "Mon Sep 12 23:54:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Spafford:1986:RASb,
author = "Eugene H. Spafford and John C. Flaspohler",
title = "A Report on the Accuracy of Some Floating Point Math
Functions on Selected Computers",
journal = j-LOGIN,
volume = "11",
number = "2",
pages = "31--56",
month = mar # "\slash " # apr,
year = "1986",
CODEN = "LOGNEM",
ISSN = "1044-6397 (print), 2169-9364 (electronic)",
bibdate = "Tue Feb 20 15:42:13 MST 1996",
bibsource = "ftp://ftp.uu.net/library/bibliography;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Georgia Institute of Technology",
fjournal = ";login: the USENIX Association newsletter",
}
@Article{Stewart:1986:CNC,
author = "G. W. Stewart",
title = "Corrigendum: ``{A} Note on Complex Division''",
journal = j-TOMS,
volume = "12",
number = "3",
pages = "285",
month = sep,
year = "1986",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/7921.356182",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 21:20:12 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Stewart:1985:NCD}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Strobach:1986:NFL,
author = "P. Strobach",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP '86}",
title = "New forms of least squares lattice algorithms and a
comparison of their round-off error characteristics",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "573--576",
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Two versions of the most recently introduced ``pure
order recursive'' LS lattice algorithm are discussed in
this paper. An analysis of the round-off error
characteristics of the new order recursive lattice
method is performed and a comparison is made \ldots{}",
}
@Article{Stummel:1986:SOP,
author = "F. Stummel",
title = "Strict optimal a posteriori error and residual bounds
for {Gaussian} elimination in floating-point
arithmetic",
journal = j-COMPUTING,
volume = "37",
number = "2",
pages = "103--124",
year = "1986",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65F05 (65G05)",
MRnumber = "88b:65047",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "Alfonso Laratta",
}
@Manual{Sun:1986:FPG,
title = "Floating-point programmer's guide for the {Sun}
workstation",
publisher = "Sun Microsystems, Inc.",
address = "Mountain View, CA, USA",
edition = "Revision {A} of 19 {September} 1986.",
pages = "various",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units.; Floating-point
arithmetic.",
remark = "``Part Number 800-1552-10.''",
}
@Article{Thun:1986:RNS,
author = "R. Thun",
title = "On residue number system decoding",
journal = "Acoustics, Speech, and Signal Processing [see also
IEEE Transactions on Signal Processing], IEEE
Transactions on",
volume = "34",
number = "5",
pages = "1346--1347",
month = oct,
year = "1986",
CODEN = "????",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26200",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The use of a residue number system (RNS) in digital
systems and especially filter designs is facilitated by
efficient algorithms for the conversion from RNS to
binary numbers. The conversion is generally based on
the Chinese remainder theorem or the \ldots{}",
}
@Article{Troutman:1986:DSF,
author = "W. W. Troutman and P. W. Diodato and A. K. Goksel and
Mean-Sea Tsay and R. H. Krambeck",
title = "Design of a Standard Floating-Point Chip",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "21",
number = "3",
pages = "396--399",
month = jun,
year = "1986",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:53 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "Some aspects of design of a VLSI floating-point chip,
which provides the WE{\reg}32100 microprocessor with
math acceleration capabilities, are described. The chip
is implemented in 1.75-$\mu$m twin-tub CMOS II
technology [2] and contains \ldots{}",
}
@Article{Truong:1986:TCD,
author = "T. K. Truong and J. J. Chang and I. S. Hsu and D. Y.
Pei and I. S. Reed",
title = "Techniques for Computing the Discrete {Fourier}
Transform Using the Quadratic Residue {Fermat} Number
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-35",
number = "11",
pages = "1008--1012",
month = nov,
year = "1986",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1986.1676704",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 14:09:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676704",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Twaddell:1986:HPM,
author = "W. Twaddell",
title = "Higher performance marks floating-point chips",
journal = j-COMP-DESIGN,
volume = "25",
number = "8",
pages = "24--30",
day = "15",
month = apr,
year = "1986",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "19171",
catcode = "B.7.1; C.4",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Advanced
technologies",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Advanced technologies; Computer Systems
Organization, PERFORMANCE OF SYSTEMS",
fjournal = "Computer Design",
genterm = "DESIGN; PERFORMANCE",
guideno = "1986-03952",
journalabbrev = "Comput. Des.",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer
Systems Organization; C.4 PERFORMANCE OF SYSTEMS",
}
@InProceedings{Vaccaro:1986:SDF,
author = "J. Vaccaro and B. Johnson and C. Nowacki",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '86}",
title = "A systolic discrete {Fourier} transform using residue
number systems over the ring of {Gaussian} integers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1157--1160",
month = aug,
year = "1986",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A VLSI implementation of a bit-serial systolic
architecture for a DFT processor has been developed
which performs residue number system (RNS) processing
over the ring of Gaussian integers. An architecture for
a 128-point DFT using the chirp z-transform algorithm
is described, and its use in an R2FFT architecture to
obtain a 16,384-point transform is illustrated. Based
on three custom-designed chips, the processor is
capable of transforming data at a continuous 2 MHz
rate. The use of RNS techniques and systolic arrays
provides two dimensions of parallelism, resulting in
hardware of low complexity and high speed. The overall
system has great flexibility in dynamic range, and can
be used in many signal processing applications.",
}
@MastersThesis{Verma:1986:DEF,
author = "Deepak Verma",
title = "Design of an efficient floating point vector
coprocessor of an advanced microcomputer system",
type = "Thesis ({M.S.})",
school = "Department of Computer Engineering and Science, Case
Western Reserve University",
address = "Cleveland, OH 44106, USA",
pages = "viii + 121",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Waterhouse:1986:TMW,
author = "William C. Waterhouse",
title = "The Teaching of Mathematics: Why Square Roots are
Irrational",
journal = j-AMER-MATH-MONTHLY,
volume = "93",
number = "3",
pages = "213--214",
month = mar,
year = "1986",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:15 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@TechReport{Weitek:1986:WSW,
author = "{Weitek Corporation}",
title = "{WTL} 1164\slash {WTL} 1165 64-bit {IEEE}
Float\-ing-Point Multiplier\slash Divider and {ALU}",
institution = pub-WEITEK,
address = pub-WEITEK:adr,
month = jul,
year = "1986",
bibdate = "Thu Nov 8 14:50:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Wichmann:1986:FPI,
author = "Brian A. Wichmann",
title = "Floating point interval arithmetic for validation",
institution = "National Physical Laboratory, Division of Information
Technology and Computing",
address = "Teddington Middlesex",
pages = "i + 12",
year = "1986",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "NPL report; DITC 76/86",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Floating-point arithmetic.",
}
@Article{Wollenberg:1986:SRD,
author = "R. Wollenberg and R. Milnikel",
title = "{Schnelles Radizierverfahren durch Tabellenzugriff}
\toenglish {Fast Square-rooting Method by Means of
Table Lookup} \endtoenglish",
journal = j-ELECTRONIK,
volume = "6",
pages = "79--82",
year = "1986",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@InProceedings{Agrawal:1987:CEF,
author = "J. C. Agrawal and P. S. Sehdev",
title = "Comparison and Evaluation of Floating Point
Representations in {IBM\slash 370} and {VAX-11\slash
780}",
crossref = "Zunde:1987:EFI",
pages = "353--369",
year = "1987",
bibdate = "Wed Sep 14 20:23:44 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Agarwal:1987:CNS,
author = "Ramesh C. Agarwal and James W. Cooley and Fred G.
Gustavson and James B. Shearer and Gordon Slishman and
Bryant Tuckerman",
title = "Clarification: {``New scalar and vector elementary
functions for the IBM System/370''} [{IBM J. Res.
Develop. {\bf 30} (1986), no. 2, 126--144}]",
journal = j-IBM-JRD,
volume = "31",
number = "2",
pages = "274--274",
month = mar,
year = "1987",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.312.0274",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "76W05",
MRnumber = "MR894626",
bibdate = "Mon Feb 12 08:07:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
http://www.research.ibm.com/journal/",
note = "See \cite{Agarwal:1986:NSV}.",
acknowledgement = ack-nhfb,
ajournal = "IBM J. Res. Develop.",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Ahmad:1987:IDA,
author = "M. Ahmad",
title = "Implementable Decimal Arithmetic Algorithms for
Micro\slash Minicomputers",
journal = j-MICROPROC-MICROPROG,
volume = "19",
number = "2",
pages = "119--128",
month = feb,
year = "1987",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessing and Microprogramming",
keywords = "decimal floating-point arithmetic",
}
@Article{Anonymous:1987:MAU,
author = "Anonymous",
title = "Multiply-Addition --- An Ultra High Performance
Dataflow",
journal = j-IBM-TDB,
volume = "30",
number = "3",
pages = "982--987",
month = aug,
year = "1987",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Thu Oct 17 12:06:22 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
keywords = "FMA; fused multiply-add",
remark = "Author(s) unknown; I cannot find an online copy of
this paper. This may be the first publication on the
fused multiply-add operation, first implemented in
hardware in early 1990 on the IBM POWER CPU, and
standardized in IEEE 754-2008.",
}
@Book{ANSI:1987:AIS,
author = "{ANSI\slash IEEE}",
title = "{ANSI\slash IEEE Std 854-1987: An American National
Standard: IEEE Standard for Radix-Independent
Floating-Point Arithmetic}",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "v + 14",
day = "5",
month = oct,
year = "1987",
ISBN = "0-7381-1167-8",
ISBN-13 = "978-0-7381-1167-4",
bibdate = "Thu Mar 02 09:40:18 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised 1994. INSPEC Accession Number: 3095617.",
price = "US\$44.00",
URL = "http://ieeexplore.ieee.org/iel1/2502/1121/00027840.pdf;
http://ieeexplore.ieee.org/xpl/standardstoc.jsp?isnumber=1121&isYear=1987",
acknowledgement = ack-nhfb,
}
@Article{Ardalan:1987:FPR,
author = "S. Ardalan and S. Alexander",
title = "Fixed-point roundoff error analysis of the
exponentially windowed {RLS} algorithm for time-varying
systems",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "35",
number = "6",
pages = "770--783",
month = jun,
year = "1987",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A fixed-point roundoff error analysis of the
exponentially windowed RLS algorithm is presented. It
is shown that a tradeoff exists in the choice of the
forgetting factor {\lambda}. In order to reduce the
sensitivity of the algorithm to additive noise, {\&}
\ldots{}",
}
@MastersThesis{Azmi:1987:FPS,
author = "Aqil M. Azmi",
title = "A floating point system with variable-length
exponent",
type = "Thesis ({M.S.})",
school = "University of Colorado",
address = "Boulder, CO, USA",
pages = "viii + 73",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Floating-point arithmetic.",
}
@InProceedings{Balsara:1987:SSS,
author = "Paras T. Balsara and Robert M. Owens",
title = "Systolic and Semi-Systolic Digit Serial Multipliers",
crossref = "Irwin:1987:PSC",
pages = "169--173",
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Balsara_Owens.pdf",
abstract = "Digit serial data transmission can be used to an
advantage in the design of special purpose processors
where communication issues dominate and where digit
pipelining can be used to maintain high data rates.
VLSI signal processing is one such problem domain. We
propose designs of systolic and semi-systolic digit
serial multipliers. These multipliers are programmable
i.e., one operand is pre-stored in the multiplier and
the other operand is fed in a digit serial fashion..
The VLSI implementation of the systolic multiplier is
also given. This systolic multiplier is used in our
VLSI signal processing system.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@MastersThesis{Baranyk:1987:EBP,
author = "Michael L. Baranyk",
title = "Extensions beyond the proposed {IEEE} standard number
754 for binary floating point arithmetic",
type = "Thesis ({M.S.})",
school = "Marquette University",
address = "Milwaukee, WI, USA",
pages = "various",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Binary system (Mathematics); Floating-point
arithmetic.; Institute of Electrical and Electronics
Engineers. --- IEEE; standard 754.",
}
@InProceedings{Barrett:1987:FAR,
author = "Geoff Barrett",
title = "A formal approach to rounding",
crossref = "Irwin:1987:PSC",
pages = "247--254",
year = "1987",
bibdate = "Wed Nov 24 12:49:55 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Barrett.pdf",
abstract = "This paper presents a formal description of rounding,
as specified in the IEEE Standard, and an algorithm to
perform the task along with its proof of correctness.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@TechReport{Barrett:1987:FMA,
author = "Geoff Barrett",
title = "Formal methods applied to a floating point number
system",
type = "Technical monograph",
number = "PRG 58",
institution = "Oxford University Computing Laboratory",
address = "Oxford, England",
pages = "47",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Binary system (Mathematics).; Floating-point
arithmetic.; Formal languages.",
}
@Article{Boettner:1987:QA,
author = "H. B{\"o}ttner",
title = "{Quadratwurzel-Algorithmus} \toenglish {Square-Root
Algorithms} \endtoenglish",
journal = j-MC,
volume = "5",
pages = "58",
year = "1987",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@InCollection{Bohlender:1987:DFP,
author = "G. Bohlender and T. Teufel",
title = "A Decimal Floating-Point Processor for Optimal
Arithmetic",
crossref = "Kaucher:1987:CAS",
pages = "31--58",
year = "1987",
bibdate = "Fri Nov 28 11:46:56 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Boisvert:1987:AAH,
author = "Ronald F. Boisvert",
title = "{Algorithm 651}: Algorithm {HFFT}\emdash High-Order
Fast-Direct Solution of the {Helmholtz} Equation",
journal = j-TOMS,
volume = "13",
number = "3",
pages = "235--249",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/29380.214342",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65V05",
MRnumber = "918 578",
bibdate = "Sun Sep 4 21:40:33 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Johnson:1987:CES}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p235-boisvert/",
abstract = "HFFT is a software package for solving the Helmholtz
equation on bounded two- and three-dimensional
rectangular domains with Dirichlet, Neumann, or
periodic boundary conditions. The software is the
result of combining new fourth-order accurate compact
finite difference (HODIE) discretizations and a
fast-direct solution technique (the Fourier method). In
this paper we briefly describe the user interface to
HFFT and present an example of its usage and several
details of its implementation.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; theory; verification",
subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
ANALYSIS, Partial Differential Equations, Elliptic
equations. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Algorithm analysis.",
}
@Article{Bose:1987:DAR,
author = "B. Bose",
title = "$2$-dimensional arithmetic residue check codes",
journal = j-COMPUT-MATH-APPL,
volume = "13",
number = "5--6",
pages = "547--554",
month = "????",
year = "1987",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:01:00 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122187900824",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Bose:1987:FMD,
author = "B. K. Bose and L. Pei and G. S. Taylor and D. A.
Patterson",
title = "Fast Multiply and Divide for a {VLSI} Floating-Point
Unit",
crossref = "Irwin:1987:PSC",
pages = "87--93",
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Bose_Pei_Taylor_Patterson.pdf",
abstract = "This paper presents the design of a fast and
area-efficient multiply-divide unit used in building a
VLSI floating-point processor (FPU), conforming to the
IEEE standard 754. Details of the algorithms,
implementation techniques and design tradeoffs are
presented. The multiplier and divider are implemented
in 2 micron CMOS technology with two layers of metal,
and occupy 23 square mm (23\% of the entire FPU). We
expect to perform extended-precision multiplication and
division in 1.1 and 2.8 microseconds, respectively.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@PhdThesis{Braune:1987:HSF,
author = "K. Braune",
title = "{Hochgenaue Standardfunktionen f{\"u}r reelle und
komplexe Punkte und Intervalle in beliebigen
Gleitpunktrastern} \toenglish {High-Accuracy Elementary
Functions for Real and Complex Points and Intervals in
Arbitrary Floating-Point Systems} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1987",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{Breuer:1987:NMR,
author = "P. T. Breuer",
title = "A New Method for Real Rational Uniform Approximation",
crossref = "Mason:1987:AAB",
pages = "265--284",
year = "1987",
bibdate = "Thu Sep 01 12:25:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Carter:1987:SAT,
author = "Tony M. Carter",
title = "Structured Arithmetic Tiling of Integrated Circuits",
crossref = "Irwin:1987:PSC",
pages = "41--48",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Carter.pdf",
abstract = "Robertson's Theory of Decomposition and Structured
Tiling (an IC design technique) are combined in a
structured arithmetic circuit design method. This
method, extended by a set of inverse operators and a
set of multiply operators, is used with computer-aided
design tools to automate the design of arithmetic
circuits.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Cavallaro:1987:CAS,
author = "Joseph R. Cavallaro and Franklin T. Luk",
title = "{CORDIC} Arithmetic for an {SVD} Processor",
crossref = "Irwin:1987:PSC",
pages = "113--120",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cavallaro_Luk.pdf",
abstract = "Arithmetic issues in the calculation of the Singular
Value Decomposition (SVD) are discussed. Traditional
algorithms using hardware division and square root are
replaced with the special purpose CORDIC algorithms for
computing vector rotations and inverse tangents. The
CORDIC $ 2 \times 2 $ SVD processor can be twice as
fast as one assembled from traditional hardware units.
A prototype VISI implementation of a CORDIC SVD
processor array is planned for use in real-time signal
processing applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Chandra:1987:ACR,
author = "D. V. Chandra",
title = "Accumulation of coefficient roundoff error in fast
{Fourier} transforms implemented with logarithmic
number system",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "35",
number = "11",
pages = "1633--1636",
month = nov,
year = "1987",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "When a fast Fourier transform (FFT) is implemented on
a digital computer or with special-purpose hardware,
quantization errors will arise due to finite word
lengths in the digital system. This correspondence
presents an analysis of error \ldots{}",
}
@Article{Chen:1987:MFP,
author = "Chang-Fuu Chen",
title = "A modified floating-point code for voice coding and
its applications",
journal = j-J-CHINESE-INST-ENG,
volume = "10",
number = "4",
pages = "421--427",
month = jul,
year = "1987",
CODEN = "CKCKDZ",
ISSN = "0253-3839",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Tatung Institute of Technology, Taipei, Taiwan",
bibno = "43559",
catcode = "E.4; I.2.7; I.2.10; I.5.4",
CRclass = "E.4 Data compaction and compression; I.2.7 Natural
Language Processing; I.2.7 Speech recognition and
understanding; I.2.10 Vision and Scene Understanding;
I.2.10 Modeling and recovery of physical attributes;
I.5.4 Applications; I.5.4 Signal processing",
descriptor = "Data, CODING AND INFORMATION THEORY, Data compaction
and compression; Computing Methodologies, ARTIFICIAL
INTELLIGENCE, Natural Language Processing, Speech
recognition and understanding; Computing Methodologies,
ARTIFICIAL INTELLIGENCE, Vision and Scene
Understanding, Modeling and recovery of physical
attributes; Computing Methodologies, PATTERN
RECOGNITION, Applications, Signal processing",
fjournal = "Journal of the Chinese Institute of Engineers =
Chung-kuo kung ch'eng hsueh kan",
genterm = "THEORY; ALGORITHMS; HUMAN FACTORS; DESIGN",
guideno = "1988-11733",
journalabbrev = "J. Chin. Inst. Eng.",
subject = "E. Data; E.4 CODING AND INFORMATION THEORY; I.
Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE;
I. Computing Methodologies; I.2 ARTIFICIAL
INTELLIGENCE; I. Computing Methodologies; I.5 PATTERN
RECOGNITION",
}
@InProceedings{Ciminiera:1987:PMB,
author = "Luigi Ciminiera",
title = "Parallel Multipliers Based on Horizontal Compressors",
crossref = "Irwin:1987:PSC",
pages = "63--69",
month = may,
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ciminiera.pdf",
abstract = "Two new implementations of parallel multipliers, based
on iterative arrays of logic cells are presented in
this paper. Both are able to compute the product of two
$n$ bit numbers with a delay of $n$ cells, rather $ 2 n
- 1 $ as in classical structures. The high speed
operation is obtained by using pure horizontal
compressors, to accelerate the horizontal signal
propagation, and by adopting a suitable array
structure, to shorten the vertical signal propagation.
The cost and performance advantages over similar
structures based on vertical compressors are
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Clenshaw:1987:LIA,
author = "C. W. Clenshaw and Frank W. J. Olver",
title = "Level-Index Arithmetic Operations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "24",
number = "2",
pages = "470--485",
month = apr,
year = "1987",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0724034",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65G05 (65G99)",
MRnumber = "881377",
MRreviewer = "F. Szidarovszky",
bibdate = "Sun Nov 12 06:18:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In a recent paper the authors described a system for
the internal representation of numbers in a computer,
based on repeated exponentiations. The main objective
in introducing this system is to eradicate the problems
of overflow and underflow. The present paper supplies
algorithms for performing the four basic arithmetical
operations in the new system. The algorithm are
accompanied by error analyses, which show that the
algorithms can be executed with fixed-point arithmetic.
Illustrative examples are included.",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004); Frank William John Olver (15 December 1924--23
April 2013)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@InProceedings{Colagrossi:1987:NAT,
author = "A. Colagrossi and A. Miola",
title = "A Normalization Algorithm for Truncated $p$-{ADIC}
Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "212--216",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Colagrossi_Miola.pdf",
abstract = "This paper presents a new algorithmic approach to cope
with the problems related to the generation and the
manipulation of the pseudo-Hensel-codes in the p-adic
arithmetic. After reviewing some classical properties
and the results of the Hensel code arithmetic, a new
algorithm to manipulate pseudo-Hensel-codes is
presented, discussed and compared with two existing
methods. The lower cost of the proposed new algorithm
will result from the comparison.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Cosnard:1987:FAC,
author = "M. Cosnard and A. Guyot and B. Hochet and Jean-Michel
Muller and H. Ouaouicha and P. Paul and E. Zysman",
title = "The {FELIN} Arithmetic Coprocessor Chip",
crossref = "Irwin:1987:PSC",
pages = "107--112",
month = may,
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cosnard_Guyot_Hochet_Muller_Ouaouicha_Paul_Zysman.pdf",
abstract = "We describe a general VLSI architecture for the
computation of arithmetic expressions including
floating-point transcendental functions. This
architecture, is divided in three parts: a
communication machine, the control part of a
computation machine and the operative part of this
computation machine. In order to compute the most usual
transcendental functions, we introduced some general
algorithms, presented briefly here, including as a
particular case the CORDIC scheme. Our major
architecture goals were regularity, parametrization and
automatic design. The final chip is designed in a 2-Alu
CMOS technology, and its name is FELIN (``Fonctions
EL{\'e}mentaires INt{\'e}gr{\'e}es'' is the French for
``integrated elementary functions'').",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@TechReport{Crockett:1987:PFF,
author = "Thomas W. Crockett",
title = "Performance of {Fortran} Floating-Point Operations on
the {Flex/32} Multicomputer",
type = "{ICASE} Interim Report",
number = "4",
institution = "ICASE, NASA Langley Research Center",
address = "Hampton, VA, USA",
pages = "????",
year = "1987",
bibdate = "Wed Sep 14 20:24:43 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib;
Parallel/ovr.bib",
series = "NASA contractor report; 178364 ICASE interim report; 4
NASA contractor report; NASA CR-178364.",
acknowledgement = ack-nj # " and " # ack-nhfb,
govtdocnumber = "NAS 1.26:178364 830-H-14 (MF)",
keywords = "Computer networks; FORTRAN (Computer program
language)",
remark = "Distributed to depository libraries in microfiche.
Microfiche. [Washington, D.C.?: National Aeronautics
and Space Administration], 1987. 1 microfiche.",
}
@InCollection{Crowell:1987:FPA,
author = "Charles Crowell",
title = "Floating-point arithmetic with the {TMS32020}",
crossref = "Lin:1987:DSP",
pages = "245--268",
year = "1987",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$30.67",
acknowledgement = ack-nhfb,
bibno = "42623",
catcode = "J.2; C.5.3; G.1.0",
CRclass = "J.2 Mathematics and statistics; C.5.3 Microcomputers;
C.5.3 TMS 32010; G.1.0 General; G.1.0 Computer
arithmetic",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Mathematics and statistics; Computer
Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers, TMS 32010; Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic",
genterm = "MEASUREMENT; ALGORITHMS",
guideno = "1988-01737",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Demmel:1987:EAA,
author = "James W. Demmel",
title = "On error analysis in arithmetic with varying relative
precision",
crossref = "Irwin:1987:PSC",
pages = "148--152",
year = "1987",
bibdate = "Thu Aug 23 06:14:44 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
DOI = "https://doi.org/10.1109/ARITH.1987.6158694",
URL = "http://www.netlib.org/na-digest/91/v91n39",
abstract = "Recently Clenshaw\slash Olver and Iri\slash Matsui
proposed new floating point arithmetics which seek to
eliminate overflows and underflows from most
computations. Their common approach is to redistribute
the available numbers to spread out the largest and
smallest numbers much more thinly than in standard
floating point, thus achieving a larger range at the
cost of lower precision at the ends of the range. The
goal of these arithmetics is to eliminate much of the
effort needed to write code which is reliable despite
over\slash underflow. In this paper we argue that for
many codes this eliminated effort will reappear in the
error analyses needed to ascertain or guarantee the
accuracy of the computed solution. Thus reliability
with respect to over\slash underflow has been traded
for reliability with respect to roundoff. We also
propose a hardware flag, analogous to the ``sticky
flags'' of the IEEE binary floating point standard, to
do some of this extra error analysis automatically.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
remark = "Comments on SLI arithmetic proposed by Olver, Lozier,
and Turner, and on Kulisch and Miranker's interval
arithmetic and its implementation in IBM's ACRITH
product.",
}
@TechReport{Dion:1987:MFA,
author = "Jeremy Dion and David Reeves Boggs and Norman P.
Jouppi",
title = "{MultiTitan}: four architecture papers",
institution = "Digital, Western Research Laboratory",
address = "Palo Alto, CA, USA",
pages = "various",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "WRL research report. Digital Equipment Corporation.
Western Research Laboratory; 87-8 Digital Equipment
Corporation. Western Research Laboratory. WRL research
report; 87/8.",
acknowledgement = ack-nhfb,
keywords = "Titan (Computer)",
}
@InProceedings{DuCroz:1987:DFP,
author = "J. {Du Croz} and M. Pont",
title = "The Development of a Floating-Point Validation
Package",
crossref = "Irwin:1987:PSC",
pages = "255--255",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
remark = "Paper not received in time for publication.",
}
@Article{Duff:1987:EAP,
author = "Iain S. Duff and Jacques Laminie and Alain Lichnewsky
and Fran{\c{c}}ois Thomasset",
title = "An experiment with arithmetic precision in linear
algebra computations",
journal = j-INT-J-NUM-METH-FLUIDS,
volume = "7",
number = "????",
pages = "1077--1092",
year = "1987",
bibdate = "Mon Jan 02 17:53:34 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0363",
}
@Manual{Duhamel:1987:ASR,
author = "Bob Duhamel",
title = "{Atari} System Reference Manual",
address = "6915 Casselberry Way, San Diego, CA 92119, USA",
year = "1987",
bibdate = "Sat Mar 04 16:04:10 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See Chapter 11: The Floating Point Arithmetic
Package.",
URL = "http://atrey.karlin.mff.cuni.cz/~pavel/atari/atr11.html;
http://web.archive.org/web/20040606074520/trident.mcs.kent.edu/~clisowsk/8bit/atrpref.html",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "The ROM O/S on the Atari 6502 handles decimal
floating-point values stored in six-byte fields. The
first byte contains the sign and an excess-64 exponent,
followed by five bytes containing ten BCD digits. The
O/S provides for conversion to and from ASCII string
representation, to and from binary integers, add,
subtract, multiple, divide, log(), log10(), exp(),
exp10(), and polynomial evaluation.",
}
@Article{Dunham:1987:PMA,
author = "C. B. Dunham",
title = "Provably Monotone Approximations {II}",
journal = j-SIGNUM,
volume = "22",
number = "3",
pages = "30--31",
month = jul,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Sep 13 09:01:31 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@Article{Ercegovac:1987:FCR,
author = "M. D. Ercegovac and T. Lang",
title = "On-the-fly conversion of redundant into conventional
representations",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "7",
pages = "895--897",
month = jul,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676986",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ercegovac:1987:LSC,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "On-Line Scheme for Computing Rotation Factors",
crossref = "Irwin:1987:PSC",
pages = "196--203",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ercegovac_Lang.pdf",
abstract = "An integrated radix-2 on-line algorithm for computing
rotation factors for matrix transformations is
presented. The inputs and outputs are in parallel form,
conventional 2's complement, floating-point
representation. The exponents are computed using
conventional arithmetic while the significands are
processed using on-line algorithms. The conventional
result is obtained by using an on-the-fly conversion
scheme. The rotation factors are computed in $ 9 + n $
clock cycles for $n$-bit significands. The clock period
is kept small by the use of carry-save adder schemes.
The implementation and performance of the algorithm are
discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Fandrianto:1987:AHS,
author = "Jan Fandrianto",
title = "Algorithms for High Speed Shared Radix 4 Division and
Radix 4 Square-Root",
crossref = "Irwin:1987:PSC",
pages = "73--79",
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Fandrianto.pdf",
abstract = "An algorithm to implement radix four division and
radix four square-root in a shared hardware for IEEE
standard for binary floating point format will be
described. The algorithm is best suited to be
implemented in either off-the-shelf components or being
a portion of a VLSI floating-point chip. Division and
square-root bits are generated by a non-restoring
method while keeping the partial remainder, partial
radicand, quotient and root all in redundant forms. The
core iteration involves a 8-bit carry look-ahead adder,
a multiplexer to convert two's complement to sign
magnitude, a 19-term next quotient\slash root
prediction PLA, a divisor\slash root multiple selector,
and a carry save adder. At the end, two iterations of
carry look-ahead adder across the length of th,e
mantissa are required to generate the quotient\slash
root in a correctly rounded form. Despite its
simplicity in the hardware requirement, the algorithm
takes only about 30 cycles to compute double precision
division or square-root. Finally, extending the
algorithm to radix eight or higher division\slash
square-root will be discussed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8; correct rounding; floating-point arithmetic",
}
@Periodical{FPS:1987:AR,
author = "{Floating Point Systems, Inc.}",
key = "FPS",
title = "Annual report",
publisher = "Floating Point Systems, Inc.",
address = "Portland, OR, USA",
pages = "various",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer industry --- United States --- Periodicals.;
Floating Point Systems, Inc. --- Periodicals.",
remark = "Description based on: 1987.",
}
@Article{Froggatt:1987:FPC,
author = "Terry Froggatt",
title = "Fixed-point conversion, multiplication, and division
in {Ada}",
journal = j-SIGADA-LETTERS,
volume = "7",
number = "1",
pages = "71--81",
month = jan # "\slash " # feb,
year = "1987",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:24 MDT 2003",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://portal.acm.org/;
http://www.adahome.com/Resources/Bibliography/articles.ref;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "languages; theory",
subject = "D.3.2 Software, PROGRAMMING LANGUAGES, Language
Classifications, Ada \\ G.1.0 Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic",
}
@Article{Grosse:1987:UCB,
author = "Eric Grosse and Cleve Moler",
title = "Underflow can be Harmful",
journal = j-SIAM-NEWS,
volume = "20",
number = "6",
pages = "1",
year = "1987",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Feb 8 10:30:07 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Article{Guyot:1987:WBE,
author = "Alain Guyot and Bertrand Hochet and Jean-Michel
Muller",
title = "A Way to Build Efficient Carry-Skip Adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "10",
pages = "1144--1152",
month = oct,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676855",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676855",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hamada:1987:NRN,
author = "Hozumi Hamada",
title = "A New Real Number Representation and Its Operation",
crossref = "Irwin:1987:PSC",
pages = "153--157",
month = may,
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hamada.pdf",
abstract = "A new internal representation is proposed for real
numbers. It has been named URR for universal
representation of real numbers. This approach is based
on a bisection method which is applied to real number
intervals. With this method, the point of division
increases or decreases in a double exponential manner
in the global range. The main characteristics of the
method are as follows. First, overflow\slash underflow
does not, in practice, occur. Second, since the data
format does not depend on the length but on the value
of the data, a transformation operation is virtually
not needed between systems of long and short data.
Finally, only one bit of resolution is lost compared
with the fixed point form. In addition, arithmetic
operations are slightly complicated compared with
conventional representation, but they present no
special difficulties. This new method is thus the most
suitable internal form as an interface not only between
computers but also between computers and digital
systems which deal with real numbers or physical
(scalar) values.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Han:1987:FAE,
author = "Tackdon Han and David A. Carlson",
title = "Fast Area-Efficient {VLSI} Adders",
crossref = "Irwin:1987:PSC",
pages = "49--56",
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Han_Carlson.pdf",
abstract = "In this paper, we study area-time tradeoffs in VLSI
for prefix computation using graph representations of
this problem. Since the problem is intimately related
to binary addition the results we obtain lead to the
design of area-time efficient VLSI adders. This is a
major goal of our work: to design {\em very low
latency\/} addition circuitry that is also {\em area
efficient}. To this end, we present a new graph
representation for prefix computation that leads to the
design of a fast, area-efficient binary adder. The new
graph is a combination of previously known graph
representations for prefix computation, and its area is
close to known lower bounds on the VLSI area of
parallel prefix graphs. Using it, we are able to design
VLSI adders having area $ A = O(n \log n) $ whose delay
time is the lowest possible value, i.e., the fastest
possible area-efficient VLSI adder.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Book{Herz-Fischler:1987:MHD,
author = "Roger Herz-Fischler",
title = "A mathematical history of division in extreme and mean
ratio",
publisher = "Wilfrid Laurier University Press",
address = "Waterloo, ON, Canada",
pages = "xvi + 191",
year = "1987",
ISBN = "0-88920-152-8",
ISBN-13 = "978-0-88920-152-1",
LCCN = "A481.H47 1987",
bibdate = "Thu Jul 10 08:02:28 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$65.00",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
}
@Book{Hildebrand:1987:INA,
author = "Francis Begnaud Hildebrand",
title = "Introduction to numerical analysis",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "Second",
pages = "xiii + 669",
year = "1987",
ISBN = "0-486-65363-3 (paperback)",
ISBN-13 = "978-0-486-65363-1 (paperback)",
LCCN = "QA297 .H54 1987",
bibdate = "Fri Aug 20 09:19:58 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/description/dover032/87005370.html",
acknowledgement = ack-nhfb,
remark = "Unabridged, slightly corrected republication of
\cite{Hildebrand:1974:INA}.",
subject = "Numerical analysis",
}
@Article{Himmeroeder:1987:CKC,
author = "H.-J. Himmer{\"o}der and R. M. Toschke",
title = "{c't-KAT-Ce. Ein 68000-Einplatinenrechner, Teil 3:
REAL-Arithmetik} \toenglish {c't-KAT-Ce. A 68000
Single-Board Computer} \endtoenglish",
journal = j-CT,
volume = "1",
pages = "152--158",
year = "1987",
ISSN = "0724-8679",
bibdate = "Sat Feb 24 09:05:58 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "C T: Magazin f{\"u}r Computer Technik (Hannover)",
}
@InProceedings{Hochet:1987:SSL,
author = "Bertrand Hochet and Patrice Quinton and Yves Robert",
title = "Systolic Solution of Linear Systems over {$ \mathrm
{GF}(p) $} with Partial Pivoting",
crossref = "Irwin:1987:PSC",
pages = "161--168",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hochet_Quinton_Robert.pdf",
abstract = "We propose two systolic architectures for the Gaussian
triangularization and the Gauss--Jordan diagonalization
of large dense $ n \times n $ matrices over $ \mathrm
{GF}(p) $, where $p$ is a prime number. The solution of
large dense linear systems over $ \mathrm {GF}(p) $ is
the major computational step in various algorithms
issued from arithmetic number theory and computer
algebra. The two proposed architectures implement the
elimination with partial pivoting, although the
operation of the array remains purely systolic. The
last section is devoted to the design and layout of a
CMOS 8 by 8 Gauss--Jordan diagonalization systolic chip
over $ \mathrm {GF}(2) $.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Homewood:1987:ITT,
author = "Mark Homewood and David May and David Shepherd and
Roger Shepherd",
title = "The {IMS T800} Transputer",
journal = j-IEEE-MICRO,
volume = "7",
number = "5",
pages = "10--26",
month = sep # "\slash " # oct,
year = "1987",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1987.305012",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Parallel/transputer.bib; Science Citation Index
database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliationaddress = "Inmos Ltd, Bristol, Engl",
classcodes = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips)",
classification = "714; 722; 723; 921",
corpsource = "Inmos Ltd., Bristol, UK",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "architecture; capability; communication links;
computer architecture; computer graphics; computer
programming languages; computers, microcomputer;
Design; floating-point arithmetic; floating-point unit
design; graphics; IMS T800 transputer; integrated
circuits, VLSI; microprocessor chips; performance;
scientific computer; supercomputers; telecommunication
links",
treatment = "P Practical; R Product Review",
}
@InCollection{HP:1987:IPH,
author = "{Hewlett Packard}",
booktitle = "{HP-71} Reference Manual",
title = "The {IEEE} Proposal for Handling Math Exceptions",
publisher = "Hewlett Packard Company",
address = "Palo Alto, CA, USA",
pages = "338--345",
month = oct,
year = "1987",
bibdate = "Fri Nov 28 17:12:16 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Mfg. \#0071-90110, Reorder \#0071-90010. First edition
October 1983. Manual available from {\em The Museum of
HP Calculators}.",
URL = "http://www.hpmuseum.org/",
abstract = "The IEEE Radix Independent Floating-Point Proposal
divides all of the floating-point ``exceptional
events'' encountered in calculations into five classes
of {\em math exceptions\/}: invalid operation, division
by zero, overflow, underflow, and inexact result.
Associated with each math exception is a flag that is
set by the HP-71 whenever an exception is encountered.
These flags remain set until you clear them. Each of
these flags can be accessed by its number or its
name.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@MastersThesis{Hu:1987:CDT,
author = "Timothy Hu",
title = "Circuit design techniques for a floating-point
processor: research project",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "70",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hull:1987:TIC,
author = "T. E. Hull and M. S. Cohen",
title = "Toward an Ideal Computer Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "131--138",
year = "1987",
bibdate = "Fri Nov 28 11:41:31 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hull_Cohen.pdf",
abstract = "A new computer arithmetic is described. Closely
related built-in functions are included. A user's point
of view is taken, so that the emphasis is on what
language features are available to a user. The main new
feature is flexible precision control of decimal
floating-point arithmetic. It is intended that the
language facilities be sufficient for describing
numerical processes one might want to implement, while
at the same time being simple to use, and implementable
in a reasonably efficient manner. Illustrative examples
are based on experience with an existing software
implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8; decimal floating-point arithmetic",
}
@Article{IEEE:1987:ISB,
author = "{IEEE}",
title = "{IEEE} Standard for Binary Floating-Point Arithmetic",
journal = j-SIGPLAN,
volume = "22",
number = "2",
pages = "9--25",
month = feb,
year = "1987",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1109/IEEESTD.1985.82928",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Fri Sep 09 12:55:55 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Book{IEEE:1987:RIS,
editor = "{IEEE}",
title = "{854-1987 (R1994) IEEE Standard for Radix-Independent
Floating-Point Arithmetic}",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "16",
year = "1987",
DOI = "https://doi.org/10.1109/IEEESTD.1987.81037",
ISBN = "1-55937-859-X",
ISBN-13 = "978-1-55937-859-8",
bibdate = "Mon Apr 24 07:02:34 2000",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised 1994.",
price = "US\$44.00",
URL = "http://standards.ieee.org/reading/ieee/std_public/description/busarch/854-1987_desc.html",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "floating point arithmetic; Floating-point arithmetic.;
Standards",
remark = "At head of title: An American National Standard.
``Approved March 12, 1987 IEEE Standards Board;
Approved September 10, 1987 American National Standards
Institute.''",
}
@MastersThesis{Jensen:1987:CIS,
author = "Debby Jensen",
title = "Control implementation for the {SPUR} floating point
coprocessor: research project",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley. Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "76",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Johnson:1987:AES,
author = "Kenneth C. Johnson",
title = "{Algorithm 650}: Efficient Square Root Implementation
on the 68000",
journal = j-TOMS,
volume = "13",
number = "2",
pages = "138--151",
month = jun,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/328512.328520",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15",
MRnumber = "898 489",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Johnson:1987:CES}.",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Johnson:1987:CES,
author = "Kenneth C. Johnson",
title = "Corrigendum: {``Algorithm 650: efficient square root
implementation on the 68000'' [ACM Trans. Math.
Software {\bf 13} (1987), no. 2, 138--151]}",
journal = j-TOMS,
volume = "13",
number = "3",
pages = "320--320",
month = sep,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/29380.356210",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "320. 65D15",
MRnumber = "918 582",
bibdate = "Sat Feb 8 10:30:18 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Kahan:1987:BCC,
author = "W. Kahan",
title = "Branch Cuts for Complex Elementary Functions or Much
Ado About Nothing's Sign Bit",
crossref = "Iserles:1987:SAN",
volume = "9",
pages = "165--211",
year = "1987",
MRclass = "65E05",
MRnumber = "88k:65027",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Inst. Math. Appl. Conf. Ser. New Ser.",
URL = "http://people.freebsd.org/~das/kahan86branch.pdf;
http://www.cs.berkeley.edu/~dbindel/class/cs279/",
acknowledgement = ack-nhfb # " and " # ack-nj,
}
@Unpublished{Kahan:1987:CWF,
author = "W. Kahan",
title = "Checking whether floating-point division is correctly
rounded",
year = "1987",
bibdate = "Mon Apr 25 05:40:03 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Lecture notes.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; floating-point arithmetic; rounding
errors",
}
@Misc{Kahan:1987:DPI,
author = "W. Kahan",
title = "Doubled-precision {IEEE Standard 754} floating-point
arithmetic",
howpublished = "Manuscript",
month = feb,
year = "1987",
bibdate = "Thu May 09 07:25:40 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
remark = "Cited in \cite{Higham:1993:AFP}.",
}
@TechReport{Kahan:1987:HAE,
author = "W. Kahan",
title = "Handling Arithmetic Exceptions",
type = "Report",
institution = inst-BERKELEY-MATH-EECS,
address = inst-BERKELEY-MATH-EECS:adr,
day = "14",
month = may,
year = "1987",
bibdate = "Mon Aug 26 10:42:10 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.arithmazium.org/classroom/lib//Kahan_Handling_Arithmetic_Exceptions.pdf",
abstract = "An {\em Exception\/} arises when an operation
performed by a computer has to produce a result to
which some people might reasonably take exception.
Examples are {\em Division by Zero}, {\em Overflow\/ }
and Floating-Point {\em Underflow}. Though most (but
not all) exceptions must be rare, too rare to be topics
cf everyday conversation, they are not so rare that
computer programmers and users can ignore them
altogether. This paper presents proposals, many of them
now implemented on a few computers, to handle
arithmetic exceptions in a generally satisfactory way
at a tolerable cost. The proposals are designed to be
fully compatible with concurrent, overlapped, parallel,
pipelined and vectorized computing on new hardware that
will be designed to support them without {\em precise
interrupts}. {\em Flags\/} and {\em Modes\/} are
proposed to help programmers cope with exceptions; {\em
Retrospective Diagnostics\/} are proposed to help most
of the rest of us, who aspire to use computers without
having to program them. The features of IEEE Standards
754 and 854 are supported by but not obligatory for the
proposals.",
acknowledgement = ack-nhfb,
}
@Book{Kane:1987:MRR,
author = "Gerry Kane",
title = "{MIPS R2000 RISC} Architecture",
publisher = pub-PH,
address = pub-PH:adr,
year = "1987",
ISBN = "0-13-584749-4",
ISBN-13 = "978-0-13-584749-7",
LCCN = "QA76.8.M52 K36 1987",
bibdate = "Wed Dec 15 17:51:38 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kao:1987:ISM,
author = "Rom-Shen Kao and Fred J. Taylor",
title = "Implementation of the Single Modulus Complex {ALU}",
crossref = "Irwin:1987:PSC",
pages = "21--27",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kao_Taylor.pdf",
abstract = "Recently the complex residue number system, or RNS,
has been a subject of intense study. One special
embodiment of this theory is the single modulus complex
RNS processor which suggests both implementation and
performance advantages. In this paper these conjectures
are tested in the context of a CMOS gate array design
and are found to be valid.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Kirchner:1987:AVP,
author = "R. Kirchner and U. Kulisch",
title = "Arithmetic for Vector Processors",
crossref = "Irwin:1987:PSC",
pages = "256--269",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kirchner_Kulisch.pdf",
abstract = "In electronic computers the elementary arithmetic
operations are these days generally approximated by
floating-point operations of highest accuracy. Vector
processors and parallel computers often provide
additional operations like ``multiply and add'',
``accumulate'' or ``multiply and accumulate''. Also
these operations shall always deliver the correct
answer whatever the data are. The user should not be
obliged to execute an error analysis for operations
predefined by the manufacturer. In the first part of
this paper we discuss circuits which allow a fast and
correct computation of sums and scalar products making
use of a matrix shaped arrangement of adders and
pipeline technology. In the second part a variant is
discussed which permits a drastic reduction in the
number of adders required. The methods discussed in
this paper can also be used to build a fast arithmetic
unit for micro computers in VLSI-technology.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Kirchner:1987:SVS,
author = "Reinhard Kirchner and Ulrich Kulisch",
title = "{Schaltungsanordnung und Verfahren zur schnellen
Berechnung von Summen und Skalarprodukten von
Gleitkommazahlen mit maximaler Genauigkeit mittels
Pipelinetechnik. (German)} [Circuit diagrams and
methods for fast computation of sums and scalar
products of floating point numbers with maximal
accuracy via pipeline technique]",
journal = "Beitr{\"a}ge zur angewandten Mathematik und
Statistik",
publisher = pub-HANSER,
address = pub-HANSER:adr,
pages = "139--177",
year = "1987",
MRclass = "68Q25 (68Q10)",
MRnumber = "986 782",
bibdate = "Fri Dec 08 12:20:44 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Koopman:1987:TF,
author = "P. Koopman",
title = "Transcendental Functions",
journal = j-FORTH-DIMENSIONS,
volume = "9",
number = "4",
pages = "21--22",
month = dec,
year = "1987",
CODEN = "FODMD5",
ISSN = "0884-0822",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Forth Dimensions",
}
@InProceedings{Kornerup:1987:BSA,
author = "Peter Kornerup and David W. Matula",
title = "A Bit-Serial Arithmetic Unit for Rational Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "204--211",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kornerup_Matula.pdf",
abstract = "We describe a binary implementation of an algorithm of
Gosper to compute the sum, difference, product,
quotient and certain rational functions of two rational
operands applicable to integrated approximate and exact
rational computation. The arithmetic unit we propose is
an eight register computation cell with bit, serial
input and output employing the binary lexicographic
continued fraction (LCF) representation of the rational
operands., The operands and results are processed in a
most-significant-bit first on-line fashion with bit
level logic leading to less delay in the computation
cell when compared to operation on the full partial
quotients of the standard continued fraction
representation. Minimization of delay is investigated
with the aim of supporting greater throughput in
cascaded parallel computation with such computation
cells.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@PhdThesis{Kraemer:1987:ISF,
author = "W. Kr{\"a}mer",
title = "Inverse Standardfunktionen f{\"u}r reelle und komplexe
Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
f{\"u}r beliebige Datenformate \toenglish {Inverse
Elementary Functions for Real and Complex Interval
Arguments with A-Priori Error Estimates for Arbitrary
Data Formats} \endtoenglish",
type = "Dissertation",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
year = "1987",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
author-dates = "1952--2014",
}
@InProceedings{Kuninobu:1987:DHS,
author = "Shigeo Kuninobu and Tamotsu Nishiyama and Hisakazu
Edamatsu and Takashi Taniguchi and Naofumi Takagi",
key = "KNE87",
title = "Design of High Speed {MOS} Multiplier and Divider
Using Redundant Binary Representation",
crossref = "Irwin:1987:PSC",
pages = "80--86",
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kuninobu_Nishiyama_Edamatsu_Taniguchi_Takagi.pdf",
abstract = "A high speed multiplier and divider for MOS LSI based
on a new algorithm is presented. When we implement the
multiplier and the divider in LSI. the features such as
high speed operation, small number of transistors and
easy layout are the most important factors. A
computational algorithm using a redundant binary
representation has several excellent features such as
high speed addition operations. We improved the
algorithm and the method of implementation. and
designed an advanced multiplier and divider with the
above mentioned features. We expect that our multiplier
and divider are excellent compared with multipliers
using the Booth algorithm and the Wallace tree. and
with divider using the SRT method, respectively.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Lange:1987:ITA,
author = "Eberhard Lange",
title = "Implementation and Test of the {ACRITH} Facility in a
{System}\slash 370",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "9",
pages = "1088--1096",
month = sep,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009539",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:55 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009539",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "floating-point testing",
}
@Article{Leavitt:1987:APF,
author = "Randal Leavitt",
title = "Adjustable Precision Floating Point Arithmetic in
{Ada}",
journal = j-SIGADA-LETTERS,
volume = "7",
number = "5",
pages = "63--78",
month = sep # "\slash " # oct,
year = "1987",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:26 MDT 2003",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://portal.acm.org/;
http://www.adahome.com/Resources/Bibliography/articles.ref;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "design; performance; theory",
subject = "D.3.2 Software, PROGRAMMING LANGUAGES, Language
Classifications, Ada \\ G.1.0 Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic",
}
@Article{Lien:1987:RCI,
author = "B. Lien and G. Tang",
title = "Reversed {Chebyshev} implementation of {McClellan}
transform and its roundoff error",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "35",
number = "10",
pages = "1435--1439",
month = oct,
year = "1987",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A new structure, called the reversed Chebyshev
structure, for the fixed point implementation of the
FIR filters designed with the McClellan transformation
is presented. It shows the best roundoff noise
performance among the existing ones for both \ldots{}",
}
@InProceedings{Lin:1987:NFP,
author = "Haixiang X. Lin and Henk J. Sips",
title = "A Novel Floating-Point Online Division Algorithm",
crossref = "Irwin:1987:PSC",
pages = "188--195",
month = may,
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Lin_Sips.pdf",
abstract = "This paper describes a new online division
(reciprocal) algorithm for (maximally) redundant
floating-point numbers of arbitrary radix. The
algorithm works for normalized, quasi-normalized, and
pseudo-normalized numbers and can therefore be applied
in chained online computations. The online delay of the
proposed algorithm is the smallest reported so far. The
algorithm consists of two steps: the first $m$ digits
of the result are generated by a simple table lookup
method; the remaining $ n - m $ digits are generated by
using an adapted Newton--Raphson iteration method. In
the second step, the online digits are created by using
a fast and simple selection mechanism.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@MastersThesis{Liu:1987:BEF,
author = "Zhi-Shun Alex Liu",
title = "{Berkeley} Elementary Function Test Suite: Research
Project",
type = "{Master of Science, Plan II}",
school = "Computer Science Division, Department of Electrical
Engineering and Computer Science, Univerity of
California at Berkeley",
address = "Berkeley, CA, USA",
month = dec,
year = "1987",
bibdate = "Mon Sep 12 23:52:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "BeEF test suite; floating-point testing",
}
@Article{Lo:1987:HGA,
author = "H.-Y. Lo and J.-L. Chen",
title = "A Hardwired Generalized Algorithm for Generating the
Logarithm Base-$k$ by Iteration",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "11",
pages = "1363--1367",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009477",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 08:08:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Maenner:1987:FIB,
author = "R. Maenner",
title = "A Fast Integer Binary Logarithm of Large Arguments",
journal = j-IEEE-MICRO,
volume = "7",
number = "6",
pages = "41--45",
month = nov # "\slash " # dec,
year = "1987",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1987.304914",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Magenheimer:1987:IMD,
author = "Daniel J. Magenheimer and Liz Peters and Karl Pettis
and Dan Zuras",
title = "Integer multiplication and division on the {HP
Precision Architecture}",
journal = j-SIGPLAN,
volume = "22",
number = "10",
pages = "90--99",
month = oct,
year = "1987",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:15 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Makarenko:1987:VMM,
author = "Darrell Makarenko and Jonathan Schaeffer",
title = "A {VLSI} multiprecision matrix multiplier and
polynomial evaluator",
journal = j-J-PAR-DIST-COMP,
volume = "4",
number = "6",
pages = "619--628",
month = dec,
year = "1987",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Alberta, Edmonton, Alberta, Can",
classification = "713; 722; C4140 (Linear algebra); C4240 (Programming
and algorithm theory); C5230 (Digital arithmetic
methods)",
corpsource = "Department of Computer Science, Alberta University,
Edmonton, Alta., Canada",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "32 bit; 32-bit multiplication; algebra; band-matrix
multiplication; bit-serial; computational complexity;
computers --- Multiplying Circuits; Design; digital
arithmetic; evaluations; full-matrix multiplication;
integrated circuits, VLSI; linear-space evaluations;
linear-time; mathematical techniques --- Polynomials;
matrix; matrix multiplier; multiply and accumulate
cells; multiprecision matrix multiplier; polynomial
evaluator; polynomials; two dimensional array; two's
complement numbers; VLSI; VLSI multiprecision; VLSI
multiprecision polynomial evaluator",
treatment = "P Practical",
}
@InProceedings{Manzoul:1987:QCN,
author = "Mahmoud A. Manzoul",
title = "A quaternary complex number {CCD} adder (abstract
only)",
crossref = "Davis:1987:PAC",
pages = "434--434",
year = "1987",
DOI = "https://doi.org/10.1145/322917.323095",
bibdate = "Sat Aug 22 09:06:07 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Complex number arithmetic occurs frequently in digital
signal processing and power systems analysis. Normally,
complex numbers are given two binary words, with one
word for each component (real and imaginary).
Therefore, the standard binary implementation of
complex numbers requires several real arithmetic
operations. Besides, the two components of each complex
number must be tracked down at every stage of the
computation. Different digital representations for
complex numbers have been proposed in an effort to
reduce these problems. Knuth [1] has proposed an
unconventional single component representation of
complex numbers whereby the radix is chosen to be (2j)
with the digit set comprised of the first four positive
integers (0, 1, 2, 3). This is in contrast with the
conventional two components representation with binary
radix whether in Cartesian or Polar coordinates.
Knuth's representation leads to simple and interesting
arithmetic in the complex field [2] [3].",
acknowledgement = ack-nhfb,
}
@Article{Mariella:1987:IDF,
author = "Ray Mariella",
title = "Integers Don't Float",
journal = j-DDJ,
volume = "12",
number = "12",
pages = "48--??",
month = dec,
year = "1987",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Mays:1987:IDA,
author = "Michael E. Mays",
title = "Iterating the Division Algorithm",
journal = j-FIB-QUART,
volume = "25",
number = "3",
pages = "204--213",
month = aug,
year = "1987",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:00:58 MDT 2011",
bibsource = "http://www.fq.math.ca/25-3.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/25-3/mays.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Book{McMcusersmanual:1987:MMF,
author = "{Motorola, Inc.}",
title = "{MC68881\slash MC68882} floating-point coprocessor
user's manual",
publisher = pub-PH,
address = pub-PH:adr,
pages = "various",
year = "1987",
ISBN = "0-13-566936-7 (pbk.)",
ISBN-13 = "978-0-13-566936-5 (pbk.)",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Motorola 68881
(Microprocessor); Motorola 68882 (Microprocessor)",
remark = "Spine title: MC68881/MC68882 user's manual.
``MC68881UM/AD REV 1''--Cover.",
}
@Article{Monahan:1987:AGC,
author = "John F. Monahan",
title = "An Algorithm for Generating Chi Random Variables",
journal = j-TOMS,
volume = "13",
number = "2",
pages = "168--172",
month = jun,
year = "1987",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/328512.328522",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65C10",
MRnumber = "88d:65013",
bibdate = "Sat Nov 19 13:08:24 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Johnson:1987:CES,Monahan:1988:CAG}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Montgomery:1987:SPE,
author = "Peter L. Montgomery",
title = "Speeding the {Pollard} and elliptic curve methods of
factorization",
journal = j-MATH-COMPUT,
volume = "48",
number = "177",
pages = "243--264",
month = jan,
year = "1987",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y05 (11A51 68Q40)",
MRnumber = "88e:11130",
MRreviewer = "Kevin S. McCurley",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
JSTOR database",
note = "See improvement \cite{Kim:2024:MCA}.",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C1160 (Combinatorial mathematics); C4240 (Programming
and algorithm theory)",
corpsource = "Syst. Dev. Corp., Santa Monica, CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computational complexity; elliptic curve; elliptic
curve method; elliptic curve methods; factorization;
Lenstra method; Monte Carlo methods; number; number
theory; parametrisation; Pollard methods; polynomial
preconditioning; theory; Williams method",
treatment = "T Theoretical or Mathematical",
}
@Book{Motorola:1987:MMF,
author = "Motorola",
title = "{MC68881\slash MC68882} Floating-Point Coprocessor
User's Manual",
publisher = pub-PH,
address = pub-PH:adr,
pages = "various",
year = "1987",
ISBN = "0-13-566936-7",
ISBN-13 = "978-0-13-566936-5",
LCCN = "QA76.8.M69 M3 1987",
bibdate = "Fri Dec 08 13:03:15 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Mutrie:1987:FEA,
author = "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
Char",
title = "Floating-point error analysis using symbolic algebraic
computation",
type = "Research report",
number = "CS-87-08",
institution = "University of Waterloo, Faculty of Mathematics",
address = "Waterloo, Ont., Canada",
pages = "13",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Roundoff errors.",
remark = "Supported in part by the Natural Sciences and
Engineering Research Council of Canada.",
}
@Misc{Nakano:1987:MAD,
author = "Hiraku Nakano",
title = "Method and apparatus for division using interpolation
approximation",
howpublished = "United States Patent 4,707,798",
day = "17",
month = nov,
year = "1987",
bibdate = "Tue Jan 08 22:36:28 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/4707798.html",
abstract = "A divide method and a divide apparatus for use in a
data processing system. The divisor and dividend are
normalized in a normalization circuit. A table unit
stores a plurality of approximate reciprocal divisors
and differences between adjacent approximate reciprocal
divisors and is addressed by the high-order bits of the
normalized divisor. The approximate reciprocal divisor
read out from the table unit is, in an interpolation
approximation circuit, changed into an interpolation
approximated approximate reciprocal divisor in
accordance with a plurality of bits following the
high-order bits and the difference. A multiplication
unit multiplies the interpolation approximated
approximate reciprocal divisor by the normalized
dividend to output a quotient.",
acknowledgement = ack-nhfb,
}
@Article{Nelsen:1987:PSR,
author = "Roger B. Nelsen and James E. Schultz",
title = "The Probability that the {``Sum} of the Rounds''
Equals the {``Round} of the Sum''",
journal = j-COLLEGE-MATH-J,
volume = "18",
number = "5",
pages = "390--396",
month = nov,
year = "1987",
CODEN = "????",
DOI = "https://doi.org/10.1080/07468342.1987.11973061",
ISSN = "0746-8342 (print), 1931-1346 (electronic)",
ISSN-L = "0746-8342",
bibdate = "Thu Feb 14 09:50:35 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
URL = "http://www.jstor.org/stable/2686963;
http://www.tandfonline.com/doi/abs/10.1080/07468342.1987.11973061",
acknowledgement = ack-nhfb,
fjournal = "College Mathematics Journal",
journal-URL = "https://maa.tandfonline.com/loi/ucmj20;
https://www.jstor.org/journal/collmathj",
keywords = "rounding in fixed-point addition",
onlinedate = "30 Jan 2018",
remark = "See also \cite{Hopkins:2016:WMN} for a later
independent derivation of part of this work.",
}
@Article{Obermaier:1987:SCI,
author = "A. Obermaier",
title = "{Sin und cosin mit Integerarithmetik} \toenglish {Sine
and Cosine with Integer Arithmetic} \endtoenglish",
journal = j-MC,
volume = "6",
pages = "108--112",
year = "1987",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@InProceedings{Olver:1987:CCA,
author = "F. W. J. Olver",
title = "A Closed Computer Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "139--143",
month = may,
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver.pdf",
abstract = "Two closely related new systems of computer arithmetic
are proposed. It is shown that both are closed under
arithmetic operations in finite-precision arithmetic,
thereby offering a permanent solution to the problems
of overflow and underflow. Other advantages of the new
systems pertaining to precision are described, and
there is also a brief discussion of possible ways of
hardware implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Olver:1987:ILI,
author = "F. W. J. Olver and P. R. Turner",
title = "Implementation of Level-Index Arithmetic Using Partial
Table Look-Up",
crossref = "Irwin:1987:PSC",
pages = "144--147",
month = may,
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver_Turner.pdf",
abstract = "This paper is concerned with finding fast efficient
algorithms for performing level-index arithmetic. The
approach used combines the advantages of parallel
processing with the use of table look-up. The latter is
used only for short words and the result is a potential
implementation with $ \li $ operation times comparable
with floating-point long multiplications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Owens:1987:AC,
author = "Robert Michael Owens and Mary Jane Irwin",
title = "The Arithmetic Cube",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "11",
pages = "1342--1348",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009473",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009473",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Papachristou:1987:ATL,
author = "Christos A. Papachristou",
title = "Associative Table Lookup Processing for Multioperand
Residue Arithmetic",
journal = j-J-ACM,
volume = "34",
number = "2",
pages = "376--396",
month = apr,
year = "1987",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Sat Oct 22 00:20:03 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Misc/IMMD_IV.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Parhami:1987:CTL,
author = "B. Parhami",
title = "On the Complexity of Table Lookup for Iterative
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "10",
pages = "1233--1236",
month = oct,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676863",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676863",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Parhami:1987:SUC,
author = "Behrooz Parhami",
title = "Systolic Up\slash Down Counters with Zero and Sign
Detection",
crossref = "Irwin:1987:PSC",
pages = "174--178",
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Parhami.pdf",
abstract = "Although a state encoding scheme for systolic counters
has been presented earlier, several important practical
problems such as zero test, sign detection, overflow,
underflow, and modulo-$n$ (cyclic) counting have not
been dealt with adequately. In this paper, design
principles for unary and binary systolic up\slash down
counters are presented. The unary counters, which are
attractive when dealing with relatively small counts,
are based on the systolic stack concept. The binary
counters use conventional binary number representation,
with several tags associated with each bit position.
The binary counter design presented can be generalized
to counters with higher-radix state encodings.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Peng:1987:ISM,
author = "Victor Peng and Sridhar Samudrala and Moshe
Gavrielov",
title = "On the Implementation of Shifters, Multipliers, and
Dividers in {VLSI} Floating Point Units",
crossref = "Irwin:1987:PSC",
pages = "95--102",
year = "1987",
bibdate = "Wed Nov 14 18:22:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Peng_Samudrala_Gavrielov.pdf",
abstract = "Several options for the implementation of
combinatorial shifters, multipliers, and dividers for a
VLSI floating point unit are presented and compared.
The comparisons are made in the context of a single
chip implementation in light of the constraints imposed
by currently available MOS technology.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Perlmutter:1987:A,
author = "D. Perlmutter and A. K.-W. Yuen",
title = "The 80387 and its Applications",
journal = j-IEEE-MICRO,
volume = "7",
number = "4",
pages = "42--57",
month = jul # "\slash " # aug,
year = "1987",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1987.304880",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Pfeiffer:1987:ADP,
author = "F. W. Pfeiffer",
title = "Automatic differentiation in {PROSE}",
journal = j-SIGNUM,
volume = "22",
number = "1",
pages = "2--8",
month = jan,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:14 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A programming language is presented in which has the
feature that first and second order partial derivatives
of a function can be calculated using differentiation
arithmetic. The language syntax allows the user to
specify which variables each function is required to be
differentiated with respect to. Model examples are
provided.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "differentiation arithmetic; languages; point
algorithm; program transformation; theory",
subject = "D.3.2 Software, PROGRAMMING LANGUAGES, Language
Classifications \\ F.4.3 Theory of Computation,
MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Formal
Languages, Algebraic language theory",
}
@InProceedings{Piuri:1987:FTS,
author = "Vincenzo Piuri",
title = "Fault-Tolerant Systolic Arrays: An Approach Based upon
Residue Arithmetic",
crossref = "Irwin:1987:PSC",
pages = "230--238",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Piuri.pdf",
abstract = "Much attention has been recently given to VLSI and WSI
processing arrays: systolic arrays are often adopted to
execute a wide class of algorithms, e.g., for matrix
arithmetic or signal and image processing. In this
paper a fault-tolerant architecture is proposed to
allow reliable computation of systolic arrays by using
physical redundancy and residue number coding. Such
architecture supplies also information for fast
reconfiguration.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Prado:1987:FSR,
author = "J. Prado and R. Alcantara",
title = "A fast square-rooting algorithm using a digital signal
processor",
journal = j-PROC-IEEE,
volume = "75",
number = "2",
pages = "262--264",
month = feb,
year = "1987",
CODEN = "IEEPAD",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
summary = "The computation of square roots is required in signal
processing applications, such as adaptive filtering
using transversal filters or lattice filters, spectral
estimation, and many other fields of engineering
sciences. Actually, all the existing \ldots{}",
}
@Article{Purdy:1987:IDL,
author = "C. N. Purdy and G. B. Purdy",
title = "Integer Division in Linear Time with Bounded Fan-In",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "5",
pages = "640--644",
month = may,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676952",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:52 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676952",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Rall:1987:ISC,
author = "L. B. Rall",
title = "An introduction to the scientific computing language
{Pascal-SC}",
journal = j-COMPUT-MATH-APPL,
volume = "14",
number = "1",
pages = "53--69",
year = "1987",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(87)90181-7",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Oct 13 22:36:01 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Microcomputers are now widely used for small-scale
scientific, engineering, and statistical computing.
Pascal-SC (Pascal for Scientific Computing) is a
language developed specifically for this purpose. Its
most important features are: (i) accurate
floating-point arithmetic for real, complex, and
interval numbers, vectors, and matrices, with
controlled rounding if desired; (ii) the convenience of
operator notation for numerical data types and the
ability to accept user-defined operators for
nonstandard data types to make programs easier to
write, read, and document; and (iii) compatibility with
ordinary Pascal, so that Pascal programming techniques
and programs already written in Pascal can be used
immediately. In PascalSC, solutions of linear systems
of equations, inverses of matrices, and eigenvalues and
eigenvectors are computed with guaranteed error bounds,
and scalar products of vectors and sums of arbitrary
length of floating-point numbers are computed to the
closest floating-point number, or rounded upward or
downward as desired. These basic features of Pascal-SC
will be described, together with some applications.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Rauch:1987:MCH,
author = "K. Rauch",
title = "Math chips: How they work: Augmenting microprocessors,
they speed up math operations while giving systems
designers a variety of performance, cost, and
integration options",
journal = j-IEEE-SPECTRUM,
volume = "24",
number = "7",
pages = "25--30",
month = jul,
year = "1987",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.1987.6448961",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Mon Jan 20 06:41:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "computer architecture; Coprocessors; desktop
computers; digital arithmetic; math chips; mathematics
coprocessors; microprocessor chips; numeric processors;
operation speed; Process control; Program processors;
satellite computers; standard building blocks;
Standards; Workstations; workstations",
}
@MastersThesis{Reddy:1987:STF,
author = "Chakradher Ayyalaper Reddy",
title = "A self-testing and testable floating point divider",
type = "Thesis ({M.S.})",
school = "Mississippi State University. Department of Electrical
Engineering",
address = "Mississippi State, MS 39762, USA",
pages = "viii + 103",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point testing; Integrated circuits;
Mississippi State University; Testing.; Very large
scale integration",
}
@InProceedings{Redinbo:1987:PCT,
author = "G. Robert Redinbo",
title = "Protecting Convolution-Type Arithmetic Array
Calculations with Generalized Cyclic Codes",
crossref = "Irwin:1987:PSC",
pages = "219--225",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Redinbo.pdf",
abstract = "Fault-tolerance in dense high-speed arithmetic units
that calculate convolutions between arrays of data is
introduced through cyclic codes which are defined over
the rings and fields commonly employed by such units.
New systematic encoding and data manipulation
techniques make the application of these generalized
cyclic codes to error detection straightforward and
efficient. The necessary overhead parity computations
have complexity proportional to the number of parity
symbols squared, whereas the error-detecting capability
for both random and burst errors is directly related to
this parity number'.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Rehmer:1987:DIM,
author = "Karl Rehmer",
title = "Development and Implementation of the {Magnavox}
Generic {Ada} Basic Mathematics Package",
journal = j-SIGADA-LETTERS,
volume = "7",
number = "3",
pages = "73--83",
month = may # "\slash " # jun,
year = "1987",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:25 MDT 2003",
bibsource = "ftp://ftp.uu.net/library/bibliography;
http://portal.acm.org/;
http://www.adahome.com/Resources/Bibliography/articles.ref;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "design; floating point, real arithmetic; languages;
theory; verification",
subject = "D.2.2 Software, SOFTWARE ENGINEERING, Tools and
Techniques, Software libraries \\ D.3.2 Software,
PROGRAMMING LANGUAGES, Language Classifications, Ada
\\
G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE",
}
@InProceedings{Robertson:1987:EDC,
author = "James E. Robertson",
title = "Error-Detection and Correction for Addition and
Subtraction through Use of Higher Radix Extensions of
{Hamming} Codes",
crossref = "Irwin:1987:PSC",
pages = "226--229",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Robertson.pdf",
abstract = "The properties of Hamming codes for error detection
and correction can be extended from the binary parity
check to addition, modulo $ 2 r $. Malfunctions in
hardware during addition, modulo $ 2 r $, can be
detected and corrected. Since carry-save and
signed-digit addition, radix $r$, are included in
addition, modulo $ 2 r $, this extension of Hamming
codes makes possible new techniques for detection and
correction of hardware malfunctions during signed-digit
and carry-save addition.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Rolfe:1987:FIS,
author = "Timothy J. Rolfe",
title = "On a Fast Integer Square Root Algorithm",
journal = j-SIGNUM,
volume = "22",
number = "4",
pages = "6--11",
month = oct,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "algorithms; performance; theory",
subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Number-theoretic computations",
}
@Article{Rysavy:1987:MSC,
author = "M. Rysav{\'y}",
title = "{MISHA} --- a system for calculations with arbitrary
arithmetic precision",
journal = j-COMP-PHYS-COMM,
volume = "47",
number = "2--3",
pages = "351--359",
month = nov # "\slash " # dec,
year = "1987",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(87)90120-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 10:28:21 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0010465587901202",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Scheidt:1987:DFP,
author = "J. K. Scheidt and C. W. Schelin",
title = "Distributions of floating point numbers",
journal = j-COMPUTING,
volume = "38",
number = "4",
pages = "315--324",
year = "1987",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G10",
MRnumber = "88g:65046",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
reviewer = "J. A. Grant",
}
@InProceedings{Scherson:1987:VCO,
author = "Isaac D. Scherson and Yiming Ma",
title = "Vector Computations on Orthogonal Memory Access
Multiprocessor System",
crossref = "Irwin:1987:PSC",
pages = "28--36",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Scherson_Ma.pdf",
abstract = "An Orthogonal Memory Access system allows a
multiplicity of processors to concurrently access
distinct rows or columns of a rectangular array of data
elements. The resulting tightly-coupled
multi-processing system is feasible with current
technology and has even been suggested for VLSI as a
``reduced mesh''. In this paper we introduce the
architecture and concentrate on its application to a
number of basic vector and. numerical computations.
Matrix multiplication, L-U decomposition. polynomial
evaluation and solutions to linear systems and partial
differential equations, all show a speed-up of $ O(n) $
for a $n$-processor system. The flexibility in the
choice of the number of PEs makes the architecture a
strong competitor in the world of special-purpose
parallel systems. Actually, we prove that the machine
exhibits the same performance as any other system with
the same number of processors within a factor of 3.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8; numerical analysis; parallel algorithms;
parallel architecture; performance analysis; time
complexity",
}
@InProceedings{Schumacher:1987:CAI,
author = "G{\"u}nter Schumacher",
title = "Computer Arithmetic and Ill-Conditioned Algebraic
Problems",
crossref = "Irwin:1987:PSC",
pages = "270--276",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Schumacher.pdf",
abstract = "n/a",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
remark = "Text illegible because of large white streak on each
page.",
}
@InProceedings{Sharma:1987:ATE,
author = "Ramautar Sharma",
title = "Area-Time Efficient Arithmetic Elements for {VLSI}
Systems",
crossref = "Irwin:1987:PSC",
pages = "58--62",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Sharma.pdf",
abstract = "Algorithms for the high speed binary arithmetic
operations of addition and multiplication in a VLSI
environment are analyzed for area-time efficiency. It
is shown that some schemes for addition and
multiplication, although good for stand-alone designs,
fail to provide both area and time efficiencies
simultaneously. Solutions that yield area-time
efficient practical implementations of these arithmetic
functions are described.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InProceedings{Shenoy:1987:AST,
author = "A. Shenoy and R. Kumaresan",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing, {ICASSP '87}",
title = "An accurate scaling technique in improved residue
number system arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1414--1417",
month = "????",
year = "1987",
DOI = "https://doi.org/10.1109/TC.1987.1676868",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
keywords = "residue arithmetic; residue number system",
summary = "A fast and accurate magnitude scaling technique in the
residue number system (RNS) is proposed. This technique
obtains the residues of the scaled integer, when scaled
by a product of a subset of the moduli, in
approximately log n cycles, where n is \ldots{}",
}
@Article{Shyu:1987:CIM,
author = "H. C. Shyu and T. K. Truong and I. S. Reed",
title = "A Complex Integer Multiplier Using the
Quadratic-Polynomial Residue Number System with Numbers
of Form $ 22 n + 1 $",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "10",
pages = "1255--1258",
month = oct,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676868",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676868;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35260",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A quadratic-polynomial Fermat residue number system
(QFNS) can be used to compute the complex
multiplications needed to perform a DFT. The advantage
of such a QFNS is that complex multiplication can be
accomplished with only two integer \ldots{}",
}
@InCollection{Simar:1987:FPA,
author = "R. {Simar, Jr.}",
title = "Floating-point arithmetic with the {TMS32010}",
crossref = "Lin:1987:DSP",
pages = "213--244",
year = "1987",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "42622",
catcode = "J.2; C.5.3; G.1.0",
CRclass = "J.2 Mathematics and statistics; C.5.3 Microcomputers;
C.5.3 TMS 32010; G.1.0 General; G.1.0 Computer
arithmetic",
descriptor = "Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Mathematics and statistics; Computer
Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers, TMS 32010; Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic",
genterm = "MEASUREMENT; ALGORITHMS",
guideno = "1988-01736",
pubcite = "Englewood Cliffs, NJ",
pubname = "Prentice-Hall, Inc.",
subject = "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of
Computing; G.1 NUMERICAL ANALYSIS",
}
@InProceedings{Smith:1987:SAE,
author = "S. G. Smith and P. B. Denyer",
title = "Synthesis of Area-Efficient {VLSI} Architectures for
Vector and Matrix Multiplication",
crossref = "Irwin:1987:PSC",
pages = "13--20",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Smith_Denyer.pdf",
abstract = "A methodology is presented for synthesis of
area-efficient, high-performance VLSI modules for
vector and matrix multiplication. Three fundamental
computational elements are employed in the composition
of these architectures: memory register, multiplexer
(1-from-2 data selector), and carry-save add-shift
computer. Two's complement serial\slash parallel
carry-save accumulation provides performance, while the
use of symmetric-coded distributed arithmetic
eliminates redundant computation to effect
area-savings.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@InCollection{Spangler:1987:RMM,
author = "R. A. Spangler",
title = "Revealing the mystery---the machine and how it
functions",
crossref = "Anbar:1987:CM",
pages = "9--46",
year = "1987",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "State University of New York at Buffalo, Buffalo",
bibno = "22925",
catcode = "C.0; B.0",
content = "In this paper, the author tries to describe the way a
digital computer works: from gates, through
instructions, data encoding, and interrupts, to
peripherals of more than a dozen types. He tries to do
this in 29 pages plus a nine-page appendix on
semiconductor technology. He tries to do it for an
audience described in the book's foreword as \par
(1) physicians who were educated in the pre-computer
era, (2) medical students and house staff being
educated now, (3) computer professionals interested in
medical applications, and (4) readers outside of the
medical profession and the computer science community
who are interested in the role of automation in health
care.\par
This is a tall order. The paper comes impressively
close to filling it. In clearly-written prose, Spangler
takes the reader through the overall structure of a
computer; its major components; information, binary
numbers (including floating point), and character
codes; word length issues; gates, combinatorial
circuits and flip-flops; instruction sets, including
subroutines and interrupts; and peripheral devices,
with emphasis on mass storage.\par
A necessary byproduct of covering all this material in
such a short space is a condensed, economical writing
style. Statements are made and concept",
CRnumber = "8802-0079",
descriptor = "Computer Systems Organization, GENERAL; Hardware,
GENERAL",
genterm = "DESIGN",
pubcite = "Rockville, MD",
pubname = "Computer Science Press, Inc.",
reviewer = "E. Mallach",
subject = "C. Computer Systems Organization; C.0 GENERAL; B.
Hardware; B.0 GENERAL",
waffil = "State University of New York at Buffalo, Buffalo",
}
@Manual{Sun:1987:SAM,
key = "Sun Microsystems",
title = "The {SPARC} Architecture Manual",
organization = pub-SUN,
address = pub-SUN:adr,
edition = "Part No: 800-1399-07",
month = aug # " 8",
year = "1987",
bibdate = "Wed Sep 14 23:02:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Takagi:1987:LED,
author = "Naofumi Takagi and Shuzo Yajima",
title = "On-Line Error-Detectable High-Speed Multiplier Using
Redundant Binary Representation and Three-Rail Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "11",
pages = "1310--1317",
month = nov,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009470",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009470",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Taylor:1987:RAI,
author = "Fred J. Taylor",
title = "A residue arithmetic implementation of the {FFT}",
journal = j-J-PAR-DIST-COMP,
volume = "4",
number = "2",
pages = "191--208",
month = apr,
year = "1987",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Florida, Gainesville, FL, USA",
classification = "723; 921; C4190 (Other numerical methods); C4240
(Programming and algorithm theory); C5230 (Digital
arithmetic methods); C5260 (Digital signal processing);
C5470 (Performance evaluation and testing)",
corpsource = "Department of Electr. Eng., Coll. of Eng., Florida
University, Gainesville, FL, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "complex arithmetic; complexity; computational
complexity; computer metatheory; computerised signal
processing; digital arithmetic; discrete Fourier
transform (DFT); evaluation; Fast Fourier Transforms;
fast Fourier transforms; FFT; FFT system; management
system; mathematical techniques; mathematical
transformations; performance; residue arithmetic;
residue arithmetic number system; sign; sign
management; single-modulus complex residue number
system; speed",
treatment = "T Theoretical or Mathematical; X Experimental",
}
@Article{Thompson:1987:FME,
author = "T. Thompson",
title = "Fast Math --- a first look at {Motorola}'s 68882 math
coprocessor",
journal = j-BYTE,
volume = "12",
number = "12",
pages = "120--121",
month = dec,
year = "1987",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@Article{Thompson:1987:IEF,
author = "P. Thompson",
title = "Implementing an Elementary Function Library",
journal = j-SIGNUM,
volume = "22",
number = "2",
pages = "2--5",
month = apr,
year = "1987",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Tu:1987:RLD,
author = "Paul K. G. Tu and Milo{\v{s}} D. Ercegovac",
title = "A Radix-4 On-Line Division Algorithm",
crossref = "Irwin:1987:PSC",
pages = "181--187",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Tu_Ercegovac.pdf",
abstract = "We present an on-line algorithm for radix-4 floating
point division. The divisor is first transformed in to
a range such that the quotient digits are computed as a
function of the scaled partial remainder only.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Turner:1987:DDI,
author = "Peter R. Turner",
title = "The Distribution of l.s.d. and Its Implications for
Computer Design",
journal = j-MATH-GAZ,
volume = "71",
number = "455",
pages = "26--31",
month = mar,
year = "1987",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.2307/3616283",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibdate = "Tue Oct 30 23:36:58 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic
distribution; overflow; underflow; Zipf's Law",
}
@InProceedings{Umeo:1987:DTO,
author = "Hiroshi Umeo",
title = "A Design of Time-Optimum and Register-Number-Minimum
Systolic Convolver",
crossref = "Irwin:1987:PSC",
pages = "5--12",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Umeo.pdf",
abstract = "We present an optimum bit-parallel\slash
word-sequential systolic convolver. Our design is the
best one among the previous many convolvers in the
sense that its optimality in time and space
performances is simultaneously attained without
augmenting any global control, broadcasting,
preloading, and\slash or multi sequential or parallel
I/O ports, which were allowed in most of the previous
designs. As an application of our convolver we give a
systolic polynomial divider which can compute the
polynomial division in exactly $ n + O(1) $ steps on $
[\min (n - m, m) / 2] + O(1) $ systolic cells, for the
division of any degree n polynomial by any degree $m$
polynomial ($ n \geq m $).",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Ushio:1987:CRE,
author = "T. Ushio and C. Hsu",
title = "Chaotic rounding error in digital control systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "34",
number = "2",
pages = "133--139",
month = feb,
year = "1987",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Chaotic behavior due to the round-off effect in
digital control systems is called the chaotic rounding
error. First, we model digital control systems with
finite-wordlength digital compensators by mixed
mappings. A mixed mapping system is described
\ldots{}",
}
@Article{Vachss:1987:CMF,
author = "R. Vachss",
title = "The {Cordic} Magnification Function",
journal = j-IEEE-MICRO,
volume = "7",
number = "5",
pages = "83--84",
month = sep # "\slash " # oct,
year = "1987",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.1987.305021",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Vitek:1987:EFA,
author = "V. Vitek",
title = "Enumeration in floating-point arithmetic",
journal = "ASR - Bulletin INORGA",
volume = "21",
number = "6",
pages = "301--305",
month = "????",
year = "1987",
ISSN = "0231-8954",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper studies the computer representation of
numbers in floating-point arithmetic and algebraic
operations with these numbers with respect to the
validity of basic algebraic laws. Methods for the
handling of emergency situations are given: overflow
and underflow, illustrated using the example of the
computation of a member of the binomial expansion. (6
Refs.)",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
keywords = "Algebraic operations; Computer representation;
Floating-point arithmetic; Overflow; Underflow",
pubcountry = "Czechoslovakia",
thesaurus = "Carry logic; Digital arithmetic; Error handling",
}
@InProceedings{Wang:1987:EEF,
author = "Kai Hwang and H. C. Wang and Z. Xu",
title = "Evaluating Elementary Functions with {Chebyshev}
Polynomials on Pipeline Nets",
crossref = "Irwin:1987:PSC",
pages = "121--128",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hwang_Wang_Xu.pdf",
abstract = "Fast evaluation of vector-valued elementary functions
plays a vital role in many real-time applications. In
this paper, we present a pipeline networking approach
to designing a Chebyshev polynomial evaluator for the
fast evaluation of elementary functions over a string
of arguments. In particular, pipeline nets are employed
to perform the preprocessing and postprocessing of
various elementary functions to boost the overall
system performance. Design tradeoffs are analyzed among
representational accuracy, processing speed and
hardware complexity.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Manual{WeitekCorporation:1987:WFP,
title = "{WTL} 1167 floating point coprocessor: preliminary
data",
organization = "{Weitek Corporation}",
address = "Sunnyvale, CA, USA",
pages = "54",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Intel 80386
(Microprocessor) --- Programming.",
remark = "August 1988.",
}
@MastersThesis{Williams:1987:FPL,
author = "Robert Leslie Williams",
title = "A floating point loop engine architecture using
pattern generation",
type = "Thesis ({M.S.})",
school = "University of New Mexico",
address = "Albuquerque, NM, USA",
pages = "ix + 92",
year = "1987",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Computer engineering.",
}
@InProceedings{Williams:1987:STC,
author = "T. E. Williams and M. Horowitz and R. L. Alverson and
T. S. Yang",
title = "A self-timed chip for division",
crossref = "Losleben:1987:ARV",
pages = "75--96",
year = "1987",
bibdate = "Mon Sep 16 16:35:03 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Wu:1987:FDS,
author = "I-Chen Wu",
title = "A Fast {$1$-D} Serial-Parallel Systolic Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "10",
pages = "1243--1247",
month = oct,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.1676865",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676865",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wu:1987:TRF,
author = "Chwan-Ghia Wu and Lih-Ren Tzeng and Tien-Shou Wu",
title = "Time-Redundant Fault-Masking in {ALUs}",
crossref = "Irwin:1987:PSC",
pages = "239--243",
year = "1987",
bibdate = "Fri Nov 16 21:39:46 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Wu_Cheng_Wu.pdf",
abstract = "A new error correction scheme for bit-sliced ALUs is
presented. The method adopted for fault location is an
extension of a concurrent error detection scheme called
RESO (Recomputing with Shifted Operands). The term
bit-slice is used in the generic sense and the length
of the slice may be one or more bits. The proposed
scheme requires two consecutive computation steps for
normal operations and the possible locations of faults,
if any, can be located provided that the failures are
confined to a certain number of adjacent bit-slices.
The fault-free bit-slices of the ALU are thus figured
out. The final and effective computation is then
carried out through those identified fault-free
bit-slices. A circular structure is proposed to realize
this concept.",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Article{Zaccone:1987:ENP,
author = "Richard J. Zaccone and Jesse L. Barlow",
title = "Eliminating the Normalization Problem in Digit On-Line
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "1",
pages = "36--46",
month = jan,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009447",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009447",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Zurawski:1987:DHS,
author = "J. H. P. Zurawski and J. B. Gosling",
title = "Design of a High-Speed Square Root Multiply and Divide
Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-36",
number = "1",
pages = "13--23",
month = jan,
year = "1987",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1987.5009445",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 09:28:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Aberth:1988:PNA,
author = "Oliver Aberth",
title = "Precise Numerical Analysis",
publisher = pub-WCB,
address = pub-WCB:adr,
pages = "x + 225",
year = "1988",
ISBN = "0-697-06760-2",
ISBN-13 = "978-0-697-06760-9",
LCCN = "QA297 .A28 1988",
bibdate = "Thu Nov 8 14:50:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Aberth addresses elementary issues of precise floating
point computations using variable precision range
arithmetic. Numbers are represented as a variable
precision number $ \pm $ a range. Rational arithmetic
is also considered. Chapters are devoted to
\begin{enumerate} \item rootfinding, \item polynomial
rootfinding, \item numerical linear algebra, \item
differentiation and integration, and \item ordinary
differential equations. \end{enumerate} Differentiation
is handled by a codelist approach like [Rall81a], and
applications to Taylor series are given. Interval
techniques for ordinary differential equations are
based on using an {\it a priori\/} bound to capture
remainder terms. Several methods are illustrated,
including Taylor series methods.",
acknowledgement = ack-nj,
comment = "Text for a one semester, junior level course in
numerical analysis. Includes PC disk with software
written in PBASIC. Sound introductory level discussion
of code lists and error capture techniques.",
keywords = "differentiation; differentiation arithmetic; general
numerical analysis; integration; interval techniques;
linear algebra; ordinary differential equations.;
variable precision arithmetic",
}
@Article{Alt:1988:FEP,
author = "Ren{\'e} Alt",
title = "Floating-point error propagation in iterative methods.
Stochastic methods in round-off error analysis",
journal = j-MATH-COMP-SIM,
volume = "30",
number = "6",
pages = "505--517",
year = "1988",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
MRclass = "65G05 (65F10)",
MRnumber = "90f:65067",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics and Computers in Simulation",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
reviewer = "D. Bini",
}
@Article{Alt:1988:FPE,
author = "R. Alt",
title = "Floating-point error propagation in iterative
methods",
journal = j-MATH-COMP-SIM,
volume = "30",
number = "6",
pages = "505--517",
month = dec,
year = "1988",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "56847",
catcode = "G.1.0",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
fjournal = "Mathematics and Computers in Simulation",
genterm = "THEORY; ALGORITHMS",
guideno = "1988-12109",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
journalabbrev = "Math. Comput. Simul.",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}
@Article{AMD:1988:IFP,
author = "{Advanced Micro Devices}",
title = "{IEEE} floating-point format",
journal = j-MICROPROC-MICROSYS,
volume = "12",
number = "1",
pages = "13--23",
month = jan # "\slash " # feb,
year = "1988",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
bibno = "23",
categories = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
K. Computing Milieux; K.1 THE COMPUTER INDUSTRY; G.1.0
General; G.1.0 Computer arithmetic; K.1 Standards",
content = "DESIGN; STANDARDIZATION; THEORY",
CRnumber = "1988-12470",
fjournal = "Microprocessors and Microsystems",
guideno = "1",
subject = "mathematics of computing, numerical analysis, general,
computer arithmetic; computing milieux, the computer
industry, standards",
wsub = "Jesse L. Barlow",
}
@Article{An:1988:CRE,
author = "S. H. An and K. Yao",
title = "Convergent and roundoff error properties of reflection
coefficients in adaptive spatial recursive least
squares lattice algorithm",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "2",
pages = "241--246",
month = feb,
year = "1988",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "The spatial recursive least-squares lattice (RLSL)
algorithm is considered and the convergent properties
as well as the finite-precision roundoff effects of the
reflection coefficients are studied in detail. It is
shown that when the forgetting \ldots{}",
}
@Article{Anderson:1988:MRE,
author = "Ned Anderson",
title = "Minimum relative error approximations for $ 1 / t $",
journal = j-NUM-MATH,
volume = "54",
number = "2",
pages = "117--124",
month = nov,
year = "1988",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01396969",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D15",
MRnumber = "90a:65037",
MRreviewer = "Mariano Gasca",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Corp. Res., Digital Equipment Corp., Hudson, MA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "approximation theory; functional equation; geometric
convergence rates; iterative methods; minimum relative
error approximations; polynomial approximations;
polynomials",
treatment = "T Theoretical or Mathematical",
}
@Book{Apple:1988:ANM,
author = "{Apple Computer, Inc.}",
title = "{Apple} Numerics Manual",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xxvi + 294",
year = "1988",
ISBN = "0-201-17738-2",
ISBN-13 = "978-0-201-17738-1",
LCCN = "QA76.8.A662 A767 1988",
bibdate = "Wed Sep 07 21:06:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$29.95",
series = "The Apple technical library",
acknowledgement = ack-nhfb,
keywords = "Apple II (computer) --- programming; computation by
computer systems --- floating point representation;
Macintosh (computer) --- programming; numerical
calculations --- data processing; SANE (Standard Apple
Numeric Environment)",
}
@Article{Bailey:1988:EHS,
author = "David H. Bailey",
title = "Extra high speed matrix multiplication on the
{Cray-2}",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "9",
number = "3",
pages = "603--607",
month = may,
year = "1988",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0909040",
ISSN = "0196-5204",
ISSN-L = "0196-5204",
MRclass = "65F30 (65G05 65W05)",
MRnumber = "937 496",
bibdate = "Mon Mar 31 10:00:04 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
acknowledgement = ack-nhfb,
classification = "C7310 (Mathematics)",
corpsource = "Ames Res. Center, NASA, Moffett Field, CA, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "Cray-2; floating-point operations; library routines;
mathematics computing; matrix algebra; matrix
multiplication; memory bank contention; numerical
stability",
onlinedate = "May 1988",
treatment = "P Practical",
}
@InProceedings{Bandyopadhyay:1988:SAF,
author = "S. Bandyopadhyay and G. A. Jullien and A. Sengupta",
booktitle = "Proceedings of the International Conference on
Systolic Arrays, 1988. 25--27 May 1988",
title = "A systolic array for fault tolerant digital signal
processing using a residue number system approach",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "577--586",
year = "1988",
CODEN = "????",
DOI = "https://doi.org/10.1109/ARRAYS.1988.18094",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Fault detection and correction using the Chinese
remainder theorem for decoding is investigated. It is
shown that this approach is well suited for
implementation by VLSI circuits for digital signal
processing using systolic architectures. A systolic
\ldots{}",
}
@Article{Banning:1988:PRF,
author = "Craig Banning",
title = "Perfectly Rounded Floats",
journal = j-CUJ,
volume = "6",
number = "2",
pages = "14--??",
month = feb,
year = "1988",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Barany:1988:FEI,
author = "T. E. Barany",
title = "Fast evaluation of integer roots in microcontroller
systems",
journal = j-MICROPROC-MICROSYS,
volume = "12",
number = "6",
pages = "341--344",
month = jul # "--" # aug,
year = "1988",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Fri Dec 08 13:06:02 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@TechReport{Barlow:1988:EAU,
author = "Jesse Louis Barlow and Richard J. Zaccone",
title = "Error analysis in unnormalized floating point
arithmetic",
type = "Technical report",
number = "CS-88-33",
institution = "Pennsylvania State University, Department of Computer
Science",
address = "University Park, PA, USA",
pages = "12",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "Supported by the National Science Foundation.
Supported by the Office of Naval Research.",
}
@TechReport{Barlowe:1988:EAU,
author = "Jesse L. Barlowe",
title = "Error analysis in unnormalized floating point
arithmetic",
type = "Technical report",
number = "CS-88-10",
institution = "Pennsylvania State University, Department of Computer
Science",
address = "University Park, PA, USA",
pages = "14",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Errors.",
remark = "Supported by the National Science Foundation.
Supported by the Office of Naval Research.",
}
@InProceedings{BenChorin:1988:NPC,
author = "S. Ben-Chorin",
title = "{NS32532-NS32580} processor cluster delivers high
floating-point performance",
crossref = "Midcon:1988:MCP",
pages = "243--248",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The NS32580 Floating-Point Controller (FPC) teams with
Weitek's WTL3164 Floating-Point Data Path (FPDP) device
and the NS32532 CPU to achieve a floating-point
performance that complements the NS32532's 15 MIPS
peak-integer performance. Due to a pipelined
coprocessor interface and the floating-point controller
design, this processor cluster achieves a peak
floating-point performance of 15 MFLOPs for both
single-precision (32-bit) and double-precision (64-bit)
floating-point instructions, such as add, subtract and
multiply. This high-performance is accomplished without
sacrificing software compatibility with the previous
Series 32000 processor clusters, including precise
floating-point exceptions.",
acknowledgement = ack-nhfb,
affiliation = "Nat. Semicond. Corp., Santa Clara, CA, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture)",
keywords = "Floating-Point Controller; Floating-Point Data Path;
Floating-point performance; NS32532 CPU; NS32580;
Pipelined coprocessor interface; Processor cluster;
WTL3164",
thesaurus = "Computer architecture; Microprocessor chips",
}
@InProceedings{Bewick:1988:ANB,
author = "G. Bewick and P. Song and G. De Micheli and M. Flynn",
title = "Approaching a nanosecond: a 32-bit adder",
crossref = "IEEE:1988:PII",
pages = "221--226",
year = "1988",
DOI = "https://doi.org/10.1109/ICCD.1988.25695",
bibdate = "Mon Dec 24 09:52:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Birman:1988:DHS,
author = "M. Birman and G. Chu and L. Hu and J. McLeod and N.
Bedard and F. Ware and L. Torban and C. M. Lim",
title = "Design of a high-speed arithmetic datapath",
crossref = "IEEE:1988:PII",
pages = "214--216",
year = "1988",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Blaker:1988:FPB,
author = "David Mark Blaker",
title = "Floating point bit-sequential arithmetic units",
type = "Thesis ({M.S.})",
school = "Lehigh University",
address = "Bethlehem, PA, USA",
pages = "vi + 73",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Floating-point arithmetic.",
}
@Article{Bohlender:1988:IFA,
author = "Gerd Bohlender",
title = "Is floating-point arithmetic still adequate?",
journal = "Systems analysis and simulation",
volume = "46",
publisher = "Akademie-Verlag",
address = "Berlin, Germany",
pages = "105--108",
year = "1988",
MRclass = "68N15 (65G99)",
MRnumber = "976 389",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxjournal = "Math. Res.",
xxx = "I (Berlin, 1988)",
}
@TechReport{Bose:1988:VDT,
author = "Bidyut Kumar Bose",
title = "{VLSI} design techniques for floating-point
computation",
type = "Report",
number = "UCB/CSD 88/469",
institution = "University of California, Berkeley, Computer Science
Division",
address = "Berkeley, CA, USA",
pages = "vi + 173",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Integrated circuits ---
Very large scale integration.",
}
@MastersThesis{Brooks:1988:VIF,
author = "Kelvin R. Brooks",
title = "The {VLSI} implementation of a floating-point
multiplier",
type = "Thesis ({M.S.})",
school = "North Carolina A\&T State University",
address = "Greensboro, NC, USA",
pages = "x + 78",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electric engineering.; Integrated circuits --- Very
large scale integration.",
}
@Article{Brosnan:1988:MED,
author = "T. J. Brosnan and N. R. {Strader II}",
title = "Modular error detection for bit-serial
multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "9",
pages = "1043--1052",
month = sep,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2255",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2255",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Byington:1988:HGB,
author = "Carl Byington",
title = "How to get better floating-point results",
journal = j-BYTE,
volume = "13",
number = "3",
pages = "229--236",
month = mar,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "44973",
catcode = "C.5.3; G.1.0; D.1.m",
CRclass = "C.5.3 Microcomputers; G.1.0 General; G.1.0 Computer
arithmetic; D.1.m Miscellaneous",
descriptor = "Computer Systems Organization, COMPUTER SYSTEM
IMPLEMENTATION, Microcomputers; Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic; Software, PROGRAMMING TECHNIQUES,
Miscellaneous",
fjournal = "BYTE Magazine",
genterm = "DESIGN; RELIABILITY",
guideno = "1988-05276",
subject = "C. Computer Systems Organization; C.5 COMPUTER SYSTEM
IMPLEMENTATION; G. Mathematics of Computing; G.1
NUMERICAL ANALYSIS; D. Software; D.1 PROGRAMMING
TECHNIQUES",
}
@Article{Callahan:1988:EII,
author = "D. Callahan and J. Cocke and K. Kennedy",
title = "Estimating interlock and improving balance for
pipelined architectures",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "4",
pages = "334--358",
month = aug,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
corpsource = "Department of Computer Science, Rice University,
Houston, TX, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "arithmetic; bandwidth; digital arithmetic; DO loops;
execution order constraints; fine-grain parallelism;
floating-point; memory; parallel architectures;
pipeline; pipeline balance; pipeline interlock;
pipelined architectures; processing",
treatment = "P Practical",
}
@Article{Capocelli:1988:EVN,
author = "R. M. Capocelli and R. Giancarlo",
title = "Efficient {VLSI} networks for converting an integer
from binary system to residue number system and vice
versa",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "11",
pages = "1425--1430",
month = nov,
year = "1988",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/31.14466",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=565",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "VLSI networks for converting integers from binary to
residue number systems are presented Both direct and
reverse conversion are treated. The networks are
improvements, with respect to area or time or both, of
previously proposed \ldots{}",
}
@TechReport{Cappello:1988:SSSa,
author = "Peter R. Cappello and Willard L. Miranker",
title = "Systolic super summation with reduced hardware",
type = "Technical report",
number = "TRCS88-27",
institution = "University of California, Santa Barbara, College of
Engineering Department of Computer Science",
address = "Santa Barbara, CA, USA",
pages = "8",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; computer science
--- mathematics; floating-point arithmetic",
remark = "``A principle limitation in accuracy for scientific
computation performed with floating-point arithmetic
may be traced to the computation of repeated sums, such
as those which arise in inner products. A design is
proposed for a systolic super summer, a cellular piece
of hardware for the summation of floating-point
numbers. The apparatus receives floating-point
summands, converting them into a fixed-point form by a
sieve-like cellular array. The emerging fixed-point
numbers then are summed in a pipelined array of long
accumulators. The architectural regularity of the sieve
makes it ideal for implementation in VLSI circuit
technology.'' Supported by the Office of Naval
Research.",
}
@Misc{Cappello:1988:SSSb,
author = "Peter R. Cappello and Willard L. Miranker",
title = "Systolic super summation device",
howpublished = "US Patent 4751665",
day = "14",
month = jun,
year = "1988",
bibdate = "Mon Dec 29 16:20:01 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/4751665/fulltext.html",
abstract = "A cellular architecture for a systolic super summer
for high throughput performance of repeated sums of
floating-point numbers. The summer receives pipelined
inputs of streams of summands, converts the
floating-point summands into a fixed-point form by a
sieve-like pipelined cellular network , and sums the
emerging fixed-point numbers in a corresponding network
of extremely long accumulators. The throughput per unit
area of the hardware approaches that of a tree network,
but without the long wires and signal propagation that
are intrinsic to tree networks.",
acknowledgement = ack-nhfb,
}
@Article{Capps:1988:OAL,
author = "C. David Capps and R. Aaron Falk and Theodore L.
Houk",
title = "Optical Arithmetic\slash Logic Unit Based on Residue
Arithmetic and Symbolic Substitution",
journal = j-APPL-OPTICS,
volume = "27",
number = "9",
pages = "1682--1686",
month = may,
year = "1988",
CODEN = "APOPAI",
ISSN = "0003-6935",
bibdate = "Fri Jun 24 18:13:20 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There has been difficulty in achieving a fully
parallel, digital optical adder or multiplier. The
primary obstacle is the carry operation inherent in any
fixed-radix number system. The concepts of residue
number representation and symbolic substitution can be
combined to produce a parallel optical arithmetic/logic
unit.",
acknowledgement = ack-nhfb,
fjournal = "Applied Optics",
journal-URL = "http://www.osapublishing.org/ao/browse.cfm",
}
@Article{Cardarilli:1988:SPD,
author = "G. C. Cardarilli and R. Lojacono and G. Martinelli and
M. Salerno",
title = "Structurally passive digital filters in residue number
systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "2",
pages = "149--158",
month = feb,
year = "1988",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/31.1716",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=107",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "The possibility of realizing structural passive
digital filters in terms of residue number systems
(RNS) is considered. For this purpose, an algorithm is
proposed for realizing the RNS rotator, which
represents the basic element of these filters.
\ldots{}",
}
@Article{Cavallaro:1988:CAS,
author = "Joseph R. Cavallaro and Franklin T. Luk",
title = "{CORDIC} arithmetic for an {SVD} processor",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "271--290",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
classification = "721; 722; 723; 921; C5230 (Digital arithmetic
methods); C5440 (Multiprocessor systems and
techniques)",
corpsource = "Sch. of Electr. Eng., Cornell University, NY, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Algorithms; computer architecture; computer
programming; computers, digital --- Computational
Methods; CORDIC arithmetic; Decomposition; digital
arithmetic; hardware division; inverse tangents;
mathematical techniques --- Algorithms; parallel
processing; real-time; rotations; signal processing
applications; Singular Value; singular value
decomposition; special-purpose arithmetic techniques;
square root; SVD processor; vector; vector rotations;
VLSI implementation",
treatment = "P Practical",
}
@Article{Chaitin:1988:RA,
author = "Gregory J. Chaitin",
title = "Randomness in Arithmetic",
journal = j-SCI-AMER,
volume = "259",
number = "1",
pages = "80--85 (Intl. ed. 52--57)",
month = jul,
year = "1988",
CODEN = "SCAMAC",
DOI = "https://doi.org/10.1038/scientificamerican0788-80",
ISSN = "0036-8733 (print), 1946-7087 (electronic)",
ISSN-L = "0036-8733",
bibdate = "Wed May 22 15:04:14 MDT 2013",
bibsource = "Distributed/QLD/1988.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciam1980.bib",
URL = "http://www.nature.com/scientificamerican/journal/v259/n1/pdf/scientificamerican0788-80.pdf",
acknowledgement = ack-nhfb,
country = "USA",
date = "01/07/93",
descriptors = "Randomness; Arithmetic",
enum = "9449",
fjournal = "Scientific American",
journal-URL = "http://www.nature.com/scientificamerican",
keywords = "algorithmic information theory; computability theory;
halting problem; incompleteness theorem; number theory;
Pascal's triangle; randomness",
remark = "(VBI-001989)",
xxnewdata = "1998.01.30",
}
@Article{Chen:1988:GCM,
author = "M. C. Chen",
title = "The generation of a class of multipliers: synthesizing
highly parallel algorithms in {VLSI}",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "3",
pages = "329--338",
month = mar,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2170",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2170",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Cheng:1988:ATM,
author = "Kuo-kuang Cheng and Robert R. Seban",
title = "Algorithm theory and the microarchitecture of an
optimal {VLSI} floating point divider",
institution = "Department of Computer Science, College of Engineering
and Applied Sciences, Arizona State University",
address = "Tempe, AZ, USA",
pages = "17",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "CR-R; 89028 TR; 88-032 Report (Arizona State
University. College of Engineering and Applied
Sciences); 89:28. Technical report (Arizona State
University. Department of Computer Science); 88-032.",
acknowledgement = ack-nhfb,
remark = "``December 22, 1988.''",
}
@Article{Cody:1988:AMS,
author = "W. J. Cody",
title = "{Algorithm 665}: {MACHAR}: a Subroutine to Dynamically
Determine Machine Parameters",
journal = j-TOMS,
volume = "14",
number = "4",
pages = "303--311",
month = dec,
year = "1988",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/50063.51907",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 22:33:58 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p303-cody/",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Portability. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic.",
}
@InCollection{Cody:1988:FPS,
author = "W. J. Cody",
title = "Floating-point standards --- theory and practice",
crossref = "Moore:1988:RCR",
pages = "99--107",
year = "1988",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Argonne National Laboratory, Argonne, IL",
bibno = "60186",
catcode = "B.7.1; K.1",
CRclass = "B.7.1 Types and Design Styles; K.1 Standards",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles; Computing Milieux, THE COMPUTER INDUSTRY,
Standards",
genterm = "THEORY; RELIABILITY; STANDARDIZATION; RELIABILITY",
guideno = "1988-01977",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; K. Computing
Milieux; K.1 THE COMPUTER INDUSTRY",
waffil = "Ohio State University, Columbus",
}
@Article{Cosentino:1988:FTS,
author = "R. J. Cosentino",
title = "Fault tolerance in a systolic residue arithmetic
processor array",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "7",
pages = "886--890",
month = jul,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2239",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2239",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Davila:1988:FPA,
author = "J. M. Davila and A. J. Phillips and D. Tabak",
title = "Floating Point Arithmetic on a {RISC}",
journal = j-MICROPROC-MICROPROG,
volume = "23",
number = "1--5",
pages = "179--184",
month = mar,
year = "1988",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Thu Sep 1 10:15:06 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessing and Microprogramming",
}
@MastersThesis{Duerksen:1988:CAP,
author = "Joel L. Duerksen",
title = "A comparative analysis of the performance of floating
point and integer based line drawing algorithms for
raster displays",
type = "Thesis ({M.S.})",
school = "Department of Computer Science, Ball State
University",
address = "Muncie, IN 47306, USA",
pages = "ix + 206",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Computer graphics.",
}
@Article{Dunham:1988:PMA,
author = "C. B. Dunham",
title = "Provably Monotone Approximations {III}",
journal = j-SIGNUM,
volume = "23",
number = "1",
pages = "10--10",
month = jan,
year = "1988",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Sep 13 09:05:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "theory",
subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation",
}
@Article{Duprat:1988:HPE,
author = "Jean Duprat and Jean-Michel Muller",
title = "Hardwired polynomial evaluation",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "291--309",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "CNRS, Grenoble, Fr",
classification = "721; 722; 723; 921; C4130 (Interpolation and
function approximation); C5230 (Digital arithmetic
methods)",
corpsource = "Inst. Nat. Polytech. de Grenoble, France",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "computer architecture; computers, digital ---
Circuits; digital arithmetic; elementary functions;
hardwired polynomial evaluation; mathematical
functions; mathematical techniques; Polynomials;
polynomials; special-purpose circuits; VLSI
implementation",
treatment = "P Practical",
}
@InProceedings{Ercegovac:1988:LAD,
author = "M. D. Ercegovac and T. Lang",
title = "On-Line Arithmetic: a Design Methodology and
Applications in Digital Signal Processing",
crossref = "Brodersen:1988:VSP",
volume = "3",
pages = "252--263",
year = "1988",
bibdate = "Fri Dec 08 10:42:22 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[66--77]{Swartzlander:1990:CAb}.",
acknowledgement = ack-nhfb,
}
@Article{Ercegovac:1988:LSC,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "On-line scheme for computing rotation factors",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "209--227",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of California, Los Angeles, CA, USA",
classification = "721; 722; 723; 921; C5230 (Digital arithmetic
methods)",
corpsource = "Department of Computer Science, California University,
Los Angeles, CA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algorithm; Algorithms; clock period; computer
programming; computers, digital --- Computational
Methods; computing rotation factors; digital
arithmetic; floating-point; low-precision estimates;
mathematical techniques --- Algorithms; matrix
transformations; on-line algorithm; online scheme;
radix-2 online; representation; rotation factors
computing; systolic arrays",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Fam:1988:ECM,
author = "A. T. Fam",
title = "Efficient complex matrix multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "7",
pages = "877--879",
month = jul,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2236",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2236",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Farnum:1988:CSF,
author = "Charles Farnum",
title = "Compiler Support for Floating-Point Computation",
journal = j-SPE,
volume = "18",
number = "7",
pages = "701--709",
month = jul,
year = "1988",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 24 19:46:39 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}
@Article{Fiske:1988:RAP,
author = "S. Fiske and W. J. Dally",
title = "The reconfigurable arithmetic processor",
journal = j-COMP-ARCH-NEWS,
volume = "16",
number = "2",
pages = "30--36",
month = may,
year = "1988",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:45 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Fitzpatrick:1988:PVF,
author = "S. Fitzpatrick",
title = "Processeur {\`a} virgule flottante {\`a} 33 {Mflops}
\toenglish {33 Mflops Floating-Point Processor}
\endtoenglish",
journal = "Electronique Industrielle",
volume = "148",
pages = "30--32",
day = "15",
month = sep,
year = "1988",
bibdate = "Sat Oct 24 15:01:51 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Fuccio:1988:DAS,
author = "M. L. Fuccio and R. N. Gadenz and C. J. Garen and J.
M. Huser and B. Ng and S. P. Pekarich and K. D. Ulery",
title = "The {DSP32C}: {AT\&T}'s Second-Generation
Floating-Point Digital Signal Processor",
journal = j-IEEE-MICRO,
volume = "8",
number = "6",
pages = "30--48",
month = nov # "\slash " # dec,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.16779",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "The WEDSP32C high-performance, programmable digital
signal processor supports 32-bit floating-point
arithmetic and is upwardly compatible with its
predecessor, the WEDSP32. Because it is implemented in
0.75-$\mu$m (effective channel length) CMOS technology
\ldots{}",
}
@Article{Gibson:1988:GBA,
author = "J. K. Gibson",
title = "A generalisation of {Brickell}'s algorithm for fast
modular multiplication",
journal = j-BIT,
volume = "28",
number = "4",
pages = "755--763",
month = dec,
year = "1988",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01954895",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68Q25 (68P25 68U99)",
MRnumber = "89m:68058",
MRreviewer = "Ricardo Baeza-Yates",
bibdate = "Wed Jan 4 18:52:20 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=28&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=28&issue=4&spage=755",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Grehan:1988:BBL,
author = "R. Grehan and T. Thompson",
title = "{Borland} beefs up its languages",
journal = j-BYTE,
volume = "13",
number = "10",
pages = "151--154",
month = oct,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages); C6150C (Compilers,
interpreters and other processors); C6150G (Diagnostic,
testing, debugging and evaluating systems)",
fjournal = "BYTE Magazine",
keywords = "Borland International; Built-in source-level
debuggers; Command-line interface version; Expanded
memory; Floating-point emulation; High-speed assembler;
In-line assembly language support; Integrated
development environment; Line-oriented environment;
Premier development languages; Stand-alone debugger;
TASM; Turbo Assembler; Turbo C; Turbo Debugger; Turbo
language; Turbo Pascal",
thesaurus = "C language; Pascal; Program assemblers; Program
compilers; Program debugging; Software packages",
}
@Article{Grehan:1988:FPCa,
author = "Rick Grehan",
title = "Floating-Point Without a Coprocessor",
journal = j-BYTE,
volume = "13",
number = "9",
pages = "313--319",
month = sep,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
bibno = "47602",
catcode = "C.3; G.0",
descriptor = "Computer Systems Organization, SPECIAL-PURPOSE AND
APPLICATION-BASED SYSTEMS; Mathematics of Computing,
GENERAL",
fjournal = "BYTE Magazine",
genterm = "DESIGN; THEORY; MANAGEMENT",
guideno = "1988-05346",
subject = "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
AND APPLICATION-BASED SYSTEMS; G. Mathematics of
Computing; G.0 GENERAL",
}
@Article{Grehan:1988:FPCb,
author = "R. Grehan",
title = "Floating-Point Without a Coprocessor, Part 2",
journal = j-BYTE,
volume = "13",
number = "10",
pages = "293--297 (or 293--298??)",
month = oct,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
classification = "C1160 (Combinatorial mathematics); C6110 (Systems
analysis and programming); C7310 (Mathematics)",
fjournal = "BYTE Magazine",
keywords = "Addition; Binary floating-point mathematics package;
Division; Floating-point accumulators; Floating-point
number manipulation; Maths chip emulation;
Multiplication; Number input/output; Primary math
operations; Pseudocode routines; Subtraction",
thesaurus = "Input-output programs; Mathematics computing; Number
theory; Programming; Software packages",
}
@MastersThesis{Helminen:1988:AFP,
author = "Brenda K. Helminen",
title = "An analysis of the floating point and communication
performance of the {FPS} {T-Series} hypercube",
type = "Thesis ({M.S.})",
school = "Michigan Technological University",
address = "Houghton, MI, USA",
pages = "viii + 69",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Michigan Technological University. --- Theses
({M.S.}).; MTU Computer Science. --- Thesis ({M.S.}).",
}
@MastersThesis{Ho:1988:ADI,
author = "Naven Chuen Wing Ho",
title = "Analysis and design of an instantaneous floating point
amplifier",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering, Cullen College
of Engineering, University of Houston",
address = "Houston, TX, USA",
pages = "xv + 185",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Amplifiers (Electronics); Seismic waves --- Data
processing.",
}
@Book{Holt:1988:BR,
editor = "Wayne E. Holt and Steven M. Cooper and Jason M. Goertz
and Scott E. Levine and Joanna L. Mosher and Stanley R.
{Sieler, Jr.} and Jacques {Van Damme}",
title = "Beyond {RISC}\emdash An Essential Guide to
Hewlett--Packard Precision Architecture",
publisher = pub-SRNI,
address = pub-SRNI:adr,
pages = "xvii + 342",
year = "1988",
ISBN = "0-9618813-7-2",
ISBN-13 = "978-0-9618813-7-5",
LCCN = "QA76.8.H66 B49 1988",
bibdate = "Thu Sep 15 11:34:06 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hsu:1988:CVA,
author = "I. S. Hsu and T. K. Truong and L. J. Deutsch and I. S.
Reed",
title = "A comparison of {VLSI} architecture of finite field
multipliers using dual, normal, or standard bases",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "6",
pages = "735--739",
month = jun,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2212",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2212",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Iacobovici:1988:HFC,
author = "S. Iacobovici",
title = "High-performance floating-point coprocessor for the
{NS32532 CPU}",
crossref = "Wescon:1988:WCR",
pages = "1.3/1--6",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The need to match the integer processing performance
of the NS32532 CPU with the floating-point performance
teams the NS32580 floating-point controller with
Weitek's WTL3164 floating-point data path to achieve a
peak performance of 15 MFLOPS for single- or
double-precision. Using a pipelined slave protocol this
solution is software compatible with existing Series
32000 software base and supports precise exception
handling. Together, NS32532-NS32580-WTL3164 provide a
high-performance, well-balanced solution for scientific
applications, as well as number crunching, graphics and
image processing.",
acknowledgement = ack-nhfb,
affiliation = "National Semicond. Corp., Santa Clara, CA, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
keywords = "15 MFLOPS; Double-precision; Exception handling;
Floating-point coprocessor; Graphics; Image processing;
NS32532 CPU; NS32580 floating-point controller;
Pipelined slave protocol; Processing performance;
Scientific applications; Series 32000 software; Single
precision arithmetic; WTL3164 floating-point data
path",
numericalindex = "Computer speed 1.5E+07 FLOPS",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Article{Iacobovici:1988:PIH,
author = "S. Iacobovici",
title = "A pipelined interface for high floating-point
performance with precise exceptions",
journal = j-IEEE-MICRO,
volume = "8",
number = "3",
pages = "77--87",
month = may # "\slash " # jun,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.542",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "Two options are presented that were considered for a
pipelined interface between a central processing unit
(CPU) and a floating-point coprocessor (FPU), along
with the CPU recovery mechanisms that provide precise
floating-point exceptions for each \ldots{}",
}
@Article{Irwin:1988:SIP,
author = "M. J. Irwin",
title = "Special issue on parallelism in computer arithmetic",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "205--208",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C5440
(Multiprocessor systems and techniques)",
corpsource = "Pennsylvania State University, University Park, PA,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "computer arithmetic; digital arithmetic; lookahead
adders; parallel processing; parallelism; pipelined
arithmetic processors; VLSI systems",
treatment = "G General Review; P Practical",
}
@Article{Jenkins:1988:SCP,
author = "W. K. Jenkins and E. J. Altman",
title = "Self-checking properties of residue number error
checkers based on mixed radix conversion",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "2",
pages = "159--167",
month = feb,
year = "1988",
CODEN = "ICSYBT",
DOI = "https://doi.org/10.1109/31.1717",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=107",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "residue arithmetic; residue number system",
summary = "It has been shown previously that a mixed-radix
converter can be modified to perform all the essential
functions of an error checker for error detection and
correction in residue number system hardware
architectures. Since the computations in a \ldots{}",
}
@PhdThesis{Johnstone:1988:DFP,
author = "Paul Johnstone",
title = "Decimal floating point representation",
type = "Thesis ({Ph.D.})",
school = "Tulane University",
address = "New Orleans, LA 70118, USA",
pages = "vi + 101",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Binary system (Mathematics); decimal floating-point
arithmetic; Floating-point arithmetic.",
}
@TechReport{Jouppi:1988:MFA,
author = "Norman Paul Jouppi and Jeremy Dion and David Reeves
Boggs and Michael J. K. Nielsen",
title = "{MultiTitan}: four architecture papers",
institution = "Digital Western Research Laboratory",
address = "Palo Alto, CA, USA",
edition = "[Revised]",
pages = "various",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "WRL research report; 87/8",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; MultiTitan (Computer)",
remark = "``April 10, 1988.'' MultiTitan central processor unit
/ Norman P. Jouppi --- MultiTitan floating point unit /
Norman P. Jouppi --- MultiTitan cache control unit /
Jeremy Dion --- MultiTitan intra-processor bus / David
Boggs, Jeremy Dion, Michael J. K. Nielsen.",
}
@TechReport{Jouppi:1988:UVS,
author = "Norman P. Jouppi and Jonathan Bertoni and David W.
Wall",
title = "A unified vector\slash scalar floating-point
architecture",
type = "Report",
number = "WRL TN-3",
institution = "Digital Western Research Laboratory",
address = "Palo Alto, CA, USA",
pages = "19",
year = "1988",
bibdate = "Thu May 09 08:38:06 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Joy:1988:OCT,
author = "Edward Bennett Joy and Paul R. Beaudet and Pankaj K.
Das",
title = "Optical communications techniques\slash floating point
residue number system",
institution = "School of Electrical Engineering, Georgia Institute of
Technology",
address = "Atlanta, GA, USA",
pages = "17",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer network architectures.; Computers --- Optical
equipment.",
remark = "Issued as R and D status reports [nos. 1--7], Contract
funds status reports [nos. 1--8], Final technical
report, and Final report, Project E-21-T01. Final
technical report has author: Paul R. Beaudet. Final
report has author: Pankaj K. Das. Final technical
report has title: Floating point residue number system.
Final report has title: New techniques in optical
communications and signal processing.",
}
@Article{Juffa:1988:SAF,
author = "N. Juffa",
title = "{Schnelle Algorithmen f{\"u}r Sin und Cos} \toenglish
{Fast Algorithms for Sin and Cos} \endtoenglish",
journal = j-MC,
volume = "5",
pages = "105--107",
year = "1988",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Misc{Kahan:1988:AFP,
author = "William Kahan",
title = "Arithmazium: The Floating Point Expos{\'e}",
howpublished = "Web site",
month = may # "\slash " # jul,
year = "1988",
bibdate = "Wed Jun 05 09:50:01 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This site includes 27 lectures with notes and videos
for CS 279 (Computer System Support for Scientific and
Engineering Computation). The class handouts amount to
more than 2000 pages.",
URL = "https://www.arithmazium.org/classroom/wk88_toc.html",
acknowledgement = ack-nhfb,
}
@TechReport{Kahan:1988:CSS,
author = "W. Kahan and David Goldberg",
title = "Computer System Support for Scientific and Engineering
Computation",
type = "Report",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
day = "26",
month = jul,
year = "1988",
bibdate = "Mon Aug 26 10:39:23 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised 14 June 1990.",
URL = "http://www.arithmazium.org/classroom/lib//Lecture_25_notes_slides.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kahaner:1988:BRP,
author = "D. K. Kahaner",
title = "Benchmarks for `real' programs",
journal = j-SIAM-NEWS,
pages = "A-61",
month = nov,
year = "1988",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Mon Sep 16 16:15:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@InProceedings{Kanada:1988:VMA,
author = "Yasumasa Kanada",
booktitle = "Proceedings of Supercomputing 88. Vol. {II}: Science
and Applications",
title = "Vectorization of multiple-precision arithmetic program
and 201,326,000 decimal digits of {$ \pi $}
calculation",
crossref = "Martin:1988:SPN",
volume = "2",
pages = "117--128",
year = "1988",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
abstract = "More than 200 million decimal places of {$ \pi $} were
calculated using an arithmetic geometric mean formula
independently discovered by E. Salamin and R. P. Brent
in 1976. Correctness of the calculation was verified
through Borwein's quartic convergent formula developed
in 1983. The computation took CPU times of 5 hours 57
minutes for the main calculation and 7 hours 30 minutes
for the verification calculation on the HITAC S-820
model 80 supercomputer with 256 MB of main memory and 3
GB of high speed semiconductor storage, Extended
Storage, to shorten I/O time.\par Computation was
completed in 27th of January 1988. At that day two
programs generated values up to $ 3 \times 2^{26} $,
about 201 million. The two results agreed except for
the last 21 digits. These results also agree with the
133,554,000 places of calculation of $ \pi $ which was
done by the author in January 1987. Compare to the
record in 1987, 50\% more decimal digits were
calculated with about $ 1 / 6 $ of CPU time.\par
Computation was performed with real arithmetic based
vectorized Fast Fourier Transform (FFT) multiplier and
newly vectorized multiple-precision add, subtract and
(single word) constant multiplication programs.
Vectorizations for the later cases were realized
through first order linear recurrence vector
instruction on the S-820. Details of the computation
and statistical tests on the first 200 million digits
of $ \pi - 3 $ are reported.",
acknowledgement = ack-nhfb,
classification = "C4190 (Other numerical methods); C7310
(Mathematics)",
corpsource = "Comput. Centre, Tokyo University, Japan",
keywords = "arithmetic geometric mean formula; Borwein's quartic
convergent formula; fast Fourier transform; fast
Fourier transforms; first order linear recurrence
vector instruction; HITAC S-820 model 80 supercomputer;
mathematics computing; multiple-precision arithmetic
program; multiplier; parallel processing; pi
calculation; S-820; vectorization",
sponsororg = "IEEE; ACM SIGARCH",
treatment = "P Practical",
}
@InProceedings{Kanada:1988:VMP,
author = "Yasumasa Kanada",
booktitle = "Proceedings of Supercomputing 88. Vol. {II}: Science
and Applications",
title = "Vectorization of multiple-precision arithmetic program
and 201,326,000 decimal digits of {$ \pi $}
calculation",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "117--128",
year = "1988",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "More than 200 million decimal places of {\pi} were
calculated using an arithmetic geometric mean formula
independently discovered by E. Salamin and R. P. Brent
in 1976. Correctness of the calculation was verified
through Borwein's quartic convergent formula developed
in 1983. The computation took CPU times of 5 hours 57
minutes for the main calculation and 7 hours 30 minutes
for the verification calculation on the HITAC S-820
model 80 supercomputer with 256 MB of main memory and 3
GB of high speed semiconductor storage, Extended
Storage, to shorten I/O time.\par
Computation was completed in 27th of January 1988. At
that day two programs generated values up to $ 3 \times
2^{26} $, about 201 million. The two results agreed
except for the last 21 digits. These results also agree
with the 133,554,000 places of calculation of $ \pi $
which was done by the author in January 1987. Compare
to the record in 1987, 50\% more decimal digits were
calculated with about $ 1 / 6 $ of CPU
time.\par
Computation was performed with real arithmetic based
vectorized Fast Fourier Transform (FFT) multiplier and
newly vectorized multiple-precision add, subtract and
(single word) constant multiplication programs.
Vectorizations for the later cases were realized
through first order linear recurrence vector
instruction on the S-820. Dertails of the computation
and statistical tests on the first 200 million digits
of $ \pi - 3 $ are reported.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kida:1988:FPP,
author = "H. Kida and M. Watabe and T. Nakamikawa and S.
Morinaga and S. Kawasaki and H. Inayoshi",
title = "A floating point processing unit for the {GMICRO}
{CPU}",
crossref = "Sakamura:1988:TPO",
bookpages = "xi + 384",
pages = "301--316",
year = "1988",
DOI = "https://doi.org/10.1007/978-4-431-68081-9_21",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes the architecture and implementation of a
newly developed floating point processing unit (FPU).
It was developed as a high performance 32-bit
coprocessor of the 32-bit GMICRO microprocessor, which
satisfies the IEEE 754 Standard for Binary
Floating-Point Arithmetic. High performance was
achieved by the high speed coprocessor's interface with
the GMICRO CPU and the pipeline processing. The
coprocessor's interface was designed to minimize
CPU-FPU communication overhead caused by transferring
commands, operands and coprocessor information.
Furthermore, to improve operation speed, the FPU
performs pipeline processing named command pipeline.
The FPU has three main elements, the bus control unit,
format conversion unit, and execution control unit. In
order to perform high speed calculations, each element
in the chip is designed to operate in parallel. (5
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Hitachi Ltd., Tokyo, Japan",
classification = "C5220 (Computer architecture)",
confdate = "1988",
conflocation = "Japan",
keywords = "32 Bit; Coprocessor; Floating point processing unit;
FPU; GMICRO CPU; GMICRO microprocessor; IEEE 754;
Standard for Binary Floating-Point Arithmetic",
numericalindex = "Word length 3.2E+01 bit",
pubcountry = "Japan",
thesaurus = "Computer architecture; Microprocessor chips",
}
@Article{Kirchner:1988:AAV,
author = "R. Kirchner and U. Kulisch",
title = "Accurate arithmetic for vector processors",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "250--270",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ Kaiserslautern, West Ger",
classification = "721; 722; 723; C5230 (Digital arithmetic methods);
C5440 (Multiprocessor systems and techniques)",
corpsource = "Fachbereich Inf., Kaiserslautern University, West
Germany",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "arithmetic operations; Computational Methods; computer
systems, digital --- Parallel Processing; computers;
computers, digital; computers, microcomputer; digital
arithmetic; dot products; implementation techniques;
local memory; microcomputers; parallel; parallel
processing; pipelined compound operations; sums; vector
processors; VLSI technology",
treatment = "P Practical",
}
@Article{Knuth:1988:FM,
author = "Donald E. Knuth",
title = "{Fibonacci} multiplication",
journal = j-APPL-MATH-LETT,
volume = "1",
number = "1",
pages = "57--60",
year = "1988",
CODEN = "AMLEEL",
ISSN = "0893-9659 (print), 1873-5452 (electronic)",
ISSN-L = "0893-9659",
MRclass = "11B39",
MRnumber = "89f:11031",
MRreviewer = "W. Herget",
bibdate = "Fri Mar 22 18:03:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/08939659",
}
@Article{Kornerup:1988:LAU,
author = "Peter Kornerup and David W. Matula",
title = "An on-line arithmetic unit for bit-pipelined rational
arithmetic",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "310--330",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Odense Univ, Odense, Den",
classification = "722; 723; 921; C5230 (Digital arithmetic methods)",
corpsource = "Odense University, Denmark",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algorithm of Gosper; Algorithms; binary version;
bit-pipelined rational arithmetic; computer metatheory
--- Binary Sequences; computer programming; computers,
digital --- Computational Methods; difference; digital
arithmetic; functions; mathematical techniques ---
Algorithms; on-line arithmetic unit; online arithmetic
unit; product; quotient; rational; sum",
treatment = "P Practical",
}
@InProceedings{Krishnan:1988:IRN,
author = "R. Krishnan",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 7--9 June 1988",
title = "Implementation of recursive and nonrecursive digital
filters using the single multiplexed {ROM} in the
quadratic residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1297--1300",
year = "1988",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1988.15166",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Recursive and nonrecursive digital filters have been
implemented using the proposed single-multiplexed
dual-clock computational module (SDCM) in the bit-slice
architecture. The amount of memory requirements has
been reduced to 50\% required for the \ldots{}",
}
@InProceedings{Krishnan:1988:SCR,
author = "R. Krishnan",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-88, 11--14} April 1988",
title = "A single-channel {ROM}-based complex digital filter
implementation in the quadratic residue number
systems",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1842--1845",
year = "1988",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1988.196981",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The implementation of complex digital filters using
the quadratic residue number system (QRNs) and modified
quadratic residue number system (MQRNS) is considered.
These QRNS/MQRNS-based filter architectures are
memory-intensive because the lookup- \ldots{}",
}
@InProceedings{Lai:1988:FAI,
author = "K. Lai and J. Valerio",
title = "The floating-point architecture of {Intel's 80960}",
crossref = "Wescon:1988:WCR",
pages = "1.5/1--3",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Intel 80960KB is a microprocessor with hardware
floating-point support integrated on-chip. In a
departure from previous microprocessors, the 80960KB
incorporates full floating-point support within the
processor instead of relying on a coprocessor. As
floating-point speeds increase, the off-chip
coprocessor interface becomes a significant performance
bottleneck. Additionally, component and system cost,
board space, and cleanliness of architecture are other
good reasons to have on-chip floating-point support.
The implementation delivers accurate results with good
performance: 1.1 single-precision Linpack MFLOPS, and
4.1 single-precision mega-Whetstones per second. (0
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Intel Corp., Hillsboro, OR, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods)",
keywords = "1.1 MFLOPS; Board space; Cleanliness; Component costs;
Floating-point architecture; Intel 80960KB; Linpack;
Microprocessor; On-chip floating-point support;
Performance; System cost",
numericalindex = "Computer speed 1.1E+06 FLOPS",
thesaurus = "Computer architecture; Digital arithmetic;
Microprocessor chips",
}
@InProceedings{Lai:1988:IFS,
author = "K. Lai and J. Valerio",
title = "Integrated floating-point solution for the {Intel
80960KB}",
crossref = "Midcon:1988:MCP",
pages = "249--251",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Intel 80960KB is a microprocessor with hardware
floating-point support integrated on-chip. In a
departure from previous microprocessors, the 80960KB
incorporates full floating-point support within the
processor instead of relying on a coprocessor. As
floating-point speeds increase, the off-chip
coprocessor interface becomes a significant performance
bottleneck. Additionally, component and system cost,
board space, and cleanliness of architecture are other
good reasons to have on-chip floating-point support.
The implementation delivers accurate results with good
performance: 1.1 single precision Linpack MFLOPS, and
4.1 single precision mega Whetstones per second. (0
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Intel Corp., Hillsboro, OR, USA",
classification = "C5130 (Microprocessor chips)",
keywords = "Floating-point support; Integrated floating point;
Intel 80960KB; Microprocessor; Onchip floating point",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Article{Lawson:1988:SRR,
author = "Charles L. Lawson",
title = "Series reversion as the reversed chain rule",
journal = j-SIGNUM,
volume = "23",
number = "1",
pages = "7--9",
month = jan,
year = "1988",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:16 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Lawson gives Fortran subroutines for differentiation
arithmetic. A subroutine SWPRO for products corresponds
to Chang's ATS [Chang74a]. The chain rule is
implemented by repeated calls to SWPRO. Series
reversion for implicit functions is implemented by
reversing the chain rule. An application is given to
Keppler's equation, $ M - E + e \sin (E) = 0 $.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "design; differentiation arithmetic; implicit
functions; languages; theory",
subject = "D.3.3 Software, PROGRAMMING LANGUAGES, Language
Constructs, Modules, packages \\ G.4 Mathematics of
Computing, MATHEMATICAL SOFTWARE \\ D.3.3 Software,
PROGRAMMING LANGUAGES, Language Constructs, Procedures,
functions, and subroutines",
}
@TechReport{Liu:1988:BEF,
author = "Zhi-Shun Alex Liu",
title = "{Berkeley} Elementary Function Test Suite",
institution = "Computer Science Division, Department of Electrical
Engineering and Computer Science, Univerity of
California at Berkeley",
address = "Berkeley, CA, USA",
pages = "ii + 59",
day = "30",
month = dec,
year = "1988",
bibdate = "Mon Sep 12 23:52:34 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.netlib.org/fp/ucbtest.tgz;
http://www.ucbtest.org/zaliu-papers/zaliu-beef-doc.pdf",
abstract = "A suite of programs is presented to test how
accurately the elementary transcendental functions exp,
log, sin, cos and atan have been implemented in a
computer's run-time library. The suite is written in
the language C and designed to run on any computer with
binary floating-point arithmetic rounded in a
reasonable way. The suite makes no appeal to
extra-precise arithmetic; the tests use only whatever
arithmetic capabilities are present in the environment
where the transcendental functions are to be used.
Despite this limitation, the tests run fast and deliver
indication of accuracy to within a small fraction of an
ULP (Unit in the Last Place) of the functions under
test. This account includes the proofs of the test
suite's claims to accuracy.",
acknowledgement = ack-nj,
keywords = "BeEF test suite; floating-point testing",
}
@InProceedings{Lu:1988:MCF,
author = "P. Y. Lu and A. Jain and J. Kung and P. H. Ang",
title = "A 30-{MFLOP} 32b {CMOS} Floating-Point Processor",
crossref = "IEEE:1988:IIS",
pages = "28, 29, 285",
year = "1988",
bibdate = "Fri Dec 08 13:04:40 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Luk:1988:AAB,
author = "Franklin T. Luk and Haesun Park",
title = "An analysis of algorithm-based fault tolerance
techniques",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "2",
pages = "172--184",
month = apr,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
classification = "722; 723; C4110 (Error analysis in numerical
methods); C4140 (Linear algebra); C5230 (Digital
arithmetic methods); C5470 (Performance evaluation and
testing)",
corpsource = "Sch. of Electr. Eng., Cornell University, Ithaca, NY,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algorithm-based fault tolerance; analysis;
computation; computer programming --- Algorithms;
computer systems, digital; decomposition; error
analysis; Fault Tolerant Capability; fault tolerant
computing; floating point error; Gaussian elimination;
Gaussian elimination with pairwise pivoting; LU; lu
decomposition; matrix algebra; pairwise pivoting; qr
decomposition; QR decomposition; rank-one perturbation;
rounding errors; roundoff errors; systolic array;
transient error; unified checksum scheme",
treatment = "T Theoretical or Mathematical",
}
@MastersThesis{Lyu:1988:PFP,
author = "Chung-nan Lyu",
title = "Pipelined floating point divider with built-in testing
circuits",
type = "Thesis ({M.S.})",
school = "Ohio University",
address = "Athens, OH, USA",
pages = "90",
month = jun,
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point testing; parallel processing
(electronic computers)",
}
@Article{Magenheimer:1988:IMD,
author = "Daniel J. Magenheimer and Liz Peters and Karl W.
Peters and Dan Zuras",
title = "Integer Multiplication and Division on the {HP
Precision Architecture}",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "8",
pages = "980--990",
month = aug,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2248",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Aug 04 16:38:15 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Marchyulaitis:1988:SRN,
author = "Saulyus Marchyula{\u\i}tis",
title = "Summation of real numbers in arithmetic with a
floating point. {A} probability approach to determining
the variance of absolute round-off error. ({Russian})",
journal = "Statist. Problemy Upravleniya",
volume = "82",
pages = "57--68",
year = "1988",
MRclass = "65G05 (65C20)",
MRnumber = "89k:65056",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
language = "Russian",
}
@Article{Maurer:1988:DVW,
author = "P. M. Maurer",
title = "Design Verification of the {WE} 32106 Math Accelerator
Unit",
journal = j-IEEE-DES-TEST-COMPUT,
volume = "5",
number = "3",
pages = "11--21",
month = jun,
year = "1988",
ISSN = "0740-7475 (print), 1558-1918 (electronic)",
ISSN-L = "0740-7475",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Design \& Test of Computers",
}
@Article{McLellan:1988:DCF,
author = "E. J. McLellan and G. M. Wolrich and R. A. J.
Yodlowski",
title = "Development of the {CVAX} floating-point chip",
journal = j-DEC-TECH-J,
volume = "??",
number = "7",
pages = "109--120",
month = aug,
year = "1988",
CODEN = "DTJOEL",
ISSN = "0898-901X",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Digital Technical Journal",
}
@InProceedings{Melear:1988:IFP,
author = "C. Melear",
title = "An integrated floating point unit for a {RISC}
architecture",
crossref = "Wescon:1988:WCR",
pages = "1.2/1--8",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "RISC architectures require multiple bus structures
that allow for instructions, operands, and results to
all travel about the processor on each clock cycle.
Thus, by putting the floating point unit on these
multiple bus structures, it can receive instructions
and operands on each clock cycle. Some number of cycles
later, as more floating point instructions are issued,
floating point results can also be sent out on the
destination bus, yielding burst execution rates equal
to the clock rate. The present clock rate is 20 MHz and
will be increased eventually to the 40 MHz area. At 20
MHz, sustained execution rates of 7 MFLOPS are typical.
Performance rates of 10.5 MWhetstones have also been
demonstrated (20 MHz clock). The floating point unit is
only one part of the RISC processor. By combining all
the aspects of software, memory system interfacing and
high performance hardware like the 88100 floating point
unit, mainframe performance moves one step closer to
the desktop computer world.",
acknowledgement = ack-nhfb,
affiliation = "Motorola, Austin, TX, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods)",
keywords = "20 MHz; 7 MFLOPS; 88100 Floating point unit; Burst
execution rates; Clock cycle; Clock rate; Desktop
computer; Execution rates; Memory system interfacing;
Multiple bus structures; Performance rates; RISC
architecture",
numericalindex = "Frequency 2.0E+07 Hz; Computer speed 7.0E+06 FLOPS",
thesaurus = "Digital arithmetic; Microprocessor chips; Reduced
instruction set computing",
}
@Article{Milnikel:1988:SRF,
author = "R. Milnikel and R. Wollenberg",
title = "{Schnelles Radizierverfahren f{\"u}r Gleitkommazahlen
im IEEE-Format} \toenglish {Fast Square-rooting method
for Floating-point Numbers in IEEE Format}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "8",
pages = "114--1122",
year = "1988",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{Monahan:1988:CAG,
author = "John F. Monahan",
title = "Corrigendum: ``{An} Algorithm for Generating Chi
Random Variables''",
journal = j-TOMS,
volume = "14",
number = "1",
pages = "111--111",
month = mar,
year = "1988",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/42288.356228",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "111. 65C10",
MRnumber = "89d:65006, 88d:65013",
bibdate = "Fri Mar 28 10:45:16 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Monahan:1987:AGC}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Manual{Motorola:1988:GPF,
title = "96-bit general purpose floating-point digital-signal
processor technical summary",
organization = "Motorola, Inc.",
address = "Phoenix, AZ, USA",
pages = "23",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Motorola semiconductor technical data",
acknowledgement = ack-nhfb,
keywords = "Integrated circuits.; Signal processing --- Digital
techniques.",
remark = "Caption title. ``BR574/D.''",
}
@Book{Motorola:1988:MFP,
author = "{Motorola, Inc.Staff}",
title = "{MC} 68881 and 68882 Floating-Point Coprocessor User's
Manual",
publisher = pub-PH,
address = pub-PH:adr,
month = feb,
year = "1988",
ISBN = "0-13-566936-7",
ISBN-13 = "978-0-13-566936-5",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$22.50",
acknowledgement = ack-nhfb,
language = "eng",
}
@Article{Nakamura:1988:SCP,
author = "S. Nakamura and K.-Y. Chu",
title = "A single chip parallel multiplier by {MOS}
technology",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "3",
pages = "274--282",
month = mar,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2164",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2164",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Nikolos:1988:EDT,
author = "D. Nikolos and A. M. Paschalis and G. Philokyprou",
title = "Efficient design of totally self-checking checkers for
all low-cost arithmetic codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "7",
pages = "807--814",
month = jul,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2226",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2226",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Normand:1988:PSP,
author = "J. M. Normand",
title = "{Percola}: a special purpose programmable 64-bit
floating-point processor",
crossref = "ACM:1988:ICS",
pages = "55--65",
year = "1988",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$49.00",
URL = "http://doi.acm.org/10.1145/55364.55370",
acknowledgement = ack-nhfb,
affiliation = "Centre d'Etudes Nucl{\'e}aires, Saclay, France",
bibno = "55370",
catcode = "G.3; C.5.1; C.5.3; J.2; G.3; B.6.3",
CRclass = "G.3 Random number generation; C.5.1 Large and Medium
(``Mainframe'') Computers; C.5.1 Super (very large)
computers; C.5.3 Microcomputers; C.5.3 Motorola 68000;
J.2 Physics; G.3 Statistical computing; B.6.3 Design
Aids; B.6.3 Optimization",
descriptor = "Mathematics of Computing, PROBABILITY AND STATISTICS,
Random number generation; Computer Systems
Organization, COMPUTER SYSTEM IMPLEMENTATION, Large and
Medium (``Mainframe'') Computers, Super (very large)
computers; Computer Systems Organization, COMPUTER
SYSTEM IMPLEMENTATION, Microcomputers, Motorola 68000;
Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Physics; Mathematics of Computing,
PROBABILITY AND STATISTICS, Statistical computing;
Hardware, LOGIC DESIGN, Design Aids, Optimization",
genterm = "ALGORITHMS; DESIGN",
guideno = "1988-15563",
subject = "G. Mathematics of Computing; G.3 PROBABILITY AND
STATISTICS; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; C. Computer Systems
Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; J.
Computer Applications; J.2 PHYSICAL SCIENCES AND
ENGINEERING; G. Mathematics of Computing; G.3
PROBABILITY AND STATISTICS; B. Hardware; B.6 LOGIC
DESIGN",
waffil = "Rennes",
wauthedit = "Lenfant, J.",
wsub = "Conference Proceedings",
}
@Article{Oklobdzija:1988:IAV,
author = "Vojin G. Oklobdzija and Earl R. Barnes",
title = "On implementing addition in {VLSI} technology",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "6",
pages = "716--728",
month = dec,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Yorktown Heights, NY, USA",
classification = "713; 714; 723; B1265B (Logic circuits); B2570D (CMOS
integrated circuits); C5210 (Logic design methods);
C5230 (Digital arithmetic methods)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "addition; Arithmetic Algorithms; arithmetic
algorithms; carry-lookahead; CMOS integrated circuits;
CMOS technology; Computer Aided Design; Computer
Programming--Algorithms; digital arithmetic; estimates;
integrated; Integrated Circuits, VLSI; logic circuits;
logic design; Logic Levels; logic levels; quick;
recurrence solver schemes; Semiconductor Devices, MOS;
Single-chip VLSI Processor; VLSI; VLSI Implementation;
VLSI technology; VLSI-; VLSI-cmos Technology",
treatment = "P Practical",
}
@InProceedings{Papadourakis:1988:VDP,
author = "G. M. Papadourakis and J. Condorodis",
booktitle = "1988 International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP-88, 11--14} April 1988",
title = "A {VLSI} design of processing element for
reconfigurable systolic architectures based on {LNS}",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2080--2083",
year = "1988",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The design and development of a processing element
(PE) in an orthogonal systolic architecture, using the
state of the art in VLSI technology, is presented. The
goal was to create a high-speed, high-precision PE
which would be adaptive to a highly \ldots{}",
}
@Article{Papamichalis:1988:TFP,
author = "P. Papamichalis and R. {Simar, Jr.}",
title = "The {TMS320C30} Floating-Point Digital Signal
Processor",
journal = j-IEEE-MICRO,
volume = "8",
number = "6",
pages = "13--29",
month = nov # "\slash " # dec,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.16778",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "The 320C30 is a fast processor with a large memory
space and floating-point-arithmetic capabilities. The
authors describe the 320C30 architecture in detail,
discussing both the internal organization of the device
and the external interfaces. They also \ldots{}",
}
@InProceedings{Perlman:1988:AFP,
author = "R. M. Perlman",
title = "The {Am29027} --- a floating-point accelerator for the
{Am29000} streamlined instruction processor",
crossref = "Wescon:1988:WCR",
pages = "1.4/1--7",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Am29000, a 32-bit RISC processor, sets new
standards of performance for integer processing. A 25
MHz Am29000 with cache can achieve in excess of 35600
Dhrystones. Even with simple video DRAM memory, the
Am29000 has a performance of 24300 Dhrystones. Although
the Am29000 contains no hardware dedicated to
floating-point computation, it can emulate
floating-point operations in software at speeds that
were heretofore achieved only by dedicated
floating-point coprocessors. For numerically-intensive
applications, the Am29000 can be augmented with the
Am29027 arithmetic accelerator. The Am29027 is a
single-chip floating-point unit that performs single-,
double-, and mixed-precision operations, and completely
implements IEEE standard 754 for those operations
supported. The Am29027 offers two operating modes: a
low-latency mode, for scalar operations, and a pipeline
mode, for vector and matrix calculations. When
configured in pipeline mode, the AM29027 can achieve a
peak throughput of 16 MFLOPS.",
acknowledgement = ack-nhfb,
affiliation = "Adv. Micro Devices, Sunnyale, CA, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
keywords = "16 MFLOPS; 32 Bit; Am29000 streamlined instruction
processor; Am29027 arithmetic accelerator; Cache;
Floating-point operations; IEEE standard 754;
Low-latency mode; Matrix calculations; Mixed-precision
operations; Pipeline mode; RISC processor; Scalar
operations; Vector calculations; Video DRAM memory",
numericalindex = "Word length 3.2E+01 bit; Computer speed 1.6E+07
FLOPS",
thesaurus = "Digital arithmetic; Microprocessor chips; Pipeline
processing; Reduced instruction set computing",
}
@Article{Pichat:1988:APC,
author = "M. A. Pichat",
title = "All possible computed results in correct
floating-point summation. Stochastic methods in
round-off error analysis",
journal = j-MATH-COMP-SIM,
volume = "30",
number = "6",
pages = "541--552",
year = "1988",
CODEN = "MCSIDR",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
MRclass = "65G05",
MRnumber = "90d:65090",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics and Computers in Simulation",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
reviewer = "Luciano Biasini",
}
@MastersThesis{Pier:1988:IPA,
author = "Richard Michael Pier",
title = "An {IBM PC\slash AT}-based floating point imaging
workstation architecture",
type = "Thesis ({M.S.E.E.})",
school = "University of Washington",
address = "Seattle, WA, USA",
pages = "vi + 35",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; IBM Personal Computer AT.;
Image processing --- Equipment and supplies.;
Microcomputer workstations.",
}
@Article{Pitas:1988:FPE,
author = "I. Pitas and M. G. Strintzis",
title = "Floating point error analysis of two-dimensional, fast
{Fourier} transform algorithms",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "35",
number = "1",
pages = "112--115",
month = jan,
year = "1988",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "Floating-point error is conducted for three algorithms
commonly used for the calculation of two-dimensional
fast Fourier transforms (FFTs), namely, the
conventional row-column FFT, the vector-radix FFT, and
the polynomial-transform FFT. The respective \ldots{}",
}
@Article{Plauger:1988:PFP,
author = "P. J. Plauger",
title = "Properties of floating-point arithmetic",
journal = j-COMP-LANG-MAG,
volume = "5",
number = "3",
pages = "17--22",
month = mar,
year = "1988",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@InProceedings{Prandolini:1988:VIB,
author = "R. Prandolini and S. Sridharan",
title = "{VLSI} implementation of a block floating point
coprocessor for the {TMS320} fixed point digital signal
processor",
crossref = "IREE:1988:AMC",
pages = "33--40",
year = "1988",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The design of a co-processor which can be interfaced
to the TMS32020 fixed-point digital signal processor is
described. The co-processor enables efficient
implementation of block floating-point arithmetic for
digital filtering using the TMS32020.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Electr. and Electron. Syst. Eng., Queensland
Inst. of Technol., Brisbane, Qld., Australia",
classification = "B1265F (Microprocessors and microcomputers); B1270F
(Digital filters); B2570 (Semiconductor integrated
circuits); C5130 (Microprocessor chips); C5240 (Digital
filters); C5260 (Digital signal processing)",
keywords = "Block floating point coprocessor; Block floating-point
arithmetic; Digital filtering; TMS320 fixed point
digital signal processor; VLSI implementation",
thesaurus = "Digital filters; Digital signal processing chips;
VLSI",
}
@Article{Prather:1988:CET,
author = "R. E. Prather",
title = "Comparison and Extension of Theories of {Zipf} and
{Halstead}",
journal = j-COMP-J,
volume = "31",
number = "3",
pages = "248--252",
month = jun,
year = "1988",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
acknowledgement = ack-nhfb,
affiliation = "Trinity Univ, San Antonio, TX, USA",
affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
classcodes = "C6110B (Software engineering techniques)",
classification = "723",
corpsource = "Comput. and Inf. Sci., Trinity University, San
Antonio, TX, USA",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "behavioural psychology; computer programming; computer
software; empirical law; Halstead metrics; Halstead's
hypothesis; length estimates; Measurements;
probabilistic hypothesis; process; programming;
software engineering; software metrication; software
science; Zipf metrics; Zipf's law",
treatment = "T Theoretical or Mathematical",
}
@Book{Press:1988:NRC,
author = "W. H. Press and B. P. Flannery and S. A. Teukolsky and
W. T. Vetterling",
title = "Numerical Recipes in {C}: The Art of Scientific
Computing",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xxii + 735",
year = "1988",
ISBN = "0-521-43724-5",
ISBN-13 = "978-0-521-43724-0",
LCCN = "QA76.73.C15 N865 1988",
bibdate = "Thu Sep 01 10:34:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Rajanala:1988:ISP,
author = "Arunkumar V. Rajanala",
title = "{IEEE 754} single precision standard compatible
floating point processor implemented using silicon
compiler technology",
type = "Thesis ({M.S.})",
school = "Oregon State University",
address = "Corvallis, OR, USA",
pages = "77",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
}
@InProceedings{Randal:1988:FPC,
author = "V. T. Randal and J. L. Schmalzel and A. P. Shepherd",
title = "Floating-Point Computation Using a Microcontroller",
crossref = "Harris:1988:PAI",
pages = "1243--1244",
year = "1988",
bibdate = "Wed Sep 07 22:02:38 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Razaz:1988:TPM,
author = "M. Razaz and J. L. Schonfelder",
title = "Test Procedures for Measurement of Floating-Point
Characteristics of Computing Environments",
journal = j-COMP-J,
volume = "31",
number = "1",
pages = "12--16",
month = feb,
year = "1988",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Mar 25 13:51:56 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of Birmingham, Birmingham, Engl",
affiliationaddress = "Univ of Birmingham, Birmingham, Engl",
classcodes = "C5470 (Performance evaluation and testing)",
classification = "723",
corpsource = "Department of Electron. and Electr. Eng., Birmingham
University, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "arithmetic; arithmetic processors; CDC; computer
testing; computers, digital; computing environments;
conversion test; DEC; digital arithmetic;
floating-point arithmetic; floating-point
characteristics; floating-point testing; IBM; ICL;
mantissa; minimum representable number; nominal
decimal; normalisation base; number representation;
operations; parameters; performance evaluation;
precision; precision-dependent; procedures;
representation test; test; Testing",
treatment = "P Practical",
}
@InProceedings{Ries:1988:MFP,
author = "P. S. Ries",
title = "An 8 {MFLOP} Floating-Point Coprocessor for a {RISC}
Microprocessor",
crossref = "Electro:1988:ECR",
pages = "48/1/1--8",
year = "1988",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Robertazzi:1988:BOF,
author = "T. G. Robertazzi and S. C. Schwartz",
title = "Best {``Ordering''} for Floating-Point Addition",
journal = j-TOMS,
volume = "14",
number = "1",
pages = "101--110",
month = mar,
year = "1988",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/42288.42343",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G99 (65V05)",
MRnumber = "89b:65117",
bibdate = "Sat Nov 19 13:08:22 1994",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p101-robertazzi/",
acknowledgement = ack-nhfb,
affiliation = "State University of New York at Stony Brook, Stony
Brook; Princeton University, Princeton, NJ",
bibno = "42343",
catcode = "G.1.0",
content = "This paper compares a variety of methods for
accumulating a floating-point sum. Wilkinson pointed
out that if we compute the $\sum^n_{i = 1} x_i$ in
strictly increasing order in magnitude of the $x_i$,
then we obtain a better bound on the rounding error
than if the sum is computed in random order
[1].\par
The authors discuss five different accumulation
strategies. They compare these accumulation strategies
for when the $x_i$ are uniformly distributed and for
when they are exponentially distributed. First they
compare a random order for summing the $x_i$, summing
in decreasing order of magnitude, and summing in
increasing order of magnitude. Not surprisingly,
summing in increasing order of magnitude is the best
and summing in decreasing order of magnitude is the
worst. In fact, it is not difficult to show this for
any class of distributions where the mean and variance
exist.\par
The interesting results in the paper concern two other
accumulation strategies. Both of these are shown to be
better than summing in increasing order of magnitude
for both the uniform and exponential distribution.
Fortunately, one of these strategies is the tree sum
(or fan-in sum) that is often used in parallel
computation. The paper calls this strategy the
``adjacency'' ordering.",
CRclass = "G.1.0 General; G.1.0 Computer arithmetic",
CRnumber = "8810-0794",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
genterm = "ALGORITHMS; PERFORMANCE",
journal-URL = "https://dl.acm.org/loi/toms",
journalabbrev = "ACM Trans. Math. Softw.",
keywords = "accurate floating-point summation; algorithms;
performance",
review = "ACM CR 8810-0794",
reviewer = "Jesse L. Barlow",
subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic",
}
@Article{Rowen:1988:MRF,
author = "Chris Rowen and Mark Johnson and Paul Ries",
title = "The {MIPS R3010} Floating-Point Coprocessor",
journal = j-IEEE-MICRO,
volume = "8",
number = "3",
pages = "53--62",
month = may # "\slash " # jun,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.540",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "Compendex database;
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliationaddress = "MIPS Computer Systems, Sunnyvale, CA, USA",
classcodes = "B1265F (Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); C5130
(Microprocessor chips); C5220 (Computer architecture);
C5230 (Digital arithmetic methods)",
classification = "714; 722; 723",
corpsource = "MIPS Comput. Syst., Sunnyvale, CA, USA",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "32-bit R31010 floating-point coprocessor; accelerator
chip; computer architecture; computer systems, digital
--- Parallel Processing; computers, microcomputer;
Design; design techniques; digital arithmetic;
floating-point; instruction set computing; integrated
circuits, VLSI; microprocessor chips; million
instruction per second (MIPS) processor; MIPS R3010
floating-point coprocessor; reduced;
reduced-instruction-set-computer;
reduced-instruction-set-computer (RISC); VLSI",
summary = "A description is given of the R3010 floating-point
accelerator chip, a coprocessor that is based on
advanced reduced-instruction-set-computer (RISC)
architecture and VLSI design techniques and provides
high-speed floating-point operation. The 75000-
\ldots{}",
treatment = "P Practical",
xxauthor = "C. Rowen and P. Ries and M. Johnson",
}
@InProceedings{Roylance:1988:EMS,
author = "G. Roylance",
title = "Expressing Mathematical Subroutines Constructively",
crossref = "ACM:1988:PAC",
pages = "8--13",
year = "1988",
bibdate = "Thu Sep 01 11:52:13 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Santoro:1988:PIA,
author = "M. Santoro and M. Horowitz",
booktitle = "Digest of Technical Papers, {IEEE} International
Solid-State Circuits Conference",
title = "A pipelined $ 64 \times 64 $ b iterative array
multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "35--36",
month = feb,
year = "1988",
bibdate = "Mon Dec 24 10:19:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Schatte:1988:ASC,
author = "Peter Schatte",
title = "On the almost sure convergence of floating-point
mantissas and {Benford}'s law",
journal = j-MATH-NACHR,
volume = "135",
pages = "79--83",
year = "1988",
CODEN = "MTMNAQ",
ISSN = "0025-584X",
MRclass = "60F15 (11K31)",
MRnumber = "89g:60114",
bibdate = "Fri Dec 08 12:49:25 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
reviewer = "S. A. Book",
}
@Article{Schatte:1988:MDC,
author = "P. Schatte",
title = "On Mantissa Distribution in Computing and {Benford}'s
Law",
journal = j-J-INFO-PROC-CYBERNETICS-EIK,
volume = "24",
number = "9",
pages = "443--455",
month = "????",
year = "1988",
CODEN = "JICYE5",
ISSN = "0863-0593",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of Information Processing and Cybernetics:
EIK",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Scherson:1988:MOA,
author = "Isaac D. Scherson and Smil Ruhman",
title = "Multi-operand arithmetic in a partitioned associative
architecture",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "6",
pages = "655--668",
month = dec,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Princeton, NJ, USA",
classification = "722; 723; 921; C5220 (Computer architecture); C5230
(Digital arithmetic methods)",
corpsource = "Department of Electr. Eng., Princeton University, NJ,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "16-bit precision; Analysis; Associative
Multiplication; associative multiplication; common
filter vector; Computer Architecture; Computer
Metatheory; concurrency; Convolution; convolution; Data
Storage, Digital--Associative; digital arithmetic;
Disjoint Data Sets; disjoint data sets; Filter Vectors;
Mathematical Techniques; Multi-operand Arithmetic;
multioperand arithmetic; multiplier bits; parallel
architectures; parallel processing; Partitioned
Associative Architecture; partitioned associative
architecture",
treatment = "P Practical",
}
@InProceedings{Schwarz:1988:CLI,
author = "Jerry Schwarz",
title = "A {C++} Library for Infinite Precision Floating
Point",
crossref = "USENIX:1988:UPC",
bookpages = "362",
pages = "271--281",
year = "1988",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "ftp://ftp.uu.net/library/bibliography;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Real library supports infinite precision floating
point computation in C++. Arbitrary precision rational
arithmetic and transcendental functions are
supported.",
acknowledgement = ack-nhfb,
affiliation = "AT\&T Bell Laboratories, Murray Hill",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
confdate = "17--21 Oct. 1988",
conflocation = "Denver, CO, USA",
keywords = "C++ library; Infinite precision floating point;
Rational arithmetic; Real library; Transcendental
functions",
thesaurus = "C language; Digital arithmetic; Object-oriented
programming; Subroutines",
}
@Article{Scott:1988:CMM,
author = "Michael Scott",
title = "{CUG247} --- {M.I.R.A.C.L.} --- a Multi-Pre\-ci\-sion
Arithmetic Library",
journal = j-CUJ,
volume = "6",
type = "{CUG} New Release",
number = "5",
pages = "76--??",
month = may,
year = "1988",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Shepherd:1988:LEC,
author = "Roger Shepherd and Charles Farnum",
title = "Letter to the {Editor}: Compiler support for
floating-point computation",
journal = j-SPE,
volume = "18",
number = "12",
pages = "1193--1194",
month = dec,
year = "1988",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380181208",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Sep 10 12:36:39 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "30 Oct 2006",
}
@Article{Simon:1988:SP,
author = "Barry Simon and Richard M. Wilson",
title = "Supercalculators on the {PC}",
journal = j-NAMS,
volume = "35",
number = "7",
pages = "978--1001",
month = sep,
year = "1988",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Wed Jun 12 16:56:18 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
mynote = "September",
}
@Article{Smith:1988:ASD,
author = "S. G. Smith and P. B. Denyer",
title = "Advanced serial-data computation",
journal = j-J-PAR-DIST-COMP,
volume = "5",
number = "3",
pages = "228--249",
month = jun,
year = "1988",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliationaddress = "Univ of Edinburgh, Edinburgh, Scotl",
classification = "716; 718; 721; 722; 723; C5230 (Digital arithmetic
methods)",
corpsource = "Department of Electr. Eng., Edinburgh University, UK",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "arithmetic operations; bit-parallel architectures;
Computational Methods; computational modules; computer
architecture; computers, digital; digital arithmetic;
dynamic range; high-; multiwire; multiwire techniques;
performance computer arithmetic; serial data
architectures; serial data computation; serial-data
architectures; signal processing --- Digital
Techniques; symmetric-coded distributed arithmetic;
techniques",
treatment = "P Practical",
}
@Article{Sohie:1988:DSP,
author = "G. R. L. Sohie and K. L. Kloker",
title = "A Digital Signal Processor with {IEEE} Floating-Point
Arithmetic",
journal = j-IEEE-MICRO,
volume = "8",
number = "6",
pages = "49--67",
month = nov # "\slash " # dec,
year = "1988",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.16780",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "A overview is given of Motorola's DSP96002, a digital
signal processor that implements IEEE-standard
floating-point arithmetic. It is designed for graphics,
image processing, spectral analysis and scientific
computing applications. Performance peaks \ldots{}",
}
@Article{Sridharan:1988:BFP,
author = "S. Sridharan and G. Dickman",
title = "Block floating-point implementation of digital filters
using the {DSP56000}",
journal = j-MICROPROC-MICROSYS,
volume = "12",
number = "6",
pages = "299--308",
month = aug,
year = "1988",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Queensland Institute of Technology, Queensland,
Australia; Queensland Institute of Technology,
Queensland, Australia",
bibno = "49397",
catcode = "G.m; I.5.4; C.3; C.5.3",
CRclass = "I.5.4 Applications; I.5.4 Signal processing; C.3
Signal processing systems; C.5.3 Microcomputers; C.5.3
Microprocessors",
descriptor = "Mathematics of Computing, MISCELLANEOUS; Computing
Methodologies, PATTERN RECOGNITION, Applications,
Signal processing; Computer Systems Organization,
SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal
processing systems; Computer Systems Organization,
COMPUTER SYSTEM IMPLEMENTATION, Microcomputers,
Microprocessors",
fjournal = "Microprocessors and Microsystems",
genterm = "ALGORITHMS; DESIGN",
guideno = "1988-12500",
journalabbrev = "Microprocess. Microsyst.",
subject = "G. Mathematics of Computing; G.m MISCELLANEOUS; I.
Computing Methodologies; I.5 PATTERN RECOGNITION; C.
Computer Systems Organization; C.3 SPECIAL-PURPOSE AND
APPLICATION-BASED SYSTEMS; C. Computer Systems
Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION",
}
@Book{Startz:1988:IPC,
author = "Richard Startz",
title = "8087\slash 80287\slash 80387 for the {IBM PC} and
Compatibles: Applications and Programming with
{Intel}'s Math Coprocessors",
publisher = pub-BRADY,
address = pub-BRADY:adr,
edition = "Third",
pages = "xviii + 296",
year = "1988",
ISBN = "0-13-246604-X",
ISBN-13 = "978-0-13-246604-2",
LCCN = "QA76.8.I2923 S79 1988",
bibdate = "Wed Sep 14 20:23:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Stasinski:1988:MRE,
author = "R. Stasinski and E. Lukasik",
booktitle = "Acoustics, Speech, and Signal Processing, 1988.
{ICASSP-88., 1988} International Conference on. 11--14
April 1988",
title = "Minimization of rounding errors in {WFTA} programs",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1423--1426",
year = "1988",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Two ideas linked with high-precision computation of
WFTAs (Winograd-Fourier transform algorithm) using
fixed-point arithmetic are analyzed. Use of the best,
optimized small-N DFT (discrete Fourier transform)
modules is considered. The sizes \ldots{}",
}
@Article{Stouraitis:1988:FPL,
author = "Thanos Stouraitis and Fred J. Taylor",
title = "Floating-point to logarithmic encoder error analysis",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "7",
pages = "858--863",
month = jul,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2232",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Ohio State University of University, Columbus;
University of Florida, Gainesville",
ajournal = "IEEE Trans. Comput.",
bibno = "48698",
catcode = "F.2.1; G.m; C.1.m",
CRclass = "F.2.1 Numerical Algorithms and Problems; F.2.1
Number-theoretic computations; C.1.m Miscellaneous",
descriptor = "Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
Number-theoretic computations; Mathematics of
Computing, MISCELLANEOUS; Computer Systems
Organization, PROCESSOR ARCHITECTURES, Miscellaneous",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
genterm = "DESIGN; THEORY; VERIFICATION",
guideno = "1988-08687",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
journalabbrev = "IEEE Trans. Comput.",
subject = "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
G.m MISCELLANEOUS; C. Computer Systems Organization;
C.1 PROCESSOR ARCHITECTURES",
summary = "The logarithmic number (LNS), which supports
high-speed, high-precision arithmetic, is envisioned as
a possible arithmetic coprocessor attachment to a
floating-point (FLP) processor. An error analysis of an
FLP-to-LNS encoder is presented. Analytic \ldots{}",
}
@Manual{Sun:1988:PG,
title = "Programmer's guides",
publisher = "Sun Microsystems",
address = "Mountain View, CA, USA",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "12 volumes in 1 case.",
acknowledgement = ack-nhfb,
keywords = "Operating systems (Computers); Sun computers ---
Programming.; SunOS (Computer operating system)",
remark = "Title from container. Contents sheet has title: 4.0
programmer's guides minibox. ``Revision A, of 9 May
1988.''--Contents. ``825-1050-10.''--Contents. C
programmer's guide --- Assembly language reference for
the Sun-2 and Sun-3 --- Programming utilities and
libraries --- Debugging tools --- Network programming
--- Writing device drivers --- Floating point
programmer's guide --- SunView 1 programmer's guide ---
SunView 1 system programmer's guide --- Pixrect
reference manual --- SunCGI reference manual ---
SunCore reference manual.",
}
@Article{Taylor:1988:BLN,
author = "F. J. Taylor and R. Gill and J. Joseph and J. Radke",
title = "A 20 Bit Logarithmic Number System Processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-37",
number = "2",
pages = "190--199",
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2148",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 19:49:19 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The architecture and performance of a 20-bit
arithmetic processor based on the logarithmic number
system (LNS) is described. The processor performed LNS
multiplication and division rapidly and with a low
hardware complexity. Addition and subtraction in the
LNS require the support of a table lookup unit. A
scheme is proposed to minimize this complexity using a
partitioned memory (ROM) and a PLA (programmable logic
array). For performance evaluation, the target
technology is integrated Schottky logic. The processor
is shown to compare well with, if not to outperform,
existing floating point (FLP) processors of equivalent
range and precision. The speed-power-product ratio of
an equivalent FLP processor, compared with that of the
LNS processor, is reported to be 20 to 1 in the case of
the square and square-root operation and 1 to 1 in the
case of addition and subtraction. For multiplication
and division, this ratio is about 5 to 1.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Taylor:1988:HFP,
author = "Fred J. Taylor",
title = "Hybrid floating point\slash logarithmic number system
arithmetic processor",
howpublished = "United States Patent 4,720,809",
day = "19",
month = jan,
year = "1988",
bibdate = "Tue Jan 08 21:48:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/4720809.html",
abstract = "A hybrid arithmetic processor which combines
attributes of conventional floating point (F.P.)
arithmetic with logarithmic number system (LNS)
arithmetic. The arithmetic processor includes an input
section (forward code converter) for converting input
operands in F.P. format to intermediate operands in LNS
format, an LNS arithmetic section for performing an
arithmetic operation on the LNS intermediate operands
and providing an intermediate output in LNS format, and
an output section (inverse code converter) for
converting the LNS intermediate output to an output in
F.P. format. Significantly, output is provided in
normalized floating point format but without the need
for a time-consuming exponent alignment operation.
Arithmetic operations, including addition and
multiplication, are accomplished at a high speed, which
speed moreover is constant and independent of the data.
An efficient accumulator structure and the structure of
an ultra-fast numeric processor are disclosed.",
acknowledgement = ack-nhfb,
}
@InProceedings{Thistle:1988:PAH,
author = "M. R. Thistle and B. J. Smith",
title = "A processor architecture for {Horizon}",
crossref = "IEEE:1988:PSN",
volume = "1",
pages = "35--41",
year = "1988",
bibdate = "Thu Apr 16 07:55:03 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5220 (Computer architecture); C5440 (Multiprocessor
systems and techniques)",
corpsource = "Supercomput. Res. Center, Lanham, MD, USA",
keywords = "floating-point operations; Horizon; horizontal
instruction set; parallel architectures; parallel
machines; processor architecture; scalable
shared-memory MIMD computer; scalable shared-memory
multiple-instruction-stream-multiple-data-stream
computer; scalar processors; three-dimensional
nearest-neighbor network",
sponsororg = "IEEE; ACM",
treatment = "P Practical",
}
@TechReport{Tsao:1988:AST,
author = "Nai-kuan Tsao",
title = "On the accuracy of solving triangular systems in
parallel",
institution = "National Aeronautics and Space Administration; For
sale by the National Technical Information Service",
address = "Washington, DC, USA",
pages = "????",
year = "1988",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "NASA technical memorandum; 101384 ICOMP; 88-19",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.15:101384 0830-D (MF)",
keywords = "Algorithms.; Error analysis.; Errors.; Floating point
arithmetic.",
remark = "Distributed to depository libraries in microfiche.
Microfiche. [Washington, D.C.: National Aeronautics and
Space Administration, 1989] 1 microfiche.",
}
@Article{Venkaiah:1988:CMS,
author = "V. Ch Venkaiah and S. K. Sen",
title = "Computing a matrix symmetrizer exactly using modified
multiple modulus residue arithmetic",
journal = j-J-COMPUT-APPL-MATH,
volume = "21",
number = "1",
pages = "27--40",
month = jan,
year = "1988",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042788903858",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Voelzke:1988:FSAa,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 1: Standards und
Strukturen} \toenglish {Floating-point Arithmetic and
its IEEE Specification. Part 1: Standards and
Structures} \endtoenglish",
journal = j-MC,
volume = "10",
pages = "123--129",
year = "1988",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:39 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Voelzke:1988:FSAb,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 2: Entwurf eines
Flie{\ss}kommapakets} \toenglish {Floating-point
Arithmetic and its IEEE Specification. Part 2: Design
of a Floating-Point Package} \endtoenglish",
journal = j-MC,
volume = "11",
pages = "78--95",
year = "1988",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Voelzke:1988:FSAc,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 3: Die verwendeten
Algorithmen} \toenglish {Floating-point Arithmetic and
its IEEE Specification. Part 3: The Algorithms Used}
\endtoenglish",
journal = j-MC,
volume = "12",
pages = "95--108",
year = "1988",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Weyland:1988:LCS,
author = "Nicholas J. Weyland and Edward A. Puckett",
title = "Lossless coding for sources of floating-point and
fixed-precision numbers",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "34",
number = "4",
pages = "882--888",
month = jul,
year = "1988",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/18.9791",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
MRclass = "94A29",
MRnumber = "89i:94023",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
summary = "A procedure for constructing binary models for sources
of floating-point and fixed-precision numbers is given
and used together with the minimum description length
principle to find optimal models. These models are used
to design noiseless source code \ldots{}",
}
@Article{Wilson:1988:FPS,
author = "Pete Wilson",
title = "Floating-Point Survival Kit",
journal = j-BYTE,
volume = "13",
number = "3",
pages = "217--217",
month = mar,
year = "1988",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Oct 31 18:51:38 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
}
@Article{Wilson:1988:NDP,
author = "Fred Wilson",
title = "A Note on Division of Positive Integers",
journal = j-SIGMICRO,
volume = "19",
number = "1--2",
pages = "4--4",
month = jun,
year = "1988",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/62197.1096672",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:39 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/62197.1096672",
abstract = "At the risk of flaunting a marginal grasp of the
obvious I would like to make a few observations on the
division of fixed point numbers.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Wilson:1988:NFP,
author = "R. Wilson",
title = "Newest floating-point processors blur architectural
distinctions",
journal = j-COMP-DESIGN,
volume = "27",
number = "8",
pages = "32--43",
day = "15",
month = apr,
year = "1988",
CODEN = "CMPDAM",
ISSN = "0010-4566",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
bibno = "44373",
catcode = "B.7.1; C.1.1; C.1.1",
CRclass = "B.7.1 Types and Design Styles; B.7.1 Memory
technologies; C.1.1 Single Data Stream Architectures;
C.1.1 RISC; C.1.1 Single Data Stream Architectures;
C.1.1 CISC",
descriptor = "Hardware, INTEGRATED CIRCUITS, Types and Design
Styles, Memory technologies; Computer Systems
Organization, PROCESSOR ARCHITECTURES, Single Data
Stream Architectures, RISC; Computer Systems
Organization, PROCESSOR ARCHITECTURES, Single Data
Stream Architectures, CISC",
fjournal = "Computer Design",
genterm = "PERFORMANCE; DESIGN",
guideno = "1988-05955",
journalabbrev = "Comput. Des.",
subject = "B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer
Systems Organization; C.1 PROCESSOR ARCHITECTURES; C.
Computer Systems Organization; C.1 PROCESSOR
ARCHITECTURES",
}
@Article{Wollard:1988:TSS,
author = "K. Wollard",
title = "Technology '88: Solid state",
journal = j-IEEE-SPECTRUM,
volume = "25",
number = "1",
pages = "44--46",
month = jan,
year = "1988",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.4483",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Mon Jan 20 06:41:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "16 Mbit; 4 Mbit; application-specific ICs; Consumer
electronics; digital integrated circuits; Electronics
industry; EPROM; floating-point digital signal
processors; GaAs-Si; Government; high-density
packaging; integrated circuit technology; Japan;
Manufacturing industries; Microprocessors; Production;
Semiconductor device manufacture; solid state; Solid
state circuits; Trade agreements; US",
}
@Book{Young:1988:SNMa,
author = "David M. Young and Robert Todd Gregory",
title = "A Survey of Numerical Mathematics",
volume = "I",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "x + 492 + A22 + B16 + I18",
year = "1988",
ISBN = "0-486-65691-8",
ISBN-13 = "978-0-486-65691-5",
LCCN = "QA297.Y63 1972",
MRclass = "65-02",
MRnumber = "92b:65005b",
bibdate = "Wed Jan 17 10:30:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Corrected reprint of the 1973 original.",
URL = "http://www.zentralblatt-math.org/zmath/en/search/?an=0732.65002",
ZMnumber = "0732.65002",
acknowledgement = ack-nhfb,
tableofcontents = "1: Numerical Analysis as a Subject Area \\
1.1 Introduction \\
1.2 Some pitfalls in computation \\
1.3 Mathematical and computer aspects of an algorithm
\\
1.4 Numerical instability of algorithms and
ill-conditioned problems \\
1.5 Typical problems of interest to the numerical
analyst \\
1.6 Iterative methods \\
2: Elementary Operations with Automatic Digital
Computers \\
2.1 Introduction \\
2.2 Binary arithmetic \\
2.3 Conversion from base $D$ to base $B$ representation
\\
2.4 Representation of integers on a binary computer \\
2.5 Floating-point representations \\
2.6 Computer-representable numbers \\
2.7 Floating-point arithmetic operations \\
2.8 Fortran analysis of a floating-point number \\
2.9 Calculation of elementary functions \\
3: Surveillance of Number Ranges \\
3.1 Introduction \\
3.2 Allowable number ranges \\
3.3 Basic real arithmetic operations \\
3.4 The quadratic equation \\
3.5 Complex arithmetic operations \\
4: Solution of Equations \\
4.1 Introduction \\
4.2 Attainable accuracy \\
4.3 Graphical methods \\
4.4 The method of bisection \\
4.5 The method of false position \\
4.6 The secant method \\
4.7 General properties of iterative methods \\
4.8 Generation of iterative methods \\
4.9 The Newton method \\
4.10 Muller's method \\
4.11 Orders of convergence of iterative methods \\
4.12 Acceleration of the convergence \\
4.13 Systems of nonlinear equations \\
5: Roots of Polynomial Equations \\
5.1 Introduction \\
5.2 General properties of polynomials \\
5.3 The Newton method and related methods \\
5.4 Muller's method and Cauchy's method \\
5.5 Location of the roots \\
5.6 Root acceptance and refinement \\
5.7 Matrix related methods: the modified Bernoulli
method \\
5.8 Matrix related methods: the IP method \\
5.9 Polyalgorithms \\
5.10 Other methods \\
6: Interpolation and Approximation \\
6.1 Introduction \\
6.2 Linear interpolation \\
6.3 Convergence and accuracy of linear interpolation
\\
6.4 Lagrangian interpolation \\
6.5 Convergence and accuracy of Lagrangian
interpolation \\
6.6 Interpolation with equal intervals \\
6.7 Hermite interpolation \\
6.8 Limitations on polynomial interpolation: smooth
interpolation \\
6.9 Inverse interpolation \\
6.10 Approximation by polynomials \\
6.11 Least squares approximation by polynomials \\
6.12 Rational approximation \\
6.13 Trigonometric interpolation and approximation \\
6.14 Interpolation in two variables \\
7: Numerical Differentiation and Quadrature \\
7.1 Introduction \\
7.2 The method of undetermined weights \\
7.3 Numerical differentiation \\
7.4 Numerical quadrature --- equal intervals \\
7.5 The Euler--MacLaurin formula \\
7.6 Romberg integration \\
7.7 Error determination \\
7.8 Numerical quadrature --- unequal intervals \\
8: Ordinary Differential Equations \\
8.1 Introduction \\
8.2 Existence and uniqueness \\
8.3 Analytic methods \\
8.4 Integral equation formulation --- the Picard method
of successive approximations \\
8.5 The Euler method \\
8.6 Methods based on numerical quadrature \\
8.7 Error estimation for predictor-corrector methods
\\
8.8 A numerical example \\
8.9 Runge--Kutta methods \\
8.10 Methods based on numerical differentiation \\
8.11 Higher-order equations and systems of first-order
equations \\
8.12 The use of high-speed computers \\
Appendix A \\
Appendix B \\
Appendix C \\
Bibliography \\
Index",
}
@InProceedings{Yuen:1988:IFP,
author = "A. K. Yuen",
title = "{Intel}'s floating-point processors",
crossref = "Electro:1988:ECR",
pages = "48/5/1--7",
year = "1988",
bibdate = "Wed Sep 7 22:32:00 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Zhou:1988:NBS,
author = "B. B. Zhou",
title = "A new bit-serial systolic multiplier over {$ \mathrm
{GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "37",
number = "6",
pages = "749--751",
month = jun,
year = "1988",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.2216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 9 08:33:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2216",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Zoicas:1988:PBG,
author = "A. Zoicas and K. Grohe and C. Kellerhoff",
title = "{PC} based general-purpose floating-point {DSP $ \mu
$PD77230} board with various analog front end options
and application software packages",
crossref = "Lacoume:1988:SPI",
pages = "1233--1236 vol.3",
year = "1988",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "3 vol.",
abstract = "The EBIBM-77230 FFT is a software and hardware DSP
engineering environment incorporated in a PC in the
form of a plug-in board. It offers no downgrade from
the ideal in terms of its processing power, which
amounts of 27 MFLOPs, its open architecture, standard
cross-software support and interfaces to popular
commercial DSP packages. A variety of analog front-end
options and supervisor modules (for stand-alone
operation) can be hooked onto the board itself thereby
opening its application to most DSP areas. A math
library, which features interfaces to most high level
languages (C, Fortran, Pascal, Basic), brings
workstation computational power to the PC. The
EBIBM-77230 FFT bridges the gap between fast high
precision number crunching and an accessible
user-friendly environment. The turn-around time from an
idea to its real-time execution is thus minimised and
cost-wise it is an economic solution in relation to
most DSP working environments.",
acknowledgement = ack-nhfb,
affiliation = "NEC Electron. GmbH, Dusseldorf, West Germany",
classification = "B1265F (Microprocessors and microcomputers); B6140
(Signal processing and detection); C5130
(Microprocessor chips); C5150 (Other circuits for
digital computers); C7410F (Communications)",
keywords = "27 MFLOPS; Analog front end; Application software
packages; Basic; C; DSP engineering environment;
EBIBM-77230 FFT; Fortran; General purpose floating
point DSP; High level languages; Interfaces; Math
library; Microprocessor D77230 board; Open
architecture; Pascal; PC; Personal computer; Plug-in
board; Supervisor modules",
numericalindex = "Computer speed 2.7E+07 FLOPS",
thesaurus = "Add-on boards; Computerised signal processing;
Microcomputer applications; Microprocessor chips;
Software packages",
}
@InProceedings{Ahmed:1989:EEF,
author = "H. M. Ahmed",
title = "Efficient Elementary Function Generation with
Multipliers",
crossref = "Ercegovac:1989:PSC",
pages = "52--59",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ahmed.pdf",
acknowledgement = ack-nhfb # " and " # ack-nj,
keywords = "ARITH-9",
}
@Article{Amit:1989:MRE,
author = "G. Amit and U. Shaked",
title = "Minimization of roundoff errors in digital
realizations of {Kalman} filters",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "37",
number = "12",
pages = "1980--1982",
month = dec,
year = "1989",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A comparison between D. Williamson's method (IEEE
Trans. Autom. Contr., vol.AC-30, p.930-9, 1985) and the
0-1 method for the design of the digital Kalman filter
is made. The 0-1 method is shown to be much better than
Williamson's method and the \ldots{}",
}
@InProceedings{Arison:1989:SAN,
author = "D. Arison and A. Genusov and L. Gerzberg",
title = "System applications of a new 32-bit floating-point
{DSP} processor",
crossref = "Chen:1989:TSA",
pages = "890--897 vol.2",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present the ZR34325, a novel
floating-point vector signal processor in the context
of system applications. The ZR34325 represents the
first full IEEE floating-point integrated array
processor on silicon, supplemented with the pertinent
scalar and control flow capabilities. The ZR34325
directly executes embedded DSP (digital signal
processing) and array processing primitives on
multidimensional arrays. Furthermore, an integrated
development environment which includes a system
software simulation, vectorized and parametric DSP,
arithmetic and matrix library, C-based
assembler/linker, and hardware development tools
facilities top-down complete application development.
The ZR34325 enables very efficient multiprocessor
multitasking schemes for tasks where execution time is
either data independent or data dependent. The authors
show the top-down integrated design methodology via
sample signal/image processing application examples
such as Kalman filtering, spectral analysis, and
constant false alarm rate processing for radar
applications as well as two-dimensional image
filtering.",
acknowledgement = ack-nhfb,
affiliation = "Zoran Corp., Santa Clara, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5260 (Digital signal
processing)",
keywords = "32 Bit; Arithmetic library; C-based assembler/linker;
Digital signal processing; False alarm rate processing;
Floating-point DSP processor; Image filtering; Kalman
filtering; Matrix library; Multidimensional arrays;
Radar; Spectral analysis; Vector signal processor;
ZR34325",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Computerised signal processing; Digital signal
processing chips; Parallel processing",
}
@InProceedings{Arnold:1989:RLN,
author = "M. G. Arnold and T. A. Bailey and J. R. Cowles and J.
J. Cupal",
title = "Redundant logarithmic number systems",
crossref = "Ercegovac:1989:PSC",
pages = "144--151",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Arnold.pdf",
abstract = "A new number system that offers advantages over
conventional floating-point and sign/logarithm number
systems is described. Called redundant logarithmic
arithmetic, it relies, like conventional logarithmic
arithmetic, on table lookups to make the arithmetic
unit simpler than an equivalent floating-point unit.
The cost of 32-b subtraction in a redundant logarithmic
number system is lower than that of previously
published logarithmic subtraction methods. Another
advantage of a redundant logarithmic number system is
that a single arithmetic unit can use the same hardware
to add, subtract, or multiply in similar times. (25
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Wyoming University, Laramie, WY, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Add; ARITH-9; Floating-point; Multiply; Number system;
Redundant logarithmic arithmetic; Sign/logarithm number
systems; Subtract; Table lookups",
thesaurus = "Digital arithmetic; Table lookup",
}
@Article{Ashton:1989:AFP,
author = "C. Ashton",
title = "The {Am29C327} floating point processor",
journal = "Electronic Product Design",
volume = "10",
number = "3",
pages = "51--59",
month = mar,
year = "1989",
bibdate = "Wed Sep 7 22:32:01 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Azmi:1989:TFP,
author = "A. M. Azmi and F. Lombardi",
title = "On a tapered floating point system",
crossref = "Ercegovac:1989:PSC",
pages = "2--9",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Azmi.pdf",
abstract = "R. Morris (see IEEE Trans. Comput., vol. TC-20, p.
1578--1579, 1971), suggested adding an extra field to
the fixed floating point system, so that exponents can
be stored more efficiently. The exponents are stored in
the smallest possible space, passing the extra bits to
the mantissa. The extra field is used to monitor the
current length of the exponent. The gain in precision
and/or exponent range outweighs the overhead of the
extra field and the processing speed. The authors
provide implementation details, error analysis, and
some future research ideas. Simulation results are
provided for comparison purposes.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Colorado
University, Boulder, CO, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ARITH-9; Error analysis; Exponents; Tapered floating
point system",
thesaurus = "Digital arithmetic",
}
@Article{Bailey:1989:FPA,
author = "D. H. Bailey and H. D. Simon and J. T. Barton",
title = "Floating Point Arithmetic in Future Supercomputers",
journal = j-IJSA,
volume = "3",
number = "3",
pages = "86--90",
month = "Fall",
year = "1989",
CODEN = "IJSAE9",
ISSN = "0890-2720",
bibdate = "Thu Aug 22 17:56:36 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover library database",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Supercomputer Applications",
journal-URL = "http://hpc.sagepub.com/content/by/year",
}
@Article{Baran:1989:MST,
author = "N. Baran",
title = "The {Mac SE} takes off",
journal = j-BYTE,
volume = "14",
number = "2",
pages = "113--116",
month = feb,
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:54:09 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5430 (Microcomputers)",
fjournal = "BYTE Magazine",
keywords = "16 MHz; 2 MBytes; 4 MBytes; 68030 CPU; 68882
Floating-point unit; Apple Macintosh SE/30; Built-in
memory management unit; FPU; Logic board; Mac SE/30;
MMU; Motorola 68030 processor; SIMM-mounted ROMs;
Single in-line memory module RAM chips",
numericalindex = "Frequency 1.6E+07 Hz; Memory size 2.1E+06 Byte;
Memory size 4.2E+06 Byte",
thesaurus = "Apple computers; Microcomputers",
}
@Article{Bardin:1989:IUI,
author = "B. Bardin and C. Colket and D. Smith",
title = "Implementation of unsigned integers in {Ada}",
journal = j-SIGADA-LETTERS,
volume = "9",
number = "1",
pages = "47--70",
month = jan # "\slash " # feb,
year = "1989",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Thu Mar 20 07:41:09 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C6130 (Data handling
techniques)",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; address arithmetic; digital arithmetic; full
range; logical operations; modular arithmetic; numeric
literals; symbol manipulation; unsigned integers",
treatment = "P Practical",
}
@Article{Barrett:1989:FMA,
author = "Geoff Barrett",
title = "Formal methods applied to a floating-point number
system",
journal = j-IEEE-TRANS-SOFTW-ENG,
volume = "15",
number = "5",
pages = "611--621",
month = may,
year = "1989",
CODEN = "IESEDJ",
DOI = "https://doi.org/10.1109/32.24710",
ISSN = "0098-5589 (print), 1939-3520 (electronic)",
ISSN-L = "0098-5589",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A formalization of the IEEE standard for binary
floating-point arithmetic (ANSI/IEEE Std. 754-1985) is
presented in the set-theoretic specification language
Z. The formal specification is refined into four
sequential components, which unpack the operands,
perform the arithmetic, and pack and round the result.
This refinement follows proven rules and so
demonstrates a mathematically rigorous method of
program development. In the course of the proofs,
useful internal representations of floating-point
numbers are specified. The procedures presented form
the basis for the floating-point unit of the Inmos IMS
T800 transputer.",
acknowledgement = ack-nhfb,
affiliation = "Oxford University, Oxford, UK",
bibno = "65476",
catcode = "F.3.1; C.5.3; D.2.1; D.2.0; B.2.0; B.5.1",
content = "It is paradoxical that no programming language can be
completely defined unless it has a formally defined
syntax, yet at the same time, languages have informal
semantic descriptions. This is most evident in
arithmetic, in which the closest thing to a formal
description lies in the IEEE standard for binary
floating point arithmetic adopted by ANSI in 1985. The
standard is written in natural language, with the
attendant possibility of ambiguity and inconsistency.
The author of this paper has given a formal version of
the standard in the Z specification language, which can
be thought of as a structured version of predicate
logic. After giving a cogent argument for the use of
formal methods in standardization, the author presents
a stage-by-stage development of the formal description
of the standard; while doing this, he stresses the
modularity of the description, as exemplified by the
separation of normal and exceptional conditions.\par
As he introduces the concepts of Z, the author gives
brief explanations of the notation, but for a beginner
in the field, the paper is best read in conjunction
with the original standard and a description of
Z.\par
A very powerful argument for the formal approach lies
in the specification's use. The INMOS T800 floating
point unit was developed by means of a series of
refinements of the formal specification; the",
CRclass = "F.3.1 Specifying and Verifying and Reasoning about
Programs; F.3.1 Specification techniques; C.5.3
Microcomputers; C.5.3 INMOS Transputer; D.2.1
Requirements/Specifications; D.2.1 Z; D.2.0 General;
D.2.0 Standards; B.2.0 General; B.5.1 Design; B.5.1
Arithmetic and logic units",
CRnumber = "9004-0316",
descriptor = "Theory of Computation, LOGICS AND MEANINGS OF
PROGRAMS, Specifying and Verifying and Reasoning about
Programs, Specification techniques; Computer Systems
Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers, INMOS Transputer; Software, SOFTWARE
ENGINEERING, Requirements/Specifications, Z; Software,
SOFTWARE ENGINEERING, General, Standards; Hardware,
ARITHMETIC AND LOGIC STRUCTURES, General; Hardware,
REGISTER-TRANSFER-LEVEL IMPLEMENTATION, Design,
Arithmetic and logic units",
fjournal = "IEEE Transactions on Software Engineering",
genterm = "ALGORITHMS; DOCUMENTATION; LANGUAGES; STANDARDIZATION;
THEORY",
guideno = "1989-06803",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
journalabbrev = "IEEE Trans. Softw. Eng.",
reviewer = "Simon Thompson",
subject = "F. Theory of Computation; F.3 LOGICS AND MEANINGS OF
PROGRAMS; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; D. Software; D.2
SOFTWARE ENGINEERING; D. Software; D.2 SOFTWARE
ENGINEERING; B. Hardware; B.2 ARITHMETIC AND LOGIC
STRUCTURES; B. Hardware; B.5 REGISTER-TRANSFER-LEVEL
IMPLEMENTATION",
}
@InProceedings{Bedard:1989:WFD,
author = "N. Bedard and M. Birman and G. Chu and L. Hu and C. M.
Lim and J. McLeod and L. Torban and F. Ware",
title = "The {Weitek} 64-bit floating-point datapath unit",
crossref = "Chen:1989:TSA",
pages = "898--902 (vol. 2)",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors describe the WTL 3165 and WTL 3364,
jointly referred to as the WTL 3X64, which are each
64-bit floating-point data path units designed for
high-speed operation in pipelined environment while
making possible full compliance with the IEEE standard
for binary floating-point arithmetic. It also provides
full interruptibility, even in a pipelined environment.
The architecture and performance of the 3X64 are
described, and a detailed block diagram is presented.",
acknowledgement = ack-nhfb,
affiliation = "Weitek Corp., Sunnyvale, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods); C5260 (Digital signal
processing)",
keywords = "64 Bit; Architecture; Binary floating-point
arithmetic; Computerised signal processing; DSP chip;
Floating-point data path units; Interruptibility;
Pipelined environment; Weitek; WTL 3165; WTL 3364; WTL
3X64",
numericalindex = "Word length 6.4E+01 bit",
thesaurus = "CMOS integrated circuits; Computerised signal
processing; Digital arithmetic; Digital signal
processing chips; Parallel architectures; Pipeline
processing",
}
@Book{Beliankov:1989:NPO,
author = "A. Ia Beliankov",
title = "Nekotorye primeneniia otsenochnoi (``gruboi'')
arifmetiki",
publisher = "VTS AN SSSR",
address = "Moskva, Russia",
pages = "35",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Soobshcheniia po vychislitelnoi matematike",
acknowledgement = ack-nhfb,
keywords = "Algebras, Linear.; Computer arithmetic.;
Floating-point arithmetic.",
remark = "At head of title: Akademiia nauk SSSR. Vychislitelnyi
tsentr.",
}
@InProceedings{Benschneider:1989:MUP,
author = "B. J. Benschneider and W. J. Bowhill and E. M. Cooper
and M. N. Gavrielov and P. E. Gronowski and V. K.
Maheshwari and V. Peng and J. D. Pickholtz and S.
Samudrala",
title = "A 50 {MHz} Uniformly Pipelined 64b Floating-Point
Arithmetic Processor",
crossref = "Wuorinen:1989:DTP",
pages = "50--51, 288",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A description is given of a uniformly pipelined,
50-MHz, 64-b floating-point arithmetic processor
implemented in a 1.5- mu m (drawn) CMOS technology
which performs single- and double-precision
floating-point operations and integer multiplication as
defined by a superminicomputer architecture standard.
The chip is composed of an interface section and a
five-segment execution core. The core insists of a
divider, bypassed in all instruction except division,
and four fully pipelined stages that are uniformly
utilized in the execution of all instructions. The
performance is summarized. First pass silicon has been
functionally verified at 50 MHz with a set of over one
million vectors.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Digital Equipment Corp., Hudson, MA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
confdate = "15-17 Feb. 1989",
conflocation = "New York, NY, USA",
confsponsor = "IEEE; University of Pennsylvania",
keywords = "1.5 Micron; 50 MHz; 64 Bit; CMOS technology; Divider;
Double-precision floating-point operations;
Five-segment execution core; Floating-point arithmetic
processor; Fully pipelined stages; Integer
multiplication; Interface section; Single-precision
floating point; Superminicomputer architecture
standard",
numericalindex = "Frequency 5.0E+07 Hz; Word length 6.4E+01 bit; Size
1.5E-06 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
@Article{Benschneider:1989:PMC,
author = "Bradley J. Benschneider and William J. Bowhill and
Elizabeth M. Cooper and Moshe N. Gavrielov and Paul E.
Gronowski and Vijay K. Maheshwari and Victor Peng and
Jeffrey D. Pickholtz and Sridhar Samudrala",
title = "A pipelined {50-MHz} {CMOS} 64-bit floating-point
arithmetic processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1317--1323",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 135K transistor, uniformly pipelined 50-MHz CMOS
64-bit floating-point arithmetic processor chip is
described. The execution unit is capable of sustaining
pipelined performance of one 32-bit or 64-bit result
every 20 ns for all operations except double-precision
multiply (40 ns) and divide. The chip employs an
exponent difference prediction scheme and a unified
leading-one and sticky-bit computation logic for the
addition and subtraction operations. A hardware
multiplier using a radix-8 modified Booth algorithm and
a divider using a radix-2 SRT algorithm are employed.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Digital Equipment Corp., Hudson, MA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "20 Ns; 40 Ns; 50 MHz; 64 Bit; Addition; CMOS; Divider;
Execution unit; Exponent difference prediction scheme;
Floating-point arithmetic processor; Hardware
multiplier; Microprocessor; Processor chip; Radix-2 SRT
algorithm; Radix-8 modified Booth algorithm; Sticky-bit
computation logic; Subtraction; Unified leading-one;
Uniformly pipelined",
numericalindex = "Word length 6.4E+01 bit; Frequency 5.0E+07 Hz; Time
2.0E-08 s; Time 4.0E-08 s",
summary = "A 135K transistor, uniformly pipelined 50-MHz CMOS
64-bit floating-point arithmetic processor chip is
described. The execution unit is capable of sustaining
pipelined performance of one 32-bit or 64-bit result
every 20 ns for all operations except \ldots{}",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
@Misc{Bleher:1989:MCA,
author = "J. Hartmut Bleher and Axel T. Gerlicher and Siegfried
M. Rump and Dieter K. Unkauf",
title = "Method and circuit arrangement for adding floating
point numbers",
howpublished = "US Patent 4866651",
day = "12",
month = sep,
year = "1989",
bibdate = "Mon Dec 29 16:18:28 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/4866651/fulltext.html",
abstract = "For successively adding a series of floating point
numbers, a floating point adder stage (FIG. 2) is used
which, in addition to the sum of two floating point
operands, emits the remainder, truncated from the
smaller operand, as a floating point number. For
obtaining an exact sum of the operands, these
remainders are summed in the form of intermediate sums.
A circuit arrangement for parallel operation comprises
series-connected floating point adder stages (FIG. 6),
the intermediate sum occurring at the output of each
stage and the intermediate remainder being buffered.
Remainders are in each case passed on to the next
stage, their value decreasing until they are zero. A
serially operating arrangement (FIG. 8) comprises a
single adder stage (30) and a register stack (34) for
buffering the intermediate sums and the final result. A
remainder occurring is stored in a remainder register
(32) at the output of the adder stage and added to the
intermediate sums until the remainder is zero.
Subsequently, a fresh operand is applied to the input
of the adder stage.",
acknowledgement = ack-nhfb,
}
@InProceedings{Boddie:1989:FDC,
author = "J. R. Boddie and R. N. Gadenz and C. J. Garen and J.
M. Huser and B. Ng and S. P. Pekarich",
title = "A 32-bit floating-point {DSP} with {C} compiler",
crossref = "Chen:1989:TSA",
pages = "880--884 vol.2",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A novel digital signal processor (the DSP32C) has been
developed which performs 32-bit floating point
operations at a rate of 25 MFLOPS (million
floating-point operations per second) and can be
programmed using a standard C compiler. The authors
present an overview of the architecture and instruction
set with emphasis on the enhancements over its
predecessor, the DSP32. The performance is expressed
with common signal processor benchmarks. The
application development environment is described which
highlights the C compiler and hardware development
system. Finally, an application example illustrates the
power and ease of this DSP.",
acknowledgement = ack-nhfb,
affiliation = "AT\&T Bell Lab., Holmdel, NJ, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5260 (Digital signal processing); C6150C
(Compilers, interpreters and other processors)",
keywords = "25 MFLOPS; 32 Bit; Architecture; C compiler;
Computerised signal processing; DSP32C; Floating point
digital signal processor; Instruction set",
numericalindex = "Word length 3.2E+01 bit; Computer speed 2.5E+07
FLOPS",
thesaurus = "CMOS integrated circuits; Computerised signal
processing; Digital signal processing chips; Program
compilers",
}
@TechReport{Bohlender:1989:FST,
author = "Gerd Bohlender and Gudenberg, J. Wolff von (Jurgen
Wolff) and Willard L. Miranker",
title = "Floating-point systems for theorem proving",
type = "Research report",
number = "RC 15101 (\#67356)",
institution = "IBM T.J. Watson Research Center",
address = "Yorktown Heights, NY, USA",
pages = "14",
day = "2",
month = nov,
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There are a number of existing floating-point systems
(programming languages and libraries) which allow the
computer user to produce computation with guarantees.
These systems may be conveniently used as a component
in theorem proving. Following a brief description of
the methodology which underlies these systems, we
tabulate them, indicating some properties and noting
where they may be obtained for use. A brief appendix
supplies an introduction to the formalism of the
methodology.",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@InProceedings{Brackert:1989:DLM,
author = "R. H. {Brackert, Jr.} and M. D. Ercegovac and A. N.
{Willson, Jr.}",
title = "Design of an on-line multiply-add module for recursive
digital filters",
crossref = "Ercegovac:1989:PSC",
pages = "34--41",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Brackert.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Brightman:1989:ASF,
author = "T. Brightman",
title = "Advancing the Standard in Floating-Point Performance",
journal = j-HIGH-PERFORM-SYST,
volume = "10",
number = "11",
pages = "59, 62--64",
month = nov,
year = "1989",
CODEN = "HPSYEA",
ISSN = "0279-2834",
bibdate = "Wed Dec 13 18:25:43 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Cyrix FasMath 83D87 is a floating-point
coprocessor chip that combines Intel 80387 socket and
software compatibility with the high performance of
Weitek's industry-leading coprocessor. The chip is a
VLSI CMOS integrated circuit built initially using
1.2-micron double-layer-metal, single-layer-polysilicon
process technology. It was designed to minimize
complications in the design of high-performance desktop
and laptop computer systems.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Cyrix Corp., Richardson, TX, USA",
chemicalindex = "Si/int Si/el",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips)",
fjournal = "High performance systems",
keywords = "Cyrix FasMath 83D87; Desktop computer systems;
Double-layer-metal; Floating-point coprocessor chip;
Intel 80387; Laptop computer systems; Math coprocessor;
Si; Single-layer-polysilicon process technology; Socket
compatibility; Software compatibility; VLSI CMOS
integrated circuit",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Satellite computers; VLSI",
}
@Article{Buell:1989:MIA,
author = "D. Buell and R. Ward",
title = "A Multiprecise Integer Arithmetic Package",
journal = j-J-SUPERCOMPUTING,
volume = "3",
number = "??",
pages = "89--107",
month = "????",
year = "1989",
CODEN = "JOSUED",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Sun Sep 11 21:56:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@InProceedings{Carter:1989:CHH,
author = "T. M. Carter",
title = "{Cascade}: hardware for high\slash variable precision
arithmetic",
crossref = "Ercegovac:1989:PSC",
pages = "184--191",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Carter.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Chan:1989:ADC,
author = "P. K. Chan and M. D. F. Schlag",
title = "Analysis and design of {CMOS Manchester} adders with
variable carry-skip",
crossref = "Ercegovac:1989:PSC",
pages = "86--95",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Chan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Chen:1989:DRN,
author = "J. T. Chen and W. K. Jenkins",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Design of a residue number system digital correlator
for real-time processing in ultrasonic blood flow
measurements",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "208--211",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1989.100328",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design of a high-speed digital correlator for
implementing the real-time correlation function
required in an ultrasonic blood flowmeter is presented.
In order to achieve the necessary real-time processing
rates, a residue number system (RNS) \ldots{}",
}
@Article{Chen:1989:FCN,
author = "S. G. Chen and P. Y. Hsieh",
title = "Fast Computation of the {$N$ th} Root",
journal = j-COMPUT-MATH-APPL,
volume = "17",
number = "10",
pages = "1423--1427",
year = "1989",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Sep 15 18:41:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxmonth = "(none)",
}
@Article{Chen:1989:FCTa,
author = "S.-G. Chen and P. Y. Hsieh",
title = "Fast computation of the {$N$}-th root",
journal = j-COMPUT-MATH-APPL,
volume = "17",
number = "10",
pages = "1423--1427",
month = "????",
year = "1989",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(89)90024-2",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:01:11 MST 2017",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122189900242",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From the abstract: ``A new class of iterative methods
for computing a differentiable function is proposed,
which is based on Pad{\'e} approximation to Taylor's
series of the function. It leads to a faster algorithm
than Newton's method for $ x^{1 / N} $ and a different
interpretation of Newton's method.''",
}
@MastersThesis{Chinn:1989:DIA,
author = "Patty Chinn",
title = "The design, implementation, and applications of an
{ACT8837} floating point processor in an image
processing hardware subsystem",
type = "Thesis ({M.S.E.E.})",
school = "University of Washingto",
address = "Seattle, WA, USA",
pages = "vi + 45 + 1",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Image processing --- Digital techniques.",
}
@Book{Chow:1989:MXR,
editor = "Paul Chow",
title = "The {MIPS-X RISC} Microprocessor",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xxiv + 231",
year = "1989",
ISBN = "0-7923-9045-8",
ISBN-13 = "978-0-7923-9045-9",
LCCN = "QA76.8.M524 M57 1989",
bibdate = "Tue Dec 14 23:27:43 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
series = "The Kluwer international series in engineering and
computer science",
ZMnumber = "0706.68010",
acknowledgement = ack-nhfb,
keywords = "MIPS-X (microprocessor); VLSI, computer architecture,
and digital signal processing SECS 81",
}
@InProceedings{Clenshaw:1989:LIA,
author = "C. W. Clenshaw and F. W. J. Olver and P. R. Turner",
title = "Level-index arithmetic: An introductory survey",
crossref = "Turner:1989:NAP",
pages = "95--168",
year = "1989",
DOI = "https://doi.org/10.1007/BFb0085715",
bibdate = "Tue Oct 09 09:58:20 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Clenshaw:1989:RSU,
author = "C. W. Clenshaw and Peter R. Turner",
title = "Root squaring using level-index arithmetic",
journal = j-COMPUTING,
volume = "43",
number = "2",
pages = "171--185",
month = jun,
year = "1989",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02241860",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G99 (65H05)",
MRnumber = "1 034 362",
bibdate = "Sun Nov 12 06:18:24 2023",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
author-dates = "Charles William Clenshaw (15 March 1926--23 September
2004)",
fjournal = "Computing. Archives for Scientific Computing",
journal-URL = "http://link.springer.com/journal/607",
subject-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
xxtitle = "{Das Graeffe-Verfahren mit H{\"o}henindexarithmetik}",
}
@TechReport{Cody:1989:AXF,
author = "W. J. Cody",
title = "Algorithm {XXX}: Functions to Support the {IEEE}
Standard for Binary Floating-Point Arithmetic",
number = "MCS-P90-0789",
institution = "Mathematics and Computer Science Division, Argonne
National Laboratory",
address = "Argonne, IL, USA",
pages = "??",
month = jul,
year = "1989",
bibdate = "Thu Sep 01 10:38:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Dadda:1989:PC,
author = "Luigi Dadda",
title = "Polyphase convolvers",
crossref = "Ercegovac:1989:PSC",
pages = "78--85",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Dadda.pdf",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-9",
}
@Article{Dadda:1989:SIM,
author = "Luigi Dadda",
title = "On serial-input multipliers for two's complement
numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "9",
pages = "1341--1345",
month = sep,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.29478",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=29478",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
author-dates = "29 April 1923--26 October 2012",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Dally:1989:MOF,
author = "W. J. Dally",
title = "Micro-optimization of floating-point operations",
journal = j-COMP-ARCH-NEWS,
volume = "17",
number = "2",
pages = "283--289",
month = apr,
year = "1989",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:39 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{DAngelo:1989:DEA,
author = "S. D'Angelo and G. R. Sechi",
title = "Definition of elementary arithmetic operations by
using {ACM}",
journal = j-SIGMICRO,
volume = "20",
number = "3",
pages = "160--162",
month = aug,
year = "1989",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/75395.75414",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:41 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/75395.75414",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Misc{Darley:1989:FPI,
author = "Henry M. Darley and Michael C. Gill and Dale C. Earl
and Dinh T. Ngo and Paul C. Wang and Maria B. L. Hipona
and Jim Dodrill",
title = "Floating Point\slash Integer Processor with Divide and
Square Root Functions",
day = "31",
month = oct,
year = "1989",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 4,878,190 held by Texas Instruments.
Expired 2008-01-29.",
URL = "https://patentimages.storage.googleapis.com/bb/ca/c5/ed5ce0fc874200/US4878190.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{deLange:1989:DMA,
author = "A. A. J. de Lange and A. J. van der Hoeven and E. F.
Deprettere and P. Dewilde and J. Bu",
title = "The design of a 50 Mflop arithmetic chip for massively
parallel pipelined {DSP} algorithms: the floating point
pipeline {CORDIC} processor",
crossref = "IEE:1989:EEC",
pages = "410--414",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper describes a high performance VLSI CORDIC
arithmetic chip. It performs 15 10/sup 6/ rotations/sec
(50 Mflops) and can be applied as a processing element
in parallel/pipelined processor structures (systolic
and wavefront arrays) for real time/high speed signal
processing algorithms and matrix computation
applications. The authors present a novel optimized
(floating point) CORDIC algorithm, and architecture,
its performance and layout. Algorithm, architecture,
performance and layout are parametrized which allows
automatic generation of the chip layout for any
required chip performance, accuracy and dynamic range
of arithmetic operations.",
acknowledgement = ack-nhfb,
affiliation = "Delft University of Technol., Netherlands",
classification = "B1265F (Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); C5220 (Computer
architecture); C5230 (Digital arithmetic methods);
C5260 (Digital signal processing)",
keywords = "50 MFLOPS; Chip layout automatic generation; Dynamic
range; Floating point pipeline CORDIC processor; High
speed signal processing algorithm; Matrix computation
applications; Parallel structure; Pipelined processor
structure; Real time signal processing; Systolic
arrays; VLSI CORDIC arithmetic chip; Wavefront arrays",
numericalindex = "Computer speed 5.0E+07 FLOPS",
thesaurus = "Digital arithmetic; Digital signal processing chips;
Parallel architectures; Pipeline processing; VLSI",
}
@TechReport{Demmel:1989:FPE,
author = "J. Demmel",
title = "On Floating Point Errors in {Cholesky}",
type = "{LAPACK} Working Note",
number = "14",
institution = inst-UT-CS,
address = inst-UT-CS:adr,
month = oct,
year = "1989",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "UT-CS-89-87, October 1989.",
URL = "http://www.netlib.org/lapack/lawns/lawn14.ps;
http://www.netlib.org/lapack/lawnspdf/lawn14.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Dennis:1989:AAD,
author = "A. M. Dennis and C. B. Marshall and I. A. Burgess",
booktitle = "{IEE} Colloquium on Signal Processing Applications of
Finite Field Mathematics, 1 June 1989",
title = "Algorithm and architecture design for the
implementation of high order {FIR} filters using the
residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1/1--1/5",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266615",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The computational speed requirements of future signal
processing algorithms necessitate the use of special
purpose multiprocessor systems implemented using VLSI
technology. Finite field arithmetic and algorithms
offer an extra degree of freedom in \ldots{}",
}
@InProceedings{Dowling:1989:MVF,
author = "E. Dowling and M. Griffin and M. Lynch and F. Taylor",
title = "A multi-purpose {VLSI} floating-point array
processor",
crossref = "Chen:1989:TSA",
pages = "730--734 vol.2",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 3*3 single-instruction multiple-data (SIMD) array
processor for the IBM PC/AT is described. This array
processor is a modified bus-connected architecture
(MBCA) using TI's SN74ACT8847 64-bit VLSI
floating-point units for processing elements. The array
processor can operate four different modes of
operation: scalar, vector processor, full utilization,
and simulated systolic. In full utilization mode, this
array processor can sustain a 90-MFLOP computational
rate. System software is also discussed, and attention
is given to how it will be used with the SIGLAB
programming environment.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Florida University,
Gainesville, FL, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5430
(Microcomputers); C5440 (Multiprocessor systems and
techniques)",
keywords = "64 Bit; 90 MFLOPS; Full utilization mode; IBM PC/AT;
Modes of operation; Modified bus-connected
architecture; SIGLAB programming environment; SIMD;
Single-instruction multiple-data; SN74ACT8847; VLSI
floating-point array processor",
numericalindex = "Word length 6.4E+01 bit; Computer speed 9.0E+07
FLOPS",
thesaurus = "CMOS integrated circuits; IBM computers;
Microcomputers; Microprocessor chips; Parallel
architectures; Parallel processing; VLSI",
}
@TechReport{Dritz:1989:RPS,
author = "K. W. Dritz",
title = "Rationale for the Proposed Standard for a Generic
Package of Elementary Functions for {Ada}",
type = "Report",
number = "ANL-89/2 Rev. 1",
institution = "Argonne National Laboratory, Mathematics and Computer
Science Division",
address = "Argonne, IL, USA",
pages = "??",
month = oct,
year = "1989",
bibdate = "Thu Sep 01 12:08:24 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Dunham:1989:ICA,
author = "C. B. Dunham",
title = "Improvement of complex arithmetic by use of double
elements",
journal = j-SIGNUM,
volume = "24",
number = "4",
pages = "3--7",
month = oct,
year = "1989",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:18 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "algorithms; theory",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Matrix inversion \\ G.1.0
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic",
}
@Article{Dunham:1989:PAH,
author = "C. B. Dunham",
title = "Perturbation Analysis of {Horner}'s Method for Nice
Cases",
journal = j-SIGNUM,
volume = "24",
number = "2 and 3",
pages = "8--9",
month = apr # "/" # jul,
year = "1989",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Dunham:1989:S,
author = "C. B. Dunham",
title = "Summation",
journal = j-SIGNUM,
volume = "24",
number = "1",
pages = "14--15",
month = jan,
year = "1989",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Sep 13 08:58:48 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "accurate floating-point summation",
}
@InProceedings{Duprat:1989:SRA,
author = "Jean Duprat and Yves Herreros and Jean-Michel Muller",
title = "Some results about on-line computation of functions",
crossref = "Ercegovac:1989:PSC",
pages = "112--118",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Duprat.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Elleithy:1989:ARA,
author = "K. M. Elleithy and M. A. Bayoumi and K. P. Lee",
title = "{$ \theta (\log N) $} architectures for {RNS}
arithmetic decoding",
crossref = "Ercegovac:1989:PSC",
pages = "202--209",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Elleithy.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Ercegovac:1989:FRD,
author = "M. D. Ercegovac and T. Lang",
title = "On-the-fly rounding for division and square root",
crossref = "Ercegovac:1989:PSC",
pages = "169--173",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "In division and square root implementation based on
digit-recurrence algorithms, the result is obtained in
digit-serial form, from most significant digit to least
significant. To reduce the complexity of the
result-digit selection and to allow the \ldots{}",
}
@InProceedings{Ercegovac:1989:FSC,
author = "Milo{\v{s}} D. Ercegovac and Algirdas Avi{\v{z}}ienis
and Earl Swartzlander",
title = "Foreword: {9th Symposium on Computer Arithmetic
(ARITH9)}",
crossref = "Ercegovac:1989:PSC",
pages = "v--v",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Ercegovac:1989:IMC,
author = "M. D. Ercegovac and T. Lang",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Implementation of module combining multiplication,
division, and square root",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "150--153",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The implementation of a module that performs radix-$2$
multiplication, division, and square root is presented.
The module is compact because most of the components
are shared by all three operations, the complexity
being similar to that of a radix-$2$ \ldots{}",
}
@InProceedings{Ercegovac:1989:RSR,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "Radix-4 square root without initial {PLA}",
crossref = "Ercegovac:1989:PSC",
pages = "162--168",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_radix4.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "A systematic derivation of a radix-$4$ square root
algorithm using redundance in the partial residuals and
the result is presented. Unlike other similar schemes,
the algorithm does not use a table-lookup or
programmable logic array (PLA) for the \ldots{}",
}
@InProceedings{Fandrianto:1989:AHS,
author = "Jan Fandrianto",
title = "Algorithms for high-speed shared radix 8 division and
radix 8 square root",
crossref = "Ercegovac:1989:PSC",
pages = "68--75",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fandrianto.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-9",
summary = "An algorithm for performing radix-$8$ division and
square root in a shared hardware is described. To
achieve short iteration cycle time, it utilizes an
optimized `next quotient/root prediction PLA' generally
used in a radix-$4$ SRT division with minimal
\ldots{}",
}
@InBook{Feldstein:1989:NAP,
author = "Alan Feldstein and Richard H. Goodman",
title = "Some aspects of floating point computation",
crossref = "Turner:1989:NAP",
pages = "169--181",
year = "1989",
DOI = "https://doi.org/10.1007/BFb0085718",
MRclass = "65G05",
MRnumber = "022 264",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The floating point format is widely used in computing
because it allows for the representation of numbers
with greatly varying magnitude. This paper introduces
some general aspects of floating point representation
and includes a discussion of the implications of
balanced and unbalanced exponent ranges. A statistical
approach is presented in order to analyze the error in
floating point computations. The shortening of computer
words is discussed and is applied to study aspects of
the fraction error and the relative error.",
acknowledgement = ack-nhfb,
}
@InProceedings{Fowler:1989:AHS,
author = "D. L. Fowler and J. E. Smith",
title = "An accurate, high speed implementation of division by
reciprocal approximation",
crossref = "Ercegovac:1989:PSC",
bookpages = "xv + 247",
pages = "60--67",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fowler.pdf",
abstract = "While unlimited accuracy is theoretically possible, it
is very important to minimize the number of iteration
steps to improve performance and/or to reduce hardware
requirements. Consequently, there is an important
accuracy/speed/cost tradeoff in reciprocal
approximation implementations. A reciprocal
approximation implementation is discussed, with special
attention given to these tradeoffs. An interpolation
method is used to ensure that an initial approximation,
held in a ROM table, is as accurate as possible. A
method for implementing the iteration steps is given.
Special instructions are used so that maximum accuracy
can be carried between iteration operations. For 64-b
floating-point operands (53-b mantissa), a table lookup
and only two iterations are required, and high accuracy
is maintained. The rounded reciprocal rarely differs
from a true round-to-nearest value based on an infinite
precision result. When the results do differ (less than
once every 1000 calculations), the difference in
accuracy is shown to be less than 0.025 of a least
significant bit (LSB).",
acknowledgement = ack-nhfb,
affiliation = "Astronaut. Corp. of America, Madison, WI, USA",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
confdate = "6-8 Sept. 1989",
conflocation = "Santa Monica, CA, USA",
confsponsor = "IEEE; IFIP; University of California",
keywords = "ARITH-9; Division; Hardware requirements; High speed
implementation; Interpolation; Reciprocal
approximation; ROM table; Rounded reciprocal; Table
lookup",
thesaurus = "Digital arithmetic; Interpolation; Table lookup",
}
@Article{Fried:1989:ONC,
author = "S. Fried",
title = "Optimizing numeric coprocessing",
journal = j-BYTE,
volume = "14",
number = "11",
pages = "221--224",
month = "????",
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:47:21 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C5470
(Performance evaluation and testing)",
fjournal = "BYTE Magazine",
keywords = "Addition; Compiler optimizations; CPU code;
Floating-point operations; Multiplication; Numeric
coprocessing; Optimisation; Weitek 3167",
thesaurus = "Computer testing; Digital arithmetic; Performance
evaluation; Satellite computers",
}
@InProceedings{Fu:1989:PMI,
author = "B. Fu and A. Saini and P. P. Gelsinger",
title = "Performance and Microarchitecture of the i486{\TM}
Processor",
crossref = "IEEE:1989:PII",
pages = "182--187",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The i486 microprocessor includes a carefully tuned,
five-stage pipeline with an integrated 8-kB cache. A
variety of techniques previously associated only with
RISC (reduced-instruction-set computer) processors are
used to execute the average instruction in 1.8 clocks.
This represents a 2.5* reduction from its predecessor,
the 386 microprocessor. The pipeline and clock count
comparisons are described in detail. In addition, an
onchip floating-point unit is included which yields a
4* clock count reduction from the 387 numeric
coprocessor. The microarchitecture enhancements and
optimizations used to achieve this goal, most of which
are non-silicon-intensive, are discussed. All
instructions of the 386 microprocessor and the 387
numeric coprocessor are implemented in a completely
compatible fashion.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Intel Corp., Santa Clara, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips)",
confdate = "2-4 Oct. 1989",
conflocation = "Cambridge, MA, USA",
confsponsor = "IEEE",
keywords = "386 Microprocessor; 387 Numeric coprocessor; Clock
count; Five-stage pipeline; I486 processor; Intel;
Microarchitecture; Onchip floating-point unit;
Performance",
thesaurus = "Microprocessor chips",
}
@Article{Fujiyama:1989:FD,
author = "T. Fujiyama and Y. Shimazu and T. Tokuda and S.
Tsujimichi",
title = "A 24-bit floating-point {DSP}",
journal = "Mitsubishi Denki Giho",
volume = "63",
number = "12",
pages = "59--62",
month = "????",
year = "1989",
ISSN = "0369-2302",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors report on a new high-speed 24-bit floating
point DSP (digital signal processor) and its
development tools. The DSP features a short 75 ns
instruction cycle and low 750 mW power dissipation.
Other features include a large memory space, internal
RAM that can be configured as a cache, and speed
control via an internal clock prescaler that is
accessed by a special instruction. The DSP is suitable
for application in audio and image processing,
communications and numerical control.",
acknowledgement = ack-nhfb,
affiliation = "Mitsubishi Electr. Corp., Tokyo, Japan",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5260 (Digital signal
processing)",
keywords = "24 Bit; 24-Bit floating-point DSP; 75 Ns; 750 MW;
Audio processing; Communications; Development; Digital
signal processor; DSP chips; Image processing;
Instruction cycle; Internal clock prescaler; Memory;
Numerical control; Power dissipation; RAM; Speed
control",
language = "Japanese",
numericalindex = "Power 7.5E-01 W; Time 7.5E-08 s; Word length 2.4E+01
bit",
pubcountry = "Japan",
thesaurus = "Computerised signal processing; Digital signal
processing chips",
}
@InProceedings{Gamberger:1989:ISN,
author = "D. Gamberger",
title = "Incompletely specified numbers in the residue number
system-definition and applications",
crossref = "Ercegovac:1989:PSC",
pages = "210--215",
year = "1989",
DOI = "https://doi.org/10.1109/ARITH.1989.72828",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Gamberger.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9; residue arithmetic; residue number system",
summary = "Incompletely specified numbers in the residue number
system (RNS) are defined in order to make
multiplicative inverse computation of a number
regardless of its magnitude possible. Incompletely
specified RNS is the general RNS model in which
\ldots{}",
}
@InProceedings{Games:1989:AIQ,
author = "R. A. Games and D. Moulin and S. D. O'Neil and J. J.
Rushanan",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "Algebraic-integer quantization an residue number
system processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "948--951",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266586",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The algebraic-integer number representation, in which
the signal sample is represented by a set of (typically
four to eight) small integers, combines with residue
number system (RNS) processing to produce processors
composed of simple parallel \ldots{}",
}
@InProceedings{Goel:1989:RTA,
author = "B. D. Goel and M. M. Jamali and S. C. Kwatra",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Real time architecture for vector quantization in
residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "204--207",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1989.100327",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A fast and simplified systolic array architecture for
real-time implementation of vector quantization is
proposed. The proposed architecture uses the residue
number system (RNS) for arithmetic operations. The
arithmetic operations can be precomputed \ldots{}",
}
@TechReport{Goldberg:1989:FCS,
author = "David Goldberg",
title = "Floating-point and computer systems",
type = "Technical report",
number = "CSL-89-9",
institution = "Xerox Corp., Palo Alto Research Center",
address = "Palo Alto, CA, USA",
pages = "58",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "``August 1989.'' ``A version of this paper will appear
in Computing Surveys.''",
}
@InProceedings{Gonnella:1989:ACF,
author = "J. Gonnella and J. Periard",
booktitle = "{IEEE} Military Communications Conference, 1989.
{MILCOM '89}. Conference Record. Bridging the Gap.
Interoperability, Survivability, Security, 1989",
title = "The application of core functions to residue number
system signal processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "604--608",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MILCOM.1989.103996",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors briefly outline core-based residue number
system (RNS) processing. An RNS adaptive array
processor using Choleski decomposition and forward
elimination/back substitution is described as an
example. The RNS adaptive processor was \ldots{}",
}
@MastersThesis{Gordon:1989:RDF,
author = "Stephen E. Gordon",
title = "Recursive digital filtering with digital differential
analyzers and floating point incremental coders",
type = "Thesis ({M.S.E.C.E.})",
school = "University of Massachusetts at Amherst",
address = "Amherst, MA, USA",
pages = "xi + 123",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics)",
}
@Article{Grassmann:1989:PAR,
author = "Winfried K. Grassmann",
title = "A probabilistic analysis of rounding errors of
floating point numbers. {Eighteenth Manitoba Conference
on Numerical Mathematics and Computing (Winnipeg, MB,
1988)}",
journal = j-CONG-NUM,
volume = "68",
pages = "171--182",
year = "1989",
ISSN = "0384-9864",
MRclass = "65G05",
MRnumber = "90d:65089",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Congressus Numerantium",
}
@Article{Grehan:1989:FPR,
author = "R. Grehan",
title = "Floating-Point Revisited",
journal = j-BYTE,
volume = "14",
number = "4",
pages = "311--318",
month = apr,
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 1 10:15:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "BYTE Magazine",
}
@InProceedings{Griffin:1989:ESR,
author = "M. Griffin and M. Sousa and F. Taylor",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "Efficient scaling in the residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1075--1078",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266618",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A unified residue number system scaling technique that
allows the designer a great deal of flexibility in
choosing the scale factor is presented. The technique
is based on the L({\&}epsi;+{\delta})-CRT (Chinese
remainder theorem). By embedding \ldots{}",
}
@InProceedings{Griffin:1989:RNS,
author = "M. F. Griffin and F. J. Taylor",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "A residue number system reduced instruction set
computer ({RISC}) concept",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2581--2584",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266995",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A reduced-instruction-set RNS (residue number system)
processor is proposed for digital signal processing
algorithms. Issues leading toward a RNS RISC are
examined, namely suitable RNS algorithms. It is argued
that this is a reasonable next step in \ldots{}",
}
@Article{Groeger:1989:DRG,
author = "Detlef Gr{\"o}ger",
title = "{Zur Division mit Rest auf Gleitkommarechnern.
(German)} [On division with remainder on floating point
computers]",
journal = j-MATH-SEMESTERBER,
volume = "36",
number = "1",
pages = "106--111",
year = "1989",
ISSN = "0720-728x (print), 1432-1815 (electronic)",
ISSN-L = "0720-728X",
MRclass = "65G99 (11Y16)",
MRnumber = "90g:65070",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Semesterberichte",
language = "German",
}
@InProceedings{Guyot:1989:JLM,
author = "Alain Guyot and Bertrand Hochet and Jean-Michel
Muller",
title = "{JANUS}, an on-line multiplier\slash divider for
manipulating large numbers",
crossref = "Ercegovac:1989:PSC",
pages = "106--111",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Guyot.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Hoffmann:1989:PAR,
author = "C. M. Hoffmann",
title = "The Problems of Accuracy and Robustness in Geometric
Computation",
journal = j-COMPUTER,
volume = "22",
number = "3",
institution = "Purdue U",
pages = "31--39, 41",
month = mar,
year = "1989",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Sep 14 07:29:35 MDT 1996",
bibsource = "Graphics/rosenfeld/1989.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Misc/IMMD_IV.bib",
acknowledgement = ack-nhfb,
affiliation = "Computer Science Dept., Purdue University, West
Lafayette, IN, USA",
classification = "C1160 (Combinatorial mathematics); C4190 (Other
numerical methods); C4290 (Other computer theory)",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "Accuracy; Degeneracies avoidance; Degenerate
positions; Floating-point computation; Geometric
computation; Geometric operations; Interacting numeric
data; Interacting symbolic data; Limited-precision
rational arithmetic; Linear elements; Model, IMAGE PART
MEASUREMENT; Numerical precision; Perturbation-free
methods; Purely symbolic representations;
Representation; Robustness; Symbolic data alteration",
thesaurus = "Computational geometry",
}
@InProceedings{Hohne:1989:PHP,
author = "R. A. Hohne and R. Siferd",
booktitle = "Proceedings of the {IEEE 1989} National Aerospace and
Electronics Conference, {NAECON 1989}, 22--26 May
1989",
title = "A programmable high performance processor using the
residue number system and {CMOS} {VLSI} technology",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "41--43",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/NAECON.1989.40188",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors describe the general architecture of RNS
(residue number system) processors, the VLSI
implementation of the associated hardware, and finally,
an RNS processor designed by the authors. The 2-{\mu}m
CMOS implementation of the processor \ldots{}",
}
@Article{Hollingsworth:1989:CPI,
author = "Walter Hollingsworth and Howard Sachs and Alan Jay
Smith",
title = "The {Clipper\TM} Processor: Instruction Set
Architecture and Implementation",
journal = j-CACM,
volume = "32",
number = "2",
pages = "200--219",
month = feb,
year = "1989",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Mon Sep 26 13:49:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "design; measurement; performance",
review = "ACM CR 9002-0119",
subject = "C.5.3 Computer Systems Organization, COMPUTER SYSTEM
IMPLEMENTATION, Microcomputers, CLIPPER \\ C.1.1
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Single Data Stream Architectures,
Single-instruction-stream, single-data-stream
processors (SISD) \\ C.4 Computer Systems Organization,
PERFORMANCE OF SYSTEMS \\ C.0 Computer Systems
Organization, GENERAL, Instruction set design",
}
@Article{Hoshi:1989:RPV,
author = "T. Hoshi and K. Koya and A. Kuwata and T. Uno and M.
Kashimura and T. Kuwata and T. Nishigouri and K. Obuchi
and N. Morikawa",
title = "{RISC} processor {V}/sub {R}/3000",
journal = j-NEC-TECH-J,
volume = "42",
number = "11",
pages = "34--38",
month = dec,
year = "1989",
CODEN = "NECGEZ",
ISSN = "0285-4139",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Outlines NEC's first RISC type microprocessor, the
V/sub R/3000 and its developmental environment. V/sub
R/3000 is fully compatible with the R3000 developed by
MIPS Computer Systems, USA. It offers one of the
fastest microprocessor systems in the world, together
with a floating point processor V/sub R/3010 that is
fully compatible with the R3010.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture)",
fjournal = "NEC Technical Journal = NEC giho",
keywords = "Floating point processor; NEC; RISC type
microprocessor; V/sub R/3000; V/sub R/3010",
language = "Japanese",
pubcountry = "Japan",
thesaurus = "Microprocessor chips; Reduced instruction set
computing",
}
@InProceedings{Hu:1989:ARM,
author = "Y. H. Hu and S. Naganathan",
title = "Angle Recoding Method for Efficient Implementation of
the {CORDIC} Algorithm",
crossref = "IEEE:1989:IISa",
pages = "175--178 (Vol. 1)",
year = "1989",
bibdate = "Thu Sep 01 11:41:20 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Huck:1989:ACA,
author = "Jerome C. Huck and Michael J. Flynn",
title = "Analyzing Computer Architectures",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 188",
year = "1989",
ISBN = "0-8186-8857-2, 0-8186-4857-0 (microfiche),
0-8186-8857-2 (casebound)",
ISBN-13 = "978-0-8186-8857-7, 978-0-8186-4857-1 (microfiche),
978-0-8186-8857-7 (casebound)",
LCCN = "QA76.9.A73 H83 1989",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society order number 857. IEEE catalog
number EH0285-7. SAN 264-620X.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Husby:1989:FPE,
author = "D. Husby and R. Atac and A. Cook and J. Deppe and M.
Fischler and I. Gaines and T. Nash and T. Pham and T.
Zmuda and E. Eichten and G. M. Hockney and P. B.
Mackenzie and H. B. Thacker and D. Toussaint",
title = "A floating point engine for lattice gauge
calculations",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "36",
number = "1",
pages = "734--737",
month = feb,
year = "1989",
CODEN = "IRNSAM",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
LCCN = "TK6540 .I573 Jan-June 1988",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0105825",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
summary = "The Fermilab Advanced Computer Program Multiple Array
Processor System, which dedicated to solving problems
in the field of quantum chromodynamics, is discussed. A
typical system with 256 processors, 2.5 Gb of memory,
and 64 Gb of online tape storage \ldots{}",
}
@InProceedings{Hwang:1989:OAU,
author = "Kai Hwang and D. K. Panda",
title = "Optical arithmetic using high-radix symbolic
substitution rules",
crossref = "Ercegovac:1989:PSC",
pages = "226--232",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Hwang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Book{IEC:1989:IBF,
author = "{IEC}",
title = "{IEC 60559 (1989-01)}: Binary floating-point
arithmetic for microprocessor systems",
publisher = pub-IEC,
address = pub-IEC:adr,
pages = "45",
year = "1989",
bibdate = "Mon Apr 24 06:17:57 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This Standard was formerly known as IEEE 754.",
price = "US\$86.00",
URL = "http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=019113",
acknowledgement = ack-nhfb,
remark = "Working Draft, 1997-11-21, WG14/N794 J11/97-158 of the
ISO C9X Standard references ``Binary floating-point
arithmetic for microprocessor systems, second edition
(IEC 559:1993)''. However, I cannot locate that edition
at the IEC Web site. The 1997 renumbering of IEC
Standards by the addition of 60000 indicates that this
document should now be IED 60559:1993, but only the
1989 version is listed in the IEC catalog.",
}
@MastersThesis{Intwala:1989:BFP,
author = "Jaiprakash D. Intwala",
title = "{8085A} based floating point arithmetic system",
type = "Thesis ({M.S.})",
school = "California State University, Northridge",
address = "Northridge, CA, USA",
pages = "viii + 81",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jain:1989:SLU,
author = "V. K. Jain and D. L. Landia and C. E. Alvarez",
title = "Systolic {L-U} Decomposition Array With a New
Reciprocal Cell",
crossref = "IEEE:1989:PII",
pages = "460--465",
year = "1989",
bibdate = "Sun Sep 11 20:59:19 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Jamieson:1989:SNR,
author = "M. J. Jamieson",
title = "Short Notes: Rapidly Converging Iterative Formulae for
Finding Square Roots and their Computational
Efficiencies",
journal = j-COMP-J,
volume = "32",
number = "1",
pages = "93--94",
month = feb,
year = "1989",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/32.1.93",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65H05",
MRnumber = "89k:65063",
bibdate = "Tue Dec 4 14:48:26 MST 2012",
bibsource = "Compendex database;
http://comjnl.oxfordjournals.org/content/32/1.toc;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This work generalizes the Pythagorean sums in
\cite{Dubrulle:1983:CNM,Moler:1983:RSR}.",
URL = "http://comjnl.oxfordjournals.org/content/32/1/93.full.pdf+html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/93.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/94.tif",
abstract = "A derivation is given of rapidly converging iterative
formulae for finding square roots which include, as
special cases, some recently published examples. Their
computational efficiencies are investigated for
sequential and parallel implementation. It is concluded
that the most efficient method is equivalent to
sequential application of the Newton Raphson formula; a
simple modification is suggested which brings the
advantage of root bracketing at little extra
computational cost.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Glasgow University,
UK",
affiliationaddress = "Glasgow, Scotl",
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
classification = "723; 921; B0290F (Interpolation and function
approximation); C4130 (Interpolation and function
approximation)",
corpsource = "Department of Computer Science, Glasgow University,
UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "computational; Computational efficiencies;
Computational Efficiency; Computer Metatheory;
Convergence; convergence of numerical methods;
Converging iterative formulae; converging iterative
formulae; efficiencies; formula; function
approximation; Iterative Methods; iterative methods;
Newton Raphson; Newton Raphson formula, Mathematical
Techniques; Parallel implementation; parallel
implementation; Square Roots; Square roots; square
roots",
thesaurus = "Convergence of numerical methods; Function
approximation; Iterative methods",
treatment = "P Practical",
}
@InProceedings{Jenkins:1989:AFP,
author = "W. K. Jenkins and J. K. Yun",
booktitle = "European Conference on Circuit Theory and Design, 5--8
Sep 1989",
title = "Analysis of fixed point roundoff effects in transform
domain {LMS} adaptive filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "228--232",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "One of the disadvantages of the well known LMS FIR
adaptive digital filter is that, for a colored noise
input signals, the filter tends to converge slowly. One
way to improve the convergence rate is to prefilter the
input signal with an \ldots{}",
}
@Article{Johnson:1989:IMA,
author = "K. R. Johnson",
title = "An Iterative Method for Approximating Square Roots",
journal = j-MATH-MAG,
volume = "62",
number = "4",
pages = "253--259",
month = oct,
year = "1989",
CODEN = "MAMGA8",
ISSN = "0025-570X",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@InProceedings{Johnstone:1989:HRF,
author = "Paul Johnstone and Frederick E. Petry",
title = "Higher Radix Floating Point Representations",
crossref = "Ercegovac:1989:PSC",
pages = "128--135",
year = "1989",
DOI = "https://doi.org/10.1109/ARITH.1989.72818",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Johnstone.pdf",
abstract = "An examination is made of the feasibility of
higher-radix floating-point representations and, in
particular, decimal-based representations. Traditional
analyses of such representations have assumed the
format of a floating-point datum to be roughly
identical to that of traditional binary floating-point
encodings such as the IEEE P754 task group standard
representations. The authors relax this restriction and
propose a method of encoding higher-radix
floating-point data with range, precision, and storage
requirements comparable to those exhibited by
traditional binary representations. The results of
other authors are extended to accommodate the proposed
representation. A decimal alternative to traditional
binary representations is proposed, and the behavior of
such a system is contrasted with that of a comparable
binary system.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Telerate Syst. Inc., New Orleans, LA, USA",
classification = "C5230 (Digital arithmetic methods)",
confdate = "6-8 Sept. 1989",
conflocation = "Santa Monica, CA, USA",
confsponsor = "IEEE; IFIP; University of California",
keywords = "ARITH-9; Binary representations; decimal
floating-point arithmetic; Decimal-based
representations; encodings; higher radix floating point
representation; IEEE P754 task group standard
representations",
thesaurus = "Digital arithmetic",
}
@Article{Jones:1989:EDC,
author = "Tom Jones",
key = "C.5.1 Convex C2",
title = "Engineering design of the {Convex C2}",
journal = j-COMPUTER,
volume = "22",
number = "1",
pages = "36--44",
month = jan,
year = "1989",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Convex Computer Corp., Richardson, TX",
bibno = "58556",
catcode = "C.5.1; C.5.1; B.4.3; B.7.1; C.1.2",
content = "The Convex C220 and C240 supercomputers are 64-bit
multiprocessors that are tightly coupled through a
shared main memory. Each processor contains an
integrated vector processor. A microcoded instruction
set controls all processor features, including the
vector processor. The system is implemented in 100K
emitter-coupled logic with a cycle time of 40
nanoseconds. The C220 contains two processors, an I/O
system, and memory. The C240 contains four processors,
a larger I/O system, and memory. This paper describes
the design process of this computer family and tries to
illuminate the methods and rationale behind
project-related decisions.\par
The original C1 system was designed in early 1983 using
transistor-transistor logic and complementary
metal-oxide semiconductor (CMOS) technologies. The bulk
of the machine consisted of medium- and
small-scale-integration logic, and the vector
functional units were built with 8,000-gate CMOS
arrays. The original C1 (later dubbed the C1-XL) had no
scalar floating-point hardware but sent the operands to
the vector processor. In 1984, floating-point
add-and-multiply functional units were designed in
20,000-gate CMOS arrays, and the C1 was upgraded to the
C1-XP. That machine, with minor changes, became the
C120 when the C2 was announced.\par
This paper is unusually frank for a retrospective
design trade-off study. The author describes",
CRclass = "C.5.1 Large and Medium (``Mainframe'') Computers;
C.5.1 Super (very large) computers; C.5.1 Large and
Medium (``Mainframe'') Computers; C.5.1 Convex C2;
B.4.3 Interconnections (subsystems); B.7.1 Types and
Design Styles; B.7.1 Gate arrays; C.1.2 Multiple Data
Stream Architectures (Multiprocessors); C.1.2
Interconnection architectures",
CRnumber = "8909-0654",
descriptor = "Computer Systems Organization, COMPUTER SYSTEM
IMPLEMENTATION, Large and Medium (``Mainframe'')
Computers, Super (very large) computers; Computer
Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
Large and Medium (``Mainframe'') Computers, Convex C2;
Hardware, INPUT/OUTPUT AND DATA COMMUNICATIONS,
Interconnections (subsystems); Hardware, INTEGRATED
CIRCUITS, Types and Design Styles, Gate arrays;
Computer Systems Organization, PROCESSOR ARCHITECTURES,
Multiple Data Stream Architectures (Multiprocessors),
Interconnection architectures",
fjournal = "Computer",
genterm = "DESIGN; MANAGEMENT; PERFORMANCE; ECONOMICS",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabbrev = "Computer",
reviewer = "P. C. Patton",
subject = "C. Computer Systems Organization; C.5 COMPUTER SYSTEM
IMPLEMENTATION; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; B. Hardware; B.4
INPUT/OUTPUT AND DATA COMMUNICATIONS; B. Hardware; B.7
INTEGRATED CIRCUITS; C. Computer Systems Organization;
C.1 PROCESSOR ARCHITECTURES",
}
@Book{Jorke:1989:AAM,
author = "G{\"u}nter Jorke and Bernhard Lampe and Norbert
Wengel",
title = "{Arithmetische Algorithmen der Mikrorechentechnik}
\toenglish {Arithmetic Algorithms of Microcomputing}
\endtoenglish",
publisher = pub-VEB-VERLAG-TECHNIK,
address = pub-VEB-VERLAG-TECHNIK:adr,
pages = "323",
year = "1989",
ISBN = "3-341-00515-3",
ISBN-13 = "978-3-341-00515-6",
LCCN = "????",
bibdate = "Fri Sep 16 16:30:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxnote = "fpbiblio.txt 1.8 has order Lampe, Jorke, Wengel, but
RLIN catalog has Jorke, Lampe, Wengel.",
}
@Article{Joslin:1989:EPN,
author = "David A. Joslin",
title = "Extended {Pascal} --- numerical features",
journal = j-SIGPLAN,
volume = "24",
number = "6",
pages = "77--80",
month = jun,
year = "1989",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:40 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Extended Pascal standard, drafted by the Joint
X3J9\slash IEEE-770 Pascal Standards Committee (JPC) in
conjunction with the ISO Pascal working group
(ISO\slash IEC JTC1\slash SC22\slash WG2), completed
its second public comment period at the end of 1988.
The comments received have been considered by JPC and
the ISO group, and the standard is now almost certainly
in its final form. Earlier papers by this author
described the main features of the standard by means of
illustrative examples. This is now the first in an
occasional series of articles, by this author and other
JPC \& WG2 members, describing in more detail various
extensions which have been made to the Pascal language;
rationale is given where appropriate. This paper
describes the predefined type COMPLEX, the range and
precision of type REAL, and the EXPONENTIATION
operators.",
acknowledgement = ack-nhfb,
affiliationaddress = "Middlesbrough, Engl",
classification = "723; 902",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "Complex Arithmetic; Computer Operating
Systems--Program Compilers; Computer Programming
Languages; design; Extended Pascal; languages; pascal;
standardization; Standards",
subject = "D.2.1 Software, SOFTWARE ENGINEERING,
Requirements/Specifications \\ D.3.2 Software,
PROGRAMMING LANGUAGES, Language Classifications,
Pascal",
}
@TechReport{Jouppi:1989:UVSa,
author = "Norman Paul Jouppi and Jonathan Bertoni and David
Wayne Wall",
title = "A unified vector\slash scalar floating-point
architecture",
institution = "Digital Western Research Laboratory",
address = "Palo Alto, CA, USA",
pages = "v + 23",
month = jul,
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "WRL research report; 89/8",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Floating-point arithmetic.;
MultiTitan (Computer); Scalar field theory.;
Supercomputers.; Vector processing (Computer science)",
}
@Article{Jouppi:1989:UVSb,
author = "N. P. Jouppi and J. Bertoni and D. W. Wall",
title = "A unified vector\slash scalar floating-point
architecture",
journal = j-COMP-ARCH-NEWS,
volume = "17",
number = "2",
pages = "134--143",
month = apr,
year = "1989",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:39 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Misc{Kahan:1989:PCA,
author = "W. Kahan",
title = "Paradoxes in Concepts of Accuracy",
howpublished = "Lecture notes from Joint Seminar on Issues and
Directions in Scientific Computation, Berkeley",
year = "1989",
bibdate = "Sat Sep 17 18:40:08 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kak:1989:BAS,
author = "S. C. Kak and A. O. Barbir",
booktitle = "Proceedings of the Twenty-First Southeastern Symposium
on System Theory, 26--28 March 1989",
title = "The {Brahmagupta} algorithm for square rooting",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "456--459",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An algorithm for square root evaluation is introduced.
Novel features of the algorithm include suitability for
parallel processing and multi-initial guesses of the
root. An extension of the algorithm to the nth rooting
is provided. A VLSI \ldots{}",
}
@Article{Kaneko:1989:VRM,
author = "K. Kaneko and T. Okamoto and M. Nakajima and Y.
Nakakura and S. Gokita and J. Nishikawa and Y. Tanikawa
and H. Kadota",
title = "A {VLSI RISC} with {20-MFLOPS} peak, 64-bit
floating-point unit",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1331--1340",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A microprocessor designed as a processing element of a
scientific parallel computer system is described. This
chip consists of a simple integer processor core and
dedicated floating-point hardware and executes 64-bit
floating-point addition, subtraction \ldots{}",
}
@Article{Kaneko:1989:VRP,
author = "K. Kaneko and T. Okamoto and M. Nakajima and Y.
Nakakura and S. Gokita and J. Nishikawa and Y. Tanikawa
and H. Kadota",
title = "A {VLSI RISC} with 20-{MFLOPS} peak, 64-bit
floating-point unit",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1331--1340",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A microprocessor designed as a processing element of a
scientific parallel computer system is described. This
chip consists of a simple integer processor core and
dedicated floating-point hardware and executes 64-bit
floating-point addition, subtraction, and
multiplication at a rate of every 50 ns and division
every 350 ns. The processor, which employs RISC
architecture and Harvard-style bus organization,
executes most of the 47 instructions in one 50-ns
cycle. The chip is fabricated in 1.2- mu m n-well CMOS
technology, containing 440K transistors in a
14.4*13.5-mm/sup 2/ die. The authors provide an
overview of the processor, especially focusing on the
functions for a parallel system, floating-point
hardware, and the new divide algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Semicond. Research Center, Matsushita Electr. Ind.
Co., Ltd., Osaka, Japan",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "1.2 Micron; 20 MFLOPS; 350 Ns; 50 Ns; 64 Bit;
Addition; Dedicated floating-point hardware; Division;
Floating-point unit; Harvard-style bus organization;
Integer processor core; Microprocessor; Multiplication;
N-well CMOS technology; RISC architecture; Scientific
parallel computer system; Subtraction; VLSI",
numericalindex = "Computer speed 2.0E+07 FLOPS; Word length 6.4E+01
bit; Time 5.0E-08 s; Time 3.5E-07 s; Size 1.2E-06 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Parallel processing; Reduced
instruction set computing; VLSI",
}
@InProceedings{Kawarai:1989:OPM,
author = "S. Kawarai and T. Murakami",
booktitle = "Acoustics, Speech, and Signal Processing, 1989.
{ICASSP-89., 1989} International Conference on. 23--26
May 1989",
title = "An optimization procedure to minimize the roundoff
noise in cascade floating-point digital filters",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "884--887",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors study the roundoff errors in
floating-point arithmetic and present an optimization
procedure for cascade floating-point digital filters.
Applying the isosceles trapezoidal distribution to the
error analysis of cascade floating-point \ldots{}",
}
@Article{Kawasaki:1989:FPV,
author = "S. Kawasaki and M. Watabe and S. Morinaga",
title = "A floating-point {VLSI} chip for the {TRON}
architecture: an architecture for reliable numerical
programming",
journal = j-IEEE-MICRO,
volume = "9",
number = "3",
pages = "26--44",
month = may # "\slash " # jun,
year = "1989",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.31476",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "A description is given of the Gmicro/FPU
(floating-point unit), a chip that provides
floating-point instructions for both the Gmicro/200 and
the Gmicro/300 microprocessors. The VLSI
central-processing-unit architecture, for which it is
designed, \ldots{}",
}
@InProceedings{Koc:1989:SAI,
author = "{\c{C}}. K. Ko{\c{c}} and P. R. Cappello",
title = "Systolic arrays for integer {Chinese} remaindering",
crossref = "Ercegovac:1989:PSC",
pages = "216--223",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Koc.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Kohn:1989:ISM,
author = "L. Kohn and N. Margulis",
title = "The {i860} 64-bit supercomputing microprocessor",
crossref = "ACM:1989:PSN",
pages = "450--456",
year = "1989",
bibdate = "Wed Apr 15 19:32:44 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture)",
corpsource = "Intel Corp., Santa Clara, CA, USA",
keywords = "64 bit; caches; floating point unit; i860 64-bit
supercomputing microprocessor; Intel; memory
management; microprocessor chips; multiplier units;
parallel architectures; parallelism; pipelined adder;
pipelining; reduced instruction set computing; RISC
based microprocessor; three-dimensional graphics",
sponsororg = "ACM; IEEE",
treatment = "P Practical",
}
@InProceedings{Kohn:1989:TM,
author = "L. Kohn and S.-W. Fu",
title = "A 1,000,000 Transistor Microprocessor",
crossref = "Wuorinen:1989:DTP",
pages = "54--55, 290",
year = "1989",
bibdate = "Wed Sep 7 22:32:01 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Komori:1989:FPE,
author = "S. Komori and H. Takata and T. Tamura and F. Asai and
T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
and H. Nishikawa and H. Terada",
title = "A 40-{MFLOPS} 32-bit floating-point processor with
elastic pipeline scheme",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1341--1347",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present a 40-MFLOPS 32-bit floating-point
processor (FP) which is a component chip for a
data-driven single-board processor. The FP is the first
practical LSI chip which has introduced the elastic
pipeline scheme. All parts in the FP are autonomously
controlled by self-timed circuits, and no system clock
is needed for processing. The elastic pipeline scheme
provides data buffering capability and stabilization of
circuit operation at the same time. Pipelining has been
extensively utilized so that high throughput over
40-MFLOPS can be achieved. An automatic power
conservation technique, called `latch mode control', is
also described.",
acknowledgement = ack-nhfb,
affiliation = "LSI Res. and Dev. Lab., Misubishi Electr. Corp.,
Hyogo, Japan",
classification = "B1265F (Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); C5130
(Microprocessor chips)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "32 Bit; 40 MFLOPS; Automatic power conservation;
Component chip; Data buffering capability; Data-driven
single-board processor; Elastic pipeline scheme;
Floating-point processor; Latch mode control; LSI chip;
Microprocessor; Self-timed circuits; Stabilization",
numericalindex = "Computer speed 4.0E+07 FLOPS; Word length 3.2E+01
bit",
thesaurus = "Large scale integration; Microprocessor chips;
Pipeline processing",
}
@InProceedings{Komori:1989:MBFa,
author = "S. Komori and H. Takata and T. Tamura and F. Asai and
T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
and H. Nishikawa and H. Terada",
title = "A 40 {MFLOPS} 32-bit Floating-Point Processor",
crossref = "Wuorinen:1989:DTP",
pages = "46--47, 286",
year = "1989",
bibdate = "Wed Sep 7 22:32:01 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Komori:1989:MBFb,
author = "S. Komori and H. Takata and T. Tamura and F. Asai and
T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
and H. Nishikawa and H. Terada",
title = "A {40-MFLOPS} 32-bit floating-point processor with
elastic pipeline scheme",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1341--1347",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "The authors present a 40-MFLOPS 32-bit floating-point
processor (FP) which is a component chip for a
data-driven single-board processor. The FP is the first
practical LSI chip which has introduced the elastic
pipeline scheme. All parts in the FP are \ldots{}",
}
@InProceedings{Komori:1989:MFP,
author = "S. Komori and H. Takata and T. Tamura and F. Asai and
T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
and H. Nishikawa and H. Terada",
title = "A 40 {MFLOPS} 32-bit floating-point processor",
crossref = "Wuorinen:1989:DTP",
pages = "46--47, 286",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 40 MFLOPS (million floating-point operations per
second), 32-bit floating-point processor (FP) for a
single-board data-driven processor is developed using a
pipeline configuration called the elastic pipeline
structure. Because there is no need to add controls for
pipeline flushing by virtue of the data-driven
processing principle, it is possible to employ
extensively subdivided pipeline stages. The elastic
mode of data transfer between pipeline stages and
distributed execution controls along the pipeline
result in minimum deterioration of the inherent logic
switching speed. The structure of the FP is shown
together with details of the ALU (arithmetic logic
unit) block. The fabrication process and chip
specifications are summarized.",
acknowledgement = ack-nhfb,
affiliation = "Mitsubishi Electr. Corp., Hyogo, Japan",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
keywords = "32 Bit; 40 MFLOPS; ALU; Chip specifications; CMOS
chip; Data transfer; Distributed execution controls;
Elastic pipeline structure; Fabrication process;
Floating-point processor; Logic switching speed;
Pipeline configuration; Single-board data-driven
processor; Subdivided pipeline stages",
numericalindex = "Computer speed 4.0E+07 FLOPS; Word length 3.2E+01
bit",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
@InProceedings{Kornerup:1989:ERB,
author = "Peter Kornerup and David W. Matula",
title = "Exploiting Redundancy in Bit-Pipelined Rational
Arithmetic",
crossref = "Ercegovac:1989:PSC",
pages = "119--126",
year = "1989",
DOI = "https://doi.org/10.1109/ARITH.1989.72817",
bibdate = "Wed Nov 14 18:29:43 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Kornerup.pdf",
abstract = "The authors develop and analyze a redundant
continued-fraction representation of the rationals in
the implementation of an arithmetic unit for computing
the sum, difference, product, quotient, and other
useful functions of two rational operands. Their
representation of operands and results allows the
computations of the unit to be performed in a signed
bit-serial, online fashion. Several such units can then
be interconnected for the computation of more
complicated expressions in a pipelined manner.
Redundancy is used to help achieve a small bounded
online delay and uniform throughput",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Krishna:1989:NAC,
author = "H. Krishna and Kuo Yu Lin",
booktitle = "Twenty-Third Asilomar Conference on Signals, Systems
and Computers, 1989",
title = "New algorithms for correcting errors in redundant
residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "653--657",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266586",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InProceedings{Krishnan:1989:CBN,
author = "R. Krishnan",
booktitle = "Twenty-Third Asilomar Conference on Signals, Systems
and Computers, 1989",
title = "Conventional binary number system ({BNS}) versus
residue number system ({RNS}) digital signal processing
architecture suitable for complex digital filtering",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "873--877",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266586",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InProceedings{Krishnan:1989:ESA,
author = "R. Krishnan",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "An efficient systolic array {VLSI} cell architecture
for the implementation of transversal filter based on
the quadratic residue number systems",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2585--2588",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266996",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The author presents efficient direct and indirect
implementations of transversal filter architectures
using the quadratic residue number system (QRNS). In
the case of the direct transversal filter, a systolic
array architecture has been developed \ldots{}",
}
@Misc{Kulisch:1989:CGS,
author = "Ulrich Kulisch and Reinhard Kirchner",
title = "Circuitry for generating sums, especially scalar
products",
howpublished = "US Patent 4866653",
day = "12",
month = sep,
year = "1989",
bibdate = "Mon Dec 29 16:20:01 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/4866653/fulltext.html",
abstract = "Circuitry for the summation, especially for
generation, of scalar products, to which one summand in
floating-point representation is conveyed per machine
cycle (ZT), in which, after conversion into fixed point
representation, it is received in a summing unit with
an accumulator (AS1,-AS4) comprising the whole exponent
range. The accumulator is subdivided into row sections,
which are longer than the mantissa of the summands.
Partial exponents (EPK1,-EPK4) generated in an exponent
analyzer (EXA) control the mantissa positioner (PM) or
are allocated to the mantissas and delivered
continuously and cycle-wise to transfer registers
(RE1,-RE4; RVS1,-RVS4; RNS1, RNS4), controlling
summation row-wise. The carriers are allocated to the
accumulator sections and intermediately stored in carry
memory sections (CS1,-CS4) and are not added digit
positionwise to the contents of each adjacent memory
section until the sum is output, further carries being
continuously processed. Afterwards the rounded result
mantissa (ME) is generated in transfer registers (RA1,
RA2, RPR) arranged downstream and the result exponent
(EE) is generated in an exponent generator (EXG).",
acknowledgement = ack-nhfb,
}
@InProceedings{Lai:1989:HNS,
author = "F. S. Lai and C. E. Wu",
title = "A hybrid number system multiplier for graphics and
complex arithmetic applications",
crossref = "IEEE:1989:ISV",
pages = "352--356",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A hybrid multiplier design which supports 32-bit
floating-point, 24-bit fixed-point and 32-bit
logarithmic number systems is described. Except for
additions and subtractions, floating-point operations
such as multiplication, division, and square root are
all performed in the logarithmic number system domain.
A modified squaring approach is adopted for fixed-point
multiplications with little extra hardware. The
performance of this multiplier is shown to be superior
to that of conventional binary multipliers for most
graphics and digital signal processing applications,
and the size of the multiplier is comparable to that of
conventional multipliers in terms of silicon area.",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res Center, Yorktown-Heights, NY,
USA",
classification = "B1265B (Logic circuits); C5230 (Digital arithmetic
methods); C5260 (Digital signal processing); C5540
(Terminals and graphic displays)",
keywords = "Complex arithmetic; Digital signal processing;
Division; Fixed-point multiplications; Floating-point
operations; Graphics; Hybrid number system multiplier;
Logarithmic number; Modified squaring approach;
Multiplication; Square root",
thesaurus = "Computer graphic equipment; Computerised signal
processing; Digital arithmetic; Multiplying circuits",
}
@InProceedings{Langston:1989:DBT,
author = "J. L. Langston and K. Hinman",
booktitle = "{IEEE} Military Communications Conference, 1989.
{MILCOM '89}. Conference Record. Bridging the Gap.
Interoperability, Survivability, Security, 1989",
title = "Digital beamforming techniques and processors based on
quadratic residue number system techniques",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "609--614",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MILCOM.1989.103997",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A very-high-performance digital beamforming processor
has been implemented using ASICs (application-specific
integrated circuits) fabricated in readily available
commercial CMOS process technology by using QRNS
(quadratic residue number system) \ldots{}",
}
@TechReport{Lee:1989:FIR,
author = "Jeong-A Lee and Tomas Lang",
title = "Floating-point implementation of redundant {CORDIC}
for {QR} decomposition",
type = "Technical report",
number = "CSD-890044",
institution = "Computer Science Dept., University of California",
address = "Los Angeles, CA, USA",
pages = "15 + 8",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Decomposition method.; Matrices.",
remark = "``July 1989.'' Supported by the National Science
Foundation.",
}
@Article{Lee:1989:MGR,
author = "Corinna Lee",
title = "Multistep Gradual Rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "4",
pages = "595--600",
month = apr,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.21152",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://dlib.computer.org/tc/books/tc1989/pdf/t0593.pdf;
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=21152;
http://www.computer.org/tc/tc1989/t0595abs.htm",
abstract = "A value $V$ is to be rounded to an arbitrary precision
resulting in the value $ V' $. Conventional rounding
technique uses one step to accomplish this.
Alternatively, {\em multistep rounding\/} uses several
steps to round the value $V$ to successively shorter
precisions with the final rounding step producing the
desired value $ V' $. This alternate rounding method is
one way to implement, with the minimum of hardware, the
denormalization process that the IEEE Floating-Point
Standard 754 requires when underflow occurs. There are
certain cases for which multistep rounding produces a
different result than single-step rounding. To prevent
such a {\em step error}, the author introduces a
rounding procedure called {\em gradual rounding} that
is very similar to conventional rounding with the
addition of two tag bits associated with each
floating-point register.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "double rounding",
}
@Article{Lee:1989:QCC,
author = "Jon Lee",
title = "A quirk of the {CRAY CFT77} compiler: {IF} (logical)
in lieu of {IF} (arithmetic)",
journal = j-J-SUPERCOMPUTING,
volume = "3",
number = "4",
pages = "351--355",
month = dec,
year = "1989",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/BF00128170",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Wed Jul 6 11:13:01 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=3&issue=4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=3&issue=4&spage=351",
acknowledgement = ack-nhfb,
affiliation = "Flight Dynamics Lab., Wright-Patterson AFB, OH, USA",
classification = "C5440 (Multiprocessor systems and techniques); C6110
(Systems analysis and programming); C6150C (Compilers,
interpreters and other processors); C7440 (Civil and
mechanical engineering)",
corpsource = "Flight Dynamics Lab., Wright-Patterson AFB, OH, USA",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
keywords = "CFT77 compiler; CIVIC; computational fluid dynamics
code; conditional IF exit; DO-loops; homogeneous
turbulence; optimised code; parallel programming;
program compilers; vectorization",
treatment = "X Experimental",
}
@Book{Levy:1989:CPA,
author = "Henry M. Levy and Richard H. {Eckhouse, Jr.}",
title = "Computer programming and architecture: the {VAX}",
publisher = pub-DP,
address = pub-DP:adr,
edition = "Second",
pages = "xix + 444",
year = "1989",
ISBN = "1-55558-015-7",
ISBN-13 = "978-1-55558-015-5",
LCCN = "QA76.8.V32 L48 1989",
bibdate = "Wed Sep 14 22:51:31 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lewis:1989:ADB,
author = "D. M. Lewis and L. K. Yu",
title = "Algorithm design for a 30-bit integrated logarithmic
processor",
crossref = "Ercegovac:1989:PSC",
pages = "192--199",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lewis.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Lin:1989:LCA,
author = "H. Lin and H. J. Sips",
title = "On-line {CORDIC} algorithms",
crossref = "Ercegovac:1989:PSC",
pages = "26--33",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lin.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Lo:1989:CED,
author = "J.-C. Lo and S. Thanawastien and T. R. N. Rao",
title = "Concurrent error detection in arithmetic and logical
operations using {Berger} codes",
crossref = "Ercegovac:1989:PSC",
pages = "233--240",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lo.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Lu:1989:VMI,
author = "P. Y. Lu and K. Dawallu",
title = "A {VLSI} Module for {IEEE} Floating-Point
Multiplication\slash Division\slash Square Root",
crossref = "IEEE:1989:PII",
bookpages = "xvii + 587",
pages = "366--368",
year = "1989",
bibdate = "Wed Nov 06 12:08:38 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The major objective of this VLSI module design is to
determine how to modify a fast floating-point
multiplier so that it can perform division and square
root in accordance with IEEE standards. This has been
achieved by applying the Newton-Ralphson iteration only
on the mantissa and adjusting the iterated result by a
rounding algorithm. Using 1.0- mu m CMOS standard cell
technology, the total area of this module is
approximately 7.0 mm*6.5 mm, which is just 25\% larger
than the floating-point multiplier. The module can
compute multiplication, division, and square root in 3,
31, and 43 cycles, respectively. The cycle time, under
nominal conditions, is expected to be 20 ns. (2
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "LSI Logic Corp., Menlo Park, CA, USA",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C4130 (Interpolation and function
approximation); C5230 (Digital arithmetic methods)",
keywords = "1 Micron; 20 Ns; 7 To 6.5 mm; CMOS standard cell
technology; Cycle time; Fast floating-point multiplier;
Floating point division; Floating point square root;
IEEE standards; Iterated result; Mantissa; Multiplier
modification; Newton-Ralphson iteration; Rounding
algorithm; VLSI module design",
numericalindex = "Time 2.0E-08 s; Size 1.0E-06 m; Size 6.5E-03 to
7.0E-03 m",
thesaurus = "Cellular arrays; CMOS integrated circuits; Digital
arithmetic; Dividing circuits; Iterative methods;
Modules; Multiplying circuits; VLSI",
}
@InProceedings{Malarkey:1989:RNS,
author = "E. C. Malarkey and G. E. Marx and J. D. Fogarty and D.
Mergerian and H. K. Hahn and J. C. Bradley and P. R.
Beaudet and R. Fenton",
booktitle = "{IEEE} Military Communications Conference, 1989.
{MILCOM '89}. Conference Record. Bridging the Gap.
Interoperability, Survivability, Security, 1989",
title = "Residue-number-system-based optical adaptive
processor",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "620--623",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MILCOM.1989.103999",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "An optical adaptive processor with 4 degrees of
freedom is under development. This processor is based
upon the use of optical lookup tables and operates
within the residue number system to provide adaptive
tap weights for nulling applications. The \ldots{}",
}
@InProceedings{Mansour:1989:CAS,
author = "Y. Mansour and B. Schieber and P. Tiwari",
booktitle = "30th Annual Symposium on Foundations of Computer
Science, 1989",
title = "The complexity of approximating the square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "325--330",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors prove upper and lower bounds for
approximately computing the square root using a given
set of operations. The bounds are extended to hold for
approximating the kth root, for any fixed k. Several
tools from approximation \ldots{}",
}
@Article{Marshall:1989:TUT,
author = "Mark Marshall",
title = "Techniques for user testing of the 68882",
journal = j-MICROPROC-MICROSYS,
volume = "13",
number = "6",
pages = "382--386",
month = jul # "\slash " # aug,
year = "1989",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Sat Nov 9 08:26:18 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "NCR Corp., Wichita, KS",
bibno = "72545",
catcode = "B.5.3; C.5.3; B.5.1",
content = "This short, clearly written paper describes how NCR
Corporation developed a series of programs to test the
Motorola 68882 floating-point coprocessor for
Motorola's 68020 and 68030 microprocessors. Integrated
circuits are tested for two reasons: to ensure that a
properly working unit meets its specifications, and to
ensure that a particular unit works properly. As
Marshall points out, manufacturers cannot always be
relied upon to perform either of these tests perfectly.
The programs described in this paper have been used
both to monitor the quality of incoming parts and to
verify that device mask or specification changes do not
effect the part's usability for NCR's
purposes.\par
This paper describes the methods by which NCR's
2700-instruction, 550,000-clock cycle test program was
developed and how it works. Since the internal workings
of the 68882 are not visible to the user, NCR adopted
the functional testing approach. Of particular interest
is NCR's sequential approach to the testing proper,
which assumes that ``no element is functional unless
previously tested.'' While the specifics of each step
vary from one microprocessor to another, the principles
still apply.\par
This is not a research paper. It does not disclose
startling new results or advance the frontiers of human
knowledge. It does show how state-of-the-art
engineering practice can achieve desirable \ldots{}",
CRclass = "B.5.3 Reliability and Testing; B.5.3 Test generation;
C.5.3 Microcomputers; B.5.1 Design",
CRnumber = "9006-0473",
descriptor = "Hardware, REGISTER-TRANSFER-LEVEL IMPLEMENTATION,
Reliability and Testing, Test generation; Computer
Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers; Hardware, REGISTER-TRANSFER-LEVEL
IMPLEMENTATION, Design",
fjournal = "Microprocessors and Microsystems",
genterm = "ALGORITHMS; DESIGN; VERIFICATION",
guideno = "1989-09211",
journalabbrev = "Microprocess. Microsyst.",
keywords = "floating-point testing",
reviewer = "E. Mallach",
subject = "B. Hardware; B.5 REGISTER-TRANSFER-LEVEL
IMPLEMENTATION; C. Computer Systems Organization; C.5
COMPUTER SYSTEM IMPLEMENTATION; B. Hardware; B.5
REGISTER-TRANSFER-LEVEL IMPLEMENTATION",
}
@Article{Mastrovito:1989:VDM,
author = "E. D. Mastrovito",
title = "{VLSI} designs for multiplication over finite fields
{$ \mathrm {GF}(2^m) $}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "357",
pages = "397--309",
year = "1989",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Jun 24 21:09:00 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Maytal:1989:DCG,
author = "B. Maytal and S. Iacobovici and D. B. Alpert and D.
Biran and J. Levy and S. Y. Tov",
title = "Design considerations for a general-purpose
microprocessor",
journal = j-COMPUTER,
volume = "22",
number = "1",
pages = "66--76",
month = jan,
year = "1989",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Sat Sep 14 07:29:35 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Misc/IMMD_IV.bib",
acknowledgement = ack-nhfb,
affiliation = "Nat. Semicond., Santa Clara, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture)",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "32 Bit; Clock frequency; Data-flow monitoring
mechanisms; Floating-point operations; General-purpose
microprocessor; Instruction-flow; Market requirements;
Memory hierarchy; Memory reference transactions;
Microarchitecture; Multiprocessing support; NS 32532;
On-chip caches; Packaging technologies; Pipeline;
System interface; Target applications; VLSI",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Computer architecture; Microcomputers; Microprocessor
chips",
}
@InProceedings{Milenkovic:1989:DPG,
author = "V. Milenkovic",
booktitle = "30th Annual Symposium on Foundations of Computer
Science, 1989",
title = "Double precision geometry: a general technique for
calculating line and segment intersections using
rounded arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "500--505",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "For the first time it is shown how to reduce the cost
of performing specific geometric constructions by using
rounded arithmetic instead of exact arithmetic. By
exploiting a property of floating-point arithmetic
called monotonicity, a technique \ldots{}",
}
@Article{Milutinovic:1989:MSD,
author = "V. Milutinovic and M. Bettinger and W. Helbig",
title = "Multiplier\slash shifter design tradeoffs in a 32-bit
microprocessor",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "6",
pages = "874--880",
month = jun,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.24298",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=24298",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Molnar:1989:MBF,
author = "K. Molnar and C.-Y. Ho and D. Staver and B. Davis and
R. Jerdonek",
title = "A 40 {MHz} 64-Bit Floating-Point Co-Processor",
crossref = "Wuorinen:1989:DTP",
pages = "48--49, 287",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An arithmetic coprocessor capable of executing 64-bit
double-precision floating-point, 32-bit
single-precision floating-point, and 32-bit integer
instructions has been integrated onto a 1.0-cm*1.1-cm
chip in a 1.2- mu m, single-poly, double-metal bulk
CMOS process. The chip contains 17000 transistors and
includes a register file, two accumulators, and
separate interface, multiplication, and addition
subprocessors. The coprocessor which is the arithmetic
unit for a multichip microprocessor system, is packaged
in a 132-pin leadless ceramic chip carrier. The
coprocessor can be issued a new instruction each 25-ns
clock cycle, and 64-bit double-precision arithmetic
with full IEEE rounding is executed at a peak rate of
26.7 MFLOPs (million floating-point operations per
second). The waveforms of a store instruction operating
at 40 MHz are shown.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Gen. Electr. Corp. Res. and Dev. Center, Schenectady,
NY, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
keywords = "1.2 Micron; 26.7 MFLOPS; 32-Bit integer instructions;
40 MHz; 64 Bit; Accumulators; Addition subprocessors;
Arithmetic coprocessor; Double-metal bulk CMOS process;
Double-precision floating-point; Floating point
coprocessor; Interface subprocessor; Leadless ceramic
chip carrier; Multichip microprocessor system;
Multiplication subprocessor; Peak rate; Register file;
Single-precision floating-point; Store instruction;
Waveforms",
numericalindex = "Frequency 4.0E+07 Hz; Word length 6.4E+01 bit; Size
1.2E-06 m; Computer speed 2.67E+07 FLOPS",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips",
}
@InProceedings{Montuschi:1989:EIH,
author = "Paolo Montuschi and Luigi Cinimera",
title = "On the efficient implementation of higher radix square
root algorithms",
crossref = "Ercegovac:1989:PSC",
pages = "154--161",
year = "1989",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
summary = "Square root nonrestoring algorithms operating with a
radix higher than two (but power of 2) are discussed.
Formulas are derived delimiting the feasibility space
of the class of algorithms considered as a function of
the different parameters. This \ldots{}",
}
@Book{Moshier:1989:MPM,
author = "Stephen L. B. Moshier",
title = "Methods and Programs for Mathematical Functions",
publisher = pub-ELLIS-HORWOOD,
address = pub-ELLIS-HORWOOD:adr,
pages = "vii + 415",
year = "1989",
ISBN = "0-7458-0289-3",
ISBN-13 = "978-0-7458-0289-3",
LCCN = "QA331 .M84 1989",
MRclass = "*65D20, 26-04, 33-04, 65-02, 65C99",
bibdate = "Thu Sep 01 10:33:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\pounds 48.00",
URL = "http://www.moshier.net/;
http://www.netlib.org/cephes",
ZMnumber = "0701.65011",
acknowledgement = ack-nj,
shorttableofcontents = "Preface / vii \\
1: Floating Point Arithmetic / 1 \\
2: Approximation Methods / 75 \\
3: Software Notes / 129 \\
4: Elementary Functions / 143 \\
5: Probability Distributions and Related Functions /
201 6: Bessel Functions / 263 \\
7: Other Special Functions / 333 \\
Bibliography / 411 \\
Index / 413",
tableofcontents = "Preface / vii \\
1: Floating Point Arithmetic / 1 \\
1.1 Numeric Data Structures / 1 \\
1.2 Rounding / 5 \\
1.3 Addition and Subtraction / 6 \\
1.4 Multiplication / 7 \\
1.4.1 Long Multiplication in Binary Radix / 8 \\
1.4.2 Multiplication in Word Integer Radix / 8 \\
1.4.3 Fast Multiplication / 9 \\
1.5 Division / 10 \\
1.5.1 Long Division / 10 \\
1.5.2 Division by Taylor Series / 11 \\
1.5.3 Newton--Raphson Division / 11 \\
1.6 C Language / 12 \\
1.7 An Extended Double Arithmetic: ieee.c / 13 \\
1.8 Binary - Decimal Conversion / 46 \\
1.8.1 etoasc.c / 47 \\
1.8.2 asctoe.c / 54 \\
1.9 Analysis of Error / 58 \\
1.9.1 Roundoff and Cancellation / 58 \\
1.9.2 Error Propagation / 60 \\
1.9.3 Error as a Random Variable / 61 \\
1.9.4 Order of Summation / 62 \\
1.10 Complex Arithmetic / 62 \\
1.10.1 cmplx.c / 64 \\
1.10.2 Absolute Value: cabs.c / 67 \\
1.11 Rational Arithmetic / 69 \\
1.11.1 euclid.c / 70 \\
2: Approximation Methods / 75 \\
2.1 Power Series / 75 \\
2.2 Chebyshev Expansions / 76 \\
2.2.1 chbevl.c / 79 \\
2.3 Pad{\'e} Approximations / 80 \\
2.4 Least Maximum Approximations / 82 \\
2.4.1 Best Polynomial Approximations / 82 \\
2.4.2 Best Rational Approximations / 85 \\
2.4.3 Special Rational Forms / 87 \\
2.5 A Program to Find Best Approximations: remes.c / 88
\\
2.6 Forms of Approximation / 111 \\
2.7 Asymptotic Expansions / 113 \\
2.8 Continued Fractions / 114 \\
2.8.1 Continued Fractions from Recurrences / 115 \\
2.8.2 Recurrences from Differential Equations / 116 \\
2.8.3 Computing Continued Fractions / 117 \\
2.9 Polynomials / 117 \\
2.9.1 polevl.c / 118 \\
2.10 Newton--Raphson Iterations / 119 \\
2.10.1 Division / 120 \\
2.10.2 Exponent Separation / 121 \\
2.10.3 Square Root / 122 \\
2.10.4 sqrt.c / 123 \\
2.10.5 Longhand Square Root / 124 \\
2.10.6 esqrt.c / 124 \\
2.10.7 Cube Root / 126 \\
2.10.8 cbrt.c / 127 \\
3: Software Notes / 129 \\
3.1 Design Strategy / 129 \\
3.2 Testing / 131 \\
3.3 System Utilities / 132 \\
3.3.1 mconf.h / 132 \\
3.3.2 mtherr.c / 134 \\
3.3.3 const.c / 136 \\
3.4 Arithmetic Utilities / 137 \\
3.4.1 efloor.c / 138 \\
3.4.2 efrexp.c / 140 \\
3.4.3 eldexp.c / 140 \\
4: Elementary Functions / 143 \\
4.1 $e^x$ / 143 \\
4.1.1 exp.c / 145 \\
4.2 $\ln x$ / 147 \\
4.2.1 log.c / 149 \\
4.3 Argument Transformation for Circular Functions /
152 \\
4.4 Sine and cosine / 153 \\
4.4.1 sin.c / 154 \\
4.4.2 cos.c / 156 \\
4.5 Tangent and Cotangent / 157 \\
4.5.1 tan.c / 158 \\
4.6 Complex Circular Functions / 161 \\
4.7 $\sin^{-1} x $ / 162 \\
4.7.1 asin.c / 163 \\
4.8 $\cos^{-1} x $ / 165 \\
4.8.1 acos.c / 165 \\
4.9 $\tan^{-1} x$ / 166 \\
4.9.1 atan.c / 168 \\
4.9.2 atan2.c / 169 \\
4.10 Complex Inverse Circular Functions / 170 \\
4.11 $\sinh x$ / 170 \\
4.11.1 sinh.c / 171 \\
4.12 $\cosh x$ / 172 \\
4.12.1 cosh.c / 173 \\
4.13 $\tanh x$ / 173 \\
4.13.1 tanh.c / 174 \\
4.14 $\sinh^{-1} x $ / 175 \\
4.14.1 asinh.c / 176 \\
4.15 $\cosh^{-1} x $ / 177 \\
4.15.1 acosh.c / 178 \\
4.16 $\tanh^{-1} x$ / 179 \\
4.16.1 atanh.c / 180 \\
4.17 Power Function / 181 \\
4.17.1 Real Exponent / 182 \\
4.17.2 pow.c / 182 \\
4.17.3 Integer Exponent / 189 \\
4.17.4 powi.c / 190 \\
4.18 Testing / 192 \\
4.19 Single Precision Polynomial Approximations / 193
\\
4.19.1 $\cos x$ / 193 \\
4.19.2 $\cosh^{-1} x $ / 193 \\
4.19.3 $\exp x$ / 196 \\
4.19.4 $\ln x$ / 196 \\
4.19.5 $\sin x$ / 197 \\
4.19.6 $\sin^{-1} x $ / 197 \\
4.19.7 Square Root / 197 \\
4.19.8 $\tan x$ / 198 \\
4.19.9 $\tan^{-1} x$ / 198 \\
4.19.10 $\tanh x$ / 199 \\
4.19.11 $tanh^{-1} x$ / 199 \\
5: Probability Distributions and Related Functions /
201 \\
5.1 $n!$ / 202 \\
5.1.1 fac.c / 204 \\
5.2 $\Gamma(x)$ / 206 \\
5.2.1 gamma.c / 210 \\
5.2.2 lgam.c / 214 \\
5.3 Incomplete Gamma Integral / 217 \\
5.3.1 igamc.c / 218 \\
5.3.2 igam.c / 220 \\
5.3.3 Functional Inverse of Incomplete Gamma Integral /
221 \\
5.3.4 igami.c / 221 \\
5.4 Gamma Distribution / 222 \\
5.4.1 gdtr c / 222 \\
5.4.2 gdtrc.c / 223 \\
5.5 $\chi^2$ Distribution / 223 \\
5.5.1 chdtrc.c / 224 \\
5.5.2 chdtr.c / 224 \\
5.5.3 chdtrl.c / 224 \\
5.6 Poisson Distribution / 225 \\
5.6.1 pdtrc.c / 225 \\
5.6.2 pdtr.c / 226 \\
5.6.3 pdtri.c / 226 \\
5.7 Beta Function / 227 \\
5.7.1 beta.c / 227 \\
5.8 Incomplete Beta Integral / 229 \\
5.8.1 ibet.c / 231 \\
5.8.2 Functional Inverse of Incomplete Beta Integral /
238 \\
5.9 Beta Distribution / 241 \\
5.9.1 btdtr.c / 241 \\
5.10 Binomial Distribution / 241 \\
5.10.1 bdtrc.c / 242 \\
5.10.2 bdtr.c / 243 \\
5.10.3 bdtri.c / 244 \\
5.11 Negative Binomial Distribution / 244 \\
5.11.1 nbdtr.c / 245 \\
5.11.2 nbdtrc.c / 245 \\
5.12 F Distribution / 246 \\
5.12.1 fdtrc.c / 247 \\
5.12.2 fdtr.c / 247 \\
5.12.3 fdtrci.c / 248 \\
5.13 Student's $t$ distribution / 249 \\
5.13.1 stdtr.c / 250 \\
5.14 Gaussian Distribution / 252 \\
5.14.1 ndtr.c / 254 \\
5.14.2 erfc.c / 256 \\
5.14.3 erf.c / 257 \\
5.14.4 Functional Inverse of Gaussian Distribution /
258 \\
5.14.5 ndtri.c / 259 \\
6: Bessel Functions / 263 \\
6.1 $J_0(x)$ / 263 \\
6.1.1 jO.c / 265 \\
6.2 $Y_0(x)$ / 268 \\
6.2.1 yO.c / 269 \\
6.3 Modulus and Phase / 270 \\
6.4 $J_1(x)$ / 271 \\
6.4.1 jl.c / 272 \\
6.5 $Y_1(x)$ / 275 \\
6.5.1 yl.c / 275 \\
6.6 $J_n(x)$ / 276 \\
6.1 $I_0(x)$ / 277 \\
6.7.1 i0.c / 278 \\
6.8 $I_1(x)$ / 281 \\
6.8.1 i1.c / 283 \\
6.9 $I_\nu(x)$ / 285 \\
6.9.1 iv.c / 286 \\
6.10 $K_0(x)$ / 287 \\
6.10.1 kO.c / 287 \\
6.11 $K_1(x)$ / 291 \\
6.11.1 kl.c / 291 \\
6.12 $K_n(x)$ / 294 \\
6.12.1 kn.c / 295 \\
6.13 $J_\nu(x)$ / 299 \\
6.13.1 jv.c / 301 \\
6.14 Airy Functions / 315 \\
6.14.1 airy.c / 322 \\
6.15 $Y_n(x)$ / 328 \\
6.15.1 yn.c / 329 \\
6.16 Testing / 330 \\
7: Other Special Functions / 333 \\
7.1 Hypergeometric Functions / 333 \\
7.1.1 $_2F_1$ / 334 \\
7.1.2 hyp2fi.c / 335 \\
7.1.3 $_1F_1$ / 341 \\
7.1.4 hyplfi.c / 342 \\
7.1.5 $_2F_0$ / 346 \\
7.1.6 hyp2ffi.c / 346 \\
7.2 Struve Functions / 348 \\
7.2.1 hypl1f2.c / 348 \\
7.2.2 hyp3f0.c / 349 \\
7.2.3 yv.c / 351 \\
7.2.4 struve.c / 351 \\
7.3 $\psi(x)$ / 352 \\
7.3.1 psi.c / 354 \\
7.4 Exponential Integral / 355 \\
7.4.1 en.c / 356 \\
7.5 Sine and Cosine Integrals / 360 \\
7.5.1 sici.c / 362 \\
7.5.2 Hyperbolic Sine and Cosine Integrals / 367 \\
7.5.3 shichi.c / 370 \\
7.6 Dilogarithm / 374 \\
7.6.1 spence.c / 375 \\
7.7 Dawson's Integral / 377 \\
7.7.1 dawsn.c / 378 \\
7.8 Fresnel Integrals / 381 \\
7.8.1 fresnl.c / 383 \\
7.9 Elliptic Functions / 387 \\
7.9.1 $K(m)$ / 387 \\
7.9.2 ellpk.c / 388 \\
7.9.3 $F(\phi|m)$ / 389 \\
7.9.4 ellik.c / 390 \\
7.9.5 $E(m)$ / 392 \\
7.9.6 ellpe.c / 392 \\
7.9.7 $E(\phi|m)$ / 393 \\
7.9.8 ellie.c / 394 \\
7.9.9 Jacobian Elliptic Functions / 396 \\
7.9.10 ellpj.c / 398 \\
7.10 Zeta Functions / 400 \\
7.10.1 hurwiz.c / 400 \\
7.10.2 Riemann Zeta Function / 402 \\
7.10.3 zetac.c / 405 \\
Bibliography / 411 \\
Index / 413",
}
@Manual{Motorola:1989:DIF,
title = "{DSP96002}: {IEEE} floating-point dual-port processor:
user's manual",
organization = "{Motorola, Inc.}",
address = "Phoeniz, AZ, USA",
pages = "various",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Signal processing.",
remark = "Cover title. Spine title: DSP96002 user's manual.
``DSP96002UM/AD''--Cover.",
}
@Book{Motorola:1989:FPC,
author = "{Motorola, Inc.}",
title = "{MC68881}\slash {MC68882} Floating-Point Coprocessor
User's Manual",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Second",
pages = "various",
year = "1989",
ISBN = "0-13-567009-8",
ISBN-13 = "978-0-13-567009-5",
LCCN = "????",
bibdate = "Fri Dec 08 13:02:55 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Motorola:1989:MFP,
author = "{Motorola, Inc.Staff}",
title = "{MC} 68881 and 68882 Floating-Point Coprocessor User's
Manual",
publisher = pub-PH,
address = pub-PH:adr,
edition = "0002",
month = aug,
year = "1989",
ISBN = "0-13-567009-8",
ISBN-13 = "978-0-13-567009-5",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$27.00",
acknowledgement = ack-nhfb,
keywords = "MICROPROCESSORS; TECHNOLOGY --- COMPUTERS AND COMPUTER
TECHNOLOGY",
language = "eng",
}
@Book{Motorola:1989:MMF,
author = "{Motorola, Inc.}",
title = "{MC68881\slash MC68882} floating-point coprocessor
user's manual",
publisher = pub-PH,
address = pub-PH:adr,
edition = "Second",
pages = "various",
year = "1989",
ISBN = "0-13-567009-8 (pbk.)",
ISBN-13 = "978-0-13-567009-5 (pbk.)",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors ---
Handbooks, manuals, etc.; Motorola 68881
(Microprocessor); Motorola 68882 (Microprocessor)",
remark = "Spine title: MC68881/882 user's manual. ``MC68881UM/AD
REV 2''--Cover.",
}
@Book{Motorola:1989:MRM,
author = "Motorola",
title = "{MC88100} {RISC} Microprocessor User's Manual",
publisher = pub-MOTOROLA,
address = pub-MOTOROLA:adr,
edition = "Second",
year = "1989",
ISBN = "0-13-567090-X",
ISBN-13 = "978-0-13-567090-3",
LCCN = "QA76.8.M75 M3 1990",
bibdate = "Wed Jul 6 14:23:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Overview \\
Features \\
Introduction \\
Execution Units and Register File \\
Execution Model \\
Programming Model \\
Processor States \\
Reset State \\
Flow-Control Instructions \\
Register with 9-Bit Vector Table Index \\
Instruction Categories \\
Programming Tips \\
Instruction Set \\
Opcode Summary \\
Signal Description \\
Data Processor Bus Signals \\
Exceptions \\
Exception Overview \\
Exception Vectors and Vector Base Register (VBR) \\
Exception Priority \\
Exception Processing \\
Instruction Unit Exceptions \\
Integer Overflow Exception (Vector Offset \$48) \\
Memory Access Exceptions \\
FPU Exception Processing \\
FPU Exception Processing Registers \\
Timing Factors \\
Execution Example \\
Instruction Set Timing Summary \\
Applications Information \\
Cache Memory Management Units \\
Power and Ground Considerations \\
Master/Checker Operations \\
Synchronization Operations \\
Electrical Characteristics",
}
@Article{Mulcahy:1989:FPR,
author = "L. P. Mulcahy",
title = "On fixed-point roundoff error analysis",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "37",
number = "10",
pages = "1623",
month = oct,
year = "1989",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The author points out the existence of work published
by the author (US Department of Commerce, Tech. Rep.
AD-A086826, 57 pp., Apr. 1980) prior to the appearance
of the paper by Barnes et al. (ibid., vol.ASSP-33,
p.595-606, June 1985) covering the same \ldots{}",
}
@InProceedings{Nakayama:1989:BMF,
author = "T. Nakayama and S. Kojima and H. Harigai and H.
Igarashi and K. Tamada and T. Toba",
title = "An 80 b, 6.7 {MFLOPS} floating-point processor with
vector\slash matrix instructions",
crossref = "Wuorinen:1989:DTP",
pages = "52--53, 289",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A description is given of an 80-b CMOS VLSI
floating-point processor (FPP) in 1.2- mu m
double-metal layer CMOS which contains 433000
transistors on an 11.6-mm*14.9-mm die. It operates at
20 MHz, dissipates 1.5 W, and is assembled in a 68-lead
pin-grid-array package. The FPP is designed as a
coprocessor for 32-b microprocessors. It implements
data formats, arithmetic rounding modes, and exception
types which are defined by the IEEE 754 standard. The
chip can handle single (32 b), double (64 b), and
double-extended (80 b) floating-point data formats. The
complex-instruction-set-computer- (CISC-) like
78-instruction set includes 22 mathematical functions
such as sin, cos, arctan, exp, and log, and 24
vector/matrix operations such as add, multiply, and
inner product. The features and performance of the
device are summarized.",
acknowledgement = ack-nhfb,
affiliation = "NEC, Kawasaki, Japan",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
keywords = "1.2 Micron; 1.5 W; 20 MHz; 6.7 MFLOPS; 80 Bit;
Arithmetic rounding modes; CMOS VLSI floating-point
processor; Complex instruction set computer; Data
formats; Double-metal layer CMOS; Exception types;
Mathematical functions; Pin-grid-array package; Power
dissipation; Vector/matrix instructions",
numericalindex = "Word length 8.0E+01 bit; Computer speed 6.7E+06
FLOPS; Size 1.2E-06 m; Frequency 2.0E+07 Hz; Power
1.5E+00 W",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; VLSI",
}
@Article{Nakayama:1989:FCV,
author = "T. Nakayama and H. Harigai and S. Kojima and H. Kaneko
and H. Igarashi and T. Toba and Y. Yamagami and Y.
Yano",
title = "A 6.7-{MFLOPS} floating-point coprocessor with
vector\slash matrix instructions",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1324--1330",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An 80-bit floating-point coprocessor which implements
24 vector/matrix instructions and 22 mathematical
functions is described. This processor can execute
floating-point addition/rounding and pipelined
multiplication concurrently, under the control of
horizontal-type microinstructions. The SRT division
method and CORDIC trigonometrical algorithm are used
for a favorable cost/performance implementation. The
performance of 6.7 MFLOPS in the vector-matrix
multiplication at 20 MHz has been attained by the use
of parallel operations. The vector/matrix instruction
is about three times faster than conventional add and
multiply instructions. The chip has been fabricated in
1.2- mu m double-metal layer CMOS process containing
433000 transistors on a 11.6*14.9-mm/sup 2/ die size.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "1.2 Micron; 20 MHz; 6.7 MFLOPS; 80 Bit; CMOS process;
CORDIC trigonometrical algorithm; Double-metal layer;
Floating-point coprocessor; Horizontal-type
microinstructions; Mathematical functions; Parallel
operations; Pipelined multiplication; SRT division
method; Vector/matrix instructions; VLSI
microprocessor",
numericalindex = "Word length 8.0E+01 bit; Size 1.2E-06 m; Computer
speed 6.7E+06 FLOPS; Frequency 2.0E+07 Hz",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Instruction sets; Microprocessor chips; Parallel
architectures; Pipeline processing; Satellite
computers; VLSI",
}
@InProceedings{Nakayama:1989:MFPa,
author = "T. Nakayama and S. Kojima and H. Harigai and H.
Igarashi and K. Tamada and T. Toba",
title = "An 80b, 6.7 {MFLOPS} Floating-Point Processor with
{Vector/Matrix} Instructions",
crossref = "Wuorinen:1989:DTP",
pages = "52--53, 289",
year = "1989",
bibdate = "Fri Dec 08 13:04:53 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Nakayama:1989:MFPb,
author = "T. Nakayama and H. Harigai and S. Kojima and H. Kaneko
and H. Igarashi and T. Toba and Y. Yamagami and Y.
Yano",
title = "A 6.7-{MFLOPS} Floating-Point Coprocessor with
Vector\slash Matrix Instructions",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "5",
pages = "1324--1330",
month = oct,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "An 80-bit floating-point coprocessor which implements
24 vector/matrix instructions and 22 mathematical
functions is described. This processor can execute
floating-point addition/rounding and pipelined
multiplication concurrently, under the control
\ldots{}",
}
@InProceedings{Nowacki:1989:ABQ,
author = "C. L. Nowacki and J. D. Harris and M. N. Richard",
booktitle = "{IEEE} Military Communications Conference, 1989.
{MILCOM '89}. Conference Record. Bridging the Gap.
Interoperability, Survivability, Security, 1989",
title = "Adaptive beamforming in quadratic residue number
systems on a cluster array processor",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "624--628",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MILCOM.1989.104000",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors describe a quadratic residue number system
(QRNS) implementation of the Leverrier algorithm for
computing the adjoint and determinant of a matrix on a
prototype parallel signal processor, called the cluster
array processor (CAP). Some \ldots{}",
}
@Article{Ochs:1989:TPF,
author = "T. Ochs",
title = "Theory and practice (floating point arithmetic)",
journal = j-COMP-LANG-MAG,
volume = "6",
number = "3",
pages = "67--70, 72, 74, 77--78, 80--81",
month = mar,
year = "1989",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Tue Dec 12 09:20:14 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IEEE-754 standard for floating point arithmetic
has inherent limits. The author presents a guide to
NaNs, unnormals, underflows and signal infinite
quantities.",
acknowledgement = ack-nhfb # " and " # ack-nj,
classification = "C5230 (Digital arithmetic methods); C6150C
(Compilers, interpreters and other processors)",
fjournal = "Computer Language Magazine",
keywords = "Compilers; Floating point arithmetic; IEEE-754
standard; NaNs; Signal infinite quantities; Underflows;
Unnormals",
thesaurus = "Digital arithmetic; Program compilers",
}
@InProceedings{Petkovsek:1989:CDS,
author = "M. Petkovsek",
title = "Contiguous digit sets and local roundings",
crossref = "Ercegovac:1989:PSC",
pages = "136--143",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Petkovsek.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Pincin:1989:NAM,
author = "A. Pincin",
title = "A new algorithm for multiplication in finite fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "7",
pages = "1045--1049",
month = jul,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.30855",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=30855",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Prince:1989:FTF,
author = "Timothy Prince",
title = "Float Trig Functions For The {C} Preprocessor",
journal = j-CUJ,
volume = "7",
number = "8",
pages = "103--??",
month = aug,
year = "1989",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@InProceedings{Ramamoorthy:1989:HSA,
author = "P. A. Ramamoorthy and B. Potu",
booktitle = "International Conference on Acoustics, Speech, and
Signal Processing, {ICASSP-89, 23--26} May 1989",
title = "High-speed {ADC} using residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1063--1066",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266615",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "An ADC (analog/digital converter) architecture based
on a residue number system (RNS) and multiple folding
of the input signal is described. The number of
comparators used is equal to the sum of moduli for
obtaining the dynamic range desired. An \ldots{}",
}
@InProceedings{Rao:1989:RNF,
author = "B. D. Rao",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 8--11 May 1989",
title = "Roundoff noise in floating point state space digital
filters",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "724--727",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The roundoff noise properties of floating-point
state-space digital filters are examined. It is shown
that the roundoff noise behavior of these filters is
related to their coefficient sensitivity. Expressions
for the variance of the output roundoff \ldots{}",
}
@InProceedings{Ray:1989:MCA,
author = "G. A. Ray",
booktitle = "Proceedings of the 32nd Midwest Symposium on Circuits
and Systems, 1989",
title = "Multiple core algorithms for residue number systems",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "833--836",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1989.101984",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The core function provides an easily implemented and
efficient means for performing the traditionally
difficult residue operations. However, two problems
with core algorithms are the difficulty in choosing
core coefficients and the many iterations \ldots{}",
}
@InProceedings{Rishe:1989:LEN,
author = "Naphtali Rishe",
title = "Lexicographic Encoding of Numeric Data Fields",
crossref = "Ercegovac:1989:PSC",
pages = "241--246",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Rishe.pdf",
abstract = "This paper proposes a method of variable-radix
representation of numeric data. The method allows
compact representation of arbitrary numbers. Among its
properties is that bitwise lexicographic comparison
($<$, $>$) is consistent with correct numeric
comparison of numbers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Book{Robbins:1989:CXM,
author = "Kay A. Robbins and Steven Robbins",
title = "The {Cray X-MP}\slash {Model} 24",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 165",
year = "1989",
ISBN = "0-387-97089-4, 3-540-97089-4",
ISBN-13 = "978-0-387-97089-9, 978-3-540-97089-7",
LCCN = "QA76.8 C72 R63 1989",
bibdate = "Sat Jan 29 18:17:38 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Saffari:1989:PDW,
author = "B. Saffari",
title = "Putting {DSPs} to work",
journal = j-BYTE,
volume = "14",
number = "13",
pages = "259--272",
month = dec,
year = "1989",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:47:21 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570
(Semiconductor integrated circuits); B6140 (Signal
processing and detection); C5130 (Microprocessor
chips); C5260 (Digital signal processing)",
fjournal = "BYTE Magazine",
keywords = "Digital filters; Feature extraction; Floating-point
application-specific-IC DSPs; Image processing;
Moments; Pattern recognition architecture; Sound; Space
correction; Time",
thesaurus = "Application specific integrated circuits; Computerised
signal processing; Digital signal processing chips",
}
@InProceedings{Santoro:1989:RAI,
author = "M. R. Santoro and G. Bewick and M. A. Horowitz",
title = "Rounding Algorithms for {IEEE} Multipliers",
crossref = "Ercegovac:1989:PSC",
pages = "176--183",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Santoro.pdf",
acknowledgement = ack-nhfb # " and " # ack-nj,
keywords = "ARITH-9",
summary = "Several technology independent rounding algorithms for
multiplying normalized numbers are presented. The first
is a simple rounding algorithm suitable for software
simulation or moderate performance hardware
multipliers. The next two algorithms are \ldots{}",
}
@Article{Sasaki:1989:AAD,
author = "Tateaki Sasaki and Mutsuko Sasaki",
title = "Analysis of accuracy decreasing in polynomial
remainder sequence with floating-point number
coefficients",
journal = "J. Inform. Process.",
volume = "12",
number = "4",
pages = "394--403",
year = "1989",
MRclass = "65G05 (65Y20)",
MRnumber = "91h:65069",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schwarz:1989:IIP,
author = "Jerry Schwarz",
title = "Implementing infinite precision arithmetic",
crossref = "Ercegovac:1989:PSC",
pages = "10--17",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Schwarz.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Scott:1989:FRM,
author = "M. Scott",
title = "Fast rounding in multiprecision floating-slash
arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "7",
pages = "1049--1052",
month = jul,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.30856",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A computational algorithm is described which quickly
rounds large fractions into a fixed-length
multiprecision floating-slash representation, using
single-precision operations where possible. An easily
calculated criterion for terminating the \ldots{}",
}
@Article{Shenoy:1989:FBE,
author = "A. P. Shenoy and R. Kumaresan",
title = "Fast base extension using a redundant modulus in
{RNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "2",
pages = "292--297",
month = feb,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.16508",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=16508",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Shimazu:1989:MFP,
author = "Y. Shimazu and T. Kengaku and T. Fujiyama and E.
Teraoka and T. Ohno and T. Tokuda and O. Tomisawa and
S. Tsujimichi",
title = "A 50 {MHz} 24b Floating-Point {DSP}",
crossref = "Wuorinen:1989:DTP",
pages = "44--45, 285",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 24-bit floating-point digital signal processor (DSP)
has been developed primarily for speech processing and
communication applications. The chip uses 1.0- mu m
double-metal CMOS with tungsten silicide technology.
The instruction set is upward compatible with an 18-bit
DSP. Novel circuit design techniques allowing 40-ns
machine cycle time at 50-MHz clock and less than 600-mW
power dissipation are described. A built-in self-test
is prepared using on-chip IROM and the two 24-bit
linear feedback shift registers which are included in
I/O registers such as the data register, the serial
input registers, and the serial output registers. The
DSP design features are summarized.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
affiliation = "Mitsubishi, Hyogo, Japan",
chemicalindex = "WSi2/int Si2/int Si/int W/int WSi2/bin Si2/bin Si/bin
W/bin",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); B6130 (Speech analysis and
processing techniques); C5130 (Microprocessor chips);
C5230 (Digital arithmetic methods); C5260 (Digital
signal processing)",
keywords = "1 Micron; 24 Bit; 40 Ns; 50 MHz; 600 MW; Built-in
self-test; Circuit design techniques; Clock frequency;
Communication applications; Data register; Double-metal
CMOS; Floating-point digital signal processor; I/O
registers; Instruction set; Linear feedback shift
registers; Machine cycle time; On-chip IROM; Power
dissipation; Serial input registers; Serial output
registers; Speech processing; WSi/sub 2/ technology",
numericalindex = "Frequency 5.0E+07 Hz; Word length 2.4E+01 bit; Time
4.0E-08 s; Power 6.0E-01 W; Size 1.0E-06 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic; Digital
signal processing chips; Speech analysis and
processing",
}
@Article{Sinha:1989:FPA,
author = "B. P. Sinha and P. K. Srimani",
title = "Fast parallel algorithms for binary multiplication and
their implementation on systolic architectures",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "3",
pages = "424--431",
month = mar,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.21128",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=21128",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Sit:1989:MFP,
author = "H. P. Sit and M. R. Nofal and S. Kimn",
title = "An 80 {MFLOPS} Floating-point Engine in the {Intel}
i860{\TM} Processor",
crossref = "IEEE:1989:PII",
pages = "374--379",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The i860 processor is a 64-b microprocessor with 1.02
million transistors. It has a 64-b external data bus
and a 32-b external address bus. It is fabricated with
Intel's CHMOS IV technology (a 1- mu m double-metal
process). The die size is approximately 10 mm*15 mm.
First silicon is functional over commercial temperature
and voltage ranges with an execution speed of 40 MHz.
The floating-point engine consists of a pipelined adder
and a pipelined multiplier, incorporates a special
hardware to support the dual operation instructions,
and operates synchronously with the RISC
(reduced-instruction-set computer) core to execute up
to three operations per clock. Its high performance
lends itself well to a numeric-intensive computation
environment, including vector processing.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
affiliation = "Intel Corp., Santa Clara, CA, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips)",
keywords = "1 Micron; 10 Mm; 15 Mm; 32 Bit; 40 MHz; 64 Bit; 80
MFLOPS; 80 MFLOPS floating-point engine; CHMOS IV
technology; CMOS; Commercial temperature; Die size;
Double-metal process; Dual operation instructions;
Execution speed; Floating-point engine; Intel i860
processor; Numeric-intensive computation environment;
Pipelined adder; Pipelined multiplier;
Reduced-instruction-set computer; RISC core; Three
operations per clock; Vector processing",
numericalindex = "Word length 6.4E+01 bit; Frequency 4.0E+07 Hz; Word
length 3.2E+01 bit; Computer speed 8.0E+07 FLOPS; Size
1.0E-06 m; Size 1.0E-02 m; Size 1.5E-02 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Reduced instruction set
computing",
}
@InProceedings{Skavantzos:1989:DFC,
author = "A. Skavantzos",
booktitle = "Twenty-Third Asilomar Conference on Signals, Systems
and Computers, 1989",
title = "Designing fast convolvers for residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "497--501",
year = "1989",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1989.266586",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@Article{Smith:1989:CSB,
author = "S. G. Smith",
title = "Comments on {``A signed bit-sequential multiplier''}
by {T. Rhyne} and {N. R. Strader II}",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "9",
pages = "1328--1330",
month = sep,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.29473",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
note = "See \cite{Rhyne:1986:SBS}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=29473",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Spaderna:1989:IFP,
author = "D. Spaderna and P. Green and K. Tam and T. Datta and
M. Kumar",
title = "An integrated floating point vector processor for
{DSP} and scientific computing",
crossref = "IEEE:1989:PII",
pages = "8--13",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The architecture of a high-performance floating-point
microprocessor intended for computation-intensive
applications is presented. Utilizing a massively
parallel execution unit, very high bandwidth onchip
memory, and extensive parallel address calculation
hardware, the processor is expected to achieve peak
execution rates of 400 MFLOPS for single-precision
floating-point numbers. This type of performance is
competitive with that of popular mainframe vector
processors.",
acknowledgement = ack-nhfb,
affiliation = "Sharp Microelectron. Technol. Inc., Vancouver, WA,
USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture);
C5260 (Digital signal processing)",
keywords = "400 MFLOPS; Computation-intensive applications; DSP;
Floating-point microprocessor; Integrated floating
point vector processor; Mainframe vector processors;
Massively parallel execution unit; Onchip memory;
Parallel address calculation hardware; Peak execution
rates; Scientific computing; Single-precision
floating-point numbers",
numericalindex = "Computer speed 4.0E+08 FLOPS",
thesaurus = "Digital signal processing chips; Parallel
architectures",
}
@InProceedings{Stearns:1989:SFD,
author = "C. C. Stearns",
title = "Subtractive floating-point division and square root
for {VLSI DSP}",
crossref = "IEE:1989:EEC",
pages = "405--409",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes recent architectural developments
in VLSI design for real-time digital signal processing.
In particular, floating point division and floating
point square root architectures applicable to both
adaptive filtering, standard deviation computations,
and general purpose processing are discussed. Emphasis
here is on the internal architectures of the arithmetic
units not on their applications. The research presented
in this paper has been proven feasible and reliable
from extensive gate-level simulation and fabrication in
silicon.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B1270F
(Digital filters); B2570D (CMOS integrated circuits);
C5230 (Digital arithmetic methods); C5240 (Digital
filters); C5260 (Digital signal processing)",
keywords = "Adaptive filtering; Arithmetic units; CMOS technology;
Floating point division; Floating point square root
architectures; Gate-level simulation; General purpose
processing; Real-time digital signal processing;
Semiconductor; Standard deviation computations; VLSI
DSP",
thesaurus = "Adaptive filters; CMOS integrated circuits; Digital
arithmetic; Digital signal processing chips; VLSI",
}
@InProceedings{Stearns:1989:SFP,
author = "C. C. Stearns",
booktitle = "European Conference on Circuit Theory and Design, 5--8
Sep 1989",
title = "Subtractive floating-point division and square root
for {VLSI} {DSP}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "405--409",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper describes recent architectural developments
in VLSI design for real-time digital signal processing.
In particular, floating point division and floating
point square root architectures applicable to both
adaptive filtering, standard \ldots{}",
}
@TechReport{Tang:1989:TCA,
author = "P. T. P. Tang",
title = "Testing Computer Arithmetic by Elementary Number
Theory",
institution = "Mathematics and Computer Science Division, Argonne
National Laboratory",
pages = "??",
month = aug,
year = "1989",
bibdate = "Thu Sep 01 11:57:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
keywords = "floating-point testing",
}
@Article{Tang:1989:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Exponential
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "15",
number = "2",
pages = "144--157",
month = jun,
year = "1989",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/63522.214389",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 22:47:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/",
abstract = "Algorithms and implementation details for the
exponential function in both single- and
double-precision of IEEE 754 arithmetic are presented
here. With a table of moderate size, the
implementations need only working-precision arithmetic
and are provably accurate to within 0.54 ulp as long as
the final result does not underflow. When the final
result suffers gradual underflow, the error is still no
worse than 0.77 ulp.",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@Book{Thies:1989:PXA,
author = "Klaus-Dieter Thies",
title = "{PC\slash {XT}\slash {AT} Numerik Buch} \toenglish
{PC\slash XT\slash AT Numeric Book} \endtoenglish",
publisher = pub-TEWI,
address = pub-TEWI:adr,
pages = "xiii + 707",
year = "1989",
ISBN = "3-89362-033-8",
ISBN-13 = "978-3-89362-033-3",
LCCN = "????",
bibdate = "Sat Nov 09 10:09:41 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Tu:1989:DLD,
author = "Paul K. Tu and M. D. Ercegovac",
title = "Design of on-line division unit",
crossref = "Ercegovac:1989:PSC",
pages = "42--49",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Tu.pdf",
abstract = "A gate array implementation of a radix-2
floating-point online division algorithm is presented.
The design requires 111 equivalent gates per bit and
has a cycle time of 24 ns. For 8-b exponent and 24-b
mantissa, the design requires 2497 equivalent gates and
can fit on an LSI Logic LL9320P chip with a utilization
factor 78\%.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, California University,
Los Angeles, CA, USA",
classification = "B1265B (Logic circuits); B2570 (Semiconductor
integrated circuits); C5120 (Logic and switching
circuits); C5230 (Digital arithmetic methods)",
keywords = "24 Ns Cycle time; ARITH-9; Gate array implementation;
LSI Logic LL9320P chip; Online division unit design;
Radix-2 floating-point online division algorithm;
Utilization factor",
numericalindex = "Time 2.4E-08 s",
thesaurus = "Digital arithmetic; Large scale integration; Logic
arrays",
}
@InProceedings{Turner:1989:SIS,
author = "Peter R. Turner",
title = "A software implementation of {SLI} arithmetic",
crossref = "Ercegovac:1989:PSC",
pages = "18--24",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Turner.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@InProceedings{Turrini:1989:OGD,
author = "Silvio Turrini",
title = "Optimal group distribution in carry-skip adders",
crossref = "Ercegovac:1989:PSC",
pages = "96--103",
year = "1989",
bibdate = "Sat Nov 27 14:19:10 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Turrini.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-9",
}
@Article{Unguru:1989:BRB,
author = "Sabetai Unguru",
title = "Book Review: {{\booktitle{A Mathematical History of
Division in Extreme and Mean Ratio}} by Roger
Herz-Fischler}",
journal = j-ISIS,
volume = "80",
number = "2",
pages = "298--299",
month = jun,
year = "1989",
CODEN = "ISISA4",
ISSN = "0021-1753 (print), 1545-6994 (electronic)",
ISSN-L = "0021-1753",
bibdate = "Tue Jul 30 21:23:50 MDT 2013",
bibsource = "http://www.jstor.org/action/showPublication?journalCode=isis;
http://www.jstor.org/stable/i211193;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isis1980.bib",
URL = "http://www.jstor.org/stable/234607",
acknowledgement = ack-nhfb,
fjournal = "Isis",
journal-URL = "http://www.jstor.org/journal/isis",
}
@Article{VanVeen:1989:MBC,
author = "B. D. {Van Veen} and R. Baraniuk",
title = "Matrix based computation of floating-point roundoff
noise",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "37",
number = "12",
pages = "1995--1998",
month = dec,
year = "1989",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "A matrix-based procedure is presented for computing
the output roundoff power for filters implemented with
floating-point arithmetic. The filter's computational
structure is represented in terms of a product of
matrices, known as a factored state \ldots{}",
}
@Article{Vassiliadis:1989:GPO,
author = "S. Vassiliadis and E. M. Schwarz and D. J. Hanrahan",
title = "A General Proof for Overlapped Multiple-Bit Scanning
Multiplications",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "2",
pages = "172--183",
month = feb,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.16494",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=16494",
acknowledgement = ack-mfc # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Vassiliadis:1989:SMF,
author = "S. Vassiliadis and D. S. Lemon and M. Putrino",
title = "{S/370} sign-magnitude floating-point adder",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "24",
number = "4",
pages = "1062--1070",
month = aug,
year = "1989",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 56-bit S/370 sign-magnitude adder for floating-point
operations implemented in a four-level metal (4LM)
bipolar master-slice technology is described. The
design of the two-to-one adder is based on a carry
lookahead scheme with implicit calculation of the
end-around carry. The implementation of the
floating-point adder and the error-detecting logic
requires one chip of 7500 automatically placed and
wired NAND gates. The chip die size is 7.39 x 7.39 mm
super(2) and it is mounted on a metalized ceramic (MC)
substrate. The floating-point sign-magnitude adder chip
is used in the IBM 9370 model 60 (9375) Engineering
Scientific Accelerator (ESA) card.",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Endicott, NY, USA",
classification = "B1265B (Logic circuits); B2570B (Bipolar integrated
circuits); C5120 (Logic and switching circuits)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "algorithms; arithmetic circuits; Carry lookahead
scheme; Chip die size; design; End-around carry;
Engineering scientific accelerator card;
Error-detecting logic; floating point arithmetic;
Four-level metal bipolar master-slice technology; IBM
9370 Model 60; logic circuits; Metallized ceramic
substrate; NAND gates; S/370; Sign-magnitude
floating-point adder",
summary = "A 56 bit S/370 sign-magnitude adder for floating-point
operations implemented in a four-level metal bipolar
master-slice technology is described. The design of the
two-to-one adder is based on a carry lookahead scheme
with implicit calculation of the \ldots{}",
thesaurus = "Adders; Bipolar integrated circuits; Carry logic;
Integrated logic circuits; NAND circuits",
}
@Article{Voelzke:1989:FSAa,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 4: Die
Konvertierungsroutinen} \toenglish {Floating-point
Arithmetic and its IEEE Specification. Part 4:
Conversion Routines} \endtoenglish",
journal = j-MC,
volume = "1",
pages = "66--73",
year = "1989",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Voelzke:1989:FSAb,
author = "H. V{\"o}lzke",
title = "{Flie{\ss}komma-Arithmetik und
IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 5: Ein- und
Ausgabefunktionen} \toenglish {Floating-point
Arithmetic and its IEEE Specification. Part 5: Input
and Output Functions} \endtoenglish",
journal = j-MC,
volume = "2",
pages = "65--71",
year = "1989",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Vulchanov:1989:SCR,
author = "N. L. Vulchanov and M. M. Konstantinov",
title = "Safe calculation of the relative machine precision in
floating-point computing environments",
journal = j-C-R-ACAD-BULGARE-SCI,
volume = "42",
number = "2",
pages = "45--48",
year = "1989",
CODEN = "DBANAD",
ISSN = "0366-8681",
MRclass = "65G99",
MRnumber = "991 451",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes rendus de l'Acad{\'e}mie bulgare des
sciences",
}
@Article{Wagner:1989:EDD,
author = "Neal R. Wagner and Paul Putter",
title = "Error detecting decimal digits",
journal = j-CACM,
volume = "32",
number = "1",
pages = "106--110",
month = jan,
year = "1989",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/63238.63246",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu May 30 09:41:10 MDT 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Misc/IMMD_IV.bib;
http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/cacm1980.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/0001-0782/63246.html",
abstract = "We were recently engaged by a large mail-order house
to act as consultants on their use of check digits for
detecting errors in account numbers. Since we were not
experts in coding theory, we looked in reference books
such as Error Correcting Codes [7] and asked colleagues
who were familiar with coding theory. Uniformly, the
answer was: There is no field of order 10; the theory
only works over a field. This article relates our
experiences and presents several of the simple
decimal-oriented error detection schemes that are
available, but not widely known.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "decimal floating-point arithmetic; reliability",
review = "ACM CR 9002-0109",
subject = "{\bf B.4.5}: Hardware, INPUT/OUTPUT AND DATA
COMMUNICATIONS, Reliability, Testing, and
Fault-Tolerance, Error-checking. {\bf E.4}: Data,
CODING AND INFORMATION THEORY, Nonsecret encoding
schemes.",
}
@Article{Wang:1989:ADF,
author = "C. C. Wang",
title = "An algorithm to design finite field multipliers using
a self-dual normal basis",
journal = j-IEEE-TRANS-COMPUT,
volume = "38",
number = "10",
pages = "1457--1460",
month = oct,
year = "1989",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.35840",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 8 19:00:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=35840",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wang:1989:MBC,
author = "Song-Tine Wang and Chi-Suan Wang and Morries Wang and
Shyh-Rurong Wang and Jhy-Kun Wang and Ching-Lu Hon and
Row-Ming Yang and Wei-Hsiung Chuang and Te-Tsoung Tsai
and Ming-Yuan Jang and Gwo-Jeng Pun",
title = "A 34-{MFLOP} 32-bit {CMOS} floating point processor",
crossref = "IEEE:1989:ISV",
pages = "361--364",
year = "1989",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 34-MFLOP 32-bit floating-point processor in 2- mu m
CMOS technology is presented. In order to achieve the
high speed of floating-point operation, the authors use
such techniques as hierarchical design parallel
circuits, and a three-stage pipeline that has been
optimized with equal delay in each stage. It is shown
that the CIC81232Y (multiplier) and CIC81233Y
(arithmetic and logic circuit) are fully compatible
with WTL1232 and WTL1233 in function, but the speeds
are 1.7 times faster.",
acknowledgement = ack-nhfb,
affiliation = "Electron. Res and Service Organ., Hsing-Chu, Taiwan",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
keywords = "32 Bit; 32-Bit floating-point processor; 34 MFLOPS;
Arithmetic circuit; CIC81232Y; CIC81233Y; CMOS
technology; Hierarchical design parallel circuits;
Logic circuit; Multiplier; Three-stage pipeline",
numericalindex = "Word length 3.2E+01 bit; Computer speed 3.4E+07
FLOPS",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Microprocessor chips; Pipeline processing",
}
@MastersThesis{Ward:1989:BFP,
author = "Kenneth L. Ward",
title = "A block floating point distributed arithmetic finite
impulse response filter",
type = "Thesis ({M.S.})",
school = "University of Florida",
address = "Gainesville, FL, USA",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics); Filters (Mathematics);
Floating-point arithmetic.",
}
@Article{Wichmann:1989:SPI,
author = "B. A. Wichmann",
title = "Scientific processing in {ISO-Pascal}: a proposal to
get the benefits of mixed precision floating-point",
journal = j-SIGPLAN,
volume = "24",
number = "6",
pages = "20--22",
month = jun,
year = "1989",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:40 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Although Pascal is a very popular language for
teaching and for use on microprocessors, it has not
been very successful for scientific calculations. Apart
from the pre-eminence of FORTRAN in this application
area, several technical defects in Pascal have
inhibited its use. One defect has been the problem in
Pascal as defined by Jensen and Wirth of the inability
to handle arrays of varying size as parameters to
procedures. The level 1 option in ISO-Pascal addressed
this defect by means of conformant arrays, albeit in a
somewhat inelegant fashion. Array handling in
ISO-Pascal can now be regarded as adequate since level
1 validated compilers are available for the majority of
widely available machines. This note addresses another
defect of Pascal, that no facility is provided to
handle floating point types of more than one
precision.",
acknowledgement = ack-nhfb,
affiliationaddress = "Teddington, Engl",
classification = "723; 902",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "algorithms; Computer Programming Languages; design;
Floating Point Computation; iso-pascal; languages;
pascal; Scientific Computing; standardization;
Standards",
subject = "D.2.1 Software, SOFTWARE ENGINEERING,
Requirements/Specifications \\ D.3.2 Software,
PROGRAMMING LANGUAGES, Language Classifications, Pascal
\\ E.1 Data, DATA STRUCTURES, Arrays",
}
@Article{Wichmann:1989:TFS,
author = "B. A. Wichmann",
title = "Towards a formal specification of floating point",
journal = j-COMP-J,
volume = "32",
number = "5",
pages = "432--436",
month = oct,
year = "1989",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65G99 (65Y10)",
MRnumber = "91b:65055",
bibdate = "Wed Dec 13 18:44:32 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Although the concept of floating point is well
understood, a formal mathematical treatment appears to
be new. The paper presents a formal definition of
floating point using the Vienna Development Method
(VDM). The relationship between this definition and the
informal definition in the Ada Standard and the work of
W. S. Brown (1981) is discussed.",
acknowledgement = ack-nhfb,
affiliation = "Department of Trade and Ind., NPL, Teddington, UK",
classification = "C5230 (Digital arithmetic methods); C6110B (Software
engineering techniques)",
corpsource = "Department of Trade and Ind., NPL, Teddington, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "digital arithmetic; Floating point; floating point;
Formal specification; formal specification; Method;
Vienna Development; Vienna Development Method",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Formal specification",
treatment = "P Practical",
}
@MastersThesis{Wittman:1989:SCU,
author = "Susan Jean Wittman",
title = "Servo compensation using a floating point digital
signal processor",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology, Dept. of
Aeronautics and Astronautics",
address = "Cambridge, MA, USA",
pages = "60",
year = "1989",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by James K. Roberge",
acknowledgement = ack-nhfb,
}
@InProceedings{Zeng:1989:RNP,
author = "B. Zeng and Y. Neuvo",
booktitle = "European Conference on Circuit Theory and Design, 5--8
Sep 1989",
title = "Roundoff noise properties of lattice filters employing
floating-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "233--237",
year = "1989",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The roundoff noise properties of general lattice
filters are studied for floating-point implementations
using the concept of dummy multipliers. The main
efforts are devoted to the Gray-Markel recursive
structures. It is shown that the roundoff noise
\ldots{}",
}
@Article{Zorpette:1989:PGD,
author = "Glenn Zorpette",
title = "{Parkinson}'s gun director",
journal = j-IEEE-SPECTRUM,
volume = "26",
number = "4",
pages = "43--43",
month = apr,
year = "1989",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.24154",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Mon Jan 20 06:41:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "antiaircraft guns; Arithmetic; Automatic control;
Cities and towns; controllers; Crystallization;
electromechanical system; gun director; Guns;
Laboratories; M-9; magnetic clutches; operational
amplifiers; Operational amplifiers; position control;
potentiometer; Psychology; Springs; Telephony;
weapons",
}
@Article{Alsup:1990:MFA,
author = "M. Alsup",
title = "{Motorola}'s 88000 Family Architecture",
journal = j-IEEE-MICRO,
volume = "10",
number = "3",
pages = "48--66",
month = may # "\slash " # jun,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.56325",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Anonymous:1990:MUF,
author = "Anonymous",
title = "{Motorola} unveils 96002 floating point processor",
journal = "Integrated circuits international",
pages = "3--??",
month = jul,
year = "1990",
ISSN = "0263-6522",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Ansari:1990:MBF,
author = "Ahmad Ansari",
title = "A $ 3 \times 3 $ multipurpose bus-connected
floating-point array processor",
type = "Thesis ({M.S.})",
school = "University of Florida",
address = "Gainesville, FL, USA",
pages = "vi + 127",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Arnold:1990:RLA,
author = "M. G. Arnold and T. A. Bailey and J. R. Cowles and J.
J. Cupal",
title = "Redundant logarithmic arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1077--1086",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57046",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57046",
abstract = "A number system that offers advantages in some
situations over conventional floating point and
sign/logarithmic number systems is described. Redundant
logarithmic arithmetic, like conventional logarithmic
arithmetic, relies on table lookups to make the
arithmetic unit simpler than an equivalent floating
point unit. The cost of 32 bit subtraction in a
redundant logarithmic number system is lower than
previously published logarithmic subtraction methods.
The total memory requirement for a 29-bit redundant
logarithmic unit is 16 K words compared to 22 K words
by the best previously published conventional sign
logarithm unit, assuming similar addition techniques
are employed. A redundant logarithmic number system can
be implemented with online arithmetic, which would be
impractical for a conventional sign logarithm number
system. The disadvantages of redundant arithmetic are
typical of redundant number systems. First, the
redundancy doubles the storage requirements for data
values. Second, the representation can become
ill-conditioned, especially as a result of iterated
multiplications. Third, division and square root
operations are more difficult to implement in redundant
logarithmic arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Wyoming University,
Laramie, WY, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C1160 (Combinatorial mathematics); C1210B
(Reliability theory); C5230 (Digital arithmetic
methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "29-Bit redundant logarithmic unit; 32 Bit subtraction;
Arithmetic unit; Data values; Division;
Ill-conditioned; Iterated multiplications; Memory
requirement; Online arithmetic; Redundant logarithmic
arithmetic; Redundant logarithmic number system; Square
root; Storage requirements; Table lookups",
thesaurus = "Digital arithmetic; Number theory; Redundancy; Table
lookup",
}
@Article{Aspray:1990:BBS,
author = "William Aspray",
title = "Back to Basics: The Stored Program Concept",
journal = j-IEEE-SPECTRUM,
volume = "27",
number = "9",
pages = "51--51",
month = sep,
year = "1990",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.58457",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 12:40:28 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib",
abstract = "The history and early development of the stored
program concept are briefly described. This refers to
the ability of a calculating machine to store its
instructions in its internal memory and process them in
its arithmetic unit, so that in the course of a
computation they may be not just executed but also
modified at electronic speeds. John von Neumann, a
faculty member of the Institute for Advanced Study in
Princeton, NJ, participated in the discussions in which
the idea was elaborated, wrote the first report of the
concept, placed it in a theoretical context, and built
his own computer, which was the early model for a
number of others, including the important commercially
manufactured IBM 701. J. Presper Eckert and John
Mauchly perhaps first conceived of the stored program
concept and developed most of the plans for
implementing it in the Edvac, and later incorporated it
in the Univac and other computers produced by their
company. Several British computer scientists, notably
Maurice Wilkes, were the first to implement the idea in
machines initially designed to embody this feature.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "arithmetic unit; calculating machine; Computer aided
instruction; Computer aided manufacturing; Computer
architecture; Context modeling; Digital arithmetic;
file organisation; history; History; internal memory;
Laboratories; Military computing; Prototypes; storage
allocation; stored program concept; Virtual
manufacturing",
}
@InProceedings{Bajwa:1990:FFP,
author = "A. Bajwa and R. Steck",
title = "A fast floating point unit in the i960 general-purpose
embedded processor family",
crossref = "Wescon:1990:WCR",
pages = "218--222",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Fast, cheap floating point arithmetic is required in
many embedded processor applications. This paper
describes a next-generation floating point unit
designed as an integrated functional unit on Intel's
i960 family of 32-bit embedded RISC processors. High
performance is achieved by utilizing two separate,
concurrent floating point execution units with wide
datapaths, both internally and to general-purpose
registers. Hardware system cost is reduced by
integrating the FPU on the main processor while
software development cost is minimized by using the
i960 Numerics Architecture supported by standard i960
family development tools.",
acknowledgement = ack-nhfb,
affiliation = "Intel Corp., Hillsboro, OR, USA",
availability = "Western Periodicals Co., 13000 Rayner Street, North
Hollywood, CA 91605, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture);
C5230 (Digital arithmetic methods)",
keywords = "32 Bit; 32-Bit embedded RISC processors; Concurrent
floating point execution units; Embedded processor
applications; Fast floating point unit; Floating point
arithmetic; FPU; General-purpose embedded processor
family; General-purpose registers; I960; I960 family;
I960 Numerics Architecture; Integrated functional unit;
Intel; Wide datapaths",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Computer architecture; Digital arithmetic;
Microprocessor chips; Reduced instruction set
computing",
}
@TechReport{Barlow:1990:EAU,
author = "Jesse Louis Barlow and Richard J. Zaccone",
title = "Error analysis in unnormalized floating point
arithmetic",
type = "Technical report",
number = "CS-90-23",
institution = "Pennsylvania State University, Department of Computer
Science",
address = "University Park, PA, USA",
pages = "9",
month = apr,
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supported by the Air Force Office of Scientific
Research. Supported by the National Science Foundation.
Supported by the Office of Naval Research.",
abstract = "The need to construct architectures in VLSI has
focused attention on unnormalized floating point
arithmetic. Certain unnormalized arithmetics allow one
to `pipe on digits,' thus producing significant speed
up in computation and making the input problems of
special purpose devices such as systolic arrays easier
to solve. We consider the error analysis implications
of using unnormalized arithmetic in numerical
algorithms. We also give specifications for its
implementation. Our discussion centers on the example
of Gaussian elimination. We show that the use of
unnormalized arithmetic requires changes in the
analysis of this algorithm. We will show that only for
certain classes of matrices that include diagonally
dominant matrices (either row or column), Gaussian
elimination is as stable in unnormalized arithmetic as
in normalized arithmetic. However, if the diagonal
elements of the upper triangular matrix are post
normalized, then Gaussian elimination is as stable in
unnormalized arithmetic as in normalized arithmetic for
all matrices.",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Floating-point arithmetic.",
}
@MastersThesis{Bhargava:1990:DFP,
author = "Ish Kumar Bhargava",
title = "Design of a floating point data acquisition system and
a development system for the {NC} 4016",
type = "Electrical Engineering Thesis ({M.S.})",
school = "University of Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "ix + 107",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Birman:1990:DWS,
author = "Mark Birman and Allen Samuels and George Chu and Chuk
Ting and Larry Hu and John McLeod and John Barnes",
title = "Developing the {WTL3170\slash 3171 Sparc}
Floating-Point Coprocessors",
journal = j-IEEE-MICRO,
volume = "10",
number = "1",
pages = "55--64",
month = jan # "\slash " # feb,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.46769",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Contending with dual floating-point interfaces at both
25 and 40 MHz posed an extraordinary challenge in
coprocessor development.",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "The development of the first two members in a family
of scalable-processor-architecture (Sparc)-compatible
parts is described. With varying frequency and latency
performance, the chips work with the first two integer
unit (IU) implementations from \ldots{}",
}
@Article{Blevins:1990:BHI,
author = "D. W. Blevins and E. W. Davis and R. A. Heaton and J.
H. Feif",
title = "{BLITZEN}: a Highly Integrated Massively Parallel
Machine",
journal = j-J-PAR-DIST-COMP,
volume = "8",
number = "2",
pages = "150--160",
month = feb,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220 (Computer architecture); C5440
(Multiprocessor systems and techniques)",
corpsource = "Microelectron. Center of North Carolina, Research
Triangle Park, NC, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "1.25 micron; 20 MHz; architecture; BLITZEN; CMOS
design rules; CMOS integrated circuits; computer
architecture; global; highly integrated massively
parallel machine; IEEE standard 32-bit floating point;
local control features; memory address; microprocessor
chips; multiplication; parallel processing; static RAM;
VLSI",
treatment = "P Practical",
}
@InBook{Branham:1990:PFP,
author = "Richard L. Branham",
booktitle = "Scientific Data Analysis: An Introduction to
Overdetermined Systems",
title = "Properties of Floating-Point Numbers",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "x + 237 + 36",
pages = "1--19",
year = "1990",
DOI = "https://doi.org/10.1007/978-1-4612-3362-6_1",
ISBN = "1-4612-3362-3 (e-book), 1-4612-7981-X",
ISBN-13 = "978-1-4612-3362-6 (e-book), 978-1-4612-7981-5",
LCCN = "QA76.9.D35",
bibdate = "Sat Dec 31 11:59:38 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
remark = "This introductory chapter discusses floating-point
arithmetic in VAX binary, IBM System\slash 360
hexadecimal, and Sharp pocket calculator decimal
formats, but has no mention of IEEE 754 arithmetic. It
discusses the failure in floating-point arithmetic of
the associative, cancellation, and distributive laws of
exact arithmetic. In the context of accurate
floating-point summation, it describes Kahan's
compensated summation algorithm, Linz'
binary-subdivision summation algorithm, and Wolfe's
cascaded accumulator algorithm, all implemented in
Fortran code given in the chapter figures. It also
treats the error in summation in rounded and truncated
arithmetic, and mentions the importance of guard
digits.",
tableofcontents = "Properties of Floating-Point Numbers \\
Matrices, Norms, and Condition Numbers \\
Sparse Matrices \\
Introduction to Overdetermined Systems \\
Linear Least Squares \\
The L1 Method \\
Nonlinear Methods \\
The Singular Value Decomposition \\
Index",
}
@InProceedings{Buck:1990:PAN,
author = "P. D. Buck and S. L. Day and D. Gonzalez",
title = "Problems with {Ada} numeric routines",
crossref = "Anonymous:1990:PAN",
pages = "195--204",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Computer programmers believe that their systems will
always perform as expected. Standardization of computer
languages has been a major advance towards this goal.
The Ada language was intended to further advance this
goal by rigorously defining the language. In addition
the language was intended to improve the portability of
programs. The authors' experience shows that the
definition of the Ada language does not ensure
mathematical algorithms will function consistently
across multiple hardware environments. The method used
by the language designers to specify the floating point
data types appears to be the cause of the problem.",
acknowledgement = ack-nhfb,
affiliation = "Nat. University, San Diego, CA, USA",
classification = "C6120 (File organisation); C6130 (Data handling
techniques); C6140D (High level languages)",
keywords = "Ada; Floating point data types; Mathematical
algorithms; Multiple hardware environments; Numeric
routines; Portability",
thesaurus = "Ada; Data structures; Digital arithmetic; Software
portability; Symbol manipulation",
}
@Article{Bursky:1990:FMC,
author = "D. Bursky",
title = "Floating-point math chip delivers 200 mflops peak",
journal = j-ELECTRONIC-DESIGN,
volume = "38",
number = "4",
pages = "51--52, 54, 55",
month = feb,
year = "1990",
CODEN = "ELODAW",
ISSN = "0013-4872 (print), 1944-9550 (electronic)",
ISSN-L = "0013-4872",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "By exploiting its latest process improvements and a
three-layer metal interconnection capability, Bipolar
Integrated Technology has managed to boost
floating-point throughput three- to five-fold over its
previous-generation circuits. The new B3130, a
single-chip double-precision floating-point processor
with 64-bit data buses, can deliver up to 200 MFLOPS of
peak throughput. With more than 55000 equivalent gates
and multiple 64-bit data buses (plus eight parity bits
on each bus), the chip is the highest-complexity ECL
chip to be sold commercially. By employing a high
degree of integration, the single chip packs a 64-bit
ALU, a 54-bit parallel multiplier (for the mantissa),
and a 64-bit divide/square root unit. The chip's
architecture is optimized for vector processing, but it
can also perform scalar calculations. In addition, the
wide data buses and pipelining support eliminate the
loading and unloading bottlenecks that frequently
degrade chip performance.",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570B
(Bipolar integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "Electronic Design",
keywords = "200 MFLOPS; 64 Bit; ALU; B3130; Bipolar Integrated
Technology; Bipolar microprocessor; Divide/square root
unit; Double-precision; ECL chip; Floating-point
processor; Multiple data buses; Parallel multiplier;
Pipelining support; Scalar calculations; Three-layer
metal interconnection; Vector processing",
numericalindex = "Computer speed 2.0E+08 FLOPS; Word length 6.4E+01
bit",
thesaurus = "Bipolar integrated circuits; Digital arithmetic;
Emitter-coupled logic; Microprocessor chips; Parallel
architectures; Parallel machines; Pipeline processing;
VLSI",
}
@Article{Carter:1990:RSD,
author = "T. M. Carter and J. E. Robertson",
title = "Radix-$ 16 $ signed-digit division",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "12",
pages = "1424--1433",
month = dec,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.61063",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61063",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Carter:1990:STA,
author = "T. M. Carter and J. E. Robertson",
title = "The set theory of arithmetic decomposition",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "993--1005",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57037",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57037",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Chen:1990:DIH,
author = "J. T. Chen and W. K. Jenkins and I. A. Hein and W. D.
{O'Brien, Jr.}",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 1--3 May 1990",
title = "Design and implementation of a high speed residue
number system correlator for ultrasonic time domain
blood flow measurement",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2893--2896",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1990.112615",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design and operation of a high-speed residue
number system (RNS) digital correlator is presented for
implementing the correlation function in a real-time
ultrasonic blood flow measurement system. This
architecture allows for both high-speed \ldots{}",
}
@Article{Chren:1990:NRN,
author = "W. A. {Chren, Jr.}",
title = "A new residue number system division algorithm",
journal = j-COMPUT-MATH-APPL,
volume = "19",
number = "7",
pages = "13--29",
month = "????",
year = "1990",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:01:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219090190U",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Ciminiera:1990:HRS,
author = "L. Ciminiera and P. Montuschi",
title = "Higher radix square rooting",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "10",
pages = "1220--1231",
month = oct,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.59853",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A general discussion on nonrestoring square root
algorithms is presented, showing bounds and constraints
delimiting the space of feasible algorithms, for all
the choices of radix, digit set and representation of
the partial remainder. Two classes of \ldots{}",
}
@Article{Clinger:1990:HRF,
author = "William D. Clinger",
title = "How to Read Floating Point Numbers Accurately",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "92--101",
month = jun,
year = "1990",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/93548.93557",
ISBN = "0-89791-364-7",
ISBN-13 = "978-0-89791-364-5",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:53 MST 2003",
bibsource = "Compendex database;
ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/93542/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib",
note = "See also output algorithms in
\cite{Knuth:1990:SPW,Steele:1990:HPF,Burger:1996:PFP,Abbott:1999:ASS,Steele:2004:RHP}.",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p92-clinger/",
abstract = "Consider the problem of converting decimal scientific
notation for a number into the best binary floating
point approximation to that number, for some fixed
precision. This problem cannot be solved using
arithmetic of any fixed precision. Hence the IEEE
Standard for Binary Floating-Point Arithmetic does not
require the result of such a conversion to be the best
approximation. This paper presents an efficient
algorithm that always finds the best approximation. The
algorithm uses a few extra bits of precision to compute
an IEEE-conforming approximation while testing an
intermediate result to determine whether the
approximation could be other than the best. If the
approximation might not be the best, then the best
approximation is determined by a few simple operations
on multiple-precision integers, where the precision is
determined by the input. When using 64 bits of
precision to compute IEEE double precision results, the
algorithm avoids higher-precision arithmetic over 99\%
of the time.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Oregon University, Eugene, OR, USA",
annote = "Published as part of the Proceedings of PLDI'90.",
classification = "722; 723; C1160 (Combinatorial mathematics); C5230
(Digital arithmetic methods); C7310 (Mathematics)",
confdate = "20-22 June 1990",
conference = "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation",
conferenceyear = "1990",
conflocation = "White Plains, NY, USA",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "algorithms; Best binary floating point approximation;
Computer Programming Languages; Computers, Digital ---
Computational Methods; Decimal scientific notation;
Design; Efficient algorithm; experimentation; Fixed
precision; Floating point numbers; Floating Point
Numbers; Higher-precision arithmetic; IEEE double
precision results; IEEE Standard; IEEE-conforming
approximation; Intermediate result; Multiple-precision
integers",
meetingaddress = "White Plains, NY, USA",
meetingdate = "Jun 20--22 1990",
meetingdate2 = "06/20--22/90",
sponsor = "Assoc for Computing Machinery, Special Interest Group
on Programming Languages",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation.",
thesaurus = "Digital arithmetic; Mathematics computing; Number
theory; Standards",
}
@Article{Codenotti:1990:ATT,
author = "B. Codenotti and G. Lotti and F. Romani",
title = "Area-time trade-offs for matrix-vector
multiplication",
journal = j-J-PAR-DIST-COMP,
volume = "8",
number = "1",
pages = "52--59",
month = jan,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Inst di Elaborazione dell'Informazione-CNR",
affiliationaddress = "Pisa, Italy",
classification = "722; 723; 921; B0290H (Linear algebra); B1265B
(Logic circuits); C4140 (Linear algebra); C4240
(Programming and algorithm theory)",
corpsource = "Istituto di Elaborazione dell'Inf., CNR, Pisa, Italy",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algebra; area-time complexity; Area-Time Trade-Offs;
arithmetic; computation; computational complexity;
Computer Systems, Digital; Computers,
Digital--Computational Methods; I/O conventions;
information flow; integrated logic circuits;
Mathematical Techniques--Matrix Algebra; matrix;
Matrix-Vector Multiplication; matrix-vector
multiplication; operations; Parallel Processing; sparse
matrix; VLSI",
treatment = "T Theoretical or Mathematical",
}
@Article{Cosnard:1990:STF,
author = "Michel Cosnard and Jean Duprat and Yves Robert",
title = "Systolic triangularization over finite fields",
journal = j-J-PAR-DIST-COMP,
volume = "9",
number = "3",
pages = "252--260",
month = jul,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure de Lyon Lab LIP-IMAG",
affiliationaddress = "Lyon, Fr",
classification = "722; 723; 921; C4140 (Linear algebra); C5220
(Computer architecture); C5230 (Digital arithmetic
methods)",
corpsource = "IMAG, Ecole Normale Superieure de Lyon, France",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "architecture; arithmetic number; computer algebra;
Computer Programming--Algorithms; Computer Systems,
Digital--Parallel Processing; Computers, Digital;
digital arithmetic; finite fields; Gaussian
Elimination; Gaussian elimination; large dense linear
systems; linear algebra; Mathematical
Techniques--Linear Algebra; Modular Multiplication
Algorithm; parallel architectures; partial; pivoting;
Special Purpose Application; systolic; Systolic Arrays;
Systolic Triangularization; systolic triangularization;
theory",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Manual{Cyrix:1990:FCU,
title = "{FasMath} {CX-83S87} user's manual",
publisher = "Cyrix Corp.",
address = "Richardson, TX, USA",
pages = "115 + 5 + 3",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Cyrix CX-83X87 (Microprocessor); Floating-point
arithmetic.; Integrated circuits --- Very large scale
integration.; Metal oxide semiconductors,
Complementary.",
remark = "Running title: FasMath 83S87 user manual.",
}
@Article{Darley:1990:TFC,
author = "Merrick Darley and Bill Kronlage and David Bural and
Bob Churchill and David Pulling and Paul Wang and Rick
Iwamoto and Larry Yang",
title = "The {TMS390C602A} Floating-Point Coprocessor for
{Sparc} Systems",
journal = j-IEEE-MICRO,
volume = "10",
number = "3",
pages = "36--47",
month = may # "\slash " # jun,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.56324",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
abstract = "A recent Sparc (scalable processor architecture)
processor consists of a two-chip configuration,
containing the TMS390C601 integer unit (IU) and the
TMS390C602A floating-point unit (FPU). The second
device, an innovative coprocessor that lets the
processor execute single- or double-precision
floating-point instructions concurrently with IU
operations is described. Dedicated floating-point
hardware in the FPU increases the performance of the
system. Running at clock periods as small as 20 ns, the
chip should deliver 5.5 million double-precision
floating-point operations per second under the Linpack
benchmark (50-MHz clock rate). The FPU provides single-
and double-precision arithmetic functions: addition,
subtraction, multiplication, division, square root,
compare, and convert. To minimize its math unit's
latency, the FPU uses a highly parallel architecture
requiring separate math units to optimize additions and
multiplications. Traps stop the execution of a program
to jump to software routine for handling data-dependent
errors or to execute instructions not implemented in
the hardware. Benchmark results are presented. (4
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Texas Instrum. Inc., Dallas, TX, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "Addition; Compare; Convert; Division; Linpack
benchmark; Multiplication; Sparc systems; Square root;
Subtraction; TMS390C601 integer unit; TMS390C602A
floating-point coprocessor; TMS390C602A floating-point
unit; Two-chip configuration",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Article{Darley:1990:TFP,
author = "Merrick Darley and Bill Kronlage and David Bural and
Bob Churchill and David Pulling and Paul Wang and Rick
Iwamoto and Larry Yang",
title = "The {TMS390C602A} Floating-Point Coprocessor for
{Sparc} Systems",
journal = j-IEEE-MICRO,
volume = "10",
number = "3",
pages = "36--47",
month = may # "\slash " # jun,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.56324",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A recent Sparc (scalable processor architecture)
processor consists of a two-chip configuration,
containing the TMS390C601 integer unit (IU) and the
TMS390C602A floating-point unit (FPU). The second
device, an innovative coprocessor that lets the
processor execute single- or double-precision
floating-point instructions concurrently with IU
operations is described. Dedicated floating-point
hardware in the FPU increases the performance of the
system. Running at clock periods as small as 20 ns, the
chip should deliver 5.5 million double-precision
floating-point operations per second under the Linpack
benchmark (50-MHz clock rate). The FPU provides single-
and double-precision arithmetic functions: addition,
subtraction, multiplication, division, square root,
compare, and convert. To minimize its math unit's
latency, the FPU uses a highly parallel architecture
requiring separate math units to optimize additions and
multiplications. Traps stop the execution of a program
to jump to software routine for handling data-dependent
errors or to execute instructions not implemented in
the hardware. Benchmark results are presented. (4
Refs.)",
acknowledgement = ack-mfc # " and " # ack-nhfb,
affiliation = "Texas Instrum. Inc., Dallas, TX, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "Addition; Compare; Convert; Division; Linpack
benchmark; Multiplication; Sparc systems; Square root;
Subtraction; TMS390C601 integer unit; TMS390C602A
floating-point coprocessor; TMS390C602A floating-point
unit; Two-chip configuration",
summary = "A recent Sparc (scalable processor architecture)
processor consists of a two-chip configuration,
containing the TMS390C601 integer unit (IU) and the
TMS390C602A floating-point unit (FPU). The second
device, an innovative coprocessor that lets the
\ldots{}",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Book{Dewar:1990:MPV,
author = "Robert B. K. Dewar and Matthew Smosna",
title = "Microprocessors: a programmer's view",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xvii + 462",
year = "1990",
ISBN = "0-07-016638-2, 0-07-016639-0 (soft)",
ISBN-13 = "978-0-07-016638-7, 978-0-07-016639-4 (soft)",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microprocessors --- Programming.",
remark = "Microprocessors --- Introduction to the 80386 ---
Addressing and memory on the 80386 --- Tasking, virtual
memory, and exceptions to the 80386 --- Microprocessors
and floating-point arithmetic --- 68030 user
programming model --- 68030 supervisor state ---
Introduction to RISC architectures --- MIPS processors
--- SPARC architecture --- Intel i860 --- IBM RISC
chips --- INMOS transputer - - Future of microprocessor
design.",
}
@InProceedings{Dixon:1990:HPB,
author = "G. Dixon",
title = "A high performance block floating point {DSP}
chip-set",
crossref = "IEE:1990:ICV",
pages = "9/1--7",
year = "1990",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes the design and development of two
ASICs which form the processing kernel of a high
performance sonar signal processor; namely a 24-bit
Block Floating Point Arithmetic Unit (BFPAU), and a
Table Memory And Address Modifier (TMAAM). The system
is based upon a 24-bit block floating point data format
which is a compromise between fixed and floating point
data; possessing the advantage of reducing the data
storage requirement compared to true floating point
while allowing arithmetic to be performed in the faster
fixed-point format whilst retaining the extended
dynamic range provided by floating point. The BFPAU and
TMAAM perform the arithmetic processing; the BFPAU is
the central arithmetic processor aimed at sonar signal
processing in general and beamforming in particular,
while the TMAAM provides a range of essential support
functions such as look-up tables for trigonometric
functions, address generation, exponent control and
normalisation and program sequencing. Two blocks of
dual-port RAM provide storage for system I/O data
transfers, together with two blocks of RAM providing
working data storage for the BFPAU. A block of video
RAM is used to store address and control sequences for
the processing element.",
acknowledgement = ack-nhfb,
affiliation = "Plessey Res. Caswell, Towcester, UK",
classification = "B1265F (Microprocessors and microcomputers); B6320E
(Sonar and acoustic radar)",
keywords = "Address generation; Arithmetic processing; ASICs;
Beamforming; Block floating point DSP chip-set; Data
format; Data storage requirement; Dual-port RAM;
Dynamic range; Exponent control; Fixed-point format;
Look-up tables; Normalisation; Program sequencing;
Sonar signal processor; System I/O data transfers;
Video RAM; Working data storage",
thesaurus = "Application specific integrated circuits; Digital
signal processing chips; Random-access storage; Sonar",
}
@Article{Dotzel:1990:DMG,
author = "G{\"u}nter Dotzel",
title = "Does {Modula-2} generate racehorses? Comparison of
compiler generated code quality for floating point
arithmetic",
journal = j-SIGPLAN,
volume = "25",
number = "12",
pages = "85--88",
month = dec,
year = "1990",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:00 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A simple example serves to demonstrate the code
quality generated by two different Modula-2 compilers.
The two compilers are called the Zurich/Hamburger and
the Erlanger. The author lists the Modula-2 source
program, shows an excerpt of the machine code listing
generated by the Erlanger and presents that of the
Zurich/Hamburger. The differences in code quality
concerning instruction count, code size and execution
speed are discussed and summarized. The author also
presents the main program module used for the
benchmarks and a short description of the development
history of Modula-2 and Modula/R.",
acknowledgement = ack-nhfb,
affiliation = "ModulaWare GmbH, Erlangen, West Germany",
classification = "C6140D (High level languages); C6150C (Compilers,
interpreters and other processors); C6150G (Diagnostic,
testing, debugging and evaluating systems)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Benchmarks; Code size; Compiler generated code
quality; Development history; Erlanger; Execution
speed; Floating point arithmetic; Instruction count;
Machine code listing; Main program module; Modula-2
compilers; Modula-2 source program; Modula/R;
Zurich/Hamburger",
thesaurus = "Modula; Modula listings; Program compilers; Program
testing",
}
@Article{Dunham:1990:FFE,
author = "C. B. Dunham",
title = "Feasibility of `Perfect' Function Evaluation",
journal = j-SIGNUM,
volume = "25",
number = "4",
pages = "25--26",
month = oct,
year = "1990",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Article{Edenfield:1990:PPD,
author = "R. W. Edenfield and M. G. Gallup and W. B. {Ledbetter,
Jr.} and R. C. McGarity and E. E. Quintana and R. A.
Reininger",
title = "The 68040 Processor. {Part} 1, Design and
Implementation",
journal = j-IEEE-MICRO,
volume = "10",
number = "1",
pages = "66--78",
month = jan # "\slash " # feb,
year = "1990",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.46770",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Ercegovac:1990:FMC,
author = "M. D. Ercegovac and T. Lang",
title = "Fast multiplication without carry-propagate addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "11",
pages = "1385--1390",
month = nov,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.61047",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61047",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ercegovac:1990:RSR,
author = "M. D. Ercegovac and T. Lang",
title = "Radix-$4$ square root without initial {PLA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1016--1024",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57040",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ercegovac:1990:SRD,
author = "M. D. Ercegovac and T. Lang",
title = "Simple radix-$4$ division with operands scaling",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "9",
pages = "1204--1208",
month = sep,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57060",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57060",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Fussichen:1990:GAM,
author = "Kenneth Fussichen",
title = "Getting {Ada} into the mainstream in the 1990's",
crossref = "ACM:1990:PDB",
pages = "428--428",
year = "1990",
DOI = "https://doi.org/10.1145/255471.255572",
bibdate = "Thu Aug 07 18:17:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Ada offers a great deal to the MIS community. There
are a number of language features that provide
attractive tools to the programmer. Ada's support for
Object Orientation is far superior to that currently
afforded by IBM mainframe languages such as COBOL and
PL/1. This translates into more maintainable code,
which is the key to MIS Ada
acceptance.\par
Unfortunately, Ada introduces problems that do not
currently exist in MIS. Decimal arithmetic and string
manipulation adequate to support reporting are
inherently non-existent. I/O support is inadequate as
are DBMS bindings. Conversions are forced on non-ASCII
hosts. The compiler has the option of reordering fields
within records, rendering non-Ada utilities useless.
There is an inexcusable lack of understanding of the
targeted market.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Gallant:1990:MCI,
author = "John Gallant and Bill Travis",
title = "Math coprocessor {ICs}: Floating-point chips boost
{muP} performance",
journal = j-EDN,
volume = "35",
number = "12",
pages = "63--??",
month = jun,
year = "1990",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating-point arithmetic exacts huge penalties in CPU
computation time. Dedicated coprocessor ICs execute
this onerous task automatically and efficiently.",
acknowledgement = ack-nhfb,
fjournal = "EDN",
}
@TechReport{Gay:1990:CRB,
author = "David M. Gay",
title = "Correctly Rounded Binary-Decimal and Decimal-Binary
Conversions",
type = "Numerical Analysis Manuscript",
number = "90-10",
institution = "AT\&T Bell Laboratories",
pages = "16",
month = nov # " 30",
year = "1990",
bibdate = "Sat Apr 28 18:42:55 2001",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://cm.bell-labs.com/cm/cs/doc/90/4-10.ps.gz;
http://www.ampl.com/ampl/REFS/rounding.ps.gz;
http://www.netlib.org/fp/dtoa.c;
http://www.netlib.org/fp/g_fmt.c;
http://www.netlib.org/fp/gdtoa.tgz;
http://www.netlib.org/fp/rnd_prod.s",
acknowledgement = ack-nj,
keywords = "correct rounding; decimal floating-point arithmetic",
}
@InProceedings{Gibson:1990:CII,
author = "D. H. Gibson",
title = "Considerations for including {IEEE} floating point in
large systems",
crossref = "SHARE:1990:PSE",
pages = "47--62",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "International standards such as ANSI/IEEE Std 754-1985
floating-point arithmetic provide the potential for
application portability. The paper, beginning with a
1984 SHARE requirements statement, sets forth certain
considerations for including IEEE Std 754 floating
point in large systems. A tutorial is presented on IEEE
Std 754 floating-point arithmetic. The considerations
for integrating IEEE into a large system along with an
existing floating point representation are discussed in
three categories: architectural; implementation; usage.
Related topics are identified and discussed. The paper
concludes with a summary of the considerations. (11
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Poughkeepsie, NY, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Application portability; Floating-point arithmetic;
IEEE Std 754 floating point; SHARE",
thesaurus = "Digital arithmetic; Standards",
}
@Article{Glass:1990:MC,
author = "L. B. Glass",
title = "Math coprocessors",
journal = j-BYTE,
volume = "15",
number = "1",
pages = "337--348",
month = jan,
year = "1990",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 17:47:21 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265B (Logic circuits); B1265F (Microprocessors and
microcomputers); C5130 (Microprocessor chips); C5230
(Digital arithmetic methods)",
fjournal = "BYTE Magazine",
keywords = "Cyrix 83D87; Floating-point maths; IEEE 754
floating-point standard; Integrated Information
Technology; Intel 80287; Intel 80387; Intel 8087; Maths
coprocessors; Motorola 68881; Motorola 68882; NP-3C87;
Weitek Abacus 3167",
thesaurus = "Digital arithmetic; Microprocessor chips; Satellite
computers",
}
@InCollection{Goldberg:1990:CA,
author = "D. Goldberg",
title = "Computer Arithmetic",
crossref = "Hennessy:1990:CAQ",
chapter = "A",
pages = "A-1--A-66",
year = "1990",
bibdate = "Fri Dec 08 13:04:21 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Goodman:1990:SMR,
author = "R. H. Goodman",
title = "Some Models of Relative Error in Products",
journal = j-APPL-NUM-MATH,
volume = "6",
number = "3",
pages = "209--220",
month = mar,
year = "1990",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Thu Sep 1 10:14:16 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@MastersThesis{Goodreau:1990:DIF,
author = "Michael S. Goodreau",
title = "The design and implementation of a floating-point
format conversion integrated circuit",
type = "Thesis ({M.S.E.E.})",
school = "University of Washington",
address = "Seattle, WA, USA",
pages = "ix + 113",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.; Integrated circuits ---
Design and construction.",
}
@InCollection{Gries:1990:BDO,
author = "David Gries",
title = "Binary to Decimal, One More Time",
crossref = "Feijen:1990:BOB",
chapter = "16",
pages = "141--148",
year = "1990",
DOI = "https://doi.org/10.1007/978-1-4612-4476-9_17",
bibdate = "Sat Sep 03 09:41:32 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
note = "This paper presents an alternate proof of Knuth's
algorithm \cite{Knuth:1990:SPW} for conversion between
decimal and fixed-point binary numbers.",
URL = "https://link.springer.com/chapter/10.1007/978-1-4612-4476-9_17",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Gu:1990:TIT,
author = "Li Zhen Gu and Xing Yuan Chen",
title = "Table-driven implementation of the trigonometric
functions using {IEEE} floating point operations.
({Chinese})",
journal = "Journal of Tsinghua University",
volume = "30",
number = "3",
pages = "31--38",
year = "1990",
MRclass = "65D20 (65-04)",
MRnumber = "92a:65070",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Tsinghua Univ.",
}
@Book{Hamacher:1990:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Third",
pages = "xx + 617",
year = "1990",
ISBN = "0-07-025685-3",
ISBN-13 = "978-0-07-025685-9",
LCCN = "QA76.9.A73 H351 1990",
bibdate = "Sat May 18 14:24:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
}
@Article{Hashemian:1990:SRA,
author = "R. Hashemian",
title = "Square Rooting Algorithms for Integer and
Floating-Point Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1025--1029",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57041",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57041",
abstract = "An algorithm for evaluating the square root of
integers and real numbers is developed. The procedure
consists of two parts: one to obtain a close estimate
of the square root and the other to modify the initial
value, iteratively, until a precise root is evaluated.
The major effort in this development has been
concentrated on two objectives: high speed and no
division operation other than division by 2. The first
objective is achieved through a simple two-step
procedure for getting the first estimate, and then
modifying it by employing a fast converging iteration
technique. The second objective is also fulfilled
through applying bit-shift operation rather than
division operation. The algorithm is simulated for both
integer and real numbers, and the results are compared
to two methods being widely used. The results
(tabulated) show considerable improvement in speed
compared to these other two methods.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Department of Electr. Eng., Northern Illinois
University, Dekalb, IL, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C1160 (Combinatorial mathematics); C4130
(Interpolation and function approximation); C5230
(Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Bit-shift operation; Close estimate; Division by 2;
Fast converging iteration; Floating-point numbers;
Initial value modification; Integer numbers; Precise
root; Real numbers; Square rooting algorithms",
summary = "An algorithm for evaluating the square root of
integers and real numbers is developed. The procedure
consists of two parts: one to obtain a close estimate
of the square root and the other to modify the initial
value, iteratively, until a precise \ldots{}",
thesaurus = "Digital arithmetic; Iterative methods; Number theory",
}
@Article{Hokenek:1990:LZA,
author = "E. Hokenek and R. K. Montoye",
title = "Leading-zero anticipator ({LZA}) in the {IBM RISC
System\slash 6000} floating-point execution unit",
journal = j-IBM-JRD,
volume = "34",
number = "1",
pages = "71--77",
month = jan,
year = "1990",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents a novel technique used in the
multiply-add-fused (MAF) unit of the IBM RISC
System/6000 (RS/6000) processor for normalizing the
floating-point results. Unlike the conventional
procedures applied thus far, the so-called leading-zero
anticipator (LZA) of the RS/6000 carries out processing
of the leading zeros and ones in parallel with
floating-point addition. Therefore, the new circuitry
reduces the total latency of the MAF unit by enabling
the normalization and addition to take place in a
single cycle.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
classification = "B1265B (Logic circuits); C5230 (Digital arithmetic
methods)",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "Circuitry; Floating-point addition; IBM RISC
System/6000 floating-point execution unit; Latency;
Leading-zero anticipator; Multiply-add-fused;
Normalization; Parallel",
thesaurus = "Digital arithmetic; IBM computers; Reduced instruction
set computing",
}
@Article{Hokenek:1990:SGR,
author = "E. Hokenek and R. K. Montoye and P. W. Cook",
title = "Second-Generation {RISC} Floating Point with
Multiply-Add Fused",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "25",
number = "5",
pages = "1207--1213",
month = oct,
year = "1990",
CODEN = "IJSCBC",
DOI = "https://doi.org/10.1109/4.62143",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 440000-transistor second-generation RISC (reduced
instruction set computer) floating-point chip is
described. The pipeline latency is only two cycles, and
a double-precision result is produced every cycle.
System throughput and accuracy are increased by using a
floating-point multiply-add-fused unit, which carries
out a double-precision accumulate as a two-cycle
pipelined execution with only one rounding error. While
the cycle time (40 ns) is competitive with other CMOS
RISC systems, the floating-point performance stretches
to the range of bipolar RISC systems (7.4-13 MFLOPS
LINPACK). Leading zero anticipation makes the two-cycle
pipeline possible by nearly eliminating the additional
postnormalization time, and it allows for reduced
overall system latency. Partial decode shifters allow
complete time sharing for the multiply and data
alignment. Improved design techniques for logarithmic
addition and higher order counters for multiplication
complete this second-generation RISC floating-point
unit design.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "40 Ns; 7.4 To 13 MFLOPS; Double-precision accumulate;
Double-precision result; Floating-point chip; Higher
order counters; Logarithmic addition; Multiplication;
Multiply-add-fused unit; Partial decode shifters;
Pipeline latency; Reduced instruction set computer;
RISC; Two-cycle pipelined execution",
numericalindex = "Time 4.0E-08 s; Computer speed 7.4E+06 to 1.3E+07
FLOPS",
summary = "A 440000-transistor second-generation RISC (reduced
instruction set computer) floating-point chip is
described. The pipeline latency is only two cycles, and
a double-precision result is produced every cycle.
System throughput and accuracy are increased \ldots{}",
thesaurus = "CMOS integrated circuits; Microprocessor chips;
Pipeline processing; Reduced instruction set
computing",
}
@Article{Hong:1990:DTP,
author = "S. J. Hong",
title = "The design of a testable parallel multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "3",
pages = "411--416",
month = mar,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.48874",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48874",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Horiguchi:1990:FNR,
author = "Hiroshi Horiguchi",
title = "Floating-Point Numbers and Real Numbers",
journal = j-ADV-SOFT-SCI-TECH,
volume = "1",
number = "??",
pages = "157--??",
year = "1990",
ISSN = "1044-7997",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances in software science and technology",
}
@TechReport{IBM:1990:AXI,
author = "{IBM Corporation}",
title = "{ACRITH-XSC}: {IBM} High Accuracy Arithmetic ---
Extended Scientific Computation",
type = "Technical Report",
number = "GC33-6461-01, SC33-6462-00, SC33-6463-00,
SC33-6464-00, SC33-6466-00.",
institution = pub-IBM,
address = pub-IBM:adr,
year = "1990",
bibdate = "Thu Jan 21 17:27:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1. General Information \\
2. Reference \\
3. Sample Programs \\
4. How To Use \\
5. Syntax Diagrams",
}
@Book{IBM:1990:IRS,
editor = "Mamata Misra",
title = "{IBM RISC System\slash 6000 Technology, publication
SA23-2619-00}",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1990",
bibdate = "Wed Sep 14 23:02:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Jarvis:1990:ICA,
author = "P. Jarvis",
title = "Implementing {Cordic} Algorithms",
journal = j-DDJ,
volume = "15",
number = "10",
pages = "152--158",
month = oct,
year = "1990",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Kahan:1990:HCA,
author = "W. Kahan",
title = "How {Cray}'s arithmetic hurts scientific computation
(and what might be done about it)",
crossref = "CUG:1990:PSC",
pages = "42",
day = "14",
month = jun,
year = "1990",
bibdate = "Tue Jan 03 18:17:16 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript prepared for the Cray User Group meeting in
Toronto, Canada, April 10, 1990.",
URL = "http://754r.ucbtest.org/issues/cray-hurts-uk.pdf;
http://754r.ucbtest.org/issues/cray-hurts-ut.pdf;
http://754r.ucbtest.org/issues/cray-hurts.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:1990:PCA,
author = "William Kahan",
title = "Paradoxes in concepts of accuracy",
publisher = "Carnegie Mellon University",
address = "Pittsburgh, PA, USA",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 videocassette (60 min.)",
series = "Distinguished lecture series",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.; Floating-point arithmetic ---
Data processing.",
remark = "Lecture given February 15, 1990. VHS format. Lecturer,
William Kahan. Paradoxes expose errors in conventional
wisdom about floating-point arithmetic.",
}
@Article{Kalbasi:1990:CYT,
author = "K. Kalbasi",
title = "Can you trust your computer?",
journal = j-IEEE-POT,
volume = "9",
number = "2",
pages = "15--18",
month = apr,
year = "1990",
CODEN = "IEPTDF",
ISSN = "0278-6648 (print), 1558-1772 (electronic)",
ISSN-L = "0278-6648",
bibdate = "Wed Sep 14 19:14:21 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Potentials",
}
@Article{Katsuno:1990:BFP,
author = "A. Katsuno and H. Takahashi and H. Kubosawa and T.
Sato and A. Suga and G. Goto",
title = "A 64-bit Floating-Point Processing Unit with a
Horizontal Instruction Code for Parallel Operations",
crossref = "IEEE:1990:PII",
pages = "347--350",
year = "1990",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Khan:1990:FPA,
author = "A. Khan",
title = "Floating point architecture and implementation",
crossref = "Wescon:1990:WCR",
pages = "205--213",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Analyzes various requirements of efficient floating
point architecture and implementation. The basic
elements of architecture such as latency, repeat rate
and issue rate are defined. Handling various exceptions
in a precise manner is described. Finally, a
description of one example (MIPS R3010) is provided. (0
Refs.)",
acknowledgement = ack-nhfb,
availability = "Western Periodicals Co., 13000 Rayner Street, North
Hollywood, CA 91605, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods)",
keywords = "Elements of architecture; Floating point architecture;
Issue rate; Latency; MIPS R3010; Repeat rate;
Requirements",
thesaurus = "Computer architecture; Digital arithmetic",
}
@InProceedings{Kiernan:1990:FAE,
author = "J. M. Kiernan and T. B. Blachowiak",
title = "Fast, Accurate Elementary Functions For the {Cray
Y-MP} Computer",
crossref = "CUG:1990:PSC",
pages = "243--252",
year = "1990",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InCollection{Knuth:1990:SPW,
author = "Donald E. Knuth",
title = "A Simple Program Whose Proof Isn't",
crossref = "Feijen:1990:BOB",
chapter = "27",
pages = "233--242",
year = "1990",
bibdate = "Mon Feb 03 07:07:55 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprinted in \cite[Chapter 11]{Knuth:2010:SPD}. This
paper discusses the algorithm used in {\TeX} for
converting between decimal and scaled fixed-point
binary values, and for guaranteeing a minimum number of
digits in the decimal representation. See also
\cite{Clinger:1990:HRF,Clinger:2004:RHR} for decimal to
binary conversion,
\cite{Steele:1990:HPF,Steele:2004:RHP} for binary to
decimal conversion, and \cite{Gries:1990:BDO} for an
alternate proof of Knuth's algorithm.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Koren:1990:EEF,
author = "I. Koren and O. Zinaty",
title = "Evaluating Elementary Functions in a Numerical
Coprocessor Based on Rational Approximations",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-39",
number = "8",
pages = "1030--1037",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57042",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:30 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kornerup:1990:ARB,
author = "Peter Kornerup and David W. Matula",
title = "An algorithm for redundant binary bit-pipelined
rational arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1106--1115",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57048",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57048",
abstract = "The authors introduce a redundant binary
representation of the rationals and an associated
algorithm for computing the sum, difference, product,
quotient, and other useful functions of two rational
operands, using this representation. The algorithm
extends R.W. Gosper's (1972) partial quotient
arithmetic algorithm and allows the design of an online
arithmetic unit with computations granularized at the
signed bit level. Each input or output port can be
independently set to receive/produce operands/result in
either binary radix or the binary rational
representation. The authors investigate by simulation
the interconnection of several such units for the
parallel computation of more complicated expressions in
a tree-pipelined manner, with particular regard to
measuring individual and compounded online delays",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Laakso:1990:RFP,
author = "T. Laakso and B. Zeng and I. Hartimo and Y. Neuvo",
booktitle = "{IEEE} International Conference on Systems
Engineering, 1990",
title = "Reduction of floating-point roundoff noise in
recursive digital filters with error feedback",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "244--247",
year = "1990",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The reduction of roundoff noise in floating-point
recursive digital filters by means of error feedback is
discussed. Optimal (minimum-noise) error feedback is
formulated, and it is shown to be different from the
optimal solution in the fixed-point \ldots{}",
}
@Article{Lee:1990:OPC,
author = "Vernon A. {Lee, Jr.} and Hans-J. Boehm",
title = "Optimizing programs over the constructive reals",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "102--111",
month = jun,
year = "1990",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/93542.93558",
ISBN = "0-89791-364-7",
ISBN-13 = "978-0-89791-364-5",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:53 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/93542/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p102-lee/",
abstract = "The constructive reals provide programmers with a
useful mechanism for prototyping numerical programs,
and for experimenting with numerical algorithms.
Unfortunately, the performance of current
implementations is inadequate for some potential
applications. In particular, these implementations tend
to be space inefficient, in that they essentially
require a complete computation history to be
maintained. Some numerical analysts propose that the
programmer instead be provided with variable precision
interval arithmetic, and then be required to write code
to restart a computation when the intervals become too
inaccurate. Though this model is no doubt appropriate
at times, it is not an adequate replacement for exact
arithmetic. The correct transformation from a program
operating on the constructive reals to a reasonable
program using iterated interval arithmetic can be
nontrivial and error prone. Here we present a technique
based on program slicing to both automate this process
and reduce the amount of reexecution. Thus the
programmer is still free to use the simpler abstraction
of exact real arithmetic, but we can provide a more
efficient interval arithmetic based implementation.
Some preliminary empirical results are presented.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Rice University",
affiliationaddress = "Houston, TX, USA",
annote = "Published as part of the Proceedings of PLDI'90.",
classification = "722; 723; C6110 (Systems analysis and programming);
C6120 (File organisation); C7310 (Mathematics)",
confdate = "20-22 June 1990",
conference = "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation",
conferenceyear = "1990",
conflocation = "White Plains, NY, USA",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "algorithms; Computer Operating Systems; Computer
Programming Languages --- Design; Constructive reals;
Efficient interval arithmetic based implementation;
Empirical results; Exact real arithmetic; Numerical
algorithms; Numerical analysts; Numerical programs;
Optimizing Compilers; performance; Performance; Program
Compilers; Program slicing; Reexecution; Variable
precision interval arithmetic",
meetingaddress = "White Plains, NY, USA",
meetingdate = "Jun 20--22 1990",
meetingdate2 = "06/20--22/90",
sponsor = "Assoc for Computing Machinery, Special Interest Group
on Programming Languages",
subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Optimization. {\bf F.2.1} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic. {\bf F.2.2} Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Nonnumerical Algorithms and Problems,
Computations on discrete structures.",
thesaurus = "Data structures; Mathematics computing; Programming",
}
@Article{Ling:1990:AIM,
author = "H. Ling",
title = "An approach to implementing multiplication with small
tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "5",
pages = "717--718",
month = may,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.53588",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53588",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lozier:1990:CPL,
author = "D. W. Lozier and F. W. J. Olver",
title = "Closure and Precision in Level-Index Arithmetic",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "5",
pages = "1295--1304",
month = oct,
year = "1990",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65-04 (65G05)",
MRnumber = "91f:65002",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{MacDonald:1990:IFP,
author = "Tom MacDonald",
title = "{IEEE} Floating-Point Arithmetic and {C}",
journal = j-JCLT,
volume = "2",
number = "2",
pages = "102--112",
month = sep,
year = "1990",
ISSN = "1042-5721",
bibdate = "Thu Nov 8 14:50:33 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Journal of {C} Language Translation",
}
@Article{Mandelbaum:1990:SMD,
author = "D. M. Mandelbaum",
title = "A systematic method for division with high average bit
skipping",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "1",
pages = "127--130",
month = jan,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.46287",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:19:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=46287",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{MangaEbongue:1990:PBV,
author = "Charles {Manga Ebongue}",
title = "Processeur 32 Bits en Virgule Flottante: Techniques de
Validation Fonctionnelle, {{\'E}}lectrique et Test
{\`a} la Conception. ({French}) [32-bit Floating-Point
Processor: Techniques of Functional and Electrical
Validation and Test in the Design]",
type = "Th{\`e}se Doctoral",
school = "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
address = "Paris, France",
year = "1990",
bibdate = "Thu May 09 10:03:41 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Sous la direction de Alain Greiner.",
abstract = "Cette th{\`e}se d{\'e}veloppe deux aspects de la
conception des circuits integr{\'e}s: (1) le premier
aspect correspond {\`a} la m{\'e}thodologie
d'implantation du processeur de calcul en virgule
flottante d{\'e}velopp{\'e} au laboratoire MASI par
l'{\'e}quipe de Cao \& VLSI de l'Universit{\'e} Pierre
et Marie Curie, (2) le deuxi{\'e}me aspect pr{\'e}sente
les travaux concernant une m{\'e}thodologie de test
{\`a} la conception conduisant aussi bien {\`a} la
validation fonctionnelle et {\'e}lectrique au cours de
la conception qu'{\`a} la testabilit{\'e} apr{\`e}s
fabrication. Le premier aspect a des implications {\`a}
diff{\'e}rents niveaux: (1) au niveau assemblage par
l'introduction d'une m{\'e}thodologie de conception
sp{\'e}cifique au circuit, (2) au niveau {\'e}lectrique
pour le choix et la conception d'une biblioth{\`e}que
de cellules standards qui tient compte des
caract{\'e}ristiques dynamiques des signaux sur chaque
nud du circuit. Le deuxi{\`e}me aspect a pour
r{\'e}sultat l'introduction d'une technique originale
de recherche de vecteurs de test. De m{\^e}me, la
validation fonctionnelle de ce circuit sera
invoqu{\^e}e en r{\^e}solvant les principaux
probl{\`e}mes de coh{\'e}rence entre les masques
d{\'e}ssin{\'e}s et la liste des interconnexions.",
acknowledgement = ack-nhfb,
language = "French",
}
@Book{Mar:1990:DSP,
editor = "Amy Mar",
title = "Digital signal processing applications using the
{ADSP-2100} family",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xvi + 611",
year = "1990",
ISBN = "0-13-212978-7",
ISBN-13 = "978-0-13-212978-7",
LCCN = "TK5102.5 .D44824 1990",
bibdate = "Sat Jan 15 05:58:58 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "System requirements for computer disks: IBM PC; PC-DOS
3.0.",
subject = "Signal processing; Digital techniques;
Microprocessors",
}
@Article{Margulis:1990:IMI,
author = "N. Margulis",
title = "i860 microprocessor internal architecture",
journal = j-MICROPROC-MICROSYS,
volume = "14",
number = "2",
pages = "89--96",
month = mar,
year = "1990",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Markstein:1990:CEF,
author = "P. W. Markstein",
title = "Computation of elementary functions on the {IBM RISC
System\slash 6000} processor",
journal = j-IBM-JRD,
volume = "34",
number = "1",
pages = "111--119",
month = jan,
year = "1990",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
MRclass = "65-04 (65D20)",
MRnumber = "1 057 659",
bibdate = "Sat Jan 11 17:44:01 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The additional speed and precision of the IBM RISC
System\slash 6000 floating-point unit have motivated
reexamination of algorithms to perform division, square
root, and the elementary functions. New results are
obtained which avoid the necessity of doing special
testing to get the last bit rounded correctly in
accordance with all of the IEEE rounding modes in the
case of division and square root. For the elementary
function library, a technique is described for always
getting the last bit rounded correctly in the selected
IEEE rounding mode.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "correct rounding; Division; Elementary functions;
Floating-point unit; IBM RISC System\slash 6000
processor; IEEE rounding modes; IEEE rounding modes,
IBM RISC System/6000 processor; Square root",
thesaurus = "Digital arithmetic; IBM computers; Reduced instruction
set computing",
}
@InProceedings{Matula:1990:HPD,
author = "D. Matula",
title = "Highly parallel divide and square root algorithms for
a new generation floating point processor",
crossref = "Ullrich:1990:CCA",
pages = "??--??",
year = "1990",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{McCloud:1990:FPU,
author = "S. McCloud and D. Anderson and C. DeWitt and C. Hinds
and Y. W. Ho and D. Marquette and E. Quintana",
title = "A Floating Point Unit for the 68040",
crossref = "IEEE:1990:PII",
pages = "187--190",
year = "1990",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Mills:1990:DIH,
author = "Karl Scott Mills",
title = "The design and implementation of a high performance
floating-point image processing and graphics subsystem
for the {NeXT} computer",
type = "Thesis ({M.S.E.E.})",
school = "University of Washington",
address = "Seattle, WA, USA",
pages = "v + 60 + 3",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer graphics.; Image processing --- Digital
techniques.",
}
@Article{Montoye:1990:DIR,
author = "R. K. Montoye and E. Hokenek and S. L. Runyon",
title = "Design of the {IBM RISC System\slash 6000}
floating-point execution unit",
journal = j-IBM-JRD,
volume = "34",
number = "1",
pages = "59--70",
month = jan,
year = "1990",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.341.0059",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://www.research.ibm.com/journal/rd/341/ibmrd3401G.pdf",
abstract = "The IBM RISC System\slash 6000 (RS\slash 6000)
floating-point unit (FPU) exemplifies a
second-generation RISC CPU architecture and an
implementation which greatly increases floating-point
performance and accuracy. The key feature of the FPU is
a unified floating-point multiply-add-fused unit (MAF)
which performs the accumulate operation (A*B)+C as an
indivisible operation. The paper first discusses the
motivation for MAF, explaining in some detail why it is
an appropriate addition to the floating-point
architecture in VLSI. A summary of floating-point
operations is then given, with a discussion to
demonstrate the parallelism that is possible when the
multiply and add are fused. This is followed by a
description of the two-stage pipeline used for the
version of IEEE double-precision floating-point
arithmetic used in the RS\slash 6000 processor, with
delays consistent with its over-all superscalar
second-generation RISC architecture. Then the paper
describes the interaction of logical and physical
design required to incorporate several advances in VLSI
arithmetic while accommodating required delay and
technological (physical) constraints. The results are
then summarized.",
acknowledgement = ack-nhfb,
affiliation = "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
classcodes = "B1265B (Logic circuits); B1130B (Computer-aided
circuit analysis and design); B1265F (Microprocessors
and microcomputers); C5230 (Digital arithmetic
methods); C5220 (Computer architecture); C5210B
(Computer-aided logic design)C7410D (Electronic
engineering)",
classification = "B1130B (Computer-aided circuit analysis and design);
B1265B (Logic circuits); B1265F (Microprocessors and
microcomputers); C5210B (Computer-aided logic design);
C5220 (Computer architecture); C5230 (Digital
arithmetic methods); C7410D (Electronic engineering)",
corpsource = "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "Accumulate operation; accumulate operation;
arithmetic; CAD; circuit layout CAD; digital
arithmetic; floating-point architecture; Floating-point
architecture; generation RISC CPU architecture; IBM
computers; IBM RISC System/6000 floating-point
execution unit; IBM RISC System\slash 6000
floating-point execution unit; IEEE double-precision
floating-point; IEEE double-precision floating-point
arithmetic; indivisible; Indivisible operation; logic;
multiply-add-fused unit; operation; Parallelism;
parallelism; reduced instruction set computing;
second-; Second-generation RISC CPU architecture; stage
pipeline; Superscalar second-generation RISC
architecture; superscalar second-generation RISC
architecture; two-; Two-stage pipeline; unified
floating-point; Unified floating-point
multiply-add-fused unit; VLSI arithmetic; VLSI
arithmetic, IBM RISC System/6000 floating-point
execution unit",
thesaurus = "Circuit layout CAD; Digital arithmetic; IBM computers;
Logic CAD; Reduced instruction set computing",
treatment = "P Practical",
}
@Article{Montuschi:1990:SSR,
author = "P. Montuschi and P. M. Mezzalama",
title = "Survey of square rooting algorithms",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "137",
number = "1",
pages = "31--40",
month = jan,
year = "1990",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
summary = "The paper reviews the algorithms for the computation
of square roots for binary machines. After an initial
classification, the algorithms are analysed in detail
by considering their specific peculiarities and
properties. Finally, some comments are \ldots{}",
}
@Article{Morita:1990:FMM,
author = "Hikaru Morita",
title = "A Fast Modular-Multiplication Algorithm Based on a
Higher Radix",
journal = j-LECT-NOTES-COMP-SCI,
volume = "435",
pages = "387--??",
year = "1990",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Feb 4 12:01:59 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0435.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0435/04350387.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0435/04350387.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@MastersThesis{Mueller:1990:HCA,
author = "Volker M{\"u}ller",
title = "{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle
Standardfunktionen mittels dynamischer
Defektberechnung} \toenglish {High-accuracy CORDIC
Algorithms for Real Elementary Functions by Means of
Dynamic Error Computation} \endtoenglish",
type = "{Diplomarbeit}",
school = "Institut f{\"u}r angewandte Mathematik,
Universit{\"a}t Karlsruhe",
pages = "??",
month = dec,
year = "1990",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Murthy:1990:MPA,
author = "Narayan Murthy and Allen Stix",
title = "Multiple precision arithmetic: a programming
assignment in {CS2} applying linked lists",
journal = j-SIGCSE,
volume = "22",
number = "1",
pages = "129--133",
month = feb,
year = "1990",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/319059.323431",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sat Nov 17 18:57:12 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Ohtomo:1990:FPD,
author = "Hiroyasu Ohtomo and Hisao Ishizuka and Masahiko
Kashimura and Akio Nakajima and Tetsuhiro Hira",
title = "A 32-bit Floating Point Digital Signal Processor for
Graphics Application",
journal = j-NEC-RES-DEV,
volume = "??",
number = "99",
pages = "47--??",
month = oct,
year = "1990",
CODEN = "NECRAU",
ISSN = "0048-0436",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Nippon Electric Company research and development",
}
@InProceedings{Olson:1990:FAA,
author = "T. Olson and B. Stewart",
title = "Floating-point architecture of the Am29050",
crossref = "Wescon:1990:WCR",
pages = "214--217",
year = "1990",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Am29050 is the newest member of Advanced Micro
Devices' 29K family of RISC microprocessors. It is both
binary and pin compatible with the Am29000, and also
incorporates a high-performance floating-point unit
(FPU) on chip. The FPU, which complies with the IEEE
754 standard, consists of parallel add, multiply, and
divide/square-root units, operating on single-precision
and double-precision values. In addition to the
standard operations, the FPU implements two types of
multiply-add functions, which take three operands and
produce one result. A single register file, which is
shared between the integer and floating-point units,
can supply two 64-bit operands and write back both a
32-bit integer result and a 64-bit floating-point
result in a single cycle.",
acknowledgement = ack-nhfb,
affiliation = "Adv. Micro Devices, Austin, TX, USA",
availability = "Western Periodicals Co., 13000 Rayner Street, North
Hollywood, CA 91605, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220 (Computer architecture);
C5230 (Digital arithmetic methods)",
keywords = "29K family; 64 Bit; Advanced Micro Devices; Am29050;
Double-precision; Floating point architecture; Floating
point arithmetic; Floating-point unit; FPU; IEEE 754
standard; Multiply-add functions; Parallel add; RISC
microprocessors; Single-precision",
numericalindex = "Word length 6.4E+01 bit",
thesaurus = "Computer architecture; Digital arithmetic;
Microprocessor chips; Reduced instruction set
computing",
}
@Article{Owens:1990:BSM,
author = "R. M. Owens and M. J. Irwin",
title = "Being stingy with multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "6",
pages = "809--818",
month = jun,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.53602",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53602",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Palmore:1990:CAC,
author = "J. Palmore and C. Herring",
title = "Computer arithmetic, chaos and fractals",
journal = j-PHYSICA-D,
volume = "42",
number = "1-3",
pages = "99--110",
month = jun,
year = "1990",
CODEN = "PDNPDT",
ISSN = "0167-2789 (print), 1872-8022 (electronic)",
ISSN-L = "0167-2789",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Ninth Annual International Conference of the Center
for Nonlinear Studies on Self-Organizing, Collective
and Cooperative Phenomena in Natural and Artificial
Networks",
abstract = "The authors explore aspects of computer arithmetic
from the viewpoint of dynamical systems. They
demonstrate the effects of finite precision arithmetic
in three uniformly hyperbolic chaotic dynamical
systems: Bernoulli shifts, cat maps, and pseudorandom
number generators. They show that elementary
floating-point operations in binary computer arithmetic
possess an inherently fractal structure. Each of these
dynamical systems allows us to compare the exact
results in integer arithmetic with those obtained by
using floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Department of Math., Illinois University, Urbana, IL,
USA",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
confdate = "22-26 May 1989",
conflocation = "Los Alamos, NM, USA",
fjournal = "Physica. D, Nonlinear phenomena",
journal-URL = "http://www.sciencedirect.com/science/journal/01672789",
keywords = "Bernoulli shifts; Binary computer arithmetic; Cat
maps; Chaos; Computer arithmetic; Dynamical systems;
Elementary floating-point operations; Finite precision
arithmetic; Floating-point arithmetic; Fractal
structure; Integer arithmetic; Pseudorandom number
generators; Self-similar structure; Uniformly
hyperbolic chaotic dynamical systems",
pubcountry = "Netherlands",
thesaurus = "Chaos; Digital arithmetic; Fractals; Random number
generation; Roundoff errors",
}
@InProceedings{Pan:1990:FSI,
author = "J. Pan and K. N. Levitz",
title = "A Formal Specification of the {IEEE Floating-Point
Standard} with Application to the Verification of
Floating-Point Coprocessors",
crossref = "Chen:1990:CRT",
pages = "505--510",
year = "1990",
bibdate = "Wed Dec 13 18:41:54 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A description is given of work in progress on
verifying a floating-point coprocessor based on the
MC68881/82, with respect to the IEEE standard
floating-point arithmetic (ANSI-IEEE Std 754-1985). A
complete formalization of the IEEE floating-point
standard using the HOL (high-order-logic) specification
and verification system is presented. The specification
of floating-point numbers, floating-point arithmetic
functions, rounding schemes and post-normalization is
described. In order for the specification to be
adaptable to different implementation, several model
parameters are used in specifying all the functions.
The floating-point coprocessor is specified as a
hierarchy of interpreters. The communication with the
CPU is modeled as standard interprocessor
communication. A technique for verifying hierarchies of
communicating hardware interpreters is described. (11
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Div. of Computer Science, California University,
Berkeley, CA, USA",
availability = "IEEE Computer Society Press, Los Alamitos, CA, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
keywords = "ANSI-IEEE Std 754-1985; Communicating hardware
interpreters; CPU communication; Floating-point
coprocessors; Higher order logic specification; HOL;
IEEE standard floating-point arithmetic; Interpreter
hierarchy; Interprocessor communication; MC68881/82;
Post-normalization; Rounding schemes; Standard
formalization; Verification system",
thesaurus = "Digital arithmetic; Formal specification;
Microprocessor chips; Satellite computers; Standards",
}
@Article{Parhami:1990:GSD,
author = "Behrooz Parhami",
title = "Generalized Signed-Digit Number Systems: a Unifying
Framework for Redundant Number Representations",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "1",
pages = "89--98",
month = jan,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.46283",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Feb 15 15:47:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Signed-digit (SD) number representation systems have
been defined for any radix r ?? 3 with digit values
ranging over the set $ ( - \alpha, \ldots {}, - 1, 0,
1, \ldots {}, \alpha) $, where $ \alpha $ is an
arbitrary integer in the range $ 1 / 2 r > \alpha > r
$. Such number representation systems possess
sufficient redundancy to allow for the annihilation of
carry or borrow chains and hence result in fast
propagation-free addition and subtraction. The author
refers to the above as ordinary SD number systems and
defines generalized SD number systems which contain
them as a special symmetric subclass. It is shown that
the generalization not only provides a unified view of
all redundant number systems which have proven useful
in practice (including stored-carry and stored-borrowed
systems), but also leads to new number systems not
examined before. Examples of such new number systems
are stored-carry-or-borrow systems, stored-double-carry
systems, and certain redundant decimal
representations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Payne:1990:PLCa,
author = "M. Payne and C. Schaffert and B. Wichmann",
title = "Proposal for a language compatible arithmetic
standard",
journal = j-SIGNUM,
volume = "25",
number = "1",
pages = "2--43",
month = jan,
year = "1990",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes the proposal for an arithmetic standard
which has been submitted to the American National
Standards Institute and the International Organization
for Standardization. It is being processed by the ANSI
X3T2 committee and the ISO/IEC JTC1/SC22/WG11 working
group. The specifications cover both integer and
floating point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Digital Equipment Corp, Maynard, MA, USA",
classification = "C7310 (Mathematics)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "American National Standards Institute; ANSI X3T2
committee; Floating point arithmetic; Integer
arithmetic; International Organization for
Standardization; Language compatible arithmetic
standard",
thesaurus = "Digital arithmetic; Mathematics computing; Standards",
}
@Article{Payne:1990:PLCb,
author = "M. Payne and C. Schaffert and B. Wichmann",
title = "Proposal for a language compatible arithmetic
standard",
journal = j-SIGPLAN,
volume = "25",
number = "1",
pages = "59--86",
month = jan,
year = "1990",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:49 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The proposal for an arithmetic standard has been
submitted to the American National Standard Institute
and the International Organization for Standardization.
The proposal covers both integer and floating point
arithmetic. The underlying goal is to expedite the
production of robust numerical software which is
portable among the diverse arithmetic implementations
currently in wide-spread use. The proposal requires
that a complying system provide error detection
capabilities beyond those currently required by many
language standards. The proposal requires that a
conforming system makes the values of certain
parameters known to users, although the method for
doing so is not specified. It also required a number of
useful operations, beyond those usually implemented. It
is acceptable to implement them by subroutine calls.",
acknowledgement = ack-nhfb,
affiliation = "Digital Equipment Corp., Maynard, MA, USA",
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "American National Standard Institute; Error detection
capabilities; Floating point arithmetic; International
Organization for Standardization; Language compatible
arithmetic standard; Robust numerical software;
Subroutine calls",
thesaurus = "Digital arithmetic; High level languages; Standards",
}
@Article{Peter:1990:PZW,
author = "O. Peter",
title = "{Prozessor zieht Wurzeln} \toenglish {Processor
Extracts Roots} \endtoenglish",
journal = j-CT,
volume = "1",
pages = "300--306",
year = "1990",
ISSN = "0724-8679",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "C T: Magazin f{\"u}r Computer Technik (Hannover)",
}
@Article{Piestrak:1990:DHS,
author = "S. J. Piestrak",
title = "Design of high-speed and cost-effective self-testing
checkers for low-cost arithmetic codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "3",
pages = "360--374",
month = mar,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.48866",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48866",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Popov:1990:AFA,
author = "Wladimir Popov",
title = "On the axiomatizations of floating-point arithmetics.
Contributions to computer arithmetic and
self-validating numerical methods ({Basel, 1989})",
journal = "IMACS Ann. Comput. Appl. Math.",
volume = "7",
publisher = pub-BALTZER,
address = pub-BALTZER:adr,
pages = "55--66",
year = "1990",
MRclass = "03B70 (65G05)",
MRnumber = "93g:03024",
bibdate = "Fri Dec 08 12:21:25 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Preparata:1990:PCD,
author = "F. P. Preparata and J. E. Vuillemin",
title = "Practical cellular dividers",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "5",
pages = "605--614",
month = may,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.53574",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:01 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53574",
abstract = "A discussion is presented of parallel division
algorithms that can be classified among modified higher
radix nonrestoring online division methods, where
redundant representations are extensively utilized to
speed up the operation. The network realizations of
these algorithms are cellular, or even systolic with
exclusively local control; they have both size (area)
and time of $ O(n) $, where $n$ is the length of the
dividend representation. The same structures can also
be used as a signed, digit-serial multiplier. When
suitably equipped with some control and a few
registers, the divider\slash multiplier brings
remarkable performance to large modular arithmetic, RSA
cryptography, and greatest common divisor computations.
They are also of interest for the design of
floating-point units and signal processing
applications.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure, Paris, France",
ajournal = "IEEE Trans. Comput.",
classification = "C5230 (Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Digit-serial multiplier; Divider/multiplier;
Floating-point units; Greatest common divisor
computations; Modular arithmetic; Nonrestoring online
division methods; Parallel division algorithms;
Redundant representations; RSA cryptography; Signal
processing; Signed; Systolic",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Dividing circuits; Parallel
algorithms",
}
@Article{Prince:1990:GST,
author = "Timothy Prince",
title = "Generating Source For {{\tt <float.h>}}",
journal = j-CUJ,
volume = "8",
number = "6",
pages = "119--??",
month = jun,
year = "1990",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Pugh:1990:CBF,
author = "Kenneth Pugh",
title = "Converting {BASIC} Floating Point Files to {C}",
journal = j-CUJ,
volume = "8",
type = "Questions and Answers",
number = "5",
pages = "69--??",
month = may,
year = "1990",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@TechReport{Quach:1990:IAH,
author = "N. T. Quach and M. J. Flynn",
title = "An improved algorithm for high-speed floating-point
addition",
type = "Technical Report",
number = "CSL-TR-90-442",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = aug,
year = "1990",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Quinn:1990:REL,
author = "T. Quinn and S. Tremaine",
title = "Roundoff error in long-term planetary orbit
integrations",
journal = j-ASTRON-J,
volume = "99",
number = "3",
pages = "1016--1023",
month = mar,
year = "1990",
CODEN = "ANJOAA",
ISSN = "0004-6256 (print), 1538-3881 (electronic)",
ISSN-L = "0004-6256",
bibdate = "Tue Dec 12 09:17:24 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The dominant source of error in most long-term
integrations of the solar system is roundoff, which
leads to a fractional energy error of order $ n i_n $
where $n$ is the number of steps and $ i_n $ is the
precision of the floating-point arithmetic. The most
accurate computers are those with optimal
floating-point arithmetic, that is, arithmetic in which
the result of evaluating in arithmetic expression is
the representable number closest to the true value of
that expression. The authors argue that when
floating-point arithmetic is optimal, most of the
roundoff error arises from two sources: the approximate
representation of the numerical coefficients used in
multistep integration formulas, and the additions
required to evaluate these formulas. The authors
present an algorithm that removes these two sources of
error in computers with optimal arithmetic, and appears
to reduce the fractional energy error to of order $
n^{0.5i}_n $ (at least for $ n < $ or approximately $ =
10^7 $) , at the cost of less than a factor of $2$
increase in computing time.",
acknowledgement = ack-nhfb,
affiliation = "Canadian Inst. for Theor. Astrophys., Toronto
University, Ont., Canada",
classification = "A9510C (Celestial mechanics); A9575P (Mathematical
and computer techniques); A9630 (Planets and
satellites); C7350 (Astronomy and astrophysics)",
fjournal = "Astronomical Journal",
journal-URL = "http://iopscience.iop.org/1538-3881",
keywords = "Addition error; Approximate representation; Arithmetic
expression; Celestial mechanics; Computing time;
Floating-point arithmetic precision; Fractional energy
error; Integration steps number; Long-term planetary
orbit integrations; Multistep integration formulas;
Numerical coefficients; Optimal floating-point
arithmetic; Representable number; Roundoff error; Solar
system long-term stability; True value",
thesaurus = "Astronomical techniques; Astronomy computing;
Celestial mechanics; Error correction; Planets; Solar
system; Stability",
}
@InProceedings{Ramamoorthy:1990:MRN,
author = "P. A. Ramamoorthy and P. E. Pace and D. Styer",
booktitle = "Proceedings of the 33rd Midwest Symposium on Circuits
and Systems, 1990",
title = "A modified residue number system with applications to
signal processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1018--1021",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1990.140897",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors have developed a number system, the
modified residue number system (MRNS), which is a
direct consequence of considering the need for a more
convenient folding waveform that can be implemented
easily. Through various arrangements of the \ldots{}",
}
@InProceedings{Rao:1990:SAA,
author = "B. D. Rao",
booktitle = "Signals, Systems and Computers, 1990. 1990 Conference
Record Twenty-Fourth Asilomar Conference on. 5--7 Nov
1990",
title = "A systematic approach for the analysis of roundoff
noise in floating point digital filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "495",
year = "1990",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@Article{Rauchwerger:1990:MFPa,
author = "Lawrence Rauchwerger and Michael P. Farmwald",
title = "A multiple floating point coprocessor architecture",
journal = j-COMP-ARCH-NEWS,
volume = "18",
number = "2",
pages = "15--24",
month = jun,
year = "1990",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:46 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@InProceedings{Rauchwerger:1990:MFPb,
author = "L. Rauchwerger and P. M. Farmwald",
title = "A multiple floating point coprocessor architecture",
crossref = "IEEE:1990:MMM",
pages = "216--222",
year = "1990",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "General purpose microprocessor based computers usually
speed their arithmetic processing performance by using
a floating point co-processor. Because adding more
co-processors represents neither a technological nor a
cost problem, the authors investigated a system based
on a MIPS R2000 and 4 floating point units. They show a
block diagram of such an implementation and how two
important scientific operations can be accelerated
using a single unmodified data bus. A large percentage
of the engineering applications are solved with the
help of linear algebra methods like BLAS3 algorithms;
it is precisely for these primitives that the proposed
architecture brings significant performance gains. The
first operation described is a matrix multiplication
algorithm, its timing diagram and some results. Next a
polynomial evaluation technique is examined. Finally
they show how to use the same ideas with various other
microprocessors.",
acknowledgement = ack-nhfb,
affiliation = "Center for Supercomput. Res. and Dev., Illinois
University, Urbana-Champaign, IL, USA",
classification = "C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
keywords = "Arithmetic processing performance; BLAS3; Engineering
applications; Matrix multiplication algorithm;
Microprocessors; MIPS R2000; Multiple floating point
coprocessor architecture; Polynomial evaluation; RISC",
thesaurus = "Computer architecture; Digital arithmetic; Satellite
computers",
}
@Article{Reemtsen:1990:MFR,
author = "Rembert Reemtsen",
title = "Modifications of the First {Remez} Algorithm",
journal = j-SIAM-J-NUMER-ANAL,
volume = "27",
number = "2",
pages = "507--518",
month = apr,
year = "1990",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0727031",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65D15",
MRnumber = "91a:65039",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Reif:1990:OSI,
author = "John H. Reif and Stephen R. Tate",
title = "Optimal Size Integer Division Circuits",
journal = j-SIAM-J-COMPUT,
volume = "19",
number = "5",
pages = "912--924",
month = oct,
year = "1990",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68Q40 (68Q15 68Q25)",
MRnumber = "91h:68092",
MRreviewer = "Helmut Alt",
bibdate = "Mon Nov 29 11:01:37 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/19/5;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@PhdThesis{Rowan:1990:FSA,
author = "Thomas Harvey Rowan",
title = "Functional stability analysis of numerical
algorithms",
type = "{Ph.D.} thesis",
school = "University of Texas at Austin",
address = "Austin, TX, USA",
pages = "xii + 206",
month = may,
year = "1990",
bibdate = "Mon Oct 21 18:08:52 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://search.proquest.com/pqdtglobal/docview/303865032",
abstract = "The standard technique for detecting instability in
numerical algorithms is backward error analysis. The
analysis is difficult and tedious when performed by
hand, while attempts to automate it have always placed
severe restrictions on the tested numerical algorithms.
A new approach for detecting instability, functional
stability analysis, removes these restrictions by
treating numerical algorithms as black boxes. The
approach consists of two parts. The first part uses the
relationship between the forward error, the backward
error, and a problem's condition to define a function
that estimates a lower bound on the backward error. In
the second part, a new optimization method maximizes
the function. A numerical algorithm is unstable if the
maximization shows that the backward error can become
large. Since numerical algorithms are treated as black
boxes, functional stability analysis normally requires
little more than an executable version of a numerical
algorithm to determine if it is unstable.",
acknowledgement = ack-nhfb,
advisor = "Alan K. Cline",
}
@Article{Sam:1990:GMR,
author = "H. Sam and A. Gupta",
title = "A generalized multibit recoding of two's complement
binary numbers and its proof with application in
multiplier implementations",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1006--1015",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57039",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Schatte:1990:SBF,
author = "Peter Schatte",
title = "On the stochastic behaviour of the floating point
mantissas of sums",
journal = "J. Inform. Process. Cybernet.",
volume = "26",
number = "4",
pages = "249--254",
year = "1990",
MRclass = "60F99 (11K99)",
MRnumber = "91m:60065",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
reviewer = "Eugenijus Manstavi{\v{c}}ius",
}
@Article{Schimandle:1990:MBC,
author = "James Schimandle",
title = "{Microsoft BASIC}'s and {C}'s Floating Point Formats",
journal = j-CUJ,
volume = "8",
type = "Letter",
number = "7",
pages = "139--??",
month = jul,
year = "1990",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Sheppard:1990:EYF,
author = "Gene Sheppard",
title = "Evaluating Your Floating Point Library",
journal = j-CUJ,
volume = "8",
number = "8",
pages = "121--??",
month = aug,
year = "1990",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Silverman:1990:PPA,
author = "Robert D. Silverman",
title = "Parallel polynomial arithmetic over finite rings",
journal = j-J-PAR-DIST-COMP,
volume = "10",
number = "3",
pages = "265--270",
month = nov,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "MITRE Corp",
affiliationaddress = "Bedford, Ma, USA",
classification = "723; 921; C4130 (Interpolation and function
approximation); C4240 (Programming and algorithm
theory); C5230 (Digital arithmetic methods)",
corpsource = "Mitre Corp., Bedford, MA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Alliant FX/8; Chinese remainder; Chinese Remainder
Theorem; Computer Systems, Digital--Parallel
Processing; Computers, Digital--Computational Methods;
Convolution Algorithms; digital arithmetic; Finite
Rings; finite rings; Mathematical Techniques; message
passing; message passing parallel computer;
multiplication; parallel algorithms; parallel
computers; parallel polynomial arithmetic; performance;
polynomial; Polynomial Arithmetic; Polynomials;
polynomials; residue number systems; shared memory;
Symult S2010; theorem",
treatment = "P Practical",
}
@InProceedings{Silverstein:1990:USM,
author = "Joel D. Silverstein and Steven E. Sommars and
Yio-Chian Tao",
title = "The {UNIX} System Math Library, a Status Report",
crossref = "USENIX:1990:PWU",
pages = "117--131",
year = "1990",
bibdate = "Thu Sep 01 11:51:21 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Sips:1990:NML,
author = "Henk J. Sips and Hai Xiang Lin",
title = "A new model for on-line arithmetic with an application
to the reciprocal calculation",
journal = j-J-PAR-DIST-COMP,
volume = "8",
number = "3",
pages = "218--230",
month = mar,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Delft Univ of Technology",
affiliationaddress = "Delft, Neth",
classification = "722; 723; 921; C4130 (Interpolation and function
approximation); C5230 (Digital arithmetic methods)",
corpsource = "Delft University of Technol., Netherlands",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "adapted Newton--Raphson; approximation method;
Approximation Theory; arithmetic; attainable on-;
computation pipelining; Computational Models; Computer
Systems, Digital--On Line Operation; conditional
on-line; cycle times; delay; delays; Digital
Arithmetic; digital arithmetic; exact function value;
functions; iteration; iteration method; iterative;
Iterative Methods; iterative methods; line delay;
Mathematical Techniques; on-line arithmetic; on-line
computation; on-line digits; online arithmetic;
overlapping computation; pipeline; processing;
reciprocal calculation; seed table; step; table
look-up",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Skelton:1990:GSE,
author = "R. E. Skelton and D. Williamson",
booktitle = "Proceedings of the 29th {IEEE} Conference on Decision
and Control, 1990",
title = "Guaranteed state estimation accuracies with roundoff
error",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "297--298",
year = "1990",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Kalman filter theory is modified to accommodate
roundoff errors in state computation. Two problems are
solved: (i) choosing the wordlength required for each
state computation to guarantee specified estimation
accuracies of multiple output variables \ldots{}",
}
@TechReport{Slishman:1990:FPR,
author = "G. Slishman",
title = "Fast and Perfectly Rounding Decimal\slash Hexadecimal
Conversions",
type = "Research Report",
number = "RC-15683",
institution = pub-IBM-WATSON,
address = pub-IBM-WATSON:adr,
year = "1990",
bibdate = "Fri Apr 21 07:04:09 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Steele:1990:HPF,
author = "Guy L. {Steele Jr.} and Jon L. White",
title = "How to Print Floating-Point Numbers Accurately",
journal = j-SIGPLAN,
volume = "25",
number = "6",
pages = "112--126",
month = jun,
year = "1990",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/93548.93559",
ISBN = "0-89791-364-7",
ISBN-13 = "978-0-89791-364-5",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:15:53 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/93542/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib",
note = "See also input algorithm in
\cite{Clinger:1990:HRF,Clinger:2004:RHR}, and a faster
output algorithm in \cite{Burger:1996:PFP} and
\cite{Knuth:1990:SPW}, IBM S/360 algorithms in
\cite{Abbott:1999:ASS} for both IEEE 754 and S/360
formats, and a twenty-year retrospective in
\cite{Steele:2004:RHP}. In electronic mail dated Wed,
27 Jun 1990 11:55:36 EDT, Guy Steele reported that an
intrepid pre-SIGPLAN 90 conference implementation of
what is stated in the paper revealed 3 mistakes:
\begin{itemize} \item[1.] Table~5 (page 124):\par
\noindent insert {\tt k <-- 0} after assertion, and
also delete {\tt k <-- 0} from Table~6. \item[2.]
Table~9 (page 125):\par \noindent \begin{tabular} {ll}
for & {\tt -1:USER!({"}{"});} \\
substitute & {\tt -1:USER!({"}0{"});} \end{tabular}\par
\noindent and delete the comment. \item[3.] Table~10
(page 125):\par \noindent \begin{tabular}{ll} for &
{\tt fill(-k, "0")}\\
substitute & {\tt fill(-k-1, "0")} \end{tabular}
\end{itemize}
\def\EatBibTeXPeriod#1{\ifx#1.\else#1\fi}\EatBibTeXPeriod",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p112-steele/",
abstract = "Algorithms are presented for accurately converting
floating-point numbers to decimal representation. The
key idea is to carry along with the computation an
explicit representation of the required rounding
accuracy. The authors begin with the simpler problem of
converting fixed-point fractions. A modification of the
well-known algorithm for radix-conversion of
fixed-point fractions by multiplication explicitly
determines when to terminate the conversion process; a
variable number of digits are produced. They derive two
algorithms for free-format output of floating-point
numbers. Finally, they modify the free-format
conversion algorithm for use in fixed-format
applications. Information may be lost if the fixed
format provides too few digit positions, but the output
is always correctly rounded. On the other hand, no
`garbage digits' are ever produced, even if the fixed
format specifies too many digit positions (intuitively,
the `4/3 prints as 1.333333328366279602' problem does
not occur).",
acknowledgement = ack-nhfb,
affiliation = "Thinking Machines Corp",
affiliationaddress = "Cambridge, MA, USA",
classification = "722; 723; C5230 (Digital arithmetic methods); C7310
(Mathematics)",
confdate = "20-22 June 1990",
conference = "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation",
conferenceyear = "1990",
conflocation = "White Plains, NY, USA",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "algorithms; computer programming languages; computers,
digital --- computational methods; conversion process;
correct rounding; decimal decimal representation;
design; digit positions; explicit representation;
fixed-format applications; fixed-point fractions;
floating point numbers; floating-point arithmetic;
floating-point numbers; free-format conversion
algorithm; free-format output; garbage digits;
performance; radix-conversion; rounding accuracy;
verification",
remark = "Published as part of the Proceedings of PLDI'90.",
sponsor = "Assoc for Computing Machinery, Special Interest Group
on Programming Languages",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic.",
thesaurus = "Digital arithmetic; Mathematics computing",
xxabstract = "We present algorithms for accurately converting
floating-point numbers to decimal representation. The
key idea is to carry along with the computation an
explicit representation of the required rounding
accuracy. We begin with the simpler problem of
converting fixed-point fractions. A modification of the
well-known algorithm for radix-conversion of
fixed-point fractions by multiplication explicitly
determines when to terminate the conversion process; a
variable number of digits are produced. We then derive
two algorithms for free-format output of floating-point
numbers. Finally, we modify the free-format conversion
algorithm for use in fixed-format applications.",
}
@Article{Su:1990:ASS,
author = "C.-C. Su and H.-Y. Lo",
title = "An algorithm for scaling and single residue error
correction in residue number systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1053--1064",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57044",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57044;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2065",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "An algorithm for scaling and single residue digit
error correction is proposed. This algorithm is fully
based on mixed radix conversion (MRC). The redundant
digits of MRC can be used to establish a lookup table
to correct single residue digit \ldots{}",
}
@InProceedings{Sun:1990:FAM,
author = "Jenn-Dong Sun and H. Krishna",
booktitle = "Conference Record Twenty-Fourth Asilomar Conference on
Signals, Systems and Computers, 5--7 Nov 1990",
title = "Fast Algorithms for Multiple Errors Detection and
Correction in Redundant Residue Number Systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "831",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1990.140897",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@Book{Tabak:1990:RS,
author = "Daniel Tabak",
title = "{RISC} Systems",
publisher = pub-JW,
address = pub-JW:adr,
pages = "xii + 300",
year = "1990",
ISBN = "0-471-92694-9",
ISBN-13 = "978-0-471-92694-8",
LCCN = "QA76.9.A73.T294 1990",
bibdate = "Wed Aug 10 11:51:06 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$49.95",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
}
@Article{Tang:1990:AET,
author = "Ping Tak Peter Tang",
title = "Accurate and Efficient Testing of the Exponential and
Logarithm Functions",
journal = j-TOMS,
volume = "16",
number = "3",
pages = "185--200",
month = sep,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65-04 (65G99)",
MRnumber = "1 070 797",
bibdate = "Sun Sep 04 23:14:59 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/79505.79506;
http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
abstract = "Table-driven techniques can be used to test highly
accurate implementation of EXP LOG. The largest error
observed in EXP and LOG accurately to within 1/500 unit
in the last place are reported in our tests. Methods to
verify the tests' reliability are discussed. Results of
applying the tests to our own as well as to a number of
other implementations of EXP and LOG are presented.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; languages; verification",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Certification and testing. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Portability.",
}
@TechReport{Tang:1990:SSI,
author = "P. T. P. Tang",
title = "Some Software Implementations of the Functions Sine
and Cosine",
number = "Report ANL-90/3",
institution = "Argonne National Laboratory",
address = "Argonne, IL, USA",
pages = "27",
month = apr,
year = "1990",
bibdate = "Mon Sep 12 23:55:17 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Tang:1990:TDIa,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the Logarithm Function
in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "16",
number = "4",
pages = "378--400",
month = dec,
year = "1990",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sun Sep 04 23:26:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
abstract = "Algorithms and implementation details for the
logarithm functions in both single and double precision
of IEEE 754 arithmetic are presented here. With a table
of moderate size, the implementation need only working-
precision arithmetic and are provably accurate to
within 0.57 ulp.",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; design; performance; reliability;
standardization; theory; verification",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@TechReport{Tang:1990:TDIb,
author = "P. T. P. Tang",
title = "Table-driven Implementation of the Expm1 Function in
{IEEE} Floating-Point Arithmetic",
number = "Preprint MCS-P144-0390",
institution = "Argonne National Laboratory",
address = "Argonne, IL, USA",
pages = "??",
month = mar,
year = "1990",
bibdate = "Mon Sep 12 23:55:14 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@TechReport{Teetz:1990:SNS,
author = "Ingo Teetz and Thomas Fischer and Walter Issel",
title = "{Die Sprache NBSF fur die strukturelle Beschreibung
von Schaltkreisen.: Eine Darstellung am Beispiel eines
Gleitkomma-Prozessors}",
type = "Report",
number = "R-Math-01/90 0233-2876",
institution = "Akademie der Wissenschaften der DDR,
Karl-Weierstrass-Institut fur Mathematik",
address = "Berlin, Germany",
pages = "vii + 79",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer hardware description languages.;
Floating-point arithmetic.; NBSF (Computer hardware
description language)",
remark = "Summary in English and German.",
}
@InCollection{Trefethen:1990:PSP,
author = "L. N. Trefethen and M. H. Gutknecht",
title = "{Pad{\'e}}, Stable {Pad{\'e}}, and
{Chebyshev--Pad{\'e}} Approximation",
crossref = "Mason:1990:AAI",
pages = "??--??",
year = "1990",
bibdate = "Thu Sep 01 12:23:25 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Tricker:1990:ERP,
author = "A. R. Tricker",
title = "The effect of rounding on the power level of certain
normal test statistics",
journal = j-J-APPL-STAT,
volume = "17",
number = "2",
pages = "219--228",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1080/757582833",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:16:18 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "5 Jun 2011",
}
@Article{Tricker:1990:ERSa,
author = "A. R. Tricker",
title = "The effect of rounding on the significance level of
certain normal test statistics",
journal = j-J-APPL-STAT,
volume = "17",
number = "1",
pages = "31--38",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1080/757582644",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:16:16 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "18 Jul 2011",
}
@Article{Tricker:1990:ERSb,
author = "A. R. Tricker",
title = "The effect of rounding on the significance level and
power of certain test statistics for non-normal data",
journal = j-J-APPL-STAT,
volume = "17",
number = "3",
pages = "329--340",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1080/02664769000000005",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Tue Sep 6 11:16:20 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "28 Jul 2006",
}
@Article{vanderVorst:1990:CBP,
author = "H. A. {van der Vorst}",
title = "The convergence behaviour of preconditioned {CG} and
{CG-S} in the presence of rounding errors",
journal = j-LECT-NOTES-MATH,
volume = "1457",
pages = "126--136",
year = "1990",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0090905",
ISBN = "3-540-53515-2 (print), 3-540-46746-7 (e-book)",
ISBN-13 = "978-3-540-53515-7 (print), 978-3-540-46746-5
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
MRclass = "65F35",
MRnumber = "1101632 (92a:65141)",
MRreviewer = "Seymour Bachmuth",
bibdate = "Fri May 9 19:07:18 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1990.bib;
MathSciNet database",
URL = "http://link.springer.com/chapter/10.1007/BFb0090905/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0090897",
book-URL = "http://www.springerlink.com/content/978-3-540-46746-5",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
MRauthor = "H. A. {van der Vorst}",
mynote = "Not copied. No actual error analysis. Just
explanations based on his paper with van der Sluis
(don't reference Greenbaum!).",
}
@MastersThesis{VanElsen:1990:OCL,
author = "Lucien William {Van Elsen}",
title = "An optimizing compiler for low-level floating point
operations",
type = "Thesis ({B.S.})",
school = "Massachusetts Institute of Technology, Dept. of
Electrical Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "v + 56",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by William J. Dally.",
acknowledgement = ack-nhfb,
}
@Article{Vuillemin:1990:ERC,
author = "J. E. Vuillemin",
title = "Exact real computer arithmetic with continued
fractions",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1087--1105",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57047",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:04 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57047",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Wallis:1990:IFP,
editor = "Peter J. L. Wallis",
title = "Improving Floating-Point Programming",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xvi + 191",
year = "1990",
ISBN = "0-471-92437-7",
ISBN-13 = "978-0-471-92437-1",
LCCN = "QA76.6 .I446 1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$60.00",
acknowledgement = ack-nhfb,
keywords = "Computation by computer systems --- Floating point
representation; Electronic digital computers ---
Programming.; Floating-point arithmetic.;
Floating-point arithmetic., Compiling (Electronic
computers)",
}
@Article{Weber:1990:EHP,
author = "Ken Weber",
title = "An experiment in high-precision arithmetic on shared
memory multiprocessors",
journal = j-SIGSAM,
volume = "24",
number = "2",
pages = "22--40",
month = apr,
year = "1990",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Wed Oct 5 08:31:59 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "??",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Wigley:1990:MRR,
author = "N. M. Wigley and G. A. Jullien",
title = "On modulus replication for residue arithmetic
computations of complex inner products",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "8",
pages = "1065--1076",
month = aug,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.57045",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:03 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57045",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wingler:1990:TMI,
author = "Eric Wingler",
title = "The Teaching of Mathematics: An Infinite Product
Expansion for the Square Root Function",
journal = j-AMER-MATH-MONTHLY,
volume = "97",
number = "9",
pages = "836--839",
month = nov,
year = "1990",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:09 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@MastersThesis{Wong:1990:PFP,
author = "Kar-pang Wong",
title = "The precision of floating point computation in digital
computer",
type = "Thesis ({M.S. in Computer Science})",
school = "University of Wisconsin, Milwaukee",
address = "Milwaukee, WI, USA",
pages = "vii + 45",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Electronic digital computers --- Programming.;
Floating-point arithmetic.",
}
@Article{Wong:1990:QNF,
author = "P. W. Wong",
title = "Quantization noise, fixed-point multiplicative
roundoff noise, and dithering",
journal = j-IEEE-TRANS-ACOUST-SPEECH,
volume = "38",
number = "2",
pages = "286--300",
month = feb,
year = "1990",
CODEN = "IETABA",
ISSN = "0096-3518",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Acoustics, Speech, and Signal
Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
summary = "The author considers the characteristics of the error
resulting when a continuous amplitude signal $x_n$ is
quantized and then multiplied by a constant multiplier
a under fixed-point roundoff arithmetic. It is shown
that \ldots{}",
}
@Article{Yager:1990:SNM,
author = "T. Yager",
title = "{Sony NeWS} and {MIPS Magnum}: a double shot of
{RISC}",
journal = j-BYTE,
volume = "15",
number = "13",
pages = "172--175",
month = dec,
year = "1990",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 18:39:30 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5430 (Microcomputers)",
fjournal = "BYTE Magazine",
keywords = "20 MHz; 25 MHz; Fast color graphics; Floating-point
acceleration; High-density 3/sup 1///sub 2/-inch floppy
disk; MIPS Magnum 3000; MIPS R3000 RISC CPU chip set;
Quarter-inch cartridge tape drives; RISC/OS; Sony NeWS
3710; System V release 4; Thick-wire Ethernet port;
Unix workstations; X Window System",
numericalindex = "Frequency 2.0E+07 Hz; Frequency 2.5E+07 Hz",
thesaurus = "Computer evaluation; Microcomputers; Workstations",
}
@MastersThesis{Yang:1990:PRN,
author = "George Chia-Jin Yang",
title = "A parametric roundoff noise analysis of second-order
state-space digital filters with floating-point
arithmetic",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vii + 67",
year = "1990",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics).; Floating-point
arithmetic.",
}
@Article{Yeh:1990:RTI,
author = "H.-G. Yeh",
title = "Real-Time Implementation of a Narrow-Band {Kalman}
Filter with a Floating-Point Processor {DSP32}",
journal = j-IEEE-TRANS-IND-ELECTRON,
volume = "37",
number = "1",
pages = "13--18",
month = feb,
year = "1990",
CODEN = "ITIED6",
DOI = "https://doi.org/10.1109/41.45838",
ISSN = "0278-0046 (print), 1557-9948 (electronic)",
ISSN-L = "0278-0046",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Industrial Electronics",
summary = "The author presents experimental results from two
studies. First, a real-time narrowband Kalman filter is
implemented with a floating-point digital processor
DSP32. The real-time capability of this narrowband
filter is investigated by varying parameters \ldots{}",
}
@Article{Yoon:1990:MTP,
author = "Hyunsoo Yoon and Kyungsook Y. Lee and Amos Bahiri",
title = "On the modulo {$M$} translators for the prime memory
system",
journal = j-J-PAR-DIST-COMP,
volume = "8",
number = "1",
pages = "72--76",
month = jan,
year = "1990",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Ohio State Univ",
affiliationaddress = "Columbus, OH, USA",
classification = "722; 723; C5230 (Digital arithmetic methods)",
corpsource = "Department of Comput. and Inf. Sci., Ohio State
University, Columbus, OH, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "array processor; binary number system; Burroughs
Scientific Processor; Burroughs Scientific Processor
(bsp); casting out nine rule; Computer Operating
Systems; Computer Systems Programming--Utility
Programs; Computer Systems, Digital--Parallel
Processing; conflict-free access; decimal
floating-point arithmetic; decimal number system;
digital arithmetic; Modulo M Computation; modulo M
translators; parallel algorithms; prime memory system;
Program Translators; SIMD Architecture; SIMD shared
memory parallel processor",
treatment = "P Practical",
}
@Article{Zarowski:1990:AMH,
author = "C. J. Zarowski and H. C. Card",
title = "On addition and multiplication with {Hensel} codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "39",
number = "12",
pages = "1417--1423",
month = dec,
year = "1990",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.61062",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 14:20:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61062",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Zelniker:1990:PBD,
author = "G. S. Zelniker and F. J. Taylor",
booktitle = "Conference Record Twenty-Fourth Asilomar Conference on
Signals, Systems and Computers, 5--7 Nov 1990",
title = "Prime Blocklength Discrete {Fourier} Transforms
Utilising the Polynomial Residue Number System",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "314",
year = "1990",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1990.140897",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InCollection{Aberth:1991:CHO,
author = "Oliver Aberth",
title = "The Conversion of a High Order Programming Language
from Floating-Point Arithmetic to Range Arithmetic",
crossref = "Meyer:1991:CAP",
pages = "1--4",
year = "1991",
DOI = "https://doi.org/10.1007/978-1-4613-9092-3_1",
bibdate = "Fri Sep 22 18:54:58 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Adali:1991:FPR,
author = "T. Adali and S. H. Ardalan",
booktitle = "Acoustics, Speech, and Signal Processing, 1991.
{ICASSP-91., 1991} International Conference on. 14--17
April 1991",
title = "Fixed-point roundoff error analysis of the {RLS}
algorithm with time-varying channels",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1865--1868",
year = "1991",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors derive the steady-state mean square
prediction error expression for the fixed-point RLS
(recursive least squares) algorithm for the case of
time-varying channel estimation, which is modeled as a
first-order Markov tapped delay line. It \ldots{}",
}
@Article{Alia:1991:VMM,
author = "G. Alia and E. Martinelli",
title = "A {VLSI} modulo $m$ multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "7",
pages = "873--878",
month = jul,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83626",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83626",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Alverson:1991:IDU,
author = "Robert Alverson",
title = "Integer Division Using Reciprocals",
crossref = "Kornerup:1991:PIS",
pages = "186--190",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Alverson.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10; correct rounding; floating-point
arithmetic",
remark = "Demonstrates a correctly-rounded algorithm for integer
division that requires six floating-point
multiplications and a table lookup. For comparison,
\cite{Markstein:2000:IEF} shows an algorithm that needs
seven multiply-adds and a reciprocal approximation.",
}
@Article{Anido:1991:IDI,
author = "M. Lois Anido",
title = "Improving the division instruction of
application-specific {RISCs}",
journal = j-MICROPROC-MICROPROG,
volume = "32",
number = "1-5",
pages = "13--21",
month = aug,
year = "1991",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "17th EUROMICRO Symposium on Microprocessing and
Microprogramming. Hardware and Software Design
Automation.",
abstract = "Presents the development and application of a signed
radix-4 division algorithm to a RISC architecture,
where the internal ALU Manchester carry adder is used
to maintain the partial remainder in irredundant form.
There are division algorithms which are faster than the
one described in this paper, however they usually make
use of a redundant representation of the partial
remainder and require carry-save adders which are not
normally used in the integer execution unit of RISCs.
The method presented in this contribution employs 3x
divisor multiples and uses a reduced next divisor
multiple estimate table which is implemented by a small
and fast logic. Alternative radix-4 schemes with
quotient digits (-2,-1,0,1,2) require large and slow
PLAs for quotient digit generation. Additionally, there
is no need for positive and negative quotient registers
because quotient bits are generated on-the-fly by a
small-sized logic, concurrently with partial remainder
formation. This method also deals directly with signed
two's complement numbers, eliminating the need for
additional instructions for sign conversion. The
application of this radix-4 division algorithm provides
a two-bits-at-a-time division instruction, instead of
the traditional single bit approach used in some RISCs.
The speedup achieved can be very important in many
numerically intensive applications, in which the use of
floating-point units is not essential.",
acknowledgement = ack-nhfb,
affiliation = "Univ. Federal do Rio de Janeiro, Brazil",
classification = "C5220 (Computer architecture); C5230 (Digital
arithmetic methods)",
confdate = "2-5 Sept. 1991",
conflocation = "Vienna, Austria",
fjournal = "Microprocessing and Microprogramming",
keywords = "3X divisor multiples; Application-specific RISCs;
Binary division; Division instruction; Internal ALU
Manchester carry adder; Irredundant form; Logic;
Numerically intensive applications; Partial remainder;
Quotient bits; Quotient digits; Reduced next divisor
multiple estimate table; RISC architecture; Signed
radix-4 division algorithm; Signed two's complement
numbers; Speedup",
pubcountry = "Netherlands",
thesaurus = "Application specific integrated circuits; Digital
arithmetic; Reduced instruction set computing",
}
@Article{Anonymous:1991:FDC,
author = "Anonymous",
title = "{60M-flops}, floating-point {DSP} chip",
journal = j-EDN,
volume = "36",
number = "13",
pages = "80--??",
month = jun,
year = "1991",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "EDN",
}
@Article{Anonymous:1991:SIS,
author = "Anonymous",
title = "{SCAN-1991: International Symposium on Computer
Arithmetic and Scientific Computation}",
journal = j-J-COMPUT-APPL-MATH,
volume = "34",
number = "2",
pages = "N13--N14",
day = "4",
month = apr,
year = "1991",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:20:48 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704279190071Q",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Arambepola:1991:CVA,
author = "B. Arambepola",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 11--14 June 1991",
title = "Common {VLSI} architecture for a practically useful
residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2951--2954",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1991.176164",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "An architecture is presented for carrying out modulo
arithmetic in a practically useful residue number
system. An important feature of this is that it allows
a single hardware design to be used for all moduli. An
application of this architecture is \ldots{}",
}
@Book{Arvo:1991:GGI,
author = "James Arvo",
title = "Graphics gems {II}",
volume = "2",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xxxii + 643",
year = "1991",
ISBN = "0-12-064480-0",
ISBN-13 = "978-0-12-064480-3",
LCCN = "T385 .G6972 1991",
bibdate = "Mon Aug 24 17:12:23 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Graphics Gems",
URL = "http://www.sciencedirect.com/science/book/9780080507545",
ZMnumber = "0774.68010",
abstract = "\booktitle{Graphics Gems II} is a collection of
articles shared by a diverse group of people that
reflect ideas and approaches in graphics programming
which can benefit other computer graphics programmers.
This volume presents techniques for doing well-known
graphics operations faster or easier. The book contains
chapters devoted to topics on two-dimensional and
three-dimensional geometry and algorithms, image
processing, frame buffer techniques, and ray tracing
techniques. The radiosity approach, matrix techniques,
and numerical and programming techniques are likewise
discussed.",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
tableofcontents = "Foreword / Andrew Glassner \\
The Area of a Simple Polygon / Jon Rokne \\
Intersection of Line Segments / Mukesh Prasad \\
Distance from a Point to a Line / Jack C. Morrison \\
An Easy Bounding Circle / Jon Rokne \\
The Smallest Circle Containing the Intersection of Two
Circles / Jon Rokne \\
Appolonius's 10th Problem / Jon Rokne \\
A Peano Curve Generation Algorithm / Ken Musgrave \\
Space-Filling Curves and a Measure of Coherence /
Douglas Voorhies \\
Scanline Coherent Shape Algebra / Jonathan E. Steinhart
\\
Image Smoothing and Sharpening by Discrete Convolution
/ Dale A. Schumacher \\
A Comparison of Digital Halftoning Techniques / Dale A.
Schumacher \\
Color Dithering / Spencer W. Thomas and Rod G. Bogart
\\
Fast Anamorphic Image Scaling / Dale A. Schumacher \\
Real Pixels / Greg Ward \\
A Fast 90-Degree Bitmap Rotator / Sue-Ken Yap \\
Rotation of Run-Length Encoded Image Data / Jeff Holt
\\
Adaptive Run-Length Encoding / Andrew S. Glassner \\
Image File Compression Made Easy / Alan W. Paeth \\
An Optimal Filter for Image Reconstruction / Nelson Max
\\
Noise Thresholding in Edge Images / John Schlag \\
Computing the Area, the Circumference, and the Genus of
a Binary Digital Image / Hanspeter Bieri and Andreas
Kohler \\
Efficient Inverse Color Map Computation / Spencer W.
Thomas \\
Efficient Statistical Computations for Optimal Color
Quantization / Xiaolin Wu \\
A Random Color Map Animation Algorithm / Ken Musgrave
\\
A Fast Approach to PHIGS PLUS Pseudo Color Mapping /
James Hall and Terence Lindgren \\
Mapping RGB Triples onto 16 Distinct Values / Alan W.
Paeth \\
Television Color Encoding and ``Hot'' Broadcast Colors
/ David Martindale and Alan W. Paeth \\
An Inexpensive Method of Setting the Monitor White
Point / Gary W. Meyer \\
Some Tips for Making Color Hardcopy / Ken Musgrave \\
Area of Planar Polygons and Volume of Polyhedra /
Ronald N. Goldman \\
Getting Around on a Sphere / Clifford A. Shaffer \\
Exact Dihedral Metrics for Common Polyhedra / Alan W.
Paeth \\
A Simple Viewing Geometry / Andrew S. Glassner \\
View Correlation / Rod G. Bogart \\
Maintaining Winged-Edge Models / Andrew S. Glassner \\
Quadtree\slash Octree-to-Boundary Conversion / Claudio
Montani and Roberto Scopigno \\
Three-Dimensional Homogeneous Clipping of Triangle
Strips / Patrick-Gilles Maillot \\
InterPhong Shading / Nadia Magnenat Thalmann, Daniel
Thalmann and Hong Tong Minh \\
Fast Ray-Convex Polyhedron Intersection / Eric Haines
\\
Intersecting a Ray with an Elliptical Torus / Joseph M.
Cychosz \\
Ray-Triangle Intersection Using Binary Recursive
Subdivision / Douglas Voorhies and David Kirk \\
Improved Ray Tagging for Voxel-Based Ray Tracing /
David Kirk and James Arvo \\
Efficiency Improvements for Hierarchy Traversal in Ray
Tracing / Eric Haines \\
A Recursive Shadow Voxel Cache for Ray Tracing / Andrew
Pearce \\
Avoiding Incorrect Shadow Intersections for Ray Tracing
/ Andrew Pearce \\
A Body Color Model: Absorption of Light through
Translucent Media / Mark E. Lee and Samuel P. Uselton
\\
More Shadow Attenuation for Ray Tracing Transparent or
Translucent Objects / Mark E. Lee and Samuel P. Uselton
\\
Implementing Progressive Radiosity with User-Provided
Polygon Display Routines / Shenchang Eric Chen \\
A Cubic Tetrahedral Adaptation of the Hemi-Cube
Algorithm / Jeffrey C. Beran-Koehn and Mark J. Pavicic
\\
Fast Vertex Radiosity Update / Filippo Tampieri \\
Radiosity via Ray Tracing / Peter Shirley \\
Detection of Shadow Boundaries for Adaptive Meshing in
Radiosity / Fran{\c{c}}ois Sillion \\
Decomposing a Matrix into Simple Transformations /
Spencer W. Thomas \\
Recovering the Data from the Transformation Matrix /
Ronald N. Goldman \\
Transformations as Exponentials / Ronald N. Goldman \\
More Matrices and Transformations: Shear and
Pseudo-Perspective / Ronald N. Goldman \\
Fast Matrix Inversion / Kevin Wu \\
Quaternions and $4 \times 4$ Matrices / Ken Shoemake
\\
Random Rotation Matrices / James Arvo \\
Classifying Small Sparse Matrices / James Arvo \\
Bit Picking / Ken Shoemake \\
Faster Fourier Transform / Ken Shoemake \\
Of Integers, Fields, and Bit Counting / Alan W. Paeth
and David Schilling \\
Using Geometric Constructions to Interpolate
Orientation with Quaternions / John Schlag \\
A Half-Angle Identity for Digital Computation: The Joys
of the Halved Tangent / Alan W. Paeth \\
An Integer Square Root Algorithm / Christopher J.
Musial \\
Fast Approximation to the Arctangent / Ron Capelli \\
Fast Sign of Cross Product Calculation / Jack Ritter
\\
Interval Sampling / Ken Shoemake \\
A Recursive Implementation of the Perlin Noise Function
/ Greg Ward \\
Least-Squares Approximations to B{\'e}zier Curves and
Surfaces / Doug Moore and Joe Warren \\
Beyond B{\'e}zier Curves / Ken Shoemake \\
A Simple Formulation for Curve Interpolation with
Variable Control Point Approximation / John Schlag \\
Symmetric Evaluation of Polynomials / Terence Lindgren
\\
Menelaus's Theorem / Hans-Peter Seidel \\
Geometrically Continuous Cubic B{\'e}zier Curves /
Hans-Peter Siedel \\
A Good Straight-Line Approximation of a Circular Arc /
Christopher J. Musial \\
Great Circle Plotting / Alan W. Paeth \\
Fast Anti-Aliased Circle Generation / Xiaolin Wu \\
Graphics Gems C Header File \\
2D and 3D Vector C Library \\
Corrected and Indexed \\
Useful C Macros for Vector Operations / Steve
Hollasch",
xxtableofcontents = "Foreword \\
Preface \\
Mathematical Notation \\
Pseudo-Code \\
Contributors \\
I: 2D Geometry and Algorithms \\
Introduction \\
1: The Area of a Simple Polygon \\
2: Intersection of Line Segments \\
3: Distance from a Point to a Line \\
4: An Easy Bounding Circle \\
5: The Smallest Circle Containing the Intersection of
Two Circles \\
6: Appolonius's 10th Problem \\
7: A Peano Curve Generation Algorithm \\
8: Space-Filling Curves and a Measure of Coherence \\
9: Scanline Coherent Shape Algebra \\
II: Image Processing \\
Introduction \\
1: Image Smoothing and Sharpening by Discrete
Convolution \\
2: A Comparison of Digital Halftoning Techniques \\
3: Color Dithering \\
4: Fast Anamorphic Image Scaling \\
5: Real Pixels \\
6: A Fast 90-Degree Bitmap Rotator \\
7: Rotation of Run-Length Encoded Image Data \\
8: Adaptive Run-Length Encoding \\
9: Image File Compression Made Easy \\
10: An Optimal Filter for Image Reconstruction \\
11: Noise Thresholding in Edge Images \\
12: Computing the Area, the Circumference, and the
Genus of a Binary Digital Image \\
III: Frame Buffer Techniques \\
Introduction \\
1: Efficient Inverse Color Map Computation \\
2. Efficient Statistical Computations for Optimal Color
Quantization \\
3: A Random Color Map Animation Algorithm \\
4: A Fast Approach to PHIGS PLUS Pseudo Color Mapping
\\
5: Mapping RGB Triples onto 16 Distinct Values \\
6: Television Color Encoding and ``Hot'' Broadcast
Colors \\
7: An Inexpensive Method of Setting the Monitor White
Point \\
8: Some Tips for Making Color Hardcopy \\
IV: 3D Geometry and Algorithms \\
Introduction \\
1: Area of Planar Polygons and Volume of Polyhedra \\
2: Getting Around on a Sphere \\
3: Exact Dihedral Metrics for Common Polyhedra \\
4: A Simple Viewing Geometry \\
5: View Correlation \\
6: Maintaining Winged-Edge Models \\
7: Quadtree\slash Octree-to-Boundary Conversion \\
8: Three-Dimensional Homogeneous Clipping of Triangle
Strips \\
9: InterPhong Shading \\
V: Ray Tracing \\
Introduction \\
1: Fast Ray-Convex Polyhedron Intersection \\
2: Intersecting a Ray with an Elliptical Torus \\
3: Ray-Triangle Intersection Using Binary Recursive
Subdivision \\
4: Improved Ray Tagging for Voxel-Based Ray Tracing \\
5: Efficiency Improvements for Hierarchy Traversal in
Ray Tracing \\
6: A Recursive Shadow Voxel Cache for Ray Tracing \\
7: Avoiding Incorrect Shadow Intersections for Ray
Tracing \\
8: A Body Color Model: Absorption of Light through
Translucent Media \\
9: More Shadow Attenuation for Ray Tracing Transparent
or Translucent Objects \\
VI: Radiosity \\
Introduction \\
1: Implementing Progressive Radiosity with
User-Provided Polygon Display Routines \\
2: A Cubic Tetrahedral Adaptation of the Hemi-Cube
Algorithm \\
3: Fast Vertex Radiosity Update \\
4: Radiosity via Ray Tracing \\
5: Detection of Shadow Boundaries for Adaptive Meshing
in Radiosity \\
[data unavailable] \ldots{}",
}
@Article{Balsara:1991:DSM,
author = "Poras T. Balsara and Robert M. Owens and Mary Jane
Irwin",
title = "Digit serial multipliers",
journal = j-J-PAR-DIST-COMP,
volume = "11",
number = "2",
pages = "156--162",
month = feb,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of Texas at Dallas",
affiliationaddress = "Richardson, TX, USA",
classification = "713; 723; B2570 (Semiconductor integrated circuits);
C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
corpsource = "Erik Jonsson Sch. of Eng. and Computer Science, Texas
University, Richardson, TX, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "communication; Computers, Digital; data; digit
pipelined multipliers; digit pipelining; digit serial
multipliers; digital arithmetic; Integrated Circuits,
VLSI; Multiplying Circuits; multiplying circuits;
parallel; pipeline processing; Pipelined Multipliers;
processing; programmable multipliers; semisystolic;
Signal Processing --- Digital Techniques; special
purpose computers; special purpose processors;
systolic; systolic multiplier; Systolic Multipliers;
transmission; VLSI; VLSI signal processing",
treatment = "P Practical",
}
@Article{Barrenechea:1991:NEH,
author = "M. J. Barrenechea",
title = "Numeric exception handling",
journal = j-PROGRAM-J,
volume = "9",
number = "3",
pages = "40--42, 44--49",
month = may # "--" # jun,
year = "1991",
ISSN = "0747-5861",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Numeric exception handling is a facet of compiler
runtime support that is not well understood by many
application programmers, or even by some compiler
vendors. Floating-point errors have puzzled programmers
for too long. The author demystifies the IEEE 754 and
854 floating-point standards and explains how the Intel
80287/80387 and i860 chips fit into the puzzle. He
gives some techniques for handling numeric exceptions
in C++.",
acknowledgement = ack-nhfb,
affiliation = "Microway Inc., Plymouth, MA, USA",
classification = "C6110 (Systems analysis and programming)",
fjournal = "Programmer's Journal",
keywords = "C++; Compiler runtime support; Floating point errors;
Floating-point standards; I860 chips; IEEE 754; IEEE
854; Intel 80287/80387; Numeric exceptions",
thesaurus = "C language; C listings; Standards",
}
@Article{Barsi:1991:MAB,
author = "Ferruccio Barsi",
title = "Mod $m$ arithmetic in binary systems",
journal = j-INFO-PROC-LETT,
volume = "40",
number = "6",
pages = "303--309",
year = "1991",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68M07 (68Q35)",
MRnumber = "MR1156823 (92m:68009)",
bibdate = "Thu Nov 8 14:50:34 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Bartholomew-Biggs:1991:AST,
author = "M. C. Bartholomew-Biggs",
title = "{Ada} Software for Teaching Modern Computer
Arithmetic",
journal = j-SIGNUM,
volume = "26",
number = "3",
pages = "17--26",
month = jul,
year = "1991",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/122649.122651",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:20 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes three Ada packages which support the
teaching of some recent and important ideas in
numerical computation. The first is designed to enable
students to write and use applications programs
demonstrating the behavior of floating point arithmetic
with different precisions and roundings. It also
underpins the other two packages which provide simple
computational tools for interval arithmetic and for
accurate arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Numerical Optimisation Centre, Hatfield Polytech.,
UK",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods); C7430 (Computer engineering);
C7810C (Computer-aided instruction)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Accurate arithmetic; Ada software; Computer
arithmetic; Floating point arithmetic; Interval
arithmetic; Numerical computation; Precisions;
Roundings; Students; Teaching",
thesaurus = "Computer aided instruction; Computer science
education; Digital arithmetic; Numerical analysis;
Software packages; Teaching",
xxpages = "16--26",
}
@Article{BartholomewBiggs:1991:AST,
author = "M. C. Bartholomew-Biggs",
title = "{Ada} software for teaching modern computer
arithmetic",
journal = j-SIGNUM,
volume = "26",
number = "3",
pages = "16--26",
month = jul,
year = "1991",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes three Ada packages which support the
teaching of some recent and important ideas in
numerical computation. The first is designed to enable
students to write and use applications programs
demonstrating the behavior of floating point arithmetic
with different precisions and roundings. It also
underpins the other two packages which provide simple
computational tools for interval arithmetic and for
accurate arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Numerical Optimisation Centre, Hatfield Polytech.,
UK",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods); C7430 (Computer engineering);
C7810C (Computer-aided instruction)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Accurate arithmetic; Ada software; Computer
arithmetic; Floating point arithmetic; Interval
arithmetic; Numerical computation; Precisions;
Roundings; Students; Teaching",
thesaurus = "Computer aided instruction; Computer science
education; Digital arithmetic; Numerical analysis;
Software packages; Teaching",
}
@Article{Bartoloni:1991:MFU,
author = "A. Bartoloni and C. Battista and S. Cabasino and N.
Cabibbo and F. Del Prete and F. Marzano and P. S.
Paolucci and R. Sarno and G. Salina and G. M. Todesco
and M. Torelli and R. Tripiccione and W. Tross and E.
Zanetti",
title = "{MAD}, a floating-point unit for massively-parallel
processors",
journal = "Particle World",
volume = "2",
number = "3",
pages = "65--73",
month = "????",
year = "1991",
ISSN = "1043-6790",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors describe in detail the architecture and
implementation of the MAD chip. It is a floating point
unit, used as the elementary processing element of the
APE100 array processor. The design has been accurately
tailored to the requirements of a SIMD floating point
intensive machine.",
acknowledgement = ack-nhfb,
affiliation = "Roma University, Italy",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods); C7320 (Physics and
Chemistry)",
keywords = "APE100 array processor; Architecture; Elementary
processing element; Floating-point unit;
Massively-parallel processors; SIMD floating point
intensive machine",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Microprocessor chips; Parallel
architectures; Physics computing",
}
@InProceedings{Beal:1991:GAP,
author = "D. Beal and C. Lambrinoudakis",
title = "{GPFP}: an array processing element for the next
generation of massively parallel supercomputer
architectures",
crossref = "IEEE:1991:PSA",
pages = "348--357",
year = "1991",
bibdate = "Wed Apr 15 16:28:01 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5220P (Parallel architecture); C5230 (Digital
arithmetic methods)",
corpsource = "Department of Computer Science, Queen Mary and
Westfield Coll., London University, UK",
keywords = "1.6 micron; 2.5 GFLOPS; 50 MHz; 50-MHz clock; ALU;
arithmetic and logic unit; array processing element;
CMOS integrated circuits; CMOSIC; cost-effective extra
functionality; digital arithmetic; floating point
arithmetic; general purpose with floating point
support; GPFP; MasPar; massively parallel SIMD arrays;
massively parallel supercomputer architectures;
microprocessor chips; on-chip memory; parallel
architectures; processing element; VLSI",
sponsororg = "IEEE; ACM",
treatment = "P Practical",
}
@TechReport{Beebe:1991:ASR,
author = "Nelson H. F. Beebe",
title = "Accurate Square Root Computation",
institution = inst-CSC,
address = inst-CSC:adr,
pages = "23",
day = "4",
month = feb,
year = "1991",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supplemental class notes prepared for Mathematics
118.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bohlender:1991:DFP,
author = "G. Bohlender",
title = "Decimal floating-point arithmetic in binary
representation",
crossref = "Kaucher:1991:CAS",
pages = "13--27",
year = "1991",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The binary representation of decimal floating-point
numbers permits an efficient implementation of the
proposed radix independent IEEE standard for
floating-point arithmetic, as far as storage space is
concerned. Unfortunately the left and right shifts
occurring in the arithmetic operations are very
complicated and slow in this representation. The paper
proposes methods which speed up these shifts; in
particular a kind of carry look-ahead technique is used
for division. These methods can be combined to
construct a decimal shifter which is needed in an ALU
for decimal arithmetic.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe University,
Germany",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ALU; Binary representation; Carry look-ahead; Decimal
arithmetic; decimal floating-point arithmetic; Decimal
floating-point numbers; Decimal shifter; Division;
Floating-point arithmetic; IEEE standard; Left shifts;
Radix independent; Right shifts; Storage space",
thesaurus = "Digital arithmetic; Standards",
}
@InProceedings{Bohlender:1991:SEF,
author = "G. Bohlender and W. Walter and P. Kornerup and D. W.
Matula",
title = "Semantics for exact floating point operations",
crossref = "Kornerup:1991:PIS",
pages = "22--26",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boldo:2003:RCT} for some special cases that
this paper may have overlooked.",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Bohlender.pdf",
abstract = "Semantics are given for the four elementary arithmetic
operations and the square root, to characterize what
are termed exact floating point operations. The
operands of the arithmetic operations and the argument
of the square root are all floating point numbers in
one format. In every case, the result is a pair of
floating point numbers in the same format with no
accuracy lost in the computation. These semantics make
it possible to realize the following principle: it
shall be a user option to discard any information in
the result of a floating point arithmetic operation.
The reliability and portability previously associated
with only mathematical software implementations in
integer arithmetic can thus be attained exploiting the
generally higher efficiency of floating point
hardware.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe University,
Germany",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
keywords = "accurate floating-point summation; argument; ARITH-10;
elementary arithmetic operations; exact floating point
operations; floating point arithmetic; floating point
hardware; floating point numbers; integer arithmetic;
mathematical software; operands; portability;
reliability; semantics; square root",
thesaurus = "Digital arithmetic; Number theory",
}
@InProceedings{Bohlender:1991:SPH,
author = "Gerd Bohlender and Andreas Kn{\"o}fel",
title = "A Survey of Pipelined Hardware Support for Accurate
Scalar Products",
crossref = "Kaucher:1991:CAS",
pages = "29--43",
year = "1991",
bibdate = "Sat Sep 17 19:05:23 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bohlender:1991:VEI,
author = "Gerd Bohlender",
title = "A Vector Extension of the {IEEE} Standard for
Floating-Point Arithmetic",
crossref = "Kaucher:1991:CAS",
pages = "3--12",
year = "1991",
bibdate = "Wed Dec 13 18:41:16 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IEEE standard for floating-point arithmetic aims
at improving security, accuracy, reliability, and
compatibility of floating-point computations. However,
the standard only specifies single, double, and
extended precision operations for real operands.
Therefore, often only these operations are available in
hardware on customary floating-point processors. Vector
and matrix operations, complex operations, and interval
operations, in contrast have to be simulated in the
traditional way, using sequences of rounded operations.
This method leads to an unnecessary loss of accuracy
and efficiency. As floating-point processors more and
more evolve into vector processors for sophisticated
numerical applications, the same aims should be
satisfied for all operations on the customary numerical
data types. The paper proposes a vector extension of
the IEEE standard which leads to improved operations in
higher numerical spaces.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe University,
Germany",
classification = "C5220P (Parallel architecture); C5230 (Digital
arithmetic methods)",
keywords = "Floating-point arithmetic; Floating-point processors;
IEEE standard; Numerical data types; Vector
processors",
thesaurus = "Digital arithmetic; Standards; Vector processor
systems",
}
@TechReport{Boughton:1991:CSG,
author = "G. A. {Boughton (editor)}",
title = "{Computation Structures Group} Progress Report
1990--91",
type = "{CSG} Memo",
number = "337",
institution = "MIT Laboratory for Computer Science",
address = "Cambridge, MA, USA",
month = jun,
year = "1991",
bibdate = "Wed Jan 29 16:27:14 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Utilities for accurate reading and printing of double
precision floating point numbers (cited in
\cite{Steele:2004:RHP}).",
}
@Article{Briggs:1991:PCF,
author = "Keith Briggs",
title = "A Precise Calculation of the {Feigenbaum} Constants",
journal = j-MATH-COMPUT,
volume = "57",
number = "195",
pages = "435--439",
month = jul,
year = "1991",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y60 (39B12 58F14 65Q05)",
MRnumber = "91j:11117",
MRreviewer = "Jeffrey O. Shallit",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290F (Interpolation and function approximation);
B0290K (Nonlinear and functional equations); C4130
(Interpolation and function approximation); C4150
(Nonlinear and functional equations)",
corpsource = "Department of Math., La Trobe University, Bundoora,
Vic., Australia",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Feigenbaum constants; Feigenbaum functional equation;
functional equations; iteration; iterative methods;
multiple precision floating point; period-doubling
bifurcations; real functions",
treatment = "T Theoretical or Mathematical",
}
@Article{Bromley:1991:FAT,
author = "Mark Bromley and Steven Heller and Tim McNerney and
Guy L. {Steele Jr.}",
title = "{Fortran} at ten gigaflops: the {Connection Machine}
convolution compiler",
journal = j-SIGPLAN,
volume = "26",
number = "6",
pages = "145--156",
month = jun,
year = "1991",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu May 13 12:37:27 MDT 1999",
bibsource = "http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p145-bromley/",
abstract = "The authors have implemented a prototype of a
specialized compiler module and associated run-time
support that allows a Fortran user to achieve sustained
floating-point performance of over 10 gigaflops on the
Connection Machine Model CM-2. This improves
substantially over the previous record of 5.6
gigaflops, which was achieved by means of hand-crafted
low-level coding techniques. The compiler module
processes array assignment statements of a certain
form: the right-hand side must be a sum of products and
the products must use the Fortran 90 array shifting
intrinsics in a certain stylized pattern. Such
assignment statements are suitable for expressing array
convolution (stencil) computations and can be executed
efficiently by chained multiply-add operations.",
acknowledgement = ack-nhfb,
affiliation = "Thinking Machines Corp., Cambridge, MA, USA",
classification = "C5440 (Multiprocessor systems and techniques); C6110
(Systems analysis and programming); C6140D (High level
languages); C6150C (Compilers, interpreters and other
processors)",
confdate = "26-28 June 1991",
conflocation = "Toronto, Ont., Canada",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Array assignment statements; Array convolution;
Chained multiply-add operations; Connection Machine
convolution compiler; Connection Machine Model CM-2;
Fortran 90 array shifting intrinsics; Fortran user;
Hand-crafted low-level coding techniques; languages;
performance; Run-time support; Specialized compiler
module; Sustained floating-point performance",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Compilers.",
thesaurus = "FORTRAN; Parallel machines; Parallel programming;
Program compilers",
}
@Book{Brunner:1991:VAR,
editor = "Richard A. Brunner and Dileep P. Bhandarkar and
others",
title = "{VAX} Architecture Reference Manual",
publisher = pub-DP # " and " # pub-PH,
address = pub-DP:adr # " and " # pub-PH:adr,
pages = "xv + 560",
year = "1991",
ISBN = "1-55558-057-2 (Digital Press), 0-13-929522-4
(Prentice-Hall)",
ISBN-13 = "978-1-55558-057-5 (Digital Press), 978-0-13-929522-5
(Prentice-Hall)",
LCCN = "QA76.8.V32 V39 1991",
bibdate = "Wed Nov 01 08:09:54 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Bruss:1991:RMF,
author = "Rolf-J{\"u}rgen Br{\"u}{\ss}",
title = "{RISC}\emdash The {MIPS-R3000} Family",
publisher = pub-SIEMENS,
address = pub-SIEMENS:adr,
pages = "340",
year = "1991",
ISBN = "3-8009-4103-1",
ISBN-13 = "978-3-8009-4103-2",
LCCN = "QA76.5 R48 1991",
bibdate = "Sat Jan 29 23:10:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bryant:1991:CVI,
author = "R. E. Bryant",
title = "On the complexity of {VLSI} implementations and graph
representations of {Boolean} functions with application
to integer multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "2",
pages = "205--213",
month = feb,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.73590",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73590",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Calvetti:1991:REF,
author = "Daniela Calvetti",
title = "Roundoff error for floating point representation of
real data",
journal = j-COMMUN-STAT-THEORY-METH,
volume = "20",
number = "8",
pages = "2687--2695",
year = "1991",
CODEN = "CSTMDC",
DOI = "https://doi.org/10.1080/03610929108830658",
ISSN = "0361-0926 (print), 1532-415X (electronic)",
ISSN-L = "0361-0926",
MRclass = "62E99 (65C20)",
MRnumber = "93d:62031",
bibdate = "Wed Jan 27 05:39:04 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Statistics: Theory and Methods",
journal-URL = "http://www.tandfonline.com/loi/lsta20",
reviewer = "Evdokia Xekalaki",
}
@Article{Calvetti:1991:SRE,
author = "Daniela Calvetti",
title = "A stochastic roundoff error analysis for the {Fast
Fourier Transform}",
journal = j-MATH-COMPUT,
volume = "56",
number = "194",
pages = "755--774",
month = apr,
year = "1991",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65T20 (65G05)",
MRnumber = "91m:65341",
MRreviewer = "Harald E. Krogstad",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
JSTOR database",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "B0290Z (Other numerical methods); B0290B (Error
analysis in numerical methods); C4190 (Other numerical
methods); C4110 (Error analysis in numerical methods)",
corpsource = "Dept. of Math., Southern Colorado Univ., Pueblo, CO,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "addition; discrete Fourier transform; error analysis;
expected value; fast Fourier transform; fast Fourier
transforms; linear forms; multiplication; stochastic
roundoff error analysis; variance",
treatment = "T Theoretical or Mathematical",
}
@Book{Catanzaro:1991:STP,
editor = "Ben J. Catanzaro",
title = "The {SPARC} Technical Papers",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 501",
year = "1991",
ISBN = "0-387-97634-5, 3-540-97634-5",
ISBN-13 = "978-0-387-97634-1, 978-3-540-97634-9",
LCCN = "QA76.9.A73 S65 1991",
bibdate = "Wed Feb 9 01:57:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Celarier:1991:AML,
author = "Donald A. Celarier and Donald W. Sando",
title = "An {Ada} math library for real-time avionics",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "274--284",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:43 MDT 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "C7460 (Aerospace engineering); C7150 (Military); C7310
(Mathematics); C6140D (High level languages)",
corpsource = "Boeing Defense and Space Group, Seattle, WA, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "accuracy testing; Ada; Ada math library; aerospace
computing; applications; avionics; computing;
implementation; library; mathematics computing;
military; military avionics processor; real-time
avionics; real-time systems; subroutines",
treatment = "P Practical",
}
@Article{Chai:1991:MCF,
author = "P. Chai and T. Chuk and Y. H. Fong and L. Hu and K. Ng
and J. Prabhu and A. Quek and A. Samuels and J. Yeun",
title = "A 120 {MFLOPS CMOS} Floating-Point Processor",
crossref = "IEEE:1991:PIC",
pages = "15.1/1--4",
year = "1991",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Chan:1991:DOC,
author = "Pak K. Chan and Martine D. F. Schlag and Clark D.
Thomborson and Vojin G. Oklobdzija",
title = "Delay optimization of carry-skip adders and block
carry-lookahead adders",
crossref = "Kornerup:1991:PIS",
pages = "154--164",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Chance:1991:EPA,
author = "R. J. Chance",
title = "The effect of processor architecture on an efficient
floating point table look-up algorithm",
journal = j-MICROPROC-MICROSYS,
volume = "15",
number = "8",
pages = "411--416 (or 411--415??)",
month = oct,
year = "1991",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "R J Chance investigates the performance that can be
achieved using linear interpolation and partitioning
techniques in look-up tables",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "Microprocessors and Microsystems",
}
@Article{Chang:1991:PLA,
author = "Yuh-Huu Chang and Ching-Kae Tzou and N. J. Bershad",
title = "Postsmoothing for the {LMS} algorithm and a fixed
point roundoff error analysis",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "4",
pages = "959--962",
month = apr,
year = "1991",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The effect of post-algorithm smoothing on digital
implementations of the least mean square (LMS)
algorithm is studied. An expression is derived for the
mean square error (MSE) with post-algorithm (PA)
smoothing but without finite wordlength effects.
\ldots{}",
}
@Article{Chassaing:1991:DSP,
author = "Chassaing and Horning",
title = "Digital Signal Processing with Fixed- and
Floating-Point Processors",
journal = j-COED,
volume = "II",
number = "1",
pages = "1--4",
month = jan,
year = "1991",
CODEN = "CWLJDP",
ISSN = "0736-8607",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "CoED",
}
@InProceedings{Chatelin:1991:AAA,
author = "F. Chatelin and V. Frayss{\'e}",
title = "Analysis of arithmetic algorithms: a statistical
study",
crossref = "Kornerup:1991:PIS",
pages = "10--16",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chatelin.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Chen:1991:BDR,
author = "F. Chen and C. S. Chen",
title = "A {20~b} dynamic-range floating-point data acquisition
system",
journal = j-IEEE-TRANS-IND-ELECTRON,
volume = "38",
number = "1",
pages = "10--14",
month = feb,
year = "1991",
CODEN = "ITIED6",
DOI = "https://doi.org/10.1109/41.103477",
ISSN = "0278-0046 (print), 1557-9948 (electronic)",
ISSN-L = "0278-0046",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Industrial Electronics",
summary = "The design and engineering of a floating-point
data-acquisition system are described. The system has
both automatic gain and software-programmable gain
adjustment features. In automatic gain adjustment mode,
the gain is set automatically dependent on \ldots{}",
}
@Article{Chiang:1991:FNR,
author = "Jen-Shiun Chiang and Mi Lu",
title = "Floating-point numbers in residue number systems",
journal = j-COMPUT-MATH-APPL,
volume = "22",
number = "10",
pages = "127--140",
month = "????",
year = "1991",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65Y10",
MRnumber = "92h:65212",
bibdate = "Wed Dec 13 18:13:40 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Introduce a new type of the residue number system
(RNS), floating-point RNS, which can significantly
increase the range of the numbers represented by RNS.
The concept of the RNS floating-point arithmetics are
presented, and the approaches to perform these
arithmetic operations are proposed. The introduced
methods are simple, efficient and easy to implement. (6
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Texas A\&M University,
College Station, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Floating-point RNS; Residue number system; RNS",
pubcountry = "UK",
thesaurus = "Digital arithmetic",
}
@Article{Chiang:1991:FPNa,
author = "Jen-Shiun Chiang and Mi Lu",
title = "Floating-point numbers in residue number systems",
journal = j-COMPUT-MATH-APPL,
volume = "22",
number = "10",
pages = "127--140",
month = "????",
year = "1991",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65Y10",
MRnumber = "92h:65212",
bibdate = "Wed Dec 13 18:13:40 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Introduce a new type of the residue number system
(RNS), floating-point RNS, which can significantly
increase the range of the numbers represented by RNS.
The concept of the RNS floating-point arithmetics are
presented, and the approaches to perform these
arithmetic operations are proposed. The introduced
methods are simple, efficient and easy to implement. (6
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Texas A\&M University,
College Station, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Floating-point RNS; Residue number system; RNS",
pubcountry = "UK",
thesaurus = "Digital arithmetic",
}
@Article{Chiang:1991:FPNb,
author = "Jen-Shiun Chiang and Mi Lu",
title = "Floating-point numbers in residue number systems",
journal = j-COMPUT-MATH-APPL,
volume = "22",
number = "10",
pages = "127--140",
month = "????",
year = "1991",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:01 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219190200N",
abstract = "Introduce a new type of the residue number system
(RNS), floating-point RNS, which can significantly
increase the range of the numbers represented by RNS.
The concept of the RNS floating-point arithmetics are
presented, and the approaches to perform these
arithmetic operations are proposed. The introduced
methods are simple, efficient and easy to implement.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Texas A and M University,
College Station, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Floating-point RNS; Residue number system; RNS",
pubcountry = "UK",
thesaurus = "Digital arithmetic",
}
@InProceedings{Chiang:1991:GDA,
author = "J.-S. Chiang and M. Lu",
title = "A general division algorithm for residue number
systems",
crossref = "Kornerup:1991:PIS",
pages = "76--83",
year = "1991",
DOI = "https://doi.org/10.1109/ARITH.1991.145537",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chiang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10; residue arithmetic; residue number system",
summary = "A general algorithm for signed number division in
residue number systems (RNSs) is presented. A parity
checking technique is used to accomplish the sign and
overflow detection in this algorithm. Compared with
conventional methods of sign and \ldots{}",
}
@Article{Cmelik:1991:AMS,
author = "Robert F. Cmelik and Shing I. Kong and David R. Ditzel
and Edmund J. Kelly",
title = "An Analysis of {MIPS} and {SPARC} Instruction Set
Utilization on the {SPEC} Benchmarks",
journal = j-SIGPLAN,
volume = "26",
number = "4",
pages = "290--301 (or 290--302??)",
month = apr,
year = "1991",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The dynamic instruction counts of MIPS and SPARC are
compared using the SPEC benchmarks. MIPS typically
executes more user-level instructions than SPARC. This
difference can be accounted for by architectural
differences, compiler differences, and library
differences. The most significant differences are that
SPARC's double-precision floating point load/store is
an architectural advantage in the SPEC floating point
benchmarks while MIPS's compare-and-branch instruction
is an architectural advantage in the SPEC integer
benchmarks. After the differences in the two
architectures are isolated, it appears that although
MIPS and SPARC each have strengths and weaknesses in
their compilers and library routines, the combined
effect of compilers and library routines does not give
either MIPS or SPARC a clear advantage in these
areas.",
acknowledgement = ack-nhfb,
affiliation = "Sun Microsyst. Inc., Mountain View, CA, USA",
classification = "C5220 (Computer architecture); C5470 (Performance
evaluation and testing); C6140B (Machine-oriented
languages)",
confdate = "8-11 April 1991",
conflocation = "Santa Clara, CA, USA",
confsponsor = "IEEE; ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Architectural differences; Compare-and-branch
instruction; Compiler differences; Double-precision
floating point load/store; Dynamic instruction counts;
Instruction set utilization; Library differences; MIPS;
SPARC; SPEC floating point benchmarks; SPEC integer
benchmarks; User-level instructions",
thesaurus = "Instruction sets; Performance evaluation; Reduced
instruction set computing",
}
@InProceedings{Cody:1991:KAA,
author = "W. J. Cody",
title = "Keynote Address: Arithmetic Standards: The Long Road",
crossref = "Kornerup:1991:PIS",
pages = "ix--ix",
year = "1991",
bibdate = "Sat Nov 17 08:46:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_keynote.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Cody:1991:PEP,
author = "W. J. Cody",
title = "Performance Evaluation of Programs Related to the Real
Gamma Function",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "46--54",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65Y20)",
MRnumber = "91m:65052",
bibdate = "Sun Sep 04 23:33:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/103147.103153;
http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/",
abstract = "Methods are presented for evaluating the performance
of programs for the functions $ \Gamma (x) $, $ \ln
\Gamma (x) $, and $ \psi (x) $. Accuracy estimates are
based on comparisons using the manipulation theorem.
Ideas for checking robustness are also given, and
details on specific implementations of test programs
are included.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "measurement; performance; reliability",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Certification and testing.",
}
@Article{Cody:1991:UTS,
author = "W. J. Cody and L. Stoltz",
title = "The Use of {Taylor} Series to Test Accuracy of
Function Programs",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "55--63",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65Y20)",
MRnumber = "91m:65053",
bibdate = "Sun Sep 04 23:36:36 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/103147.103154;
http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/",
abstract = "This paper discusses the use of local Taylor series
expansions for determining the accuracy of computer
programs for special functions. The main example is
testing of programs for exponential integrals.
Additional applications include testing of programs for
certain Bessel functions, Dawson's integral, and error
functions.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; measurement; performance; verification",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
}
@Article{Compan:1991:GPS,
author = "A. Compan and P. Debaud and V. Delorme and J. A.
Fran{\c{c}}ois and H. Mehrez and F. Pecheux",
title = "{GAF}: a portable standard-cell floating point adder
generator using the {CXgen} function library",
journal = j-MICROPROC-MICROPROG,
volume = "32",
number = "1",
pages = "637--644",
month = aug,
year = "1991",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Microprocessing and Microprogramming",
}
@Book{Counihan:1991:F,
author = "Martin Counihan",
title = "{Fortran 90}",
publisher = pub-PITMAN,
address = pub-PITMAN:adr,
pages = "309",
year = "1991",
ISBN = "0-273-03073-6",
ISBN-13 = "978-0-273-03073-7",
LCCN = "QA76.73.F25 C68 1991",
bibdate = "Sun May 02 07:48:16 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "See \cite{ANSI:ftn92}.",
acknowledgement = ack-nhfb,
keywords = "Fortran 90 (computer program language); Programming
languages; {Fortran 90} (Computer program language)",
libnote = "Not yet in my library.",
tableofcontents = "1: Introduction \\
1.1: Fortran 90 / 1 \\
1.2: Programs and Programming / 2 \\
2: What is Fortran 90? \\
2.1: Program Structure / 5 \\
2.2: Intrinsic Procedures / 6 \\
2.3: Statement Types / 7 \\
2.4: What Fortran 90 Isn't / 7 \\
2.5: New Features in Fortran 90 / 8 \\
Notes / 10 \\
3: Getting Started \\
3.1: The Character Set / 11 \\
3.2: A Simple Program / 14 \\
3.3: Arithmetic Operators / 18 \\
Exercises 3A / 19 \\
3.4: Names and Other Lexical Tokens / 20 \\
3.5: Fortran Source Form / 21 \\
Exercises 3B / 24 \\
Notes / 25 \\
4: Intrinsic Data Types \\
4.1: Integers / 26 \\
4.2: Real Numbers / 29 \\
Exercises A / 31 \\
4.3: Simple Form of the Type Declaration Statement / 32
\\
4.4: Kinds Real Numbers / 32 \\
4.5: Complex Numbers / 33 \\
4.6: Logical Data; Logical and Relational Operators /
35 \\
4.7: Characters and Strings / 38 \\
Exercises 4B / 40 \\
Notes / 42 \\
5: Some Intrinsic Procedures \\
5.1: An Intrinsic Subroutine / 43 \\
5.2: Mathematical Functions / 44 \\
5.3: Numeric Functions / 46 \\
Exercises 5A / 50 \\
Notes / 52 \\
6: More About Characters \\
6.1: Declaring Character Data / 53 \\
6.2: Character Constants / 54 \\
6.3: Character Operators / 55 \\
6.4: Intrinsic Character Functions / 56 \\
6.5: Substrings / 59 \\
Exercises / 61 \\
Notes / 62 \\
7: Arrays \\
7.1: Declaring Arrays / 63 \\
7.2: Using Arrays / 65 \\
7.3: Array Constructors / 67 \\
7.4: Array Sections / 68 \\
7.5: Array Sections, Character Strings and Substrings /
70 \\
7.6: Where / 72 \\
7.7: Arrays and Intrinsic Functions / 73 \\
Exercises 7B / 74 \\
8: Execution Control \\
8.1: The ``CASE'' Construct / 76 \\
8.2: The ``IF'' Construct / 80 \\
Exercises / 81 \\
8.3: The ``DO'' Construct / 82 \\
8.4: Stop / 88 \\
Exercises 8B / 88 \\
Notes / 89 \\
9: Functions and Subroutines (1) \\
9.1: Functions / 90 \\
Exercises 9A / 93 \\
9.2: Subroutines / 93 \\
9.3: Procedures and Arrays / 96 \\
Exercises 9B / 99 \\
Notes / 100 \\
10: More Intrinsic Procedures; Statement Labels \\
10.1: Intrinsic Subroutines / 102 \\
10.2: Functions for Use with Arrays / 104 \\
Exercises 10A / 110 \\
10.3: Numeric Inquiry Functions and Floating-Point
Manipulation Functions / 110 \\
10.4: Statement Labels and ``GO TO'' / 111 \\
Notes / 114 \\
11: Modules \\
11.1: Data Modules / 116 \\
Module Procedures / 120 \\
11.3: More About ``USE'' Statements / 124 \\
Exercises / 126 \\
Notes / 127 \\
12: Functions and Subroutines (2) \\
12.1: Recursive Procedures / 128 \\
Exercises 12A / 130 \\
12.2: Interface Blocks / 131 \\
12.3: Argument Keywords / 132 \\
12.4: More About Arguments: ``PRESENT'' / 133 \\
12.5: Functions / 134 \\
12.6: Operators / 135 \\
12.7: Generic Names / 138 \\
12.8: Parallel Processing / 141 \\
Exercises 12B / 142 \\
Notes / 143 \\
13: The Type Declaration Statement \\
13.1: General Form of the TDS / 144 \\
13.2: Character Length Selectors / 147 \\
13.3: Attribute Specifications / 149 \\
13.4: Array Specifications / 152 \\
13.5: The Entity Declaration List / 157 \\
13.6: Summary / 158 \\
Exercises 13A / 159 \\
Notes / 161 \\
14: Derived Types \\
14.1: Derived-Type Definition / 164 \\
14.2: Structure Constructors / 166 \\
14.3: Structure Components / 168 \\
Exercises 14A / 169 \\
14.4: Structures of Structures / 170 \\
Exercises 14B / 171 \\
14.5: Functions and Operators with Derived Types / 172
\\
14.6: Defined Assignment / 174 \\
Exercises 14C / 178 \\
Notes / 180 \\
15: Arrays and Pointers \\
15.1: Array Element Order, Array Constructors; RESHAPE
/ 181 \\
15.2: Vector Subscripts / 184 \\
15.3: Allocatable Arrays / 187 \\
Exercises 15A / 190 \\
15.4: LBOUND, SHAPE and SIZE / 190 \\
Exercises 15B / 191 \\
15.5: Simple Pointers / 192 \\
15.6: Pointers as Structures and as Structure
Components / 197 \\
15.7: Pointers and Procedures / 204 \\
15.8: Array Pointers / 205 \\
Exercises 15C / 207 \\
Notes / 208 \\
16: Input and Output; Data Format Specifications \\
16.1: Data Transfer Statements / 209 \\
16.2: The Item List / 210 \\
16.3: List-Directed Input / 212 \\
16.4: List-Directed Output / 216 \\
16.5: Explicit Formats / 217 \\
Exercises 16A / 219 \\
16.6: Data Edit Descriptors and Character Edit
Descriptors / 219 \\
16.7: Control Edit Descriptors / 223 \\
Exercises 16B / 225 \\
16.8: Namelists / 226 \\
16.9: Unformatted / 228 \\
16.10: The TRANSFER Function / 229 \\
16.11: Summary / 231 \\
Notes / 232 \\
17: File Handling \\
17.1: Units, Files and Records / 233 \\
17.2: Opening and Closing Files / 235 \\
17.3: BACKSPACE, ENDFTLE and REWIND / 240 \\
17.4: Control Specifications for / 240 \\
17.5: The ``INQUIRE'' Statement / 242 \\
17.6: Internal Files / 246 \\
Exercises 17A / 248 \\
Notes / 249 \\
18: Bits \\
18.1: Inside Integers / 250 \\
18.2: Bit Logic / 251 \\
18.3: A Warning / 252 \\
Exercises 18A / 253 \\
19: Programming Conventions and Program Architecture:
Putting It All Together \\
19.1: Coding Conventions / 254 \\
19.2: Towards Fortran 90 / 255 \\
Fortran 90 Recommended Statements / 256 \\
Intrinsic Functions / 257 \\
19.3: Program Unit Structure / 258 \\
19.4: Program Structure / 261 \\
19.5: Final Remarks / 262 \\
Answers to Selected Exercises / 263 \\
Appendices \\
A: Fortran 90 Statements \\
B: Intrinsic Procedures / 286 \\
C: Intrinsic Procedures: Names / 292 \\
D: Argument Keywords in Intrinsic Procedures / 294 \\
E: Edit Descriptors / 297 \\
F: The ASCII Character Set / 301 \\
Index / 304",
}
@Article{Cox:1991:TSS,
author = "Christopher L. Cox and James A. Knisely",
title = "A tridiagonal system solver for distributed memory
parallel processors with vector nodes",
journal = j-J-PAR-DIST-COMP,
volume = "13",
number = "3",
pages = "325--331",
month = nov,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Clemson Univ",
affiliationaddress = "Clemson, SC, USA",
classification = "721; 722; 723; 921; C4140 (Linear algebra); C5220P
(Parallel architecture); C5230 (Digital arithmetic
methods); C5470 (Performance evaluation and testing);
C7310 (Mathematics)",
corpsource = "Department of Math. Sci., Clemson University, SC,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "algebraic routine; algorithm; computer; Computer
Programming languages--fortran; Computer
Programming--Algorithms; Computer Systems, Digital;
Cyclic reduction algorithms; Data Storage, Digital;
digital arithmetic; Distributed memories; distributed
memory parallel; divide and conquer strategy; Floating
Point Systems FPS T-20; FORTRAN; Intel iPSC/2-VX;
linear algebra; Mathematical Techniques--Matrix
Algebra; mathematics computing; odd-even cyclic
reduction; parallel architectures; Parallel Processing;
partitioning; performance evaluation; processors;
programs; redundancy; scaled speedup; tridiagonal
system solver; Tridiagonal systems; Vector nodes;
vector nodes; vector processors",
treatment = "A Application; P Practical",
}
@Article{Crenshaw:1991:SRS,
author = "J. W. Crenshaw",
title = "Square roots are simple?",
journal = j-EMBED-SYS-PROG,
volume = "4",
number = "11",
pages = "30--52",
month = nov,
year = "1991",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Wed Sep 14 19:14:52 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Embedded Systems Programming",
}
@Article{Davida:1991:FPA,
author = "George I. Davida and Bruce Litow",
title = "Fast Parallel Arithmetic via Modular Representation",
journal = j-SIAM-J-COMPUT,
volume = "20",
number = "4",
pages = "756--765",
month = aug,
year = "1991",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68Q10",
MRnumber = "92c:68046",
bibdate = "Mon Nov 29 11:01:48 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/20/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@MastersThesis{Davies:1991:FPS,
author = "Davies, T. C. (Tudor Craddock)",
title = "A floating point systolic array processing element
using serial communication",
type = "Thesis ({M.Eng.})",
school = "Royal Military College of Canada",
address = "Kingston, ON, Canada",
year = "1991",
ISBN = "0-315-60644-4",
ISBN-13 = "978-0-315-60644-9",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "2 microfiches. University Microfilms order no.
UMI00285885",
series = "National Library of Canada = Bibliotheque nationale du
Canada; Canadian theses = Theses canadiennes",
acknowledgement = ack-nhfb,
}
@Article{Davis:1991:CC,
author = "Warren Davis and Kan Yabumoto",
title = "A coprocessor for a coprocessor?",
journal = j-DDJ,
volume = "16",
number = "5",
pages = "16--28, 84--88",
month = may,
year = "1991",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 09:11:02 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "When fast graphics aren't fast enough, the TI 34020
graphics coprocessor employs its own coprocessor -- the
34082 FPU -- for even higher system performance.",
acknowledgement = ack-nhfb,
affiliation = "Pixelab Inc., Lisle, IL, USA",
classification = "C5130 (Microprocessor chips); C5540 (Terminals and
graphic displays)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "Built-in graphics-related instructions; Floating point
coprocessor; General-purpose microprocessor; Graphics
System Processor; Programmable graphics coprocessor;
Texas Instruments; TMS34020; TMS34082; Video control
circuitry",
thesaurus = "Assembly language listings; C listings; Computer
graphic equipment; Microprocessor chips; Satellite
computers; Texas Instruments computers",
}
@PhdThesis{Deb:1991:BFF,
author = "Kalyanmoy Deb",
title = "Binary and floating-point function optimization using
messy genetic algorithms",
type = "Thesis ({Ph.D.})",
school = "Department of Engineering Mechanics, University of
Alabama",
address = "Tuscaloosa, AL, USA",
pages = "xvii + 166",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms.; Combinatorial optimization.",
}
@InProceedings{deLange:1991:DIF,
author = "Alfons A. J. de Lange and Ed F. Deprettere",
title = "Design and implementation of a floating-point
quasi-systolic general purpose {CORDIC} rotator for
high-rate parallel data and signal processing",
crossref = "Kornerup:1991:PIS",
pages = "272--281",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lange.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Demmel:1991:OIA,
author = "James W. Demmel",
title = "On the odor of {IEEE} arithmetic",
journal = j-NA-DIGEST,
volume = "91",
number = "39",
day = "29",
month = sep,
year = "1991",
bibdate = "Thu Aug 23 06:19:41 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Rebuttal to \cite{Grcar:1991:IAS}.",
URL = "http://www.netlib.org/na-digest/91/v91n39",
acknowledgement = ack-nhfb,
fjournal = "NA Digest",
}
@InProceedings{Dongarra:1991:GBP,
author = "J. J. Dongarra and A. Karp and K. Miura and H. D.
Simon",
title = "{Gordon Bell Prize} lectures (supercomputer
applications)",
crossref = "IEEE:1991:PSA",
pages = "328--337",
year = "1991",
bibdate = "Wed Apr 15 16:28:01 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5440 (Multiprocessor systems and techniques)",
corpsource = "Department of Computer Science, Tennessee University,
Knoxville, TN, USA",
keywords = "128-node Intel iPSC/860; compiler speedup; Connections
Machine; electronic structure; floating point
processors; Fortran 77; Fortran 90; grid generation
program; parallel processing; partial differential
equation; price/performance award; scientific and
engineering problems; supercomputers",
sponsororg = "IEEE; ACM",
treatment = "G General Review; P Practical",
}
@Article{Dunham:1991:ABA,
author = "C. Dunham",
title = "Applications of Best Approximation",
journal = j-SIGNUM,
volume = "26",
number = "2",
pages = "2--10",
month = apr,
year = "1991",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Duprat:1991:NRR,
author = "Jean Duprat and Yvan Herreros and Sylvanus Kla",
title = "New redundant representations of complex numbers and
vectors",
crossref = "Kornerup:1991:PIS",
pages = "2--9",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Duprat.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Duprat:1991:WND,
author = "J. Duprat and Jean-Michel Muller",
title = "Writing numbers differently for faster calculation",
journal = j-TECHNIQUE-SCI-INFORMATIQUES,
volume = "10",
number = "3",
pages = "211--224",
month = "????",
year = "1991",
CODEN = "TTSIDJ",
ISSN = "0752-4072, 0264-7419",
ISSN-L = "0752-4072",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Instead of Avizienis' or the carry save methods a
borrow save (BS) notation is proposed. Examples are
given of BS addition, subtraction, shifting and
multiplication with the necessary elementary cells
being proposed and circuits for testing zero and sign
being described. Floating point arithmetic is
explained, involving pseudo normalisation and
applications are covered including the Cordic
algorithm.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure de Lyon, France",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Technique et science informatiques : TSI",
keywords = "Addition; Borrow save; Carry save methods; Cordic
algorithm; Floating point arithmetic; Multiplication;
Pseudo normalisation; Shifting; Subtraction; Zero",
language = "French",
pubcountry = "France",
thesaurus = "Digital arithmetic",
}
@Article{Ercegovac:1991:MPM,
author = "Milo{\v{s}} D. Ercegovac and Tomas Lang",
title = "Module to perform multiplication, division, and square
root in systolic arrays for matrix computations",
journal = j-J-PAR-DIST-COMP,
volume = "11",
number = "3",
pages = "212--221",
month = mar,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of California Los Angeles",
affiliationaddress = "Los Angeles, CA, USA",
classification = "722; 723; 921; C4140 (Linear algebra); C5220
(Computer architecture); C5230 (Digital arithmetic
methods)",
corpsource = "Department of Computer Science, California University,
Los Angeles, CA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Applications; carry-save; complexity; Computer
Programming --- Algorithms; Computers; digital
arithmetic; division; matrix algebra; Matrix
Computations; matrix computations; module;
multiplication; Multiplication/Division/Square Root
Module; Normalization; On-The-Fly Conversion; radix-2
divider; result-digit selection; Rounding;
signed-digit; square root; Systolic Arrays; systolic
arrays",
treatment = "P Practical",
}
@Article{Even:1991:SMM,
author = "Shimon Even",
title = "Systolic Modular Multiplication",
journal = j-LECT-NOTES-COMP-SCI,
volume = "537",
pages = "619--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:48:02 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0537.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0537/05370619.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0537/05370619.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Ferguson:1991:AMA,
author = "Warren E. {Ferguson, Jr.} and Tom Brightman",
title = "Accurate and Monotone Approximations of Some
Transcendental Functions",
crossref = "Kornerup:1991:PIS",
pages = "237--244",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Ferguson.pdf",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "ARITH-10",
}
@Article{Ferguson:1991:SMC,
author = "Warren E. {Ferguson, Jr.}",
title = "Selecting math coprocessors",
journal = j-IEEE-SPECTRUM,
volume = "28",
number = "7",
pages = "38--41",
month = jul,
year = "1991",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.83469",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Sep 01 16:17:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "floating-point arithmetic",
remark = "Contains performance-comparison tables for Cyrix,
Intel, Motorola, and Weitek floating-point coprocessor
chips.",
}
@InProceedings{Fleurkens:1991:HLD,
author = "H. Fleurkens and R. Tangelder",
title = "The high level design of the long accumulator chip",
crossref = "IEEE:1991:PFC",
pages = "299--301",
year = "1991",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors discuss an architecture and its high level
description of a long accumulator chip suited for the
exact calculation of the inner products of floating
point numbers. A highly parallel implementation is
developed using eight independent adder stations, which
add products to two circular long accumulators. A
dispatcher schedules each product to the best available
station. To validate this architecture and to calculate
its performance, a high level description is created.
This description is made with ESCHER+, an interactive
schematic entry tool with a built-in simulator. The
resulting description showed to be the basis for the
further implementation of the chip.",
acknowledgement = ack-nhfb,
affiliation = "Eindhoven University of Technol., Netherlands",
classification = "B1130B (Computer-aided circuit analysis and design);
B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5210B (Computer-aided logic design); C5220P
(Parallel architecture); C5230 (Digital arithmetic
methods); C7410D (Electronic engineering)",
keywords = "Built-in simulator; ESCHER+; Floating point numbers;
High level description; High level design; Highly
parallel implementation; Inner products calculation;
Interactive schematic entry tool; Long accumulator
chip",
thesaurus = "Circuit CAD; Digital arithmetic; Integrated logic
circuits; Logic CAD; Parallel architectures",
}
@Article{Fossmeier:1991:ALH,
author = "R. F{\"o}{\ss}meier",
title = "{Zur Axiomatisierung logarithmischer und
halblogarithmischer Zahlensysteme}. ({German}) [{On}
the axiomatization of logarithmic and semi-logarithmic
number systems]",
journal = j-COMPUTING,
volume = "46",
number = "2",
pages = "175--182",
month = jun,
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G99",
MRnumber = "92e:65064",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
abstract = "In the history of numerical analysis there have been
various approaches to gain stricter control of
numerical computation by axiomatization of
approximative arithmetic systems. In the case of
floating-point-like systems, the limitations to this
approach originate essentially in the fact that
addition is not associative. By suitably weakening the
axiomatic system of the real numbers the author arrives
at a system which can be fulfilled by approximative
arithmetic structures. Comparisons show that structures
fulfilling this system cannot be arbitrarily distant
from reasonable approximative structures. This shows
that it is possible to describe approximative
structures by approximations of the laws of the
original structure.",
acknowledgement = ack-nhfb,
affiliation = "Inst. f{\"u}r Inf., Tech. University of Munchen,
Germany",
classification = "723; 921; C4100 (Numerical analysis)",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput Vienna New York",
keywords = "Approximative arithmetic structures; Axiomatization;
computers, digital --- Computational Methods;
Floating-Point Arithmetic; Logarithmic; mathematical
techniques; Number systems; Number Systems; Numerical
analysis; Semi-logarithmic number systems",
language = "German",
pubcountry = "Austria",
thesaurus = "Number theory; Numerical analysis",
}
@Article{Fossmeier:1991:ALS,
author = "R. Fossmeier",
title = "On the axiomatization of logarithmic and
semi-logarithmic number systems",
journal = j-COMPUTING,
volume = "46",
number = "2",
pages = "175--182",
month = "????",
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the history of numerical analysis there have been
various approaches to gain stricter control of
numerical computation by axiomatization of
approximative arithmetic systems. In the case of
floating-point-like systems, the limitations to this
approach originate essentially in the fact that
addition is not associative. By suitably weakening the
axiomatic system of the real numbers the author arrives
at a system which can be fulfilled by approximative
arithmetic structures. Comparisons show that structures
fulfilling this system cannot be arbitrarily distant
from reasonable approximative structures. This shows
that it is possible to describe approximative
structures by approximations of the laws of the
original structure.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Inf., Tech. University of Munchen, Germany",
classification = "C4100 (Numerical analysis)",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "Approximative arithmetic structures; Axiomatization;
Logarithmic; Number systems; Numerical analysis;
Semi-logarithmic number systems",
language = "German",
pubcountry = "Austria",
thesaurus = "Number theory; Numerical analysis",
}
@Article{Foster:1991:PM,
author = "Kenneth R. Foster",
title = "Prepackaged math",
journal = j-IEEE-SPECTRUM,
volume = "28",
number = "11",
pages = "44--50",
month = nov,
year = "1991",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.99016",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Wed Jan 15 16:15:28 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib;
https://www.math.utah.edu/pub/tex/bib/macsyma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Chemical analysis; Data engineering; Data
visualization; Differential equations; Graphics; Hard
disks; manipulation; mathematical problems; mathematics
computing; matrices; matrix algebra; Packaging;
Personal communication networks; software packages;
Software packages; Workstations",
}
@InProceedings{Frougny:1991:RNN,
author = "Christiane Frougny",
title = "Representation of numbers in nonclassical numeration
systems",
crossref = "Kornerup:1991:PIS",
pages = "17--21",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Frougny.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Gal:1991:AEM,
author = "Shmuel Gal and Boris Bachelis",
title = "An Accurate Elementary Mathematical Library for the
{IEEE} Floating Point Standard",
journal = j-TOMS,
volume = "17",
number = "1",
pages = "26--45",
month = mar,
year = "1991",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D20 (65-04 65D15)",
MRnumber = "92a:65069",
bibdate = "Sun Sep 04 23:33:02 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://doi.acm.org/10.1145/103147.103151;
http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/",
abstract = "The algorithms used by the IBM Israel Scientific
Center for the elementary mathematical library using
the IEEE standard for binary floating point arithmetic
are described. The algorithms are based on the
``accurate tables method.'' This methodology achieves
high performance and produces very accurate results. It
overcomes one of the main problems encountered in
elementary mathematical functions computations:
achieving last bit accuracy. The results obtained are
correctly rounded for almost all argument
values.\par
Our main idea in the accurate tables method is to use
``nonstandard tables,'' which are different from the
natural tables of equally spaced points in which the
rounding error prevents obtaining last bit accuracy. In
order to achieve a small error we use the following
idea: Perturb the original, equally spaced, points in
such a way that the table value (or tables values in
case we need several tables) will be very close to
numbers which can be exactly represented by the
computer (much closer than the usual double precision
representation). Thus we were able to control the error
introduced by the computer representation of real
numbers and extended the accuracy without actually
using extended precision arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; correct rounding; floating-point
arithmetic; theory",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation.",
}
@InProceedings{Gamberger:1991:NAI,
author = "Dragan Gamberger",
title = "New approach to integer division in residue number
systems",
crossref = "Kornerup:1991:PIS",
pages = "84--91",
year = "1991",
DOI = "https://doi.org/10.1109/ARITH.1991.145538",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Gamberger.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10; residue arithmetic; residue number system",
summary = "A novel division algorithm that is especially
appropriate for residue number systems (RNSs) is
presented. It makes use of the fact that the
multiplicative inverse element of a divisor which is
relatively prime to system moduli can be easily
\ldots{}",
}
@Article{Gladshtein:1991:MDD,
author = "M. A. Gladshtein",
title = "A method of designing a decimal arithmetic processor",
journal = j-AUTO-CTL-COMP-SCI,
volume = "25",
number = "6",
pages = "51--56",
month = "????",
year = "1991",
CODEN = "ACCSCE",
ISSN = "0132-4160",
ISSN-L = "0146-4116",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The advantages and drawbacks of binary numeric coding
in digital computers are considered. This type of
coding has is shown to be ineffective in processing
large data arrays especially when represented in the
floating-point form. Also, the low efficiency of
conventionally employed decimal computational
procedures using the so-called corrections is noted. It
is proposed, in designing digital computers, to
renounce the principle of binary computations in favor
of decimal operations on the basis of stored addition
and multiplication tables using binary-decimal numeric
coding. A version of circuit design for a decimal
processor, algorithms and microprograms for addition
and multiplication operations are described. Advantages
inherent in the method proposed are analyzed. (10
Refs.)",
acknowledgement = ack-nhfb,
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
fjournal = "Automatic Control and Computer Sciences",
keywords = "Addition tables; BCD code; Binary numeric coding;
Binary-decimal numeric coding; Circuit design; Decimal
arithmetic processor; decimal floating-point
arithmetic; Decimal operations; Digital computers;
Microprograms; Multiplication tables",
pubcountry = "Latvia",
remark = "English translation of: Avtomatika i Vychislitel'naya
Tekhnika",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@Article{Goldberg:1991:CWE,
author = "David Goldberg",
title = "Corrigendum: {``What Every Computer Scientist Should
Know About Floating-Point Arithmetic''}",
journal = j-COMP-SURV,
volume = "23",
number = "3",
pages = "413--413",
month = sep,
year = "1991",
CODEN = "CMSVAN",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Sun Sep 25 09:58:43 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann:1992:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Goldberg:1991:WEC,
author = "David Goldberg",
title = "What Every Computer Scientist Should Know About
Floating-Point Arithmetic",
journal = j-COMP-SURV,
volume = "23",
number = "1",
pages = "5--48",
month = mar,
year = "1991",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/103162.103163",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:40:16 MDT 2008",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also
\cite{Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW}.",
URL = "http://www.acm.org/pubs/toc/Abstracts/0360-0300/103163.html",
abstract = "Floating-point arithmetic is considered an esoteric
subject by many people. This is rather surprising,
because floating-point is ubiquitous in computer
systems: almost every language has a floating-point
datatype; computers from PCs to supercomputers have
floating-point accelerators; most compilers will be
called upon to compile floating-point algorithms from
time to time; and virtually every operating system must
respond to floating-point exceptions such as overflow.
This paper presents a tutorial on the aspects of
floating-point that have a direct impact on designers
of computer systems. It begins with background on
floating-point representation and rounding error,
continues with a discussion of the IEEE floating-point
standard, and concludes with examples of how computer
system builders can better support floating point.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Xerox Palo Alto Res. Center, CA, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
keywords = "algorithms; compilers; computer scientist; computer
systems; denormalized number; design; exception;
floating-point; floating-point accelerators;
floating-point algorithms; floating-point datatype;
floating-point exceptions; floating-point
representation; floating-point standard; gradual
underflow; guard digit; IEEE floating-point standard;
languages; NaN; operating system; overflow; PCs;
relative error; rounding error; rounding mode;
standardization; supercomputers; ulp; underflow",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf K.1}:
Computing Milieux, THE COMPUTER INDUSTRY, Standards.
{\bf C.0}: Computer Systems Organization, GENERAL,
Instruction set design. {\bf G.1.0}: Mathematics of
Computing, NUMERICAL ANALYSIS, General, Numerical
algorithms.",
thesaurus = "digital arithmetic; roundoff errors",
}
@TechReport{Golubev:1991:FPM,
author = "Yu. F. Golubev and I. A. Seregin and R. Z.
Kha{\u\i}rullin",
title = "The floating point method in problems of the
optimization of motion during the descent of a
spacecraft into the atmosphere. ({Russian})",
type = "{Inst. Prikl. Mat.} Preprint",
number = "50",
institution = "Akad. Nauk SSSR",
pages = "28",
year = "1991",
MRclass = "65K10 (49N55 70-08 70Q05)",
MRnumber = "166 839",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Gonnella:1991:ACF,
author = "J. Gonnella",
title = "The application of core functions to residue number
systems",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "1",
pages = "69--75",
month = jan,
year = "1991",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.80766",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2655",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "A theory of core functions is presented, and the
application of this theory to the difficult residue
number system (RNS) operations is described. Potential
applications for special-purpose core-based RNS
processors include adaptive array processing,
\ldots{}",
}
@Article{Gotze:1991:SRD,
author = "J. G{\"o}tze and U. Schwiegelshohn",
title = "A Square Root and Division Free {Givens} Rotation for
Solving Least Squares Problems on Systolic Arrays",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "12",
number = "4",
pages = "800--807",
month = jul,
year = "1991",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65F20 (65F25)",
MRnumber = "92a:65125",
bibdate = "Sat Oct 24 13:20:45 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
}
@Article{Grcar:1991:IAS,
author = "Joe Grcar",
title = "{IEEE} Arithmetic Stinks",
journal = j-NA-DIGEST,
volume = "91",
number = "33",
day = "18",
month = aug,
year = "1991",
bibdate = "Thu Aug 23 06:22:13 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See rebuttal \cite{Demmel:1991:OIA}.",
URL = "http://www.netlib.org/na-digest/91/v91n33",
acknowledgement = ack-nhfb,
fjournal = "NA Digest",
}
@Article{Griffin:1991:REA,
author = "C. Griffin and P. Rao and F. Taylor",
title = "Roundoff error analysis of the discrete {Wigner}
distribution using fixed-point arithmetic",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "9",
pages = "2096--2098",
month = sep,
year = "1991",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The issue of roundoff noise effects in the
implementation of the discrete Wigner distribution
using fixed-point arithmetic is addressed. The
sign-magnitude number representation is assumed
throughout the analysis. The measure of roundoff noise
\ldots{}",
}
@Article{Gusev:1991:NCS,
author = "A. V. Gusev and I. V. Melezhnikov",
title = "Noise in a Constant-Current {SQUID} with a Floating
Operating Point",
journal = j-TELECOMM-RADIO-ENG,
volume = "46",
number = "8",
pages = "125--127",
year = "1991",
CODEN = "TCREAG",
ISSN = "0040-2508 (print), 1943-6009 (electronic)",
ISSN-L = "0040-2508",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Telecommunications and Radio Engineering",
}
@InProceedings{Guyot:1991:OAV,
author = "Alain Guyot",
title = "{OCAPI}: Architecture of a {VLSI} Coprocessor for the
{GCD} and the Extended {GCD} of Large Numbers",
crossref = "Kornerup:1991:PIS",
pages = "226--231",
year = "1991",
bibdate = "Sat Nov 17 08:46:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Guyot.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Hamza:1991:MBD,
author = "K. M. Hamza and M. A. H. Abdul-Karim",
title = "Microprocessor Based Direct Square Root Extractor",
journal = "Modelling",
volume = "34",
number = "1",
pages = "45--48",
month = "????",
year = "1991",
bibdate = "Thu Sep 1 10:15:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Heidtmann:1991:ASA,
author = "K. D. Heidtmann",
title = "Arithmetic spectrum applied to fault detection for
combinational networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "3",
pages = "320--324",
month = mar,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.76409",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=76409",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Holmes:1991:FSD,
author = "Ian Holmes",
title = "A feasibility study into the design of a 64-bit
floating point processor",
type = "Thesis ({M.Sc. in Electronics})",
school = "University of Southampton, Department of Electronics
and Computer Science",
address = "Southampton, UK",
year = "1991",
bibdate = "Thu May 09 08:35:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Horiguchi:1991:HFN,
author = "Hiroshi Horiguchi and Tsutomu Tayama and Kazuaki
Kajitori",
title = "{Hamada} Floating-Point Numbers and Real Numbers",
journal = j-ADV-SOFT-SCI-TECH,
volume = "2",
number = "??",
pages = "123--??",
year = "1991",
ISSN = "1044-7997",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances in software science and technology",
}
@Article{Horiguchi:1991:PEP,
author = "Susumu Horiguchi and Takeo Nakada",
title = "Performance Evaluation of Parallel Fast {Fourier}
Transform on a Multiprocessor Workstation",
journal = j-J-PAR-DIST-COMP,
volume = "12",
number = "2",
pages = "158--163",
month = jun,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4190 (Other numerical methods); C4240 (Programming
and algorithm theory); C5440 (Multiprocessor systems
and techniques)",
corpsource = "Department of Inf. Sci., Tohoku University, Sendai,
Japan",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "algorithms; cache protocols; fast Fourier transform;
fast Fourier transforms; FFT; floating-; multiprocess
operating system; multiprocessing systems;
multiprocessor workstation; multithread operating
system; operating systems; parallel; parallel FFT;
performance; performance evaluation; point
coprocessors",
treatment = "P Practical",
}
@Misc{Hough:1991:TBC,
author = "David G. Hough and Vern Paxson",
title = "Testbase: base conversion test program",
howpublished = "World-Wide Web document",
day = "20",
month = jul,
year = "1991",
bibdate = "Wed May 26 07:22:52 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Paxson:1991:PTI}.",
URL = "http://www.netlib.org/fp/testbase",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@InProceedings{Hsiao:1991:CHA,
author = "Shen-Fu Hsiao and Jean-Marc Delosme",
title = "The {CORDIC Householder} algorithm",
crossref = "Kornerup:1991:PIS",
pages = "256--263",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hsiao.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Hu:1991:ERC,
author = "X. Hu and R. G. Harber and S. C. Bass",
title = "Expanding the Range of Convergence of the {CORDIC}
Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "1",
pages = "13--21",
month = jan,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.67316",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 00:50:12 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hui:1991:DFD,
author = "S. Hui and D. P. Brown",
booktitle = "{IEEE} Pacific Rim Conference on Communications,
Computers and Signal Processing, 9--10 May 1991",
title = "Digital filter design with a combination of fixed
point and residue number systems",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "331--334",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/PACRIM.1991.160746",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new design method using a combination of fixed-point
and RNS (residue number system) arithmetics is
presented. It is proven that an IIR digital filter can
be efficiently implemented in a system that combines
both fixed-point and RNS arithmetics. \ldots{}",
}
@InProceedings{Hull:1991:SVP,
author = "T. E. Hull and M. S. Cohen and C. B. Hall",
title = "Specifications for a variable-precision arithmetic
coprocessor",
crossref = "Kornerup:1991:PIS",
pages = "127--131",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hull.pdf",
abstract = "The authors have been developing a programming system
intended to be especially convenient for scientific
computing. Its main features are variable precision
(decimal) floating-point arithmetic and convenient
exception handling. The software implementation of the
system has evolved over a number of years, and a
partial hardware implementation of the arithmetic
itself was constructed and used during the early stages
of the project. Based on this experience, the authors
have developed a set of specifications for an
arithmetic coprocessor to support such a system. These
specifications are described. An outline of the
language features and how they can be used is also
provided, to help justify the particular choice of
coprocessor specifications. The authors also indicate
what other hardware features would be most helpful to
the systems programmer, especially for implementation
of the exception handling.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Toronto University,
Ont., Canada",
classification = "B1265B (Logic circuits); B1265F (Microprocessors and
microcomputers); B2570 (Semiconductor integrated
circuits); C5120 (Logic and switching circuits); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
keywords = "ARITH-10; decimal floating-point arithmetic; Exception
handling; Floating-point arithmetic; Programming
system; Scientific computing; Variable-precision
arithmetic coprocessor",
thesaurus = "Digital arithmetic; Logic circuits; Microprocessor
chips; Satellite computers",
}
@Book{Ince:1991:SQR,
author = "D. (Darrel) Ince",
title = "Software quality and reliability tools and methods",
publisher = "Chapman and Hall",
address = "London, UK",
pages = "178",
year = "1991",
ISBN = "0-442-31314-4, 0-412-37810-8",
ISBN-13 = "978-0-442-31314-2, 978-0-412-37810-2",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Unicom applied information technology reports; [6]",
acknowledgement = ack-nhfb,
keywords = "Computer software --- Quality control.; Computer
software --- Reliability.; Software --- Quality
control",
remark = "Aspects of path testing and mutation testing / M.R.
Woodward --- Quality-- an integrated approach / A.
Smith --- Quality management and software engineering /
R. Hailstone --- The role of verification and
validation tools in the production of critical software
/ J.T. Webb --- The real importance of software quality
and the role of quality systems / A. Voss --- Software
testing tools / E. Fergus \ldots{} [et al.] --- FPV-- a
floating point validation package / J. Du Croz ---
Building in quality through the use of software tools /
P.A.V. Hall --- Software requirements analysis, formal
methods and software prototyping / D. Ince ---
Increasing software quality by objectives and residual
fault prognosis / K. Moller --- Towards a software
quality control environment / M. Adam \ldots{} [et al.]
--- Expert system software quality problems / S. Ronchi
and M. Martignano --- Quality assurance management for
real-time software systems: the experience of the
Spanish Civil Aviation Administration / J.P. Buendia,
C. Bravo --- The PRX/A software reliability
investigation / A.E.J. van Delft.",
}
@InCollection{Iri:1991:HAD,
author = "M. Iri",
editor = "A. Griewank and G. F. Corliss",
booktitle = "Automatic Differentiation of Algorithms: Theory,
Implementation, and Application",
title = "History of automatic differentiation and rounding
error estimation",
crossref = "Griewank:1991:ADA",
pages = "3--16",
year = "1991",
bibdate = "Thu May 27 07:45:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Jain:1991:CSN,
author = "Suneel Jain",
title = "Circular scheduling: a new technique to perform
software pipelining",
journal = j-SIGPLAN,
volume = "26",
number = "6",
pages = "219--228",
month = jun,
year = "1991",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:07 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p219-jain/",
abstract = "With the advent of deeply pipelined RISC processors,
static instruction scheduling by the compiler has
become extremely important to obtain high processor
performance. This is especially true for floating point
code. The author suggests using a new algorithm called
circular scheduling to perform software pipelining.
Software pipelining has previously been investigated
mostly for VLIW architectures. The algorithm described
is shown to be quite effective for a scalar
architecture. Register renaming, an idea that
originates from dynamic instruction scheduling, is used
in conjunction with this algorithm to augment its
performance. The techniques described here have been
implemented as part of a commercial, production quality
optimizing compiler for a RISC architecture. The
resulting performance improvement has verified the
feasibility and practicality of the techniques.",
acknowledgement = ack-nhfb,
affiliation = "MIPS Comput. Syst. Inc., Sunnyvale, CA, USA",
classification = "C5220 (Computer architecture); C6110 (Systems
analysis and programming); C6150C (Compilers,
interpreters and other processors); C6150J (Operating
systems)",
confdate = "26-28 June 1991",
conflocation = "Toronto, Ont., Canada",
confsponsor = "ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "algorithms; Circular scheduling; Deeply pipelined RISC
processors; Dynamic instruction scheduling;
experimentation; performance; Production quality
optimizing compiler; RISC architecture; Scalar
architecture; Software pipelining; Static instruction
scheduling; VLIW architectures",
subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Compilers. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Optimization.",
thesaurus = "Parallel programming; Pipeline processing; Program
compilers; Reduced instruction set computing;
Scheduling",
}
@InProceedings{Jain:1991:NRS,
author = "V. K. Jain and G. E. Perez and J. M. Wills",
title = "Novel reciprocal and square-root {VLSI} cell:
architecture and application to signal processing",
crossref = "IEEE:1991:VCA",
volume = "2",
pages = "1201--1204",
year = "1991",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
summary = "A novel high-speed cell, capable of performing a
square-root or a reciprocal function in two clock
cycles, is presented. Its performance signifies an
estimated three-fold increase in speed over existing
approaches. Furthermore, since both functions
\ldots{}",
}
@TechReport{Kahan:1991:APL,
author = "William Kahan and J. W. Thomas",
title = "Augmenting a Programming Language with Complex
Arithmetic",
number = "NCEG/91-039, UCB/CSD 91/667",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
pages = "8",
day = "15",
month = nov,
year = "1991",
bibdate = "Mon Dec 26 21:13:51 GMT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript",
acknowledgement = ack-nhfb,
}
@Article{Kahan:1991:ARL,
author = "W. Kahan",
title = "Analysis and Refutation of the {LCAS}",
journal = j-SIGNUM,
volume = "26",
number = "3",
pages = "2--15",
month = jul,
year = "1991",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Fri Jan 5 07:58:42 MST 1996",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/signum.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "LCAS (Language Compatible Arithmetic Standard)",
}
@InProceedings{Kantabutra:1991:DOC,
author = "Vitit Kantabutra",
title = "Designing optimum carry-skip adders",
crossref = "Kornerup:1991:PIS",
pages = "146--153",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kantabutra.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Kim:1991:ERB,
author = "Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee",
title = "Efficient residue-to-binary conversion technique with
rounding error compensation",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "38",
number = "3",
pages = "315--317",
month = mar,
year = "1991",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "An improved scaled-decoding technique (defined as
residue-to-binary conversion of which outputs are
scaled by a constant) for hardware implementations in
the residue number system (RNS) is presented. The
technique is based on the Chinese remainder \ldots{}",
}
@InProceedings{Kim:1991:NIC,
author = "S. W. Kim and T. Stouraitis",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 11--14 June 1991",
title = "New implementations of converters for the residue and
quadratic residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2959--2962",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1991.176166",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Full adder (FA)-based converters are proposed for
efficiently performing complex number calculations. The
basic idea is to use FA arrays to decompose 2 i terms
into 2 j terms, where j{$<$}i, by modulo arithmetic.
\ldots{}",
}
@Book{Klatte:1991:PSB,
author = "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
Ch. Ullrich",
title = "{PASCAL-XSC: Sprachbeschreibung mit Beispielen}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 345",
year = "1991",
ISBN = "0-387-53714-7",
ISBN-13 = "978-0-387-53714-6",
LCCN = "QA76.73.P2 P42 1991",
bibdate = "Mon Dec 18 09:37:18 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation is available as
\cite{Klatte:1991:PXP}.",
acknowledgement = ack-nhfb,
}
@Book{Klatte:1991:PXP,
author = "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
Ch. Ullrich",
title = "{PASCAL-XSC}: {A PASCAL} Extension for Scientific
Computation",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 344",
year = "1991",
ISBN = "0-387-55137-9 (New York), 3-540-55137-9 (Berlin)",
ISBN-13 = "978-0-387-55137-1 (New York), 978-3-540-55137-9
(Berlin)",
LCCN = "QA76.73.P2 P4213 1992",
bibdate = "Thu Nov 8 14:50:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation of \cite{Klatte:1991:PSB}.",
price = "DM64.00",
acknowledgement = ack-nhfb,
referred = "[Corl91a].",
}
@InProceedings{Knofel:1991:FHU,
author = "Andreas Kn{\"o}fel",
title = "Fast hardware units for the computation of accurate
dot products",
crossref = "Kornerup:1991:PIS",
pages = "70--74",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Knofel.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Knowles:1991:APD,
author = "S. Knowles",
title = "Arithmetic Processor Design for the {T9000}
Transputer",
crossref = "SPIE:1991:PSI",
pages = "230--243",
year = "1991",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Koc:1991:FAG,
author = "Cetin K. Koc and Sarath N. Arachchige",
title = "A fast algorithm for {Gaussian} elimination over
{GF(2)} and its implementation on the {GAPP}",
journal = j-J-PAR-DIST-COMP,
volume = "13",
number = "1",
pages = "118--122",
day = "1",
month = sep,
year = "1991",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of Houston",
affiliationaddress = "Houston, TX, USA",
classification = "722; 723; 921; C4140 (Linear algebra); C4240
(Programming and algorithm theory)",
corpsource = "Department of Electr. Eng., Houston University, TX,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "1s location; Algorithms; algorithms; arithmetic
parallel processor; binary matrix; binary search;
Binary search technique; bit operations; bit-array;
columns; computational complexity; Computer
Programming; Computer Systems, Digital--Parallel
Processing; Galois fields; GAPP; Gaussian elimination;
geometric; Geometric arithmetic parallel processors;
GF(2); Large binary matrices; Mathematical
Techniques--Matrix Algebra; matrix algebra; ones
location; parallel; Triangularization; triangularize;
vertical memory",
treatment = "T Theoretical or Mathematical",
}
@Article{Koc:1991:IAM,
author = "{\c{C}}etin K. Ko{\c{c}}",
title = "An improved algorithm for mixed-radix conversion of
residue numbers",
journal = j-COMPUT-MATH-APPL,
volume = "22",
number = "8",
pages = "63--71",
month = "????",
year = "1991",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:04 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219190014U",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@MastersThesis{Kohprasert:1991:FAC,
author = "Teera Kohprasert",
title = "32-bit floating-point arithmetic coprocessor design
using {VHDL}",
type = "Thesis ({M.S.})",
school = "Florida Institute of Technology",
address = "Melbourne, FL, USA",
pages = "xiv + 456",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic and logic units --- Design and
construction.; VHDL (Computer hardware description
language).",
}
@Article{Kostopoulos:1991:ACB,
author = "D. K. Kostopoulos",
title = "An Algorithm for the Computation of Binary
Logarithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "11",
pages = "1267--1270",
month = nov,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.102831",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Kramer:1991:EFA,
author = "David Kramer and Isaac D. Scherson",
title = "The effect of {FPU} architecture on a dynamic
precision algorithm for the solution of differential
equations",
type = "Technical report",
number = "91-73",
institution = "Information and Computer Science, University of
California, Irvine",
address = "Irvine, CA, USA",
pages = "18",
year = "1991",
LCCN = "Z699 .C3 no. 91-73",
bibdate = "Fri Jan 5 11:51:46 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kuhnel:1991:OPS,
author = "Lars K{\"u}hnel",
title = "Optimal purely systolic addition",
crossref = "Kornerup:1991:PIS",
pages = "172--179",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kuhnel.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Kurokawa:1991:CGU,
author = "T. Kurokawa and T. Mizukoshi",
title = "Computer graphics using logarithmic number systems",
journal = "IEICE Transactions",
volume = "E74",
number = "2",
pages = "447--451",
month = feb,
year = "1991",
ISSN = "0917-1673",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Logarithmic arithmetic (LA) is a very fast
computational method for real numbers. Its precision is
better than a floating point arithmetic of equivalent
word length and range. This paper shows a method to use
LA in computer graphics-picture generation of almost
any kind. Various experiments are done-from curve
drawing to 3D image generation. The results are all
excellent for quality and speed.",
acknowledgement = ack-nhfb,
affiliation = "Department of Ind. Eng., Aichi Inst. of Technol.,
Toyota, Japan",
classification = "C5230 (Digital arithmetic methods); C6130B (Graphics
techniques)",
keywords = "3D image generation; Computer graphics; Curve drawing;
Fast computational method for real numbers; Logarithmic
arithmetic; Logarithmic number systems; Picture
generation; Precision; Word length",
pubcountry = "Japan",
thesaurus = "Computer graphics; Digital arithmetic",
}
@Article{Lai:1991:HNS,
author = "F.-S. Lai and C.-F. E. Wu",
title = "A hybrid number system processor with geometric and
complex arithmetic capabilities",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "8",
pages = "952--962",
month = aug,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83639",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83639",
abstract = "The architecture, design, and performance of a hybrid
number system processor are described. The processor
performs multiplication, division, square root, and
square in the logarithmic number system (LNS) domain.
However, the input, output, addition, and subtraction
are all executed in the 32-b IEEE standard
floating-point number system. With the LNS multiplier
and pipelined architecture, the processor is able to
perform the geometric and complex arithmetic very
effectively. The processor is also shown to compare
well to an existing 32-b floating-point DSP (digital
signal processor) chip. For the same level of CMOS
technology, the performance ratios between the hybrid
number system and the floating-point processor are
shown to be 6.4:1 and 8:1 for division and square root,
respectively; for the complex FFT (fast Fourier
transform) algorithm, the ratio is around 2:1. (27
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C5230 (Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Complex arithmetic; Division; Floating-point number
system; Geometric; Hybrid number system processor;
Logarithmic number system; Multiplication; Square;
Square root",
thesaurus = "Digital arithmetic",
}
@Article{Lee:1991:FPPa,
author = "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
Briggs",
title = "The Floating Point Performance of a superscalar
{SPARC} Processor",
journal = j-COMP-ARCH-NEWS,
volume = "19",
number = "2",
pages = "28--37",
month = apr,
year = "1991",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:40 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Co-published in {\em Operating Systems Review}, {\bf
28}(3S).",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Lee:1991:FPPb,
author = "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
Briggs",
title = "The floating-point performance of a superscalar
{SPARC} processor",
journal = j-OPER-SYS-REV,
volume = "25",
number = "3S",
pages = "28--37",
month = apr,
year = "1991",
CODEN = "OSRED8",
ISSN = "0163-5980 (print), 1943-586X (electronic)",
ISSN-L = "0163-5980",
bibdate = "Sat Aug 26 15:24:15 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Operating Systems Review",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J597",
}
@Article{Lee:1991:FPPc,
author = "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
Briggs",
title = "The Floating-Point Performance of a Superscalar
{SPARC} Processor",
journal = j-SIGPLAN,
volume = "26",
number = "4",
pages = "28--37",
month = apr,
year = "1991",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The floating point performance of superscalar SPARC
processors is evaluated based on empirical data from 12
benchmarks. This evaluation is done in the context of
two software instruction scheduling optimizations: loop
unrolling and software pipelining, and for three
machine models: 1-scalar, 2-scalar and 4-scalar. The
authors also consider the effect of the memory system
on the performance improvements. Superscalar hardware
alone exhibit little performance improvement without
software optimization. Of the two scheduling methods,
software pipelining more effectively takes advantage of
increased hardware parallelism, and achieves near
optimal speedup on the 4-scalar machine model. The
performance of loop unrolling is restricted by the
limited number of floating point registers in the SPARC
architecture. The best performance level is obtained by
applying both optimization techniques. A superscalar
SPARC processor can provide improved floating point
performance but with significant software and hardware
development costs.",
acknowledgement = ack-nhfb,
affiliation = "Sun Microsyst. Inc., Mountain View, CA, USA",
classification = "C5220 (Computer architecture); C5470 (Performance
evaluation and testing)",
confdate = "8-11 April 1991",
conflocation = "Santa Clara, CA, USA",
confsponsor = "IEEE; ACM",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Benchmarks; Development costs; Floating point
performance; Floating point registers; Hardware
parallelism; Loop unrolling; Memory system; N-scalar
machine models; Optimal speedup; Software instruction
scheduling optimizations; Software pipelining; SPARC
architecture; Superscalar SPARC processor",
thesaurus = "Optimisation; Parallel architectures; Performance
evaluation; Pipeline processing; Scheduling",
}
@InProceedings{Lee:1991:SCF,
author = "Jeong-A. Lee and Tom{\'a}s Lang",
title = "{SVD} by constant-factor-redundant-{CORDIC}",
crossref = "Kornerup:1991:PIS",
pages = "264--271",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lee.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Letcher:1991:GNC,
author = "John H. Letcher",
title = "Getting numeric coprocessors up to speed",
journal = j-DDJ,
volume = "16",
number = "5",
pages = "36, 38, 40, 42",
month = may,
year = "1991",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 09:11:02 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "Memory-mapped math coprocessors can boost performance
without sacrificing compatibility.",
acknowledgement = ack-nhfb,
affiliation = "Tulsa University, OK, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "80*86 Integer CPU; Floating point coprocessors;
Numeric coprocessors; Processing speeds",
thesaurus = "Digital arithmetic; Microprocessor chips; Satellite
computers",
}
@Article{Lo:1991:BHS,
author = "H.-Y. Lo and T. C. Yang",
title = "Balanced high-speed residue number {VLSI} multiplier
with error detection",
journal = "Circuits, Devices and Systems, IEE Proceedings G",
volume = "138",
number = "3",
pages = "421--423",
month = jun,
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/78.80821",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6544",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A balanced residue number VLSI multiplier is proposed
which eliminates the extra delay for an unbalanced
residue multiplier. The number of adding stages used in
the VLSI multiplier is reduced from three to two. The
authors also describe how \ldots{}",
}
@Article{Lyashenko:1991:PAR,
author = "N. N. Lyashenko and M. S. Nikulin",
title = "Probability Analysis of Round-Off Errors in
Floating-Point Arithmetic",
journal = j-THEORY-PROBAB-APPL,
volume = "35",
number = "1",
pages = "66--74",
month = "????",
year = "1991",
CODEN = "TPRBAU",
DOI = "https://doi.org/10.1137/1135006",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Tue Apr 1 10:40:31 MDT 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/35/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib",
acknowledgement = ack-nhfb,
fjournal = "Theory of Probability and its Applications",
journal-URL = "http://epubs.siam.org/tvp",
onlinedate = "January 1991",
}
@InProceedings{Lynch:1991:RCA,
author = "Tom Lynch and Earl {Swartzlander, Jr.}",
title = "The redundant cell adder",
crossref = "Kornerup:1991:PIS",
pages = "165--170",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lynch.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Lyons:1991:FMF,
author = "Ken Lyons",
title = "A fast method for finding an integer square root",
crossref = "Koopman:1991:PST",
pages = "27--30",
year = "1991",
bibdate = "Tue May 4 05:57:50 MDT 1999",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
acknowledgement = ack-nhfb,
}
@InProceedings{MacKenzie:1991:FMS,
author = "Donald MacKenzie",
title = "Formal methods and the sociology of proof",
crossref = "Morris:1991:RWP",
pages = "115--124",
year = "1991",
DOI = "https://doi.org/10.1007/978-1-4471-3756-6_6",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper begins by asking whether a sociology of
mathematical knowledge is possible. Having answered in
the affirmative (drawing examples from the history of
mathematics), it goes on to discuss the development of
a similar analysis of the mathematical aspects of
computer science. A brief vignette is presented: the
processes of negotiation of the IEEE floating-point
arithmetic specifications. Then the discussion moves on
to the verification of software and hardware. If the
sociology of mathematics is correct, then formal proofs
can be seen as social, not just in the processes of
their acceptance, but also in their internal structure.
Placed in the context of pressure for formal
verification of safety-critical and security-critical
systems, this argument led the author and colleagues to
the prediction that litigation involving the nature of
mathematical proof was bound to occur. That prediction
has now been borne out.",
acknowledgement = ack-nhfb,
affiliation = "Department of Sociol., Edinburgh University, UK",
classification = "C0230 (Economic, social and political aspects);
C4240 (Programming and algorithm theory); C6110B
(Software engineering techniques)",
keywords = "Computer science; Formal proofs; Formal verification;
IEEE floating-point arithmetic specifications;
Litigation; Mathematical aspects; Mathematical
knowledge; Negotiation; Safety-critical systems;
Security-critical systems; Sociology of proof;
Verification",
thesaurus = "Economic and sociologic effects; Formal verification;
Safety; Security of data; Software reliability; Theorem
proving",
}
@Article{MacKenzie:1991:IAL,
author = "Donald MacKenzie",
title = "The Influence of the {Los Alamos} and {Livermore
National Laboratories} on the Development of
Supercomputing",
journal = j-ANN-HIST-COMPUT,
volume = "13",
number = "2",
pages = "179--201",
month = apr # "\slash " # jun,
year = "1991",
CODEN = "AHCOE5",
ISSN = "0164-1239",
bibdate = "Fri Nov 1 15:29:15 MST 2002",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/super.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
Contents1st database",
URL = "http://dlib.computer.org/an/books/an1991/pdf/a2179.pdf;
http://www.computer.org/annals/an1991/a2179abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
remark = "The author has this remark about Metropolis on page
194: ``What are the architectural consequences of this
kind of influence? [of Los Alamos on computer design]
One apparent in Stretch is that machine's noisy mode
facility (Los Alamos interviews). The inspiration of
these was Los Alamos Nicholas Metropolis, who in the
1950s developed what he called significance arithmetic:
the attempt to determine the consequences, for the
reliability of results, of errors caused by the need to
represent numbers by words of finite length. In noisy
mode the effects of truncation were handled differently
from in normal operation so as to allow errors caused
by truncation to be detected.
By definition of ordinary normalized [floating-point]
operations, numbers are frequently extended on the
right by attaching zeros. During addition the $n$-digit
operand that is not preshifted is extended with n
zeros, so as to provide the extra positions to which
the preshifted operand can be added. Any operand or
result that is shifted left to be normalized requires a
corresponding number of zeros to be shifted in at the
right. Both sets of zeros tend to produce numbers
smaller in absolute value than they would have been if
more digits had been carried. In the noisy mode these
numbers are simply extended with 1s instead of zeros
(1s in a binary machine, 9s in a decimal machine). Now
all numbers tend to be too large in absolute value. The
true value, if there had been no significance loss,
should lie between these two extremes. Hence, two runs,
one made without and one made with the noisy mode,
should show differences in result that indicate which
digits may have been affected by significance loss
(Buchholz 1962, p. 102).''
See \cite{Buchholz:1962:PCS} for more information about
the Stretch noisy mode.",
}
@Book{MacKenzie:1991:NAC,
author = "Donald MacKenzie and Edinburgh Pict",
title = "Negotiating arithmetic, construction proof: the
sociology of mathematics and information technology",
volume = "38",
publisher = "Research Centre for Social Sciences, University of
Edinburgh",
address = "Edinburgh",
pages = "27",
year = "1991",
ISBN = "1-872287-42-5",
ISBN-13 = "978-1-872287-42-3",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Edinburgh PICT working paper",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic; Computer security; Floating-point
arithmetic",
}
@Article{Marcus:1991:HSR,
author = "Marvin Marcus and Markus Sandy",
title = "{Hadamard} Square Roots",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "1",
pages = "49--69",
month = jan,
year = "1991",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A57 (15A18 15A48 15A52 47B15 60H25)",
MRnumber = "92a:15027",
MRreviewer = "Zdzis{\l}aw W. Trzaska",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Markstein:1991:WFF,
author = "V. Markstein and P. Markstein and T. Nguyen and S.
Poole",
title = "Wide Format Floating-Point Math Libraries",
crossref = "IEEE:1991:PSA",
pages = "130--138",
year = "1991",
DOI = "https://doi.org/10.1145/125826.125903",
bibdate = "Wed Dec 13 18:34:51 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present the performance and accuracy
evaluations of eleven transcendental functions found in
64- and 128-bit floating-point formats in math
libraries on the Cray Y-MP, the IBM 3090E/VF, the
Convex C-240, the Hewlett--Packard 9000/720, and the
IBM System/6000. Both architecture and algorithms are
shown to impact the results.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "ISQUARE, Inc., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods); C5470
(Performance evaluation and testing); C7310
(Mathematics)",
confdate = "18-22 Nov. 1991",
conflocation = "Albuquerque, NM, USA",
confsponsor = "IEEE; ACM",
keywords = "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
Cray Y-MP; Floating-point formats; Hewlett--Packard
9000/720; IBM 3090E/VF; IBM System/6000; Math
libraries; Performance; Transcendental functions; Wide
format floating point math libraries",
numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
thesaurus = "Digital arithmetic; Mathematics computing; Parallel
processing; Performance evaluation",
}
@Article{McQuillan:1991:HPV,
author = "S. E. McQuillan and J. V. McCanny and R. F. Woods",
title = "High performance {VLSI} architecture for division and
square root",
journal = j-ELECT-LETTERS,
volume = "27",
number = "1",
pages = "19--21",
day = "3",
month = jan,
year = "1991",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "A novel high performance bit parallel architecture to
perform square root and division is proposed. Relevant
VLSI design issues have been addressed. By employing
redundant arithmetic and a semisystolic schedule, the
throughput has been made \ldots{}",
}
@InProceedings{McQuillan:1991:VAM,
author = "S. E. McQuillan and J. V. McCanny",
booktitle = "1991 International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP-91, 14--17} April 1991",
title = "A {VLSI} architecture for multiplication, division and
square root",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1205--1208",
year = "1991",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A high-performance VLSI architecture to perform
combined multiply-accumulate, divide, and square root
operations is proposed. The circuit is highly regular,
requires only minimal control, and can be reconfigured
for every cycle. The execution time \ldots{}",
}
@PhdThesis{Mehrez:1991:AVP,
author = "Habib Mehrez",
title = "Des architectures {VLSI} pipelin{\'e}s pour les
algorithmes num{\'e}riques {\`a} flots de donn{\'e}es
en repr{\'e}sentations arithm{\'e}tiques virgule fixe
et virgule flottante. ({French}) [{Pipelined VLSI}
architectures for numerical algorithms for numerical
data in fixed- and floating-point arithmetic]",
type = "Th{\`e}se Doctoral",
school = "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
address = "Paris, France",
year = "1991",
bibdate = "Thu May 09 10:10:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Sous la direction de Alain Greiner.",
abstract = "Dans cette th{\`e}se, on se propose d'exposer
certaines reflexions et contributions dans le
d{\'e}veloppement et la recherche en architectures VLSI
pour l'implantation des algorithmes de traitement
num{\'e}rique {\`a} flots des donn{\'e}es. On exposera
en particulier une m{\'e}thodologie g{\'e}n{\'e}rale
d'implantation concr{\'e}tis{\'e}e par des {\'e}tudes
et des r{\'e}alisations des architectures
sp{\'e}cifiques {\`a} la transform{\'e}e de Fourier
rapide (TFR ou FFT). Ces architectures concernent aussi
bien des traitements arithm{\'e}tiques en virgule fixe
qu'en virgule flottante et seront de type pipelin{\'e}s
serie systolique. Des propositions d'implantation des
op{\'e}rateurs arithm{\'e}tiques de base et des chemins
des donn{\'e}es seront developp{\'e}es ainsi que les
{\'e}valuations des performances et de leur
complexit{\'e} correspondantes. Il sera discut{\'e} des
facteurs de classification et d'interactions entre les
aspects fonctionnels et algorithmiques, les aspects
structurels et architecturaux et finalement les aspects
li{\'e}s aux implantations VLSI. Ces derniers aspects
concernent notamment les compromis et les choix
logiques, {\'e}lectriques et topologiques. La
m{\'e}thode de conception est bas{\'e}e sur
l'utilisation d'une biblioth{\`e}que de cellules
standards qui inclut la technique LSSD, de test et
testabilit{\'e}, au moment de la conception des
circuits VLSI.",
acknowledgement = ack-nhfb,
language = "French",
}
@InProceedings{Mehta:1991:HSM,
author = "Mayur Mehta and Vijay Parmar and Earl {Swartzlander,
Jr.}",
title = "High-speed multiplier design using multi-input counter
and compressor circuits",
crossref = "Kornerup:1991:PIS",
pages = "43--50",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Mehta.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Manual{Microsoft:1991:MCC,
author = "{Microsoft Corporation}",
title = "{Microsoft C, C++}: version 7.0: programming
techniques for {MS-DOS} and {Windows} operating
systems",
organization = "Microsoft Corp.",
address = "Redmond, WA, USA",
pages = "xix + 323",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Microsoft C++.; Microsoft C.; MS - DOS (Computer
file); Windows (Computer programs)",
remark = "Improving program performance: optimizing your
programs; using precompiled header files; reducing
program size with p-code; managing memory in C;
managing memory in C++; using the inline assembler;
controlling floating-point math operations --- Special
environments: compiling with the QuickWin windows
library; communicating with graphics; creating charts
and graphs; programming with mixed languages; writing
portable C programs --- P-code instruction tables. [The
book] describes how to take advantage of the special
features of Microsoft C/C++. The topics covered by this
manual include language extensions, special-purpose
library functions, and the interaction between
programming strategies and compiler options. This
manual is not a reference for the tools included with
Microsoft C/C++. -Introd.",
}
@Article{Montuschi:1991:OAE,
author = "P. Montuschi and M. Mezzalama",
title = "Optimal Absolute Error Starting Values for
{Newton--Raphson} Calculation of Square Root",
journal = j-COMPUTING,
volume = "46",
number = "1",
pages = "67--86",
year = "1991",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65H05 (65G99)",
MRnumber = "92a:65161",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
affiliation = "Politecnico di Torino",
affiliationaddress = "Torino, Italy",
classification = "723; 921",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput Vienna New York",
keywords = "Absolute Error; Computer Programming --- Algorithms;
Mathematical Techniques; Newton--Raphson Method;
Optimization; Square Roots",
}
@InProceedings{Montuschi:1991:SRD,
author = "Paolo Montuschi and Luigi Ciminiera",
title = "Simple radix 2 division and square root with skipping
of some addition steps",
crossref = "Kornerup:1991:PIS",
pages = "202--209",
year = "1991",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
summary = "The authors present a novel algorithm for shared radix
2 division and square root whose main characteristic is
the ability to avoid any addition when the digit 0 has
been selected. The solution presented uses a redundant
representation of the \ldots{}",
}
@Article{Mulder:1991:AMC,
author = "J. M. Mulder and N. T. Quach and M. J. Flynn",
title = "An area model for on-chip memories and its
application",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "26",
number = "2",
pages = "98--105",
month = feb,
year = "1991",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@InProceedings{Muller:1991:EAF,
author = "Michael M{\"u}ller and Christine R{\"u}b and Wolfgang
R{\"u}lling",
title = "Exact accumulation of floating-point numbers",
crossref = "Kornerup:1991:PIS",
pages = "64--69",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Muller.pdf",
abstract = "The authors present a new idea for designing a chip
which computes the exact sum of arbitrarily many
floating-point numbers, i.e., it can accumulate the
floating-point numbers without cancellation. Such a
chip is needed to provide a fast implementation of
Kulisch arithmetic. This is a new theory of
floating-point arithmetic which makes it possible to
compute least significant bit accurate solutions to
even ill-conditioned numerical problems. The proposed
approach avoids the disadvantages of previously
suggested designs which are too large, too slow, or
consume too much power. The crucial point is a
technique for a fast carry resolution in a long
accumulator. It can also be implemented in software.",
acknowledgement = ack-nhfb,
affiliation = "Max-Planck-Inst., Saarbrucken, Germany",
classification = "B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5230 (Digital arithmetic methods)",
keywords = "Accumulator; ARITH-10; Chip; Exact accumulation; Exact
sum; Fast carry resolution; Floating-point arithmetic;
Floating-point numbers; Ill-conditioned numerical
problems; Kulisch arithmetic; Least significant bit
accurate solutions",
thesaurus = "Adders; Digital arithmetic",
}
@InProceedings{Muller:1991:FSC,
author = "Jean-Michel Muller and Peter Kornerup and David W.
Matula",
title = "Foreword: {10th Symposium on Computer Arithmetic,
Grenoble, France, June 26--28, 1991}",
crossref = "Kornerup:1991:PIS",
pages = "v--v",
year = "1991",
bibdate = "Sat Nov 17 08:46:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Mundie:1991:OOR,
author = "David A. Mundie and David A. Fisher",
title = "Optimized Overload Resolution and Type Matching for
{Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "3",
pages = "83--90",
month = "Spring",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:41 MDT 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "C6140D (High level languages); C5230 (Digital
arithmetic methods)",
conflocation = "Redondo Beach, CA, USA; 30 April-2 May 1990",
conftitle = "1st International Symposium on Environments and Tools
for Ada",
corpsource = "Incremental Syst. Corp., Pittsburgh, PA, USA; Computer
Sci. Dept., University of Wisconsin, Madison, WI, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; computational methods; digital arithmetic;
incremental environment; microprogramming interval
arithmetic; nodes; overload resolution; pruning
heuristics; recursive strategy; tree; type matching",
sponsororg = "IEEE",
treatment = "P Practical; A Application",
}
@PhdThesis{Mutrie:1991:TSS,
author = "Mark P. W. Mutrie",
title = "Towards a Symbolic System for Floating-Point Error
Analysis",
school = "University of Waterloo",
year = "1991",
bibdate = "Thu Nov 8 14:50:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Myczkowski:1991:SMA,
author = "J. Myczkowski and G. Steele",
title = "Seismic modeling at {15 Gigaflops} on the {Connection
Machine}",
crossref = "IEEE:1991:PSA",
pages = "316--326",
year = "1991",
bibdate = "Wed Apr 15 16:28:01 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "A9130 (Seismology); C4170 (Differential equations);
C5440 (Multiprocessor systems and techniques); C7340
(Geophysics)",
corpsource = "Thinking Machines Corp., Cambridge, MA, USA",
keywords = "14 GFLOPS; acoustic wave equation; CM-2 supercomputer;
Connection Machine; difference equations; finite
difference algorithm; floating point unit; geophysics
computing; instruction sequence; interprocessor grid
communication; massively parallel machine; memory
interface; parallel processing; seismic modelling code;
seismology; sponge boundary conditions; stencil
compiler",
sponsororg = "IEEE; ACM",
treatment = "A Application; P Practical",
}
@Article{Nagal:1991:PEM,
author = "T. Nagal",
title = "Performance evaluation of mathematical functions",
journal = j-SUPERCOMPUTER,
volume = "8",
number = "8",
pages = "46--56",
month = nov,
year = "1991",
CODEN = "SPCOEL",
ISSN = "0168-7875",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Supercomputer",
}
@InProceedings{Nakano:1991:MBM,
author = "H. Nakano and M. Nakajima and Y. Nakahura and T.
Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
Kishida and H. Kadora",
title = "A 80 {MFLOPS} 64-bit Microprocessor for Parallel
Computer",
crossref = "IEEE:1991:PIC",
pages = "15.2/1--4",
year = "1991",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Nelson:1991:SPM,
editor = "Greg Nelson",
title = "Systems Programming with {Modula-3}",
publisher = pub-PH,
address = pub-PH:adr,
pages = "ix + 267",
year = "1991",
ISBN = "0-13-590464-1",
ISBN-13 = "978-0-13-590464-0",
LCCN = "QA76.66 .S87 1991",
bibdate = "Mon Sep 12 08:08:01 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A description of the Modula 3 programming language by
the committee that designed it, with an entertaining
appendix on how various design decisions were made.
Section 3.4 describes three floating-point interfaces
that provide parameters of the underlying
floating-point system, access primitives, and exception
handling.",
acknowledgement = ack-nj,
}
@Article{Ochs:1991:NRU,
author = "T. Ochs",
title = "Numerics for the rest of us",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "10",
pages = "113--127",
month = oct,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Ochs:1991:NTR,
author = "T. Ochs",
title = "Numeric types, representations, and other fictions",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "8",
pages = "93--101",
month = aug,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Ochs:1991:RF,
author = "T. Ochs",
title = "A rotten foundation",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "2",
pages = "103--107",
month = feb,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:05 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Ochs:1991:SRF,
author = "T. Ochs",
title = "Son of rotten foundation: The sequel",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "3",
pages = "85--91",
month = mar,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Fri Dec 08 13:04:29 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{OGrady:1991:HOA,
author = "E. Pearse O'Grady and Baek-Kyu K. Young",
title = "A Hardware-Oriented Algorithm for Floating-Point
Function Generation",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "2",
pages = "237--241",
month = feb,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.73596",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73596",
abstract = "An algorithm is presented for performing accurate,
high-speed, floating-point function generation for
univariate functions defined at arbitrary breakpoints.
Rapid identification of the breakdown interval, which
includes the input argument, is the key operation in
the algorithm. A hardware implementation which makes
extensive use of read\slash write memories illustrates
the algorithm.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Okabe:1991:LDC,
author = "Y. Okabe and N. Takagi and S. Yaima",
key = "OTY91",
title = "Log-Depth Circuits for Elementary Functions Using
Residue Number System",
journal = j-ELECTRON-COMMUN-JPN,
volume = "74",
number = "8",
pages = "31--37",
year = "1991",
CODEN = "ECOJAL",
ISSN = "0424-8368",
bibdate = "Mon May 19 15:16:09 1997",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan",
}
@InProceedings{Orup:1991:HRH,
author = "Holger Orup and Peter Kornerup",
title = "{A} high-radix hardware algorithm for calculating the
exponential {$ M^E \bmod N $}",
crossref = "Kornerup:1991:PIS",
pages = "51--56",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Orup.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Ozawa:1991:FND,
author = "K. Ozawa",
title = "A Fast {$ O(n^2) $} Division Algorithm for
Multiple-Precision Floating-Point Numbers",
journal = j-INFO-PROC,
volume = "14",
number = "3",
pages = "354--356",
month = "????",
year = "1991",
bibdate = "Thu Sep 1 10:15:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Ozawa:1991:FOD,
author = "K. Ozawa",
title = "A Fast {$ O(n^2) $} Division Algorithm for
Multiple-Precision Floating-Point Numbers",
journal = j-J-INF-PROCESS,
volume = "14",
number = "3",
pages = "354--356",
month = "????",
year = "1991",
CODEN = "JIPRDE",
ISSN = "0387-6101",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A fast O(n/sup 2/) algorithm is derived for the
division of multiple-precision floating-point numbers,
where $n$ is the number of digits in each of the
numbers. This algorithm, which is a modification of the
conventional pencil-and-paper technique, is as fast as
the conventional $ O(n^2) $ multiplication and 2.67
times faster than the algorithm based on the Newton
method.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Coll. of Gen. Educ.,
Tohoku University, Miyagi, Japan",
classification = "C4240 (Programming and algorithm theory)",
fjournal = "Journal of Information Processing",
keywords = "Fast O(n/sup 2/) division algorithm;
Multiple-precision floating-point numbers; Newton
method",
pubcountry = "Japan",
thesaurus = "Algorithm theory; Digital arithmetic",
}
@InProceedings{Parikh:1991:RBE,
author = "Shrikant N. Parikh and David W. Matula",
title = "A redundant binary {Euclidean GCD} algorithm",
crossref = "Kornerup:1991:PIS",
pages = "220--225",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Parikh.pdf",
abstract = "An efficient implementation of the Euclidean GCD
(greatest common divisor) algorithm employing the
redundant binary number system is described. The time
complexity is O(n), utilizing O(n)4-2 signed 1-b adders
to determine the GCD of two n-b integers. The process
is similar to that used in SRT division. The efficiency
of the algorithm is competitive, to within a small
factor, with floating point division in terms of the
number of shift and add/subtract operations. The
novelty of the algorithm is based on properties derived
from the proposed scheme of normalization of signed bit
fractions. The implementation is well suited for
systolic hardware design.",
acknowledgement = ack-nhfb,
affiliation = "IBM, Westlake, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ARITH-10; Euclidean GCD; Floating point division;
Greatest common divisor; Redundant binary number
system; Signed bit fractions; Systolic hardware design;
Time complexity",
thesaurus = "Computational complexity; Digital arithmetic",
}
@InProceedings{Paterson:1991:SMC,
author = "Michael S. Paterson and Uri Zwick",
title = "Shallow multiplication circuits",
crossref = "Kornerup:1991:PIS",
pages = "28--34",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Peterson.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Misc{Paxson:1991:PTI,
author = "Vern Paxson and W. Kahan",
title = "A Program for Testing {IEEE} Binary--Decimal
Conversion",
howpublished = "World-Wide Web document",
month = may,
year = "1991",
bibdate = "Wed Jan 29 17:59:29 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.ee.lbl.gov/testbase-report.ps.Z;
ftp://ftp.ee.lbl.gov/testbase.tar.Z",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; floating-point
testing",
}
@InProceedings{Piestrak:1991:DRG,
author = "Stanis{\l}aw J. Piestrak",
title = "Design of Residue Generators and Multioperand Modular
Adders Using Carry-Save Adders",
crossref = "Kornerup:1991:PIS",
pages = "100--107",
year = "1991",
bibdate = "Sat Nov 17 08:46:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Piestrak.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Plauger:1991:AF,
author = "P. J. Plauger",
title = "Approximating functions",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "6",
pages = "17--25",
month = jun,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Plauger:1991:EP,
author = "P. J. Plauger",
title = "Economizing polynomials",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "7",
pages = "21--27",
month = jul,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Plauger:1991:FPA,
author = "P. J. Plauger",
title = "Floating-Point Arithmetic",
journal = j-EMBED-SYS-PROG,
volume = "4",
number = "8",
pages = "95--99",
month = aug,
year = "1991",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Thu Sep 1 10:14:15 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Embedded Systems Programming",
}
@Article{Plauger:1991:FPP,
author = "P. J. Plauger",
title = "Floating-Point Primitives",
journal = j-JCLT,
volume = "3",
number = "2",
pages = "89--100",
month = sep,
year = "1991",
ISSN = "1042-5721",
bibdate = "Thu Nov 8 14:50:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "The Journal of {C} Language Translation",
}
@Article{Plauger:1991:HTF,
author = "P. J. Plauger",
title = "The Header {{\tt <float.h>}}",
journal = j-CUJ,
volume = "9",
type = "{Standard C}",
number = "1",
pages = "9--??",
month = jan,
year = "1991",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Plauger:1991:WW,
author = "P. J. Plauger",
title = "Washing the watchers",
journal = j-COMP-LANG-MAG,
volume = "8",
number = "9",
pages = "23--32",
month = sep,
year = "1991",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 1 10:15:07 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@InProceedings{Priest:1991:AAP,
author = "Douglas M. Priest",
title = "Algorithms for Arbitrary Precision Floating Point
Arithmetic",
crossref = "Kornerup:1991:PIS",
pages = "132--143",
year = "1991",
DOI = "https://doi.org/10.1109/ARITH.1991.145549",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Priest.pdf",
abstract = "The author presents techniques for performing
computations of very high accuracy using only
straightforward floating-point arithmetic operations of
limited precision. The validity of these techniques is
proved under very general hypotheses satisfied by most
implementations of floating-point arithmetic. To
illustrate the applications of these techniques, an
algorithm is presented which computes the intersection
of a line and a line segment. The algorithm is
guaranteed to correctly decide whether an intersection
exists and, if so, to produce the coordinates of the
intersection point accurate to full precision. The
algorithm is usually quite efficient; only in a few
cases does guaranteed accuracy necessitate an expensive
computation.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Department of Math., California University, Berkeley,
CA, USA",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
keywords = "accurate floating-point summation; ARITH-10;
coordinates; floating point arithmetic; intersection
point; line intersection; line segment",
thesaurus = "Digital arithmetic; Number theory",
}
@Article{Pugh:1991:TFV,
author = "Kenneth Pugh and Hugo Calleens",
title = "{{\tt float}}s Versus {{\tt double}}s",
journal = j-CUJ,
volume = "9",
type = "Questions and Answers",
number = "6",
pages = "117--??",
month = jun,
year = "1991",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@TechReport{Quach:1991:DIS,
author = "N. Quach and M. Flynn",
title = "Design and implementation of the {SNAP} floating-point
adder",
type = "Technical Report",
number = "CSL-TR-91-501",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = dec,
year = "1991",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@TechReport{Quach:1991:FIR,
author = "N. Quach and N. Takagi and M. J. Flynn",
title = "On Fast {IEEE} Rounding",
type = "Technical Report",
number = "CSL-TR-91-459",
institution = "Stanford University",
address = "Stanford, CA, USA",
pages = "v + 27",
month = jan,
year = "1991",
bibdate = "Sun Dec 10 14:08:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://i.stanford.edu/pub/cstr/reports/csl/tr/91/459/CSL-TR-91-459.pdf",
abstract = "A systematic general rounding procedure is proposed.
This procedure consists of 2 steps: constructing a
rounding table and selecting a prediction scheme.
Optimization guidelines are given in each step to
minimize the hardware used. This procedure-based
rounding method has the additional advantage that
verification and generalization are trivial. Two
rounding hardware models are described. The first is
shown to be identical to that reported by Santoro, et
al. The second is more powerful, providing solutions
where the first fails. Applying this approach to the
IEEE rounding modes for high-speed conventional binary
multipliers reveals that round to infinity is more
difficult to implement than the round to nearest mode;
more adders are potentially needed. Round to zero
requires the least amount of hardware. A generalization
of this procedure to redundant binary multipliers
reveals two major advantages over conventional binary
multipliers. First, the computation of the sticky bit
consumes considerably less hardware. Second,
implementing round to positive and minus infinity modes
does not require the examination of the sticky bit,
removing a possible worst-case path. A generalization
of this approach to addition produces a similar
solution to that reported by Quach and Flynn. Although
generalizable to other kinds of rounding as well as
other arithmetic operations, we only treat the case of
IEEE rounding for addition and multiplication; IEEE
rounding because it is the current standard on
rounding, addition and multiplication because they are
the most frequently used arithmetic operations in a
typical scientific computation.",
acknowledgement = ack-nhfb,
keywords = "high-speed floating-point adders; high-speed parallel
multipliers; IEEE rounding; redundant binary
multipliers; redundant binary representation",
}
@TechReport{Quach:1991:LOP,
author = "N. T. Quach and M. J. Flynn",
title = "Leading one prediction --- implementation,
generalization, and application",
type = "Technical Report",
number = "CSL-TR-91-463",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = mar,
year = "1991",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Raja:1991:NDT,
author = "Paruvachi V. R. Raja",
title = "Novel Design Techniques for {RNS} Systolic {VLSI}
Arrays",
journal = j-LECT-NOTES-COMP-SCI,
volume = "507",
pages = "206--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon May 13 08:51:55 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Rao:1991:ARN,
author = "B. D. Rao",
booktitle = "Acoustics, Speech, and Signal Processing, 1991.
{ICASSP-91., 1991} International Conference on. 14--17
April 1991",
title = "Analysis of roundoff noise in floating point digital
filters",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1893--1896",
year = "1991",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A systematic approach for the analysis of roundoff
noise in floating point digital filters is presented.
The analysis is based on a high level model developed
to deal with the errors in the inner product operation.
The model consists of an efficient \ldots{}",
}
@Article{Rees:1991:RRA,
author = "Jonathan Rees and William Clinger and others",
title = "The revised$^4$ report on the algorithmic language
{Scheme}",
journal = "ACM SIGPLAN Lisp Pointers",
volume = "4",
number = "3",
pages = "1--55",
month = jul # "\slash " # sep,
year = "1991",
bibdate = "Wed Jan 29 16:50:56 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``the result [of a
binary-to-decimal conversion] is expressed using the
minimum number of digits\ldots{}''",
}
@Article{Rump:1991:CAI,
author = "Siegfried M. Rump",
title = "A Class of Arbitrarily Ill-Conditioned Floating-Point
Matrices",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "4",
pages = "645--653",
month = oct,
year = "1991",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F35 (15A12 65G05)",
MRnumber = "92d:65076",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Scott:1991:MCS,
author = "T. J. Scott",
title = "Mathematics and computer science at odds over real
numbers",
journal = j-SIGCSE,
volume = "23",
number = "1",
pages = "130--139",
month = mar,
year = "1991",
CODEN = "SIGSD3",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
bibdate = "Tue Dec 12 09:20:21 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "22nd SIGCSE Technical Symposium on Computer Science
Education.",
abstract = "Discusses the `real numbers' data type as implemented
by `floating point' numbers. Floating point
implementations and a theorem that characterizes their
truncations are presented. A teachable floating point
system is presented, chosen so that most problems can
be worked out with paper and pencil. Then major
differences between floating point number systems and
the continuous real number system are presented.
Important floating point formats are next discussed.
Two examples derived from actual computing practice on
mainframes, minicomputers, and PCs are presented. The
paper concludes with a discussion of where floating
point arithmetic should be taught in standard courses
in the ACM curriculum.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Western Illinois
University, Macomb, IL, USA",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods)",
confdate = "7-8 March 1991",
conflocation = "San Antonio, TX, USA",
confsponsor = "ACM",
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
keywords = "ACM curriculum; Computer science; Floating point
arithmetic; Floating point formats; Floating point
number systems; Real number data types; Standard
courses; Teaching; Truncations",
thesaurus = "Computer science education; Data structures; Digital
arithmetic; Educational courses; Number theory",
}
@TechReport{Seznec:1991:OCE,
author = "Andre Seznec and Karl Courtel",
title = "{OPAC}: a cost-effective floating-point coprocessor =
Le coprocessor num{\'e}rique {OPAC}",
institution = "Institut National de Recherche en Informatique et en
Automatique",
address = "Le Chesnay, France",
pages = "24",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Rapports de recherche. Institut National de Recherche
en Informatique et en Automatique; 1461 Rapports de
recherche (Institut national de recherche en
informatique et en automatique (France)); 1461.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
remark = "Abstracts in English and French. ``Mai 1991.''
Abstract: ``The effective performance of RISC
microprocessors on numerical applications remains on
the order of a few megaflops/s. In this paper, we show
that the static addressing of the registers in standard
RISC floating-point coprocessors is one of the main
bottleneck [sic] for performance. In the architecture
of the coprocessor OPAC, we propose an alternative
using only FIFO queues for storing intermediate results
and reusable operands. Performance close to
multiplication-accumulation every cycle is expected on
a large set of numerical applications at a reasonable
hardware cost.'' Supported in part by the CNRS PRC-AMN
Supported in part by the French Ministry of Defense.",
}
@TechReport{Seznec:1991:OFP,
author = "Andre Seznec and Karl Courtel",
title = "{OPAC}: a floating-point coprocessor dedicated to
compute-bound kernels = {OPAC}: un coprocesseur
flottant dedi{\'e} au calcul matriciel",
type = "Rapports de recherche",
number = "1555",
institution = "Institut National de Recherche en Informatique et en
Automatique",
address = "Le Chesnay, France",
pages = "27",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Array processors.; Kernel functions.; Parallel
programming (Computer science)",
remark = "Abstracts in English and French. ``October 7, 1991.''
Abstract: ``In various application domains, programmers
are not specialists of parallel programming, but are
demanding for performance that cannot be reached
without using parallelism. Nevertheless, in many
applications, the main part of the computations may be
encapsulated in compute-bounds kernels with [sic]
exhibit high potential parallelism. Achieving high
performance on compute-bound primitives at a low
hardware cost has became [sic] an important challenge.
In this paper, we present the architecture of the OPAC
floating-point operator. OPAC has been designed in
order to be the basic cell in a multi-cell
floating-point coprocessor dedicated to the execution
of the most useful compute-bound kernels. The peak
performance of one floating-point multiply-add per
cycle per cell obtained on the OPAC prototype may be
approached in a microprocessor environment on a
multi-cell OPAC floating-point coprocessor on a large
set of numerical applications.'' Supported in part by
the French ministry of defense. Supported in part by
the CNRS (PRC-ANM and GCIS)",
}
@Article{Shaeffer:1991:HEP,
author = "D. L. Shaeffer and J. R. Kimbrough and S. M. Denton
and J. L. Kaschmitter and J. W. Wilburn and R. W. Davis
and N. J. Colella and D. B. Holtkamp",
title = "High energy proton {SEU} test results for the
commercially available {MIPS R3000} microprocessor and
{R3010} floating point unit",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "38",
number = "6",
pages = "1421--1428",
month = dec,
year = "1991",
CODEN = "IRNSAM",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
keywords = "floating-point testing",
summary = "Proton single event upset (SEU) cross sections and
proton total dose hardness of commercially available
MIPS R3000 microprocessors (CPU) and R3010 floating
point units (FPU) were obtained by exposing these parts
to 256 MeV protons from the linear accelerator
\ldots{}",
}
@Article{Shand:1991:HSL,
author = "M. Shand and P. Bertin and J. Vuillemin",
title = "Hardware speedups in long integer multiplication",
journal = j-COMP-ARCH-NEWS,
volume = "19",
number = "1",
pages = "106--113",
month = mar,
year = "1991",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:33 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Book{Siewiorek:1991:AST,
author = "Daniel P. Siewiorek and Philip John {Koopman, Jr.}",
title = "The Architecture of Supercomputers\emdash Titan, {A}
Case Study",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 202",
year = "1991",
ISBN = "0-12-643060-8",
ISBN-13 = "978-0-12-643060-8",
LCCN = "QA76.5 S536 1991",
bibdate = "Sun Jan 23 17:54:38 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Skavantzos:1991:PRN,
author = "A. Skavantzos and F. J. Taylor",
title = "On the polynomial residue number system [digital
signal processing]",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "39",
number = "2",
pages = "376--382",
month = feb,
year = "1991",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.80821",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2656",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "The theory of the polynomial residue number system
(PRNS), a system in which totally parallel polynomial
multiplication can be achieved provided that the
arithmetic takes place in some carefully chosen ring,
is examined. Such a system is defined by \ldots{}",
}
@Article{Smith:1991:AFP,
author = "David M. Smith",
title = "{Algorithm 693}: {A FORTRAN} Package for
Floating-Point Multiple-Precision Arithmetic",
journal = j-TOMS,
volume = "17",
number = "2",
pages = "273--283",
month = jun,
year = "1991",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/108556.108585",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Dec 13 18:36:25 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p273-smith/",
abstract = "FM is a collection of FORTRAN-77 routines which
performs floating-point multiple-precision arithmetic
and elementary functions. Results are almost always
correctly rounded, and due to improved algorithms used
for elementary functions, reasonable efficiency is
obtained.",
acknowledgement = ack-nhfb,
affiliation = "Loyola Marymount University, Los Angeles, CA, USA",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods); C7310
(Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Accuracy; correct rounding; Elementary functions;
floating-point arithmetic; Floating-point
multiple-precision arithmetic; FM; FORTRAN-77 routines;
Mathematical library; Portable software; Rounding off",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 77.",
thesaurus = "Digital arithmetic; Function approximation;
Mathematics computing; Software packages; Subroutines",
}
@Article{Sorensen:1991:OEC,
author = "D. C. Sorensen and Ping Tak Peter Tang",
title = "On the Orthogonality of Eigenvectors Computed by
Divide and Conquer Techniques",
journal = j-SIAM-J-NUMER-ANAL,
volume = "28",
number = "6",
pages = "1752--1775",
month = dec,
year = "1991",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15 (65G05)",
MRnumber = "92h:65065",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database; Parallel/par.lin.alg.bib;
Theory/Matrix.bib",
note = "Pages 1759--1761 discuss implementation of useful
primitives for higher-precision arithmetic: DPAdd2(),
DPAdd3(), DPDiv().",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
kwds = "nla, eig, prll, symmetric matrix",
}
@PhdThesis{Sparmann:1991:SBT,
author = "U. Sparmann",
title = "Structure Based Test Methods for Arithmetic Circuits",
type = "{Ph.D.} thesis",
school = "Computer Science Department, University of Saarland",
address = "Saarbr{\"u}cken, Germany",
year = "1991",
bibdate = "Tue Mar 13 10:30:20 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "In German.",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
remark = "Cited in \cite{Mueller:2000:CAC}.",
}
@Article{Squire:1991:ANS,
author = "Jon S. Squire",
title = "{Ada} numerics standardization and testing",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
address = "New York, NY, USA",
pages = "1--286",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada (Computer program language); floating-point
testing",
remark = "A special edition from SIGAda \ldots{} presented by
SIGAda Numerics Working Group and Ada-Europe Numerics
Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
Rapporteur Group.",
tableofcontents = "Introduction to the proposed standard for the
elementary functions in Ada / Kenneth W. Dritz\\
Proposed standard for a generic package of elementary
functions for Ada / edited by Kenneth W. Dritz\\
Rationale for the proposed standard for a generic
package of elementary functions for Ada; Proposed
standard for a generic package of primitive functions
for Ada; Rationale for the proposed standard for a
generic package of primitive functions for Ada /
Kenneth W. Dritz\\
Proposed standard for packages of real and complex type
declarations and basic operations for Ada (including
vector and matrix types) / edited by Graham S.
Hodgson\\
Rationale for the proposed standard for packages of
real and complex type declarations and basic operations
for Ada (including vector and matrix types) / Graham S.
Hodgson. Proposed standard for a generic package of
complex elementary functions / edited by Jon S. Squire
\\
Rationale for the proposed standard for a generic
package of complex elementary functions / Jon S. Squire
\\
A portable generic elementary function package in Ada
and an accurate test suite / Ping Tak Peter Tang \\
Towards validation of generic elementary functions and
other standard Ada numerics packages / Jon S. Squire\\
Floating point attributes in Ada / Dik T. Winter\\
An Ada math library for real-time avionics / Donald A.
Celarier and Donald W. Sando\\
Predefined floating point type names, uniformity
rapporteur group UI-48 / edited by Jon S. Squire.",
}
@InProceedings{Steidley:1991:FPA,
author = "C. W. Steidley",
title = "Floating point arithmetic basic exercises in
mathematical reasoning for computer science majors",
crossref = "ASEE:1991:CCW",
pages = "191--197 vol.1",
year = "1991",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The author gives examples demonstrating how an
unsuspecting user of floating point arithmetic on
computers may be misled by results. Specifically, there
are cases where the fundamental rules of arithmetic
break down. Thus, it is even more imperative that
fledgling computer scientists have some insight into
the machinations of floating point arithmetic on
computers.",
acknowledgement = ack-nhfb,
affiliation = "Central Washington University, Ellensburg, WA, USA",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods)",
keywords = "Computer science majors; Computers; Floating point
arithmetic; Mathematical reasoning",
thesaurus = "Computer science education; Digital arithmetic",
}
@Article{Takagi:1991:RCM,
author = "N. Takagi and T. Asada and S. Yajima",
title = "Redundant {CORDIC} Methods with a Constant Scale
Factor for Sine and Cosine Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-40",
number = "9",
pages = "989--995",
month = sep,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83660",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Takagi:1991:RMM,
author = "Naofumi Takagi",
title = "{A} radix-$4$ modular multiplication hardware
algorithm efficient for iterative modular
multiplications",
crossref = "Kornerup:1991:PIS",
pages = "35--42",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Takagi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@TechReport{Tang:1991:TLAa,
author = "Ping Tak Peter Tang",
title = "Table-Lookup Algorithms for Elementary Functions and
Their Error Analysis",
type = "Technical Report",
number = "MCS-P194-1190",
institution = "Argonne National Laboratory",
address = "Argonne, IL, USA",
pages = "????",
year = "1991",
bibdate = "Thu Jan 30 16:25:10 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Tang:1991:TLAb,
author = "Ping Tak Peter Tang",
title = "Table-Lookup Algorithms for Elementary Functions and
Their Error Analysis",
crossref = "Kornerup:1991:PIS",
pages = "232--236",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tang.pdf",
acknowledgement = ack-nj # " and " # ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Taylor:1991:TFA,
author = "V. E. Taylor and A. Ranade and D. G. Messerschmitt",
title = "Three-dimensional finite-element analyses:
implications for computer architectures",
crossref = "IEEE:1991:PSA",
pages = "786--795",
year = "1991",
bibdate = "Wed Apr 15 16:28:01 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra); C4185 (Finite element
analysis); C4240P (Parallel programming and algorithm
theory); C5220P (Parallel architecture); C6110P
(Parallel programming); C6120 (File organisation)",
corpsource = "Department of Electr. Eng. and Computer Science,
California University, Berkeley, CA, USA",
keywords = "columns; computer architectures; data path design;
data structure; data structures; finite element
analysis; floating-point units; matrix algebra; memory
bandwidth; parallel architectures; parallel
programming; programming theory; rows; sparse matrices;
sparsity pattern",
sponsororg = "IEEE; ACM",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{teRiele:1991:NLB,
author = "H. J. J. {te Riele}",
title = "A new lower bound for the {de Bruijn-Newman}
constant",
journal = j-NUM-MATH,
volume = "58",
number = "6",
pages = "661--667",
year = "1991",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "30D10 (11M26 30D15 65E05)",
MRnumber = "92c:30030",
MRreviewer = "George L. Csordas",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
B0290R (Integral equations); C4130 (Interpolation and
function approximation); C4180 (Integral equations)",
corpsource = "Centre for Math. and Computer Science, Amsterdam,
Netherlands",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "complex zeros; de Bruijn-Newman constant;
high-precision floating-point computations; integral
equations; Jensen polynomial; lover bound; polynomials;
Riemann hypothesis; Sturm sequence",
treatment = "T Theoretical or Mathematical",
}
@Manual{TI:1991:TDH,
title = "{TMS34082} designer's handbook",
organization = "{Texas Instruments Incorporated}",
address = "Dallas, TX, USA",
edition = "Revised",
pages = "various",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer graphics --- Equipment and supplies.;
Floating-point arithmetic --- Computer simulation.;
Integrated circuits --- Very large scale integration
--- Handbooks,; manuals, etc.",
remark = "``Datapath VLSI products''--Cover. ``2564007-9721
revision A, May 1991''--T.p.",
}
@Manual{TI:1991:TFDa,
title = "{TMS320} floating-point {DSP} optimizing {C} compiler
user's guide",
organization = "{Texas Instruments Incorporated}",
address = "Dallas, TX, USA",
edition = "Revised",
pages = "various",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Compilers (Computer programs).; manuals, etc.; Signal
processing --- Digital techniques --- Equipment and;
supplies.; Texas Instruments TMS320 series
microprocessors --- Handbooks",
remark = "``Microprocessor development systems''--Cover.
``2576391-9721 revision A, October 1991''--T.p.",
}
@Manual{TI:1991:TFDb,
title = "{TMS320} floating-point {DSP} assembly language tools
user's guide",
organization = "{Texas Instruments Incorporated}",
address = "Dallas, TX, USA",
edition = "Revised",
pages = "various",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Assembler language (Computer program language).;
Handbooks, manuals, etc.; Signal processing --- Digital
techniques --- Equipment and; supplies.; Texas
Instruments TMS320 series microprocessors ---
Programming --",
remark = "``Microprocessor development systems''--Cover.
``2576328-9721 revision A, September 1991''--T.p.",
}
@Manual{TI:1991:TST,
title = "{TMS34082} software tool kit user's guide",
organization = "Texas Instruments Incorporated",
address = "Dallas",
edition = "2547321-9721 revision.",
pages = "various",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer storage devices.; TMS34082 Floating-Point
Processor.",
remark = "``Datapath VLSI products''--Cover. ``SSCA001''--P. [4]
of cover.",
}
@InProceedings{Tomabechi:1991:DMD,
author = "N. Tomabechi",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 11--14 June 1991",
title = "Design method of defect-tolerant {WSI} systems based
on the residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3082--3085",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1991.176199",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A design method is proposed for defect-tolerant WSI
arithmetic systems based on the RNS (residue number
system). The yield analysis has shown that the features
of the RNS are very well suited for the defect recovery
of WSIs. In the RNS, addition and \ldots{}",
}
@TechReport{Tsang:1991:SDC,
author = "Annie Tsang and Manfred Olschanowsky",
title = "A Study of {DataBase 2} Customer Queries",
type = "Technical Report",
number = "TR 03.413",
institution = "IBM Santa Teresa Laboratory",
address = "San Jose, CA, USA",
month = apr,
year = "1991",
bibdate = "Mon Mar 06 08:07:19 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "This report surveys the numeric data types used in
commercial databases by 51 major organizations, and
finds that 98.6\% of the numeric data are decimal.",
}
@Article{Tsubokawa:1991:FEA,
author = "Hiroshi Tsubokawa and Hajime Kubota and Shigeo
Tsujii",
title = "Floating-Point Error Analysis for Recursive
Least-Square Algorithm Using {UD} Factorization",
journal = j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI,
volume = "74",
number = "6",
pages = "1--10",
year = "1991",
CODEN = "ECJSER",
ISSN = "1042-0967 (print), 1520-6440 (electronic)",
ISSN-L = "1042-0967",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan. Part 3,
Fundamental electronic science",
}
@InProceedings{Tu:1991:ALA,
author = "Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac",
title = "Application of on-line arithmetic algorithms to the
{SVD} computation: preliminary results",
crossref = "Kornerup:1991:PIS",
pages = "246--255",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tu.pdf",
abstract = "A scheme for the singular value decomposition (SVD)
problem, based on online arithmetic, is discussed. The
design, using radix-2 floating-point online operations,
implemented in the LSI HCMOS gate-array technology, is
compared with a compatible conventional arithmetic
implementation. The preliminary results indicate that
the proposed online approach achieves a speedup of
2.4-3.2 with respect to the conventional solutions,
with 1.3-5.5 more gates and more than 6 times fewer
interconnections.",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ARITH-10; Floating-point online operations; Online;
Online arithmetic; Radix-2; Singular value
decomposition",
thesaurus = "Digital arithmetic",
}
@Article{Tu:1991:GAI,
author = "Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac",
title = "Gate Array Implementation of On-Line Algorithms for
Floating-Point Operations",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "3",
number = "4",
pages = "307--318",
month = oct,
year = "1991",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/BF00936903",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present gate array designs of on-line arithmetic
units for radix-2 floating-point addition,
multiplication and division operations. Performance and
complexity characteristics of the implementations of
on-line arithmetic units are discussed and compared
with those of the compatible conventional
floating-point algorithms implemented in the same
technology.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Turner:1991:IAE,
author = "Peter R. Turner",
title = "Implementation and analysis of extended {SLI}
operations",
crossref = "Kornerup:1991:PIS",
pages = "118--126",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Turner.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Umemura:1991:FNL,
author = "K. Umemura",
title = "Floating-point number {LISP}",
journal = j-SPE,
volume = "21",
number = "10",
pages = "1015--1026",
month = oct,
year = "1991",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Tue Dec 12 09:26:54 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A floating-point-number-oriented LISP has been
developed. Though it performs type checking on every
numeric operation, it runs as fast as Fortran for
simple differential-equation problems. The author
describes the implementation, provides some
measurements of its efficiency and discusses the
feasibility of this type of implementation.",
acknowledgement = ack-nhfb,
affiliation = "Software Labs., NTT Corp., Tokyo, Japan",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6140D (High level languages);
C7310 (Mathematics)",
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "Floating-point-number-oriented LISP; Numeric
operation; Simple differential-equation problems; Type
checking",
pubcountry = "UK",
thesaurus = "Digital arithmetic; LISP; Mathematics computing;
Symbol manipulation",
}
@Article{Umemura:1991:FPN,
author = "Kyoji Umemura",
title = "Floating-point Number {LISP}",
journal = j-SPE,
volume = "21",
number = "10",
pages = "1015--1026",
month = oct,
year = "1991",
CODEN = "SPEXBL",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A floating-point-number-oriented LISP has been
developed. Though it performs type checking on every
numeric operation, it runs as fast as Fortran for
simple differential-equation problems. The author
describes the implementation, provides some
measurements of its efficiency and discusses the
feasibility of this type of implementation.",
acknowledgement = ack-nhfb,
affiliation = "Software Labs., NTT Corp., Tokyo, Japan",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C6140D (High level languages);
C7310 (Mathematics)",
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "Floating-point-number-oriented LISP; Numeric
operation; Simple differential-equation problems; Type
checking",
pubcountry = "UK",
thesaurus = "Digital arithmetic; LISP; Mathematics computing;
Symbol manipulation",
}
@Article{Vassiliadis:1991:HWM,
author = "S. Vassiliadis and E. M. Schwarz and B. M. Sung",
title = "Hard-wired multipliers with encoded partial products",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "11",
pages = "1181--1197",
month = nov,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.102823",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=102823",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Vishin:1991:FPP,
author = "Sanjay Vishin",
title = "A floating point primitive classifier for the ray
casting machine",
type = "Typescript. Thesis ({M.S.})",
school = "Duke University. Department of Computer Science",
address = "Durham, NC 27708, USA",
pages = "ix + 79",
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer graphics.; Floating-point arithmetic.;
Geometry, Analytic --- Solid --- Data processing.;
Image processing.",
}
@InProceedings{Vuillemin:1991:CTA,
author = "J. E. Vuillemin",
title = "Constant time arbitrary length synchronous binary
counters",
crossref = "Kornerup:1991:PIS",
pages = "180--183",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Vuillemin.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Walter:1991:FMM,
author = "Colin D. Walter",
title = "Faster Modular Multiplication by Operand Scaling",
journal = j-LECT-NOTES-COMP-SCI,
volume = "576",
pages = "313--??",
year = "1991",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:48:11 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0576.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0576/05760313.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0576/05760313.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Wigley:1991:FMR,
author = "N. W. Wigley and G. A. Jullien",
title = "Flexible modulus residue number system for complex
digital signal processing",
journal = j-ELECT-LETTERS,
volume = "27",
number = "16",
pages = "1436--1438",
month = aug,
year = "1991",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2666",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "The quadratic residue number system (QRNS) is often
used for integer calculation on complex data streams. A
finite polynomial ring mapping technique is presented
that removes the $4k + 1$ prime divisor restriction of
the QRNS, albeit with an \ldots{}",
}
@InProceedings{Wigley:1991:SMR,
author = "N. Wigley and G. A. Jullien and D. Reaume and W. C.
Miller",
title = "Small moduli replications in the {MRRNS}",
crossref = "Kornerup:1991:PIS",
pages = "92--99",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Wigley.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Williams:1991:NBC,
author = "Ted E. Williams and Mark A. Horowitz",
title = "{A} 160 ns 54 bit {CMOS} division implementation using
self-timing and symmetrically overlapped {SRT} stages",
crossref = "Kornerup:1991:PIS",
pages = "210--217",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Williams.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Williams:1991:ZOS,
author = "Ted E. Williams and Mark A. Horowitz",
title = "A zero-overhead self-timed 160-ns 54-b {CMOS}
divider",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "26",
number = "11",
pages = "1651--1661",
month = nov,
year = "1991",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Winter:1991:FPA,
author = "Dik T. Winter",
title = "Floating point attributes in {Ada}",
journal = j-SIGADA-LETTERS,
volume = "11",
number = "7",
pages = "244--273",
month = "Fall",
year = "1991",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:43 MDT 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
abstract = "The Ada programming language offers a number of
facilities to simplify the writing of portable
programs. One of these is the concept of attributes.
Many types and objects carry with them a set of
attributes that a program may interrogate to get
information about the actual implementation. The author
is concerned with the set of attributes belonging to
floating point types. One should hope that the floating
point attributes give correct results. In fact, they
are compile time constants. A little experimentation
shows that that is not true. Many systems deliver
incorrect attributes in a number of cases. Also, due to
the inappropriate definition of some of the attributes,
many attributes deliver results that are misleading.
The author considers the floating point attributes the
language gives and shows that indeed some definitions
are inappropriate. A program that verifies the validity
of the results given by a system is also presented. (3
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Centrum voor Wiskunde en Inf., Amsterdam,
Netherlands",
classcodes = "C6140D (High level languages); C6110B (Software
engineering techniques); C6150G (Diagnostic, testing,
debugging and evaluating systems); C5230 (Digital
arithmetic methods)",
classification = "C5230 (Digital arithmetic methods); C6110B (Software
engineering techniques); C6140D (High level languages);
C6150G (Diagnostic, testing, debugging and evaluating
systems)",
corpsource = "Centrum voor Wiskunde en Inf., Amsterdam,
Netherlands",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; Ada programming language; compile; Compile time
constants; digital arithmetic; Floating point
attributes; floating point attributes; Floating point
types; floating point types; Objects; objects;
portability; Portable programs; portable programs;
program verification; software; time constants; Types;
types; Validity; validity",
thesaurus = "Ada; Digital arithmetic; Program verification;
Software portability",
treatment = "P Practical",
}
@InProceedings{Wong:1991:FDU,
author = "Derek C. Wong and Michael J. Flynn",
title = "Fast division using accurate quotient approximations
to reduce the number of iterations",
crossref = "Kornerup:1991:PIS",
pages = "191--201",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Wong.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@Article{Yan:1991:RFA,
author = "Tak W. Yan",
title = "A Rational Function Arithmetic and Simplification
System in {Common Lisp}",
journal = j-SIGSAM,
volume = "25",
number = "4",
pages = "4--6",
month = oct,
year = "1991",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Fri Feb 8 18:27:01 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics); C6140D (High level languages)",
corpsource = "California University, Berkeley, CA, USA",
fjournal = "SIGSAM Bulletin",
issue = "98",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
keywords = "arithmetic simplification; Common Lisp;
exponentiation; freely-distributed computer algebra;
LISP; Lisp prefix form; mathematics computing;
multiplication; multivariate rational function;
rational addition; rational expressions; symbol
manipulation; system",
treatment = "P Practical",
}
@InProceedings{Yassine:1991:FAB,
author = "H. M. Yassine",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, 11--14 June 1991",
title = "Fast arithmetic based on residue number system
architectures",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2947--2950",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1991.176163",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new approach is described for transforming residue
numbers into equivalent decimal numbers. The approach
is based on the periodicity inherent in residue numbers
and uses matrix techniques to achieve high-speed
residue-to-decimal conversion. In \ldots{}",
}
@Article{Yassine:1991:IMR,
author = "H. M. Yassine and W. R. Moore",
title = "Improved mixed-radix conversion for residue number
system architectures",
journal = "Circuits, Devices and Systems, IEE Proceedings G",
volume = "138",
number = "1",
pages = "120--124",
month = feb,
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/78.80821",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2864",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Processor architectures, based on arithmetic cells
using residue number systems, are inherently parallel,
modular and fault isolating. The fundamental
characteristic of a residue number system is its being
an unweighted numbering system. The authors \ldots{}",
}
@InProceedings{Yokoo:1991:OUF,
author = "Hidetoshi Yokoo",
title = "Overflow\slash underflow-free floating-point number
representations with self-delimiting variable-length
exponent field",
crossref = "Kornerup:1991:PIS",
pages = "110--117",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Yokoo.pdf",
abstract = "A class of new floating-point representations of real
numbers, based on representations of the integers, is
described. In the class, every representation uses a
self-delimiting representation of the integers as a
variable length field, and neither overflow nor
underflow appears in practice. The adopted
representations of the integers are defined
systematically, so that representations of numbers
greater than one have both exponent-significant and
integer-fraction interpretations. Since representation
errors are characterized by the length function of an
underlying representation of the integers, systems
superior in precision can be easily selected from the
proposed class.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Gunma University,
Japan",
classification = "C1160 (Combinatorial mathematics); C5230 (Digital
arithmetic methods)",
keywords = "ARITH-10; Exponent-significant; Floating-point number
representations; Integer-fraction; Integers; Length
function; Real numbers; Representation errors;
Self-delimiting variable-length exponent field",
thesaurus = "Digital arithmetic; Number theory",
}
@Article{Yoshida:1991:PRT,
author = "N. Yoshida and E. Goto and S. Ichikawa",
title = "Pseudorandom Rounding for Truncated Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "40",
number = "9",
pages = "1065--1067",
month = sep,
year = "1991",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.83650",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 12:52:23 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83650",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "An economical, unbiased, overflow-free rounding scheme
for multiplication of multiple-precision floating-point
numbers is proposed. The scheme, called pseudorandom
rounding, saves multiplications of lower bits and makes
use of statistical properties \ldots{}",
}
@TechReport{Yu:1991:FCF,
author = "Tsung Lun Yu and William B. Ribbens",
title = "A floating-point coprocessor for fault detection and
isolation in electronically controlled internal
combustion engines",
number = "{GLCTTR} 03-91/1",
institution = "Great Lakes Center for Truck Transportation Research",
address = "Ann Arbor, MI, USA",
pages = "68",
month = sep,
year = "1991",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Fault location (Engineering); Floating-point
arithmetic.; Internal combustion engines --- Defects.;
Microprocessors.; Motor vehicles --- Electronic
equipment.",
remark = "Performed in cooperation with the University
Transportation Centers Program by Vehicle Electronics
Laboratory, University of Michigan.",
}
@Article{Zelniker:1991:RCF,
author = "G. Zelniker and F. J. Taylor",
title = "A Reduced Complexity Finite Field {ALU}",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "38",
number = "12",
pages = "1571--1573",
month = dec,
year = "1991",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Jun 24 19:51:42 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "arithmetic logic unit (ALU)",
}
@Article{Zeng:1991:AFP,
author = "B. Zeng and Y. Neuvo",
title = "Analysis of floating point roundoff errors using dummy
multiplier coefficient sensitivities",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "38",
number = "6",
pages = "590--601",
month = jun,
year = "1991",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
summary = "A simple method for analyzing roundoff errors in
floating-point digital filters is presented. The method
is based on the coefficient sensitivities of dummy
multipliers with gains of one and connects the roundoff
error analysis to coefficient sensitive \ldots{}",
}
@PhdThesis{Zeng:1991:ARR,
author = "Bing Zeng",
title = "Analysis and reduction of roundoff errors in
floating-point recursive digital filters",
volume = "72",
type = "Avhandling (doktorgrad)",
school = "Tampereen teknillinen korkeakoulu",
address = "Tampere, Finland",
pages = "45 + 80",
year = "1991",
ISBN = "951-721-697-1",
ISBN-13 = "978-951-721-697-5",
bibdate = "Thu May 09 08:15:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Julkaisuja",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhang:1991:ADN,
author = "D. Zhang and G. A. Jullien and W. C. Miller and Earl
{Swartzlander, Jr.}",
title = "Arithmetic for digital neural networks",
crossref = "Kornerup:1991:PIS",
pages = "58--63",
year = "1991",
bibdate = "Sat Nov 27 12:40:58 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Zhang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-10",
}
@InProceedings{Zhang:1991:HSE,
author = "C. N. Zhang and H. D. Cheng",
booktitle = "Reliable Systems and Applications. 5th Annual European
Computer Conference. Proceedings. {CompEuro 91}.
Advanced Computer Technology, 13--16 May 1991",
title = "A high speed error correcting converter for residue
number processing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "816--820",
year = "1991",
CODEN = "????",
DOI = "https://doi.org/10.1109/CMPEUR.1991.257495",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A novel pipelined systolic design for residue error
correction using the Chinese remainder theorem (CRT) is
described. This design has a higher throughput compared
to previous methods and minimum time latency. The
design also has overflow detection \ldots{}",
}
@Article{Zhang:1991:HSS,
author = "C. N. Zhang and H. D. Cheng",
title = "High-speed single error correcting convertor for
residue number processing",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "138",
number = "4",
pages = "177--182",
month = jul,
year = "1991",
CODEN = "ICDTEA",
DOI = "https://doi.org/10.1109/78.80821",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2686",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
keywords = "residue arithmetic; residue number system",
summary = "A pipelined systolic design for residue error
correction using the Chinese remainder theorem is
described which has a higher throughput compared with
previous methods and minimum time latency. In addition,
the design has the capability of overflow \ldots{}",
}
@Article{Ziv:1991:FEE,
author = "Abraham Ziv",
title = "Fast Evaluation of Elementary Mathematical Functions
with Correctly Rounded Last Bit",
journal = j-TOMS,
volume = "17",
number = "3",
pages = "410--423",
month = sep,
year = "1991",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/114697.116813",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Sep 1 10:15:31 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p410-ziv/",
acknowledgement = ack-nj,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; correct rounding; floating-point
arithmetic; standardization; theory",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Efficiency.",
}
@Article{Acha:1992:LOF,
author = "J. I. Acha and J. Calvo",
title = "Low-frequency oscillator for floating-point digital
signal processor chips",
journal = j-ELECT-LETTERS,
volume = "28",
number = "17",
pages = "1582--??",
month = aug,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{Anonymous:1992:FPa,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "11",
number = "8",
pages = "58--??",
month = aug,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "OpenGL: The NeWs of 3D Graphics?",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1992:FPb,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "11",
number = "11",
pages = "62--??",
month = nov,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Software with a View.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1992:FPc,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "11",
number = "10",
pages = "101--??",
month = oct,
year = "1992",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A Helping Hand for FEA.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Manual{ANSI:ftn92,
title = "{American National Standard Programming Language
Fortran Extended X3.198--1992}",
organization = pub-ANSI,
address = pub-ANSI:adr,
year = "1992",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
acknowledgement = ack-nhfb,
xxnote = "This US Standard is identical to the international
standard, ISO 1539:1991. See also
\cite{Adams:1992:FHC,Brainerd:1990:PGF,Counihan:1991:F,Metcalf:1990:FE}.",
}
@Article{Arazi:1992:BDC,
author = "B. Arazi and D. Naccache",
title = "Binary-to-Decimal Conversion Based on the Divisibility
of $ 2^8 - 1 $ by 5",
journal = j-ELECT-LETTERS,
volume = "28",
number = "3",
pages = "2151--2152",
month = nov,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "decimal floating-point arithmetic",
}
@Article{Arnold:1992:AFI,
author = "M. G. Arnold and T. A. Bailey and J. R. Cowles and M.
D. Winkel",
title = "Applying features of {IEEE 754} to sign\slash
logarithm arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "1040--1050",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156547",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156547",
abstract = "Various features found in standard floating point
arithmetic (IEEE 754) are examined in light of their
appropriateness for sign/logarithm arithmetic. The
emphasis is on a 32-b word size comparable to IEEE 754
single precision, although other word sizes are
possible. A multilayer sign/logarithm format is
considered. The lowest layer, similar to previous
implementations, would provide only normalized
representations but would not provide representations
for zero, denormalized values, infinities, and NaNs.
The highest layer would provide most of the features
found in IEEE 754, including zeros, denormalized
values, infinities, and NaNs. Novel algorithms for
implementing logarithmic denormalized arithmetic are
presented. Simulation results show that the error
characteristics of the proposed logarithmic
denormalized arithmetic algorithms are similar to those
of the denormalized floating point arithmetic in IEEE
754.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Wyoming University,
Laramie, WY, USA",
ajournal = "IEEE Trans. Comput.",
classification = "B0250 (Combinatorial mathematics); B1265B (Logic
circuits); C1160 (Combinatorial mathematics); C5230
(Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "32 Bit; Denormalized values; IEEE 754; Infinities;
Logarithmic denormalized arithmetic algorithms;
Multilayer sign/logarithm format; NaNs; Sign/logarithm
arithmetic; Standard floating point arithmetic; Zeros",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Digital arithmetic; Number theory; Standards",
}
@TechReport{Bailey:1992:ATF,
author = "David H. Bailey",
title = "Automatic Translation of {Fortran} Programs to
Multiprecision",
type = "{RNR} Technical Report",
number = "RNR-91-025",
institution = "NAS Applied Research Branch, NASA Ames Research
Center",
address = "Moffett Field, CA 94035",
day = "17",
month = apr,
year = "1992",
bibdate = "Mon Sep 12 23:55:57 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Bailey:1992:PHP,
author = "David H. Bailey",
title = "A Portable High Performance Multiprecision Package",
type = "{RNR} Technical Report",
number = "RNR-90-022",
institution = "NAS Applied Research Branch, NASA Ames Research
Center",
address = "Moffett Field, CA 94035",
day = "29",
month = may,
year = "1992",
bibdate = "Mon Sep 12 23:56:03 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Baker:1992:LCE,
author = "H. G. Baker",
title = "Less Complex Elementary Functions",
journal = j-SIGPLAN,
volume = "27",
number = "11",
pages = "15--16",
month = nov,
year = "1992",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Sep 08 08:11:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Bakhrakh:1992:NIF,
author = "S. M. Bakhrakh and S. V. Velichko and N. E.
Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
Yu. G. Fedorova and V. I. Kheifets",
title = "Numerical investigation of floating-point arithmetic
operations. ({Russian})",
journal = j-PROGRAMMIROVANIE,
volume = "6",
pages = "13--17",
year = "1992",
CODEN = "PROGD3",
ISSN = "0132-3474, 0361-7688",
MRclass = "65G05",
MRnumber = "1 227 941",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "English translation appears in
\cite{Bakhrakh:1993:NIF}.",
acknowledgement = ack-nhfb,
fjournal = "Programmirovanie",
language = "Russian",
}
@TechReport{Bewick:1992:BMU,
author = "G. Bewick and M. J. Flynn",
title = "Binary multiplication using partially redundant
multiples",
type = "Technical Report",
number = "CSL-TR-92-528",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jun,
year = "1992",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@TechReport{Blair:1992:PMD,
author = "M. Blair and S. Obenski and P. Bridickas",
title = "{Patriot} missile defense: Software problem led to
system failure at {Dhahran, Saudi Arabia}",
type = "Report",
number = "GAO/IMTEC-92-26",
institution = "Information Management and Technology Division, United
States General Accounting Office",
address = "Washington, DC, USA",
year = "1992",
bibdate = "Sat Apr 01 07:34:33 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.gao.gov/assets/220/215614.pdf;
http://www.gao.gov/products/IMTEC-92-26",
abstract = "Pursuant to a congressional request, GAO reviewed the
facts associated with the failure of a Patriot missile
defense system in Dhahran, Saudi Arabia, during
Operation Desert Storm.\par
GAO found that: (1) the Patriot battery at Dhahran
failed to track and intercept a Scud missile due to a
software problem in the system's weapons control
computer; (2) the software problem caused an inaccurate
tracking calculation which became worse the longer the
system operated; (3) at the time of the incident, the
battery had operated continuously for over 100 hours
and the inaccuracy was serious enough to cause the
system to look in the wrong place for the incoming
Scud; (4) two weeks before the incident, Army officials
received Israeli data indicating some loss in accuracy
after the system had been running for 8 consecutive
hours; (5) the Army had never used the Patriot to
defend against tactical ballistic missiles or expected
the Patriot to operate continuously for long periods of
time; and (6) Army officials modified the software, but
the new software did not reach Dhahran until the day
after the incident. \ldots{} The precision of a
computer's calculations depends on the number of bits
in its registers. Since the Patriot's registers are
only 24 bits long, precision beyond 24 bits is not
possible unless the software is specifically written to
adjust for such hardware limitations. Computers built
today have registers that contain as many as 64 bits,
permitting calculations with far greater precision.
\ldots{} During the conflict the Patriot's software was
modified six times. Patriots had to be shut down for at
least 1 to 2 hours to install each software
modification.",
acknowledgement = ack-nhfb,
remark = "From the report: ``Because of the way the Patriot
computer performs its calculations and the fact that
its registers are only 24 bits long, the conversion of
time from an integer to a real number cannot be any
more precise than 24 bits. This conversion results in a
loss of precision causing a less accurate time
calculation. The effect of this inaccuracy on the range
gate's calculation is directly proportional to the
target's velocity and the length of time the system has
been running. Consequently, performing the conversion
after the Patriot has been running continuously for
extended periods causes the range gate to shift away
from the center of the target, making it less likely
that the target, in this case a Scud, will be
successfully intercepted. \ldots{} On February 25,
Alpha Battery had been in operation for over 100
consecutive hours. Because the system had been on so
long, the resulting inaccuracy in the time calculation
caused the range gate to shift so much that the system
could not track the incoming Scud. Consequently, Alpha
Battery did not engage the Scud, which then struck an
Army barracks and killed 28 American soldiers.''",
xxremark = "Report of integer overflow in a timer that made the
guidance system erroneous; the ultimate solution proved
to be to reboot the guidance computer every few hours,
before the overflow.",
}
@Article{Bohlender:1992:PAF,
author = "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
Kulisch and R. Lohner and W. V. Walter",
title = "Proposal for Accurate Floating-Point Vector
Arithmetic",
journal = j-MATH-SCI-ENG,
volume = "189",
number = "??",
pages = "87--104",
year = "1992",
CODEN = "MTSEAT",
ISSN = "0076-5392",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics in Science and Engineering",
}
@Article{Borwein:1992:MHP,
author = "Jonathan M. Borwein and Mark A. Limber",
title = "{Maple} as a High Precision Calculator",
journal = j-MAPLE-TECH-NEWS,
volume = "0",
number = "8",
pages = "39--44",
month = "Fall",
year = "1992",
ISSN = "1061-5733",
ISSN-L = "1061-5733",
bibdate = "Fri May 09 22:33:19 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
URL = "http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
fjournal = "Maple technical newsletter",
journal-URL = "http://web.mit.edu/maple/www/plibrary/mtn.html",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}
@Article{Brosgol:1992:ADA,
author = "Benjamin M. Brosgol and Robert I. Eachus and David E.
Emery",
title = "An {Ada} Decimal Arithmetic Capability",
journal = "CrossTalk: The Journal of Defense Software
Engineering",
volume = "36",
publisher = "Software Technology Support Center",
address = "Hill AFB, Odgen, UT, USA",
month = sep,
year = "1992",
bibdate = "Fri Nov 28 16:01:38 2003",
bibsource = "http://www.stsc.hill.af.mil/crosstalk/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.iste.uni-stuttgart.de/ps/AdaBasis/pal_1195/ada/ajpo/work-grp/ev-team/ev-info/summary.txt",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
pagecount = "8 (approx)",
xxCODEN = "none",
xxISSN = "none",
}
@InProceedings{Brosgol:1992:DAA,
author = "Benjamin M. Brosgol and Robert I. Eachus and David E.
Emery",
title = "Decimal arithmetic in {Ada}",
crossref = "Katwijk:1992:AMT",
pages = "138--149",
year = "1992",
DOI = "https://doi.org/10.1007/3-540-55585-4_1",
bibdate = "Thu Aug 07 17:11:50 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Calvetti:1992:SRE,
author = "Daniela Calvetti",
title = "A Stochastic Roundoff Error Analysis for the
Convolution",
journal = j-MATH-COMPUT,
volume = "59",
number = "200",
pages = "569--582",
month = oct,
year = "1992",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G05 (44A35 65T20)",
MRnumber = "93a:65061",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
JSTOR database; Theory/Matrix.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4190 (Other numerical methods); C4110 (Error analysis
in numerical methods)",
corpsource = "Dept. of Pure and Appl. Math., Stevens Inst. of
Technol., Hoboken, NJ, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "accuracy; convolution; error analysis; fast Fourier
transforms; Radix-2 fast Fourier transforms; roundoff
errors; stochastic roundoff error analysis",
kwds = "nla, fft, convolution, rounding error, stochastic
analysis",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Clarkson:1992:SED,
author = "K. L. Clarkson",
title = "Safe and effective determinant evaluation",
crossref = "IEEE:1992:ASF",
pages = "387--395",
year = "1992",
bibdate = "Tue Nov 22 05:54:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Cosentino:1992:AMJ,
author = "R. J. Cosentino and J. J. Vaccaro",
title = "Adaptation of the {Mactaggart} and {Jack} Complex
Multiplication Algorithm for Floating-Point Operators",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "10",
pages = "1324--1326",
month = oct,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.166608",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166608",
abstract = "With a suitable treatment of the exponents in the
input operands, a hardware implementation of the
Mactaggart and Jack fixed-point complex multiplication
algorithm can also calculate a floating-point product
with no loss in accuracy from the greater dynamic range
of the floating-point inputs. This floating-point
technique can be extended to any sum to two products
operation, such as encountered in matrix multiplication
and vector cross-products.",
acknowledgement = ack-nhfb,
affiliation = "Mitre Corp., Bedford, MA, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C5230 (Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Floating-point operators; Hardware implementation;
Jack complex multiplication algorithm; Mactaggart
complex multiplication; Matrix multiplication; Vector
cross-products",
summary = "With a suitable treatment of the exponents in the
input operands, a hardware implementation of the
Mactaggart and Jack fixed-point complex multiplication
algorithm can also calculate a floating-point product
with no loss in accuracy from the greater \ldots{}",
thesaurus = "Digital arithmetic",
}
@Article{Dao-Trong:1992:SCI,
author = "S. Dao-Trong and K. Helwig",
title = "A single-chip {IBM System}\slash 390 floating-point
processor in {CMOS}",
journal = j-IBM-JRD,
volume = "36",
number = "4",
pages = "733--749",
month = jul,
year = "1992",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Dao-Trong:1992:SIS,
author = "S. Dao-Trong and K. Helwig",
title = "A single-chip {IBM} System\slash 390 floating-point
processor in {CMOS}",
journal = j-IBM-JRD,
volume = "36",
number = "4",
pages = "733--750",
month = jul,
year = "1992",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{DaoTrong:1992:SIS,
author = "S. Dao-Trong and K. Helwig",
title = "A single-chip {IBM} system\slash 390 floating-point
processor in {CMOS}",
journal = j-IBM-JRD,
volume = "36",
number = "4",
pages = "733--749",
month = jul,
year = "1992",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A floating-point processor with the IBM System/390
architecture is implemented in one CMOS VLSI chip
containing over 70000 cells (equivalent inverters),
using a transistor channel length of 0.5 mu m. All
floating-point instructions are hard-wired, including
the binary integer multiplications. The chip is
implemented in a 1- mu m technology with three layers
of metal. All circuits are realized in standard cells
except for a floating-point register and a multiplier
array macro, which are custom designed to save chip
area. Instructions are performed in a five-stage
pipeline with a maximum operating frequency of 37 MHz.
The chip measures 12.7 mm*12.7 mm, and dissipates 2 W.
It is part of the chip set which forms the core of the
IBM Enterprise System/9000 Type 9221 entry-level
models.",
acknowledgement = ack-nhfb,
affiliation = "IBM Germany, Boeblingen, Germany",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods)",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "37 MHz; Binary integer multiplications; Chip set;
CMOS; Equivalent inverters; Five-stage pipeline; IBM
Enterprise System/9000; Single-chip IBM system/390
floating-point processor; Transistor channel length",
numericalindex = "Frequency 3.7E+07 Hz",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Equipment evaluation; IBM computers; Microprocessor
chips",
}
@MastersThesis{Daumas:1992:BIR,
author = "Marc Daumas",
title = "Basis for the implementation of a reliable dot
product",
type = "{Master}'s Thesis",
school = "Southern Methodist University",
address = "Dallas, Texas",
year = "1992",
bibdate = "Wed Nov 24 12:42:59 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Davarakis:1992:PPA,
author = "C. T. Davarakis and D. G. Maritsas",
title = "A Probabilistic Parallel Associative Search and Query
Set of Algorithms",
journal = j-J-PAR-DIST-COMP,
volume = "14",
number = "1",
pages = "37--49",
month = jan,
year = "1992",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 19:06:31 MDT 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Computer Technology Inst",
affiliationaddress = "Patras, Greece",
classification = "723; 921; 922; C1230 (Artificial intelligence);
C4240P (Parallel programming and algorithm theory);
C5470 (Performance evaluation and testing); C7310
(Mathematics)",
corpsource = "Department of Comput. Eng., Comput. Technol. Inst.,
Patras, Greece",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Algorithms; arithmetic applications; Associative
searching; Computer Programming; computing; Data
Storage, Digital--Associative; digital arithmetic;
extrema algorithm; extrema queries; generic associative
process; heuristic programming; heuristics; high
performance systems; Mathematical
Techniques--Heuristic; mathematics; multilayer
associative process; parallel algorithms; parallel
associative search; parallel threshold; performance
evaluation; Primitive algorithms; primitive algorithms;
probabilistic; Probability; query set of algorithms;
symbol manipulation; symbolic applications; threshold
searches; time performance",
treatment = "A Application; P Practical",
}
@InProceedings{Dawid:1992:BSC,
author = "H. Dawid and G. Fettweis",
title = "Bit-level systolic carry-save array division",
crossref = "IEEE:1992:GCG",
pages = "484--488 vol.1",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A bit-level systolic carry-save division array that
allows bit-level pipelining, just as for carry-save
array multipliers, is presented. This architecture
leads to very fast, efficient and regular division
implementations as needed in digital signal processing
(DSP) applications such as speech processing or
cryptography. The architecture is very well suited for
integer division as well as for the division of
normalized fixed-point mantissas used in floating-point
number system implementations.",
acknowledgement = ack-nhfb,
affiliation = "Aachen University of Technol., Germany",
classification = "B1265B (Logic circuits); C5130 (Microprocessor
chips); C5230 (Digital arithmetic methods); C5260
(Digital signal processing)",
keywords = "Bit-level pipelining; Carry-save array multipliers;
Cryptography; Digital signal processing; DSP;
Floating-point number system; Integer division;
Normalized fixed-point mantissas; Speech processing;
Systolic carry-save array division",
thesaurus = "Digital arithmetic; Systolic arrays",
}
@Article{Dawson:1992:RLS,
author = "Jeffrey Dawson and Mary Payne and Craig Schaffert",
title = "The Role of {LIA-1} in Software Portability",
journal = j-SIGNUM,
volume = "27",
number = "4",
pages = "9--12",
month = oct,
year = "1992",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:22 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "LIA is now an International Standard, ISO/IEC
10967-1:1994; it is ``92 pages of small print, densely
mathematical, not counting 8 pages of front matter, and
it is not available electronically.'' Its adoption has
been rather controversial.",
abstract = "The second committee draft of language independent
arithmetic-Part 1: Integer and floating point
arithmetic is now available. This document was formerly
called the Language Compatible Arithmetic Standard
(LCAS) and is now referred to as LIA-1. This draft was
prepared by ISO/IEC JTC1/SC22/WG11, with assistance
from standards committees in several countries. The
authors explain the goals of the standard and methods
for achieving those goals. They present them to clear
up previous misunderstandings, misconceptions, and
misrepresentations of the purpose of the standard. (0
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Digital Equipment Corp., Maynard, MA, USA",
classification = "C0310F (Software development management); C6110B
(Software engineering techniques); C7310
(Mathematics)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Floating point arithmetic; Integer arithmetic; ISO/IEC
JTC1/SC22/WG11; Language independent arithmetic; LIA-1;
Software portability; Standard",
thesaurus = "Mathematics computing; Software portability;
Standards",
}
@Book{DEC:1992:AAH,
author = "Digital Equipment Corporation",
title = "{Alpha} Architecture Handbook",
publisher = pub-DP,
address = pub-DP:adr,
year = "1992",
bibdate = "Mon Jan 18 15:08:40 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Demmel:1992:LWN,
author = "James Demmel",
title = "{LAPACK} working note 49 draft: a specification for
floating point parallel prefix",
type = "Technical report",
number = "CS-92-167",
institution = "University of Tennessee, Computer Science Dept.",
address = "Knoxville, TN, USA",
pages = "8 + 1",
month = may,
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Parallel prefix is a useful operation for various
linear algebra operations, including solving bidiagonal
systems of equations and finding the eigenvalues of a
symmetric tridiagonal matrix. However, the simplest
implementations of parallel prefix for the operations
of scalar floating point add and scalar floating point
multiply are inadequate to solve these important
problems. This is because they are too susceptible to
over/underflow, and because they apparently cannot
solve the general two term recurrence needed to find
eigenvalues. In this note we propose a specification
for parallel prefix operations overcoming these
drawbacks.",
acknowledgement = ack-nhfb,
keywords = "Linear algebraic groups.",
}
@TechReport{Demmel:1992:SFP,
author = "J. Demmel",
title = "A Specification for Floating Point Parallel Prefix",
type = "LAPACK Working Note",
number = "49",
institution = inst-UT-CS,
address = inst-UT-CS:adr,
month = may,
year = "1992",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "UT-CS-92-167, May 1992.",
URL = "http://www.netlib.org/lapack/lawns/lawn49.ps;
http://www.netlib.org/lapack/lawnspdf/lawn49.pdf",
acknowledgement = ack-nhfb,
}
@Article{Devine:1992:RTT,
author = "M. L. Devine",
title = "Real time trigonometric function evaluation",
journal = j-MICROPROC-MICROSYS,
volume = "16",
number = "8",
pages = "417--425",
month = aug,
year = "1992",
CODEN = "MIMID5",
ISSN = "0141-9331 (print), 1872-9436 (electronic)",
ISSN-L = "0141-9331",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Microprocessors and Microsystems",
}
@Article{Dimauro:1992:NMF,
author = "G. Dimauro and S. Impedovo and G. Pirlo",
title = "A new magnitude function for fast numbers comparison
in the residue number system",
journal = j-MICROPROC-MICROPROG,
volume = "35",
number = "1--2",
pages = "97--104",
month = sep,
year = "1992",
CODEN = "MMICDT",
DOI = "https://doi.org/10.1016/0165-6074(92)90300-V",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Thu Nov 18 09:52:10 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper a new magnitude function, called the
`diagonal function', has been defined from a Residue
Number System to the integers. The `diagonal function'
provides an efficient technique for fast magnitude
comparison of numbers in the residue representation.
The superiority of this technique with respect to the
approaches based on the Chinese Remainder Theorem and
on the Mixed Radix Transformation is shown.",
acknowledgement = ack-nhfb,
fjournal = "Microprocessing and Microprogramming",
}
@MastersThesis{Du:1992:CAB,
author = "Sihai Du",
title = "Cellular automata based floating-point adder and
multiplier with a single transition rule",
type = "Thesis ({M.S.C.E.})",
school = "Wright State University",
address = "Dayton, OH, USA",
pages = "ix + 68",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Cellular automata --- Research.; Computer Simulation.;
Floating-point arithmetic --- Research.",
}
@Article{Dunham:1992:SFW,
author = "Charles B. Dunham",
title = "Surveyor's Forum: {``What Every Computer Scientist
Should Know About Floating-Point Arithmetic''}",
journal = j-COMP-SURV,
volume = "24",
number = "3",
pages = "319--319",
month = sep,
year = "1992",
CODEN = "CMSVAN",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Sun Sep 25 10:14:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Wichmann:1992:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@InProceedings{Duprat:1992:DOF,
author = "J. Duprat and M. Fiallos-Aguilar and Jean-Michel
Muller and H. J. Yeh",
title = "Delays of on-line floating point operators in
borrow-save representation",
crossref = "Quinton:1992:APV",
pages = "273--278",
year = "1992",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "On-line computation using redundant notations to
represent numbers is an interesting field of computer
arithmetic. In these systems, different operators can
operate together in a digit level pipelining mode. In
integer or fixed-point format, implementations of the
main operations have been proposed. This paper focuses
on a floating point format. The authors show that, more
so in addition than in multiplication, critical loss of
information due to the variation of the length of the
mantissas can be avoided by partial normalizations.
Furthermore, these normalizations do not break the
circulation of the digit though they do delay the
operations even more.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Normale Superieure de Lyon, France",
classification = "C5230 (Digital arithmetic methods); C5440
(Multiprocessor systems and techniques)",
keywords = "Borrow-save representation; Computer arithmetic;
Delays; Digit level pipelining mode; Floating point
format; Mantissas; On-line floating point operators;
Partial normalizations; Redundant notations",
thesaurus = "Delays; Digital arithmetic; Pipeline processing",
}
@Article{Duprat:1992:SPF,
author = "J. Duprat and M. Fiallos Aguilar",
title = "On the Simulation of Pipelining of Fully Digit On-Line
Floating-Point Adder Networks on Massively Parallel
Computers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "??",
number = "634",
pages = "707--712",
year = "1992",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Ercegovac:1992:FRC,
author = "M. D. Ercegovac and T. Lang",
title = "On-the-fly rounding [computing arithmetic]",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "12",
pages = "1497--1503",
month = dec,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.214659",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214659",
abstract = "In implementations of operations based on
digit-recurrence algorithms such as division,
left-to-right multiplication and square root, the
result is obtained in digit-serial form, from most
significant digit to least significant. To reduce the
complexity of the result-digit selection and allow the
use of redundant addition, the result-digit has values
from a signed-digit set. As a consequence, the result
has to be converted to conventional representation,
which can be done on-the-fly as the digits are
produced, without the use of a carry-propagate adder.
The authors describe three ways to modify this
conversion process so that the result is rounded. The
resulting operation is fast because no carry-propagate
addition is needed. The schemes described apply also to
online arithmetic operations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fagin:1992:LIM,
author = "Barry S. Fagin",
title = "Large Integer Multiplication on Hypercubes",
journal = j-J-PAR-DIST-COMP,
volume = "14",
number = "4",
pages = "426--430",
month = apr,
year = "1992",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Apr 12 17:13:17 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4230M (Multiprocessor interconnection); C4240P
(Parallel programming and algorithm theory); C5230
(Digital arithmetic methods)",
corpsource = "Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "Connection Machine; digital arithmetic; Fermat Number
Transform; hypercube networks; hypercubes; integer
multiplication; parallel algorithms; polynomial
transforms; transforms",
treatment = "T Theoretical or Mathematical",
}
@Article{Filanovsky:1992:SCA,
author = "I. M. Filanovsky and H. P. Baltes",
title = "Simple {CMOS} analog square-rooting and squaring
circuits",
journal = j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
volume = "39",
number = "4",
pages = "312--315",
month = apr,
year = "1992",
CODEN = "ITCAEX",
ISSN = "1057-7122 (print), 1558-1268 (electronic)",
ISSN-L = "1057-7122",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I:
Fundamental Theory and Applications",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
summary = "Two closely related CMOS circuits are described. In
the first circuit, the input signal is a current, and
the output is a voltage proportional to the square root
of input current. In the second circuit, the input is a
voltage, and the output is the \ldots{}",
}
@Article{Fujii:1992:FCL,
author = "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
T. Demura and G. Ootomo",
title = "A Floating-Point Cell Library and a {100-MFLOPS} Image
Signal Processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "27",
number = "7",
pages = "1080--1088",
month = jul,
year = "1992",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Fujii:1992:FPC,
author = "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
T. Demura and G. Ootomo",
title = "A floating-point cell library and a {100-Mflops} image
signal processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "27",
number = "7",
pages = "1080--1088",
month = jul,
year = "1992",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A novel floating-point cell library for image signal
processors that includes a floating-point arithmetic
logic unit (ALU), a floating-point multiplier (MPY), an
instruction RAM, and a data register file is
considered. It has been designed for high-speed
\ldots{}",
}
@Article{Gamberger:1992:IIM,
author = "D. Gamberger",
title = "Inversion of integer matrices in residue number
system",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "139",
number = "5",
pages = "465--468",
month = sep,
year = "1992",
CODEN = "ICDTEA",
DOI = "https://doi.org/10.1109/78.157231",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4186",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
keywords = "residue arithmetic; residue number system",
summary = "The presented algorithm makes use of the recently
introduced incompletely specified residue number
system. This system enables the operations necessary in
the inversion process to be done quickly, completely in
parallel for different moduli, even if \ldots{}",
}
@Article{Goldberg:1992:DFD,
author = "D. Goldberg",
title = "The design of floating-point data types",
journal = j-LOPLAS,
volume = "1",
number = "2",
pages = "138--151",
month = jun,
year = "1992",
CODEN = "ALPSE8",
ISSN = "1057-4514 (print), 1557-7384 (electronic)",
ISSN-L = "1057-4514",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The issues involved in designing the floating-point
part of a programming language are discussed. Looking
at the language specifications for most existing
languages might suggest that this design involves only
trivial issues, such as whether to have one or two
types of REALs or how to name the functions that
convert from INTEGER to REAL. It is shown that there
are more significant semantic issues involved. After
discussing the tradeoffs for the major design
decisions, they are illustrated by presenting the
design of the floating-point part of the Modula-3
language.",
acknowledgement = ack-nhfb,
affiliation = "Xerox Palo Alto Res. Center, CA, USA",
classification = "C6120 (File organisation)",
fjournal = "ACM Letters on Programming Languages and Systems",
keywords = "Design; Floating-point data types; Language
specifications; Modula-3 language; Programming
language; REALs",
thesaurus = "Data structures; Digital arithmetic",
}
@Article{Gray:1992:UMF,
author = "A. Gray and R. Knill",
title = "Using {Mathematica} to Find Closed Form Expressions
for Approximations to the Square Root of $x$",
journal = j-MATHEMATICA-EDUC,
volume = "1",
number = "4",
pages = "12--13",
month = "Summer",
year = "1992",
ISSN = "1065-2965",
bibdate = "Sat Apr 6 16:22:43 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-ble,
fjournal = "Mathematica in Education",
}
@InProceedings{Hartwig:1992:AFQ,
author = "F. Hartwig and A. Lacroix",
title = "Analysis of floating-point quantization errors using
stochastic models",
crossref = "Vandewalle:1992:SPV",
pages = "247--250 vol.1",
year = "1992",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Some results concerning the single quantizer with
limited exponent wordlength are presented. In addition
to roundoff, the authors present a generalization for
magnitude truncation. The method is also applied to
digital filters. The theoretical results are tested in
comparison with simulation results.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Phys., J. W. Goethe-University,
Frankfurt am Main, Germany",
classification = "B0240Z (Other and miscellaneous); B0290B (Error
analysis in numerical methods); B1265H (A/D and D/A
convertors); B6140 (Signal processing and detection);
C1140Z (Other and miscellaneous); C5230 (Digital
arithmetic methods); C5240 (Digital filters)",
keywords = "Digital filters; Digital signal processing devices;
Floating-point quantization errors; Limited exponent
wordlength; Magnitude truncation; Roundoff; Simulation
results; Stochastic models; Theoretical results",
thesaurus = "Analogue-digital conversion; Digital arithmetic;
Digital filters; Error analysis; Signal processing;
Stochastic processes",
}
@InProceedings{Hartwig:1992:MFA,
author = "F. Hartwig and A. Lacroix",
title = "Multi-operand floating-point addition utilizing
operand sorting",
crossref = "White:1992:IIS",
pages = "1800--1803 vol.4",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In many signal processing applications repeated
additions have to be calculated with a considerable
number of operands. It is known that proper sorting of
operands has a positive influence on the precision of
the result of multioperand floating-point additions.
This is investigated for different operand statistics
and for proper sorting strategies. In addition to
successive addition techniques, adder trees are
included in the investigation. The densities of the
addition errors for different floating-point addition
methods are compared.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fuer Angewandte Phys., J. W. Goethe-University,
Frankfurt am Main, Germany",
classification = "C1260 (Information theory); C5230 (Digital
arithmetic methods); C5260 (Digital signal processing);
C6130 (Data handling techniques)",
keywords = "Adder trees; Addition errors densities; Floating-point
addition; Floating-point addition methods; Multioperand
floating-point additions; Operand sorting; Operand
statistics; Repeated additions; Signal processing;
Sorting strategies; Successive addition techniques",
thesaurus = "Digital arithmetic; Signal processing; Sorting",
}
@Article{Hasan:1992:BSS,
author = "M. A. Hasan and V. K. Bhargava",
title = "Bit-serial systolic divider and multiplier for finite
fields {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "972--980",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156540",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156540",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hasan:1992:MCL,
author = "M. A. Hasan and M. Wang and V. K. Bhargava",
title = "Modular construction of low complexity parallel
multipliers for a class of finite fields {$ \mathrm
{GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "962--971",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156539",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156539",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hegeman:1992:AF,
author = "Frederick W. Hegeman",
title = "Arithmetic In Factorial-Base",
journal = j-CUJ,
volume = "10",
number = "2",
pages = "73--??",
month = feb,
year = "1992",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Hoehfeld:1992:LLN,
author = "M. Hoehfeld and S. E. Fahlman",
title = "Learning with limited numerical precision using the
cascade-correlation algorithm",
journal = j-IEEE-TRANS-NEURAL-NETW,
volume = "3",
number = "4",
pages = "602--611",
month = jul,
year = "1992",
CODEN = "ITNNEP",
DOI = "https://doi.org/10.1109/72.143374",
ISSN = "1045-9227 (print), 1941-0093 (electronic)",
ISSN-L = "1045-9227",
bibdate = "Fri Sep 22 17:49:00 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Neural Networks",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=72",
}
@InProceedings{Hoff:1992:FCH,
author = "J. R. Hoff and G. W. Foster",
title = "A full custom, high speed, floating point adder",
crossref = "Alley:1992:CRI",
pages = "450 vol.1",
year = "1992",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Summary form only. A high-speed pipelined floating
point adder for use by the Solenoidal Detector
Collaboration (SDC) at the Superconducting Super
Collider (SSC) is discussed. The adder uses a unique
floating point format. The chip is designed to be a
two-stage pipeline and to operate at a peak speed of at
least 63 MHz. Static rather than dynamic logic was
desired, to permit operation at lower speeds and to
ease system testing. The chip is implemented using
Orbit Semiconductor's 1.2 mu m n-well process.
Simulations indicate that the device will operate at 63
MHz. Initial testing performed at Fermilab, limited by
test equipment, indicates speeds of at least 63 MHz,
with some tests demonstrating speeds in excess of 150
MHz.",
acknowledgement = ack-nhfb,
affiliation = "Fermilab, Batavia, IL, USA",
classification = "A2980C (Computer systems); B1265B (Logic circuits);
B7430 (Counting circuits and electronics); C5120 (Logic
and switching circuits); C5230 (Digital arithmetic
methods); C7320 (Physics and Chemistry)",
keywords = "150 MHz; 63 MHz; Fermilab; Floating point adder; High
speed; Orbit Semiconductor; Pipelined; SDC; Simulation;
Static logic; System testing; Testing; Two-stage
pipeline",
numericalindex = "Frequency 6.3E+07 Hz; Frequency 1.5E+08 Hz",
thesaurus = "Adders; Digital arithmetic; Nuclear electronics;
Physics computing; Pipeline processing",
}
@Article{Hohfeld:1992:PRN,
author = "Markus H{\"o}hfeld and Scott E. Fahlman",
title = "Probabilistic rounding in neural network learning with
limited precision",
journal = j-NEUROCOMPUTING,
volume = "4",
number = "6",
pages = "291--299",
month = dec,
year = "1992",
CODEN = "NRCGEO",
DOI = "https://doi.org/10.1016/0925-2312(92)90014-g",
ISSN = "0925-2312 (print), 1872-8286 (electronic)",
ISSN-L = "0925-2312",
bibdate = "Fri Sep 22 17:46:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Neurocomputing",
journal-URL = "http://www.sciencedirect.com/science/journal/09252312",
}
@Article{Horiguchi:1992:FNR,
author = "Hiroshi Horiguchi and Tsutomu Tayama",
title = "Floating-Point Numbers and Real Numbers {II}",
journal = j-ADV-SOFT-SCI-TECH,
volume = "3",
number = "??",
pages = "151--156",
year = "1992",
ISSN = "1044-7997",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Advances in software science and technology",
}
@MastersThesis{Hoyt:1992:MFP,
author = "Brian S. Hoyt",
title = "The {Macintosh} floating point arithmetic
visualization system",
type = "Thesis ({M.S.--Electrical Engineering})",
school = "Bucknell University",
address = "Lewisburg, PA, USA",
pages = "ix + 88",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Supervised by Richard J. Zaccone. Describes the
design, development, implementation, and use of MacFavs
(Macintosh Floating point arithmetic visualization
system). MacFavs uses simulation, visual displays, and
animations to allow students to see actual machine
representations of floating point numbers.",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Macintosh (Computer);
Numerical analysis --- Computer-assisted instruction.",
}
@Article{Hudak:1992:RPL,
author = "Paul Hudak and Simon Peyton Jones and Philip Wadler
and Brian Boutel and Jon Fairbairn and Joseph Fasel and
Mar{\'\i}a M. Guzm{\'a}n and Kevin Hammond and John
Hughes and Thomas Johnsson and Dick Kieburtz and
Rishiyur Nikhil and Will Partain and John Peterson",
title = "Report on the programming language {Haskell}: a
non-strict, purely functional language (Version 1.2)",
journal = j-SIGPLAN,
volume = "27",
number = "5",
pages = "Ri--Rx, R1--R163",
month = may,
year = "1992",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:21 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Haskell is a general purpose, purely functional
programming language incorporating many recent
innovations in programming language research, including
higher-order functions, non-strict semantics, static
polymorphic typing, user-defined algebraic datatypes,
pattern-matching, list comprehensions, a module system,
and a rich set of primitive datatypes, including lists,
arrays, arbitrary and fixed precision integers, and
floating-point numbers. Haskell is both the culmination
and solidification of many years of research on
functional languages-the design has been influenced by
languages as old as ISWIM and as new as Miranda. The
report defines the syntax for Haskell programs and an
informal abstract semantics for the meaning of such
programs.",
acknowledgement = ack-nhfb,
affiliation = "Yale University, New Haven, CT, USA",
classification = "C6140D (High level languages)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Abstract semantics; Arrays; Fixed precision integers;
Floating-point numbers; Functional programming
language; Haskell; Higher-order functions; List
comprehensions; Lists; Module system; Non-strict
semantics; Pattern-matching; Primitive datatypes;
Static polymorphic typing; Syntax; User-defined
algebraic datatypes",
thesaurus = "Functional programming; High level languages",
}
@Article{IFIF:1992:CVD,
author = "{IFIP Working Group 2.5 (Numerical Software)}",
title = "Comments on version 3.1 of draft {ISO\slash IEC
10967:1991 Language Compatible Arithmetic}",
journal = j-SIGNUM,
volume = "27",
number = "1",
pages = "2--3",
month = jan,
year = "1992",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:21 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@InProceedings{Jackson:1992:DTF,
author = "P. B. Jackson",
title = "Developing a toolkit for floating-point hardware in
the {Nuprl} proof development system",
crossref = "Prinetto:1992:CHD",
pages = "401--419",
year = "1992",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Describes current work in building a toolkit of
theorems, definitions and tactics in the Nuprl proof
development system for the verification of
floating-point hardware designs. The approach
emphasizes reasoning over a wide range of levels of
abstraction within a single system. For example the
specification of the IEEE's floating point standard
makes free use of rational arithmetic, as well as
talking explicitly about the input and output
bit-vectors of floating-point circuits.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Cornell University,
Ithaca, NY, USA",
classification = "C4210 (Formal logic); C5230 (Digital arithmetic
methods); C6110B (Software engineering techniques);
C6115 (Programming support)",
keywords = "Floating-point hardware; Nuprl proof development
system; Rational arithmetic; Reasoning; Toolkit;
Verification",
thesaurus = "Digital arithmetic; Formal specification; Software
tools; Theorem proving",
}
@Article{Jacobson:1992:ETF,
author = "David Jacobson",
title = "Engineer's Toolbox: Floating Point in {Mathematica}",
journal = j-MATHEMATICA-J,
volume = "2",
number = "3",
pages = "42--46",
month = "Summer",
year = "1992",
CODEN = "????",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
ISSN-L = "1047-5974",
bibdate = "Sat Nov 6 13:33:40 MDT 2010",
bibsource = "http://www.mathematica-journal.com/issue/v2i3/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mathematica-journal.com/issue/v2i3/tutorials/toolbox/index.html",
abstract = "Mathematica provides both traditional machine-level
floating point numbers and software-implemented
variable-precision floating-point numbers. There are
two different notions of precision: an estimate of the
maximum possible relative error, which is propagated
through arithmetic operations based on the precision of
the operands; and the number of digits used to
represent the significand (mantissa). Mathematica links
the first notion to the second, throwing away digits
that it cannot prove are significant. In iterative
calculations the precision can ratchet down a little
each iteration, until there is nothing left.",
acknowledgement = ack-nhfb,
fjournal = "Mathematica Journal",
journal-URL = "http://www.mathematica-journal.com/",
}
@Article{Jaffar:1992:AMC,
author = "Joxan Jaffar and Peter J. Stuckey and Spiro Michaylov
and Roland H. C. Yap",
title = "An abstract machine for {CLP$ (\mathcal {R}) $}",
journal = j-SIGPLAN,
volume = "27",
number = "7",
pages = "128--139",
month = jul,
year = "1992",
CODEN = "SINODQ",
ISBN = "0-89791-475-9",
ISBN-13 = "978-0-89791-475-8",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
LCCN = "QA76.7.S53 1992",
bibdate = "Sun Dec 14 09:16:22 MST 2003",
bibsource = "Compendex database; http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/143095/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/143095/p128-jaffar/",
abstract = "An abstract machine is described for the CLP$
(\mathcal {R}) $ programming language. It is intended
as a first step toward enabling CLP$ (\mathcal {R}) $
programs to be executed with efficiency approaching
that of conventional languages. The core Constraint
Logic Arithmetic Machine (CLAM) extends the Warren
Abstract Machine (WAM) for compiling Prolog with
facilities for handling real arithmetic constraints.
The full CLAM includes facilities for taking advantage
of information obtained from global program analysis.",
acknowledgement = ack-nhfb,
affiliation = "IBM T. J. Watson Research Cent",
affiliationaddress = "Yorktown Heights, NY, USA",
annote = "Published as part of the Proceedings of PLDI'92.",
classification = "723.1",
conference = "Proceedings of the ACM SIGPLAN '92 Conference on
Programming Language Design and Implementation",
conferenceyear = "1992",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
journalabr = "SIGPLAN Not",
keywords = "Abstract machine; algorithms; Computer programming;
Computer programming languages; Constraint logic
arithmetic machine; design; Global program analysis;
languages; Program compilers; prolog (programming
language)",
meetingaddress = "San Francisco, CA, USA",
meetingdate = "Jun 17--19 1992",
meetingdate2 = "06/17--19/92",
sponsor = "ACM",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, Prolog. {\bf D.1.6} Software,
PROGRAMMING TECHNIQUES, Logic Programming. {\bf D.3.3}
Software, PROGRAMMING LANGUAGES, Language Constructs
and Features, Data types and structures. {\bf D.3.4}
Software, PROGRAMMING LANGUAGES, Processors,
Optimization.",
}
@InProceedings{Jain:1992:AEA,
author = "V. K. Jain and G. E. Perez and E. E. Swartzlander",
title = "Arithmetic Error Analysis of a New Reciprocal Cell",
crossref = "IEEE:1992:IIC",
pages = "106--109",
year = "1992",
bibdate = "Thu Sep 08 00:34:18 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{James:1992:DRC,
author = "Shelton L. James",
title = "A distributed remote computational server",
type = "Thesis ({M.S.})",
school = "University of Missouri, Columbia",
address = "Columbia, MO, USA",
pages = "vi + 183",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Distributed operating systems (Computers); Electronic
networks.; Floating-point systems.; OSI (Computer
network standard)",
}
@InProceedings{Johnstone:1992:RNA,
author = "P. Johnstone and F. E. Petry",
title = "Rational number approximation in higher radix floating
point systems",
crossref = "IEEE:1992:PIS",
pages = "501--504 vol.2",
year = "1992",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recent research has shown that hybrid non-binary
floating point bases, particularly decimal-based
systems, can match or exceed the error performance of
more traditional binary systems. The authors address a
more general question of whether such bases offer any
further advantages in the domain of rational number
approximation. They consider the effect of the choice
of floating point base on rational number approximation
in systems which exhibit the typical characteristics of
floating point representations, normalized encodings,
limited exponent range, and storage allocated in a
fixed number of bits per datum. The frequency with
which terminating and representable results can be
expected is considered for binary, decimal, and other
potentially interesting bases (base 30 and base 210).",
acknowledgement = ack-nhfb,
affiliation = "Telerate Syst. Inc., New Orleans, LA, USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Base 10; Base 2; Base 210; Base 30; Bits per datum;
decimal floating-point arithmetic; Error performance;
Floating point representations; Fractions; Higher radix
floating point systems; Limited exponent range;
Normalized encodings; Rational number approximation;
Storage allocated",
thesaurus = "Digital arithmetic",
}
@Article{Kahan:1992:ARL,
author = "W. Kahan",
title = "Analysis and Refutation of the {LCAS}",
journal = j-SIGPLAN,
volume = "27",
number = "1",
pages = "61--74",
month = jan,
year = "1992",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Aug 18 02:37:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "LCAS (Language Compatible Arithmetic Standard)",
}
@Unpublished{Kahan:1992:FPE,
author = "W. Kahan",
title = "Floating-Point Exception-Handling",
institution = inst-BERKELEY-CS,
address = inst-BERKELEY-CS:adr,
pages = "2",
day = "31",
month = jul,
year = "1992",
bibdate = "Mon Apr 25 18:24:02 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Manuscript",
acknowledgement = ack-nhfb,
}
@Article{Kahaner:1992:SJC,
author = "D. K. Kahaner and U. Wattenberg",
title = "{Supercomputing-Japan}: a competitive assessment",
journal = j-IEEE-SPECTRUM,
volume = "29",
number = "9",
pages = "42--47",
month = sep,
year = "1992",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.155708",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Jan 16 07:37:23 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "5 to 8 GFLOPS; Arithmetic; Central Processing Unit;
Computer industry; Hardware; high-speed single
processor systems; Home computing; Information
technology; intuitive information processing; Japanese
supercomputers; Manufacturing industries; Ministry of
International Trade and Industry; National electric
code; parallel machines; Real-World Computing Program;
research initiatives; Supercomputers; Telephony; US
machines; vector processing functions",
}
@InProceedings{Kalliojarvi:1992:DRN,
author = "K. Kalliojarvi and Y. Neuvo",
title = "Distribution of roundoff noise in binary
floating-point addition",
crossref = "White:1992:IIS",
volume = "4",
bookpages = "3028",
pages = "1796--1799",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A method for deriving the distribution of relative
round off error in addition of two binary
floating-point numbers is introduced. The distribution
is needed in the calculation of variance of the
relative roundoff error in floating-point addition. The
resulting distribution depends on the statistics of the
addends and the rounding strategy chosen. As an
example, the distribution is derived for the addition
of two uncorrelated numbers from Gaussian distribution.
The result was verified by simulation.",
acknowledgement = ack-nhfb,
affiliation = "Signal Process. Lab., Tampere University of Technol.,
Finland",
classification = "C1260 (Information theory); C5230 (Digital
arithmetic methods); C5260 (Digital signal
processing)",
keywords = "Addends; Binary floating-point addition; Calculation
of variance; Distribution of relative round off error;
Gaussian distribution; Relative roundoff error;
Rounding strategy; Roundoff noise; Simulation; Two
uncorrelated numbers",
thesaurus = "Digital arithmetic; Digital simulation; Roundoff
errors; Signal processing",
}
@Book{Kane:1992:MRA,
author = "Gerry Kane and Joe Heinrich",
title = "{MIPS RISC} Architecture",
publisher = pub-PH,
address = pub-PH:adr,
year = "1992",
ISBN = "0-13-590472-2",
ISBN-13 = "978-0-13-590472-5",
LCCN = "QA76.8.M52 K37 1992",
bibdate = "Wed Dec 15 10:35:45 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
acknowledgement = ack-nhfb,
keywords = "computer architecture; MIPS R2000 series
microprocessors; reduced instruction set computers",
tableofcontents = "RISC Architecture: An Overview \\
MIPS Processor Architecture Overview \\
CPU Instruction Set Summary \\
Memory Management System \\
Caches \\
Exception Processing \\
FPU Overview \\
FPU Instruction Set Summary and Instruction Pipeline
\\
Floating Point Exceptions \\
Appendixes \\
Index",
}
@Book{Klatte:1992:PXP,
author = "Rudi Klatte and Ulrich Kulisch and Michael Neaga and
Dietmar Ratz and Christian Ullrich",
title = "{PASCAL-XSC}: language reference with examples",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 344",
year = "1992",
DOI = "https://doi.org/10.1007/978-3-642-77277-1",
ISBN = "3-540-55137-9 (Berlin), 0-387-55137-9 (New York)",
ISBN-13 = "978-3-540-55137-9 (Berlin), 978-0-387-55137-1 (New
York)",
LCCN = "QA76.73.P2 P4213 1992",
bibdate = "Thu Jan 21 17:16:51 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Translated by G. F. Corliss and others.",
price = "DM 64.00",
abstract = "The programming language PASCAL-XSC (PASCAL eXtension
for Scientific Computation) significantly simplifies
programming in the area of scientific and technical
computing. PASCAL-XSC provides a large number of
predefined data types with arithmetic operators and
predefined functions of highest accuracy for real and
complex numbers, for real and complex intervals, and
for the corresponding vectors and matrices. Thus
PASCAL-XSC makes the computer more powerful concerning
the arithmetic. Through an implementation in C,
compilers for PASCAL-XSC are available for a large
variety of computers such as personal computers,
workstations, mainframes, and supercomputers.
PASCAL-XSC provides a module concept, an operator
concept, functions and operators with general result
type, overloading of functions, procedures, and
operators, dynamic arrays, access to subarrays,
rounding control by the user, and accurate evaluation
of expressions. The language is particularly suited for
the development of numerical algorithms that deliver
highly accurate and automatically verified results. A
number of problem-solving routines with automatic
result verification have already been implemented.
PASCAL-XSC contains Standard PASCAL. It is immediately
usable by PASCAL programmers. PASCAL-XSC is easy to
learn and ideal for programming education. The book can
be used as a textbook for lectures on computer
programming. It contains a major chapter with sample
programs, exercises, and solutions. A complete set of
syntax diagrams, detailed tables, and indices complete
the book.",
acknowledgement = ack-nhfb,
language = "English.",
remark = "Translation of: PASCAL-XSC.",
subject = "Pascal (Computer program language)",
tableofcontents = "1 Introduction \\
1.1 Typography \\
1.2 Historical Remarks and Motivation \\
1.3 Advanced Computer Arithmetic \\
1.4 Connection with Programming Languages \\
1.5 Survey of PASCAL-XSC \\
2 Language Reference \\
2.1 Basic Symbols \\
2.2 Identifiers \\
2.3 Constants, Types, and Variables \\
2.4 Expressions \\
2.5 Statements \\
2.6 Program Structure \\
2.7 Subroutines \\
2.8 Modules \\
2.9 String Handling and Text Processing \\
2.10 How to Use Dynamic Arrays \\
3 The Arithmetic Modules \\
3.1 The Module C\_ARI \\
3.2 The Module I\_ARI \\
3.3 The Module CI\_ARI \\
3.4 The Module MV\_ARI \\
3.5 The Module MVC\_ARI \\
3.6 The Module MVI\_ARI \\
3.7 The Module MVCI\_ARI \\
3.8 The Hierarchy of the Arithmetic Modules \\
3.9 A Complete Sample Program \\
4 Problem-Solving Routines \\
5 Exercises with Solutions \\
5.1 Test of Representability \\
5.2 Summation of Exponential Series \\
5.3 Influence of Rounding Errors \\
5.4 Scalar Product \\
5.5 Boothroyd/Dekker Matrices \\
5.6 Complex Functions \\
5.7 Surface Area of a Parallelepiped \\
5.8 Parallelism and Intersection of Lines \\
5.9 Transposed Matrix, Symmetry \\
5.10 Rail Route Map \\
5.11 Inventory Lists \\
5.12 Complex Numbers and Polar Representation \\
5.13 Complex Division \\
5.14 Electric Circuit \\
5.15 Alternating Current Measuring Bridge \\
5.16 Optical Lens \\
5.17 Interval Evaluation of a Polynomial \\
5.18 Calculations for Interval Matrices \\
5.19 Differentiation Arithmetic \\
5.20 Newton's Method with Automatic Differentiation \\
5.21 Measurement of Time \\
5.22 Iterative Method \\
5.23 Trace of a Product Matrix \\
5.24 Calculator for Polynomials \\
5.25 Interval Newton Method \\
5.26 Runge-Kutta Method \\
5.27 Rational Arithmetic \\
5.28 Evaluation of Polynomials \\
A Syntax Diagrams \\
B Indices and Lists \\
B.1 Syntax Diagrams \\
B.2 Reserved Words \\
B.3 Predefined Identifiers \\
B.4 Operators \\
B.4.1 Basic Operators \\
B.4.2 Arithmetic Operators \\
B.4.3 Relational Operators for the Arithmetic Types \\
B.4.4 Assignment Operators \\
B.5 Predefined Functions \\
B.6 Transfer Functions \\
B.7 Predefined Procedures \\
B.8 \#-Expressions \\
B.8.1 Real and Complex \#-Expressions \\
B.8.2 Real and Complex Interval \#-Expressions \\
Bibliography \\
Index",
}
@Article{Koc:1992:AAS,
author = "{\c{C}}etin K. Ko{\c{c}} and Ching-Yu Hung",
title = "Adaptive $m$-ary segmentation and canonical recoding
algorithms for multiplication of large binary numbers",
journal = j-COMPUT-MATH-APPL,
volume = "24",
number = "3",
pages = "3--12",
month = aug,
year = "1992",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:08 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219290209Z",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Kola:1992:MQP,
author = "M. Kol{\'a}r and T. Sasaki",
title = "Multivariate quotient by power-series division",
journal = j-SIGSAM,
volume = "26",
number = "3",
pages = "17--20",
month = aug,
year = "1992",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Fri Feb 8 18:27:02 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@InProceedings{Kontro:1992:FAS,
author = "J. Kontro and K. Kalliojarvi and Y. Neuvo",
title = "Floating-point arithmetic in signal processing",
crossref = "White:1992:IIS",
pages = "1784--1791 vol.4",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The use of floating-point arithmetic in digital signal
processing is considered. An introduction to
floating-point arithmetic based on the IEEE
floating-point standards is given. Finite wordlength
effects of these arithmetic systems are presented.
Floating-point hardware is discussed. The emphasis is
on audio applications. As an example, amplitude
distributions and signal-to-noise ratios of quantized
music are considered, and audio standards using
floating-point arithmetic are presented.",
acknowledgement = ack-nhfb,
affiliation = "Signal Process. Lab., Tampere University of Technol.,
Finland",
classification = "B1265F (Microprocessors and microcomputers); B6140
(Signal processing and detection); B6450 (Audio
equipment and systems); C1260 (Information theory);
C5130 (Microprocessor chips); C5230 (Digital arithmetic
methods); C5260 (Digital signal processing)",
keywords = "Amplitude distributions; Audio applications; Audio
standards; Digital signal processing; Finite wordlength
effects; Floating-point arithmetic; Hardware; IEEE
floating-point standards; Quantized music;
Signal-to-noise ratios",
thesaurus = "Audio equipment; Audio signals; Digital arithmetic;
Digital signal processing chips; Roundoff errors;
Signal processing",
}
@Article{Kontro:1992:USF,
author = "J. Kontro and K. Kalliojarvi and Y. Neuvo",
title = "Use of Short Floating-Point Formats in Audio
Applications",
journal = j-IEEE-TRANS-CONSUMER-ELECTRONICS,
volume = "38",
number = "3",
pages = "200--207",
month = aug,
year = "1992",
CODEN = "ITCEDA",
ISSN = "0098-3063 (print), 1558-4127 (electronic)",
ISSN-L = "0098-3063",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Consumer Electronics",
summary = "Use of short floating-point formats that are shorter
than the IEEE floating-point standard (ANSI/IEEE S+A
754-1985), 24+8-b, in digital audio applications is
studied. The performance of these formats is analyzed
in different parts of the digital audio \ldots{}",
}
@Article{Krishna:1992:CTA,
author = "H. Krishna and K.-Y. Lin and J.-D. Sun",
title = "A coding theory approach to error control in redundant
residue number systems. {I}. Theory and single error
correction",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "39",
number = "1",
pages = "8--17",
month = jan,
year = "1992",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.204106",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "A coding theory approach to error control in redundant
residue number systems (RRNSs) is presented. The
concepts of Hamming weight, minimum distance, weight
distribution, and error detection and correction
capabilities in redundant residue number \ldots{}",
}
@Article{Krishnan:1992:CGF,
author = "R. Krishnan and G. A. Jullien and W. C. Miller",
title = "Computation of generalized {FIR} filter structure
using the modified quadratic residue number system",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "39",
number = "1",
pages = "58--62",
month = jan,
year = "1992",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.204110",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "The systematic approach for generating the generalized
number theoretic FIR filter structure based on the
complex number theoretic z-transform is presented. A
step-by-step computational method that can be used in
the implementation and \ldots{}",
}
@InProceedings{Kubosawa:1992:BFP,
author = "H. Kubosawa and A. Katsuno and H. Takahashi and T.
Sato and A. Suga and G. Goto",
title = "A 64-bit floating point processing unit for a {RISC}
microprocessor",
crossref = "Anonymous:1992:EAP",
pages = "270--273",
year = "1992",
DOI = "https://doi.org/10.1109/EUASIC.1992.228042",
bibdate = "Thu Mar 02 09:45:28 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/iel2/416/5911/00228042.pdf",
acknowledgement = ack-nhfb,
keywords = "25MHz SPARC S-25 microprocessor; CMOS; PGA; RISC",
}
@InProceedings{Kutuso:1992:EMO,
author = "K. N. Kutuso and H. M. Yassine",
booktitle = "Proceedings of the 35th Midwest Symposium on Circuits
and Systems, 1992",
title = "Effect of moduli ordering of mixed radix conversion
methods in residue number systems",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "678--680",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1992.271232",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The effect of moduli ordering in different methods for
converting residue numbers to decimal numbers using the
mixed radix approach is investigated. The number of
operations involved in the conversion process of
residue numbers to their decimal \ldots{}",
}
@InProceedings{Lacroix:1992:DDM,
author = "A. Lacroix and F. Hartwig",
title = "Distribution densities of the mantissa and exponent of
floating point numbers",
crossref = "White:1992:IIS",
pages = "1792--1795 vol.4",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "6 vol.",
abstract = "The relations between the probability densities of
real numbers and the corresponding mantissa and
exponent densities in the floating point number format
are investigated. Assumptions about continuity of the
probability density of real numbers lead to certain
restrictions in terms of the density of the mantissa. A
few real number densities of practical importance were
treated analytically and experimentally. During
arithmetic operations like addition and multiplication
which are essential for signal processing the operand
density is altered. The effect concerning the densities
of mantissa and exponent of the result is discussed.
The reciprocal density of the mantissas plays a central
role. Applications in roundoff-noise-analysis of signal
processing with finite wordlength are considered. (5
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Inst. fuer Angewandte Phys., J. W. Goethe-University,
Frankfurt am Main, Germany",
classification = "B1270F (Digital filters); B6140 (Signal processing
and detection); C1260 (Information theory); C5230
(Digital arithmetic methods); C5240 (Digital filters);
C5260 (Digital signal processing)",
keywords = "Addition; Arithmetic operations; Exponent densities;
Finite wordlength; Floating point number format;
Floating point numbers; Mantissa densities;
Multiplication; Operand density; Probability densities;
Real numbers; Reciprocal density;
Roundoff-noise-analysis; Signal processing",
thesaurus = "Digital arithmetic; Digital filters; Roundoff errors;
Signal processing",
}
@Article{Lang:1992:HRS,
author = "T. Lang and P. Montuschi",
title = "Higher radix square root with prescaling",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "996--1009",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156542",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156542",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A scheme for performing higher radix square root based
on prescaling of the radicand is presented to reduce
the complexity of the result-digit selection. The
scheme requires several steps, namely multiplication
for prescaling the radicand, square \ldots{}",
}
@Article{Lee:1992:ACR,
author = "J. H. M. Lee and M. H. {van Emden}",
title = "Adapting {$ {\rm CLP}(\sc {R}) $} to floating-point
arithmetic",
journal = "Fifth generation computer systems, vol 1",
volume = "2",
publisher = "Ohm",
address = "Tokyo, Japan",
pages = "996--1003",
year = "1992",
MRclass = "68N15 (68N17 68Q40)",
MRnumber = "93m:68027",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Lee:1992:FPP,
author = "K. Lee",
title = "On the Floating Point Performance of the i860
Microprocessor",
journal = j-INT-J-HIGH-SPEED-COMPUTING,
volume = "4",
number = "4",
pages = "251--268",
month = dec,
year = "1992",
CODEN = "IHSCEZ",
ISSN = "0129-0533",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Speed Computing",
journal-URL = "http://www.worldscientific.com/worldscinet/ijhsc",
}
@Book{Leighton:1992:IPA,
author = "Frank Thomson Leighton",
title = "Introduction to Parallel Algorithms and Architectures:
Arrays, Trees, Hypercubes",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xviii + 831",
year = "1992",
ISBN = "1-55860-117-1",
ISBN-13 = "978-1-55860-117-8",
LCCN = "QA76.5 .L45 1992",
bibdate = "Mon Sep 16 16:21:01 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$54.95",
acknowledgement = ack-nhfb,
}
@Article{Li:1992:CSC,
author = "Zhenyu Li and Victor Milenkovic",
title = "Constructing Strongly Convex Hulls Using Exact or
Rounded Arithmetic",
journal = j-ALGORITHMICA,
volume = "8",
number = "5--6",
pages = "345--364",
year = "1992",
CODEN = "ALGOEJ",
ISSN = "0178-4617 (print), 1432-0541 (electronic)",
ISSN-L = "0178-4617",
MRclass = "68U05 (52B55)",
MRnumber = "MR1195157 (93k:68104)",
MRreviewer = "Nikolaj M. Korneenko",
bibdate = "Mon Jan 22 05:31:33 MST 2001",
bibsource = "dblp-journals-algorithmica.bib;
http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica8.html#LiM92;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica;
MathSciNet database",
note = "1990 Computational Geometry Symposium (Berkeley, CA,
1990)",
acknowledgement = ack-nhfb,
fjournal = "Algorithmica. An International Journal in Computer
Science",
journal-URL = "http://link.springer.com/journal/453",
keywords = "exact arithmetic; floating-point arithmetic; rounding
errors",
oldlabel = "LiM92",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/algorithmica/LiM92",
}
@Article{Lim:1992:SPM,
author = "Y. C. Lim",
title = "Single-precision multiplier with reduced circuit
complexity for signal processing applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "10",
pages = "1333--1336",
month = oct,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.166611",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166611",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Liu:1992:QBS,
author = "K. J. R. Liu and E. Frantzeskakis",
booktitle = "Workshop on {VLSI} Signal Processing, V, 1992",
title = "Qrd-based Square Root Free and Division Free
Algorithms and Architectures",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "459--468",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@Article{Lozier:1992:RPC,
author = "D. W. Lozier and P. R. Turner",
title = "Robust Parallel Computation in Floating-Point and
{SLI} Arithmetic. {Robuste Parallel-Verarbeitung in
Gleitkomma-und SLI-Arithmetik}",
journal = j-COMPUTING,
volume = "48",
number = "3-4",
pages = "239--258 (or 239--257??)",
year = "1992",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65Y05 (65-04 65G05)",
MRnumber = "93e:65161",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Lozier:1992:RPV,
author = "D. W. Lozier and P. R. Turner",
title = "{Robuste Parallel-Verarbeitung in Gleitkomma- und
SLI-Arithmetik}. ({German}) [{Robust} Parallel
Computation in Floating-Point and {SLI} Arithmetic]",
journal = j-COMPUTING,
volume = "48",
number = "3--4",
pages = "239--257",
month = sep,
year = "1992",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65Y05 (65-04 65G05)",
MRnumber = "93e:65161",
bibdate = "Mon Oct 11 20:38:38 MDT 1999",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Lozier:1992:SLI,
author = "Daniel W. Lozier and P. R. Turner",
title = "Symmetric Level-Index Arithmetic in Simulation and
Modeling",
journal = j-J-RES-NATL-BUR-STAND,
volume = "97",
number = "4",
pages = "471--485",
month = jul,
year = "1992",
CODEN = "JRNBAG",
DOI = "https://doi.org/10.6028/jres.097.020",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
bibdate = "Fri Jul 09 07:24:16 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/jres/097/jresv97n4p471_A1b.pdf",
abstract = "This paper begins with a general introduction to the
symmetric level-index, SLI, system of number
representation and arithmetic. This system provides a
robust framework in which experimental computation can
be performed without the risk of failure due to
overflow/underflow or to poor scaling of the original
problem. There follows a brief summary of some existing
computational experience with this system to illustrate
its strengths in numerical, graphical and parallel
computational settings. An example of the use of SLI
arithmetic to overcome graphics failure in the modeling
of a turbulent combustion problem is presented. The
main thrust of this paper is to introduce the idea of
SLI-linear least squares data fitting. The use of
generalized logarithm and exponential functions is seen
to offer significant improvement over the more
conventional linear regression tools for fitting data
from a compound exponential decay such as the decay of
radioactive materials.",
acknowledgement = ack-nhfb,
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
keywords = "computer graphics; generalized logarithms and
exponentials; least-squares data-fitting; overflow,
underflow, and scaling; parallel computing; symmetric
level-index arithmetic.",
}
@Article{Lu:1992:NDA,
author = "M. Lu and J.-S. Chiang",
title = "A novel division algorithm for the residue number
system",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "1026--1032",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156545",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156545;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4052",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A novel general algorithm for signed number division
in the residue number system (RNS) is presented. The
parity checking technique used for sign and overflow
detection in this algorithm is more efficient and
practical than conventional methods. \ldots{}",
}
@InProceedings{Lynch:1992:FCA,
author = "Thomas W. Lynch and Earl E. {Swartzlander, Jr.}",
title = "A Formalization for Computer Arithmetic",
crossref = "Atanassova:1992:CAE",
pages = "137--145",
year = "1992",
bibdate = "Sat Sep 17 19:09:42 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From the abstract: ``The formalism, when applied to
IEEE Std 754 shows that the non-trapping mode can
produce incorrect numeric and non-numeric results.''",
acknowledgement = ack-nhfb,
}
@Misc{Lynch:1992:HSD,
author = "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
T. Hurson",
title = "High speed divider with square root capability",
year = "1992",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,128,891.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{Maguire:1992:MD,
author = "J. Maguire",
title = "{MC8810}: Datapath",
crossref = "Juj:1992:NCR",
pages = "193--197",
year = "1992",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@MastersThesis{Makhdumi:1992:CCS,
author = "Shazia Makhdumi",
title = "Comparison of current switch bipolar circuits for high
performance floating point arithmetic",
type = "Thesis ({M.S.})",
school = "Massachusetts Institute of Technology, Dept. of
Electrical Engineering and Computer Science",
address = "Cambridge, MA, USA",
pages = "107",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Mar:1992:DSP,
editor = "Amy Mar",
title = "Digital signal processing applications using the
{ADSP}-2100 family",
publisher = pub-PH,
address = pub-PH:adr,
pages = "????",
year = "1992",
ISBN = "0-13-219726-X (vol. 1), 0-13-178567-2 (vol. 2)",
ISBN-13 = "978-0-13-219726-7 (vol. 1), 978-0-13-178567-0 (vol.
2)",
LCCN = "TK5102.9 .D53 1992",
bibdate = "Sat Jan 15 05:58:58 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Vol. 2: edited by Jere Babst. System requirements for
computer disks: IBM-compatible PC; DOS 3.0 or higher;
high-density disk drive.",
subject = "Signal processing; Digital techniques;
Microprocessors",
}
@Article{McQuillan:1992:VMH,
author = "S. E. McQuillan and J. V. McCanny",
title = "{VLSI} module for high-performance multiply, square
root and divide",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "139",
number = "6",
pages = "505--510",
month = nov,
year = "1992",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
summary = "A high-performance VLSI architecture to perform
multiply-accumulate, division and square root
operations is proposed. The circuit is highly regular,
requires only minimal control and ean be pipelined
right down to the bit level. The system can also
\ldots{}",
}
@TechReport{MenissierMorain:1992:CNR,
author = "V. M{\'e}nissier-Morain",
title = "{CAML} numbers reference manual",
number = "141",
institution = "Inst. Nat. Recherche Inf. Autom.",
address = "Le Chesnay, France",
pages = "157",
month = jul,
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An overview is given of the arithmetic of the
functional language CAML V3.1. This arithmetic includes
floating point numbers, arbitrary large integers and
rationals and a complete set of primitives. Its
implementation relies on the efficient BigNum package
(J.-C. Herve et al., 1989).",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods); C6110 (Systems
analysis and programming); C6140D (High level
languages); C7310 (Mathematics)",
keywords = "Arbitrary large integers; Arithmetic; BigNum package;
Floating point numbers; Functional language CAML;
Primitives; Rationals",
pubcountry = "France",
thesaurus = "Digital arithmetic; Functional programming; High level
languages; Mathematics computing",
}
@Book{Menninger:1992:NWN,
author = "Karl Menninger",
title = "Number Words and Number Symbols: a Cultural History of
Numbers",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xiii + 480",
year = "1992",
ISBN = "0-486-27096-3",
ISBN-13 = "978-0-486-27096-8",
LCCN = "QA141.2 .M4513 1992",
bibdate = "Fri Nov 28 18:29:23 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Meredith:1992:NPF,
author = "Roger W. Meredith",
title = "Numeric precision in {FORTRAN} computing",
journal = j-COMPUT-PHYS,
volume = "6",
number = "5",
pages = "506--512",
month = sep # "\slash " # oct,
year = "1992",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.168438",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:36 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.168438",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Mikami:1992:NDO,
author = "N. Mikami and M. Kobayashi and Y. Yokoyama",
title = "A New {DSP}-Oriented Algorithm for Calculation of the
Square Root Using a Nonlinear Digital Filter",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "7",
pages = "1663--1669",
month = jul,
year = "1992",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "A high-speed algorithm for calculating the square root
is proposed. This algorithm, which can be regarded as
calculation of the step response of a kind of nonlinear
IIR filter, requires no divisions. Therefore, it is
suitable for a VLSI digital \ldots{}",
}
@Article{Mitchell:1992:VFA,
author = "H. B. Mitchell",
title = "Very fast accurate square-root algorithm for use with
gradient edge operators",
journal = j-ELECT-LETTERS,
volume = "28",
number = "10",
pages = "922--923",
day = "7",
month = may,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "Commonly used gradient edge operators such as the
Sobel, Prewitt and Roberts operators all required a
square root operation; this is, however,
computationally intensive and, consequently, simple but
very inaccurate approximations are often used
\ldots{}",
}
@InProceedings{Montuschi:1992:DAC,
author = "P. Montuschi and L. Ciminiera and A. Giustina",
title = "A Division Architecture Combining {Newton--Raphson}
Approximations and Direct Methods Iterations",
crossref = "Singh:1992:CRT",
pages = "376--380",
year = "1992",
bibdate = "Wed Dec 13 18:19:38 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors consider the possibility of designing
architectures which combine in the best possible way
the convergence with the square advantages of the
Newton--Raphson method with the precision
characteristics of the digit-by-digit algorithms so as
to obtain units which satisfy the IEEE 754 floating
point standard requirements. This is a general method
which can be extended with simple and minor changes
also to square root. Attention is focused on a possible
implementation of this design methodology for division.
The evaluation shows that the proposed unit offers an
alternative architecture for division which provides
interesting performances.",
acknowledgement = ack-nj,
affiliation = "Dipartimento di Autom. e Inf., Politecnico di Torino,
Italy",
classification = "B0290F (Interpolation and function approximation);
B1265B (Logic circuits); C4130 (Interpolation and
function approximation); C5230 (Digital arithmetic
methods)",
keywords = "Convergence; Digit-by-digit algorithms; Direct methods
iterations; Division architecture; IEEE 754 floating
point standard; Newton--Raphson method; Square
advantages; Square root",
thesaurus = "Convergence of numerical methods; Digital arithmetic;
Dividing circuits; Iterative methods",
}
@Article{Montuschi:1992:DRD,
author = "P. Montuschi and L. Ciminiera",
title = "Design of a radix $4$ division unit with simple
selection table",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "12",
pages = "1606--1611",
month = dec,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.214670",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214670",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Moore:1992:PRP,
author = "David L. Moore",
title = "Programming the 29050 ({RISC} programming)",
journal = j-DDJ,
volume = "17",
number = "1",
pages = "34, 36, 38, 40, 42",
month = jan,
year = "1992",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 10:06:23 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5220 (Computer architecture); C6110 (Systems
analysis and programming); C6140B (Machine-oriented
languages)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "29000 Family; AM29050; Assembly language programming;
Flat address space; Floating-point operations;
Registers; RISC processors",
thesaurus = "Assembly language; Microprogramming; Reduced
instruction set computing",
}
@Book{Morgan:1992:NM,
author = "Don Morgan",
title = "Numerical Methods: Real-time and Embedded Systems
Programming",
publisher = pub-MT,
address = pub-MT:adr,
pages = "496",
year = "1992",
ISBN = "1-55851-232-2 (book only), 1-55851-233-0 (disk only),
1-55851-234-9 (book and disk set)",
ISBN-13 = "978-1-55851-232-0 (book only), 978-1-55851-233-7 (disk
only), 978-1-55851-234-4 (book and disk set)",
LCCN = "QA76.6 .M669 1992",
bibdate = "Wed Sep 14 19:16:35 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$34.95",
acknowledgement = ack-nj,
}
@Article{Mou:1992:OSA,
author = "Z.-J. Mou and F. Jutand",
title = "{`Overturned-stairs'} adder trees and multiplier
design",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "940--948",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156536",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156536",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Mutrie:1992:AFE,
author = "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
Char",
title = "An approach for floating-point error analysis using
computer algebra",
crossref = "Wang:1992:PII",
pages = "284--293",
year = "1992",
bibdate = "Thu Mar 12 08:39:32 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/issac.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p284-mutrie/",
acknowledgement = ack-nhfb,
keywords = "algorithms",
subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Algorithms, Algebraic algorithms. {\bf G.1.0}
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic. {\bf I.1.3} Computing
Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
Languages and Systems, Maple. {\bf G.2.2} Mathematics
of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph
algorithms.",
}
@PhdThesis{Mutrie:1992:TSS,
author = "Mark P. W. Mutrie",
title = "Towards a symbolic system for floating-point error
analysis",
type = "Thesis ({Ph.D.})",
publisher = "National Library of Canada = Bibliotheque nationale du
Canada",
school = "University of Waterloo",
address = "Waterloo, ON, Canada",
year = "1992",
ISBN = "0-315-72486-2",
ISBN-13 = "978-0-315-72486-0",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "8 microfiches. University Microfilms order no.
UMI00359027",
series = "Canadian theses = Theses canadiennes",
acknowledgement = ack-nhfb,
}
@Article{Nakano:1992:AHS,
author = "H. Nakano and M. Nakajima and Y. Nakakura and T.
Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
Kishida",
title = "An accurate, high speed implementation of division by
the quasi-unity divisor method",
journal = j-IFIP-TRANS-A,
volume = "A-12",
pages = "261--267",
month = "????",
year = "1992",
CODEN = "ITATEC",
ISSN = "0926-5473",
bibdate = "Thu Dec 14 15:33:50 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Algorithms, Software, Architecture. Information
Processing 92. IFIP 12th World Computer Congress.",
abstract = "A first-order convergent division algorithm is
generally thought to be accurate but slow. Using a
large look-up table and a multiplier improves speed.
Since a partial quotient is not negative and iterations
use only one formula, an iteration is carried out in
the form of a partial carry and a partial sum. This
paper describes a new developed division algorithm with
the above-mentioned characteristics. This algorithm is
compared to other similar algorithms. In a hardware
implementation, this algorithm is applied to the 53-bit
significand part of a floating-point double precision
divider. The execution time is division of 8 or 9
cycles.",
acknowledgement = ack-nhfb,
affiliation = "Corporate R and D, Matsushita Electric Industrial Co.
Ltd., Osaka, Japan",
classification = "C5230 (Digital arithmetic methods)",
confdate = "7-11 Sept. 1992",
conflocation = "Madrid, Spain",
confsponsor = "IFIP",
fjournal = "IFIP Transactions. A. Computer Science and
Technology",
keywords = "53-Bit significand part; First-order convergent
division algorithm; Floating-point double precision
divider; Look-up table; Multiplier; Partial carry;
Partial sum; Quasi-unity divisor method",
pubcountry = "Netherlands",
thesaurus = "Digital arithmetic; Table lookup",
}
@Article{Nakano:1992:FPB,
author = "H. Nakano and M. Nakajima and Y. Nakakura and T.
Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
Kishida and H. Kadota",
title = "An 80-{FLOPS} (Peak) 64-b Microprocessor for Parallel
Computer",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "27",
number = "3",
pages = "365--372",
month = mar,
year = "1992",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Wed Sep 7 22:32:42 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Ng:1992:ARH,
author = "K. C. Ng",
title = "Argument Reduction for Huge Arguments: Good to the
Last Bit",
journal = "SunPro",
volume = "??",
number = "??",
day = "13",
month = jul,
year = "1992",
bibdate = "Thu Sep 1 10:16:08 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Work in progress.",
URL = "http://www.validlab.com/arg.pdf",
acknowledgement = ack-nj,
keywords = "range reduction",
}
@InProceedings{Nishimura:1992:FPR,
author = "S. Nishimura",
booktitle = "Proceedings of the 35th Midwest Symposium on Circuits
and Systems, 1992",
title = "A fixed-point roundoff error analysis of adaptive
notch filters",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "373--376",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Methods to analyze the convergence and steady-state
characteristics of an adaptive notch filter when the
effects of fixed-point arithmetic are taken into
account are presented. The adaptive detection of a
sinusoid with white Gaussian noise is \ldots{}",
}
@Article{Obaidat:1992:DMA,
author = "Mohammad S. Obaidat and Saleh A. Bleha",
title = "A Decimal Multiplication Algorithm for
Microcomputers",
journal = j-COMPUT-ELECTR-ENG,
volume = "18",
number = "5",
pages = "357--363",
month = sep,
year = "1992",
CODEN = "CPEEBQ",
ISSN = "0045-7906 (print), 1879-0755 (electronic)",
ISSN-L = "0045-7906",
bibdate = "Thu Sep 1 10:16:11 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computers and Electrical Engineering",
keywords = "decimal floating-point arithmetic",
}
@Article{Ochs:1992:SIR,
author = "T. Ochs",
title = "This sine is also right!",
journal = j-COMP-LANG-MAG,
volume = "9",
number = "1",
pages = "89--93",
month = jan,
year = "1992",
CODEN = "COMLEF",
ISSN = "0749-2839",
bibdate = "Thu Sep 01 10:44:04 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Computer Language Magazine",
}
@Article{Okada:1992:AQE,
author = "Kazuho Okada and Yasuaki Kuroe",
title = "Analysis of Quantization Errors in Digital Control
Systems Using Floating-Point Arithmetic--Considering
Computational Order in Controller",
journal = j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI,
volume = "75",
number = "6",
pages = "1--??",
month = jun,
year = "1992",
CODEN = "ECJSER",
ISSN = "1042-0967 (print), 1520-6440 (electronic)",
ISSN-L = "1042-0967",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and communications in Japan. Part 3,
Fundamental electronic science",
}
@Article{Orton:1992:NFT,
author = "G. A. Orton and L. E. Peppard and S. E. Tavares",
title = "New fault tolerant techniques for residue number
systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "11",
pages = "1453--1464",
month = nov,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.177315",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:21 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=177315;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4475",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "Previously proposed error detection algorithms for the
residue number system require a complete recombination.
A weighted approximation via the Chinese remainder
theorem is shown to be sufficient to detect 100\% of
single errors. This makes real-time \ldots{}",
}
@InProceedings{Paliouras:1992:SDP,
author = "V. Paliouras and D. Soudris and T. Stouraitis",
booktitle = "{IEEE} International Symposium on Circuits and
Systems. {ISCAS '92}. Proceedings, 3--6 May 1992",
title = "Systematic derivation of the processing element of a
systolic array based on residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "815--818",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1992.230097",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A systematic methodology for synthesizing optimal VLSI
residue number system architectures using full adders
(FAs) as the basic building block is introduced. The
design methodology derives array architectures starting
from the algorithmic level. \ldots{}",
}
@TechReport{Pan:1992:CWU,
author = "V. Y. Pan",
title = "Can we utilize the cancellation of the most
significant digits?",
type = "Report",
number = "TR 92 061",
institution = "The International Computer Science Institute",
address = "Berkeley, CA, USA",
year = "1992",
bibdate = "Mon Mar 06 17:00:31 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Park:1992:MED,
author = "Haesun Park",
title = "On Multiple Error Detection in Matrix
Triangularizations Using Checksum Methods",
journal = j-J-PAR-DIST-COMP,
volume = "14",
number = "1",
pages = "90--97",
month = jan,
year = "1992",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
MRclass = "65F05 (65F25)",
MRnumber = "92i:65060",
bibdate = "Mon Apr 14 08:15:42 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Univ of Minnesota",
affiliationaddress = "Minneapolis, MN, USA",
classification = "722; 723; 921; 922; C4110 (Error analysis in
numerical methods); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods); C5470 (Performance
evaluation and testing)",
corpsource = "Department of Computer Science, Minnesota University,
Minneapolis, MN, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
journalabr = "J Parallel Distrib Comput",
keywords = "Checksum methods; checksum methods; Codes,
Symbolic--Error Detection; Computer Systems,
Digital--Fault Tolerant Capability; correct rounding;
detection; digital arithmetic; error; error analysis;
error correction; errors; floating-point arithmetic;
floating-point error analysis; Gaussian elimination; LU
decomposition; Mathematical Techniques; matrix; Matrix
Algebra; Matrix triangularizations; multiple error
correction; multiple error detection; pairwise
pivoting; parallel architectures; performance
evaluation; QR decomposition; rounding; transient
errors; triangularizations",
treatment = "P Practical",
}
@Article{Parker:1992:OVN,
author = "A. Parker and J. O. Hamblen",
title = "Optimal value for the {Newton--Raphson} division
algorithm",
journal = j-INFO-PROC-LETT,
volume = "42",
number = "3",
pages = "141--144",
day = "25",
month = may,
year = "1992",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Nov 11 07:31:13 1998",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "fast division; floating-point arithmetic",
}
@Article{Pichat:1992:SFR,
author = "Mich{\`e}le Pichat",
title = "Sets of floating-point results associated with an
algebraic algorithm",
journal = "Computational and applied mathematics, I (Dublin,
1991)",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "409--418",
year = "1992",
MRclass = "68M07 (65G05)",
MRnumber = "93m:68010",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Plauger:1992:SCL,
author = "P. J. Plauger",
title = "The {Standard C} Library",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiv + 498",
year = "1992",
ISBN = "0-13-838012-0",
ISBN-13 = "978-0-13-838012-0",
LCCN = "QA76.73.C15 P563 1991",
bibdate = "Wed Dec 15 10:40:47 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ansistd.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/litprog.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
abstract = "\booktitle{The Standard C Library} shows you how to
use all of the library functions mandated by the ANSI
and ISO Standards for the programming language C. To
help you understand how to use the library, this book
also shows you how to implement it. You see
approximately 9,000 lines of tested, working code that
is highly portable across diverse computer
architectures. \booktitle{The Standard C Library}
explains how the library was meant to be used and how
it can be used. It places particular emphasis on
features added to C as part of the C Standard. These
features include support for multiple locales (cultural
conventions) and very large character sets (such as
Kanji). The code presented in this book has been tested
with C compilers from Borland, Saber, Project Gnu, Sun,
UNIX, and VAX, ULTRIX. It has passed the widely used
Plum Hall Validation Suite tests for library functions.
It has also survived an assortment of public-domain
programs designed to stress C implementations and
illuminate their darker corners. The mathematical
functions are particularly well-engineered and tested.
Finally, \booktitle{The Standard C Library} shows you
many principles of library design in general. You learn
how to design and implement libraries that are highly
cohesive and reusable.",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / ix \\
Introduction / 1 \\
<assert.h> / 17 \\
<ctype.h> / 25 \\
<errno.h> / 47 \\
<float.h> / 57 \\
<limits.h> / 73 \\
<locale.h> / 81 \\
<math.h> / 127 \\
<setjmp.h> / 181 \\
<signal.h> / 193 \\
<stdarg.h> / 205 \\
<stddef.h> / 215 \\
<stdio.h> / 225 \\
<stdlib.h> / 333 \\
<string.h> / 387 \\
<time.h> / 415 \\
Interfaces / 445 \\
Names / 453 \\
Terms / 463 \\
Index / 475",
}
@TechReport{Posch:1992:MRR,
author = "K. C. Posch and R. Posch",
title = "Modulo reduction in residue number systems",
institution = "Inst., TU, Ges.",
address = "????",
pages = "16",
year = "1992",
bibdate = "Thu Nov 18 09:44:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "IIG-report-series",
URL = "http://books.google.com/books?id=YPLKHAAACAAJ",
abstract = "Residue number systems provide a good means for
extremely long integer arithmetic. Their carry-free
operations make parallel implementations feasible. Some
applications involving very long integers, such as
public key encryption, rely heavily on fast modulo
reductions. This paper shows a new combination of
residue number systems with efficient modulo reduction
methods. Two methods are compared, and the faster one
is scrutinized in detail. Both methods have the same
order of complexity, $ O(\log n) $, with $n$ denoting
the amount of registers involved.",
acknowledgement = ack-nhfb,
}
@InProceedings{Posch:1992:RNS,
author = "K. C. Posch and R. Posch",
booktitle = "Proceedings of the Fourth {IEEE} Symposium on Parallel
and Distributed Processing 1992",
title = "Residue number systems: a key to parallelism in public
key cryptography",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "432--435",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/SPDP.1992.242713",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Public key cryptography and parallel algorithms are
considered. Special attention is paid to algorithms
using long integer modulo arithmetic. A modification of
the commonly known RSA algorithm is taken as a
candidate. So far all implementations have \ldots{}",
}
@Book{Press:1992:NRC,
author = "W. H. Press and B. P. Flannery and S. A. Teukolsky and
W. T. Vetterling",
title = "Numerical Recipes in {C}: The Art of Scientific
Computing",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
edition = "Second",
pages = "xxvi + 994",
year = "1992",
ISBN = "0-521-43108-5, 0-521-43720-2",
ISBN-13 = "978-0-521-43108-8, 978-0-521-43720-2",
LCCN = "QA297 .N864 1992",
bibdate = "Thu Sep 01 22:12:07 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@PhdThesis{Priest:1992:PFP,
author = "Douglas M. Priest",
title = "On Properties of Floating Point Arithmetics: Numerical
Stability and the Cost of Accurate Computations",
type = "Thesis ({Ph.D.} in Mathematics)",
school = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "iv + 136",
month = dec,
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "UMI order number GAX93-30692.",
URL = "ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z",
abstract = "Floating point arithmetics generally possess many
regularity properties in addition to those that are
typically used in roundoff error analyses; these
properties can be exploited to produce computations
that are more accurate and cost effective than many
programmers might think possible. Furthermore, many of
these properties are quite simple to state and to
comprehend, but few programmers seem to be aware of
them (or at least willing to rely on them).\par
This dissertation presents some of these properties and
explores their consequences for computability,
accuracy, cost, and portability. For example, we
consider several algorithms for summing a sequence of
numbers and show that under very general hypotheses, we
can compute a sum to full working precision at only
somewhat greater cost than a simple accumulation, which
can often produce a sum with no significant figures at
all. This example, as well as others we present, can be
generalized further by substituting still more complex
algorithms; consequently, examples such as these oblige
us to consider more carefully the tradeoffs between
cost and accuracy.\par
At one end of the accuracy spectrum we find one of the
least obvious consequences of the properties of
floating point arithmetic: the accuracy of a
computation consisting of rational arithmetic
operations and comparisons need not be limited by the
precision of the floating point arithmetic in which it
is carried out. Of course, the more accuracy desired,
the greater the cost of the computation, and the cost
of computing a very accurate result may be quite high;
we illustrate this possibility in the case of
polynomial evaluation. At the other end of the
spectrum, however, we give an example of a problem for
which simply computing a result to a modest guaranteed
accuracy costs far less than the contortions required
to accommodate inaccurate results. As a consequence of
examples such as these, we conclude that programmers
and theorists alike must be willing to adopt a more
sophisticated view of floating point arithmetic, even
if only to consider that more accurate and reliable
computations than those presently in common use might
be possible based on stronger hypotheses than are
customarily assumed.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Dept. of
Mathematics; Dissertations; floating-point arithmetic;
University of California, Berkeley",
}
@Article{Quach:1992:HSA,
author = "N. T. Quach and M. J. Flynn",
title = "High-speed addition in {CMOS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "12",
pages = "1612--1615",
month = dec,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.214671",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Quach:1992:RFP,
author = "N. Quach and M. Flynn",
title = "A radix-64 floating-point divider",
type = "Technical Report",
number = "CSL-TR-92-529",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jun,
year = "1992",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Rao:1992:FPA,
author = "B. D. Rao",
title = "Floating point arithmetic and digital filters",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "1",
pages = "85--95",
month = jan,
year = "1992",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The roundoff noise properties of floating point
digital filters are examined. To make the analysis
tractable, a high level model to deal with the errors
in the inner product operation is developed. This model
establishes a broad connection between \ldots{}",
}
@InProceedings{Rix:1992:CFA,
author = "B. Rix and D. Timmermann and H. Hahn and B. J.
Hosticka",
title = "A {CORDIC}-based floating-point arithmetic unit",
crossref = "IEEE:1992:PIC",
bookpages = "766",
pages = "30.3/1--4",
year = "1992",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A floating-point arithmetic unit based on the CORDIC
algorithm is described. It computes a wide range of
arithmetic, trigonometric, and hyperbolic functions and
achieves a normalized peak performance of 220 MFLOPS.
The unit is implemented in 1.6- mu m double-metal CMOS
technology and packaged in a 280-pin PGA.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Duisburg University,
Germany",
classification = "B1265F (Microprocessors and microcomputers); B2570D
(CMOS integrated circuits); C5135 (Digital signal
processing chips); C5230 (Digital arithmetic methods);
C5260 (Digital signal processing)",
keywords = "1.6 Micron; 220 MFLOPS; 280-Pin PGA; CORDIC algorithm;
Double-metal CMOS technology; DSP; Floating-point
arithmetic unit; Hyperbolic functions; Trigonometric
functions",
numericalindex = "Computer speed 2.2E+08 FLOPS; Size 1.6E-06 m",
thesaurus = "CMOS integrated circuits; Digital arithmetic; Digital
signal processing chips",
}
@InProceedings{Sanz-Gonzalez:1992:OFP,
author = "J. L. Sanz-Gonzalez and F. Lopez-Ferreras",
booktitle = "Proceedings of the 3rd {AFRICON} Conference: {AFRICON
'92}",
title = "Optimal floating-point structures for low roundoff
noise digital filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "194--197",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A theoretical analysis of roundoff noise power in
floating-point realizations of digital filters is
presented. Formulas are given for single-length and
double-length accumulators. The minimal-noise
floating-point structure is found to be identical
\ldots{}",
}
@Article{Scherson:1992:BPA,
author = "I. D. Scherson and D. A. Kramer and B. D. Alleyne",
title = "Bit-parallel arithmetic in a massively-parallel
associative processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "10",
pages = "1201--1210",
month = oct,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.166599",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166599",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Schwarz:1992:ASF,
author = "E. M. Schwarz and M. J. Flynn",
title = "Approximating the Sine Function With Combinational
Logic",
crossref = "Singh:1992:CRT",
pages = "386--390",
year = "1992",
bibdate = "Thu Sep 08 08:02:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Seznec:1992:CSH,
author = "Andr{\'e} Seznec and Karl Courtel",
title = "Controlling and sequencing a heavily pipelined
floating-point operator",
journal = j-SIGMICRO,
volume = "23",
number = "1--2",
pages = "111--114",
month = dec,
year = "1992",
CODEN = "SIGMDJ",
DOI = "https://doi.org/10.1145/144965.145008",
ISSN = "0163-5751, 1050-916X",
ISSN-L = "0163-5751",
bibdate = "Fri Apr 16 10:27:43 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
URL = "https://dl.acm.org/doi/10.1145/144965.145008",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMICRO Newsletter",
journal-URL = "https://dl.acm.org/loi/sigmicro",
}
@Article{Seznec:1992:OAF,
author = "Andr{\'e} Seznec and Karl Courtel",
title = "{OPAC} (abstract): a floating-point coprocessor
dedicated to compute-bound kernels",
journal = j-COMP-ARCH-NEWS,
volume = "20",
number = "2",
pages = "427--427",
month = may,
year = "1992",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 12 09:40:43 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Seznec:1992:OFC,
author = "A. Seznec and K. Courtel",
title = "{OPAC}: a Floating-Point Coprocessor Dedicated to
Compute-Bound Kernels",
journal = j-COMP-ARCH-NEWS,
volume = "20",
number = "2",
pages = "427--427",
month = may,
year = "1992",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Simar:1992:FPP,
author = "Ray {Simar, Jr.} and Peter Koeppen and Jerald Leach
and Steve Marshall and Dave Francis and Greg Mekras and
Jeffrey Rosenstrauch and Scott Anderson",
title = "Floating-Point Processors Join Forces in Parallel
Processing Architectures",
journal = j-IEEE-MICRO,
volume = "12",
number = "4",
pages = "60--69",
month = jul # "\slash " # aug,
year = "1992",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.149737",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Achieving cost-effective design performance goals with
parallel DSP building blocks supported by extensive
software",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
summary = "The hardware architecture and software capabilities of
the TMS320C40 floating-point digital signal processor
are described. The C40 operates at 275 million
operations per second (MOPS) and transfers data at a
rate of 320 Mbytes/s with a 40-ns cycle time \ldots{}",
}
@Book{Sites:1992:AAR,
author = "Richard L. Sites and Richard Witek and others",
title = "Alpha Architecture Reference Manual",
publisher = pub-DP # " and " # pub-PH,
address = pub-DP:adr # " and " # pub-PH:adr,
year = "1992",
ISBN = "0-13-033663-7 (PH), 1-55558-098-X (DP: print)",
ISBN-13 = "978-0-13-033663-7 (PH), 978-1-55558-098-8 (DP:
print)",
LCCN = "QA76.9.A73 A46 1992",
bibdate = "Wed Jan 23 08:49:36 MST 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Foreword \\
Preface \\
Common Architecture \\
Introduction \\
Basic Architecture \\
Instruction Formats \\
Instruction Descriptions \\
System Architecture and Programming Implications \\
Common PALcode Architecture \\
Console Subsystem Overview \\
Input/Output \\
OpenVMS Alpha Software \\
Introduction to OpenVMS Alpha \\
OpenVMS PALcode Instruction Descriptions \\
OpenVMS Memory Management \\
OpenVMS Process Structure \\
OpenVMS Internal Processor Registers \\
OpenVMS Exceptions, Interrupts, and Machine Checks \\
DEC OSF/1 Alpha Software \\
Introduction to DEC OSF/1 Alpha \\
OSF/1 PALcode Instruction Descriptions \\
OSF/1 Memory Management \\
OSF/I Process Structure \\
OSF/1 Exceptions and Interrupts \\
Appendix A: Software Considerations \\
Appendix B: IEEE Floating-Point Conformance \\
Appendix C: Instruction Encodings \\
Index",
xxauthor = "{Alpha Architecture Committee}",
}
@Article{Skavantzos:1992:DCM,
author = "A. Skavantzos and T. Stouraitis",
title = "Decomposition of complex multipliers using polynomial
encoding",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "10",
pages = "1331--1333",
month = oct,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.166610",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See comments \cite{Katti:1994:CDC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166610",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Skavantzos:1992:NMM,
author = "A. Skavantzos and P. B. Rao",
title = "New multipliers modulo {$ 2^N - 1 $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "957--961",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156538",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156538",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Skavantzos:1992:TII,
author = "A. Skavantzos and N. Mitash",
booktitle = "{IEEE} Southeastcon '92, Proceedings, 12--15 April
1992",
title = "Theory and implementation issues of the 2-dimensional
polynomial residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "226--233",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/SECON.1992.202342",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The authors present 2D polynomial residue number
system techniques for parallel polynomial
multiplication in modular rings and discuss array
implementation issues of such 2D polynomial
multipliers. A specific example design is presented.
The \ldots{}",
}
@Article{Skeel:1992:REP,
author = "R. Skeel",
title = "Roundoff error and the {Patriot} missile",
journal = j-SIAM-NEWS,
volume = "25",
number = "4",
pages = "11--1",
month = jul,
year = "1992",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Apr 28 19:10:25 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.siam.org/siamnews/general/patriot.htm",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Article{Smith:1992:FPR,
author = "L. Montgomery Smith and B. W. Bomar and R. D. Joseph
and G. C. J. Yang",
title = "Floating-Point Roundoff Noise Analysis of Second-Order
State-Space Digital Filter Structures",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "39",
number = "2",
pages = "90--98",
month = feb,
year = "1992",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.205812",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE transactions on circuits and systems. 2, Analog
and digital signal processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "A parametric approach is used to determine the
roundoff noise in all real second-order floating-point
state-space realizations of a transfer function having
complex conjugate poles. The parametric roundoff noise
analysis is then verified by experiment \ldots{}",
}
@InProceedings{Soudris:1992:SDAa,
author = "D. Soudris and V. Paliouras and T. Stouraitis",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing. {ICASSP-92, 23--26} March 1992",
title = "Systematic development of architectures for
multidimensional {DSP} using the residue number
system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "397--400",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1992.226192",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A systematic methodology for mapping multidimensional
algorithms onto array processor architectures based on
the quadratic residue number system is presented. A
class of algorithms with separable functions, which can
be reduced to the computation of \ldots{}",
}
@InProceedings{Soudris:1992:SDAb,
author = "D. Soudris and V. Paliouras and T. Stouraitis",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing. {ICASSP-92, 23--26} March 1992",
title = "Systematic development of architectures for
multidimensional {DSP} using the residue number
system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "397--400",
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1992.226192",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A systematic methodology for mapping multidimensional
algorithms onto array processor architectures based on
the quadratic residue number system is presented. A
class of algorithms with separable functions, which can
be reduced to the computation of \ldots{}",
}
@Book{SPARC:1992:SAM,
author = "{SPARC International, Inc.}",
title = "The {SPARC} Architecture Manual\emdash{}Version 8",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xxix + 316",
year = "1992",
ISBN = "0-13-825001-4",
ISBN-13 = "978-0-13-825001-0",
LCCN = "QA76.9.A73 S647 1992",
bibdate = "Thu Dec 16 09:12:32 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sparmann:1992:DHQ,
author = "Uwe Sparmann",
title = "Derivation of high quality tests for large
heterogeneous circuits: floating-point operations",
journal = "Informatik",
volume = "1",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
pages = "425--439",
year = "1992",
MRclass = "94C12 (93C05)",
MRnumber = "93j:94039",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Teubner-Texte Inform.",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
reviewer = "Adrian Ad{\u{a}}sc{\u{a}}li{\c{t}}ei",
}
@Article{Srinivas:1992:SFV,
author = "S. Srinivas and K. Dybvig",
title = "Superscalar Floating-Point Vector Computation in
Scheme",
journal = j-LECT-NOTES-COMP-SCI,
volume = "??",
number = "634",
pages = "811--812",
year = "1992",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Steidley:1992:FPA,
author = "C. W. Steidley",
title = "Floating point arithmetic basic exercises in
mathematical reasoning for computer science majors",
journal = j-COMP-EDU-J,
volume = "2",
number = "4",
pages = "1--6",
month = oct # "--" # dec,
year = "1992",
CODEN = "CEJOE7",
ISSN = "1069-3769",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Efficient mathematical (numerical) computing requires
floating point computation since fixed point arithmetic
limits the range of the numbers being manipulated.
Fixed point arithmetic also adds to the complexity of
operation by demanding a great deal of scaling among
numbers with different `implicit' radix (base) points.
Thus, floating point arithmetic has become a modern
computing necessity. In 1988, Central Washington
University introduced CPSC 321 Systems Programming into
the curriculum. The course was intended to give
students an opportunity to learn more about the
hardware, architecture, and organization of computing
machines by studying and writing systems software. Some
topics considered for the initial offering of the
course included: a simple assembler, a basic loader, or
a simple compiler. However, many of these topics are
covered in other courses and after discussions with
many colleagues in the Department of Mathematics
regarding the coverage of representation and use of
decimal arithmetic on computers, it was decided that
the fundamentals of some systems programs could be
covered by introducing the basic aspects of doing
mathematics on a computer from the systems point of
view.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Southeastern Louisiana
University, Hammond, LA, USA",
classification = "C0220 (Education and training); C5230 (Digital
arithmetic methods); C6110 (Systems analysis and
programming); C7310 (Mathematics)",
fjournal = "Computers in education journal",
keywords = "Computer science majors; Computing machines; Computing
necessity; CPSC 321 Systems Programming; Curriculum;
decimal floating-point arithmetic; Floating point
arithmetic; Floating point computation; Mathematical
reasoning; Students; Systems software",
thesaurus = "Computer science education; Digital arithmetic;
Educational courses; Mathematics computing; Systems
analysis; Teaching",
}
@Article{Stetter:1992:ICR,
author = "F. Stetter",
title = "Internal computer representation of integer numbers",
journal = j-INFORMATIK-SPEKTRUM,
volume = "15",
number = "6",
pages = "352--354",
month = dec,
year = "1992",
CODEN = "INSKDW",
ISSN = "0170-6012 (print), 1432-122X (electronic)",
ISSN-L = "0170-6012",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Compares floating point and integer representations
and presents a proposal for a unified integer
representation which allows for sign. Definitions are
given of two's complement and one's complement
representations and rules are proposed for integer
addition and subtraction, multiplication and division
with various translation algorithms.",
acknowledgement = ack-nhfb,
affiliation = "Mannheim University, Germany",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Informatik Spektrum",
journal-URL = "http://link.springer.com/journal/287",
keywords = "Division; Floating point; Integer addition; Integer
numbers; Integer representations; Multiplication;
Subtraction; Unified integer representation",
language = "German",
pubcountry = "Germany",
thesaurus = "Digital arithmetic",
}
@Article{Stouraitis:1992:ECR,
author = "T. Stouraitis",
title = "Efficient convertors for residue and quadratic-residue
number systems",
journal = "Circuits, Devices and Systems, IEE Proceedings G",
volume = "139",
number = "6",
pages = "626--634",
month = dec,
year = "1992",
CODEN = "????",
DOI = "https://doi.org/10.1109/78.157231",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4741",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The quadratic-residue number system (QRNS) is known to
be efficient for complex-number calculations, since it
eliminates the need for cross-product terms and offers
high speed with small hardware complexity. However, the
conversion overhead between \ldots{}",
}
@Article{Sun:1992:CTA,
author = "J.-D. Sun and H. Krishna",
title = "A coding theory approach to error control in redundant
residue number systems. {II}. Multiple error detection
and correction",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "39",
number = "1",
pages = "18--34",
month = jan,
year = "1992",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.204107",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "For pt.I see ibid., vol.39, no.1, p.8-17 (1992). The
coding theory approach to error control in redundant
residue number systems (RRNSs) is extended by deriving
computationally efficient algorithms for correcting
multiple errors, single-burst-error, \ldots{}",
}
@Article{Takagi:1992:MMH,
author = "N. Takagi and S. Yajima",
title = "Modular multiplication hardware algorithms with a
redundant representation and their application to {RSA}
cryptosystem",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "7",
pages = "887--891",
month = jul,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.256444",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=256444",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Takagi:1992:RMM,
author = "N. Takagi",
title = "A radix-$4$ modular multiplication hardware algorithm
for modular exponentiation",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "949--956",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156537",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156537",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Tang:1992:TDI,
author = "Ping Tak Peter Tang",
title = "Table-Driven Implementation of the {{\tt Expm1}}
Function in {IEEE} Floating-Point Arithmetic",
journal = j-TOMS,
volume = "18",
number = "2",
pages = "211--222",
month = jun,
year = "1992",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/146847.146928",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65D15",
MRnumber = "1 167 891",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See independent analysis and accuracy confirmation of
this algorithm in \cite{Kramer:1998:PWC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
abstract = "Algorithms and implementation details for the function
$ e^x - 1 $ in both single and double precision of IEEE
754 arithmetic are presented here. With a table of
moderate size, the implementations need only
working-precision arithmetic and are provably accurate
to within 0.58 ulp.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Error analysis. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm analysis.",
}
@InProceedings{Teufel:1992:IFP,
author = "Thomas Teufel",
title = "Implementation of a floating-point arithmetic with an
accurate scalar product for digital signal processing",
crossref = "Atanassova:1992:CAE",
pages = "147--156",
year = "1992",
bibdate = "Sat Sep 17 19:12:26 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Thirumalaiswamy:1992:DSB,
author = "Vijayashree Thirumalaiswamy",
title = "Design and simulation of bit-serial floating point
arithmetic co-processor",
type = "Thesis ({M.S.})",
school = "University of Texas at El Paso",
address = "El Paso, TX, USA",
pages = "xii + 113",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Array processors --- Design.; Floating-point
arithmetic.",
}
@Article{Timmermann:1992:LLT,
author = "D. Timmermann and H. Hahn and B. J. Hosticka",
title = "Low Latency Time {CORDIC} Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "1010--1015",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156543",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 08 00:52:02 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Vowels:1992:D,
author = "R. A. Vowels",
title = "Division by 10",
journal = j-AUSTRALIAN-COMP-J,
volume = "24",
number = "3",
pages = "81--85",
month = aug,
year = "1992",
CODEN = "ACMJB2",
ISSN = "0004-8917",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Division of a binary integer and a binary
floating-point mantissa by 10 can be performed with
shifts and adds, yielding a significant improvement in
hardware execution time, and in software execution time
if no hardware divide instruction is available. Several
algorithms are given, appropriate to specific machine
word sizes, hardware and hardware instructions
available, and depending on whether a remainder is
required. The integer division algorithms presented
here contain a new strategy that produces the correct
quotient directly, without the need for the
supplementary correction required of
previously-published algorithms. The algorithms are
competitive in time with binary coded decimal (BCD)
divide by 10. Both the integer and floating-point
algorithms are an order of magnitude faster than
conventional division.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, R. Melbourne Inst. of
Technol. Ltd., Vic., Australia",
classification = "C7310 (Mathematics)",
fjournal = "Australian Computer Journal",
keywords = "Binary integer; decimal floating-point arithmetic;
Floating-point algorithms; Hardware execution time;
Integer division algorithms; Software execution time",
pubcountry = "Australia",
thesaurus = "Digital arithmetic; Mathematics computing",
}
@MastersThesis{Wang:1992:RAF,
author = "Jie Wang",
title = "Response analysis for floating point implementations
of linear discrete systems",
type = "Thesis ({M.S.E.E.})",
school = "University of Notre Dame",
address = "Notre Dame, IN 46556, USA",
pages = "xi + 83",
year = "1992",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Weber-Wulff:1992:REC,
author = "Debora Weber-Wulff",
title = "Rounding error changes {Parliament} makeup",
journal = "The Risks Digest",
volume = "13",
number = "37",
pages = "8--8",
year = "1992",
bibdate = "Sat Apr 28 19:12:42 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://catless.ncl.ac.uk/Risks/13.37.html#subj4",
acknowledgement = ack-nhfb,
}
@Article{Werter:1992:SLC,
author = "M. J. Werter",
title = "Suppression of limit cycles in the first-order
two-dimensional direct form digital filter with a
controlled rounding arithmetic",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "6",
pages = "1599--1601",
month = jun,
year = "1992",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The first-order two-dimensional direct-form digital
filter with magnitude truncation is known to be free
from limit cycles for a limited range of allowed filter
coefficients. In this correspondence, the quantization
technique of controlled rounding \ldots{}",
}
@Article{Wesner:1992:TS,
author = "J. Wesner",
title = "{Ein Tick schneller} \toenglish {A Tick Faster}
\endtoenglish",
journal = j-MC,
volume = "2",
pages = "80--86",
year = "1992",
ISSN = "0720-4442, 0941-777x , 0943-5409",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "MC: Die Mikrocomputer-Zeitschrift",
}
@Article{Wichmann:1992:NUF,
author = "Brian A. Wichmann",
title = "A Note on the Use of Floating Point in Critical
Systems",
journal = j-COMP-J,
volume = "35",
number = "1",
pages = "41--44",
month = feb,
year = "1992",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.body.html#AbstractWichmann",
abstract = "Floating point is a well tried technology which, it
might seem, can be used without reservation.
Unfortunately, there are dangers which arise from
faults in implementation and incorrect use. These are
often hard to locate. The paper addresses these
dangers.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "NPL, Teddington, UK",
author-1-adr = "National Physical Laboratory, Teddington, Middlesex
TW11 OLW",
classcodes = "C5230 (Digital arithmetic methods)",
classification = "C5230 (Digital arithmetic methods)",
corpsource = "NPL, Teddington, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "critical systems; digital arithmetic; faults; floating
point; Floating point; safety systems",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Safety systems",
treatment = "P Practical",
}
@Article{Wichmann:1992:SFW,
author = "Brian A. Wichmann",
title = "{Surveyor's Forum}: ``{What} Every Computer Scientist
Should Know About Floating-Point Arithmetic''",
journal = j-COMP-SURV,
volume = "24",
number = "3",
pages = "319--319",
month = sep,
year = "1992",
CODEN = "CMSVAN",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Sun Sep 25 10:14:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See
\cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Dunham:1992:SFW}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Wilkes:1992:E,
author = "Maurice V. Wilkes",
title = "{EDSAC 2}",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "14",
number = "4",
pages = "49--56",
month = oct # "--" # dec,
year = "1992",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/85.194055",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Thu Jul 12 06:22:54 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
URL = "http://dlib.computer.org/an/books/an1992/pdf/a4049.pdf;
http://www.computer.org/annals/an1992/a4049abs.htm",
acknowledgement = ack-nhfb,
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
remark = "From page 54: ``When the machine was initialized for a
new program to be run, every bit in the memory was set
to a 1, rather than to a 0. Since, according to the
format used for floating numbers, no floating number
could consist entirely of 1's, any attempt to read a
floating-point number from part of the memory that had
not been written into caused the machine to stop. Many
a programmer must have been grateful to [David J.]
Wheeler for his foresight in making this happen.''",
}
@Article{Wilt:1992:ALP,
author = "Nicholas Wilt",
title = "Assembly language programming for the 80*87",
journal = j-DDJ,
volume = "17",
number = "3",
pages = "36, 38, 40, 42, 88",
month = mar,
year = "1992",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 10:06:23 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods); C6110 (Systems analysis and
programming)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "80*87 Coprocessor; Assembly language programming;
Floating point arithmetic; Numeric coprocessors;
Optimization",
thesaurus = "Assembly language listings; Digital arithmetic;
Microprocessor chips; Optimisation; Programming;
Satellite computers",
}
@Article{Wong:1992:DSR,
author = "W. F. Wong and E. Goto",
title = "Division and square-rooting using a split multiplier",
journal = j-ELECT-LETTERS,
volume = "28",
number = "18",
pages = "1758--1759",
day = "27",
month = aug,
year = "1992",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Wed Dec 13 13:13:34 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A modification is proposed to the traditional design
of a fast floating point multiplication circuit such
that instead of just performing $ A * B $ where $A$ and
$B$ are $m$ bits long, it is also capable of performing
$ C * x_0$ and $ D * x_1$ where $C$ and $D$ are still m
bits long but $ x_0$ and $ x_1$ are $ m / 2$ bits long
using about the same amount of hardware resources but
in two thirds of the time. Such a circuit is called a
split multiplier. The authors show how such a split
multiplier can be used to compute division and $ Y
\sqrt {X}$ accurately and quickly.",
acknowledgement = ack-nhfb,
affiliation = "Goto Lab., Inst. of Phys. and Chem. Res., Saitama,
Japan",
classification = "B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5230 (Digital arithmetic methods)",
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "Division; Fast floating point multiplication circuit;
Split multiplier; Square-rooting",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Dividing circuits; Logic circuits;
Multiplying circuits",
}
@Article{Wong:1992:FDU,
author = "D. Wong and M. Flynn",
title = "Fast Division Using Accurate Quotient Approximations
to Reduce the Number of Iterations",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "981--995",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156541",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156541",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Woods:1992:HPD,
author = "R. F. Woods and S. E. McQuillan and J. Dowling and J.
V. McCanny",
booktitle = "Proceedings of Fifth Annual {IEEE} International
{ASIC} Conference and Exhibit, 1992",
title = "High performance {DSP} {ASIC} for multiply, divide and
square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "209--213",
year = "1992",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The design of a high-speed ASIC that combines the
operations of multiplication, division and square root
is described. The chip is based on a systolic array
architecture that uses a redundant number system and
allows multiplication, division, and \ldots{}",
}
@Article{Yeyios:1992:TSA,
author = "A. K. Yeyios",
title = "On two sequences of algorithms for approximating
square roots",
journal = j-J-COMPUT-APPL-MATH,
volume = "40",
number = "1",
pages = "63--72",
month = jun,
year = "1992",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Thu Sep 1 10:15:56 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Yokoo:1992:OUF,
author = "H. Yokoo",
title = "Overflow\slash Underflow-Free Floating-Point Number
Representations with Self-Delimiting Variable-Length
Exponent Field",
journal = j-IEEE-TRANS-COMPUT,
volume = "41",
number = "8",
pages = "1033--1039",
month = aug,
year = "1992",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.156546",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 10:49:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156546",
abstract = "A class of new floating-point representations of real
numbers, based on representations of the integers, is
described. In the class, every representation uses a
self-delimiting representation of the integers as a
variable length field of the exponent, and neither
overflow nor underflow appears in practice. The adopted
representations of the integers are defined
systematically, so that representation's of numbers
greater than one have both exponent-significant and
integer-fraction interpretations. Since representation
errors are characterized by the length function of an
underlying representation of the integers, superior
systems in precision can be easily selected from the
proposed class.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Gunma University,
Kiryu, Japan",
ajournal = "IEEE Trans. Comput.",
classification = "B0250 (Combinatorial mathematics); B1265B (Logic
circuits); C1160 (Combinatorial mathematics); C5230
(Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Floating-point number representations; Integer
representation; Real numbers; Self-delimiting
variable-length exponent field",
summary = "A class of new floating-point representations of real
numbers, based on representations of the integers, is
described. In the class, every representation uses a
self-delimiting representation of the integers as a
variable length field of the exponent \ldots{}",
thesaurus = "Digital arithmetic; Number theory",
}
@Article{Zelniker:1992:RMC,
author = "G. S. Zelniker and F. J. Taylor",
title = "On the reduction in multiplicative complexity achieved
by the polynomial residue number system",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "40",
number = "9",
pages = "2318--2320",
month = sep,
year = "1992",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.157231",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4075",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "The polynomial residue number system is known to
reduce the complexity of polynomial multiplication from
O(N 2) to O(N). A new interpretation of this complexity
reduction is given in the context of \ldots{}",
}
@Article{Alam:1993:RTO,
author = "M. S. Alam and M. A. Karim",
title = "Real-Time Optical Arithmetic\slash Logical
Processing",
journal = j-J-PAR-DIST-COMP,
volume = "17",
number = "3",
pages = "251--258",
month = mar,
year = "1993",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1993.1024",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:51 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production/pdf",
acknowledgement = ack-nhfb,
classification = "B4180 (Optical logic devices and optical computing
techniques); C5110D (Optical logic elements)C5120
(Logic and switching circuits); C5230 (Digital
arithmetic methods); C5270 (Optical computing
techniques)",
corpsource = "Department of Eng., Purdue University, Fort Wayne, IN,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "autocorrelation peaks; binary; coding scheme; digital
arithmetic; full adder; input joint image; joint
transform correlator; minterms; multiple outputs;
optical logic; real time logical processing; real-time
optical arithmetic; real-time systems",
treatment = "P Practical",
}
@Book{Albrecht:1993:VNT,
editor = "R. (Rudolf F.) Albrecht and G. (G{\"o}tz) Alefeld and
H. (Hans) J. Stetter",
title = "Validation numerics: theory and applications",
volume = "9",
publisher = pub-SV,
address = pub-SV:adr,
pages = "291",
year = "1993",
ISBN = "3-211-82451-0 (Wien), 0-387-82451-0 (New York)",
ISBN-13 = "978-3-211-82451-1 (Wien), 978-0-387-82451-2 (New
York)",
LCCN = "QA297 .V27 1993",
bibdate = "Thu Apr 02 09:18:32 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This volume is dedicated to Professor Dr. Ulrich
Kulisch, \ldots{} on the occasion of his 60th
birthday.",
series = "Computing (Springer-Verlag). Supplementum",
acknowledgement = ack-nhfb,
}
@MastersThesis{Alqeisi:1993:FPF,
author = "Yousuf Alqeisi",
title = "A 16-bit floating point fast {Fourier} transform
processor using {Xlinx}'s {FPGA's}",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering, Southern
Illinois University at Carbondale",
address = "Carbondale, IL, USA",
pages = "v + 60",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1993:FPa,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "1",
pages = "56--??",
month = jan,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Making a Case for Pencil Plotters.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FPb,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "5",
pages = "67--??",
month = may,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Component Technology.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FPc,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "9",
pages = "48--??",
month = sep,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "ProStep.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FPd,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "10",
pages = "98--??",
month = oct,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Open Modeling Still Going Strong.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FPe,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "12",
number = "11",
pages = "42--??",
month = nov,
year = "1993",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Cost Benefits CAD/CAM.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1993:FSB,
author = "Anonymous",
title = "The ``fastest system on the block'' label must be
qualified with new multiplatform, floating-point
benchmarks",
journal = j-PC-WEEK,
volume = "10",
number = "22",
pages = "85--??",
month = jun,
year = "1993",
ISSN = "0740-1604",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "PC Week",
}
@Book{Anonymous:1993:SRT,
author = "Anonymous",
title = "The Square Root of Two to 100,000 digits",
volume = "52",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1993",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext93/2sqrt10.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
}
@Article{Asprey:1993:PFP,
author = "T. Asprey and G. Averill and E. DeLano and R. Mason
and B. Weiner and J. Yetter",
title = "Performance features of the {PA7100} microprocessor",
journal = j-IEEE-MICRO,
volume = "13",
number = "3",
pages = "22--35",
month = may # "\slash " # jun,
year = "1993",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.216746",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Book{ASTM:1993:AES,
author = "{ASTM}",
title = "{ASTM E29-08}: Standard Practice for Using Significant
Digits in Test Data to Determine Conformance with
Specifications",
publisher = "ASTM International",
address = "West Conshohocken, PA, USA",
year = "1993",
bibdate = "Mon May 21 17:19:21 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Superseded by \cite{ASTM:2008:AES}.",
URL = "https://www.astm.org/DATABASE.CART/HISTORICAL/E29-08.htm",
acknowledgement = ack-nhfb,
remark = "Cited in \cite[ref. 32]{Carter:2013:ESF}.",
}
@Article{Bailey:1993:AMT,
author = "David H. Bailey",
title = "{Algorithm 719}: Multiprecision Translation and
Execution of {FORTRAN} Programs",
journal = j-TOMS,
volume = "19",
number = "3",
pages = "288--319",
month = sep,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/155743.155767",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Dec 13 18:37:31 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p288-bailey/",
abstract = "This paper describes two Fortran utilities for
multiprecision computation. The first is a package of
Fortran subroutines that perform a variety of
arithmetic operations and transcendental functions on
floating point numbers of arbitrarily high precision.
This package is in some cases over 200 times faster
than that of certain other packages that have been
developed for this purpose.\par
The second utility is a translator program, which
facilitates the conversion of ordinary Fortran programs
to use this package. By means of source directives
(special comments) in the original Fortran program, the
user declares the precision level and specifies which
variables in each subprogram are to be treated as
multiprecision. The translator program reads this
source program and outputs a program with the
appropriate multiprecision subroutine calls.\par
This translator supports multiprecision integer, real,
and complex datatypes. The required array space for
multiprecision data types is automatically allocated.
In the evaluation of computational expressions, all of
the usual conventions for operator precedence and mixed
mode operations are upheld. Furthermore, most of the
Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
are supported and produce true multiprecision values.",
abstract-2 = "The author describes two Fortran utilities for
multiprecision computation. The first is a package of
Fortran subroutines that perform a variety of
arithmetic operations and transcendental functions on
floating point numbers of arbitrarily high precision.
This package is in some cases over 200 times faster
than that of certain other packages that have been
developed for this purpose. The second utility is a
translator program, which facilitates the conversion of
ordinary Fortran programs to use this package. By means
of source directives (special comments) in the original
Fortran program, the user declares the precision level
and specifies which variables in each subprogram are to
be treated as multiprecision. The translator program
reads this source program and outputs a program with
the appropriate multiprecision subroutine calls. This
translator supports multiprecision integer, real, and
complex datatypes. The required array space for
multiprecision data types is automatically allocated.
In the evaluation of computational expressions, all of
the usual conventions for operator precedence and mixed
mode operations are upheld. Furthermore, most of the
Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
are supported and produce true multiprecision values.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "NASA Ames Res. Center, Moffett Field, CA, USA",
classification = "C5230 (Digital arithmetic methods); C6120 (File
organisation); C6140D (High level languages); C6150C
(Compilers, interpreters and other processors); C7310
(Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Algorithm 719; Arithmetic operations; Array space;
Complex data types; Computational expressions; Floating
point numbers; Fortran programs; Fortran subroutines;
Fortran utilities; Fortran-77 intrinsics; Mixed mode
operations; Multiprecision computation; Multiprecision
data types; Multiprecision subroutine calls;
Multiprecision translation; Operator precedence; Source
directives; Transcendental functions; Translator
program",
subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]:
Numerical Algorithms and Problems; G.1.0 [Numerical
Analysis]: General; G.1.2 [Numerical Analysis];
Approximation",
thesaurus = "Data structures; Digital arithmetic; FORTRAN;
Mathematics computing; Program interpreters;
Subroutines",
}
@InProceedings{Bailey:1993:MPM,
author = "David H. Bailey and Robert Krasny and Richard Pelz",
title = "Multiple precision, multiple processor vortex sheet
roll-up computation",
crossref = "Sincovec:1993:PSS",
pages = "52--56",
year = "1993",
bibdate = "Thu Nov 25 10:04:31 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bajard:1993:BNH,
author = "J. C. Bajard and S. Kla and Jean-Michel Muller",
title = "{BKM}: a New Hardware Algorithm for Complex Elementary
Functions",
crossref = "Swartzlander:1993:SCA",
pages = "146--153",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bajard.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Baker:1993:SLR,
author = "Henry G. {Baker, Jr.}",
title = "Safe and leakproof resource management using {Ada83}
limited types",
journal = j-SIGADA-LETTERS,
volume = "13",
number = "5",
pages = "32--42",
month = sep # "\slash " # oct,
year = "1993",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:49 MDT 2003",
bibsource = "Compendex database; http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
abstract = "Safe, leakproof and automatic resource managers are
essential to the implementation of every embedded
system, yet the standard examples of Ada83 resource
managers are either unsafe: they risk allocating the
same resource for two different purposes, leaky: they
risk permanently losing track of some resources, or
non-automatic: they require explicit deallocation,
which allows for a host of opportunities for
single-point system failures. Nevertheless, it is
possible to construct a safe, leakproof and automatic
resource manager --- at least for systems with only a
single task --- by a careful combination of certain
features of Ada83, and a careful avoidance of other
features. We illustrate our scheme with a safe,
leakproof and fully automatic dynamic-string package.
The same techniques also work for an arbitrary
precision arithmetic package [Fisher83] and for
managing the `roots' of a real-time garbage-collected
heap [Baker78] [Baker91SP] [Baker92Tread]. Suggestions
are offered to improve the use of limited private types
in Ada9X for automatic, safe and leakproof resource
management.",
acknowledgement = ack-nhfb,
affiliation = "Nimble Computer Corp",
affiliationaddress = "Encino, CA, USA",
classcodes = "C6150J (Operating systems); C6110B (Software
engineering techniques); C6120 (File organisation);
C6140D (High level languages)",
classification = "722.1; 722.4; 723.1; 723.1.1; 723.2",
conferenceyear = "1993",
corpsource = "Nimble Comput. Corp., Encino, CA, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
journalabr = "Ada Lett",
keywords = "Ada; Ada (programming language); Ada listings; Ada83
limited types; Ada83 resource; Ada9X; arbitrary
precision; Arbitrary precision arithmetic package;
arithmetic package; Automatic resource manager;
automatic resource managers; Computer operating
systems; Computer system recovery; Computer systems
programming; Data collection; data structures;
Deallocation; dynamic-string package; Embedded system;
embedded system; explicit deallocation; failures;
Information management; Interfaces (computer); Large
scale systems; leakproof resource management; limited
private types; management; managers; Program debugging;
Real time garbage collected heap; Real time systems;
real-time garbage-collected heap; real-time systems;
Resource allocation; resource allocation; Resource
management; Single point system failures; single-point
system; software reliability; storage; Storage
allocation (computer); Supervisory and executive
programs; System failure",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Bakhrakh:1993:NIF,
author = "S. M. Bakhrakh and S. V. Velichko and N. E.
Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
Yu. G. Fedorova and V. I. Kheifets",
title = "Numerical investigation of floating-point arithmetic
operations",
journal = j-PROG-COMP-SOFT,
volume = "18",
number = "6",
pages = "255--258",
year = "1993",
CODEN = "PCSODA",
ISSN = "0361-7688 (print), 1608-3261 (electronic)",
ISSN-L = "0361-7688",
bibdate = "Wed Dec 13 18:18:07 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Original Russian language paper in
\cite{Bakhrakh:1992:NIF}.",
abstract = "This article analyzes the sources of accumulated
computational error in certain computers (of ES and PS
types) in floating-point mode. Results of numerical
experiments are given. These experiments demonstrate
the influence of rounding on accumulated error. (5
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Inst. for Control Sci., Acad. of Sci., Russia",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Programming and Computer Software; translation of
Programmirovaniye (Moscow, USSR) Plenum",
journal-URL = "http://link.springer.com/journal/11086",
keywords = "Accumulated error rounding; Computational error;
Digital arithmetic; ES computers; Floating-point
arithmetic; Numerical investigation; PS computers",
pubcountry = "Russia",
remark = "English translation of: Programmirovanie",
thesaurus = "Digital arithmetic",
}
@Article{Barrera:1993:IBS,
author = "Tony Barrera and Pelle Olsson",
title = "An Integer Based Square Root Algorithm",
journal = j-BIT,
volume = "33",
number = "2",
pages = "253--261",
month = jun,
year = "1993",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01989748",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "68M07",
MRnumber = "1 326 017",
bibdate = "Wed Dec 13 18:20:52 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit33.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
abstract = "The authors propose a fast integer based method for
computing square roots of floating point numbers. This
implies high accuracy and robustness, since no
precision will be lost during the computation. Only
integer addition and shifts are necessary to obtain the
square root. Comparisons made with the modified Newton
method indicate that the suggested method is twice as
fast for computing floating point square roots. (5
Refs.)",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "AB Consonant, Uppsala, Sweden",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Floating point numbers; floating-point arithmetic;
Integer based square root algorithm; Modified Newton
method; Robustness",
pubcountry = "Denmark",
thesaurus = "Digital arithmetic",
xxpages = "254--261",
}
@Article{Bauer:1993:LCB,
author = "P. H. Bauer and J. Wang",
title = "Limit cycle bounds for floating point implementations
of second-order recursive digital filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "40",
number = "8",
pages = "493--501",
month = aug,
year = "1993",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.242338",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "It is shown that floating point realizations of
linearly stable systems can exhibit four fundamental
types of free responses. Sufficient conditions for the
existence or nonexistence of some of these periodic
response types in a given system are presented
\ldots{}",
}
@Article{Beckmann:1993:FFTa,
author = "P. E. Beckmann and B. R. Musicus",
title = "Fast fault-tolerant digital convolution using a
polynomial residue number system",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "7",
pages = "2300--2313",
month = jul,
year = "1993",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.224241",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "A fault-tolerant convolution algorithm that is an
extension of residue-number-system fault-tolerance
schemes applied to polynomial rings is described. The
algorithm is suitable for implementation on
multiprocessor systems and is able to concurrently
\ldots{}",
}
@Article{Beckmann:1993:FFTb,
author = "P. E. Beckmann and B. R. Musicus",
title = "Fast fault-tolerant digital convolution using a
polynomial residue number system",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "7",
pages = "2300--2313",
month = jul,
year = "1993",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.224241",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "A fault-tolerant convolution algorithm that is an
extension of residue-number-system fault-tolerance
schemes applied to polynomial rings is described. The
algorithm is suitable for implementation on
multiprocessor systems and is able to concurrently
\ldots{}",
}
@InProceedings{Benouamer:1993:LEA,
author = "M. O. Benouamer and P. Jaillon and D. Michelucci and
J.-M. Moreau",
title = "A Lazy Exact Arithmetic",
crossref = "Swartzlander:1993:SCA",
pages = "242--249",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Benouamer.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Bickerstaff:1993:RAM,
author = "K'Andrea C. Bickerstaff and Michael J. Schulte and
Earl E. {Swartzlander, Jr.}",
title = "Reduced Area Multipliers",
crossref = "Wah:1993:ICA",
pages = "478--489",
year = "1993",
bibdate = "Sun Mar 04 10:43:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1993-03.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Bizzan:1993:IMA,
author = "S. S. Bizzan and G. A. Jullien and N. M. Wigley and W.
C. Miller",
title = "Integer Mapping Architectures for the Polynomial Ring
Engine",
crossref = "Swartzlander:1993:SCA",
pages = "44--51",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bizzan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InCollection{Bohlender:1993:PAF,
author = "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
Kulisch and R. Lohner and W. V. Walter",
title = "Proposal for accurate floating-point vector
arithmetic",
crossref = "Adams:1993:SCA",
pages = "87--102",
year = "1993",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Many computers provide accurate and reliable scalar
arithmetic for floating point numbers. An accurate
definition of the four elementary floating-point
operations +, -, *, / is given in the IEEE standards
for floating-point arithmetic and was well established
long before. An increasing number of computers
(especially PC's and workstations) feature IEEE
arithmetic. In many numerical algorithms, however,
compound operations such as the summation of a sequence
of numbers or the dot product of two vectors are highly
common. A simulation of these compound operations by
means of elementary floating-point operations leads to
accumulation of rounding errors and may suffer from
catastrophic cancellation of leading digits. Existing
standards for floating-point arithmetic do not improve
this situation. The goal of the proposal is to define
vector operations in a manner consistent with the
elementary scalar arithmetic operations. The rounding
modes and accuracy requirements as well as the data
formats of the operands and results of the vector
operations described in the proposal are chosen to be
fully consistent with the existing scalar
floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math., Karlsruhe University,
Germany",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C7310 (Mathematics)",
keywords = "Accuracy requirements; Catastrophic cancellation;
Compound operations; Data formats; Dot product;
Elementary floating-point operations; Elementary scalar
arithmetic operations; Floating point numbers; IEEE
arithmetic; IEEE standards; Leading digits; Numerical
algorithms; Operands; Rounding errors; Rounding modes;
Scalar floating-point arithmetic; Sequence; Standards;
Summation; Vector operations",
thesaurus = "Digital arithmetic; Mathematics computing; Roundoff
errors; Standards",
}
@InProceedings{Booth:1993:ECA,
author = "Andrew D. Booth",
title = "Early Computer Arithmetic",
crossref = "Swartzlander:1993:SCA",
pages = "ix--ix",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_keynote.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
remark = "The author developed ``Booth's Algorithm'' for two's
complement multiplication, the APEXC computer at the
University of London (one of the world's first three
electronic digital computers), and the M3 series of
computers at the University of Saskatchewan (the first
all Canadian electronic computer).",
}
@InProceedings{Briggs:1993:XBM,
author = "W. S. Briggs and D. W. Matula",
title = "A $ 17 \times 69 $ Bit Multiply and Add Unit with
Redundant Binary Feedback and Single Cycle Latency",
crossref = "Swartzlander:1993:SCA",
pages = "163--170",
year = "1993",
bibdate = "Thu Jun 20 10:16:11 2002",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Briggs.pdf",
acknowledgement = ack-nj,
keywords = "ARITH-11",
}
@InProceedings{Callaway:1993:EPC,
author = "Thomas K. Callaway and Earl E. {Swartzlander, Jr.}",
title = "Estimating the Power Consumption of {CMOS} Adders",
crossref = "Swartzlander:1993:SCA",
pages = "210--216",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Callaway.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Chang:1993:REP,
author = "Long-Wen Chang",
title = "Roundoff Error Problem of the Systolic Array for
{DFT}",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "1",
pages = "395",
month = jan,
year = "1993",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "Not \ldots{}",
}
@InProceedings{Choi:1993:FPR,
author = "H. Choi and W. P. Burleson and D. S. Phatak",
booktitle = "Proceedings of 1993 International Joint Conference on
Neural Networks. {IJCNN '93-Nagoya}",
title = "Fixed-point roundoff error analysis of large
feedforward neural networks",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1947--1950",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Digital implementations of neural nets must consider
finite wordlength effects. For large sized nets, it is
particularly important to investigate the roundoff
errors in order to realize low-cost hardware
implementations while satisfying precision \ldots{}",
}
@Misc{Chu:1993:FPA,
author = "Tan V. Chu and Faraydon O. Karim and Christopher H.
Olson",
title = "Floating point arithmetic unit with size efficient
pipelined multiply-add architecture",
howpublished = "US Patent 5,241,493",
day = "31",
month = aug,
year = "1993",
bibdate = "Thu Oct 17 10:40:01 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US5241493A",
abstract = "An architecture and method relating to a floating
point operation which performs the mathematical
computation of A * B + C. The multiplication is
accomplished in two or more stages, each stage
involving corresponding sets of partial products and
concurrently accomplished incremental summations. A
pipelined architecture provides for the summation of
the least significant bits of an intermediate product
with operand C at a stage preceding entry into a full
adder. Thereby, a significant portion of the full adder
can be replaced by a simpler and smaller incrementer
circuit. Partitioning of the multiplication operation
into two or more partial product operations
proportionally reduces the size of the multiplier
required. Pipelining and concurrence execution of
multiplication and addition operation in the multiplier
provides in two cycles the results of the mathematical
operation A * B + C while using a full adder of
three-quarters normal size.",
acknowledgement = ack-nhfb,
remark = "Patent filed 16 December 1991, granted to IBM on 31
August 1993, possibly expired 16 December 2011.",
}
@Article{Cody:1993:ACP,
author = "W. J. Cody",
title = "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
for Complex Elementary Functions",
journal = j-TOMS,
volume = "19",
number = "1",
pages = "1--21",
month = mar,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/151271.151272",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 05 09:15:25 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/",
abstract = "This paper discusses CELEFUNT, a package of Fortran
programs for testing complex elementary functions.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; measurement; performance",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
}
@Article{Cody:1993:AFS,
author = "W. J. Cody and Jerome T. Coonen",
title = "{Algorithm 722}: Functions to Support the {IEEE}
Standard for Binary Floating-Point Arithmetic",
journal = j-TOMS,
volume = "19",
number = "4",
pages = "443--451",
month = dec,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/168173.168185",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p443-cody/",
abstract = "This paper describes C programs for the support
functions {\em copysign(x,y), logb(x), scalb(x,n),
nextafter(x,y), finite(x)}, and {\em isnan(x)}
recommended in the Appendix to the {\em IEEE Standard
for Binary Floating-Point Arithmetic.} In the case of
{\em logb}, the modified definition given in the later
{\em IEEE Standard for Radix-Independent Floating-Point
Arithmetic} is followed. These programs should run
without modification on most systems conforming to the
binary standard.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Argonne Nat. Lab., IL, USA",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques); C7310 (Mathematics)",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "C programs; Copysign(x,y); Finite(x); IEEE Standard
for Binary Floating-point arithmetic; Isnan(x);
Logb(x); Nextafter(x,y); Numerical software;
Scalb(x,n)",
subject = "G.1.0 [Numerical Analysis]: General -- numerical
algorithms; G.4 [Numerical Analysis]: Mathematical
Software -- certification and testing",
thesaurus = "Data handling; Digital arithmetic; Mathematics
computing; Standards",
}
@Article{Cody:1993:ASE,
author = "W. J. Cody",
title = "{Algorithm 715}: {SPECFUN}\emdash {A} Portable
{FORTRAN} Package of Special Function Routines and Test
Drivers",
journal = j-TOMS,
volume = "19",
number = "1",
pages = "22--32",
month = mar,
year = "1993",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/151271.151273",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 09 10:23:18 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remark \cite{Price:1996:RA}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p22-cody/",
abstract = "SPECFUN is a package containing transportable FORTRAN
special function programs for real arguments and
accompanying test drivers. Components include Bessel
functions, exponential integrals, error functions and
related functions, and gamma functions and related
functions.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms",
subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
SOFTWARE, Certification and testing. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Numerical algorithms.",
}
@Article{Cole:1993:SAA,
author = "T. J. Cole",
title = "Statistical Algorithms: {Algorithm AS 281}: Scaling
and Rounding Regression Coefficients to Integers",
journal = j-APPL-STAT,
volume = "42",
number = "1",
pages = "261--268",
year = "1993",
CODEN = "APSTAG",
ISSN = "0035-9254 (print), 1467-9876 (electronic)",
ISSN-L = "0035-9254",
bibdate = "Sat Apr 21 10:26:43 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
JSTOR database",
URL = "http://lib.stat.cmu.edu/apstat/281",
acknowledgement = ack-nhfb,
fjournal = "Applied Statistics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}
@InProceedings{Cortadella:1993:DSQ,
author = "Jordi Cortadella and Tom{\'a}s Lang",
title = "Division with Speculation of Quotient Digits",
crossref = "Swartzlander:1993:SCA",
pages = "87--94",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Cortadella.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Dadda:1993:MPC,
author = "Luigi Dadda and Vincenzo Piuri and Renato Stefanelli",
title = "Multi-Parallel Convolvers",
crossref = "Swartzlander:1993:SCA",
pages = "70--77",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Dadda.pdf",
acknowledgement = ack-nhfb,
author-dates = "29 April 1923--26 October 2012",
keywords = "ARITH-11",
}
@InProceedings{Daumas:1993:DFV,
author = "M. Daumas and D. W. Matula",
title = "Design of a Fast Validated Dot Product Operation",
crossref = "Swartzlander:1993:SCA",
pages = "62--69",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Daumas.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@MastersThesis{Delgado:1993:DSP,
author = "Maria Luisa Delgado",
title = "Design and simulation of a pipeline floating-point
adder",
type = "Thesis ({M.S.})",
school = "University of Texas at El Paso",
address = "El Paso, TX, USA",
pages = "x + 90",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Parallel processing
(Electronic computers)",
}
@InProceedings{Demmel:1993:FNA,
author = "James W. Demmel and Xiaoye Li",
title = "Faster numerical algorithms via exception handling",
crossref = "Swartzlander:1993:SCA",
pages = "234--241",
year = "1993",
bibdate = "Thu Jun 20 10:16:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Demmel.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@TechReport{Desaulniers:1993:BEA,
author = "H. Desaulniers and Stewart, N. F. (Neil Frederick)",
title = "Backward error analysis for floating-point operations
on rectilinear $r$-sets",
type = "Publication",
number = "816",
institution = "Universit{\'{e}} de Montr{\'{e}}al, Departement
d'informatique et de recherche operationnelle",
address = "Montr{\'{e}}al, Qu{\'{e}}bec, Canada",
pages = "64",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer-aided design.",
remark = "``January 5, 1993.'' Supported in part by the Natural
Sciences and Engineering Research Council of Canada",
}
@Article{DiClaudio:1993:SRR,
author = "E. D. {Di Claudio} and G. Orlandi and F. Piazza",
title = "A systolic redundant residue arithmetic error
correction circuit",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "4",
pages = "427--432",
month = apr,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.214689",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214689",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{DiLecce:1993:CES,
author = "V. Di Lecce and E. Di Sciascio",
title = "A comparative evaluation of solutions for inner
product",
journal = j-INT-J-MINI-MICROCOMPUTERS,
volume = "15",
number = "2",
pages = "71--77",
month = "????",
year = "1993",
CODEN = "IJMMDE",
ISSN = "0702-0481",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper proposes the design and performance
evaluation of a bit-serial processing element for inner
product computation in fine-grain architectures. Some
solutions proposed in the scientific literature for
inner product are presented and evaluated. The
processing element architecture and its operating mode
are described; a single floating-point inner product
computation can be accomplished in e*(n+1) clock cycles
(2*(n+1) in pipelined mode), supposing that mantissas
and exponents have the same length n. The VLSI
implementation of the processing element is discussed
with reference to both standard cell and full custom
design styles. A comparative evaluation with the
previously described solutions is proposed, relative to
some particularly significant parameters.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electron. Eng., Politecnico di Bari,
Italy",
classification = "B1265F (Microprocessors and microcomputers); C5135
(Digital signal processing chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods);
C5260 (Digital signal processing)",
fjournal = "International Journal of Mini and Microcomputers",
keywords = "Bit-serial processing element; Comparative evaluation;
DSP chips; Exponents; Fine-grain architectures; Full
custom design styles; Inner product; Mantissas;
Operating mode; Performance evaluation; VLSI
implementation",
thesaurus = "Digital arithmetic; Digital signal processing chips;
Performance evaluation",
}
@Article{Dimauro:1993:NTF,
author = "G. Dimauro and S. Impedovo and G. Pirlo",
title = "A new technique for fast number comparison in the
residue number system",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "5",
pages = "608--612",
month = may,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.223680",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=223680;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5840",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "A technique for number comparison in the residue
number system is presented, and its theoretical
validity is proved. The proposed solution is based on
using a diagonal function to obtain a magnitude order
of the numbers. In a first approach the \ldots{}",
}
@Article{Dittmer:1993:EUC,
author = "Ingo Dittmer",
title = "Error in {Unix} commands {\tt dc} and {\tt bc} for
multiple-precision-arithmetic",
journal = j-SIGNUM,
volume = "28",
number = "2",
pages = "8--11",
month = apr,
year = "1993",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:23 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@Book{Dowd:1993:HPC,
author = "Kevin Dowd",
title = "High Performance Computing",
publisher = pub-ORA,
address = pub-ORA:adr,
pages = "xxv + 371",
year = "1993",
ISBN = "1-56592-032-5",
ISBN-13 = "978-1-56592-032-3",
LCCN = "QA76.88 .D6 1993; QA76.9.A73 D68 1993",
bibdate = "Mon Jan 3 18:34:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hpfortran.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/ora.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$25.95",
series = "RISC architectures, optimization and benchmarks; A
Nutshell handbook",
URL = "http://www.oreilly.com/catalog/9781565920323",
acknowledgement = ack-nhfb,
subject = "Computer architecture; Electronic digital computers;
Parallel processing (Electronic computers);
Supercomputers",
tableofcontents = "Preface / xxi \\
Who Should Buy This Book? / xxii \\
What's in This Book / xxii \\
Conventions / xxiv \\
Acknowledgments / xxv \\
1 Modern Computer Architectures / 1 \\
1: What is High Performance Computing? / 3 \\
Why Worry About Performance? / 3 \\
Measuring Performance / 5 \\
The Next Step / 6 \\
2: RISC Computers / 9 \\
Why CISC? / 10 \\
Space and Time / 10 \\
Beliefs About Complex Instruction Sets / 11 \\
Memory Addressing Modes / 12 \\
Microcode / 14 \\
Making the Most of a Clock Tick / 17 \\
Pipelines / 18 \\
Instruction Pipelining / 19 \\
Why RISC? / 21 \\
Characterizing RISC / 22 \\
A Few More Words About Pipelining / 27 \\
Memory References / 27 \\
Floating Point Pipelines / 28 \\
Classes of Processors / 29 \\
Superscalar Processors / 30 \\
Superpipelined Processors / 32 \\
Long Instruction Word (LIW) / 34 \\
Other Advanced Features / 35 \\
Register Bypass / 36 \\
Register Renaming / 36 \\
Reducing Branch Penalties / 37 \\
Closing Notes / 40 \\
3: Memory / 43 \\
Memory Technology / 44 \\
Random Access Memory / 45 \\
Access Time / 47 \\
Caches / 48 \\
Direct Mapped Cache / 50 \\
Fully Associative Cache / 52 \\
Set Associative Cache / 52 \\
Uses of Cache / 54 \\
Virtual Memory / 54 \\
Page Tables / 55 \\
Translation Lookaside Buffer / 56 \\
Page Faults / 57 \\
Improving Bandwidth / 59 \\
Large Caches / 60 \\
Interleaved Memory Systems / 60 \\
Software Managed Caches / 64 \\
Memory Reference Reordering / 64 \\
Multiple References / 66 \\
Closing Notes / 67 \\
IL Porting and Tuning Software / 91 \\
4: What an Optimizing Compiler Does / 69 \\
Optimizing Compiler Tour / 70 \\
Intermediate Language Representation / 70 \\
Basic Blocks / 72 \\
Forming a DAG / 74 \\
Uses and Definitions / 76 \\
Loops / 78 \\
Object Code Generation / 80 \\
Classical Optimizations / 81 \\
Copy Propagation / 81 \\
Constant Folding / 82 \\
Dead Code Removal / 83 \\
Strength Reduction / 84 \\
Variable Renaming / 84 \\
Common Subexpression Elimination / 85 \\
Loop Invariant Code Motion / 86 \\
Induction Variable Simplification / 87 \\
Register Variable Detection / 88 \\
Closing Notes / 88 \\
5: Clarity / 93 \\
Under Construction / 94 \\
Comments / 94 \\
Clues in the Landscape / 95 \\
Variable Names / 96 \\
Variable Types / 98 \\
Named Constants / 99 \\
INCLUDE Statements / 100 \\
Use of COMMON / 101 \\
The Shape of Data / 102 \\
Closing Notes / 104 \\
6: Finding Porting Problems / 105 \\
Problems in Argument Lists / 106 \\
Aliasing / 106 \\
Argument Type Mismatch / 108 \\
Storage Issues / 110 \\
Equivalenced Storage / 111 \\
Memory Reference Alignment Restrictions / 112 \\
Closing Notes / 115 \\
7: Timing and Profiling / 119 \\
Timing / 120 \\
Timing a Whole Program / 120 \\
Timing a Portion of the Program / 124 \\
Using Timing Information / 126 \\
Subroutine Profiling / 127 \\
prof / 130 \\
gprof / 133 \\
gprofs Flat Profile / 138 \\
Accumulating the Results of Several gprof Runs / 139
\\
A Few Words About Accuracy / 140 \\
Basic Block Profilers / 140 \\
tcov / 141 \\
!prof / 142 \\
pixie / 143 \\
Closing Notes / 144 \\
8: Understanding Parallelism / 147 \\
A Few Important Concepts / 148 \\
Constants / 148 \\
Scalars / 150 \\
Vectors and Vector Processing / 150 \\
Dependencies / 153 \\
Data Dependencies / 154 \\
Control Dependencies / 159 \\
Ambiguous References / 161 \\
Closing Notes / 162 \\
9: Eliminating Clutter / 165 \\
Subroutine Calls / 166 \\
Macros / 168 \\
Procedure Inlining / 170 \\
Branches / 171 \\
Wordy Conditionals / 171 \\
Redundant Tests / 172 \\
Branches Within Loops / 173 \\
Loop Invariant Conditionals / 174 \\
Loop Index Dependent Conditionals / 175 \\
Independent Loop Conditionals / 176 \\
Dependent Loop Conditionals / 177 \\
Reductions / 178 \\
Conditionals That Transfer Control / 179 \\
A Few Words About Branch Probability / 180 \\
Other Clutter / 181 \\
Data Type Conversions / 181 \\
Doing Your Own Common Subexpression Elimination / 182
\\
Doing Your Own Code Motion / 183 \\
Handling Array Elements in Loops / 184 \\
Closing Notes / 185 \\
10: Loop Optimizations / 187 \\
Basic Loop Unrolling / 188 \\
Qualifying Candidates for Loop Unrolling / 189 \\
Loops with Low Trip Counts / 190 \\
Fat Loops / 191 \\
Loops Containing Procedure Calls / 191 \\
Loops with Branches in Them / 193 \\
Recursive Loops / 194 \\
Negatives of Loop Unrolling / 195 \\
Unrolling by the Wrong Factor / 196 \\
Register Thrashing / 196 \\
Instruction Cache Miss / 197 \\
Other Hardware Delays / 197 \\
Outer Loop Unrolling / 197 \\
Outer Loop Unrolling to Expose Computations / 199 \\
Associative Transformations / 200 \\
Reductions / 202 \\
Dot Products and daxpys / 204 \\
Matrix Multiplication / 206 \\
Loop Interchange / 208 \\
Loop Interchange to Move Computations to the Center /
208 \\
Operation Counting / 209 \\
Closing Notes / 211 \\
11: Memory Reference Optimizations / 213 \\
Memory Access Patterns / 214 \\
Loop Interchange to Ease Memory Access Patterns / 215
\\
Blocking to Ease Memory Access Patterns / 216 \\
Ambiguity in Memory References / 223 \\
Ambiguity in Vector Operations / 224 \\
Pointer Ambiguity in Numerical C Applications / 225 \\
Programs That Require More Memory Than You Have / 227
\\
Software-Managed, Out-of-Core Solutions / 227 \\
Virtual Memory / 228 \\
Instruction Cache Ordering / 231 \\
Closing Notes / 232 \\
12: Language Support for Performance / 235 \\
Subroutine Libraries / 235 \\
Vectorizing Preprocessors / 237 \\
Explicitly Parallel Languages / 243 \\
Fortran 90 / 244 \\
High Performance Fortran (HPF) / 250 \\
Explicitly Parallel Programming Environments / 251 \\
Closing Notes / 253 \\
1/L Evaluating Performance / 255 \\
13: Industry Benchmarks / 257 \\
What is a MIP? / 258 \\
VAX MIPS / 259 \\
Dhrystones / 259 \\
Floating Point Benchmarks / 261 \\
Linpack / 262 \\
Whetstone / 264 \\
The SPEC Benchmarks / 265 \\
Individual SPEC Benchmarks / 266 \\
030.matrix300 Was Deleted / 272 \\
Transaction Processing Benchmarks / 272 \\
TPC-A / 273 \\
TPC-B / 273 \\
TPC-C / 273 \\
Closing Notes / 273 \\
14: Running Your Own Benchmarks / 275 \\
Choosing What to Benchmark / 275 \\
Benchmark Run Time / 276 \\
Benchmark Memory Size / 277 \\
Kernels and Sanitized Benchmarks / 277 \\
Benchmarking Third Party Codes / 278 \\
Types of Benchmarks / 279 \\
Single Stream Benchmarks / 280 \\
Throughput Benchmarks / 282 \\
Interactive Benchmarks / 283 \\
Preparing the Code / 285 \\
Portability / 285 \\
Making a Benchmark Kit / 286 \\
Benchmarking Checklist / 287 \\
Closing Notes / 288 \\
IV. Parallel Computing / 291 \\
15: Large Scale Parallel Computing / 293 \\
Problem Decomposition / 294 \\
Data Decomposition / 295 \\
Control Decomposition / 299 \\
Distributing Work Fairly / 300 \\
Classes of Parallel Architectures / 302 \\
Single Instruction, Multiple Data / 303 \\
SIMD Architecture / 305 \\
Mechanics of Programming a SIMD Machine / 309 \\
Multiple Instruction, Multiple Data / 312 \\
Distributed Memory MIMD Architecture / 314 \\
Programming a Distributed Memory MIMD Machine / 315 \\
A Few Words About Data Layout Directives / 319 \\
Virtual Shared Memory / 320 \\
Closing Notes / 323 \\
16: Shared-Memory Multiprocessors / 325 \\
Symmetric Multiprocessing / 326 \\
Operating System Support for Multiprocessing / 327 \\
Multiprocessor Architecture / 329 \\
Shared Memory / 330 \\
Conservation of Bandwidth / 330 \\
Coherency / 332 \\
Data Placement / 334 \\
Multiprocessor Software Concepts / 334 \\
Fork and Join / 335 \\
Synchronization with Locks / 337 \\
Synchronization with Barriers / 340 \\
Automatic Parallelization / 341 \\
Loop Splitting / 341 \\
Subroutine Calls in Loops / 342 \\
Nested Loops / 342 \\
Manual Parallelism / 344 \\
Closing Notes / 345 \\
A: Processor Overview / 347 \\
B: How to Tell When Loops Can Be Interchanged / 351 \\
C: Obtaining Sample Programs and Problem Set Answers /
357 \\
FTP / 357 \\
FTPMAIL / 358 \\
BITFTP / 359 \\
UUCP / 359 \\
Figures \\
2: RISC Computers / 9 \\
2-1 Registers, a single common data path, and an adder
/ 15 \\
2-2 A pipeline / 18 \\
2-3 Three instructions in flight through one pipeline /
20 \\
2-4 Variable length instructions make pipelining
difficult / 23 \\
2-5 Variable length CISC versus fixed length RISC
instructions / 23 \\
2-6 Processor encounters a branch / 26 \\
2-7 The Branch Delay Slot --- ZERO R3 executes either
way / 27 \\
2-8 Memory references scheduled early to account for
pipeline depth / 28 \\
2-9 Decomposing a serial stream / 30 \\
2-10 RS/ 6000 functional blocks / 31 \\
2-11 MIPS R4000 Instruction Pipeline / 33 \\
2-12 Intel i860 transition between modes / 35 \\
3: Memory / 43 \\
3-1 Row--Column memory address / 46 \\
3-2 Direct mapping of memory address to RAM / 46 \\
3-3 Cache lines can come from different parts of memory
/ 49 \\
3-4 Many memory addresses map to same cache line / 51
\\
3-5 Two -way set associative cache / 53 \\
3-6 Virtual to physical address mapping / 55 \\
3-7 Simple memory system / 59 \\
3-8 Page mode cache refill / 60 \\
3-9 Multi-banked memory system / 62 \\
3-10 Cache refill from interleaved memory / 63 \\
4: What an Optimizing Compiler Does / 69 \\
4-1 Example 4-1 divided into basic blocks / 73 \\
4-2 Tuple mapped into a DAG / 74 \\
4-3 Basic Block B / 75 \\
4-4 DAG for Block B / 75 \\
4-5 Revised Basic Block B / 76 \\
4-6 Flow graph for data flow analysis / 77 \\
4-7 Flow graph with a loop in it / 79 \\
5: Clarity / 93 \\
5-1 Array C in two -dimensional memory / 103 \\
6: Finding Porting Problems / 105 \\
6-1 IEEE 754 floating point formats / 109 \\
6-2 IBM 370 floating point formats / 110 \\
6-3 Equivalence storage relationship on most computers
/ 111 \\
6-4 Misaligned variables / 113 \\
7: Timing and Pro.filing / 119 \\
7-1 The built-in csh time function / 123 \\
7-2 Sharp profile --- dominated by routine 1 / 128 \\
7-3 Flat profile --- no routine predominates / 129 \\
7-4 Simple call graph / 134 \\
7-5 FORTRAN example / 135 \\
7-6 Quantization Errors in Profiling / 140 \\
8: Understanding Parallelism / 147 \\
8-1 Vector Computer / 152 \\
8-2 A little section of your program / 159 \\
8-3 Expensive operation moved so that it's rarely
executed / 160 \\
11: Memory Reference Optimizations / 213 \\
11-1 Arrays A and B / 217 \\
11-2 How array elements are stored / 218 \\
11-3 2x2 squares / 219 \\
11-4 Picture of unblocked versus blocked references /
220 \\
11-5 Optimization performance for various sized loops /
222 \\
11-6 Vector machine memory access / 223 \\
12: Language Support for Performance / 235 \\
12-1 Linda's Tuple Space Bulletin Board / 252 \\
14: Running Your Own Benchmarks / 275 \\
14-1 Kernel benchmark / 278 \\
14-2 Single stream benchmarks / 280 \\
14-3 Computing an overall benchmark score / 281 \\
14-4 Wrong way to run a throughput benchmark / 282 \\
14-5 Benchmark stone wall / 283 \\
14-6 Interactive use benchmark / 284 \\
_15:Large Scale Parallel Computing / 293 \\
15-1 Domain decomposition / 295 \\
15-2 Cells with X's have life / 296 \\
15-3 One iteration later / 297 \\
15-4 Two examples of division of cells between four
CPUs / 298 \\
15-5 Each processor with a piece of the domain / 300
\\
15-6 Duplicated data domain / 301 \\
15-7 Iterations mapped onto SIMD nodes / 304 \\
15-8 Mapping a route through a strictly Cartesian mesh
/ 306 \\
15-9 Four nodes / 307 \\
15-10 A 3-cube and a 4-cube / 307 \\
15-11 Front-end and SIMD machine / 309 \\
15-12 KSR-1 ring of rings architecture / 322 \\
16: Shared-Memory Multiprocessors / 325 \\
16-1 A typical bus architecture / 329 \\
16-2 A $4 \times 4$ crossbar / 330 \\
16-3 High cache hit rate reduces main memory traffic /
331 \\
16-4 Multiple copies of variable A / 332 \\
16-5 Fork and join / 335 \\
16-6 Integration / 337 \\
16-7 Implementation of a spinlock / 339 \\
B: How to Tell When Loops Can Be Interchanged / 351 \\
B-1 $4 \times 4$ matrix / 352 \\
B-2 One iteration complete / 353 \\
B-3 All iterations completed / 354 \\
B-4 Movement of data in array A / 355 \\
Examples \\
4: What an Optimizing Compiler Does / 69 \\
4-1 Intermediate Language for a Single Loop / 72 \\
5: Clarity / 93 \\
5-1 Comments, asterisks, and pretty printing / 95 \\
5-2 Variable names count / 97 \\
5-3 Parameter statements \\
5-4 Declarations / 100 \\
5-5 Routine using both INCLUDE files / 100 \\
5-6 Changing the Shape of an Array / 100 \\
/ 102 \\
6: Finding Porting Problems / 105 \\
6-1 Program for creating misaligned references \\
6-2 Misaligned reference in C / 114 \\
/ 115 \\
7: Timing and Profiling / 119 \\
7-1 FORTRAN program using etime / 125 \\
7-2 etime implemented in C / 126 \\
7-3 loops.c --- a program for testing profilers / 131
\\
7-4 Profile of loops.c / 132 \\
7-5 A portion of gprof output / 135 \\
7-6 gprof flat profile / 138 \\
8: Understanding Parallelism / 147 \\
8-1 Vector Addition / 150 \\
9: Eliminating Clutter / 165 \\
9-1 Macro definition and use / 168 \\
10: Loop Optimizations / 187 \\
10-1 Loop containing a procedure call / 192 \\
10-2 Matrix multiply with daxpy inner loop / 206 \\
10-3 Matrix multiply with dot product inner loop / 206
\\
11: Memory Reference Optimizations / 213 \\
11-1 Two-dimensional vector sum / 216 \\
11-2 Outer and inner loop unrolled / 217 \\
B: How to Tell When Loops Can Be Interchanged / 351 \\
B-1 Each iteration is independent / 351 \\
B-2 Can we interchange these loops? / 352 \\
B-3 Legal alternate loop nests / 354 \\
B-4 More complicated references / 355 \\
B-5 More complicated references / 356 \\
Tables \\
6: Finding Porting Problems / 105 \\
6-1 Preferred Alignment Boundaries on Most Computers /
113 \\
15: Large Scale Parallel Computing / 293 \\
15-1 Worst Case Communication / 308 \\
A: Processor Overview / 347 \\
A-1 CPU Characteristics / 347 \\
A-2 Cache and Branch Architecture / 348 \\
A-2 Cache and Branch Architecture (continued) / 349",
}
@Article{Duncan:1993:CES,
author = "Roy Duncan and John Tunstall and Brian T. Smith and
Richard Brankin",
title = "Correspondence: Expert Systems for Re-ordering
Arithmetic Expressions?",
journal = j-FORTRAN-FORUM,
volume = "12",
number = "3",
pages = "12--14",
month = sep,
year = "1993",
CODEN = "????",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Tue Apr 23 14:50:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "35",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@Article{Duprat:1993:CAN,
author = "J. Duprat and J. Muller",
title = "The {CORDIC} Algorithm: New Results for Fast {VLSI}
Implementation",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "2",
pages = "168--178",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.204786",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:15:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Eisig:1993:DBI,
author = "David Eisig and Josh Rotstain and Israel Koren",
title = "The Design of a 64-bit Integer Multiplier\slash
Divider Unit",
crossref = "Swartzlander:1993:SCA",
pages = "171--178",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Eisig.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Eldridge:1993:HIM,
author = "S. E. Eldridge and C. D. Walter",
title = "Hardware implementation of {Montgomery}'s modular
multiplication algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "6",
pages = "693--699",
month = jun,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.277287",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=277287",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ercegovac:1993:VHR,
author = "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang and Paolo
Montuschi",
title = "Very high radix division with selection by rounding
and prescaling",
crossref = "Swartzlander:1993:SCA",
pages = "112--119",
year = "1993",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Ercegovac.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
summary = "A division algorithm in which the quotient-digit
selection is performed by rounding the shifted residual
in carry-save form is presented. To allow the use of
this simple function, the divisor (and dividend) is
prescaled to a range close to one. The \ldots{}",
}
@InProceedings{Etiemble:1993:AMV,
author = "D. Etiemble and K. Navi",
title = "Algorithms and Multi-Valued Circuits for the
Multioperand Addition in the Binary Stored-Carry Number
System",
crossref = "Swartzlander:1993:SCA",
pages = "194--201",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Etiemble.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Fortune:1993:EEA,
author = "Steven Fortune and Christopher J. {Van Wyk}",
editor = "{ACM}",
booktitle = "{Proceedings of the 9th ACM Symposium on Computational
Geometry, May 19--21, 1993, San Diego, CA, USA}",
title = "Efficient Exact Arithmetic for Computational
Geometry",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "vii + 406",
pages = "163--172",
year = "1993",
DOI = "https://doi.org/10.1145/160985.161015",
ISBN = "0-89791-582-8",
ISBN-13 = "978-0-89791-582-3",
LCCN = "QA448.D38 S96 1993",
bibdate = "Tue Nov 13 21:44:58 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Fowkes:1993:HEA,
author = "R. E. Fowkes",
title = "Hardware Efficient Algorithms for Trigonometric
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "3",
pages = "235--239",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.204796",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 1 10:16:09 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fox:1993:HLS,
author = "J. R. Fox",
title = "A higher level of synthesis ({CAD})",
journal = j-IEEE-SPECTRUM,
volume = "30",
number = "3",
pages = "43--47",
month = mar,
year = "1993",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.211955",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Jan 16 07:37:23 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "abstraction; Arithmetic; CAD; Circuit synthesis;
Clocks; design automation; Design automation; Design
engineering; design synthesis systems; Fabrication;
Hardware; hardware description languages; Logic
circuits; Logic design; Microarchitecture; software
tools; specification languages; testability; top-down
design",
}
@MastersThesis{Geraminejad:1993:DIC,
author = "Mohsen Geraminejad",
title = "Design and implementation of a 16-bit {CMOS} floating
point multiplier",
type = "Research paper ({M.S.})",
school = "Department of Electrical Engineering, Southern
Illinois University at Carbondale",
address = "Carbondale, IL, USA",
pages = "vii + 54",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gibbons:1993:FMW,
author = "Jeremy Gibbons",
editor = "John Hosking",
booktitle = "{Proceedings of the 13th New Zealand Computer Society
Conference: Applying the future today, Aotea Centre,
Auckland, 18--20 August 1993}",
title = "Formal Methods: {Why} Should {I} Care? {The}
development of the {T800} transputer floating-point
unit",
publisher = "New Zealand Computer Society",
address = "Wellington, NZ",
pages = "207--217",
year = "1993",
ISBN = "0-9597657-6-X; 0-9597657-5-1",
ISBN-13 = "978-0-9597657-6-2; 978-0-9597657-5-5",
LCCN = "????",
bibdate = "Tue Nov 13 21:37:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The term `formal methods' is a general term for
precise mathematically-based techniques used in the
development of computer systems, both hardware and
software. This paper discusses formal methods in
general, and in particular describes their successful
role in specifying, constructing and proving correct
the floating-point unit of the Inmos T800 transputer
chip.",
acknowledgement = ack-nhfb,
keywords = "Inmos T800 transputer",
}
@TechReport{Goldberg:1993:DFP,
author = "David Goldberg",
title = "The design of floating-point data types",
type = "Technical report",
number = "CSL-93-3",
institution = "Xerox Corp., Palo Alto Research Center",
address = "Palo Alto, CA, USA",
pages = "19",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Abstract data types (Computer science)",
remark = "``A version of this paper will appear in Letters on
Programming Languages and Systems.'' ``February 1993.''
Abstract: ``We discuss the issues involved in designing
the floating-point part of a programming language.
Looking at the language specifications for most
existing languages might suggest that this design
involves only trivial issues such as whether to have
one or two types of REALs or how to name the functions
that convert from INTEGER to REAL. We show that there
are more significant semantic issues involved. After
discussing the tradeoffs for the major design
decisions, we illustrate them by presenting the design
of the floating-point part of the Modula-3
language.''",
}
@TechReport{Gudeman:1993:RTI,
author = "David Gudeman",
title = "Representing Type Information in Dynamically Typed
Languages",
type = "Technical report",
number = "TR 93-27",
institution = "Department of Computer Science, The University of
Arizona",
address = "Tucson, AZ 85721, USA",
pages = "40",
month = oct,
year = "1993",
bibdate = "Wed Oct 13 08:12:36 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.cs.arizona.edu/reports/1993/TR93-27.ps;
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.4394",
abstract = "This report is a discussion of various techniques for
representing type information in dynamically typed
languages, as implemented on general-purpose machines
(and costs are discussed in terms of modern RISC
machines). It is intended to make readily available a
large body of knowledge that currently has to be
absorbed piecemeal from the literature or re-invented
by each language implementer. This discussion covers
not only tagging schemes but other forms of
representation as well, although the discussion is
strictly limited to the representation of type
information. It should also be noted that this report
does not purport to contain a survey of the relevant
literature. Instead, this report gathers together a
body of folklore, organizes it into a logical
structure, makes some generalizations, and then
discusses the results in terms of modern hardware.",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; integer arithmetic; Lisp;
Prolog; typed objects",
remark = "Discusses implementation of fast arithmetic for typed
integer and floating-point data.",
}
@Misc{Gupta:1993:NPF,
author = "S. Gupta and R. Periman and T. Lynch and B. McMinn",
title = "Normalizing pipelined floating point processing
units",
day = "30",
month = nov,
year = "1993",
bibdate = "Fri Nov 28 15:27:34 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,267,186.",
acknowledgement = ack-nhfb,
}
@InCollection{Hammer:1993:PXN,
author = "R. Hammer and M. Neaga and D. Ratz",
title = "{PASCAL-XSC}: New Concepts for Scientific Computation
and Numerical Data Processing",
crossref = "Adams:1993:SCA",
pages = "15--44",
year = "1993",
bibdate = "Wed Oct 13 22:38:56 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hasan:1993:MMO,
author = "M. A. Hasan and M. Z. Wang and V. K. Bhargava",
title = "A modified {Massey--Omura} parallel multiplier for a
class of finite fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "10",
pages = "1278--1280",
month = oct,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.257715",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=257715",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hatzinakos:1993:AFP,
author = "D. Hatzinakos",
title = "Analysis of floating point roundoff errors in the
estimation of higher-order statistics",
journal = "IEE proceedings. F, Radar and signal processing",
volume = "140",
number = "6",
pages = "371--379",
month = dec,
year = "1993",
ISSN = "0956-375X",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A floating point roundoff error analysis in the
estimation of higher-order statistics, moments or
cumulants of real stationary processes from single data
records is provided. Closed form expressions or upper
bounds are derived for the mean and \ldots{}",
}
@Book{Heinrich:1993:MRM,
author = "Joe Heinrich",
title = "{MIPS R4000} Microprocessor User's Manual",
publisher = pub-PHPTR,
address = pub-PHPTR:adr,
pages = "xxvi + 438 + A182 + B62 + C6 + D4 + E4",
year = "1993",
ISBN = "0-13-105925-4",
ISBN-13 = "978-0-13-105925-2",
LCCN = "QA76.8.M523H45 1993",
bibdate = "Wed Aug 10 11:02:27 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$34.00",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
tableofcontents = "Introduction \\
CPU Instruction Set Summary \\
The CPU Pipeline \\
Memory Management \\
CPU Exception Processing \\
Floating-Point Unit \\
Floating-Point Exceptions \\
R4000 Processor Signal Descriptions \\
Initialization Interface \\
Clock Interface \\
Cache Organization, Operation, and Coherency \\
System Interface \\
Secondary Cache Interface \\
JTAG Interface \\
R4000 Processor Interrupts \\
Error Checking and Correcting \\
CPU Instruction Set Details \\
FPU Instruction Set Details \\
Subblock Ordering \\
Output Buffer \ldots{} Di \ldots{} Dt Control Mechanism
\\
PLL Passive Components \\
R4000 Coprocessor 0 Hazards",
}
@InProceedings{Hekstra:1993:FPC,
author = "Gerben J. Hekstra and Ed F. A. Deprettere",
title = "Floating Point Cordic",
crossref = "Swartzlander:1993:SCA",
pages = "130--137",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hekstra.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Hemkumar:1993:ECM,
author = "Nariankadu D. Hemkumar and Joseph R. Cavallaro",
title = "Efficient Complex Matrix Transformations with
{CORDIC}",
crossref = "Swartzlander:1993:SCA",
pages = "122--129",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hemkumar.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Hendtlass:1993:MNIa,
author = "T. Hendtlass",
title = "Math-who needs it?",
journal = j-FORTH-DIMENSIONS,
volume = "14",
number = "6",
pages = "27--38",
month = mar # "--" # apr,
year = "1993",
CODEN = "FODMD5",
ISSN = "0884-0822",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A thorough treatment of integer, double-precision,
fixed-point, and floating-point mathematics. A
mathematician's toolbox of code is presented, and
tables compare the benefits bestowed and the penalties
extracted by the routines.",
acknowledgement = ack-nhfb,
classification = "C6140D (High level languages); C7310 (Mathematics)",
fjournal = "Forth Dimensions",
keywords = "Code toolbox; Double precision arithmetic; Fixed-point
arithmetic; Floating-point mathematics; Integer",
thesaurus = "FORTH; FORTH listings; Mathematics computing",
}
@Article{Hendtlass:1993:MNIb,
author = "T. Hendtlass",
title = "Math---who needs it?",
journal = j-FORTH-DIMENSIONS,
volume = "15",
number = "1",
pages = "38--39",
month = may # "--" # jun,
year = "1993",
CODEN = "FODMD5",
ISSN = "0884-0822",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The continuation of the source code for a Forth
program is presented (see ibid., vol.14, no.6, 1993).
The software is a math professor's toolbox of integer,
double-precision, fixed-point and floating-point
routines.",
acknowledgement = ack-nhfb,
classification = "C6110 (Systems analysis and programming); C7310
(Mathematics)",
fjournal = "Forth Dimensions",
keywords = "Double-precision; Fixed-point; Floating-point
routines; Forth program; Math; Source code; Toolbox",
thesaurus = "Digital arithmetic; FORTH listings; Mathematics
computing; Programming",
}
@Article{Higginbotham:1993:ISR,
author = "T. F. Higginbotham",
title = "The integer square root of {N} via a binary search",
journal = j-SIGCSE,
volume = "25",
number = "4",
pages = "41--45",
month = dec,
year = "1993",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/164205.164229",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sat Nov 17 18:57:24 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
abstract = "An algorithm is presented which may be used to find
the integer square root of N. The method is intended
for use on a binary computer, where only addition,
subtraction, multiplication, or division by 2 is
required. The problem arose when the author was working
on factoring large numbers, where the machine, the
Honeywell DPS 8, had double precision integer addition
and subtraction, and the simulation of multiplication
was easy. The actual factoring of the large number was
to be Fermat's Method, requiring only addition and
subtraction, but the integer square root is required in
order to test for termination. The algorithm is
implemented in FORTRAN for ease of reading. Students
enjoy the unconventional approach to solving this
problem. It isn't long before some of them think of
other unusual solutions.",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Higham:1993:AFP,
author = "Nicholas J. Higham",
title = "The accuracy of floating point summation",
journal = j-SIAM-J-SCI-COMP,
volume = "14",
number = "4",
pages = "783--799",
month = jul,
year = "1993",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/0914050",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G05 (65B10)",
MRnumber = "94a:65025",
bibdate = "Thu Aug 23 06:36:53 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://citeseer.nj.nec.com/higham93accuracy.html;
http://www.maths.man.ac.uk/~nareports/narep198.pdf;
http://www.maths.man.ac.uk/~nareports/narep198.ps.gz",
abstract = "The usual recursive summation technique is just one of
several ways of computing the sum of $n$ floating point
numbers. Five summation methods and their variations
are analyzed. The accuracy of the methods is compared
using rounding error analysis and numerical
experiments. Four of the methods are shown to be
special cases of a general class of methods, and an
error analysis is given for this class. No one method
is uniformly more accurate than the others, but some
guidelines are given on the choice of method in
particular cases.",
acknowledgement = ack-nhfb,
affiliation = "Department of Math., Manchester University, UK",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; floating point
numbers; numerical experiments; recursive summation
technique; rounding error analysis",
thesaurus = "Digital arithmetic; Error analysis",
}
@MastersThesis{Holler:1993:IFP,
author = "Paul T. Holler",
title = "Integrating a floating point unit into the {AT\&T
Hobbit} microprocessor",
type = "Thesis ({M.S.})",
school = "Lehigh University",
address = "Bethlehem, PA, USA",
pages = "viii + 85",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
}
@Article{Hopkins:1993:CEM,
author = "Tim Hopkins and John Slater",
title = "A Comment on the {Eispack} Machine Epsilon Routine",
journal = j-SIGNUM,
volume = "28",
number = "4",
pages = "2--6",
month = oct,
year = "1993",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/165639.165641",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:24 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors analyze the algorithm used to generate the
value for the machine epsilon in the Eispack suite of
routines and show that it can fail on a binary
floating-point system. The comments in the code
describing the conditions under which this method will
work are not restrictive enough and the authors provide
a replacement set of assumptions. They conclude by
suggesting how the algorithm may be modified to
overcome most of the shortcomings.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Comput. Lab., Kent University, Canterbury, UK",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Binary floating-point system; Eispack machine epsilon
routine",
thesaurus = "Digital arithmetic",
}
@TechReport{Horning:1993:SUM,
author = "Jim Horning and Bill Kalsow and Paul McJones and Greg
Nelson",
title = "Some Useful {Modula-3} Interfaces",
type = "Memo",
number = "113",
institution = "Digital Equipment Corporation, Systems Research
Center",
address = "Palo Alto, CA, USA",
month = dec,
year = "1993",
bibdate = "Wed Jan 29 16:39:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``The floating-point
reader has been implemented in \ldots{} to
Modula-3''.",
}
@Article{Hu:1993:EIS,
author = "X. Hu and S. C. Bass and R. G. Harber",
title = "An Efficient Implementation of Singular Value
Decomposition Rotation Transformations with {CORDIC}
Processors",
journal = j-J-PAR-DIST-COMP,
volume = "17",
number = "4",
pages = "360--362",
month = apr,
year = "1993",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1993.1034",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:52 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production/pdf",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra); C5230 (Digital arithmetic
methods); C7310 (Mathematics)",
corpsource = "General Motors Res. Labs., Warren, MI, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "2*2 matrices; CORDIC processors; digital arithmetic;
mathematics computing; matrix algebra; singular value
decomposition rotation transformations",
treatment = "A Application; P Practical",
}
@Book{IBM:1993:IPA,
author = "{IBM Corporation}",
title = "The {IBM PowerPC} Architecture: a New Family of {RISC}
Processors",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
year = "1993",
ISBN = "1-55860-316-6",
ISBN-13 = "978-1-55860-316-5",
LCCN = "QA76.8.P67P68 1994",
bibdate = "Sat Oct 15 12:26:00 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$49.95",
acknowledgement = ack-nhfb,
}
@Article{Ide:1993:CFP,
author = "N. Ide and H. Fukuhisa and Y. Kondo and T. Yoshida and
M. Nagamatsu and J. Mori and I. Yamazaki and K. Ueno",
title = "A {320-MFLOPS} {CMOS} Floating-Point Processing Unit
for Superscalar Processors",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "28",
number = "3",
pages = "352--361",
month = mar,
year = "1993",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Ide:1993:MCF,
author = "Nobuhiro Ide and Hiroto Fukuhisa and Yoshihisa Kondo
and Takeshi Yoshida and Masato Nagamatsu and Junji Mori
and Itaru Yamazaki and Kiyoji Ueno",
title = "A 320-{MFLOPS CMOS} Floating-Point Processing Unit for
Superscalar Processors",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "28",
number = "3",
pages = "352--361",
month = mar,
year = "1993",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A CMOS pipelined floating-point processing unit (FPU)
for superscalar processors is described. It is
fabricated using a 0.5 $\mu$m CMOS triple-metal-layer
technology on a 61 mm 2 die. The FPU has two execution
modes to meet precise scientific computations and
real-time applications. It can start two FPU operations
in each cycle, and this achieves a peak performance of
160 MFLOPS double or single precision with an 80 MHz
clock. Furthermore, the original computation mode, twin
single-precision computation, double the peak
performance and delivers 320 MFLOPS single precision.
Its full bypass reduces the latency of operations,
including load and store, and achieves an effective
throughput even in nonvectorizable computations. An
out-of-order completion is provided by using a new
exception prediction method and a pipeline stall
technique.",
}
@Article{Jahn:1993:LIF,
author = "K.-U. Jahn",
title = "Loop Invariants in Floating Point Algorithms.
{Schleifen-Invarianten in Gleitpunktalgorithmen}",
journal = j-COMPUTING,
volume = "50",
number = "3",
pages = "255--264",
year = "1993",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (65G10)",
MRnumber = "94f:65052",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "It is shown that by using directed roundings with
respect to enclosure sets for the exact values, the
loop conditions and loop invariants of numerical
algorithms can be generalized for computing in a
discrete screen. It is possible to verify the received
results. Thereby only inherent properties of the
algorithms are used, which moreover guarantee that the
loops terminate.",
acknowledgement = ack-nhfb,
classification = "C4240P (Parallel programming and algorithm theory);
C6150G (Diagnostic, testing, debugging and evaluating
systems)",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "Directed roundings; Enclosure sets; Floating point
algorithms; Loop conditions; Loop invariants",
pubcountry = "Austria",
thesaurus = "Program verification",
}
@Article{Jahn:1993:SIG,
author = "K.-U. Jahn",
title = "{Schleifen-Invarianten in Gleitpunktalgorithmen}.
({German}) [{Loop} Invariants in Floating Point
Algorithms]",
journal = j-COMPUTING,
volume = "50",
number = "3",
pages = "255--264",
month = sep,
year = "1993",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65G05 (65G10)",
MRnumber = "94f:65052",
bibdate = "Mon Oct 11 20:38:38 MDT 1999",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
abstract = "It is shown that by using directed roundings with
respect to enclosure sets for the exact values, the
loop conditions and loop invariants of numerical
algorithms can be generalized for computing in a
discrete screen. It is possible to verify the received
results. Thereby only inherent properties of the
algorithms are used, which moreover guarantee that the
loops terminate.",
acknowledgement = ack-nhfb,
classification = "C4240P (Parallel programming and algorithm theory);
C6150G (Diagnostic, testing, debugging and evaluating
systems)",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "Directed roundings; Enclosure sets; Floating point
algorithms; Loop conditions; Loop invariants",
language = "German",
pubcountry = "Austria",
thesaurus = "Program verification",
}
@InProceedings{Jebelean:1993:CSG,
author = "T. Jebelean",
title = "Comparing Several {GCD} Algorithms",
crossref = "Swartzlander:1993:SCA",
pages = "180--185",
month = jun,
year = "1993",
bibdate = "Wed Nov 14 18:46:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jebelean.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Jenkins:1993:CSL,
author = "W. K. Jenkins and B. A. Schnaufer and A. J. Mansen",
title = "Combined System-Level Redundancy and Modular
Arithmetic for Fault Tolerant Digital Signal
Processing",
crossref = "Swartzlander:1993:SCA",
pages = "28--35",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jenkins.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Johnstone:1993:RNA,
author = "P. Johnstone and F. E. Petry",
title = "Rational number approximation in higher radix floating
point systems",
journal = j-COMPUT-MATH-APPL,
volume = "25",
number = "6",
pages = "103--108",
month = mar,
year = "1993",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Mathematical researchers have long recognized that
some bases offer some representational advantages in
that they generate fewer nonterminate values when
representing arbitrary rational numbers. While such
results are true for abstract number systems, little
attention has been paid to machine based computation
and its finite resources. In the paper, such results
are considered in an environment more typical of
computer based models of number systems. Specifically,
the authors consider the effect of the choice of
floating point base on rational number approximation in
systems which exhibit the typical characteristics of
floating point representations-normalized encodings,
limited exponent range and storage allocated in a fixed
number of `bits' per datum. The frequency with which
terminate and representable results can be expected is
considered for binary, decimal, and other potentially
interesting bases.",
acknowledgement = ack-nhfb,
affiliation = "New Orleans Tech. Dev. Group, Telerate Systems Inc.,
LA, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Computer based models; decimal floating-point
arithmetic; Floating point base; Floating point
systems; Number systems; Rational number
approximation",
pubcountry = "UK",
thesaurus = "Digital arithmetic",
}
@InProceedings{Ju:1993:WCB,
author = "Chwen-Jye Ju",
title = "What can block floating-point arithmetic do for {DSP}
applications",
crossref = "Anonymous:1993:IPF",
bookpages = "1675",
pages = "641--650 vol.1",
year = "1993",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Block floating-point arithmetic for filtering was
proposed by Oppenheim two decades ago. Although it has
the advantages of both integer and floating-point
arithmetic, it is scarcely used in DSP applications
because the required signal reference level adjustment
(scaling) usually offsets its advantages. To conquer
the scaling problem, the unified indexing concept has
been proposed by the author for the M-D FFT
implementation. This paper will extend the concept to
derive the general block-oriented block floating-point
DSP algorithms. Therefore, the block floating-point
processors such as the LH9124/LH9320 can provide
self-contained solutions for some classes of DSP
applications.",
acknowledgement = ack-nhfb,
affiliation = "Sharp Microelectron. Technol. Inc., Camas, WA, USA",
classification = "B1265F (Microprocessors and microcomputers); B6140
(Signal processing and detection); C5135 (Digital
signal processing chips); C5230 (Digital arithmetic
methods); C5260 (Digital signal processing)",
keywords = "Block floating-point arithmetic; Block floating-point
processors; DSP applications; General block-oriented
block floating-point DSP algorithms; LH9124/LH9320; M-D
FFT implementation; Oppenheim; Scaling problem; Signal
reference level adjustment; Unified indexing concept",
thesaurus = "Array signal processing; Digital arithmetic; Digital
filters; Digital signal processing chips; Fast Fourier
transforms",
}
@TechReport{Karp:1993:HPD,
author = "A. H. Karp and P. Markstein",
title = "High precision division and square root",
number = "HPL-93-42",
institution = "Hewlett--Packard Lab.",
address = "Palo Alto, CA, USA",
pages = "20",
month = jun,
year = "1993",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors present division and square root
algorithms for calculations with more bits than are
handled by the floating point hardware. These
algorithms avoid the need to multiply two high
precision numbers, speeding up the last iteration by as
much as a factor of ten.",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
keywords = "Division; Floating point hardware; Square root
algorithms",
thesaurus = "Digital arithmetic",
}
@InProceedings{Kim:1993:FABa,
author = "S. W. Kim and T. Stouraitis and A. Skavantzos",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '93}, 3--6 May 1993",
title = "Full adder-based inner product step processors for
residue and quadratic residue number systems",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1821--1824",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1993.394100",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A full adder-based arithmetic unit of a modulus $m$,
called an FA-based AU$_m$, is proposed. It performs
both addition and multiplication at the same time.
Since the proposed AU$_m$'s use full adders as their
basic units, they lead to modular and regular designs
which result in lower cost and easier implementation in
VLSI.",
}
@InProceedings{Kim:1993:FABb,
author = "Seon Wook Kim and T. Stouraitis and A. Skavantzos",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '93}, 3--6 May 1993",
title = "Full adder-based inner product step processors for
residue and quadratic residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1821--1824",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/EDAC.1993.386412",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InProceedings{Kim:1993:FABc,
author = "S. W. Kim and T. Stouraitis and A. Skavantzos",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '93}, 3--6 May 1993",
title = "Full adder-based inner product step processors for
residue and quadratic residue number systems",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1821--1824",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1993.394100",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A full adder-based arithmetic unit of a modulus m,
called an FA-based AU m, is proposed. It performs both
addition and multiplication at the same time. Since the
proposed AU m's use full adders as their basic units,
they \ldots{}",
}
@InProceedings{Kim:1993:FABd,
author = "Seon Wook Kim and T. Stouraitis and A. Skavantzos",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '93}, 3--6 May 1993",
title = "Full adder-based inner product step processors for
residue and quadratic residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1821--1824",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/EDAC.1993.386412",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@InProceedings{Kirsch:1993:ABU,
author = "Bary J. Kirsch and Peter R. Turner",
title = "Adaptive Beamforming Using {RNS} Arithmetic",
crossref = "Swartzlander:1993:SCA",
pages = "36--43",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kirsch.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11; residue number system",
}
@Book{Klatte:1993:CXC,
editor = "Rudi Klatte and Ulrich Kulisch and Christian Lawo and
Michael Rauch and Andreas Wiethoff",
title = "{C-XSC}: a {C++} class library for extended scientific
computing",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 269",
year = "1993",
ISBN = "3-540-56328-8 (Berlin), 0-387-56328-8 (New York)",
ISBN-13 = "978-3-540-56328-0 (Berlin), 978-0-387-56328-2 (New
York)",
LCCN = "QA76.73.C153 C9 1993",
bibdate = "Fri Jun 24 20:05:29 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "DM74.00",
abstract = "C-XSC is a tool for the development of numerical
algorithms delivering highly accurate and automatically
verified results. It provides a large number of
predefined numerical data types and operators. These
types are implemented as C++ classes. Thus, C-XSC
allows high-level programming of numerical applications
in C and C++. The most important features of C-XSC are:
real, complex, interval, and complex interval
arithmetic; dynamic vectors and matrices; subarrays of
vectors and matrices; dotprecision data types,
predefined arithmetic operators with maximum accuracy;
standard functions of high accuracy; multiple precision
arithmetic and standard functions; rounding control for
I/O data; error handling, and library of problem
solving routines with automatic result verification.
Thus, C-XSC makes the computer more powerful concerning
the arithmetic. C-XSC is immediately usable by C
programmers, easy to learn, user-extendable, and may
also be combined with other tools. The book can be used
as a textbook and as a reference manual. It consists of
an introduction to advanced computer arithmetic, a
chapter describing the programming languages C and C++,
the major chapter ``C-XSC Reference'', sample programs,
and indices.",
acknowledgement = ack-nhfb,
remark = "This book is a translation of an unpublished German
manuscript.",
subject = "C++ (Computer program language); C-XSC; Mathematics;
Numerical analysis; Mathematics.; Numerical analysis.",
tableofcontents = "1 Introduction \\
1.1 Typography \\
1.2 C-XSC: A Class Library in the Programming Language
C++ \\
1.3 C-XSC: A Programming Environment for Scientific
Computing with Result Verification \\
1.4 Survey of C-XSC \\
2 The Programming Languages C and C++ \\
2.1 A Short Introduction to C \\
2.2 Additional Features in C++ \\
3 C-XSC Reference \\
3.1 Constants, Data Types, and Variables \\
3.2 Expressions \\
3.3 Statements \\
3.4 Error Handling \\
3.5 Pitfalls for Programming with C XSC \\
A Syntax Diagrams \\
A.1 Data Types \\
A.2 Management of Vectors and Matrices \\
A.3 Definition of Variables \\
A.4 Expressions \\
A.5 Logical Expressions \\
A.6 Type Castings \\
A.7 Assignments \\
A.8 Arithmetic Standard Functions \\
A.9 Other Functions \\
A.10 Input and Output \\
A.11 Extension of a Syntax Diagram of C++ \\
B The Structure of the C-XSC Package \\
B.1 Header Files \\
B.2 Module Libraries \\
C Error List \\
D Sample Programs \\
D.1 Rounding Control of Arithmetic Operations \\
D.2 Rounding Control of Input and Output \\
D.3 Scalar Product \\
D.4 Transpose of a Matrix \\
D.5 Trace of a Product Matrix \\
D.6 Inverse of a Matrix \\
D.7 Multiple-Precision Arithmetic \\
D.8 Interval Newton Method \\
D.9 Runge-Kutta Method \\
D.10 Complex Polynomial Arithmetic \\
D.11 Automatic Differentiation \\
E Scientific Computation with Verified Results \\
E.1 Evaluation of Polynomials \\
E.2 Matrix Inversion \\
E.3 Linear Systems of Equations \\
E.4 Eigenvalues of Symmetric Matrices \\
E.5 Fast Fourier Transform \\
E.6 Zeros of a Nonlinear Equation \\
E.7 System of Nonlinear Equations \\
E.8 Ordinary Differential Equations",
}
@Book{Koren:1993:CAA,
author = "Israel Koren",
title = "Computer Arithmetic Algorithms",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xiii + 210",
year = "1993",
ISBN = "0-13-151952-2",
ISBN-13 = "978-0-13-151952-7",
LCCN = "76.9.C62 K67 1993",
bibdate = "Thu Sep 1 10:12:51 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@InProceedings{Kornerup:1993:HRM,
author = "Peter Kornerup",
title = "High-Radix Modular Multiplication for Cryptosystems",
crossref = "Swartzlander:1993:SCA",
pages = "277--283",
year = "1993",
bibdate = "Wed Nov 14 18:46:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kornerup.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Book{Kortemeyer:1993:CPT,
author = "Gerd Kortemeyer and others",
title = "{Coprozessoren Programmierung mit Turbo Pascal und
C++: eine grundlegende Einf{\"u}hrung in die
mathematischen Coprozessoren ab 80387 und deren
Programmierung} \toenglish Coprocessor Programming with
{Turbo Pascal} and {C++}\relax \endtoenglish",
publisher = pub-IWT,
address = pub-IWT:adr,
pages = "391",
year = "1993",
ISBN = "3-88322-439-1",
ISBN-13 = "978-3-88322-439-8",
LCCN = "????",
bibdate = "Mon Sep 16 17:08:22 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Kota:1993:NAH,
author = "K. Kota and J. R. Cavallaro",
title = "Numerical Accuracy and Hardware Tradeoffs for {CORDIC}
Arithmetic for Special-Purpose Processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "7",
pages = "769--779",
month = jul,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.237718",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237718",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Krandick:1993:EMF,
author = "Werner Krandick and Jeremy R. Johnson",
title = "Efficient multiprecision floating point multiplication
with optimal directional rounding",
crossref = "Swartzlander:1993:SCA",
pages = "228--233",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Krandick.pdf",
abstract = "An algorithm is described for multiplying
multiprecision floating-point numbers. The algorithm
can produce either the smallest floating-point number
greater than or equal to the true product, or the
greatest floating-point number smaller than or equal to
the true product. Software implementations of
multiprecision floating-point multiplication can reduce
the computation time by a factor of two if they do not
compute the low-order digits of the product of the two
mantissas. However, these algorithms do not necessarily
provide optimally rounded results. The algorithms
described here is guaranteed to produce optimally
rounded results and typically obtains the same
savings.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
University, Linz, Austria",
classification = "C5230 (Digital arithmetic methods)",
confdate = "29 June-2 July 1993",
conflocation = "Windsor, Ont., Canada",
confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
Natural Sci. and Eng. Res.; Council of Canada",
keywords = "ARITH-11; Floating-point numbers; Multiprecision
floating point multiplication; Optimal directional
rounding; Optimally rounded results",
thesaurus = "Floating point arithmetic",
}
@Article{Krishna:1993:TFA,
author = "H. Krishna and J.-D. Sun",
title = "On theory and fast algorithms for error correction in
residue number system product codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "7",
pages = "840--853",
month = jul,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.237724",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237724;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6095",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "The authors develop a coding theory approach to error
control in residue number system product codes. Based
on this coding theory framework, computationally
efficient algorithms are derived for correcting single
errors, double errors, and multiple \ldots{}",
}
@Article{Lee:1993:DAE,
author = "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
title = "Design of an area efficient unit for floating-point
division and square root",
journal = j-J-KOREA-INFO-SCI-SOCIETY,
volume = "20",
number = "7",
pages = "1060--1071",
month = jul,
year = "1993",
CODEN = "HJKHDC",
ISSN = "0258-9125",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors propose an algorithm for a high
performance floating point division and square root
unit that uses a parallel multiplier. The basic
algorithm used in the design is the continued-product
normalization method. In this method, an arbitrary
number is constantly multiplied to the divisor and
dividend and dividend/divisor ends up with quotient/1
and the desired result attained. However this method
requires computation of x*(2-x) and x*(3-x)/2 and this
is quite an overhead. Therefore they propose a new
algorithm to compute (2-x) and (3-x)/2 by using the
modified Booth algorithm. When applied to the
continued-product normalization method, this algorithm
can maximize the inherent parallelism of the
continued-product normalization method, and reduce
computation time by effectively applying pipelining,
and also achieve area efficient design by eliminating
one register and one carry propagate adder needed for
computing (2-x) and (3-x)/2. When the designed unit is
used with the seed generator which has the accuracy of
2/sup -7/, division can be executed in eight cycles and
the square root operation in 13 cycles.",
acknowledgement = ack-nhfb,
classification = "B1265B (Logic circuits); C4240P (Parallel
programming and algorithm theory); C5120 (Logic and
switching circuits); C5230 (Digital arithmetic
methods)",
fjournal = "Journal of the Korea Information Science Society =
Chongbo Kwahakhoe nonmunji",
keywords = "Area efficient unit; Continued-product normalization
method; Floating-point division; Modified Booth
algorithm; Parallel multiplier; Pipelining; Seed
generator; Square root",
language = "Korean",
pubcountry = "South Korea",
thesaurus = "Adders; Digital arithmetic; Parallel algorithms",
}
@InProceedings{Lewis:1993:ALA,
author = "D. M. Lewis",
title = "An accurate {LNS} arithmetic unit using interleaved
memory function interpolator",
crossref = "Swartzlander:1993:SCA",
pages = "2--9",
year = "1993",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lewis.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
summary = "A logarithmic number system (LNS) arithmetic unit
using a new method for polynomial interpolation in
hardware is described. The use of an interleaved memory
reduces storage requirements by allowing each stored
function value to be used in \ldots{}",
}
@Misc{Lindsley:1993:DME,
author = "Brett L. Lindsley",
title = "Device and method for evaluating exponentials",
howpublished = "United States Patent 5,177,702",
day = "5",
month = jan,
year = "1993",
bibdate = "Tue Jan 08 22:31:05 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.freepatentsonline.com/5177702.html",
abstract = "A method and apparatus are described for processing an
input value to provide an output exponential value of a
desired base raised to the power of the input value.
The method includes, and the apparatus included
hardware for implementing, the steps of adjusting the
input value relative to the input value, a
predetermined base of a first exponential value, and
the desired base of the output exponential value to
obtain a first scaled value, modifying the scaled value
to obtain an approximation value, determining the first
exponential value of the approximation value,
generating an adjusted error value relative to the
first scaled value, the approximation value, and a
logarithm of the predetermined base of the first
exponential value, determining a correction value for
the first exponential value and combining the first
exponential value with the correction value to obtain,
substantially, the output exponential value having the
desired base raised to the power of the input value.",
acknowledgement = ack-nhfb,
}
@Article{Linzer:1993:IEF,
author = "E. N. Linzer and E. Feig",
title = "Implementation of Efficient {FFT} Algorithms on Fused
Multiply-Add Architectures",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "1",
year = "1993",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/TSP.1993.193130",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sun Feb 20 10:11:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}
@Article{Lo:1993:BCP,
author = "J.-C. Lo and S. Thanawastien and T. R. N. Rao",
title = "{Berger} check prediction for array multipliers and
array dividers",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "7",
pages = "892--896",
month = jul,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.237731",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See correction \cite{Lo:1996:CBC}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237731",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Louie:1993:DRD,
author = "M. E. Louie and M. D. Ercegovac",
title = "On Digit-Recurrence Division Implementations for Field
Programmable Gate Arrays",
crossref = "Swartzlander:1993:SCA",
pages = "202--209",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Louie.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Louie:1993:DRS,
author = "M. E. Louie and M. D. Ercegovac",
booktitle = "Proceedings of the {IEEE} Workshop on {FPGAs} for
Custom Computing Machines, 5--7 April 1993",
title = "A digit-recurrence square root implementation for
field programmable gate arrays",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "178--183",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Creating efficient arithmetic processors requires a
pairing of high speed arithmetic algorithms with
optimal mapping strategies for a given technology. The
authors propose bit reduction as key to an efficient
pairing process for lookup table based \ldots{}",
}
@InProceedings{Lozier:1993:UGF,
author = "D. W. Lozier",
title = "An underflow-induced graphics failure solved by {SLI}
arithmetic",
crossref = "Swartzlander:1993:SCA",
pages = "10--17",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lozier.pdf",
abstract = "Floating-point underflow is often regarded as either
harmless or as an indication that the computational
algorithm is in need of scaling. A counterexample to
this view is given of a function for which contour
plotting is difficult due to floating-point underflow.
The function arose as an asymptotic solution to a model
problem in turbulent combustion in which two chemical
species (fuel and oxidizer) mix and react in a vortex
field. Scaling is not a viable option because of
extreme sensitivity to a small physical parameter.
Standard graphics software packages produce erroneous
contours without any indication of difficulty. This
example provides support for considering symmetric
level-index arithmetic, a new form of computer
arithmetic which is immune to underflow and overflow.",
acknowledgement = ack-nhfb,
affiliation = "Nat. Inst. of Stand. and Technol., Gaithersburg, MD,
USA",
classification = "C5230 (Digital arithmetic methods); C6130B (Graphics
techniques)",
confdate = "29 June-2 July 1993",
conflocation = "Windsor, Ont., Canada",
confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
Natural Sci. and Eng. Res.; Council of Canada",
keywords = "ARITH-11; Asymptotic solution; Computer arithmetic;
Contour plotting; Floating point underflow; Graphics
failure; Graphics software packages; Turbulent
combustion",
thesaurus = "Computer graphics; Floating point arithmetic",
}
@Article{Mandelbaum:1993:SRS,
author = "D. M. Mandelbaum",
title = "Some results on a {SRT} type division scheme",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "1",
pages = "102--106",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.192218",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192218",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Maryoung:1993:DBP,
author = "James Maryoung",
title = "Development of a binary phase shift keying modem
receiver with a floating point processor {TMS320C30}",
type = "Thesis ({M.S.})",
school = "California State University, Long Beach",
address = "Long Beach, CA, USA",
pages = "xi + 265",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Signal processing --- Algorithms.; Signal processing
--- Digital techniques.",
}
@Article{Masotti:1993:FNE,
author = "G. Masotti",
title = "Floating-point numbers with error estimates",
journal = j-CAD,
volume = "25",
number = "9",
pages = "524--538",
month = sep,
year = "1993",
CODEN = "CAIDA5",
ISSN = "0010-4485 (print), 1879-2685 (electronic)",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Addresses the problem of precision in floating-point
computations. A method for estimating the errors which
affect intermediate and final results is presented, and
a synthesis of many software simulations is discussed.
The basic idea is to represent floating-point numbers
by means of a data-structure collecting value and
estimated error information. It has been found that,
under certain circumstances, the estimate of the
absolute error is accurate and has a compact
statistical distribution. It is also shown that, by
monitoring the estimated relative error during a
computation (an ad hoc definition of relative error is
used), the validity of results can be ensured. The
error estimates enable robust algorithms to be
implemented and ill-conditioned problems to be
detected. A hardware implementation of the method by
means of a special floating-point processor is
outlined. A dynamic extension of number precision,
under the control of error estimates, is also
advocated, in order to compute results within given
error bounds.",
acknowledgement = ack-nhfb,
affiliation = "Dept. di Elettr. Inf. e Sistem., Universita degli
Studi di Bologna, Bologna, Italy",
classification = "C5230 (Digital arithmetic methods)",
keywords = "Compact statistical distribution; Computer arithmetic;
Data-structure collecting value; Dynamic extension;
Dynamic precision extension; Error bounds; Error
estimates; Final results; Floating-point numbers;
Floating-point processor; Hardware implementation;
Ill-conditioned problems; Intermediate results;
Numerical accuracy; Relative error; Robust algorithms;
Software simulations; Validity",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Error statistics; Roundoff
errors",
}
@Article{Mazenc:1993:CFU,
author = "Christophe Mazenc and Xavier Merrheim and Jean-Michel
Muller",
title = "Computing functions $ \cos^{-1} $ and $ \sin^{-1} $
using {Cordic}",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "1",
pages = "118--122",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.192222",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{McClellan:1993:AFP,
author = "Scott McClellan",
title = "Alternatives to floating point representation",
type = "Honors paper",
number = "4",
institution = "United States Naval Academy Honors Paper. Dept. of
Mathematics",
pages = "various",
year = "1993",
bibdate = "Sat May 04 17:18:52 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.",
remark = "Honors paper--United States Naval Academy, 1993.",
}
@Article{McKeeman:1993:AOC,
author = "W. M. McKeeman",
title = "Avoiding Overflow in Constant Expression Evaluation",
journal = j-JCLT,
volume = "5",
number = "1",
pages = "27--31",
month = sep,
year = "1993",
ISSN = "1042-5721",
bibdate = "Fri Nov 21 14:40:20 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of {C} Language Translation",
remark = "Predicting overflow before it occurs",
}
@InProceedings{McQuillan:1993:NAV,
author = "S. E. McQuillan and J. V. McCanny and R. Hamill",
title = "New algorithms and {VLSI} architectures for {SRT}
division and square root",
crossref = "Swartzlander:1993:SCA",
pages = "80--86",
year = "1993",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-11",
summary = "Radix two algorithms for SRT division and
square-rooting are developed. For these schemes, the
result digits and the residuals are computed
concurrently and the computations in adjacent rows are
overlapped. Consequently, their performance should
\ldots{}",
}
@Article{Meier:1993:EMC,
author = "Willi Meier and Othmar Staffelbach",
title = "Efficient Multiplication on Certain Nonsupersingular
Elliptic Curves",
journal = j-LECT-NOTES-COMP-SCI,
volume = "740",
pages = "333--344",
year = "1993",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:48:51 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0740.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0740/07400333.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0740/07400333.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "CRYPTO; cryptology",
}
@InProceedings{Mellott:1993:GMG,
author = "Jonathon D. Mellott and Jeremy C. Smith and Fred J.
Taylor",
title = "The {Gauss} Machine: a {Galois}-Enhanced Quadratic
Residue Number System Systolic Array",
crossref = "Swartzlander:1993:SCA",
pages = "156--162",
year = "1993",
DOI = "https://doi.org/10.1109/ARITH.1993.378097",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Mellott.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11; residue arithmetic; residue number system",
summary = "The Gauss machine is a SIMD systolic array
architecture that takes advantage of the
Galois-enhanced residue number system (GEQRNS) to form
reduced-complexity arithmetic elements. The Gauss
machine is targeted at front-end signal and image
processing applications. A discrete prototype that
achieves a peak rating of 320 million complex
arithmetic operations per second while operating at 10
MHz has been constructed. A VLSI implementation of the
Gauss machine's processor cell has been created. The
VLSI implementation is implemented in 2.0-$\mu$m CMOS
and achieves greater than 20-MHz performance, using
less than 2.0-mm$^2$ die area. It is shown that
techniques for defect tolerance in RNS systolic arrays
can result in substantial yield enhancement, thereby
making larger than conventional (ULSI) systems
possible",
}
@InProceedings{Merrheim:1993:FEP,
author = "Xavier Merrheim and Jean-Michel Muller and Hong-Jin
Yeh",
title = "Fast Evaluation of Polynomials and Inverses of
Polynomials",
crossref = "Swartzlander:1993:SCA",
pages = "186--192",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Merrheim.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@MastersThesis{Mesfin:1993:IHP,
author = "Biniam Mesfin",
title = "Implementation of a high performance floating point
unit multiplier",
type = "Thesis ({M.A.Sc.})",
school = "University of Windsor",
address = "Windsor, ON, Canada",
year = "1993",
ISBN = "0-315-78864-X",
ISBN-13 = "978-0-315-78864-0",
LCCN = "????",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "National Library of Canada = Bibliotheque nationale du
Canada; Canadian theses = Theses canadiennes",
acknowledgement = ack-nhfb,
remark = "3 microfiches. University Microfilms order no.
UMI00399117",
}
@Article{Metzger:1993:IFR,
author = "D. Metzger",
title = "Investigation of Finite Register Length Effects on
{Winograd} {FFT} Computation Using Floating Point
Math",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "1",
pages = "449",
month = jan,
year = "1993",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}
@Manual{MicrosoftCorporation:1993:PGM,
author = "{Microsoft Corporation}",
title = "Programmer's guides: {Microsoft Visual C++}
development system for {Windows}: version 1.0",
organization = "Microsoft Corp.",
address = "Redmond, WA, USA",
pages = "various",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "C++ (Computer program language); Microsoft Visual
C++.",
remark = "C++ tutorial: introduction to C++: a first look at
C++; C++ enhancements to C; references; classes:
introduction to classes; classes and dynamic memory
allocation; more features of classes; inheritance and
polymorphism; operator overloading and conversion
functions; object-oriented design: fundamentals of
object-oriented design; design example, a windowing
class --- Class library user's guide for the Microsoft
Foundation Class Library: introducing the class
library; creating a new application with AppWizard;
creating the document, view; constructing the user
interface with App Studio; binding visual objects to
code using ClassWizard; adding a dialog box; enhancing
views, printing; adding context-sensitive help;
general-prupose classes; CObject class; collections;
files and serialization; diagnostics; exceptions;
programming with VBX controls; OLE support ---
Programming techniques: improving program performance:
using precompiled headers; managing memory for 16-bit C
programs; controlling floating-point math operations;
special environments: programming for Windows;
programming with mixed languages; writing portable C
programs. [Section one of the book], the C++ tutorial,
provides an introduction to the C++ language and
object-oriented programming. [It] assumes [the reader
is] familiar with C \ldots{} [Section two] contains a
tutorial for the Microsoft Foundation Class Library.
The class library is a set of C++ classes that
encapsulate the functionality of applications written
for the Microsoft Windows operating system \ldots{}
[Section three], programming techniques, describes how
to take advantage of the special features of Microsoft
Visual C++. The topics covered \ldots{} include
language extensions, special-purpose library functions,
and the interaction between programming strategies and
compiler options. [This section] is divided into two
parts. Part I, ``Improving Program Performance,'' helps
[the reader] write more efficient programs \ldots{}
Part 2, ``Special Environments,'' covers techniques
specific to certain programming situations. -Introds.",
}
@Article{Mikami:1993:RER,
author = "N. Mikami and M. Kobayashi and Y. Yokoyama",
title = "Roundoff-error reduction for evaluation of a function
by polynomial approximation with error feedback in
fixed-point arithmetic",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "5",
pages = "1953--1955",
month = may,
year = "1993",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The relationship between Hornor's method for
polynomial evaluation and a first-order recursive
filter with error feedback (EFB) is described. It is
shown that EFB is a useful technique for reducing the
roundoff errors that occur in evaluating a \ldots{}",
}
@InProceedings{Montuschi:1993:CSM,
author = "Paolo Montuschi and Luigi Ciminiera",
title = "$ n \times n $ Carry-Save Multipliers without Final
Addition",
crossref = "Swartzlander:1993:SCA",
pages = "54--61",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Montuschi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Montuschi:1993:RIT,
author = "P. Montuschi and L. Ciminiera",
title = "Reducing iteration time when result digit is zero for
radix $2$ {SRT} division and square root with redundant
remainders",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "2",
pages = "239--246",
month = feb,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.204797",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See remark \cite{Montuschi:1995:RRI}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204797",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A new architecture is presented for shared radix 2
division and square root whose main characteristic is
the ability to avoid any addition/subtraction, when the
digit 0 has been selected. The solution presented uses
a redundant representation of the \ldots{}",
}
@Article{Motteler:1993:APF,
author = "Frederick C. Motteler",
title = "Arbitrary Precision Floating-Point Arithmetic",
journal = j-DDJ,
volume = "18",
number = "9",
pages = "28, 30, 32, 34, 84, 86--87",
month = sep,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 03 09:15:43 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "The C library presented was developed with IEEE-754
compatibility and portability as its primary goals. Its
first application was as part of a portable cross
compiler. It is a general-purpose library that supports
single, double, double-extended, and longer IEEE-754
like formats. The library has been ported to and tested
on a variety of systems including CP/M, PCs running
MS-DOS, PCs running Coherent, Sun 3s, Sparcstations
(Sun's C compiler), and the IBM RS/6000 under AIX. The
package is K and R, ANSI C, and C++ compatible. A
table-driven tester included with the library checks if
it has compiled properly. The tester also gives an idea
of what the package is capable of doing.",
acknowledgement = ack-nhfb,
affiliation = "Zetron Inc., Redmond, WA, USA",
classification = "C5230 (Digital arithmetic methods); C7310
(Mathematics)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "C library; Coherent; CP/M; Double-extended;
Floating-point arithmetic; General-purpose library; IBM
RS/6000; IEEE-754 compatibility; IEEE-754 like formats;
MS-DOS; PCs; Portability; Portable cross compiler;
Sparcstations; Sun 3s; Table-driven tester",
thesaurus = "C listings; Digital arithmetic; Mathematics computing;
Software portability; Subroutines",
}
@Misc{Ng:1993:FV,
author = "K-C Ng",
title = "{FDLIBM} Version 5.3",
howpublished = "Web site",
year = "1993",
bibdate = "Thu Oct 17 06:21:14 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.netlib.org/fdlibm/readme",
acknowledgement = ack-nhfb,
keywords = "FDLIBM (Freely Distributable Math Library)",
}
@InProceedings{Nguyen:1993:LDR,
author = "Q. H. Nguyen and I. Kollar",
booktitle = "Instrumentation and Measurement Technology Conference,
1993. {IMTC/93}. Conference Record., {IEEE. 18--20} May
1993",
title = "Limited dynamic range of spectrum analysis due to
roundoff errors of the {FFT}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "47--50",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Roundoff errors of the block-float fast Fourier
transform (FFT) are treated. Special emphasis is given
to the case when signals containing sine waves are
analyzed. In the detection and analysis of sine waves,
root-mean-square values and overall \ldots{}",
}
@Article{North:1993:FPA,
author = "R. C. North and J. R. Zeidler and W. H. Ku and T. R.
Albert",
title = "A floating-point arithmetic error analysis of direct
and indirect coefficient updating techniques for
adaptive lattice filters",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "41",
number = "5",
pages = "1809--1823",
month = may,
year = "1993",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "The ways in which finite precision arithmetic effects
can deleteriously manifest themselves in both the
stochastic gradient and the recursive least squares
adaptive lattice filters are discussed. closed form
expressions are derived for the steady-state \ldots{}",
}
@Article{Ozawa:1993:SAE,
author = "K. Ozawa and M. Miyazaki",
title = "A summation algorithm with error correction for
parallel computers",
journal = j-SYS-COMP-JAPAN,
volume = "24",
number = "7",
pages = "62--68",
month = "????",
year = "1993",
CODEN = "SCJAEP",
ISSN = "0882-1666 (print), 1520-684X (electronic)",
ISSN-L = "0882-1666",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Proposes an algorithm to accurately compute the sum of
floating-point numbers on parallel computers. This
algorithm is an extension of the well-known recursive
doubling technique which computes the sum of n
floating-point number in log/sub 2/n parallel steps.
The time complexity of the present algorithm also is
O(logn), and the space complexity is O(n). This
algorithm enables a highly accurate result to be
obtained with guarantee. The theoretical analysis and
the numerical experiments on a parallel computer show
that this algorithm is as accurate as Kahan's, which is
the fastest and an accurate serial algorithm for the
summation of the numbers, and also that the present
algorithm is faster than Kahan's provided that two or
more processors are available.",
acknowledgement = ack-nhfb,
affiliation = "Coll. of Gen. Educ., Tohoku University, Sendai,
Japan",
classification = "C4110 (Error analysis in numerical methods); C4240P
(Parallel programming and algorithm theory)",
fjournal = "Systems and computers in Japan",
keywords = "accurate floating-point summation; correct rounding;
error correction; floating-point numbers; guaranteed
accuracy; parallel computation; parallel computers;
recursive doubling; recursive doubling technique;
round-off error analysis; space complexity; summation;
summation algorithm; time complexity",
thesaurus = "computational complexity; error correction; parallel
algorithms",
}
@PhdThesis{Pan:1993:TFVa,
author = "Jing Pan",
title = "Toward a formal verification of a floating-point
coprocessor and its composition with a central
processing unit",
type = "Thesis ({Ph.D.})",
school = "Computer Science Department, University of California,
Davis",
address = "Davis, CA, USA",
pages = "221",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Pan:1993:TFVb,
author = "Jing Pan and K. N. Levitt and M. Archer and S.
Kalvala",
title = "Towards a formal verification of a floating point
coprocessor and its composition with a central
processing unit",
journal = j-IFIP-TRANS-A,
volume = "A20",
pages = "427--447",
month = "????",
year = "1993",
CODEN = "ITATEC",
ISSN = "0926-5473",
bibdate = "Tue Dec 12 09:27:13 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Higher Order Logic Theorem Proving and its
Applications IFIP TC\slash WG10.2 International
Workshop - HOL '92.",
abstract = "The authors discuss verification (ultimately down to
the microcode level) of a microprocessor that consists
of a central processing unit that is the master of a
floating point coprocessor; the design is drawn from
the MC68881 floating point coprocessor slaved to the
MC68000, but greatly simplified. The coprocessor in
isolation is verified with respect to a specification
that captures the IEEE floating point standard. In the
authors system, CPU and floating point instructions are
allowed to execute concurrently, but the appearance to
the programmer of the composed system is that of a
sequentially executing instruction stream. The CPU and
floating point coprocessor communicate through the
four-phase handshaking protocol. The verification
involves reasoning about a form of behavioural
abstraction wherein concurrently executing instruction
steams are mapped to a sequential stream.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, California University,
Davis, CA, USA",
classification = "C4210 (Formal logic); C5130 (Microprocessor chips);
C5230 (Digital arithmetic methods); C6110B (Software
engineering techniques)",
confdate = "21-24 Sept. 1992",
conflocation = "Leuven, Belgium",
fjournal = "IFIP Transactions. A. Computer Science and
Technology",
keywords = "Behavioural abstraction; Central processing unit;
Concurrently executing instruction steams; Floating
point coprocessor; Formal verification; Four-phase
handshaking protocol; MC68000; MC68881; Microprocessor;
Reasoning; Sequentially executing instruction stream;
Specification",
pubcountry = "Netherlands",
thesaurus = "Digital arithmetic; Formal verification;
Microprocessor chips; Theorem proving",
}
@InProceedings{Panneerselvam:1993:MAF,
author = "G. Panneerselvam and B. Nowrouzian",
title = "Multiply-add fused {RISC} architectures for {DSP}
applications",
crossref = "IEEE:1993:PIP",
volume = "1",
pages = "108--111",
year = "1993",
DOI = "https://doi.org/10.1109/PACRIM.1993.407210",
bibdate = "Sun Feb 20 10:47:10 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The development of a fixed-point bit-parallel
multiply-add fused (MAF) architecture together with a
corresponding VLSI implementation is presented. The
proposed MAF implementation employs 1.2 CMOS
technology. This MAF implementation finds a variety of
practical applications in high-speed real-time digital
signal processing. The MAF implementation employs a
parallel modified Booth multiplier incorporating an
array of carry-save adders for the addition of the
intermediate partial products, and a hardware efficient
carry-skip adder for carry propagation. The performance
characteristics of the MAF implementation have been
successfully verified by an HSPICE simulation at speeds
of up to 100 MHz.",
acknowledgement = ack-nhfb,
}
@Article{Parhami:1993:IAS,
author = "B. Parhami",
title = "On the implementation of arithmetic support functions
for generalized signed-digit number systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "3",
pages = "379--384",
month = mar,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.210182",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=210182",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Parker:1993:OHS,
author = "A. Parker",
title = "Optimization of high speed function generation using
table-lookup",
journal = j-TRANS-SOC-COMP-SIM,
volume = "10",
number = "2",
pages = "105--114",
month = jun,
year = "1993",
CODEN = "TSCSEV",
ISSN = "0740-6797",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A process is presented for the use of generic operator
optimization for the evaluation of unary floating point
functions using table lookup. The process involves the
identification of an underlying architecture and the
symbolic-numeric optimization of operators to minimize
a least-squares representation of total error. The
approach is illustrated for the case of floating point
division.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Alabama
University, Huntsville, AL, USA",
classification = "C1160 (Combinatorial mathematics); C4120 (Functional
analysis); C6130 (Data handling techniques)",
fjournal = "Transactions of the Society for Computer Simulation",
keywords = "Floating point division; High speed function
generation; Least-squares representation;
Symbolic-numeric optimization; Table lookup",
thesaurus = "Equivalence classes; Function evaluation; Symbol
manipulation; Table lookup",
}
@Book{Pichat:1993:IDC,
author = "Mich{\`e}le Pichat and Jean Vignes",
title = "Ing{\'e}nierie du contr{\^o}le de la pr{\'e}cision des
calculs sur ordinateur",
publisher = "Editions Technip",
address = "Paris, France",
pages = "xvii + 233",
year = "1993",
ISBN = "2-7108-0653-3",
ISBN-13 = "978-2-7108-0653-0",
LCCN = "TJ213 .P478 1993",
bibdate = "Wed Nov 24 12:28:18 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Collection Informatique",
acknowledgement = ack-nhfb,
subject = "Automatic control; Microcomputers",
}
@Article{Plauger:1993:FCE,
author = "P. J. Plauger",
title = "Floating-Point {C} Extensions",
journal = j-CUJ,
volume = "11",
type = "{Standard C}",
number = "9",
pages = "10--??",
month = sep,
year = "1993",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Book{Plauger:1993:PPIc,
author = "P. J. Plauger",
title = "Programming on Purpose {III}: Essays on Software
Technology",
volume = "3",
publisher = pub-PHPTR,
address = pub-PHPTR:adr,
pages = "viii + 224",
year = "1993",
ISBN = "0-13-328113-2",
ISBN-13 = "978-0-13-328113-2",
LCCN = "QA76.76.D47 P53 1994",
bibdate = "Wed Jul 6 14:26:01 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$19.95",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
remark = "Originally published in the author's monthly column in
Computer language magazine, 1986-1992. Contents: Volume
I: Essays on software design -- volume II: Essays on
software people -- volume III: Essays on software
technology.",
tableofcontents = "You Must Be Joking \\
Computer Arithmetic \\
Floating-Point Arithmetic \\
The Central Folly \\
Safe Math \\
Do-It-Yourself Math Functions \\
Locking the Barn Door \\
Half a Secret \\
It's (Almost) Alive \\
The (Almost) Right Stuff \\
Instant Lies \\
What Meets the Eye \\
Technicolor and Cinemascope \\
What Meets the Ear \\
Warm Fuzzies \\
Font Follies \\
Text Editors \\
Approximating Functions \\
Economizing Polynomials \\
Technical Writing \\
All I Want to Do Is \\
Programming for the Billions \\
All Sorts of Sorts \\
Transforming Strings \\
Books for Our Times \\
Through the Grapevine \\
List of Columns \\
Bibliography \\
Index",
}
@Article{Posch:1993:BKR,
author = "K. C. Posch and R. Posch",
title = "{Basiserweiterung mit einer Konvolutionssumme in
Restklassenzahlensystemen}. ({German}) [{Base}
Extension Using a Convolution Sum in Residue Number
Systems]",
journal = j-COMPUTING,
volume = "50",
number = "2",
pages = "93--104",
year = "1993",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68M07 (11Y16)",
MRnumber = "94e:68024",
bibdate = "Mon Oct 11 20:38:38 MDT 1999",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
language = "German",
}
@Article{Pugh:1993:FPC,
author = "Kenneth Pugh",
title = "Floating Point Constants",
journal = j-CUJ,
volume = "11",
type = "Questions and Answers",
number = "10",
pages = "130--??",
month = oct,
year = "1993",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Reid:1993:LIA,
author = "John Reid",
title = "{Language Independent Arithmetic} ({LIA}) --- a {Draft
International Standard} ({DIS})",
journal = j-SIGNUM,
volume = "28",
number = "1",
pages = "2--7",
month = jan,
year = "1993",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:23 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "LIA is now an International Standard, ISO/IEC
10967-1:1994; it is ``92 pages of small print, densely
mathematical, not counting 8 pages of front matter, and
it is not available electronically.'' Its adoption has
been rather controversial.",
abstract = "The UK and US votes have been decided on the draft
international standard ISO/IEC CD 10967-1:1992:
language independent arithmetic-part 1: integer and
floating point arithmetic. The stated goals of the
draft are: to enhance the portability of numeric
programs across a wide range of numeric architectures.
To help programming languages express the semantics of
their numerical types. It defines integer and
(normalized and denormalized) floating point types. It
defines integer and (normalized and denormalized)
floating point types. It specifies the primitive
computational operations with source and destination
operands of the same type, comparison operations on two
operands of the same type, and conversions from any
arithmetic type to any other arithmetic type. The
values of parameters define the exact arithmetic
behaviour of any particular platform.",
acknowledgement = ack-nhfb,
affiliation = "Rutherford Appleton Lab., Didcot, UK",
classification = "C5230 (Digital arithmetic methods); C6140D (High
level languages)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "International standard; Language independent
arithmetic; Numeric architectures; Numeric programs;
Portability; Programming languages",
thesaurus = "Digital arithmetic; High level languages; Standards",
}
@InProceedings{Richardson:1993:ETR,
author = "S. E. Richardson",
title = "Exploiting trivial and redundant computation",
crossref = "Swartzlander:1993:SCA",
pages = "220--227",
year = "1993",
bibdate = "Thu Jun 20 10:16:15 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Richardson.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-11",
}
@Article{Ris:1993:WFP,
author = "Fred Ris and Ed Barkmeyer and Craig Schaffert and
Peter Farkas",
title = "When Floating-Point Addition Isn't Commutative",
journal = j-SIGNUM,
volume = "28",
number = "1",
pages = "8--13",
month = jan,
year = "1993",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/156301.156303",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:23 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the early 1980s, the IEEE floating-point standards
(754 for binary formats adopted in 1985 and 854 for
more general situations adopted in 1987) were
developed. There are now many more-or-less IEEE 754
conformant products on the market. A fully compliant
implementation must provide conforming representations
of floating-point values, perform arithmetic operations
as specified by the standard, provide four rounding
modes and five exception flags defined by the standard,
support infinities, NaNs, signed zeros, and unordered
comparisons, and provide access to all these features
from programming languages (as supported by the
compiler and runtime library). Not surprisingly, very
few implementations comply fully with the IEEE 754
standard in all respects. But one might imagine that if
there were such compliance one could expect bit-for-bit
identical results for a given algorithm executed on any
conforming implementation. The paper explains why this
is not always the case.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "IBM Federal Syst. Co., Boulder, CO, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "Arithmetic operations; Conforming implementation;
Exception flags; Floating-point addition;
Floating-point values; IEEE 754; IEEE floating-point
standards; Rounding modes",
thesaurus = "Digital arithmetic; Standards",
}
@InProceedings{Samani:1993:SVP,
author = "D. M. Samani and J. Ellinger and E. J. Powers and E.
E. Swartzlander",
title = "Simulation of variable precision {IEEE} floating point
using {C}++ and its application in digital signal
processor design",
crossref = "IEEE:1993:PMS",
pages = "1509--1514 vol.2",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We use a C++ class to transparently emulate
variable-precision floating point arithmetic using
standard arithmetic. This allows the determination of
an algorithm's susceptibility to errors produced by
finite-precision arithmetic and the determination of
the minimum precision necessary for stability. The
class, called Real, offers several advantages for many
applications, e.g., ALU design, signal processing,
systolic and lattice filter design, etc. Since it
supports the IEEE floating point standard, it produces
identical results on any compliant platform. An
algorithm can be adapted for simulation with minimal
effort and without interfering with normal operation.
We also consider how the acceptance of the IEEE
standard and the development of fast hardware for
microcomputers have changed common assumptions about
algorithm timing. Finally, we examine the potential use
of the new floating point DSP chips for adaptive
filtering. Historically, the computational requirements
of adaptive filters confined implementations to
specialized hardware or supercomputers. Today's DSP
chips offer a relatively inexpensive alternative. We
have implemented several adaptive filtering algorithms
that are based on Least Squares estimation criterion on
Motorola's DSP96002. Our experience indicates that the
DSP96K is a viable medium for such algorithms and one
can expect a ten-fold speed improvement over a i486
running at 50 MHz.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Texas
University, Austin, TX, USA",
classification = "B1265F (Microprocessors and microcomputers); B1270F
(Digital filters); B6140 (Signal processing and
detection); C5135 (Digital signal processing chips);
C5220P (Parallel architecture); C5230 (Digital
arithmetic methods); C5240 (Digital filters); C5260
(Digital signal processing); C6140D (High level
languages)",
keywords = "Adaptive filtering; Algorithm timing; ALU design; C++
language; Digital signal processor design; DSP chips;
Floating point arithmetic; IEEE standard; Lattice
filter; Least squares estimation criterion; Motorola
DSP96002; Real; Systolic filter; Variable precision
IEEE floating point",
thesaurus = "Adaptive filters; C language; Digital signal
processing chips; Floating point arithmetic; Lattice
filters; Least squares approximations; Systolic
arrays",
}
@InProceedings{Sarma:1993:MAR,
author = "D. D. Sarma and D. W. Matula",
title = "Measuring the Accuracy of {ROM} Reciprocal Tables",
crossref = "Swartzlander:1993:SCA",
pages = "95--102",
year = "1993",
bibdate = "Wed Nov 14 18:47:17 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Sarma.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Scannell:1993:DMM,
author = "Robert K. Scannell and John K. Hagge",
title = "Development of a Multichip Module {DSP}",
journal = j-COMPUTER,
volume = "26",
number = "4",
pages = "13--21",
month = apr,
year = "1993",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Tue May 14 16:20:44 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A highly modular processor architecture based on
off-the-shelf components supports an MCM design
implementation that delivers 400 million floating-point
operations per second in a 75-gram package.",
acknowledgement = ack-nhfb,
affiliation = "Rockwell Int., Anaheim, CA, USA",
classification = "B0170J (Product packaging); B1265F (Microprocessors
and microcomputers); B2220J (Hybrid integrated
circuits); B2570 (Semiconductor integrated circuits);
C5135 (Digital signal processing chips)",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "Cost; Highly modular processor architecture;
Interconnect-substrate design; MCM package assembly;
Multichip module DSP; Signal processor packaging
design; Size; Weight",
thesaurus = "Digital signal processing chips; Multichip modules",
}
@Article{Schorn:1993:AAR,
author = "Peter Schorn",
title = "An Axiomatic Approach to Robust Geometric Programs",
journal = j-J-SYMBOLIC-COMP,
volume = "16",
number = "2",
pages = "155--166 (or 155--165??)",
month = aug,
year = "1993",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "68U07",
MRnumber = "94k:68196",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classcodes = "C4260 (Computational geometry); C1180 (Optimisation
techniques)",
corpsource = "Inst. fur Theor. Inf., Eidgenossische Tech.
Hochschule, Zurich, Switzerland",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "axiomatic approach; computational geometry; digital
arithmetic; floating point arithmetic; geometric;
imprecise primitives; non-trivial; plane sweep
algorithm; primitives; programming; robust geometric
programs",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Schulte:1993:ERC,
author = "M. Schulte and E. Swartzlander",
title = "Exact rounding of certain elementary functions",
crossref = "Swartzlander:1993:SCA",
pages = "138--145",
year = "1993",
bibdate = "Thu Jun 20 10:16:17 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf;
http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Schulte.pdf",
abstract = "An algorithm is described which produces exactly
rounded results for the functions of reciprocal, square
root, 2/sup x/, and log 2/sup x/. Hardware designs
based on this algorithm are presented for floating
point numbers with 16- and 24-b significands. These
designs use a polynomial approximation in which
coefficients are originally selected based on the
Chebyshev series approximation and are then adjusted to
ensure exactly rounded results for all inputs. To
reduce the number of terms in the approximation, the
input interval is divided into subintervals of equal
size and different coefficients are used for each
subinterval. For floating point numbers with 16-b
significands, the exactly rounded value of the function
can be computed in 51 ns on a 20-mm/sup 2/ chip. For
floating point numbers with 24-b significands, the
functions can be computed in 80 ns on a 98-mm/sup 2/
chip.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Texas
University, Austin, TX, USA",
classification = "C4120 (Functional analysis); C5230 (Digital
arithmetic methods)",
confdate = "29 June--2 July 1993",
conflocation = "Windsor, Ont., Canada",
confsponsor = "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
Natural Sci. and Eng. Res.; Council of Canada",
keywords = "ARITH-11; Elementary functions; Exact rounding;
Floating point numbers; Polynomial approximation;
Reciprocal; Rounded results; Square root",
thesaurus = "Floating point arithmetic; Function evaluation",
}
@InProceedings{Schulte:1993:PHD,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "Parallel Hardware Designs for Correctly Rounded
Elementary Functions",
crossref = "Corliss:1993:AIC",
pages = "65--87 (or 65--88??)",
year = "1993",
bibdate = "Tue Oct 22 13:37:58 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1993:TMC,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "Truncated Multiplication with Correction Constant",
crossref = "Eggermont:1993:VSP",
pages = "388--396",
year = "1993",
bibdate = "Sun Mar 04 10:38:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1993-02.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Schwarz:1993:HRAa,
author = "E. Schwarz",
title = "High-radix algorithms for high-order arithmetic
operations",
type = "Technical Report",
number = "CSL-TR-93-559",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jan,
year = "1993",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@PhdThesis{Schwarz:1993:HRAb,
author = "Eric Mark Schwarz",
title = "High-radix algorithms for high-order arithmetic
operations",
type = "Thesis ({Ph.D.})",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "224",
month = apr,
year = "1993",
bibdate = "Mon Jan 07 22:38:06 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Many common algorithms for high-order arithmetic
operations require an initial approximation. The
Newton--Raphson algorithm starts with an approximation
and then quadratically converges on the solution. The
initial approximation determines the number of
iterations of the algorithm and is typically
implemented as a look-up table in the form of a ROM or
PLA. A novel method is suggested which describes
high-order arithmetic operations with a partial product
array. This method applies to the operations of
division, reciprocal, square root, natural logarithm,
exponential, and trigonometric functions. The partial
product array of Boolean elements which describes the
operation can be summed on an existing floating-point
multiplier. The hardware needed is only the logic gates
to create the Boolean elements in the array and a
multiplexor, and the latency is that of the multiplier.
Thus, by reusing a floating-point multiplier, a
high-precision approximation to a high-order arithmetic
operation can be implemented with a low marginal
cost.\par
This dissertation describes the implementation and
shows a method for deriving partial product arrays to
approximate arithmetic operations. Then the proposed
method is applied and evaluated for several operations.
The proposed method yields a minimum approximation of
twelve bits correct for the reciprocal operation and
sixteen bits for the square root operation. The
proposed method is shown to be as small as 0.05\% the
size (in gates) of an equivalent precision look-up
table and has up to four times the accuracy (in bits)
as an equivalent latency polynomial approximation.
Also, three new iterative algorithms to increase the
precision of the approximations and a theoretical
analysis of the partial product array representation
are detailed. Thus, high-radix algorithms of many
arithmetic operations are possible at low cost.",
acknowledgement = ack-nhfb,
keywords = "division; elementary functions; exponential;
logarithm; PPA (partial product array); reciprocal
square root; square root",
remark = "AAT 9317816. ProQuest document ID 746798521.",
}
@InProceedings{Schwarz:1993:HSA,
author = "Eric M. Schwarz and Michael J. Flynn",
title = "Hardware starting approximation for the square root
operation",
crossref = "Swartzlander:1993:SCA",
pages = "103--111",
year = "1993",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Schwarz.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-11",
summary = "A method for obtaining high-precision approximations
of high-order arithmetic operations is presented. These
approximations provide an accurate starting
approximation for high-precision iterative algorithms,
which translates into few iterations and \ldots{}",
}
@Article{Schwarz:1993:PHR,
author = "E. M. Schwarz and M. J. Flynn",
title = "Parallel high-radix nonrestoring division",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "10",
pages = "1234--1246",
month = oct,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.257709",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=257709",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Schwarz:1993:UFM,
author = "Eric Mark Schwarz and M. J. (Michael J.) Flynn",
title = "Using a floating-point multiplier's internals for
high-radix division and square root",
type = "Technical report",
number = "CSL-TR-93-554",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
pages = "iv + 45",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic.",
remark = "``January 1993.'' Abstract: ``A method for obtaining
high-precision approximations of high-order arithmetic
operations at low-cost is presented in this study.
Specifically, high-precision approximations of the
reciprocal (12 bits worst case) and square root (16
bits) operations are obtained using the internal
hardware of a floating-point multiplier without the use
of look-up tables. The additional combinatorial logic
necessary is very small due to the reuse of existing
hardware. These low-cost high-precision approximations
are used by iterative algorithms to perform the
operations of division and square root. The method
presented also applies to several other high-order
arithmetic operations. Thus, high-radix algorithms for
high-order arithmetic operations such as division and
square root are possible at low-cost.''",
}
@InProceedings{Shanbhag:1993:REAa,
author = "N. R. Shanbhag and K. K. Parhi",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS '93}, 3--6 May 1993",
title = "Roundoff error analysis of the pipelined {ADPCM}
coder",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "886--889",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Not \ldots{}",
}
@InProceedings{Shanbhag:1993:REAb,
author = "N. R. Shanbhag and K. K. Parhi",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS '93}, 3--6 May 1993",
title = "Roundoff error analysis of the pipelined {ADPCM}
coder",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "886--889",
year = "1993",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Roundoff error analysis of a pipelined adaptive
differential pulse code modulation (ADPCM) coder is
presented. The pipelined coder has been developed by
employing the relaxed look-ahead technique. It is shown
that the precision of the quantized \ldots{}",
}
@InProceedings{Shand:1993:FIR,
author = "M. Shand and J. Vuillemin",
title = "Fast Implementations of {RSA} Cryptography",
crossref = "Swartzlander:1993:SCA",
pages = "252--259",
year = "1993",
bibdate = "Wed Nov 14 18:47:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Shand.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Book{Shannon:1993:CES,
author = "Claude Elwood Shannon and N. J. A. (Neil James
Alexander) Sloane and A. D. (Aaron D.) Wyner",
title = "{Claude Elwood Shannon}: collected papers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xliv + 924",
year = "1993",
ISBN = "0-7803-0434-9",
ISBN-13 = "978-0-7803-0434-5",
LCCN = "TK5101 .S448 1993",
bibdate = "Sat Nov 20 09:04:51 MST 2010",
bibsource = "catalog.princeton.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "Claude Elwood Shannon (1916--2001)",
subject = "telecommunication; information theory; computers",
}
@Article{Sharp:1993:PRN,
author = "W. E. Sharp and Carter Bays",
title = "A portable random number generator for
single-precision floating-point arithmetic",
journal = j-COMP-GEOSCI,
volume = "19",
number = "4",
pages = "593--??",
month = apr,
year = "1993",
CODEN = "CGEODT, CGOSDN",
ISSN = "0098-3004 (print), 1873-7803 (electronic)",
ISSN-L = "0098-3004",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Geosciences",
}
@InProceedings{Shirayanagi:1993:MCM,
author = "Kiyoshi Shirayanagi",
title = "An algorithm to compute floating point {Gr{\"o}bner}
bases",
crossref = "Lee:1993:MCM",
pages = "95--106",
year = "1993",
MRclass = "68Q40 (13P10 68Q25)",
MRnumber = "94j:68129",
bibdate = "Fri Dec 8 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Shute:1993:AAB,
author = "Malcolm J. Shute",
title = "{Abotec}: an automatic back-of-the-envelope
calculator",
journal = j-SIGPLAN,
volume = "28",
number = "8",
pages = "90--98",
month = aug,
year = "1993",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:40 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The trial-and-error method, iteratively applied, is
invariably involved in any kind of design work, with
much back-of-the-envelope calculation to guide the
process. In this, the `what-if' game is a very useful
tactic in the search for unexpected solutions in
complex design spaces, made all the more effective by
the availability of automated interpreters. These are
needed to perform the tedious re-calculation of the
model each time a change is made to a small part. In
the financial world, the interpreter generally takes
the form of the spread-sheet, of which Quattro is a
fine example; in mathematics it takes the form of
packages such as Mathematica. Neither of these is
ideally tailored for engineering design, and so Abotec
was developed when the author had need of such a tool.
There are four main characteristics which fit Abotec
for its purpose: it works with floating-point numbers
throughout; it uses a richer than normal set of
arithmetic operators and functions; it uses mnemonic
labelling throughout; and, most importantly it treats
all variables as having an upper and lower bound.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Manchester University,
UK",
classification = "C6140D (High level languages); C7310 (Mathematics);
C7400 (Engineering)",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "Abotec; Arithmetic operators; Automated interpreters;
Automatic back-of-the-envelope calculator;
Back-of-the-envelope calculation; Complex design
spaces; Design work; Engineering design; Floating-point
numbers; Mnemonic labelling; Re-calculation;
Trial-and-error method; Unexpected solutions; What-if",
thesaurus = "CAD; High level languages; Mathematics computing",
}
@Article{Smith:1993:PFC,
author = "Ross Smith and Gerald Sobelman and George Luk and
Koichi Suda and Jeff Bracken",
title = "A Programmable Floating-Point Cell for Systolic Signal
Processing",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "5",
number = "1",
pages = "75--84",
month = jan,
year = "1993",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/BF01880273",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The FPC controller and the AMD Am29325 32-bit
floating-point mathematics processor form a two-chip
cell designed for one- or two-dimensional systolic
arrays which can be used to implement a wide variety of
signal processing applications. The FPC controls the
Am29325, routes data to and from it, and routes data
and control to other cells in the array. Unique
architectural features include two interchangeable data
memories, an input port which can be used as either a
local or global port, and a 32-bit instruction word
that allows concurrent use of all cell resources.
Additional features include a program memory, two data
streams, and three control streams.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@Article{Smith:1993:VFP,
author = "William Smith",
title = "Varying Floating-Point Precision",
journal = j-CUJ,
volume = "11",
number = "7",
pages = "87--??",
month = jul,
year = "1993",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Smith:1993:WDF,
author = "William Smith",
title = "Windows, {DLLs}, and Floating Point Types",
journal = j-CUJ,
volume = "11",
number = "9",
pages = "21--??",
month = sep,
year = "1993",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@InProceedings{Soulas:1993:AMC,
author = "T. Soulas and D. Villeger and V. G. Oklobdzija",
title = "An {ASIC} macro cell multiplier for complex numbers",
crossref = "IEEE:1993:PEC",
pages = "589--593",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An architecture for ASIC macro cell implementing a
complex number multiplier with applications in a
digital signal processing ASIC chip is described. The
complex numbers are packed into one 32-bit word. The
design is unique and combines shared Booth encoding for
the real and imaginary parts including only one
combined modified Wallace tree. The regular Wallace
tree and the tree of 4:2 adders for the complex
multiplier implementation are compared. The authors
took advantage of 4:2 adders in implementing the
combined bit compression tree for each part. This
design resulted in a more compact wiring structure and
balanced delays resulting in faster multiplier circuit.
The number of adders was also decreased.",
acknowledgement = ack-nhfb,
affiliation = "Ecole Superieure d'Ingenieurs en Electrotech. et
Electron., Noisy le Grand, France",
classification = "B1130B (Computer-aided circuit analysis and design);
B1265B (Logic circuits); B1265F (Microprocessors and
microcomputers); B2570D (CMOS integrated circuits);
C5120 (Logic and switching circuits); C5135 (Digital
signal processing chips); C5210B (Computer-aided logic
design); C5230 (Digital arithmetic methods); C7410D
(Electronic engineering computing)",
confsponsor = "IEEE; EDA Assoc.; AEIA, Spain; AFCET, France; AICA,
Italy; Bull SA, France; CEC ESPRIT Basic Research",
keywords = "32 Bit; ASIC macro cell multiplier; Balanced delays;
CMOS; Combined bit compression tree; Compact wiring
structure; Complex numbers; Digital signal processing
ASIC chip; Floating point number representation; Shared
Booth encoding; Wallace tree",
numericalindex = "Word length 3.2E+01 bit",
thesaurus = "Application specific integrated circuits; Cellular
arrays; CMOS logic circuits; Digital signal processing
chips; Floating point arithmetic; Integrated circuit
design; Logic arrays; Logic CAD; Multiplying circuits",
}
@Article{Subramaniam:1993:PPP,
author = "Ramesh Subramaniam and Kiran Kundargi and J. Dahms",
title = "Programming The {Pentium} Processor",
journal = j-DDJ,
volume = "18",
number = "6",
pages = "34, 36, 38, 40--42",
month = jun,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 03 09:15:41 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "Intel's recent entry into the 32-bit microprocessor
race ups the performance ante. Our authors discuss the
Pentium's superscalar, pipelined architecture, focusing
on floating-point code. John Dahms shares some of his
experiences in writing a Pentium-aware compiler.",
acknowledgement = ack-nhfb,
affiliation = "Intel, Santa Clara, CA, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C6110 (Systems analysis and
programming); C6150C (Compilers, interpreters and other
processors)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "32 Bit; 32-Bit microprocessor; Floating-point code;
High performance architecture; Intel Pentium;
Pentium-aware compiler; Programming; Superscalar
pipelined architecture",
thesaurus = "Computer architecture; Microprocessor chips;
Microprogramming; Pipeline processing; Program
compilers",
}
@InProceedings{Swartzlander:1993:FSC,
author = "Earl Swartzlander and Mary Jane Irwin and Graham
Jullien",
title = "Foreword: {11th Symposium on Computer Arithmetic,
Windsor, Ontario, Canada, June 29--July 2, 1993}",
crossref = "Swartzlander:1993:SCA",
pages = "v--v",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@InProceedings{Takagi:1993:MMA,
author = "N. Takagi",
title = "Modular Multiplication Algorithm with Triangle
Addition",
crossref = "Swartzlander:1993:SCA",
pages = "272--276",
year = "1993",
bibdate = "Wed Nov 14 18:48:15 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Takagi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Article{Thompson:1993:CCQ,
author = "William J. Thompson",
title = "Cutting Corners: Quick Square Roots and Trig
Functions",
journal = j-COMPUT-PHYS,
volume = "7",
number = "1",
pages = "18--??",
month = jan,
year = "1993",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4823136",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:39 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.4823136",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Manual{TI:1993:ITC,
title = "Interfacing {TI} clocked {FIFOs} with {TI}
floating-point digital signal processors: first-in,
first-out technology",
organization = "Texas Instruments Incorporated",
address = "S.l",
pages = "iv + 15",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer input-output equipment.; Signal processing
--- Digital techniques --- Equipment and; supplies.",
remark = "``SCAA005'' --- back cover.",
}
@Misc{TI:1993:ITT,
key = "TI '1993",
title = "Inside technology today 32-bit floating point
multi-port {DSP} \slash{} produced by {Texas
Instruments}",
howpublished = "VHS format. High-speed, multi-port DSPs can be used in
parallel processing applications to really enhance
computation time and power. A popular 6-port floating
point DSP and high speed design integration and
applications are described in this tape.",
address = "Dallas, TX, USA",
year = "1993",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "1 videocassette",
acknowledgement = ack-nhfb,
keywords = "Computer --- Circuits.; Electronic calculating
machines circuits.",
publication = "Texas Instruments Inc.",
}
@Article{Timmermann:1993:GFR,
author = "D. Timmermann and B. Rix and B. Hosticka",
title = "{Gleitkommaprozessor f{\"u}r rechenintensive
Echtzeitanwendungen} \toenglish {Floating-point
Processor for Computationally Intensive Real-Time Use}
\endtoenglish",
journal = j-ELECTRONIK,
volume = "20",
number = "??",
pages = "142--146",
month = "????",
year = "1993",
CODEN = "EKRKAR",
ISSN = "0013-5658",
bibdate = "Fri Dec 08 13:05:00 1995",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
fjournal = "Elektronik",
}
@Article{Tiwari:1993:NCP,
author = "Neeraj Tiwari and A. K. Nigam",
title = "A note on constructive procedure for unbiased
controlled rounding",
journal = j-STAT-PROB-LETT,
volume = "18",
number = "5",
pages = "415--420",
day = "2",
month = dec,
year = "1993",
CODEN = "SPLTDC",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Sun Jun 1 11:14:48 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/statproblett1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/016771529390036I",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
}
@Article{Tsuji:1993:FNS,
author = "Kumiko Tsuji",
title = "Floating-point number solutions in a simple linear
equation with addition algorithm. Numerical calculation
methods with guaranteed accuracy and their applications
({Japanese}) ({Kyoto}, 1992)",
journal = "S{\=u}rikaisekikenky{\=u}sho K{\=o}ky{\=u}roku",
volume = "831",
pages = "33--45",
year = "1993",
MRclass = "65G05",
MRnumber = "95a:65083",
bibdate = "Fri Dec 8 08:24:11 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Turner:1993:CSA,
author = "P. R. Turner",
title = "Complex {SLI} arithmetic: Representation, algorithms
and analysis",
crossref = "Swartzlander:1993:SCA",
pages = "18--25",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Turner.pdf",
abstract = "The extension of the SLI (symmetric level index)
system to complex numbers and arithmetic is discussed.
The natural form for representation of complex
quantities in SLI is in the modulus-argument form, and
this can be sensibly packed into a single 64-b word for
the equivalent of the 32-b real SLI representation. The
arithmetic algorithms prove to be very slightly more
complicated than for real SLI arithmetic. The
representation, the arithmetic algorithms, and the
control of errors within these algorithms are
described.",
acknowledgement = ack-nhfb,
affiliation = "Department of Math., US Naval Acad., Annapolis, MD,
USA",
classification = "C5230 (Digital arithmetic methods)",
keywords = "ARITH-11; Arithmetic algorithms; Complex numbers;
Modulus-argument form; Representation; SLI; SLI
arithmetic; Symmetric level index",
thesaurus = "Floating point arithmetic",
}
@Article{Vassiliadis:1993:CHW,
author = "S. Vassiliadis and E. M. Schwarz",
title = "Correction to {``Hard-wired multipliers with encoded
partial products''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "1",
pages = "127--127",
month = jan,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.192224",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192224",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Veselic:1993:FPH,
author = "Kre{\v{s}}imir Veseli{\'c} and Ivan Slapni{\v{c}}ar",
title = "Floating-Point Perturbations of {Hermitian} Matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "195",
number = "??",
pages = "81--116",
month = dec,
year = "1993",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18 15A57)",
MRnumber = "94m:65066",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Vignes:1993:SAR,
author = "J. Vignes",
title = "A stochastic arithmetic for reliable scientific
computation",
journal = j-MATH-COMP-SIM,
volume = "35",
number = "3",
pages = "233--261",
month = sep,
year = "1993",
CODEN = "MCSIDR",
DOI = "https://doi.org/10.1016/0378-4754(93)90003-D",
ISSN = "0378-4754 (print), 1872-7166 (electronic)",
ISSN-L = "0378-4754",
bibdate = "Thu Mar 24 20:56:34 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://portal.acm.org/citation.cfm?id=165789.165792",
acknowledgement = ack-nhfb,
fjournal = "Mathematics and Computers in Simulation",
journal-URL = "http://www.sciencedirect.com/science/journal/03784754",
}
@Article{vonNeumann:1993:FDR,
author = "John von Neumann",
title = "First Draft of a Report on the {EDVAC}",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "15",
number = "4",
pages = "28--75",
month = oct # "\slash " # dec,
year = "1993",
CODEN = "IAHCEX",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Thu Jul 12 06:22:55 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
note = "Edited and corrected by Michael D. Godfrey.",
URL = "http://dlib.computer.org/an/books/an1993/pdf/a4027.pdf;
http://www.computer.org/annals/an1993/a4027abs.htm",
acknowledgement = ack-nhfb,
ajournal = "IEEE Ann. Hist. Comput.",
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
xxpages = "27--??",
keywords = "floating-point arithmetic; rounding",
}
@Article{Vornberger:1993:BBM,
author = "Cal Vornberger",
title = "Beyond Bit Maps: Multiple floating objects deliver new
power and flexibility to bit-map image processing.
{Micrografx Picture Publisher} 4.0 and {Fractal Design
Painter X2} feature object layers and other useful
innovations",
journal = j-BYTE,
volume = "18",
number = "13",
pages = "165--166, 168",
month = dec,
year = "1993",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Thu Sep 12 16:34:03 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "D2010 (Business and professional); D2020 (Design and
graphics)",
fjournal = "BYTE Magazine",
keywords = "Bit maps; Ease of use; Fractal design painterX2;
Functionality; Micrografx; Object technology; Picture
Publisher 4.0",
thesaurus = "Business graphics; Desktop publishing",
}
@Article{Walter:1993:SMM,
author = "C. D. Walter",
title = "Systolic modular multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "3",
pages = "376--378",
month = mar,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.210181",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=210181",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wang:1993:SAC,
author = "Chin-Liang Wang and Jung-Lung Lin",
title = "A systolic architecture for computing inverses and
divisions in finite fields {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "42",
number = "9",
pages = "1141--1146",
month = sep,
year = "1993",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.241603",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:58:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=241603",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wei:1993:CTA,
author = "D.-Y. D. Wei and J. H. Kim and T. R. N. Rao",
title = "Complete tests in algorithm-based fault-tolerant
matrix operation on processor arrays",
crossref = "Lombardi:1993:PII",
pages = "255--262",
year = "1993",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently, F. T. Assaad and S. Dutt (1992) proposed the
hybrid checksum test method for the floating-point
matrix-matrix multiplication in ABFT environment, by
which the error coverage can be greatly increased.
However, the thresholded test in their approach is
still not avoidable in the floating-point additions
involved in matrix multiplication and the number of
error detections decrease with the increase in the
dynamic range of data, which is not totally
satisfactory. The authors present an effective method,
called concurrent floating-point checksum (CFPC) test,
which provides very convincing error
detection/correction capabilities for the part of
floating-point addition with a minimum time latency and
hardware overhead.",
acknowledgement = ack-nhfb,
affiliation = "Center for Adv. Comput. Studies, University of
Southwestern Louisiana, Lafayette, LA, USA",
classification = "B0290H (Linear algebra); B1265 (Digital
electronics); B6120B (Codes); C4140 (Linear algebra);
C5210 (Logic design methods); C5230 (Digital arithmetic
methods); C6130 (Data handling techniques)",
keywords = "concurrent floating-point checksum; error correction;
error detections; fault-tolerant matrix; floating-point
additions; floating-point matrix-matrix multiplication;
floating-point testing; hardware overhead; hybrid
checksum test; minimum time latency; processor arrays;
thresholded test",
thesaurus = "Computational complexity; Error correction; Error
detection; Fault tolerant computing; Floating point
arithmetic; Logic arrays; Logic testing; Matrix
multiplication",
}
@Book{Weste:1993:PCV,
author = "Neil H. E. Weste and Kamran Eshraghian",
title = "Principles of {CMOS VLSI} Design: a Systems
Perspective",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xxii + 713",
year = "1993",
ISBN = "0-201-53376-6",
ISBN-13 = "978-0-201-53376-7",
LCCN = "TK7874 .W46 1993",
bibdate = "Mon Sep 16 16:32:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Williams:1993:BFM,
author = "Al Williams",
title = "Bit Floating-Point Math",
journal = j-DDJ,
volume = "18",
number = "6",
pages = "70--??",
month = jun,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This approach to floating-point math uses 32-bit
instructions. Although Al uses the 80386 as an example,
these techniques can be applied to other 32-bit
processors as well.",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Williams:1993:FM,
author = "Al Williams",
title = "32-bit floating-point math",
journal = j-DDJ,
volume = "18",
number = "6",
pages = "70, 72, 74, 76, 80",
month = jun,
year = "1993",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 10 08:57:56 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "This approach to floating-point math uses 32-bit
instructions. Although Al uses the 80386 as an example,
these techniques can be applied to other 32-bit
processors as well.",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "32 Bit; 32-Bit instructions; 32-Bit processors; 386
Instruction set; 80386; Floating-point mathematics",
thesaurus = "Digital arithmetic; Microprocessor chips",
}
@InProceedings{Wrzyszcz:1993:DDCa,
author = "A. Wrzyszcz and D. Caban and E. L. Dagless",
booktitle = "Proceedings. [4th] European Conference on Design
Automation, 1993, with the European Event in {ASIC}
Design",
title = "Design of a discrete cosine transform circuit using
the residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "584--588",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/EDAC.1993.386412",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design of an integrated circuit aimed at efficient
discrete cosine transform computation is presented.
High performance is obtained through the use of
pipelining and residue arithmetic. An approach to
high-speed modular multiplication employing \ldots{}",
}
@InProceedings{Wrzyszcz:1993:DDCb,
author = "A. Wrzyszcz and D. Caban and E. L. Dagless",
booktitle = "Proceedings. [4th] European Conference on Design
Automation, 1993, with the European Event in {ASIC}
Design",
title = "Design of a discrete cosine transform circuit using
the residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "584--588",
year = "1993",
CODEN = "????",
DOI = "https://doi.org/10.1109/EDAC.1993.386412",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design of an integrated circuit aimed at efficient
discrete cosine transform computation is presented.
High performance is obtained through the use of
pipelining and residue arithmetic. An approach to
high-speed modular multiplication employing \ldots{}",
}
@Article{Zeng:1993:CFA,
author = "Chuan-Qing Zeng and Kousuke Tsukamoto and Takeo
Miyata",
title = "Charge-balancing floating-point analogue-to-digital
converter using acyclic conversion",
journal = j-INT-J-ELECTRON,
volume = "74",
number = "5",
pages = "705--??",
month = may,
year = "1993",
CODEN = "IJELA2",
ISSN = "0020-7217 (print), 1362-3060 (electronic)",
ISSN-L = "0020-7217",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Electronics Theoretical \&
Experimental",
}
@Article{Zhang:1993:EAP,
author = "C. N. Zhang and B. Shirazi and D. Y. Y. Yun",
title = "An Efficient Algorithm and Parallel Implementations
for Binary and Residue Number Systems",
journal = j-J-SYMBOLIC-COMP,
volume = "15",
number = "4",
pages = "451--462",
month = apr,
year = "1993",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1006/jsco.1993.1030",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "65G10 (65Y05)",
MRnumber = "94j:65066",
MRreviewer = "De Ren Wang",
bibdate = "Sat May 10 15:54:09 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Arithmetic units based on a Residue Number System
(RNS) are fast and simple, and therefore attractive for
use in digital signal processing and symbolic
computation applications. However, RNS suffers from
overheads of converting numbers to and from residue
system. We present a new simple and uniform computation
formula for both conversion from RNS to binary and vice
versa. Two levels of parallelism for VLSI hardware
design of the proposed algorithm are introduced.",
acknowledgement = ack-nhfb,
classcodes = "C7310 (Mathematics); C7410D (Electronic engineering)",
corpsource = "Department of Computer Science, Regina University,
Sask., Canada",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "algorithm; binary number systems; circuit CAD;
computation; digital signal processing; parallel
implementations; parallelism; residue number systems;
symbol manipulation; symbolic; VLSI; VLSI hardware
design",
treatment = "A Application; P Practical",
}
@InProceedings{Zuras:1993:SML,
author = "D. Zuras",
title = "On Squaring and Multiplying Large Integers",
crossref = "Swartzlander:1993:SCA",
pages = "260--271",
year = "1993",
bibdate = "Sat Nov 17 09:46:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Zuras.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Book{Zuse:1993:CML,
author = "Konrad Zuse",
title = "The Computer, My Life",
publisher = pub-SV,
address = pub-SV:adr,
pages = "245",
year = "1993",
ISBN = "3-540-56453-5 (Berlin), 0-387-56453-5 (New York)",
ISBN-13 = "978-3-540-56453-9 (Berlin), 978-0-387-56453-1 (New
York)",
LCCN = "TK7885.22.Z87 A3 1993",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "computer engineers --- Germany --- biography;
computers --- Germany --- history; Zuse, Konrad",
tableofcontents = "1: Ancestors and parents --- Early childhood
memories --- School days --- Metropolis --- Abitur / 1
\\
2: Studies (not without detours and byways) and general
studies --- First inventions --- The \emph{Akademische
Verein Motiv} --- Student life between science and
politics / 15 \\
3: The early years of the computer and a digression on
its prehistory --- Colleagues remember --- From
mechanics to electromechanics --- Schreyer's electronic
computing machine --- First outside contacts ---
Thoughts on the future / 33 \\
4: Outbreak of the war and first callup --- Structural
engineer in aircraft construction --- The Z2 and Z3 ---
Second callup --- \emph{Zuse Ingenieurb{\"u}ro und
Apparatebau, Berlin} --- The first process computer /
55 \\
5: Origins of the Z4 --- News from the United States
--- Attempt at a PhD dissertation --- Computing machine
for logic operations --- Final months of the war in
Berlin --- The evacuation --- Z4 completed in
G{\"o}ttingen --- Final war days in the Allg{\"a}u / 75
\\
6: End of the war --- Refugees in Hinterstein --- The
\emph{Plankalk{\"u}l} --- The computing universe ---
Automation and self-reproducing systems --- A
logarithmic computing machine --- Computer development
in Germany and the United States --- Move to Hopferau
near F{\"u}ssen --- The mill of the Patent Office / 95
\\
7: The \emph{Zuse-Ingenieurb{\"u}ro, Hopferau bei
F{\"u}ssen} --- First business partners: IBM and
Remington Rand --- The first pipelining design ---
Founding of ZUSE KG in Neukirchen --- The Z4 in the ETH
in Z{\"u}rich --- The computer in Europe: taking stock
--- Lost opportunities --- The first German contract:
the Z5 / 113 \\
8: The partners leave --- Computing machine for land
use zoning --- Electronics gains acceptance --- First
funds from the \emph{Deutsche Forschungsgemeinschaft}
--- Losing one's way (and possibly a lost opportunity)
--- The array processor --- Custom work for geodesics
--- The Graphomat Z64 --- Growth and crisis of ZUSE KG
--- The end / 133 \\
9: Free for science (again) --- Honors --- A look to
the future / 157 \\
Appendices \\
1: From Forms to Program Control / 185 \\
2: Construction of Devices / 190 \\
3: On Computer Architecture / 210 \\
4: On the Plan Calculus / 211 \\
5: Lecture on the Occasion of the Award of the Honorary
Doctorate by the Technical University of Berlin
(Extract) / 222 \\
6: The Computer Did Not Fall From Heaven / 225 \\
Notes / 229 \\
References / 231 \\
Name Index / 235 \\
Subject Index / 239 \\
Computer Index / 245",
}
@Article{Agarwal:1994:EFP,
author = "R. C. Agarwal and F. G. Gustavson and M. Zubair",
title = "Exploiting functional parallelism of {POWER2} to
design high-performance numerical algorithms",
journal = j-IBM-JRD,
volume = "38",
number = "5",
pages = "563--576",
month = sep,
year = "1994",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.almaden.ibm.com/journal/rd38-5.html#eight",
abstract = "We describe the algorithms and architecture approach
to produce high-performance codes for numerically
intensive computations. In this approach, for a given
computation, we design algorithms so that they perform
optimally when run on a target machine --- in this
case, the new POWER2* machines from the RS\slash 6000
family of RISC processors. The algorithmic features
that we emphasize are functional parallelism,
cache/register blocking, algorithmic prefetching, loop
unrolling, and algorithmic restructuring. The
architectural features of the POWER2 machine that we
describe and that lead to high performance are multiple
functional units, high bandwidth between registers,
cache, and memory, a large number of fixed- and
floating-point registers, and a large cache and TLB
(translation lookaside buffer). The paper gives two
examples that illustrate how the algorithms and
architectural features interplay to produce
high-performance codes. They are BLAS (basic linear
algebra subroutines) and narrow-band matrix routines.
These routines are included in ESSL (Engineering and
Scientific Subroutine Library); an overview of ESSL is
also given in this paper.",
acknowledgement = ack-nhfb,
affiliation = "Res. Div., IBM Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
classcodes = "C7310 (Mathematics computing); C5430 (Microcomputers);
C6140B (Machine-oriented languages); C6110P (Parallel
programming)",
classification = "C5430 (Microcomputers); C6110P (Parallel
programming); C6140B (Machine-oriented languages);
C7310 (Mathematics computing)",
corpsource = "Res. Div., IBM Thomas J. Watson Res. Center, Yorktown
Heights, NY, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "algorithmic; Algorithmic prefetching; algorithmic
restructuring; Algorithmic restructuring; algorithms;
and Scientific Subroutine Library; basic linear
algebra; Basic linear algebra subroutines; BLAS;
cache/register blocking; Cache/register blocking;
computations; Engineering; Engineering and Scientific
Subroutine Library; ESSL; floating-point registers;
Floating-point registers; functional parallelism;
Functional parallelism; high-performance codes;
High-performance codes; high-performance numerical;
High-performance numerical algorithms; IBM computers;
loop unrolling; Loop unrolling; mathematics computing;
multiple functional units; Multiple functional units;
narrow-band matrix routines; Narrow-band matrix
routines; numerically intensive; Numerically intensive
computations; parallel algorithms; POWER2 workstations;
prefetching; processors; reduced instruction set
computing; RISC; RISC processors; RS/6000 family;
software libraries; subroutines; translation lookaside
buffer; Translation lookaside buffer; workstations",
thesaurus = "IBM computers; Mathematics computing; Parallel
algorithms; Reduced instruction set computing; Software
libraries; Workstations",
treatment = "P Practical",
}
@Article{Anonymous:1994:C,
author = "Anonymous",
title = "Corrigenda",
journal = j-TOMS,
volume = "20",
number = "4",
pages = "553--553",
month = dec,
year = "1994",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 14 16:17:03 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Hull:1994:ICE}",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
xxURL = "Missing from ACM Digital Library",
}
@Article{Anonymous:1994:FPa,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "13",
number = "6",
pages = "65--??",
month = jun,
year = "1994",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Interactive Analysis Presentations.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1994:FPb,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "13",
number = "7",
pages = "85--??",
month = jul,
year = "1994",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Misplaced Value of CE.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1994:FPc,
author = "Anonymous",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "13",
number = "10",
pages = "122--??",
month = oct,
year = "1994",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Integration's Relational Dimension.",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1994:SCSa,
author = "Anonymous",
title = "Single chip supercomputer: Vector processing is key to
high performance in floating point calculations",
journal = "New electronics",
volume = "27",
number = "4",
pages = "7--??",
day = "1",
month = apr,
year = "1994",
ISSN = "0047-9624",
bibdate = "Fri Aug 23 08:32:16 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover library database",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1994:SPF,
author = "Anonymous",
title = "Signal Path: Floating-point tactics",
journal = j-ELECTRONIC-ENG-TIMES,
volume = "??",
number = "807",
pages = "78--??",
month = jul,
year = "1994",
ISSN = "0192-1541",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronic engineering times",
}
@Book{Anonymous:1994:SRT,
author = "Anonymous",
title = "The Square Root of Two to 5 million digits",
volume = "129",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1994",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext94/2sqrt10a.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
url-contents = "ZIP",
}
@Book{Apple:1994:IMP,
author = "{Apple Computers, Inc.}",
title = "Inside {Macintosh}: {PowerPC Numerics}",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xx + 300",
year = "1994",
ISBN = "0-201-40728-0",
ISBN-13 = "978-0-201-40728-0",
LCCN = "QA76.8.M3 I5622 1994",
bibdate = "Wed Sep 07 21:08:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$28.95",
acknowledgement = ack-nj,
}
@Article{Bajard:1994:BNH,
author = "J.-C. Bajard and S. Kla and Jean-Michel Muller",
title = "{BKM}: a New Hardware Algorithm for Complex Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "955--963",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295857",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@Article{Bajard:1994:SOL,
author = "J.-C. Bajard and J. Duprat and S. Kla and J.-M.
Muller",
title = "Some Operators for On-Line Radix-2 Computations",
journal = j-J-PAR-DIST-COMP,
volume = "22",
number = "2",
pages = "336--345",
month = aug,
year = "1994",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1994.1093",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:55 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1093/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1093/production/pdf",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Lab. LIP, Ecole Normale Superieure de Lyon, France",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "bit-level representation; Borrow-Save; delay; digital
arithmetic; online radix-2 computations; operators;
optimal online; radix-2 digits; representation",
treatment = "P Practical",
}
@Article{Barsi:1994:TOM,
author = "Ferruccio Barsi and M. Cristina Pinotti",
title = "Time optimal mixed radix conversion for residue number
applications",
journal = j-COMP-J,
volume = "37",
number = "10",
pages = "907--916",
month = "????",
year = "1994",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Jul 21 09:54:19 MDT 1999",
bibsource = "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_10/Vol37_10.index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_10/Vol37_10.body.html#AbstractBarsi",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica, Perugia University,
Italy",
author-1-adr = "Dipartimento at Matematica, Universita di Perugia, Via
Vanvitelli, 061OO Perugia, Italy",
author-2-adr = "Istituto di Elaborazione dell'Informazione del CNR,
Via S. Maria 46, 56100 Pisa, Italy",
classcodes = "B2570 (Semiconductor integrated circuits); C5230
(Digital arithmetic methods); C6130 (Data handling
techniques); C4240C (Computational complexity)",
classification = "B2570 (Semiconductor integrated circuits); C4240C
(Computational complexity); C5230 (Digital arithmetic
methods); C6130 (Data handling techniques)",
corpsource = "Dipartimento di Matematica, Perugia University,
Italy",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "applications; asymptotic conversion time; Chinese
Remainder Theorem; computational complexity;
constructive VLSI design; Constructive VLSI design;
conventional logic; Conventional logic; logic
circuitry; Logic circuitry; lookup; lookup table
implementations; Lookup table implementations; mixed
radix; Mixed radix notation; notation; practical ECL
IC; Practical ECL IC; residue integer conversion;
Residue integer conversion; residue number; Residue
number applications; residue number systems;
residue-to-weighted system; Residue-to-weighted system
asymptotic conversion time; table; time optimal mixed
radix conversion; Time optimal mixed radix conversion;
VLSI",
thesaurus = "Computational complexity; Residue number systems;
Table lookup; VLSI",
treatment = "P Practical",
}
@Article{Bartolucci:1994:REC,
author = "M. Bartolucci and G. R. Sechi",
title = "Rounding error in the computation of opposite sign
floating point number parametric addition: a case
study",
journal = j-MICROPROC-MICROPROG,
volume = "40",
number = "10-12",
pages = "833--839",
month = dec,
year = "1994",
CODEN = "MMICDT",
ISSN = "0165-6074 (print), 1878-7061 (electronic)",
ISSN-L = "0165-6074",
bibdate = "Thu Dec 14 15:33:45 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "20th Annual Euromicro Conference. System Architecture
and Integration.",
abstract = "Presents a study about rounding errors arising in the
addition of opposite-sign floating-point operands. The
algebraic study of the adder functionalities provides
the possibility of modifying the hardware in order to
measure the rounding error effect in terms of error
size and incoming rate.",
acknowledgement = ack-nhfb,
affiliation = "Istituto di Fisica Cosmica e Tecnologie Relative, CNR,
Milano, Italy",
classification = "C1110 (Algebra); C5230 (Digital arithmetic
methods)",
confdate = "Sept. 1994",
conflocation = "Liverpool, UK",
fjournal = "Microprocessing and Microprogramming",
keywords = "Adder functionalities; Algebraic properties; Case
study; Computational units; Error size; Errors
detection; Errors elimination; Floating-point operands;
Hardware modification; High-speed floating point
operators; Incoming rate; Opposite-sign floating-point
number parametric addition; Real time applications;
Rounding error",
pubcountry = "Netherlands",
thesaurus = "Algebra; Error detection; Floating point arithmetic;
Roundoff errors",
}
@Article{Bauer:1994:MDS,
author = "F. L. Bauer",
title = "Multiplication and dual system",
journal = j-INFORMATIK-SPEKTRUM,
volume = "17",
number = "4",
pages = "245--250",
month = aug,
year = "1994",
CODEN = "INSKDW",
ISSN = "0170-6012 (print), 1432-122X (electronic)",
ISSN-L = "0170-6012",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A history of methods of multiplication is introduced
with a table showing the assignments of Greek and
Hebrew letters to the units, tens and hundreds up to
900, with no zero. The ancient Egyptian method using
decimal-to-binary conversion with addition of
successive even multiples of the multiplicand is
explained. Napier's (1617) method of `numeri locales'
is described with the aid of a multiplication table for
algebraic symbols each representing a different power
of 2. The application of these principles in electronic
computing circuits is discussed with reference to
Braun's (1963) full-adder correction circuit and
Wallace's (1964) cascaded half-adders. Progress from
the 8*8 field multiplier chips of 1971 to the
floating-point 1.2 mu m CMOS 56*56 RISC multiplier of
1989 is summarised.",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
fjournal = "Informatik Spektrum",
journal-URL = "http://link.springer.com/journal/287",
keywords = "Algebraic symbols; Cascaded half-adders; decimal
floating-point arithmetic; Decimal-to-binary
conversion; Egyptian method; Electronic computing
circuits; Floating-point; Full-adder correction
circuit; Multiplication; Multiplier chips; Numeri
locales; RISC",
language = "German",
pubcountry = "Germany",
thesaurus = "Digital arithmetic; History; Multiplying circuits",
}
@PhdThesis{Bewick:1994:FMA,
author = "Gary Bewick",
title = "Fast Multiplication: Algorithms and Implementations",
type = "{Ph.D.} thesis",
school = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
pages = "170",
month = feb,
year = "1994",
bibdate = "Mon Dec 24 09:59:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also issued as report CSL-TR-94-617",
acknowledgement = ack-nhfb,
}
@Article{BrinchHansen:1994:MLD,
author = "Per {Brinch Hansen}",
title = "Multiple-length Division Revisited: a Tour of the
Minefield",
journal = j-SPE,
volume = "24",
number = "6",
pages = "579--601",
month = jun,
year = "1994",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380240605",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Fri Nov 28 17:07:54 2003",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/litprog.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "This paper derives an algorithm for division of long
integers, and implements it as a literate program,
although without identifier cross-references. See also
related work on division
\cite{BrinchHansen:1995:LDA,Regener:1984:MID} .",
URL = "http://brinch-hansen.net/papers/1994b.pdf",
abstract = "Long division of natural numbers plays a crucial role
in Cobol arithmetic, cryptography, and primality
testing. Only a handful of textbooks discuss the theory
and practice of long division, and none of them do it
satisfactorily. This tutorial attempts to fill this
surprising gap in the literature on computer
algorithms. We illustrate the subtleties of long
division by examples, define the problem concisely,
summarize the theory, and develop a complete Pascal
algorithm using a consistent terminology.",
acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
ajournal = "Softw. Pract. Exp.",
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "algorithms; multiple-length integer division",
onlinedate = "30 Oct 2006",
}
@InProceedings{Brosgol:1994:ISD,
author = "Benjamin M. Brosgol and Robert I. Eachus and David E.
Emery",
title = "Information Systems Development in {Ada}",
crossref = "ACM:1994:AAW",
pages = "2--16",
year = "1994",
bibdate = "Fri Nov 28 16:05:55 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we survey how to use Ada (both Ada 83
and Ada 9X) for IS applications, with a focus on two
principal issues: Specification of the information
architecture of an IS application, and Programming
techniques relevant to financial and related
applications.\par
We cover both the language features and the
supplemental packages for IS development. Special
attention will be paid to the Ada Decimal-Associated
Reusabilia (`ADAR') components for Ada 83 and
transitioning to Ada 9X.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@MastersThesis{Bull:1994:SFF,
author = "Nathan Lee Bull",
title = "A study of frequency-sampling filters realized on
floating-point digital signal processors",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vii + 56",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics)",
}
@Article{Carr:1994:IRM,
author = "S. Carr and K. Kennedy",
title = "Improving the Ratio of Memory Operations in
Floating-Point Operations in Loops",
journal = j-TOPLAS,
volume = "16",
number = "6",
pages = "1768--1810",
month = nov,
year = "1994",
CODEN = "ATPSDT",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Over the past decade, microprocessor design strategies
have focused on increasing the computational power on a
single chip. Because computations often require more
data from cache per floating-point operation than a
machine can deliver and because operations are
pipelined, idle computational cycles are common when
scientific applications are executed. To overcome these
bottlenecks, programmers have learned to use a coding
style that ensures a better balance between memory
references and floating-point operations. In our view,
this is a step in the wrong direction because it makes
programs more machine-specific. A programmer should not
be required to write a new program version for each new
machine; instead, the task of specializing a program to
a target machine should be left to the compiler. But is
our view practical? Can a sophisticated optimizing
compiler obviate the need for the myriad of programming
tricks that have found their way into practice to
improve the performance of the memory hierarchy? In
this paper we attempt to answer that question. To do
so, we develop and evaluate techniques that
automatically restructure program loops to achieve high
performance on specific target architectures. These
methods attempt to balance computation and memory
accesses and seek to eliminate or reduce pipeline
interlock. To do this, they estimate statically the
balance between memory operations and floating-point
operations for each loop in a particular program and
use these estimates to determine whether to apply
various loop transformations. Experiments with our
automatic techniques show that integer-factor speedups
are possible on kernels. Additionally, the estimate of
the balance between memory operations and computation,
and the application of the estimate are very
accurate-experiments reveal little difference between
the balance achieved by our automatic system and that
possible by hand optimization.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Michigan Technol.
University, Houghton, MI, USA",
classification = "C5230 (Digital arithmetic methods); C6120 (File
organisation); C6150C (Compilers, interpreters and
other processors)",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
keywords = "Bottlenecks; Floating-point operations; Integer-factor
speedups; Memory operations; Memory references;
Microprocessor design strategies; Pipeline interlock;
Program loops; Sophisticated optimizing compiler",
thesaurus = "Floating point arithmetic; Optimising compilers;
Pipeline processing; Program control structures;
Storage management",
}
@MastersThesis{Chandramouli:1994:DSP,
author = "V. Chandramouli",
title = "Design of a self-timed, pipelined, floating point
multiplier in gallium arsenide",
type = "Thesis ({M.S.})",
school = "Department of Computer Science, University of Utah",
address = "Salt Lake City, UT, USA",
pages = "xiii + 121",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Computer architecture.; Gallium arsenide
semiconductors.",
}
@InProceedings{Chen:1994:EDU,
author = "Sau-Gee Chen and Chieh-Chih Li",
booktitle = "Proceedings of {TENCON '94}. {IEEE} Region 10's Ninth
Annual International Conference. Theme: `Frontiers of
Computer Technology'",
title = "Efficient designs of unified $2$'s complement division
and square root algorithm and architecture",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "943--947",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Efficient unified 2's complement division and square
root algorithm, and their architectures are proposed in
this work. The designs are high speed, small area and
high compatibility. The architectures provide bit level
pipelined operation, as well \ldots{}",
}
@Article{Chesneaux:1994:ERS,
author = "J.-M. Chesneaux",
title = "The equality relations in scientific computing",
journal = j-NUMER-ALGORITHMS,
volume = "7",
number = "2-4",
pages = "129--143",
month = jul,
year = "1994",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The equality relation (more generally, the ordering
relations) in floating point arithmetic is the exact
translation of the mathematical equality relation.
Because of the propagation of round-off errors, the
floating point arithmetic is not the exact
representation of the theoretical arithmetic which is
continuous on the real numbers. This leads to some
incoherence when the equality concept is used in
floating point arithmetic. A well known example is the
detection of a zero element in the pivoting column and
equation when applying Gaussian elimination, which is
almost impossible in floating point arithmetic. The
author begins by showing the inadequacy of the equality
relation used in floating point arithmetic (the author
calls it floating point equality), and then introduces
two new concepts stochastic numbers and the equality
relation between such numbers which is called the
stochastic equality. It is shown how these concepts
allow recovery of the coherence between the arithmetic
operators and the ordering relations that was missing
in floating point computations.",
acknowledgement = ack-nhfb,
affiliation = "Laboratoire MASI, Universit{\'e} Pierre et Marie
Curie, Paris, France",
classification = "C5230 (Digital arithmetic methods); C7310
(Mathematics)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Arithmetic operators; Equality relations; Floating
point arithmetic; Floating point equality; Gaussian
elimination; Ordering relations; Pivoting column;
Round-off errors; Scientific computing; Stochastic
equality; Stochastic numbers; Zero element",
pubcountry = "Switzerland",
thesaurus = "Digital arithmetic; Mathematics computing; Roundoff
errors",
}
@InProceedings{Chren:1994:ALIa,
author = "W. A. {Chren, Jr.}",
booktitle = "Proceedings of the 37th Midwest Symposium on Circuits
and Systems, 1994",
title = "Area and latency improvements for direct digital
synthesis using the residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "269--273",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1994.519237",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Two residue number system-based direct digital
synthesizers are presented. The High-Agility Direct
Synthesizer exhibits a frequency switching latency
which is reduced by as much as 50\% below that of
traditional, binary number system-based designs.
\ldots{}",
}
@InProceedings{Chren:1994:ALIb,
author = "W. A. {Chren, Jr.}",
booktitle = "Proceedings of the 37th Midwest Symposium on Circuits
and Systems, 1994. 3--5 August 1994, Lafayette, {LA},
{USA}",
title = "Area and latency improvements for direct digital
synthesis using the residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "269--273",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1994.519237",
ISBN = "0-7803-2428-5",
ISBN-13 = "978-0-7803-2428-2",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Two residue number system-based direct digital
synthesizers are presented. The High-Agility Direct
Synthesizer exhibits a frequency switching latency
which is reduced by as much as 50\% below that of
traditional, binary number system-based designs. The
Reduced Area Direct Synthesizer has a chip area which
is reduced by more than 40\%. The area reduction is due
primarily to the decomposition of the sine ROM into
several small look-up tables, while the latency
reduction is due to the shortening of the carry paths
in the phase accumulator",
}
@Article{Cortadella:1994:HRD,
author = "J. Cortadella and T. Lang",
title = "High-Radix Division and Square-Root with Speculation",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "919--931",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295854",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295854",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
summary = "The speed of high-radix digit-recurrence dividers and
square-root units is mainly determined by the
complexity of the result-digit selection. We present a
scheme in which a simpler function speculates the
result digit, and, when this speculation is \ldots{}",
}
@TechReport{Dallaway:1994:DAC,
author = "Richard Z. Dallaway",
title = "Dynamics of Arithmetic: a Connectionist View of
Arithmetic Skills",
type = "Technical report",
number = "CSRP 306",
institution = "Univerity of Sussex",
address = "Brighton, UK",
pages = "159",
month = feb,
year = "1994",
ISSN = "1350-3162",
bibdate = "Fri Nov 28 16:36:28 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{DasSarma:1994:MAR,
author = "D. DasSarma and D. W. Matula",
title = "Measuring the Accuracy of {ROM} Reciprocal Tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "932--940",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295855",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@InProceedings{Daumas:1994:FAR,
author = "M. Daumas and C. Mazenc and X. Merrheim and J. M.
Muller",
title = "Fast and accurate range reduction for computation of
the elementary functions",
crossref = "Ames:1994:IPI",
pages = "??--??",
year = "1994",
bibdate = "Sat Jun 25 08:57:47 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "range reduction",
}
@Article{Daumas:1994:RFP,
author = "Marc Daumas and David W. Matula",
title = "Rounding of floating point intervals",
journal = j-INTERVAL-COMP,
volume = "4",
pages = "28--45",
year = "1994",
ISSN = "0135-4868",
MRclass = "65G10 (65G05)",
MRnumber = "1 332 074",
bibdate = "Fri Dec 8 08:24:03 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Interval Computations = Interval'nye vychisleniia",
xxnote = "SCAN-93 (Vienna, 1993)",
}
@Article{De:1994:FPA,
author = "M. De and B. P. Sinha",
title = "Fast parallel algorithm for ternary multiplication
using multivalued {$ I^2 L $} technology",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "5",
pages = "603--607",
month = may,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.280807",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=280807",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{delaSerna:1994:TBF,
author = "A. E. de la Serna and M. A. Soderstrand",
booktitle = "Conference Record of the Twenty-Eighth Asilomar
Conference on Signals, Systems and Computers, 1994",
title = "Trade-off between {FPGA} resource utilization and
roundoff error in optimized {CSD} {FIR} digital
filters",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "187--191",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "In this paper, we investigate the trade off between
filter order and bits of coefficient precision in
fixed-coefficient FIR digital filters utilizing
canonical signed digit (CSD) coefficient
representation. We demonstrate that the use of
optimized \ldots{}",
}
@Article{delRosario:1994:HIM,
author = "J. M. del Rosario and A. N. Choudhary",
title = "High-performance {I/O} for massively parallel
computers: problems and prospects",
journal = j-COMPUTER,
volume = "27",
number = "3",
pages = "59--68",
month = mar,
year = "1994",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Sep 13 16:03:42 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Syracuse
University, NY, USA",
classification = "B6210L (Computer communications); C5440
(Multiprocessor systems and techniques); C5620
(Computer networks and techniques); C6110P (Parallel
programming); C6150N (Distributed systems)",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "Access patterns; Compilers; File systems;
Floating-point operations per second; Hardware
technology; High-performance I/O; High-performance
storage systems; High-speed networking; I/O
infrastructure; Language interfaces; Massive parallel
processing; Massively parallel computers; Networking
technology; Operating systems; Parallel I/O problem;
Powerful supercomputers; Resource-management
approaches; Runtime system; Teraflops barrier;
Visualization systems",
thesaurus = "Computer networks; Input-output programs; Network
operating systems; Parallel machines; Parallel
programming",
}
@TechReport{Demmel:1994:CPBa,
author = "James Demmel and Inderjit Dhillon and Huan Ren",
title = "On the correctness of parallel bisection in floating
point",
type = "Report",
number = "UCB/CSD 94/805",
institution = "Computer Science Division (EECS), University of
California",
address = "Berkeley, CA, USA",
pages = "38",
month = mar,
year = "1994",
bibdate = "Thu Aug 23 06:41:11 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also known as LAPACK Working Note number 70.",
URL = "http://www.neglib.org/lapack/lawns/lawn70.ps",
acknowledgement = ack-nhfb,
}
@TechReport{Demmel:1994:CPBb,
author = "James Demmel and Inderjit Dhillon and Huan Ren",
title = "On the Correctness of Parallel Bisection in Floating
Point",
type = "LAPACK Working Note",
number = "70",
institution = inst-UT-CS,
address = inst-UT-CS:adr,
month = mar,
year = "1994",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "UT-CS-94-228, March 1994.",
URL = "http://www.netlib.org/lapack/lawns/lawn70.ps;
http://www.netlib.org/lapack/lawnspdf/lawn70.pdf",
acknowledgement = ack-nhfb,
}
@Article{Demmel:1994:FNA,
author = "James W. Demmel and Xiaoye Li",
title = "Faster Numerical Algorithms via Exception Handling",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "983--992",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295860",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
note = "This is an expanded version of
\cite{Demmel:1993:FNA}.",
URL = "http://www.cs.berkeley.edu/~xiaoye/ieee.ps.gz",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@InProceedings{Dimauro:1994:DFNa,
author = "G. Dimauro and S. Impedovo and G. Pirlo",
booktitle = "Proceedings of the 20th {EUROMICRO} Conference,
{EUROMICRO 94}. System Architecture and Integration",
title = "The `diagonal function' in non-redundant residue
number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "590--596",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/EURMIC.1994.390354",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Although the `diagonal function' of a Residue Number
System has been recently introduced as a powerful tool
to perform non modular operations, its implementation
is generally realized using an additional modulus
external to the set of system moduli. \ldots{}",
}
@InProceedings{Dimauro:1994:DFNb,
author = "G. Dimauro and S. Impedovo and G. Pirlo",
booktitle = "{EUROMICRO 94}. System Architecture and Integration.
Proceedings of the 20th {EUROMICRO} Conference",
title = "The `diagonal function' in non-redundant residue
number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "590--596",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/EURMIC.1994.390354",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Although the `diagonal function' of a Residue Number
System has been recently introduced as a powerful tool
to perform non modular operations, its implementation
is generally realized using an additional modulus
external to the set of system moduli. \ldots{}",
}
@Misc{Edelman:1994:W,
author = "Alan Edelman",
title = "When is $ x \star (1 / x) \neq 1 $ ?",
howpublished = "Web document",
day = "7",
month = dec,
year = "1994",
bibdate = "Wed Aug 07 15:04:56 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://math.mit.edu/~edelman/homepage/papers/ieee.pdf",
acknowledgement = ack-nhfb,
}
@Book{Ercegovac:1994:DSR,
author = "Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang",
title = "Division and square root: digit-recurrence algorithms
and implementations",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "x + 230",
year = "1994",
ISBN = "0-7923-9438-0",
ISBN-13 = "978-0-7923-9438-9",
LCCN = "QA76.9.C62 E73 1994",
bibdate = "Fri Mar 27 09:46:24 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Ercegovac:1994:VHR,
author = "M. D. Ercegovac and T. Lang and P. Montuschi",
title = "Very-High Radix Division with Prescaling and Selection
by Rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "909--918",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295853",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295853",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
summary = "A division algorithm in which the quotient-digit
selection is performed by rounding the shifted residual
in carry-save form is presented. To allow the use of
this simple function, the divisor (and dividend) is
prescaled to a range close to one. The \ldots{}",
xxtitle = "Very high radix division with selection by rounding
and prescaling",
}
@Article{Fagin:1994:FPG,
author = "B. Fagin and C. Renard",
title = "Field Programmable Gate Arrays and Floating Point
Arithmetic",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "2",
number = "3",
pages = "365--367",
month = sep,
year = "1994",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/92.311646",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present empirical results describing the
implementation of an IEEE Standard 754 compliant
floating-point adder/multiplier using field
programmable gate arrays. The use of FPGA's permits
fast and accurate quantitative evaluation of a variety
of circuit design tradeoffs for addition and
multiplication. PPGA's also permit accurate assessments
of the area and time costs associated with various
features of the IEEE floating-point standard, including
rounding and gradual underflow. These costs are
analyzed, along with the effects of architectural
correlation, a phenomenon that occurs when the cost of
combining architectural features exceeds the sum of
separate implementation. We conclude with an assessment
of the strengths and weaknesses of using FPGA's for
floating-point arithmetic.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, US Air Force Acad.,
Colorado Springs, CO, USA",
classification = "B1265B (Logic circuits); B2570 (Semiconductor
integrated circuits); C5120 (Logic and switching
circuits); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
keywords = "Addition; Architectural correlation; Area costs; Field
programmable gate arrays; Floating point arithmetic;
Floating-point adder; Floating-point multiplier; FPGA;
IEEE Standard 754 compliance; Multiplication; Time
costs",
summary = "We present empirical results describing the
implementation of an IEEE Standard 754 compliant
floating-point adder/multiplier using field
programmable gate arrays. The use of FPGA's permits
fast and accurate quantitative evaluation of a variety
of \ldots{}",
thesaurus = "Adders; Application specific integrated circuits;
Digital arithmetic; Logic arrays; Multiplying
circuits",
}
@Book{Farquhar:1994:MPH,
author = "Erin Farquhar and Philip Bruce",
title = "The {MIPS} Programmer's Handbook",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "viii + 408",
year = "1994",
ISBN = "1-55860-297-6",
ISBN-13 = "978-1-55860-297-7",
LCCN = "QA76.6 .F375 1994",
bibdate = "Fri May 13 18:21:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
price = "US\$36.95",
abstract = "A hands-on view of the highly successful MIPS family
of microprocessors, written for programmers developing
systems applications for the MIPS platform. The MIPS
Programmer's Handbook describes the MIPS architecture
from the perspective of assembly- and C-language
programmers, with special emphasis on issues related to
embedded applications. Engineers writing system-level
programs for MIPS-based embedded systems will find the
topic selection especially useful including the
sections on software conventions, initializing the
processor in a bare machine environment, and writing
exception handlers. For convenient use, the instruction
set reference is presented with only one page per
instruction. The authors focus on the instructions
available to assembly-language programmers, rather than
on the hardware-level instruction set documented in
data books released by vendors of the MIPS processor.
Provides enough detail for anyone doing serious
system-level programming. Also included are ten
complete program examples, with line-by-line
explanations.",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
tableofcontents = "1: Introduction \\
2: Software Conventions \\
3: Initialization \\
4: Exceptions \\
5: Instruction Set Reference \\
A: Overview of the MIPS1 Architecture \\
B: Instruction Summary \\
C: Prologue and Epilogue Templates \\
D: Include Files \\
E: Libraries \\
F: Vendors of MIPS Products",
}
@InProceedings{FiallosAguilar:1994:HPA,
author = "M. Fiallos-Aguilar",
title = "High precision arithmetic units for fine-grain
massively parallel computing",
crossref = "IEEE:1994:PFI",
pages = "403--407",
year = "1994",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we deal with new high precision
arithmetic units (AUs). These AUs are specialized in
the computation of one arithmetic operation (division,
addition, etc.), but when hundreds of them are
interconnected by a reconfigurable network, a parallel
architecture that uses massive digit-level pipelining
between floating-point arithmetic units (allowing fast
computation of scientific jobs) becomes interesting. In
this paper we present several new AUs for the fast
computation of arithmetic expressions that will be used
on a high precision massively parallel computer. (6
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Lab. LIP-IMAG, Ecole Normale Superieure de Lyon,
France",
classification = "C5220P (Parallel architecture); C5230 (Digital
arithmetic methods)",
keywords = "Arithmetic units; Fine-grain; Floating-point
arithmetic units; High precision; Massively parallel
computing; Parallel architecture",
thesaurus = "Digital arithmetic; Parallel architectures; Pipeline
arithmetic",
}
@Article{Gander:1994:AFP,
author = "H. Gander and M. Vincze and J. P. Prenninger",
title = "Application of a Floating Point Digital Signal
Processor to the Control of a Laser Tracking System",
journal = j-IEEE-TRANS-CONTROL-SYST-TECHNOL,
volume = "2",
number = "4",
pages = "290--298",
month = dec,
year = "1994",
CODEN = "IETTE2",
ISSN = "1063-6536 (print), 1558-0865 (electronic)",
ISSN-L = "1063-6536",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Control Systems Technology",
summary = "Laser tracking systems represent the most promising
technique for dynamic position measurement of
industrial robots. The Institute of Flexible Automation
at the Vienna University of Technology a new tracking
algorithm has been developed. It is shown \ldots{}",
}
@InProceedings{Gerber:1994:DPH,
author = "S. Gerber and M. Goessel",
title = "Detection of permanent hardware faults of a floating
point adder by pseudoduplication",
crossref = "Echtle:1994:PFI",
pages = "327--335",
year = "1994",
DOI = "https://doi.org/10.1007/3-540-58426-9_139",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper the detection of hardware faults by
pseudoduplication for a special floating point adder is
investigated. For a special floating point adder all
single stuck-at-0/1 faults are injected. In a first
simulation experiment for random input patterns all the
faults are determined which can be detected by
pseudoduplication. In a second experiment for sequences
of random input vectors with different length the
probability to detect an arbitrary single fault is
determined.",
acknowledgement = ack-nhfb,
affiliation = "Max-Planck-Society Fault-Tolerant Comput. Group,
Potsdam University, Germany",
classification = "B1130B (Computer-aided circuit analysis and design);
B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5210B (Computer-aided logic design); C7410D
(Electronic engineering computing)",
keywords = "Arbitrary single fault; Floating point adder;
Permanent hardware faults; Probability;
Pseudoduplication; Random input patterns; Stuck at
faults",
thesaurus = "Adders; Digital simulation; Fault location; Floating
point arithmetic; Logic CAD; Logic testing",
}
@Article{Granlund:1994:DII,
author = "Torbj{\"o}rn Granlund and Peter L. Montgomery",
title = "Division by invariant integers using multiplication",
journal = j-SIGPLAN,
volume = "29",
number = "6",
pages = "61--72",
month = jun,
year = "1994",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/178243.178249",
ISBN = "0-89791-598-4",
ISBN-13 = "978-0-89791-598-4",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:51 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/178243/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.cwi.nl/pub/pmontgom/divcnst.psa4.gz;
ftp://ftp.cwi.nl/pub/pmontgom/divcnst.psl.gz;
http://www.acm.org:80/pubs/citations/proceedings/pldi/178243/p61-granlund/",
abstract = "Integer division remains expensive on today's
processors as the cost of integer multiplication
declines. We present code sequences for division by
arbitrary nonzero integer constants and run-time
invariants using integer multiplication. The algorithms
assume a two's complement architecture. Most also
require that the upper half of an integer product be
quickly accessible. We treat unsigned division, signed
division where the quotient rounds towards zero, signed
division where the quotient rounds towards $ - \infty
$, and division where the result is known a priori to
be exact. We give some implementation results using the
C compiler GCC.",
acknowledgement = ack-nhfb,
affiliation = "Cygnus Support, Mountain View, CA, USA",
annote = "Published as part of the Proceedings of PLDI'94.",
classification = "C5230 (Digital arithmetic methods); C6110 (Systems
analysis and programming); C6150C (Compilers,
interpreters and other processors)",
confdate = "20-24 June 1994",
conflocation = "Orlando, FL, USA",
confsponsor = "ACM",
conftitle = "ACM SIGPLAN '94 Conference on Programming Language
Design and Implementation (PLDI)",
corpsource = "Cygnus Support, Mountain View, CA, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "algorithms; Arbitrary nonzero integer constants;
arbitrary nonzero integer constants; C compiler; Code
sequences; code sequences; digital arithmetic; Floating
point arithmetic; floating point arithmetic; GCC;
Integer division; integer division; Integer
multiplication; integer multiplication; Invariant
integers; invariant integers; mathematics computing;
Multiplication; multiplication; performance; program;
program compilers; programming; reduced instruction set
computing; RISC processors; Run-time invariants;
run-time invariants; Signed division; signed division;
Two's complement architecture; two's complement
architecture; Unsigned division; unsigned division",
sponsororg = "ACM",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf F.2.1}
Theory of Computation, ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY, Numerical Algorithms and Problems.
{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Compilers.",
thesaurus = "Digital arithmetic; Mathematics computing; Program
compilers; Programming; Reduced instruction set
computing",
treatment = "T Theoretical or Mathematical",
}
@Article{Grosse:1994:IRS,
author = "Eric Grosse and John D. Hobby",
title = "Improved rounding for spline coefficients and knots",
journal = j-MATH-COMPUT,
volume = "63",
number = "207",
pages = "175--194",
month = jul,
year = "1994",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65D07",
MRnumber = "94j:65019",
bibdate = "Tue Mar 25 15:38:13 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
acknowledgement = ack-nhfb,
affiliation = "Comput. Sci. Res., AT\&T Bell Labs., Murray Hill, NJ,
USA",
ajournal = "Math. Comput.",
classcodes = "B0290F (Interpolation and function approximation);
B0290B (Error analysis in numerical methods); C4130
(Interpolation and function approximation); C4110
(Error analysis in numerical methods)",
corpsource = "Comput. Sci. Res., AT\&T Bell Labs., Murray Hill, NJ,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "affine model; algorithm; error; error analysis;
infinite-precision value; knot; knots; Lovasz basis
reduction; optimal full-precision free-; parameterized
spline; quadratic error model; rounding; roundoff
errors; spline coefficients; splines (mathematics)",
treatment = "T Theoretical or Mathematical",
}
@Article{Hahn:1994:UDF,
author = "H. Hahn and D. Timmermann and B. J. Hosticka and B.
Rix",
title = "A unified and division-free {CORDIC} argument
reduction method with unlimited convergence domain
including inverse hyperbolic functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "11",
pages = "1339--1344",
month = nov,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.324568",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hartwig:1994:FPA,
author = "F. Hartwig and A. Lacroix",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS '94}, 2 June 1994",
title = "Floating point addition errors and their effect on the
roundoff noise in digital signal processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "121--124",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An improved adder model is derived which takes into
account correlations between signal and error. For
different adder strategies is shown the influence of
the improved adder model on the estimated of the
resulting \ldots{}",
}
@MastersThesis{Hauser:1994:PEH,
author = "John R. Hauser",
title = "Programmed exception handling: research project",
type = "{Master of Science, Plan II}",
school = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "82",
year = "1994",
LCCN = "T7.49.1994 H286",
bibdate = "Mon Feb 18 12:39:53 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hegland:1994:SSP,
author = "Markus Hegland",
title = "A self-sorting in-place fast {Fourier} transform
algorithm suitable for vector and parallel processing",
journal = j-NUM-MATH,
volume = "68",
number = "4",
pages = "507--547",
year = "1994",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65T20 (65Y05)",
MRnumber = "96e:65082",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "B0290Z (Other numerical methods); C4190 (Other
numerical methods); C5220P (Parallel architecture);
C5440 (Multiprocessing systems); C7310 (Mathematics
computing)",
corpsource = "Centre for Math. Anal. and its Applications,
Australian Nat. University, Canberra, ACT, Australia",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "data analysis; distributed memory computers; fast
Fourier transforms; floating point pipelines; Fujitsu
VP2200; index digit permutations; mathematics
computing; matrix recursions; parallel processing;
self-sorting in-place fast Fourier transform algorithm;
splitting formulas; uniformly long vector lengths;
vector processing; vector processor systems",
treatment = "A Application; P Practical; T Theoretical or
Mathematical",
}
@Article{Hemkumar:1994:RLC,
author = "N. D. Hemkumar and J. R. Cavallaro",
title = "Redundant and On-Line {CORDIC} for Unitary
Transformations",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "941--954",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295856",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@Article{Hester:1994:PPP,
author = "P. D. Hester and W. J. Filip",
title = "Preface: {Power2} and {PowerPC} Architecture and
Implementation",
journal = j-IBM-JRD,
volume = "38",
number = "5",
pages = "490--491",
month = sep,
year = "1994",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Mon Feb 12 08:14:00 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.almaden.ibm.com/journal/rd38-5.html#one",
abstract = "During the four years since the RISC System\slash
6000* (RS\slash 6000) announcement in February of 1990,
IBM* has strengthened its product line with
microprocessor enhancements, increased memory capacity,
improved graphics, greatly expanded I/O adapters, and
new AIX* and compiler releases. In 1991, IBM began
planning for future RS\slash 6000 systems that would
span the range from small, battery-operated products to
very large supercomputers and mainframes. As the first
step toward achieving this ``palmtop to teraFLOPS''
goal with a single architecture, IBM investigated
further optimizations for the original POWER
Architecture*. This effort led to the creation of the
PowerPC* alliance (IBM Corporation, Motorola*, Inc.,
and Apple* Computer Corporation) and the definition of
the PowerPC Architecture*. Today, the single-chip
PowerPC 601* processor is the basis of IBM's entry
systems. A more aggressively superscalar version of the
original POWER processor, the multichip POWER2*
processor, is exploited in our current IBM high-end
RISC systems. As technology continues to advance,
PowerPC implementations will provide the basis for
high-performance 64-bit super servers. This special
issue of the IBM Journal of Research and Development
focuses on the POWER2 and PowerPC portions of IBM's
wide-ranging announcement in the Fall of 1993. The new
POWER2 processor nearly doubles the performance of the
earlier high-end models. The PowerPC 601 processor was
introduced in the RISC System\slash 6000 Model 250, the
first system in the industry to use the PowerPC
Architecture created by the strategic
IBM/Motorola/Apple alliance. These workstations
achieved industry-leading performance and
price/performance on virtually every industry-standard
benchmark, including SPECint92*, SPECfp92*, Linpack,
TPP, TPC-A*, and TPC-C*. Compared to the 1990
offerings, SPEC performance nearly quadrupled,
transaction performance improved by a factor of almost
five, maximum memory capacity quadrupled, and the
maximum disk capacity grew by an order of magnitude.
The POWER2 design exploits both multichip technology
and a larger die size to execute up to six instructions
(eight operations) per clock cycle. Many of the
higher-performance POWER2-based systems provide peak
execution rates in excess of a half billion operations
per second. The paper by White and Dhawan provides an
overview of the POWER2 design. Shippy and Griffith
describe the dual fixed-point unit design, the data
cache unit, and the storage control unit. Hicks, Fry,
and Harvey describe the dual floating-point unit
design. Barreh et al. describe hardware strategies to
minimize compare-branch penalties in the instruction
cache unit. Welbon et al. describe a POWER2 hardware
performance- monitoring facility which provides
execution characteristics that can identify
opportunities for application performance improvement.
This facility can also be used to gather information
crucial to future design decisions. Two performance
papers conclude the POWER2 portion of this issue.
Franklin et al. analyze some of the key POWER2 hardware
contributions to performance on the commercial
workloads. Agarwal, Gustavson, and Zubair relate their
experiences with optimizing the high-performance
Engineering/Scientific Subroutine Library (ESSL) for
the POWER2 implementation. While POWER2 and PowerPC
implementations provide the opportunity for
high-performance systems, optimizing software is also
key in delivering end-user performance. Blainey
describes aspects of the TOBEY compiler, with special
emphasis on instruction scheduling for the RS\slash
6000 products. Heisch describes TDPR, a prototype
version of FDPR, a program restructuring tool which
improves application performance by placing frequently
executed code blocks so as to minimize instruction
cache misses and branch penalties. IBM and the PowerPC
alliance are currently developing a family of five
PowerPC designs. IBM and Motorola designers at the
Somerset Design Center in Austin will optimize
single-chip implementations of the PowerPC Architecture
for high-volume products. The high-end requirements of
the large server and workstation products will be
addressed with multichip PowerPC implementations from
IBM.\par
IBM entry-level workstation products introduced the
PowerPC 601 microprocessor, the first member of the
PowerPC family. The goal for the PowerPC 601 designers
was to quickly bring PowerPC to the market. Vaden et
al. describe the microarchitecture and performance
aspects of the PowerPC 601 processor. Brodnax et al.
discuss the PowerPC 601 circuitry and chip
implementation details. Future products are planned
that will incorporate the PowerPC 603*, PowerPC 604*,
and the 64-bit PowerPC 620* implementations as they
become available. In addition, the price and
price/performance of the PowerPC family enable
lower-cost ``RISC PCs'' to be built using PowerPC
microprocessors. These ``RISC PCs'' will be developed
by the IBM POWER Personal Systems Division.\par
The PowerPC and POWER2 systems signify a major
milestone in IBM's commitment to the ``palmtops to
teraFLOPS'' strategy. The PowerPC 601 chip extends the
entry products further into the high-volume market by
providing exceptional performance in a low-cost
single-chip microprocessor. The high-end POWER2
implementation extracts the maximum performance
achievable in today's technology, thrusting the IBM
RISC processors into the supercomputing and
large-server environments. IBM POWER Parallel Systems
extends the RS\slash 6000 processing capability by
providing IBM POWER Parallel SP2* systems with up to
512 POWER/POWER2 nodes. In addition to scalability,
four-way High Availability Cluster Multi-Processor
(HACMP) systems provide the reliability/availability
that one would expect from mainframe-class systems by
supporting a ``no single point of failure'' capability,
even when one processor is off line. This impressive
base of processing technology complements a commitment
to high-performance compilers and strong graphics
offerings.\par
This robust product line addresses the cost-driven
requirements of the entry workstation market, the
transaction and server requirements of the commercial
market, and the computation-intensive requirements of
the technical market. These hardware offerings result
from a team effort by many dedicated and talented
individuals from around the world. Their expertise and
skill in a wide range of disciplines were key to
achieving this significant step toward the goal of a
comprehensive architecture. We want to thank all those
involved in continuing the success of the RISC
System\slash 6000 line.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Article{Hicks:1994:PFU,
author = "T. N. Hicks and R. E. Fry and P. E. Harvey",
title = "{POWER2} floating-point unit: Architecture and
implementation",
journal = j-IBM-JRD,
volume = "38",
number = "5",
pages = "525--536",
month = sep,
year = "1994",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The POWER2 floating-point unit (FPU) extends the
concept of the innovative multiply-add fused (MAF) ALU
of the RISC System/6000 processor to provide a
floating-point unit that sets new standards, not only
for computation capability but for data throughput and
processor flexibility. The POWERS FPU achieves a
performance (MFLOPS) rate never accomplished before by
a personal workstation machine by: (1) integrating dual
generic MAF ALUs, (2) doubling the instruction
bandwidth and quadrupling the data bandwidth over that
of the POWER FPU, (3) adding support for additional
functions, and (4) using dynamic instruction scheduling
techniques to maximize instruction-level parallelism
not only among its own internal units but with the rest
of the CPU.",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Austin, TX, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods)",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "Data bandwidth; Dynamic instruction scheduling;
Floating-point unit; Instruction bandwidth;
Instruction-level parallelism; Multiply add fused
arithmetic logic unit; POWER2; RISC System/6000
processor",
thesaurus = "Floating point arithmetic; Microprocessor chips;
Parallel architectures; Parallel processing; Reduced
instruction set computing",
}
@InProceedings{Hilker:1994:NMM,
author = "S. Hilker and N. Phan and D. Rainey",
title = "A 3.4 ns 0.8 mu m {BiCMOS} 53*53 b multiplier tree",
crossref = "Wuorinen:1994:IIS",
pages = "292--293",
year = "1994",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A 53*53 b multiplier tree with 3.4 ns latency, 10
mm/sup 2/ active area, and 5 W power dissipation at 200
MHz and 3.6 V supply is implemented in 0.8 mu m n-well
BiCMOS with 115 AA gate oxide, 0.45 mu m effective
channel length, and 4 levels of metal. This 3.4ns
low-latency multiplier is for a floating-point unit
(FPU) on a BiCMOS RISC processor capable of performing
IEEE double precision multiply-add operations in three
pipelined stages at 200MHz (15ns latency, 5ns
throughput, 400MFLOPs peak rate) using multiply-add
fused dataflow.",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Rochester, MN, USA",
classification = "B1265B (Logic circuits); B2570K (Mixed technology
integrated circuits); C5120 (Logic and switching
circuits); C5220P (Parallel architecture); C5230
(Digital arithmetic methods)",
keywords = "0.8 Micron; 200 MHz; 3.4 Ns; 3.6 V; 400 MFLOPS; 5 W;
Effective channel length; Floating-point unit; IEEE
double precision multiply-add operations; Latency;
Multiplier tree; Multiply-add fused dataflow; N-well
BiCMOS; Pipelined stages; Power dissipation; RISC
processor",
numericalindex = "Time 3.4E-09 s; Size 8.0E-07 m; Power 5.0E+00 W;
Frequency 2.0E+08 Hz; Voltage 3.6E+00 V; Computer speed
4.0E+08 FLOPS",
thesaurus = "BiCMOS integrated circuits; Digital arithmetic;
Multiplying circuits; Parallel processing; Pipeline
processing; Reduced instruction set computing",
}
@Book{Hill:1994:GPL,
author = "Patricia Hill",
title = "The {G{\"o}del} Programming Language",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "xx + 348",
year = "1994",
ISBN = "0-262-08229-2",
ISBN-13 = "978-0-262-08229-7",
LCCN = "QA76.73.G17H55 1994",
bibdate = "Thu Sep 15 07:47:50 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Section 13.3 (pp. 206--218) defines floating-point
numbers and standard functions conforming to Version
4.0 (August 1992) of the Language Independent
Arithmetic Standard (LIAS) ISO\slash IEC CD
10967-1:1992 (JTC1/SC22/WG11 N318, ANSI X3T3 92-064).
It also conforms to the ANSI\slash IEEE Standard for
Binary Floating-Point Arithmetic 754-1985.",
acknowledgement = ack-nhfb,
}
@TechReport{Hopkins:1994:CEM,
author = "Tim Hopkins and John Slater",
title = "A Comment on the {Eispack} Machine Epsilon Routine",
type = "Technical Report",
number = "18-94",
institution = "University of Kent, Computing Laboratory, University
of Kent",
address = "Canterbury, UK",
year = "1994",
bibdate = "Tue Apr 12 12:00:52 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.kent.ac.uk/pubs/1994/74/content.ps.gz",
acknowledgement = ack-nhfb,
}
@Article{Horvath:1994:PPM,
author = "Tam{\'a}s Horv{\'a}th and Spyros S. Magliveras and
Tran van Trung",
title = "A Parallel Permutation Multiplier for a {PGM}
Crypto-Chip",
journal = j-LECT-NOTES-COMP-SCI,
volume = "839",
pages = "108--113",
year = "1994",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:49:18 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0839.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0839/08390108.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0839/08390108.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "CRYPTO; cryptology; IACR; IEEE",
}
@Article{Hsu:1994:CPF,
author = "Chau-Yun Hsu and Jui Chi Yao",
title = "Comparative performance of fast cosine transform with
fixed-point roundoff error analysis",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "42",
number = "5",
pages = "1256--1259",
month = may,
year = "1994",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "Suitable scaling schemes are chosen for the Lee's and
the Hou's (1984) fast DCT algorithms, and the relative
fixed-point roundoff error analyses are carried out,
respectively. The average output signal-to-noise ratio
are then calculated, and it is \ldots{}",
}
@Article{Hsu:1994:NFP,
author = "Chau-Yun Hsu",
title = "Novel fixed-point roundoff analysis of the
decimation-in-time {FHT}",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "42",
number = "1",
pages = "206--208",
month = jan,
year = "1994",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "A least upper bound for the increasing factor of the
magnitude of the decimation-in-time fast Hartley
transform (FHT) in fixed-point arithmetic is developed
and a new scaling model for the roundoff analysis in
the fixed-point arithmetic computation \ldots{}",
}
@Article{Hull:1994:ICE,
author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
Tang",
title = "Implementing Complex Elementary Functions Using
Exception Handling",
journal = j-TOMS,
volume = "20",
number = "2",
pages = "215--244",
month = jun,
year = "1994",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/178365.178404",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 21 15:10:29 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See correction \cite{Anonymous:1994:C}, and improved
analysis, tightened bounds, and exhibition of worst
cases for complex square roots
\cite{Jeannerod:2017:REC}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/",
abstract = "Algorithms are developed for reliable and accurate
evaluations of the complex elementary functions
required in Fortran 77 and Fortran 90, namely cabs,
csqrt, cexp, clog, csin, and ccos. The algorithms are
presented in a pseudocode that has a convenient
exception-handling facility. A tight error bound is
derived for each algorithm. Corresponding Fortran
programs for an IEEE environment have also been
developed to illustrate the practicality of the
algorithms, and these programs have been tested very
carefully to help confirm the correctness of the
algorithms and their error bounds. The results are of
these tests are included in the paper, but the Fortran
programs are not; the programs are available from
Fairgrieve, ([email protected]).",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; complex elementary functions; design;
implementation",
subject = "G.1.0 [Numerical Analysis]: General--error analysis;
numerical algorithms; G.1.2 [Numerical Analysis]:
Approximation--elementary function approximation; G.4
[Mathematics of Computing]: Mathematical
Software--algorithm analysis; reliability and
robustness; verification",
}
@Article{Hung:1994:ASD,
author = "C. Y. Hung and B. Parhami",
title = "An approximate sign detection method for residue
numbers and its application to {RNS} division",
journal = j-COMPUT-MATH-APPL,
volume = "27",
number = "4",
pages = "23--35",
month = feb,
year = "1994",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122194900523",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Hung:1994:FRD,
author = "Ching Yu Hung and Behrooz Parhami",
title = "Fast {RNS} division algorithms for fixed divisors with
application to {RSA} encryption",
journal = j-INFO-PROC-LETT,
volume = "51",
number = "4",
pages = "163--169",
day = "24",
month = aug,
year = "1994",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "94A60",
MRnumber = "1 294 308",
bibdate = "Fri Oct 25 18:39:09 2002",
bibsource = "Compendex database;
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
affiliation = "Univ of California",
affiliationaddress = "Santa Barbara, CA, USA",
classification = "722.4; 723.1; 723.2; 921.6; C4240 (Programming and
algorithm theory)C6130S (Data security); C7310
(Mathematics)",
corpsource = "Department of Electr. and Comput. Eng., California
University, Santa Barbara, CA, USA",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
journalabr = "Inf Process Lett",
keywords = "Algorithms; Chinese remainder theorem; Chinese
remainder theorem decoding and table lookup;
Computational complexity; computational complexity;
Computational complexity; Computational methods;
Computer software; Cryptography; cryptography;
Cryptography; Decoding; Digital arithmetic; digital
arithmetic; Digital arithmetic; Division; divisor
reciprocal; Exponentiation; fast RNS division
algorithms; fixed divisors; Fixed divisors; Function
evaluation; mathematics computing; Modular
multiplication; multiplication; Numbering systems;
on-line speed; ordinary integer division; Parallel
processing systems; preprocessing; Residue number
system; Residue processors; RSA encryption; Sign
detection; Table lookup; Time complexity; time
complexity; Time complexity",
treatment = "A Application; T Theoretical or Mathematical",
}
@Book{IBM:1994:IRS,
editor = "Steve White and John Reysa",
title = "{IBM RISC} System\slash 6000 Technology: Volume {II}",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1994",
bibdate = "Fri Mar 18 10:25:19 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A partial draft is available via anonymous ftp to
\path|ibminet.awdpa.ibm.com| in the PostScript file
\path|/pub/rs6kpapers/techbook.ps|.",
acknowledgement = ack-nhfb,
}
@Book{IBM:1994:OA,
author = "{IBM Corporation}",
title = "The {PowerPC} Architecture: a Specification for a New
Family of {RISC} Processors",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
edition = "Second",
pages = "xxxi + 518",
year = "1994",
ISBN = "1-55860-316-6",
ISBN-13 = "978-1-55860-316-5",
LCCN = "QA76.8.P67 P68 1994",
bibdate = "Wed Jul 6 14:15:23 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$49.95",
acknowledgement = ack-nhfb,
}
@Article{Ienne:1994:BSM,
author = "P. Ienne and M. A. Viredaz",
title = "Bit-serial multipliers and squarers",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "12",
pages = "1445--1450",
month = dec,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.338107",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=338107",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ignatowski:1994:CNA,
author = "R. Ignatowski and E. E. Swartzlander",
title = "Creating New Algorithms and Modifying Old Algorithms
to Use the Variable Precision Floating Point
Simulator",
journal = "Conference record",
pages = "152--??",
year = "1994",
ISSN = "1058-6393",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Isaacson:1994:ANM,
author = "Eugene Isaacson and Herbert Bishop Keller",
title = "Analysis of numerical methods",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xv + 541",
year = "1994",
ISBN = "0-486-68029-0 (paperback)",
ISBN-13 = "978-0-486-68029-3 (paperback)",
LCCN = "QA297 .I8 1994",
bibdate = "Fri Aug 20 09:37:14 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/description/dover031/94007740.html",
acknowledgement = ack-nhfb,
remark = "Originally published in \cite{Isaacson:1966:ANM}.
Contains new preface.",
subject = "Numerical analysis",
}
@Book{ISO:1994:IIIa,
author = "{ISO}",
title = "{ISO\slash IEC 10967-1 (1994-12)}: {Information}
technology --- {Language} independent arithmetic ---
{Part 1}: {Integer} and floating point arithmetic",
publisher = pub-ISO,
address = pub-ISO:adr,
pages = "viii + 92",
day = "15",
month = dec,
year = "1994",
bibdate = "Sun Mar 15 11:09:44 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "CHF 176, US\$136.00",
URL = "http://standards.iso.org/ittf/PubliclyAvailableStandards/c018939_ISO_IEC_10967-1_1994(E).zip;
http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=019729;
http://www.iso.ch/cate/d18939.html",
acknowledgement = ack-nhfb,
}
@TechReport{Jackson:1994:PCE,
author = "K. R. Jackson and N. S. Nedialkov",
title = "Precision Control and Exception Handling in Scientific
Computing",
type = "Technical Report",
institution = "Department of Computer Science, University of
Toronto",
address = "Toronto, ON, Canada",
pages = "8",
year = "1994",
bibdate = "Tue May 22 15:45:43 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.toronto.edu/NA/reports.html#prec.except;
http://www.cs.toronto.edu/pub/reports/na/prec.except.ps.Z",
abstract = "This paper describes convenient language facilities
for precision control and exception handling. Nedialkov
has developed a variable-precision and exception
handling library, SciLib, implemented as a numerical
class library in C++. A new scalar data type, {\em
real}, is introduced, consisting of variable-precision
floating-point numbers. Arithmetic, relational, and
input and output operators of the language are
overloaded for reals, so that mathematical expressions
can be written without explicit function calls.
Precision of computations can be changed during program
execution. The exception handling mechanism treats only
numerical exceptions and does not distinguish between
different types of exceptions.\par
The proposed precision control and exception handling
facilities are illustrated by sample SciLib programs.",
acknowledgement = ack-nhfb,
}
@InProceedings{Jain:1994:SRR,
author = "V. K. Jain and Lei Lin",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing: {ICASSP-94, 19--22} April 1994",
title = "Square-root, reciprocal, sine\slash cosine, arctangent
cell for signal and image processing",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II/521--II/524",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper discusses an efficient interpolation method
for nonlinear function generation. Based on this, a 24
bit VLSI cell, capable of computing the (1) square
root, (2) reciprocal, (3) sine/cosine, and (4)
arctangent functions, is presented for \ldots{}",
}
@Article{Jaromczyk:1994:CCH,
author = "Jerzy W. Jaromczyk and G. W. Wasilkowski",
title = "Computing convex hull in a floating point arithmetic",
journal = j-COMP-GEOM,
volume = "4",
number = "5",
pages = "283--292",
year = "1994",
ISSN = "0925-7721 (print), 1879-081X (electronic)",
ISSN-L = "0925-7721",
MRclass = "68U05",
MRnumber = "95j:68159",
bibdate = "Fri Dec 8 08:24:07 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computational Geometry. Theory and Applications",
}
@Article{Johnstone:1994:DAN,
author = "Paul Johnstone and Frederick E. Petry",
title = "Design and analysis of non-binary radix floating point
representations",
journal = j-COMPUT-ELECTR-ENG,
volume = "20",
number = "1",
pages = "39--50",
month = jan,
year = "1994",
CODEN = "CPEEBQ",
ISSN = "0045-7906 (print), 1879-0755 (electronic)",
ISSN-L = "0045-7906",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The authors examine the feasibility of higher radix
floating point representations and in particular
decimal based representations. Traditional analyses of
such representations have assumed the format of a
floating point datum to be roughly identical to that of
traditional binary floating point encodings such as the
IEEE P754 task group standard representations. We relax
this restriction and propose a method of encoding
higher radix floating point data with range, precision
and storage requirements comparable to those exhibited
by traditional binary representations. Results from W.
M. McKeeman's (1967) maximum and average relative
representational error (MRRE and ARRE) analyses, R. P.
Brent's (1973) RMS error evaluation, D. W. Matula's
(1970) ratio of significance space and gap functions,
and W. S. Brown and P. L. Richman's (1969) exponent
range estimates are extended to accommodate the
proposed representation. A decimal alternative to
traditional binary representations is proposed and the
behavior of such a system is contrasted with that of a
comparable binary system.",
acknowledgement = ack-nhfb,
affiliation = "Dow Jones Telerate, New Orleans, LA, USA",
classification = "B1265 (Digital electronics); C5230 (Digital
arithmetic methods)",
fjournal = "Computers and Electrical Engineering",
keywords = "ARRE; Average relative representational error; Decimal
alternative; Decimal based representations; decimal
floating-point arithmetic; Exponent range estimates;
Floating point datum; Gap functions; Higher radix
floating point representations; MRRE; Non-binary radix
floating point representations; RMS error evaluation;
Significance space ratio; Storage requirements",
thesaurus = "Digital arithmetic; Roundoff errors",
}
@Article{Kabuo:1994:ARS,
author = "H. Kabuo and T. Taniguchi and A. Miyoshi and H.
Yamashita and M. Urano and H. Edamatsu and S.
Kuninobu",
title = "Accurate Rounding Scheme for the {Newton--Raphson}
Method Using Redundant Binary Representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "1",
pages = "43--51",
month = jan,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.250608",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:53 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=250608",
acknowledgement = ack-nj # "\slash " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "Proposes a new algorithm of estimation and
compensation of the error effect for rounding in the
case of implementation of division and square root
using the Newton--Raphson method. The authors analyze
the error of the hardware system to confirm the
\ldots{}",
}
@Article{Kalliojarvi:1994:RCW,
author = "K. Kalliojarvi and J. Astola",
title = "Required coefficient word length in floating-point and
logarithmic digital filters",
journal = j-IEEE-SIGNAL-PROCESS-LETT,
volume = "1",
number = "3",
pages = "52--54",
month = mar,
year = "1994",
CODEN = "ISPLEM",
ISSN = "1070-9908 (print), 1558-2361 (electronic)",
ISSN-L = "1070-9908",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Signal Processing Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
summary = "The effects of coefficient quantization to the
response of a digital filter are studied. Easy-to-use
expressions for the required coefficient word length,
with which the filter response deviations are within
specified bounds, are derived for filters \ldots{}",
}
@MastersThesis{Kambi:1994:EAD,
author = "Shivaprakash Jayadev Kambi",
title = "Error analysis of digital filters realized with
floating-point arithmetic",
type = "Thesis ({M.S.})",
school = "Mississippi State University. Department of Electrical
and Computer Engineering",
address = "Mississippi State, MS 39762, USA",
pages = "viii + 82",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital filters (Mathematics); Electric filters,
Digital.; Floating-point arithmetic.; Mississippi State
University --- Thesis --- (1994)",
}
@InProceedings{Kanellakis:1994:FPR,
author = "A. Kanellakis and P. Agathoklis",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS '94}, 2 June 1994",
title = "Floating-point roundoff noise analysis of {$2$-D}
state-space digital filters",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "601--604",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "In this paper the analysis of roundoff noise in
floating point state-space realizations of $2$-D
digital filters is considered. The variance of the
roundoff noise at the output of a $2$-D digital filter
is derived. It is shown that this variance is
\ldots{}",
}
@Misc{Karp:1994:FPA,
author = "Alan H. Karp and Peter Markstein and Dennis
Brzezinski",
title = "Floating point arithmetic unit using modified
{Newton--Raphson} technique for division and square
root",
howpublished = "US Patent 5,341,321",
day = "23",
month = aug,
year = "1994",
bibdate = "Thu Oct 17 10:20:52 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Patent filed 5 May 1993, granted to Hewlett-Packard
Company on 23 August 1994. Patent expired 5-May-2013.
See criticism in \cite{Zimmermann:2005:XXX}.",
URL = "http://patft.uspto.gov/netahtml/PTO/search-bool.html;
https://patents.google.com/patent/US5341321A",
abstract = "A floating point processing system which uses a
multiplier unit and an adder unit to perform floating
point division and square root operations using both a
conventional and a modified form of the Newton--Raphson
method. The modified form of the Newton--Raphson method
is used in place of the final iteration of the
conventional Newton--Raphson so as to compute high
precision approximated results with a substantial
improvement in speed. The invention computes
approximated results faster and simplifies hardware
requirements because no multiplications of numbers of
the precision of the result are required.",
acknowledgement = ack-nhfb,
}
@Article{Katti:1994:CDC,
author = "R. Katti",
title = "Comments on {``Decomposition of Complex Multipliers
Using Polynomial Encoding''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "3",
pages = "381--383",
month = mar,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.272441",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See \cite{Skavantzos:1992:DCM}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272441",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kawahito:1994:HSA,
author = "S. Kawahito and M. Ishida and T. Nakamura and M.
Kameyama and T. Higuchi",
title = "High-speed area-efficient multiplier design using
multiple-valued current-mode circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "1",
pages = "34--42",
month = jan,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.250607",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See comments \cite{Parhami:1996:CHS}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=250607",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kim:1994:FPF,
author = "Seehyun Kim and Wonyong Sung",
title = "A Floating-Point to Fixed-Point Assembly Program
Translator for the {TMS} {320C25}",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "41",
number = "11",
pages = "730--739",
month = nov,
year = "1994",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.331543",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "A floating-point digital signal processor-like
programming environment is developed for the Texas
Instruments TMS 320C25, a fixed-point digital signal
professor. Programmers first develop an assembly
program using a hypothetical floating-point instrument
\ldots{}",
}
@Article{Kobbelt:1994:FDP,
author = "L. Kobbelt",
title = "A Fast Dot-Product Algorithm with Minimal Rounding
Errors",
journal = j-COMPUTING,
volume = "52",
number = "4",
pages = "355--369",
year = "1994",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "68Q20 (68Q25)",
MRnumber = "1 287 970",
bibdate = "Tue Oct 12 16:33:42 MDT 1999",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database; OCLC Contents1st database",
abstract = "Presents a new algorithm which computes dot-products
of arbitrary length with minimal rounding errors,
independent of the number of addends. The algorithm has
an O(n) time and O(1) memory complexity, and does not
need extensions of the arithmetic kernel, i.e., the
usual floating-point operations. A slight modification
yields an algorithm which computes the dot-product in
machine precision. Due to its simplicity, the algorithm
can easily be implemented in hardware.",
acknowledgement = ack-nhfb,
affiliation = "Inst. f{\"u}r Betriebs-und Dialogsyst., Karlsruhe
University, Germany",
classification = "721.1; 722.4; 921.1; 921.6; C4140 (Linear algebra);
C4240 (Programming and algorithm theory); C5230
(Digital arithmetic methods)",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
journalabr = "Comput Vienna New York",
keywords = "Addends; Algorithms; Arbitrary length; Arithmetic
kernel; Computational complexity; Computer arithmetic;
Computer hardware; Digital arithmetic; Dot product
computation; Errors; Exact computer arithmetic; Fast
dot-product algorithm; Floating-point operations;
Hardware implementation; Machine precision; Matrix
algebra; Matrix multiplications; Memory complexity;
Minimal rounding errors; Numerical algorithms;
Numerical methods; Stability; Summation; Time
complexity",
pubcountry = "Austria",
thesaurus = "Computational complexity; Digital arithmetic; Matrix
algebra; Numerical analysis; Roundoff errors; Vectors",
}
@Article{Kornerup:1994:SLA,
author = "P. Kornerup",
title = "A Systolic, Linear-Array Multiplier for a Class of
Right-Shift Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "892--898",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295851",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295851",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@InProceedings{Krandick:1994:EMF,
author = "W. Krandick and J. R. Johnson",
title = "Efficient multiprecision floating point multiplication
with exact rounding",
crossref = "Calmet:1994:RWC",
pages = "207--??",
year = "1994",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An algorithm is described for multiplying
multiprecision floating point numbers. The returned
result is equal to the floating point number obtained
by rounding the exact product. Software implementations
of multiprecision floating point multiplication can
reduce the computing time by a factor of two if they do
not compute the low order digits of the product of the
two mantissas. However, these algorithms do not
necessarily provide exactly rounded results. The
algorithm described in this paper is guaranteed to
produce exactly rounded results and typically obtains
the same savings. The method can be modified to take
advantage of Karatsuba's algorithm for fast integer
multiplication.",
acknowledgement = ack-nhfb,
affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
University, Linz, Austria",
classification = "C5230 (Digital arithmetic methods); C7310
(Mathematics computing)",
keywords = "Exact rounding; Fast integer multiplication;
Karatsuba's algorithm; Multiprecision floating point
multiplication; Software implementations",
thesaurus = "Digital arithmetic; Mathematics computing",
}
@Article{Laakso:1994:BFP,
author = "T. I. Laakso and L. B. Jackson",
title = "Bounds for Floating-Point Roundoff Noise",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "41",
number = "6",
pages = "424--426",
month = jun,
year = "1994",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.300204",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "The dummy multiplier model and the conventional
estimates for roundoff noise variance in floating-point
implementations are compared. Common upper and lower
bounds for the noise estimates are derived and
experimental results are presented. Although \ldots{}",
}
@Article{Laakso:1994:ELC,
author = "T. Laakso and B. Zeng and I. Hartimo and Y. Neuvo",
title = "Elimination of limit cycles in floating-point
implementations of direct-form recursive digital
filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "41",
number = "4",
pages = "308--313",
month = apr,
year = "1994",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.285707",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "This paper focuses on the limit cycle analysis of
floating-point implementations of direct form recursive
digital filters. A sufficient criterion for the absence
of zero-input limit cycles is derived for a direct-form
implementation with a single \ldots{}",
}
@Article{Ledoux:1994:TOW,
author = "C. Ledoux and J. F. Grandin",
title = "Two original weight pruning methods based on
statistical tests and rounding techniques",
journal = "Vision, Image and Signal Processing, IEE
Proceedings-",
volume = "141",
number = "4",
pages = "230--237",
month = aug,
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors focus on the use of neural networks to
approximate continuous decision functions. In this
context, the parameters to be estimated are the
synaptic weights of the network. The number of such
parameters and the quantity of data \ldots{}",
}
@Article{Lewis:1994:IMF,
author = "D. M. Lewis",
title = "Interleaved Memory Function Interpolators with
Application to an Accurate {LNS} Arithmetic Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "974--982",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295859",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295859",
abstract = "This paper describes a new method for polynomial
interpolation in hardware, with advantages demonstrated
by its application to an accurate logarithmic number
system (LNS) arithmetic unit. The use of an interleaved
memory reduces storage requirements by allowing each
stored function value to be used in interpolation
across several segments. This strategy can be shown to
always use fewer words of memory than an optimized
polynomial with stored polynomial coefficients.
Interleaved memory function interpolators are then
applied to the specific goal of an accurate logarithmic
number system arithmetic unit. Many accuracy
requirements for the LNS arithmetic unit are possible.
Although a round to nearest would be desirable, it
cannot be easily achieved. The goal suggested is to
insure that the worst case LNS relative error is
smaller than the worst case floating point (FP)
relative error. Using the interleaved memory
interpolator, the detailed design of an LNS arithmetic
unit is performed using a second order polynomial
interpolator including approximately 91K bits of ROM.
This arithmetic unit has better accuracy and less
complexity than previous LNS units.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Toronto
University, Ont., Canada",
ajournal = "IEEE Trans. Comput.",
classification = "C4110 (Error analysis in numerical methods); C4130
(Interpolation and function approximation); C5230
(Digital arithmetic methods); C5320G (Semiconductor
storage)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "32 Bit; 91 Kbit; Accuracy requirements; Accurate
logarithmic number system (LNS) arithmetic unit;
Floating point; Interleaved memory function
interpolators; Polynomial interpolation; ROM; Round to
nearest; Storage requirements",
numericalindex = "Word length 3.2E+01 bit; Storage capacity 9.3E+04
bit",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
summary = "This paper describes a new method for polynomial
interpolation in hardware, with advantages demonstrated
by its application to an accurate logarithmic number
system (LNS) arithmetic unit. The use of an interleaved
memory reduces storage requirements \ldots{}",
thesaurus = "Approximation theory; Digital arithmetic; Error
analysis; Interpolation; Polynomials; Read-only
storage",
}
@Article{Lo:1994:RFP,
author = "Jien-Chung Lo",
title = "Reliable Floating-Point Arithmetic Algorithms for
Error-Coded Operands",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "4",
pages = "400--412",
month = apr,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.278479",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=278479",
abstract = "Reliable floating-point arithmetic is vital for
dependable computing systems. It is also important for
future high-density VLSI realizations that are
vulnerable to soft-errors. However, the direct checking
of floating-point arithmetic is still an open problem.
The author presents a set of reliable floating-point
arithmetic algorithms for low-cost residue encoded and
Berger encoded operands, respectively. Closed form
equations are derived for floating-point addition,
subtraction, multiplication, and division. Given the
standard IEEE floating-point numbers, the proposed
reliable floating-point multiplication algorithms for
low-cost residue encoded operands are extremely
low-cost: it requires less than 8\% of hardware
redundancy in all cases. For reliable floating-point
addition and subtraction, the author finds the hardware
redundancy ratios of applying low-cost residue code is
about the same as that of applying Berger code: less
than 40\% of hardware redundancy for single precision
numbers and about 16\% for double precision numbers.
For reliable floating-point division, Berger encoded
operands yields hardware cost-effectiveness: about 45\%
for single precision numbers and about 36\% for double
precision numbers.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., Rhode Island University,
Kingston, RI, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C5230 (Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Berger check prediction; Berger encoded; Computer
arithmetic; Concurrent error detection; Error-coded
operands; Floating-point arithmetic; Hardware
redundancy; High-density VLSI; Low-cost residue codes;
Redundancy ratios; Reliable floating-point
multiplication; Residue encoded; Soft-errors; Standard
IEEE floating-point numbers",
summary = "Reliable floating-point arithmetic is vital for
dependable computing systems. It is also important for
future high-density VLSI realizations that are
vulnerable to soft-errors. However, the direct checking
of floating-point arithmetic is still an open
\ldots{}",
thesaurus = "Digital arithmetic; Error correction codes;
Redundancy",
}
@Book{May:1994:PAS,
editor = "Cathy May and Ed Silha and Rick Simpson and Hank
Warren",
title = "The {PowerPC} Architecture: a Specification for a New
Family of {RISC} Processors",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
edition = "Second",
pages = "xxxi + 518",
year = "1994",
ISBN = "1-55860-316-6",
ISBN-13 = "978-1-55860-316-5",
LCCN = "QA76.8.P67 P68 1994",
bibdate = "Sat Feb 24 10:55:16 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
price = "US\$49.95",
acknowledgement = ack-nhfb,
oldlabel = "IBM:1994:PAS",
tableofcontents = "Book III. PowerPC Operating Environment
Architecture \\
2. Branch Processor \\
3. Fixed-Point Processor \\
4. Storage Control \\
5. Interrupts \\
6. Timer Facilities \\
7. Synchronization Requirements for Special Registers
and for Lookaside Buffers \\
Appendix A. Optional Facilities and Instructions \\
Appendix B. Assembler Extended Mnemonics \\
Appendix C. Cross-Reference for Changed POWER Mnemonics
\\
Appendix D. New Instructions \\
Appendix E. Implementation-Specific SPRs \\
Appendix F. Interpretation of the DSISR as Set by an
Alignment Interrupt \\
Appendix G. PowerPC Operating Environment Instruction
Set",
}
@Article{McGrath:1994:OMC,
author = "Gary McGrath",
title = "Optimizing {MC68882} Code",
journal = j-DDJ,
volume = "19",
number = "6",
pages = "58, 60, 62, 64, 66, 98--99",
month = jun,
year = "1994",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 03 09:15:49 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "The MC68882 floating-point coprocessor adds 46
instructions to the MC68020/030 32-bit microprocessor,
substantially increasing the speed of floating-point
calculations. Gary examines these instructions and
finds certain combinations to be faster than others.",
acknowledgement = ack-nhfb,
affiliation = "Stanford Linear Accel. Center, Stanford University,
CA, USA",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "32 Bit; 80 Bit; 80-Bit extended precision; ANSI-IEEE
754-1985 binary floating-point arithmetic standard;
FPCP; MC68020 microprocessor; MC68030 microprocessor;
MC68882 floating-point coprocessor; Optimizing MC68882
code; Parallel operation; Pipeline architecture",
thesaurus = "Digital arithmetic; Microprocessor chips; Parallel
processing; Pipeline processing; Satellite computers",
}
@Article{Meek:1994:PLT,
author = "Brian L. Meek",
title = "Programming languages: towards greater commonality",
journal = j-SIGPLAN,
volume = "29",
number = "4",
pages = "49--57",
month = apr,
year = "1994",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:49 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6110 (Systems analysis and programming); C6140
(Programming languages)",
corpsource = "Comput. Centre, King's Coll., London, UK",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "cross-language standardisation; JTC1; language
independent arithmetic; language independent calling;
language independent datatypes; language independent
procedure calling; language independent standards;
language standardisation; OSI; programming; programming
guidelines; programming languages; programming
languages commonality; programming languages
differences; remote procedure calling; remote procedure
calls; SC22; standardisation; standards; subcommittee;
working group",
treatment = "G General Review",
}
@InProceedings{Mehlhorn:1994:IGA,
author = "Kurt Mehlhorn and Stefan Naher",
title = "The Implementation of Geometric Algorithms",
crossref = "Pehrson:1994:IPP",
volume = "1",
pages = "223--231",
year = "1994",
bibdate = "Tue Nov 13 21:47:31 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Montgomery:1994:SRP,
author = "Peter L. Montgomery",
title = "Square roots of products of algebraic numbers",
crossref = "Gautschi:1994:MCH",
pages = "567--571",
year = "1994",
bibdate = "Thu Oct 25 14:53:00 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Montuschi:1994:DUN,
author = "P. Montuschi and L. Ciminiera and A. Giustina",
title = "Division unit with {Newton--Raphson} approximation and
digit-by-digit refinement of the quotient",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "141",
number = "6",
pages = "317--324",
month = nov,
year = "1994",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The advantages of the convergence with the square of
the Newton--Raphson method are combined with the
precision characteristics of digit-by-digit algorithms
to obtain units for fast division that satisfy the IEEE
754 floating point standard requirements. A general
design methodology that leads to a class of alternative
architectures providing interesting performances for
division is presented, together with one example of
possible implementation. In particular, the proposed
implementation achieves a speedup varying from 20\% to
about 30\% in comparison with a previous architecture
by Fandrianto, with a relatively small additional
hardware cost if a multiplier is already available on
the arithmetic unit.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Autom. e Inf., Politecnico di Torino,
Italy",
classification = "C4130 (Interpolation and function approximation);
C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
fjournal = "IEE Proceedings. Computers and Digital Techniques",
keywords = "Convergence; Digit-by-digit refinement; Fast division;
Floating point standard; Newton--Raphson
approximation",
pubcountry = "UK",
thesaurus = "Dividing circuits; Floating point arithmetic;
Newton--Raphson method",
}
@Article{Montuschi:1994:RDO,
author = "P. Montuschi and L. Ciminiera",
title = "Radix-8 division with over-redundant digit set",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "7",
number = "3",
pages = "259--270",
month = may,
year = "1994",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/BF02409402",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a radix-8 divider that uses an
over-redundant digit set for the quotient in order to
obtain simple digit selection rules. We show that the
proposed enlarged set of values for the quotient digit
does not lead to increases both in the complexity and
the delay of the adder required to update the
remainder, with respect to similar solutions, since the
values allowed for the quotient digit have been
selected carefully. The digit selection process is
subdivided into two concurrent steps, each one making
reference to a secondary digit set and the resulting
implementation can be cheaper and faster than other
units which do not use over-redundant digit sets. A
performance analysis estimates a speed improvement from
25\% to 35\% with respect to a radix-8 architecture by
Fandrianto (1987, 1989), and from 21\% to 30\% with
respect to a radix-4 architecture with prescaling,
presented by Ercegovac and Lang (1990). As required
from the IEEE 754 floating point standard, the proposed
algorithm features the correct remainder of the
division.",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Autom. e Inf., Politecnico di Torino,
Italy",
classification = "B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5230 (Digital arithmetic methods)",
fjournal = "Journal of VLSI Signal Processing",
keywords = "Algorithm; Delay; Digit selection rules; IEEE 754
floating point standard; Over-redundant digit set;
Performance analysis; Quotient; Radix-8 divider;
Radix-8 division; Remainder; Speed improvement",
pubcountry = "Netherlands",
thesaurus = "Digital arithmetic; Dividing circuits",
}
@Article{Montuschi:1994:RDS,
author = "P. Montuschi and L. Ciminiera",
title = "Over-redundant digit sets and the design of
digit-by-digit division units",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "3",
pages = "269--277",
month = mar,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.272428",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272428",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Muller:1994:SCF,
author = "Jean-Michel Muller",
title = "Some characterizations of functions computable in
on-line arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "6",
pages = "752--755",
month = jun,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.286308",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=286308",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Murofushi:1994:RBR,
author = "Makoto Murofushi and Hideko Nagasaka",
title = "The relationship between the round-off errors and
{M{\o}ller}'s algorithm in the extrapolation method",
journal = j-ANN-NUM-MATH,
volume = "1",
number = "1--4",
pages = "451--458",
year = "1994",
ISSN = "1021-2655",
ISSN-L = "1021-2655",
MRclass = "65L05 (65L70)",
MRnumber = "1340673",
MRreviewer = "Haydar Ak\c{c}a",
bibdate = "Sat Feb 08 09:16:09 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Scientific computation and differential equations
(Auckland, 1993).",
acknowledgement = ack-nhfb,
ajournal = "Ann. Numer. Math.",
fjournal = "Annals of Numerical Mathematics",
}
@InProceedings{Nakamura:1994:EPV,
author = "H. Nakamura and H. Imori and Y. Yamashita and K.
Nakazawa and T. Boku and H. Li and I. Nakata",
title = "Evaluation of pseudo vector processor based on
slide-windowed registers",
crossref = "Mudge:1994:PTS",
pages = "368--377",
year = "1994",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a new scalar processor for high-speed
vector processing and its evaluation. The proposed
processor can hide long main memory access latency by
introducing slide-windowed floating-point registers
with data preloading feature and pipelined memory.
Owing to the slide-window structure, the proposed
processor can utilize more floating-point registers in
keeping upward compatibility with existing scalar
architecture. We have evaluated its performance on
Livermore Fortran Kernels. The evaluation results show
that the proposed processor drastically reduces the
penalty of main memory access compared with an ordinary
scalar processor. For example, the proposed processor
with 96 registers hides memory access latency of 70 CPU
cycles when the throughput of main memory is 8
byte/cycle. From these results, it is concluded that
the proposed architecture is very suitable for
high-speed vector processing.",
acknowledgement = ack-nhfb,
affiliation = "Inst. of Inf. Sci. and Electron., Tsukuba University,
Ibaraki, Japan",
classification = "C5220P (Parallel architecture); C5440
(Multiprocessor systems and techniques); C5470
(Performance evaluation and testing)",
keywords = "Data preloading feature; Floating-point registers;
High-speed vector processing; Livermore Fortran
Kernels; Performance; Pipelined memory; Pseudo vector
processor; Scalar processor; Slide-windowed registers",
thesaurus = "FORTRAN; Performance evaluation; Vector processor
systems",
}
@Article{Narayanaswami:1994:AE,
author = "Chandrasekhar Narayanaswami and William Luken",
title = "Approximating $ x^n $ efficiently",
journal = j-INFO-PROC-LETT,
volume = "50",
number = "4",
pages = "205--210",
day = "25",
month = may,
year = "1994",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "65D20 (41-04 65B99)",
MRnumber = "95b:65031",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "Compendex database;
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
affiliation = "IBM Advanced Workstations and Systems Div",
affiliationaddress = "Austin, TX, USA",
classification = "721.1; 723.2; 723.5; 741.2; 921.1; 921.6; B0290F
(Interpolation and function approximation); C4130
(Interpolation and function approximation); C6130B
(Graphics techniques)",
corpsource = "IBM Adv. Workstations and Syst. Div., Austin, TX,
USA",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
journalabr = "Inf Process Lett",
keywords = "$x^n$ approximation; approximation theory;
Approximation theory; Color computer graphics;
Computational complexity; Computational methods;
computer graphics; elementary functions; floating-point
arithmetic; Function evaluation; graphics modeling;
Image quality; Light intensity computation; look-up
tables; performance requirements; Polynomial
evaluation; Polynomials; polynomials; power function;
scientific applications; Semiconducting silicon; Table
lookup",
treatment = "T Theoretical or Mathematical",
}
@MastersThesis{Nedialkov:1994:PCE,
author = "Nedialko (Ned) Stoyanov Nedialkov",
title = "Precision Control and Exception Handling in Scientific
Computing",
type = "{M.Sc.} Thesis",
school = "Department of Computer Science, University of
Toronto",
address = "Toronto, ON, Canada",
pages = "51",
year = "1994",
bibdate = "Tue May 22 15:44:16 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.toronto.edu/NA/reports.html#ned-94-msc;
http://www.cs.toronto.edu/pub/reports/na/ned-94-msc.ps.Z",
acknowledgement = ack-nhfb,
}
@MastersThesis{Niescier:1994:DIC,
author = "Richard J. Niescier",
title = "Design of an {IEEE} compliant 32-bit floating point
multiplier\slash accumulator",
type = "Thesis ({M.S.})",
school = "Lehigh University",
address = "Bethlehem, PA, USA",
pages = "vii + 94",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Floating-point arithmetic.; Microprocessors.",
}
@MastersThesis{Novak:1994:AFP,
author = "Joseph Herschel Novak",
title = "An asynchronous floating point unit",
type = "Thesis ({M.S.})",
school = "Department of Computer Science, University of Utah",
address = "Salt Lake City, UT, USA",
pages = "xi + 151",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Asynchronous circuits.; Computers --- Circuits.;
Floating-point arithmetic.",
}
@TechReport{Oberman:1994:DIH,
author = "S. Oberman and N. Quach and M. Flynn",
title = "The design and implementation of a high-performance
floating-point divider",
type = "Technical Report",
number = "CSL-TR-94-599",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = jan,
year = "1994",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{Oh:1994:IPDa,
author = "S. Oh and D. Garcia",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing. {ICASSP-94, 19--22} April 1994",
title = "Implementation of a parallel {DFE} using residue
number system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "III/237--III/240",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1994.390024",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A parallel decision feedback equalizer (DFE)
implementation using residue number system (RNS) is
considered When the DFE implementation for a system
requires a wide input data width and high sampling
rates, RNS provides a speed advantage over \ldots{}",
}
@InProceedings{Oh:1994:IPDb,
author = "S. Oh and D. Garcia",
booktitle = "{IEEE} International Conference on Acoustics, Speech,
and Signal Processing. {ICASSP-94, 19--22} April 1994",
title = "Implementation of a parallel {DFE} using residue
number system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "III/237--III/240",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1994.390024",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A parallel decision feedback equalizer (DFE)
implementation using residue number system (RNS) is
considered When the DFE implementation for a system
requires a wide input data width and high sampling
rates, RNS provides a speed advantage over \ldots{}",
}
@Article{Ohta:1994:INP,
author = "S. Ohta and E. Goto and Weng Fai Wong and N. Yoshida",
title = "Improvement and new proposal on fast evaluation of
elementary functions",
journal = j-TRANS-INFO-PROCESSING-SOC-JAPAN,
volume = "35",
number = "5",
pages = "926--933",
month = may,
year = "1994",
CODEN = "JSGRD5",
ISSN = "0387-5806",
ISSN-L = "0387-5806",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp.
1570-1579, 1993) introduced fast methods for numerical
evaluation of elementary functions based on table
lookup. They are called ATA (add/table-lookup/add) and
ATA-M (add/table-lookup/add and multiply) methods for
single- and double-precision calculations respectively.
In this paper, an improvement to these methods that
shrinks the size of the table by a factor of about 3/16
is presented. Another method called the `split parallel
multiplication method', which is characterized by
simpler table lookup than ATA-M and by split and
parallel use of double-precision floating point
circuitry, is also introduced, These new methods fit on
to integrated circuits of a size comparable with
commercially available floating-point accelerators.
Methods for accelerating double-precision division,
generating uniform pseudo-random numbers in
double-precision, and accelerating the multiplication
of single-precision complex numbers using the same
circuitry are proposed.",
acknowledgement = ack-nhfb,
affiliation = "RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan",
classification = "C4120 (Functional analysis); C5230 (Digital
arithmetic methods); C6130 (Data handling techniques)",
fjournal = "Transactions of the Information Processing Society of
Japan",
keywords = "Add/table-lookup/add method;
Add/table-lookup/add/multiply method; ATA method; ATA-M
method; Double-precision calculations; Double-precision
division; Double-precision floating point circuitry;
Elementary functions evaluation; Floating-point
accelerators; Integrated circuits; Numerical
evaluation; Single-precision calculations;
Single-precision complex number multiplication; Split
parallel multiplication method; Table size; Uniform
pseudo-random number generation",
language = "Japanese",
pubcountry = "Japan",
thesaurus = "Digital arithmetic; Function evaluation; Random number
generation; Table lookup",
}
@Book{Omondi:1994:CAS,
author = "Amos R. Omondi",
title = "Computer Arithmetic Systems: Algorithms, Architecture,
and Implementation",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xvi + 520",
year = "1994",
ISBN = "0-13-334301-4",
ISBN-13 = "978-0-13-334301-4",
LCCN = "QA76.9.C62 O46 1994",
bibdate = "Sat Dec 09 11:57:03 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$40.00",
acknowledgement = ack-nhfb,
tableofcontents = "Preface \\
Preliminary notes \\
Fixed-point number systems / 3 \\
Fixed-point addition and subtraction / 13 \\
Fixed-point multiplication / 119 \\
Fixed-point division / 192 \\
Floating-point number systems and arithmetic / 293 \\
Basic floating-point operations: implementation / 345
\\
Elementary functions / 371 \\
Unconventional number systems and arithmetic / 439 \\
Bibliography / 469 \\
Appendix A: Pipelining / 489 \\
Appendix B: Design of shifters / 505 \\
Index / 514",
}
@Article{Ooyama:1994:CSC,
author = "M. Ooyama and H. Hamada",
title = "A circuit to separate and to connect the exponent part
and the mantissa part for {URR} floating point
arithmetic and its application to a {URR} processor",
journal = j-TRANS-INFO-PROCESSING-SOC-JAPAN,
volume = "35",
number = "8",
pages = "1642--1651",
month = aug,
year = "1994",
CODEN = "JSGRD5",
ISSN = "0387-5806",
ISSN-L = "0387-5806",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "To overcome overflows and underflows in computation,
several new floating-point arithmetics have been
proposed. But in these new arithmetics, a boundary
between the exponent part and the mantissa part moves
according to the exponent value and data formats are
usually more complicated. So, fast separation and
connection of the exponent and the mantissa is a key
technology to achieve fast computation of these new
arithmetics. In this paper, a circuit scheme to
separate and connect the exponent and the mantissa for
URR floating-point arithmetic based on double
exponential cut is presented. To separate the exponent
from the mantissa, this circuit scheme firstly detects
the boundary and the position is encoded to a short
code. Then barrel shifters, logical operation circuits,
and bit pattern generators controlled by the code
separate the exponent and the mantissa from URR. To
form URR from the exponent and the mantissa, a number
of bits of the exponent is counted and encoded to a
short code. The boundary can be settled by this code,
and using the same circuits controlled by the code, the
exponent part and the mantissa part are generated and
combined into URR. To achieve fast execution, these
processes are executed by the combination logic
circuits in bit parallel manner and meet to pipelined
architectures. We applied this circuit scheme to an
experimental 64 bits URR processor and verified its
realization. Its performance was also evaluated. (11
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Central Res. Lab., Hitachi Ltd., Tokyo, Japan",
classification = "B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5220P (Parallel architecture); C5230
(Digital arithmetic methods)",
fjournal = "Transactions of the Information Processing Society of
Japan",
keywords = "64 Bit; Barrel shifters; Bit parallel processing; Bit
pattern generators; Combination logic circuits; Double
exponential cut; Exponent part; Logical operation
circuits; Mantissa part; Pipelined architectures; URR
floating point arithmetic; URR processor",
language = "Japanese",
numericalindex = "Word length 6.4E+01 bit",
pubcountry = "Japan",
thesaurus = "Combinatorial circuits; Digital arithmetic; Parallel
processing; Pipeline processing",
}
@InProceedings{Paliouras:1994:SDMa,
author = "V. Paliouras and T. Stouraitis",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '94}, 2 June 1994",
title = "Systematic design of multi-modulus\slash
multi-function {Residue Number System} processors",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "79--82",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1994.409201",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A methodology for the design of novel Residue Number
System (RNS) processors is presented. It results in
ROM-less processors, which perform basic residue
arithmetic algorithms in more than one moduli channel,
either serially or concurrently. \ldots{}",
}
@InProceedings{Paliouras:1994:SDMb,
author = "V. Paliouras and T. Stouraitis",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '94}, 2 June 1994",
title = "Systematic design of multi-modulus\slash
multi-function {Residue Number System} processors",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "79--82",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1994.409201",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A methodology for the design of novel Residue Number
System (RNS) processors is presented. It results in
ROM-less processors, which perform basic residue
arithmetic algorithms in more than one moduli channel,
either serially or concurrently. \ldots{}",
}
@InProceedings{Parhami:1994:OTLa,
author = "B. Parhami and C. Y. Hung",
booktitle = "Workshop on {VLSI} Signal Processing, {VII, 1994}",
title = "Optimal table lookup schemes for {VLSI} implementation
of input\slash output conversions and other residue
number operations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "470--481",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/VLSISP.1994.574771",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue number representation has become a viable
alternative for fast, area-efficient VLSI realization
of high-performance signal processing hardware. Wider
applicability and improved cost/performance of
residue-based VLSI implementations of signal \ldots{}",
}
@InProceedings{Parhami:1994:OTLb,
author = "B. Parhami and C. Y. Hung",
booktitle = "Workshop on {VLSI} Signal Processing, {VII, 1994}",
title = "Optimal table lookup schemes for {VLSI} implementation
of input\slash output conversions and other residue
number operations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "470--481",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/VLSISP.1994.574771",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue number representation has become a viable
alternative for fast, area-efficient VLSI realization
of high-performance signal processing hardware. Wider
applicability and improved cost/performance of
residue-based VLSI implementations of signal \ldots{}",
}
@InProceedings{Parker:1994:FTLa,
author = "M. G. Parker and M. Benaissa",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '94}, 2 June 1994",
title = "Fault-tolerant linear convolution using residue number
systems",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "441--444",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1994.408997",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper proposes a fault-tolerant linear
convolution architecture using Residue Number Systems
(RNS) and Polynomial Residue Number Systems (PRNS). The
RNS and PRNS are both given error-detection capability
by the addition of redundant residue \ldots{}",
}
@InProceedings{Parker:1994:FTLb,
author = "M. G. Parker and M. Benaissa",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '94}, 2 June 1994",
title = "Fault-tolerant linear convolution using residue number
systems",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "441--444",
year = "1994",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1994.408997",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper proposes a fault-tolerant linear
convolution architecture using Residue Number Systems
(RNS) and Polynomial Residue Number Systems (PRNS). The
RNS and PRNS are both given error-detection capability
by the addition of redundant residue \ldots{}",
}
@MastersThesis{Patankar:1994:SHA,
author = "Rashmi Arun Patankar",
title = "Software and hardware approaches to data compression
of {IEEE} 64-bit floating point data",
type = "Thesis ({M.S.})",
school = "Iowa State University",
address = "Ames, IA, USA",
pages = "55",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Phatak:1994:HSD,
author = "D. S. Phatak and I. Koren",
title = "Hybrid Signed-Digit Number Systems: a Unified
Framework for Redundant Number Representations With
Bounded Carry Propagation Chains",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "880--891",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295850",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@Article{Popova:1994:EIA,
author = "Evgenija D. Popova",
title = "Extended interval arithmetic in {IEEE} floating-point
environment",
journal = j-INTERVAL-COMP,
volume = "4",
pages = "100--129",
year = "1994",
ISSN = "0135-4868",
MRclass = "65-04 (65G10)",
MRnumber = "1 332 078",
bibdate = "Fri Dec 8 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Interval Computations = Interval'nye vychisleniia",
xxnote = "SCAN-93 (Vienna, 1993)",
}
@Article{Prince:1994:TFM,
author = "Timothy Prince",
title = "{{\tt float}}-Precision Math Library",
journal = j-CUJ,
volume = "12",
number = "6",
pages = "45--??",
month = jun,
year = "1994",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@Article{Pritchard:1994:RAR,
author = "A. J. Pritchard and S. J. Sangwine and R. E. N.
Horne",
title = "Rational arithmetic representation of colour image
pixels",
journal = j-ELECT-LETTERS,
volume = "30",
number = "18",
pages = "1474--1475",
month = sep,
year = "1994",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 30 07:42:41 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@InProceedings{Rajski:1994:DRP,
author = "J. Rajski and J. Tyszer",
title = "Design of random pattern testable floating point
adders",
crossref = "IEEE:1994:PTA",
pages = "227--232",
year = "1994",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper presents a floating point adder with
enhanced testability and test response compaction
capabilities. It is shown that the testability of the
conventional adders can be improved by changing the
functionality of some of their internal modules in the
testing mode. It is also demonstrated that the floating
point units can perform an efficient test response
compaction in a built-in self test environment. (7
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng., McGill University,
Montreal, Que., Canada",
classification = "B0170E (Production facilities and engineering);
B1265B (Logic circuits); B7210B (Automatic test and
measurement systems); C5120 (Logic and switching
circuits); C5210 (Logic design methods); C5230 (Digital
arithmetic methods); C7410D (Electronic engineering
computing)",
keywords = "built-in self test environment; enhanced testability;
floating point accumulator; floating point units;
floating-point testing; functionality; internal
modules; random pattern testable floating point adders;
rotate shifter; simulation experiments; test response
compaction; testability",
thesaurus = "adders; built-in self test; design for testability;
digital simulation; floating point arithmetic; logic
design; modules; shift registers",
}
@MastersThesis{Robe:1994:SME,
author = "Edward D. Robe",
title = "{SIMULINK} modules that emulate digital controllers
realized with fixed-point or floating-point
arithmetic",
type = "Thesis ({M.S.})",
school = "Ohio University",
address = "Athens, OH, USA",
pages = "v + 130",
month = jun,
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Digital control systems.; Emulators (Computer
programs); Floating-point arithmetic.",
}
@TechReport{Rothberg:1994:ILD,
author = "Edward Rothberg and Robert Schreiber",
title = "Improved load distribution in parallel sparse
{Cholesky} factorization",
institution = "Research Institute for Advanced Computer Science, NASA
Ames Research Center; National Technical Information
Service, distributor",
address = "Moffett Field, CA, USA",
pages = "????",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "[NASA contractor report]; NASA CR-196380 RIACS
technical report; 94.13 RIACS technical report; TR
94.13.",
acknowledgement = ack-nhfb,
govtdocnumber = "NAS 1.26:196380 0830-H-14 (MF)",
keywords = "Cholesky factorization.; Computer systems
performance.; Floating point arithmetic.; Heuristic
methods.; Parallel processing (Computers).",
remark = "Distributed to depository libraries in microfiche.
Shipping list no.: 94-0871-M. Microfiche. [Washington,
D.C.: National Aeronautics and Space Administration,
1994] 1 microfiche.",
}
@Article{Schaefer:1994:POU,
author = "Mark J. Schaefer",
title = "Precise optimization using range arithmetic",
journal = j-J-COMPUT-APPL-MATH,
volume = "53",
number = "3",
pages = "341--351",
day = "30",
month = aug,
year = "1994",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:24:32 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042794900620",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@MastersThesis{Schaffer:1994:FPM,
author = "Jonathan T. Schaffer",
title = "A floating point multiplier for a superscalar
microprocessor",
type = "Thesis ({M.S.})",
school = "North Carolina State University",
address = "Raleigh, NC, USA",
pages = "viii + 104",
year = "1994",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Schorn:1994:DGC,
author = "Peter Schorn",
title = "Degeneracy in geometric computation and the
perturbation approach",
journal = j-COMP-J,
volume = "37",
number = "1",
pages = "35--42",
month = "????",
year = "1994",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Jul 21 09:54:00 MDT 1999",
bibsource = "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_01/Vol37_01.index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_01/Vol37_01.body.html#AbstractSchorn",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Theor. Inf., ETH, Zurich, Switzerland",
author-1-adr = "Institut f{\"u}r Theoretische Informatik, ETH, CH-8092
Zurich, Switzerland",
classcodes = "C4260 (Computational geometry); C4240 (Programming and
algorithm theory)",
classification = "C4240 (Programming and algorithm theory); C4260
(Computational geometry)",
corpsource = "Inst. fur Theor. Inf., ETH, Zurich, Switzerland",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algorithm construction; Algorithm construction;
algorithm theory; algorithm-dependent;
Algorithm-dependent degeneracies; approach;
computational geometry; degeneracies; Euclidean
constructions; floating; Floating point arithmetic;
geometric computation; Geometric computation;
input-output; Input-output specifications; integer
arithmetic; Integer arithmetic; lexicographic;
Lexicographic ordering; ordering; perturbation;
Perturbation approach; point arithmetic;
problem-dependent degeneracies; Problem-dependent
degeneracies; provably correct results; Provably
correct results; specifications; theory; winding
number; Winding number",
thesaurus = "Algorithm theory; Computational geometry; Perturbation
theory",
treatment = "T Theoretical or Mathematical",
}
@MastersThesis{Schoss:1994:ISF,
author = "H. Schoss",
title = "{Intervall Standardfunktionen f{\"u}r das bin{\"a}re
IEEE Zahlenformat} \toenglish {Interval Standard
Functions for the Binary IEEE Number Format}
\endtoenglish",
type = "{Diplomarbeit}",
school = "Institut f{\"u}r angewandte Mathematik,
Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
pages = "??",
month = mar,
year = "1994",
bibdate = "Fri Sep 16 16:30:40 1994",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Article{Schulte:1994:HDE,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "Hardware Designs for Exactly Rounded Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "964--973",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295858",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
abstract = "This paper presents hardware designs that produce
exactly rounded results for the functions of
reciprocal, square-root, 2/sup x/, and log/sub 2/(x).
These designs use polynomial approximation in which the
terms in the approximation are generated in parallel,
and then summed by using a multi-operand adder. To
reduce the number of terms in the approximation, the
input interval is partitioned into subintervals of
equal size, and different coefficients are used for
each subinterval. The coefficients used in the
approximation are initially determined based on the
Chebyshev series approximation. They are then adjusted
to obtain exactly rounded results for all inputs.
Hardware designs are presented, and delay and area
comparisons are made based on the degree of the
approximating polynomial and the accuracy of the final
result. For single-precision floating point numbers, a
design that produces exactly rounded results for all
four functions has an estimated delay of 80 ns and a
total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS
technology. Allowing the results to have a maximum
error of one unit in the last place reduces the
computational delay by 5\% to 30\% and the area
requirements by 33\% to 77\%.",
acknowledgement = ack-nhfb # " and " # ack-nj,
affiliation = "Department of Electr. and Comput. Eng., Texas
University, Austin, TX, USA",
ajournal = "IEEE Trans. Comput.",
classification = "B0290F (Interpolation and function approximation);
B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C4130 (Interpolation and function
approximation); C5120 (Logic and switching circuits);
C5230 (Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "1 Micron; 1.0-Micron CMOS technology; Argument
reduction; Chebyshev series approximation; Chip area;
Computational delay; Computer arithmetic; Exact
rounding; Exactly rounded elementary functions;
Hardware designs; Multi-operand adder; Parallel
multiplier; Polynomial approximation; Reciprocal;
Single-precision floating point numbers;
Special-purpose hardware; Square-root",
numericalindex = "Size 1.0E-06 m",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
thesaurus = "Approximation theory; Chebyshev approximation; CMOS
integrated circuits; Digital arithmetic; Multiplying
circuits; Polynomials; Summing circuits",
xxtitle = "Hardware Design for Exactly Rounded Elementary
Functions",
}
@Article{Schulte:1994:OIA,
author = "M. J. Schulte and J. Omar and E. E. {Swartzlander,
Jr.}",
title = "Optimal initial approximations for the
{Newton--Raphson} division algorithm",
journal = j-COMPUTING,
volume = "53",
number = "3--4",
pages = "233--242",
month = sep,
year = "1994",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65D99",
MRnumber = "1 308 764",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
MathSciNet database; OCLC Contents1st database",
note = "International Symposium on Scientific Computing,
Computer Arithmetic and Validated Numerics (Vienna,
1993).",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@InProceedings{Schulte:1994:VIA,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "A variable-precision interval arithmetic processor",
crossref = "Cappello:1994:PIC",
pages = "248--258",
year = "1994",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a special-purpose processor which
implements variable-precision, interval arithmetic.
Variable-precision arithmetic allows the precision of
the computation to be specified, based on the problem
to be solved and the required accuracy of the
computation. Interval arithmetic produces two values
for each result, such that the true result is
guaranteed to be between the two values. The distance
between the two values gives an upper bound on the
error. Direct hardware support for variable-precision,
interval arithmetic greatly improves the accuracy of
the computation, and is much faster than existing
software methods for controlling numerical error. Area
and delay estimates indicate that the processor can be
implemented on a single chip with a cycle time which is
comparable to existing IEEE double-precision floating
point processors. For computationally intensive
problems, an application-specific array of
variable-precision, interval arithmetic processors can
execute in parallel to provide high-performance and
numerically reliable results.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Comput. Eng., Texas
University, Austin, TX, USA",
classification = "B0290B (Error analysis in numerical methods); B1265F
(Microprocessors and microcomputers); C4110 (Error
analysis in numerical methods); C5130 (Microprocessor
chips); C5220P (Parallel architecture); C5230 (Digital
arithmetic methods)",
keywords = "Application-specific array; Hardware support; IEEE
double-precision floating point processors; Numerical
error; Parallel arithmetic; Special-purpose processor;
Variable-precision interval arithmetic processor",
thesaurus = "Digital arithmetic; Error analysis; Microprocessor
chips; Parallel architectures",
}
@Article{Schwandt:1994:IAD,
author = "Hartmut Schwandt",
title = "An interval arithmetic domain decomposition method for
a class of elliptic {PDEs} on nonrectangular domains",
journal = j-J-COMPUT-APPL-MATH,
volume = "50",
number = "1--3",
pages = "509--521",
day = "20",
month = may,
year = "1994",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:02:23 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042794903247",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@TechReport{Sharangpani:1994:SAF,
author = "H. P. Sharangpani and M. L. Barton",
title = "Statistical analysis of floating point flaw in the
{Pentium} processor",
institution = pub-INTEL,
address = pub-INTEL:adr,
month = nov,
year = "1994",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://home1.gte.net/deleyd/pentbug/white11.ps;
http://www.intel.com/procs/support/pentium/fdiv/white11.ps",
abstract = "A subtle flaw in the hardware divide unit of the
PentiumTM Processor was discovered by Intel.
Subsequently, a characterization of its impact to the
end-user application base was conducted. The flaw is
rare and data-dependent, and causes a reduction in
precision of the divide instruction and certain other
operations in certain cases.\par
The significance of the flaw depends upon (a) the rate
of use of specific FP instructions in the PentiumTM
CPU, (b) the data fed to them, (c) the way in which the
results of these instructions are propagated into
further computation in the application; and (d) the way
in which the final results of the application are
interpreted.\par
The thorough and detailed characterization of the flaw
and the subsequent investigations of its impact on
applications through elaborate surveys, analyses and
empirical observation lead us to the overall conclusion
that the flaw is of no concern to the vast majority of
users of Pentium processor based systems. A few users
of applications in the scientific/engineering and
financial engineering fields who require unusual
precision and invoke millions of divides per day may
need to employ either an updated Pentium processor
without the flaw or a software workaround.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "Intel Pentium divide flaw; Thomas R. Nicely",
remark = "This Intel white paper was controversial, and its
minimization of the problem was refuted by others: see
\cite{Edelman:1997:MPD}.",
}
@Article{Shippy:1994:PFD,
author = "D. J. Shippy and T. W. Griffith",
title = "{POWER2} fixed-point, data cache, and storage control
units",
journal = j-IBM-JRD,
volume = "38",
number = "5",
pages = "503--524",
month = sep,
year = "1994",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.almaden.ibm.com/journal/rd38-5.html#three",
abstract = "The POWER2* fixed-point, data cache, and storage
control units provide a tightly integrated subunit for
a second-generation high-performance superscalar RISC
processor. These functional units provide dual
fixed-point execution units and a large multiported
data cache, as well as high-performance interfaces to
memory, I/O, and the other execution units in the
processor. These units provide the following features:
dual fixed-point execution units, improved
fixed-point/floating-point synchronization, new
floating-point load and store quadword instructions,
improved address translation, improved fixed-point
multiply/divide, large multiported D-cache, increased
bandwidth into and out of the caches through wider data
buses, an improved external interrupt mechanism, and an
improved I/O DMA mechanism to support
multiple-streaming Micro Channels.*",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Austin, TX, USA",
classcodes = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5470 (Performance evaluation
and testing); C5610S (System buses); C5320G
(Semiconductor storage)",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5320G (Semiconductor storage);
C5470 (Performance evaluation and testing); C5610S
(System buses)",
corpsource = "IBM Corp., Austin, TX, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "address translation; Address translation; cache; cache
storage; data buses; Data buses; data cache; Data
cache; dual fixed-point; Dual fixed-point execution
units; execution units; external interrupt; External
interrupt mechanism; floating-; Floating-point;
mechanism; memory interface; Memory interface;
microprocessor chips; multiple-streaming micro
channels; Multiple-streaming micro channels;
multiported data; Multiported data cache; performance
evaluation; point; POWER2; reduced instruction set
computing; storage control units; Storage control
units; storage management; superscalar RISC processor;
Superscalar RISC processor; synchronisation;
synchronization; Synchronization; system buses",
thesaurus = "Cache storage; Microprocessor chips; Performance
evaluation; Reduced instruction set computing; Storage
management; Synchronisation; System buses",
treatment = "P Practical",
}
@Article{Smith:1994:PAT,
author = "James E. Smith and Shlomo Weiss",
title = "{PowerPC 601} and {Alpha 21064}: a Tale of Two
{RISCs}",
journal = j-COMPUTER,
volume = "27",
number = "6",
pages = "46--58",
month = jun,
year = "1994",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Mon Feb 3 07:28:57 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Both PowerPC and Alpha are RISC architectures, but
they have little in common beyond that. The design
philosophy of one emphasizes powerful instructions, the
other simplicity.",
acknowledgement = ack-nhfb,
affiliation = "Cray Res. Inc., Chippewa Falls, WI, USA",
affiliationaddress = "Chippewa Falls, WI, USA",
classification = "721.3; 722.1; 722.4; 723.1; C5220P (Parallel
architecture); C5440 (Multiprocessor systems and
techniques); C6140B (Machine-oriented languages)",
conferenceyear = "1994",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
journalabr = "Computer",
keywords = "Access memory; Alpha 21064; Buffering; Cache memory;
Computer software; Data storage equipment; Digital
arithmetic; Digital Equipment Corporation; Floating
point instructions; High performance;
IBM/Motorola/Apple; Implementation philosophies;
Instruction sets; Load/store architecture;
Microprocessor chips; Out of order dispatch; Parallel
processing systems; Performance; Philosophical aspects;
Pipeline processing systems; Pipelined implementations;
PowerPC 601; Processing order; Program compilers;
Program debugging; Reduced instruction set computing;
RISC implementations; RISC microprocessors; Streamlined
implementation structure; Superscalar implementations;
User interfaces; Very fast clock; Virtual storage",
publisherinfo = "IEEE Service Center",
thesaurus = "Instruction sets; Pipeline processing; Reduced
instruction set computing",
}
@Article{Smith:1994:SFT,
author = "William Smith",
title = "A Short Floating-Point Type in {C++}",
journal = j-CUJ,
volume = "12",
number = "1",
pages = "23--??",
month = jan,
year = "1994",
ISSN = "0898-9788",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C Users Journal",
}
@TechReport{Solhaug:1994:FDK,
author = "Fredrik Solhaug",
title = "Flyttalls {A/D}-konverter = Floating Point {A/D}
Converter",
type = "Hovedoppgave",
institution = "Institutt for teleteknikk, NTH",
address = "Trondheim, Norway",
year = "1994",
bibdate = "Thu May 09 08:14:17 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Srivastava:1994:ASB,
author = "A. Srivastava and A. Eustace",
title = "{ATOM}: a system for building customized program
analysis tools",
journal = j-SIGPLAN,
volume = "29",
number = "6",
pages = "196--205",
month = jun,
year = "1994",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM SIGPLAN '94 Conference on Programming Language
Design and Implementation (PLDI).",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Stockman:1994:OMM,
author = "Harlan W. Stockman",
title = "Optimizing Matrix Math On The {Pentium}",
journal = j-DDJ,
volume = "19",
number = "5",
pages = "52, 54, 56, 60, 62, 66",
month = may,
year = "1994",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Sep 03 09:15:49 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "The Pentium processor is more than just a fast 486.
Its pipeline and floating-point and integer operations
require that you pay more attention to the flow of data
on the off the FPU. Harlan presents and measures
methods for speeding up Pentium matrix-math
operations.",
acknowledgement = ack-nhfb,
affiliation = "Department of Geochem., Sandia Nat. Labs.,
Albuquerque, NM, USA",
classification = "C1180 (Optimisation techniques); C4140 (Linear
algebra); C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods); C7310 (Mathematics)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "1 MByte; 100 MHz; 256 KByte; 33 MHz; 486DX; 60 MHz; 64
Bit; 64 KByte; 8 Bit; 8-Byte boundaries; Code
optimization; Data alignment; Floating-point unit;
Gateway 486/33C; Gateway P5-60; Global register
allocation; IRIX 4.0.5H; LINPACK routines; Loop
unrolling; Matrix multiplication; Matrix operations
optimization; MIPS R4000; Pentium microprocessor chip;
Pentium-optimized compilers; Performance gains; SGI
Elan; Simultaneous linear equations; Symantec C++ 6.0
for DOS; UNIX cc version 3.1; Write-through L2 cache",
thesaurus = "Assembly language listings; Digital arithmetic;
Mathematics computing; Matrix algebra; Microprocessor
chips; Optimisation",
}
@Article{Thompson:1994:PSN,
author = "Tom Thompson and Bob Ryan",
title = "{PowerPC} 620 Soars: The newest member of the
{PowerPC} family targets the workstation market with
fast throughput and speedy floating-point performance",
journal = j-BYTE,
volume = "19",
number = "11",
pages = "113--??",
month = nov,
year = "1994",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Tue Jan 2 10:01:41 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
}
@Article{Timmermann:1994:CFP,
author = "D. Timmermann and B. Rix and H. Hahn and B. J.
Hosticka",
title = "A {CMOS} Floating-Point Vector-Arithmetic Unit",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "29",
number = "5",
pages = "634--639",
month = may,
year = "1994",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "This work describes a floating-point arithmetic unit
based on the CORDIC algorithm. The unit computes a full
set of high level arithmetic and elementary functions:
multiplication, division, (co)sine, hyperbolic
(co)sine, square root, natural logarithm \ldots{}",
}
@Article{Timmermann:1994:CFV,
author = "D. Timmermann and B. Rix and H. Hahn and B. J.
Hosticka",
title = "A {CMOS} floating-point vector-arithmetic unit",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "29",
number = "5",
pages = "634--639",
month = may,
year = "1994",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This work describes a floating-point arithmetic unit
based on the CORDIC algorithm. The unit computes a full
set of high level arithmetic and elementary functions:
multiplication, division, (co)sine, hyperbolic
(co)sine, square root, natural logarithm, inverse
(hyperbolic) tangent, vector norm, and phase. The chip
has been integrated in 1.6 mu m double-metal n-well
CMOS technology and achieves a normalized peak
performance of 220 MFLOPS.",
acknowledgement = ack-nhfb,
affiliation = "Fraunhofer Inst. of Microelectron. Circuits and Syst.,
Duisburg, Germany",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C5120 (Logic and switching circuits); C5220P
(Parallel architecture); C5230 (Digital arithmetic
methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine;
Division; Double-metal n-well CMOS technology;
Floating-point vector-arithmetic unit; Hyperbolic sine;
Inverse tangent; Multiplication; Natural logarithm;
Phase; Sine; Square root; Vector norm",
numericalindex = "Size 1.6E-06 m; Computer speed 2.2E+08 FLOPS",
thesaurus = "CMOS integrated circuits; Digital arithmetic;
Integrated logic circuits; Parallel architectures;
Pipeline processing; Vector processor systems",
}
@Article{Turner:1994:SRM,
author = "Stephen M. Turner",
title = "Square roots mod $p$",
journal = j-AMER-MATH-MONTHLY,
volume = "101",
number = "5",
pages = "443--449",
month = may,
year = "1994",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11A07",
MRnumber = "95c:11004",
MRreviewer = "David Lee Hilliker",
bibdate = "Wed Dec 3 17:17:33 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Tydeman:1994:WCT,
author = "Fred Tydeman",
title = "What causes a Trap in {IEEE-754} Floating-Point?",
journal = j-SIGNUM,
volume = "29",
number = "1",
pages = "2--4",
month = jan,
year = "1994",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:24 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the ANSI/IEEE Std 754-1985 (IEEE standard for
binary floating-point arithmetic), and the ANSI/IEEE
Std 854-1987 (IEEE standard for radix-independent
floating-point arithmetic), is signaling a trap an
`edge-triggered' or a `level-sensitive' event? The
authors discusses the question: Does it matter if an
exception is signaled by an arithmetic operation versus
a user setting a status flag?.",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Austin, TX, USA",
classification = "C5230 (Digital arithmetic methods)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
keywords = "ANSI/IEEE Std 754-1985; ANSI/IEEE Std 854-1987; Binary
floating-point arithmetic; Exception; IEEE standard;
Radix-independent floating-point arithmetic",
thesaurus = "Digital arithmetic; Standards",
}
@Article{Upton:1994:RAH,
author = "Michael Upton and Thomas Huff and Trevor Mudge and
Richard Brown",
title = "Resource allocation in a high clock rate
microprocessor",
journal = j-SIGPLAN,
volume = "29",
number = "11",
pages = "98--109",
month = nov,
year = "1994",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:57 MST 2003",
bibsource = "http://portal.acm.org/; http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/asplos/195473/p98-upton/",
abstract = "This paper discusses the design of a high clock rate
(300 MHz) processor. The architecture is described, and
the goals for the design are explained. The performance
of three processor models is evaluated using
trace-driven simulation. A cost model is used to
estimate the resources required to build processors
with varying sizes of on-chip memories, in both single
and dual issue models. Recommendations are then made to
increase the effectiveness of each of the models.",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. Eng. and Computer Science,
Michigan University, Ann Arbor, MI, USA",
classification = "C5130 (Microprocessor chips); C5220 (Computer
architecture); C5230 (Digital arithmetic methods);
C6150J (Operating systems)",
confdate = "4-7 Oct. 1994",
conflocation = "San Jose, CA, USA; 4--7 Oct. 1994",
confsponsor = "ACM; IEEE Comput. Soc",
conftitle = "Sixth International Conference on Architectural
Support for Programming Languages and Operating Systems
(ASPLOS-VI)",
corpsource = "Department of Electr. Eng. and Computer Science,
Michigan University, Ann Arbor, MI, USA",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "computer architecture; Cost model; cost model; design;
floating point arithmetic; Floating point latency;
floating point latency; High clock rate microprocessor;
high clock rate microprocessor; measurement;
microprocessor chips; Nonblocking cache; nonblocking
cache; On-chip memories; on-chip memories; performance;
performance evaluation; Pipelining; pipelining;
Prefetching; prefetching; Processor model performance;
processor model performance; Resource allocation;
resource allocation; theory; Trace-driven simulation;
trace-driven simulation; virtual machines",
sponsororg = "ACM; IEEE Comput. Soc",
subject = "{\bf C.1.2} Computer Systems Organization, PROCESSOR
ARCHITECTURES, Multiple Data Stream Architectures
(Multiprocessors), Pipeline processors**. {\bf D.4.2}
Software, OPERATING SYSTEMS, Storage Management,
Allocation/deallocation strategies. {\bf C.4} Computer
Systems Organization, PERFORMANCE OF SYSTEMS.",
thesaurus = "Computer architecture; Floating point arithmetic;
Microprocessor chips; Performance evaluation; Resource
allocation; Virtual machines",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Book{vanSomeren:1994:ARC,
author = "Alex {van Someren} and Carol Atack",
title = "The {ARM RISC} Chip: a Programmer's Guide",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xviii + 346",
year = "1994",
ISBN = "0-201-62410-9",
ISBN-13 = "978-0-201-62410-6",
LCCN = "QA76.5.V275 1994",
bibdate = "Wed Sep 14 22:16:36 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Vinnakota:1994:FCTa,
author = "B. Vinnakota and V. V. Bapeswara Rao",
title = "Fast conversion techniques for binary-residue number
systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
volume = "41",
number = "12",
pages = "927--929",
month = dec,
year = "1994",
CODEN = "ITCAEX",
DOI = "https://doi.org/10.1109/81.340862",
ISSN = "????",
ISSN-L = "1057-7122",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7979",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I:
Fundamental Theory and Applications",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
keywords = "residue arithmetic; residue number system",
summary = "An easy and efficient procedure for converting a
binary number into a residue number on moduli 2 n -1, 2
n, 2 n+1 is presented. The procedure presented reveals
an inversion technique. The paper also includes a
\ldots{}",
}
@Article{Vinnakota:1994:FCTb,
author = "B. Vinnakota and V. V. Bapeswara Rao",
title = "Fast conversion techniques for binary-residue number
systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
volume = "41",
number = "12",
pages = "927--929",
month = dec,
year = "1994",
CODEN = "ITCAEX",
DOI = "https://doi.org/10.1109/81.340862",
ISSN = "????",
ISSN-L = "1057-7122",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7979",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I:
Fundamental Theory and Applications",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
keywords = "residue arithmetic; residue number system",
summary = "An easy and efficient procedure for converting a
binary number into a residue number on moduli 2 n -1, 2
n, 2 n+1 is presented. The procedure presented reveals
an inversion technique. The paper also includes a
\ldots{}",
}
@Article{Vinnakota:1994:SBR,
author = "B. Vinnakota",
title = "Selection of bases for a residue number system",
journal = j-ELECT-LETTERS,
volume = "30",
number = "11",
pages = "836--837",
day = "26",
month = may,
year = "1994",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7164",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A procedure is presented for selecting the bases in a
residue number system (RNS) for which the conversion
procedure from RNS to decimal is simple. The conversion
procedure is not based on the Chinese remainder
\ldots{}",
}
@Article{Vuillemin:1994:CN,
author = "J. E. Vuillemin",
title = "On Circuits and Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "868--879",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295849",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@Article{Walker:1994:SMA,
author = "W. J. Walker",
title = "A summability method for the arithmetic {Fourier}
transform",
journal = j-BIT,
volume = "34",
number = "2",
pages = "304--309",
month = jun,
year = "1994",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01955877",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "42A99 (65T20)",
MRnumber = "97i:42010",
bibdate = "Wed Jan 4 18:52:23 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=34&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit34.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=34&issue=2&spage=304",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@TechReport{Walters:1994:CTR,
author = "H. R. Walters",
title = "A Complete Term Rewriting System for Decimal Integer
Arithmetic",
type = "Technical report",
number = "CS-9435",
institution = "Centrum voor Wiskunde en Informatica (CWI)",
address = "Amsterdam, The Netherlands",
pages = "9",
month = aug,
year = "1994",
bibdate = "Fri Nov 28 19:36:09 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a term rewriting system for decimal
integers with addition and subtraction. We prove that
the system is confluent and terminating.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Wang:1994:MQF,
author = "Mu-Cheng Wang and Wayne G. Nation and James B.
Armstrong and Howard Jay Siegel and Shin Dug Kim and
Mark A. Nichols and Michael Gherrity",
title = "Multiple Quadratic Forms: a Case Study in the Design
of Data-Parallel Algorithms",
journal = j-J-PAR-DIST-COMP,
volume = "21",
number = "1",
pages = "124--139",
month = apr,
year = "1994",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1994.1046",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:54 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1046/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1046/production/pdf",
acknowledgement = ack-nhfb,
classification = "C4240P (Parallel programming and algorithm theory)",
corpsource = "Department of Computer Science, City University of New
York, NY, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "communication overhead; complex arithmetic operation
count; complexity; computational complexity;
data-parallel algorithms; MasPar; memory storage; MP-1;
multiple quadratic forms; nCUBE 2; parallel algorithms;
partitioning; PASM; real-time; systems",
treatment = "P Practical",
}
@Book{Weaver:1994:SAM,
author = "David L. Weaver and Tom Germond",
title = "The {SPARC} Architecture Manual: Version 9",
publisher = pub-PHPTR,
address = pub-PHPTR:adr,
pages = "xxii + 357",
year = "1994",
ISBN = "0-13-099227-5",
ISBN-13 = "978-0-13-099227-7",
LCCN = "QA76.9.A73S648 1992",
bibdate = "Fri Jul 22 08:37:56 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
price = "US\$33.00",
URL = "http://www.sparc.org/standards/SPARCV9.pdf",
abstract = "SPARC (Scalable Processor Architecture) is the
industry's only openly defined and evolved RISC
architecture. Version 9 is the new 64-bit incarnation
of SPARC --- the most significant change since SPARC's
introduction in 1987! Unlike other RISC (Reduced
Instruction Set Computer) designs, SPARC specifies not
a hardware implementation (``chip''), but an open,
standard architecture belonging to the community of
SPARC vendors and users. The SPARC specification is
defined by the SPARC Architecture Committee, a
technical arm of the computer-maker consortium, SPARC
International. Version 9 provides 64-bit data and
addressing, support for fault tolerance, fast context
switching, support for advanced compiler optimizations,
efficient design for Superscalar processors, and a
clean structure for modern operating systems. The V9
architecture supplements, rather than replaces, the
32-bit Version 8 architecture. The non-privileged
features of Version 9 are upward-compatible from
Version 8, so 32-bit application software can execute
natively, without modification, on Version 9 systems no
special ``compatibility mode'' is required. Publication
of the Version 9 architecture marks a three-year
development effort by SPARC International member
companies from a broad cross-section of disciplines.",
acknowledgement = ack-nhfb,
tableofcontents = "Introduction \\
Overview \\
Definitions \\
Architectural Overview \\
Data Formats \\
Registers \\
Instructions \\
Traps \\
Memory Models \\
(Normative) Instruction Definitions \\
(Normative) IEEE 754-1985 Requirements for SPARC-V9 \\
(Normative) SPARC-V9 Implementation Dependencies \\
(Normative) Formal Specification of the Memory Models
\\
(Informative) Opcode Maps \\
(Informative) SPARC-V9 MMU Requirements \\
(Informative) Suggested Assembly Language Syntax \\
(Informative) Software Considerations \\
(Informative) Extending the SPARC-V9 Architecture \\
(Informative) Programming With the Memory Models \\
(Informative) Changes from SPARC-V8 to SPARC-V9 \\
Bibliography \\
Index",
}
@InProceedings{Wei:1994:REF,
author = "D.-Y. D. Wei and J. H. Kim and T. R. N. Rao",
booktitle = "Proceedings of the {IEEE} International Workshop on
Defect and Fault Tolerance in {VLSI} Systems, 1994",
title = "Roundoff error-free tests in algorithm-based fault
tolerant matrix operations on {$2$-D} processor
arrays",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "74--82",
year = "1994",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
summary = "Assaad and Dutt [1992] proposed the hybrid checksum
test method for the floating-point matrix-matrix
multiplication in ABFT environment, by which the error
coverage can be greatly increased. However, the
threshold test in their approach is still \ldots{}",
}
@Book{Weiss:1994:PPP,
author = "Shlomo Weiss and James E. Smith",
title = "{Power} and {PowerPC}: Principles, Architecture,
Implementation",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xvi + 408",
year = "1994",
ISBN = "1-55860-279-8",
ISBN-13 = "978-1-55860-279-3",
LCCN = "QA76.8.P67 W45 1994",
bibdate = "Wed Aug 10 10:06:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
price = "US\$54.95",
acknowledgement = ack-nhfb,
tableofcontents = "Foreword by Michael Slater \\
Preface \\
Modern Computer Design Concepts / 1 \\
POWER Architecture / 31 \\
POWER Implementation: Pipelines / 71 \\
POWER1 Implementation / 97 \\
POWER1 Implementation: Cache Memories / 115 \\
POWER2: The Next Generation / 135 \\
PowerPC Architecture / 173 \\
PowerPC 601 Implementation / 223 \\
PowerPC: Support for Multiprocessing / 253 \\
System Organization / 271 \\
PowerPC 601 and Alpha 21064 / 305 \\
App. A. IEEE 754 Floating-Point Standard / 333 \\
App. B. POWER Instruction Formats / 341 \\
App. C. POWER Instruction Set Sorted by Mnemonic / 349
\\
App. D. PowerPC Instruction Formats / 355 \\
App. E. PowerPC Instruction Set Sorted by Mnemonic /
365 \\
App. F. Cross Reference for Changed POWER Mnemonics /
377 \\
Bibliography / 383 \\
Index / 391",
}
@Article{White:1994:PNG,
author = "S. W. White and S. Dhawan",
title = "{POWER2}: {Next} generation of the {RISC System\slash
6000} family",
journal = j-IBM-JRD,
volume = "38",
number = "5",
pages = "493--502",
month = sep,
year = "1994",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.almaden.ibm.com/journal/rd38-5.html#two",
abstract = "Since its announcement, the IBM RISC System\slash
6000* processor has characterized the aggressive
instruction-level parallelism approach to achieving
performance. Recent enhancements to the architecture
and implementation provide greater superscalar
capability. This paper describes the architectural
extensions which improve storage reference bandwidth,
allow hardware square-root computation, and speed
floating-point-to-integer conversion. The
implementation, which exploits these extensions and
doubles the number of functional units, is also
described. A comparison of performance results on a
variety of industry standard benchmarks demonstrates
that superscalar capabilities are an attractive
alternative to aggressive clock rates.",
acknowledgement = ack-nhfb,
affiliation = "IBM Corp., Austin, TX, USA",
classcodes = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220P (Parallel architecture);
C5470 (Performance evaluation and testing)",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5220P (Parallel architecture);
C5470 (Performance evaluation and testing)",
corpsource = "IBM Corp., Austin, TX, USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "bandwidth; evaluation; floating-point-to-;
Floating-point-to-integer conversion;
Floating-point-to-integer conversion, POWER2; IBM RISC
System/6000 processor; IBM RISC System\slash 6000
processor; instruction-level; Instruction-level
parallelism; integer conversion; microprocessor chips;
parallel architectures; parallelism; performance;
POWER2; reduced instruction set computing; Square-root
computation; square-root computation; storage
reference; Storage reference bandwidth; superscalar
capability; Superscalar capability",
thesaurus = "Microprocessor chips; Parallel architectures;
Performance evaluation; Reduced instruction set
computing",
treatment = "P Practical",
}
@Article{Wichmann:1994:CSP,
author = "B. A. Wichmann",
title = "Contribution of standard programming languages to
software quality",
journal = j-SEJ,
volume = "9",
number = "1",
pages = "3--12",
month = jan,
year = "1994",
CODEN = "SEJOED",
ISSN = "0268-6961",
bibdate = "Sun Mar 15 17:49:58 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Software Engineering Journal",
remark = "Brief mention of floating-point issues in software
validation.",
}
@Misc{Williams:1994:MAM,
author = "T. Williams",
title = "Method and apparatus for multiplying denormalized
binary floating point numbers without additional
delay",
day = "13",
month = sep,
year = "1994",
bibdate = "Fri Nov 28 15:24:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,347,481.",
acknowledgement = ack-nhfb,
}
@InProceedings{Wong:1994:FEE,
author = "W. F. Wong and E. Goto",
title = "Fast evaluation of the elementary functions in double
precision",
crossref = "Mudge:1994:PTS",
pages = "349--358",
year = "1994",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the most spectacular development in computer
technology is the growth in memory density and speed.
It is with this development in mind that we intend to
tackle the old problem of computing the elementary
functions. Since the dawn of computing, the fast and
accurate computation of the elementary functions has
been a constant concern of numerical computing. It now
seems possible to use tables of sizes in the range of
megabits to aid in such computation. To this end, in
this paper, we propose a method called ATA-M (Add-Table
Lookup-Add with Multiplication) for evaluating
polynomials with the aid of tables. When applied to the
elementary functions, we obtained a set of algorithms
which computes the reciprocal, square root,
exponential, sine, cosine, logarithm, are tangent and
the hyperbolic functions in about 3 to 4 double
precision floating point multiplication time and
utilizing about 2 Mbyte of tables.",
acknowledgement = ack-nhfb,
affiliation = "Department of Inf. Syst. and Computer Science, Nat.
University of Singapore, Singapore",
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods)",
keywords = "Add-Table Lookup-Add with Multiplication; ATA-M;
Double precision; Elementary functions; Floating point
multiplication time; Hyperbolic functions; Memory
density; Memory speed; Numerical computing;
Polynomials",
thesaurus = "Digital arithmetic; Polynomials; Table lookup",
}
@Article{Wong:1994:FHB,
author = "W. F. Wong and E. Goto",
title = "Fast Hardware-Based Algorithms for Elementary Function
Computations Using Rectangular Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "3",
pages = "278--294",
month = mar,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.272429",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 7 07:13:54 MDT 2011",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429",
abstract = "As the name suggests, elementary functions play a
vital role in scientific computations. Yet due to their
inherent nature, they are a considerable computing task
by themselves. Not surprisingly, since the dawn of
computing, the goal of speeding up elementary function
computation has been pursued. This paper describes new
hardware based algorithms for the computation of the
common elementary functions, namely division,
logarithm, reciprocal square root, arc tangent, sine
and cosine. These algorithms exploit microscopic
parallelism using specialized hardware with heavy use
of truncation based on detailed accuracy analysis. The
contribution of this work lies in the fact that these
algorithms are very fast and yet are accurate. If we
let the time to perform an IEEE Standard 754 double
precision floating point multiplication be $
\tau_\times $, our algorithms to achieve roughly $ 3.68
\tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times
$, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $
6.5 \tau_\times $, for division, logarithm, square
root, exponential, are tangent and complex exponential
(sine and cosine) respectively. The trade-off is the
need for tables and some specialized hardware. The
total amount of tables required, however, is less than
128 Kbytes. We discuss the hardware, algorithmic and
accuracy aspects of these algorithms.",
acknowledgement = ack-nj # " and " # ack-nhfb,
affiliation = "Department of Inf. Syst. and Computer Science, Nat.
University of Singapore, Singapore",
ajournal = "IEEE Trans. Comput.",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Arc tangent; Common elementary functions; Cosine;
Elementary function computations; Floating point
multiplication; Hardware-based algorithms; Microscopic
parallelism; Reciprocal square root; Rectangular
multipliers; Scientific computations; Sine",
language = "English",
pubcountry = "USA",
thesaurus = "Digital arithmetic; Error analysis",
}
@Article{Yang:1994:NIPa,
author = "Ming-Chwen Yang and Ja-Ling Wu",
title = "A new interpretation of ``polynomial residue number
system''",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "42",
number = "8",
pages = "2190--2191",
month = aug,
year = "1994",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.301857",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7453",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "The authors show that the polynomial residue number
system can be interpreted in terms of the Chinese
remainder theorem for polynomials (CRTP) over a finite
ring which is useful for signal \ldots{}",
}
@Article{Yang:1994:NIPb,
author = "Ming-Chwen Yang and Ja-Ling Wu",
title = "A new interpretation of ``polynomial residue number
system''",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "42",
number = "8",
pages = "2190--2191",
month = aug,
year = "1994",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.301857",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7453",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "The authors show that the polynomial residue number
system can be interpreted in terms of the Chinese
remainder theorem for polynomials (CRTP) over a finite
ring which is useful for signal \ldots{}",
}
@Article{Yuen:1994:PMC,
author = "C. K. Yuen and M. D. Feng",
title = "Parallel multiplication: a case study in parallel
programming",
journal = j-SIGPLAN,
volume = "29",
number = "3",
pages = "12--17",
month = mar,
year = "1994",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:16:48 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C6110P (Parallel programming); C7310 (Mathematics)",
corpsource = "Department of Inf. Syst. and Computer Science, Nat.
University of Singapore, Singapore",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "AND/OR parallel problems; bottom up design method;
mathematics computing; parallel multiplication;
parallel program; parallel programming; performance
evaluation; program structure design; speculative
processing; systems analysis; top down design method;
tuplespace",
treatment = "P Practical",
}
@InProceedings{Zhang:1994:EMR,
author = "Qihong Zhang and J. H. Kim",
title = "An efficient method to reduce roundoff error in matrix
multiplication with algorithm-based fault tolerance",
crossref = "Lea:1994:PSA",
pages = "32--39",
year = "1994",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithm-Based Fault Tolerance (ABFT) schemes have
been proposed by a number of researchers recently.
Although all errors can be theoretically detected and
corrected by using these techniques, some practical
problems, especially the roundoff errors, degrade the
performance drastically. In this paper, we proposed a
new scheme called Extended Mantissa Checksum (EMC) test
in which the mantissa of the product of two input
matrices are divided into two sections and extended for
faulty detection and correction. Using this scheme, the
number of undetected errors and false alarms are
decreased largely and the error coverage is improved
significantly. In addition, the time latency is short
and the hardware overhead is small compared with other
schemes.",
acknowledgement = ack-nhfb,
affiliation = "Center for Adv. Comput. Studies, Southwestern
Louisiana University, Lafayette, LA, USA",
classification = "C1110 (Algebra); C4240P (Parallel programming and
algorithm theory); C5230 (Digital arithmetic methods)",
keywords = "Algorithm-based fault tolerance; correct rounding;
Error coverage; Extended mantissa checksum test; False
alarms; Fault correction; Fault detection; Floating
point test; Hardware overhead; Matrix multiplication;
Roundoff error; Time latency",
thesaurus = "Algorithm theory; Digital arithmetic; Error
correction; Error detection; Fault tolerant computing;
Matrix algebra; Roundoff errors",
}
@Article{Zhang:1994:TDN,
author = "M. Zhang and J. G. Delgado-Frias and S. Vassiliadis",
title = "Table driven {Newton} scheme for high precision
logarithm generation",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "141",
number = "5",
pages = "281--292",
month = sep,
year = "1994",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Based on the Newton method, a table driven iterative
scheme is proposed to compute the logarithm function.
The proposed scheme provides high performance and high
precision and it is implementable with currently
available technologies. It is shown, assuming the
availability of a parallel multiplier and an adder and
the IEEE floating point format, that a computation
delay of 12 machine cycles can be obtained with
precision of 0.761*2/sup -53/ requiring 18432 bytes of
read only memory (ROM). Based on performance and
look-up table size estimations of other existing
schemes also using table driven approaches a speed-up
of over 1.5 for the proposed scheme can be obtained.",
acknowledgement = ack-nhfb,
affiliation = "McCaw Cellular Commun. Inc., Kirkland, WA, USA",
classification = "C5230 (Digital arithmetic methods); C6130 (Data
handling techniques)",
fjournal = "IEE Proceedings. Computers and Digital Techniques",
keywords = "12 Machine cycles; Adder; High precision logarithm
generation; IEEE floating point format; Iterative
scheme; Newton method; Parallel multiplier; Table
driven",
pubcountry = "UK",
thesaurus = "Digital arithmetic; Iterative methods; Table lookup",
}
@Article{Zuras:1994:MSM,
author = "D. Zuras",
title = "More On Squaring and Multiplying Large Integers",
journal = j-IEEE-TRANS-COMPUT,
volume = "43",
number = "8",
pages = "899--908",
month = aug,
year = "1994",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.295852",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:16:49 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Selected revised and extended papers from ARITH'11
\cite{Swartzlander:1993:SCA}.",
}
@Article{Zuse:1994:PPV,
author = "K. Zuse",
title = "Past and present view on computer architecture",
journal = j-IFIP-TRANS-A,
volume = "A-52",
pages = "248--250",
month = "????",
year = "1994",
CODEN = "ITATEC",
ISSN = "0926-5473",
bibdate = "Tue Dec 12 09:29:07 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Applications and Impacts. Information Processing '94
IFIP 13th World Computer Congress.",
abstract = "The author discusses his work in developing binary
instruction stream based computers. He chose the
half-logarithmic form, where he stored only the
exponent in a logarithmic notation, which is the same
as the floating point numbers, used in today's
computers. Following this principle, he developed new
machines. He started with a mechanical working
construction. This was a storage utility which was
concentrated and enabled the storage of a thousand
words. This storage device was completed in 1936. It
occurred to him that one could also build this machine
with electrical parts. First he built small computers,
the model Z2 and immediately after this the model Z3,
which was based entirely on relays. Both machines
worked satisfactory. Then he discovered Boolean
algebra. He could now design a computer on paper. He
continued to develop machines and founded a company in
Germany where a number of machines such as the Z11 were
built.",
acknowledgement = ack-nhfb,
classification = "C0200 (General computer topics); C5220 (Computer
architecture); C5420 (Mainframes and minicomputers)",
confdate = "28 Aug.-2 Sept. 1994",
conflocation = "Hamburg, Germany",
fjournal = "IFIP Transactions. A. Computer Science and
Technology",
keywords = "Binary instruction stream based computers; Boolean
algebra; Computer architecture; Exponent; Floating
point numbers; Half-logarithmic form; Storage device;
Z11; Z2; Z3; ZUSE KG",
pubcountry = "Netherlands",
thesaurus = "Computer architecture; Digital computers; History",
}
@InProceedings{Aagaard:1995:FVP,
author = "M. Aagaard and C. Seger",
title = "The formal verification of a pipelined
double-precision {IEEE} floating-point multiplier",
crossref = "IEEE:1995:IAI",
pages = "7--10",
year = "1995",
bibdate = "Sat Jun 02 07:46:35 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Abdallah:1995:SASa,
author = "M. Abdallah and A. Skavantzos",
booktitle = "Proceedings of the Twenty-Seventh Southeastern
Symposium on System Theory, 12--14 March 1995",
title = "A systematic approach for selecting practical moduli
sets for residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "445--449",
year = "1995",
CODEN = "????",
DOI = "https://doi.org/10.1109/SSST.1995.390542",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The residue number system (RNS) is a useful tool for
digital signal processing (DSP) since it can support
parallel, carry free, high speed arithmetic. An RNS is
defined by a set of relatively prime integers called
the moduli set. The most important \ldots{}",
}
@InProceedings{Abdallah:1995:SASb,
author = "M. Abdallah and A. Skavantzos",
booktitle = "Proceedings of the Twenty-Seventh Southeastern
Symposium on System Theory, 12--14 March 1995",
title = "A systematic approach for selecting practical moduli
sets for residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "445--449",
year = "1995",
CODEN = "????",
DOI = "https://doi.org/10.1109/SSST.1995.390542",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The residue number system (RNS) is a useful tool for
digital signal processing (DSP) since it can support
parallel, carry free, high speed arithmetic. An RNS is
defined by a set of relatively prime integers called
the moduli set. The most important \ldots{}",
}
@Article{Al-Mouhamed:1995:ELF,
author = "Mayez Al-Mouhamed and Lubomir Bic",
title = "Effects of Loop Fusion and Statement Migration on the
Speedup of Vector Multiprocessors",
journal = j-J-PAR-DIST-COMP,
volume = "31",
number = "1",
pages = "56--64",
day = "15",
month = nov,
year = "1995",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1995.1144",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:58 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1144/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1144/production/pdf",
acknowledgement = ack-nhfb,
classification = "C5220P (Parallel architecture); C6150C (Compilers,
interpreters and other processors); C6150N (Distributed
systems software)",
corpsource = "Department of Comput. Eng., King Fahd University of
Pet. and Miner., Dhahran, Saudi Arabia",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "arithmetic pipelines; C240; cache reuse; commercial
optimizing compiler; load and store operations; loop
fusion; optimising compilers; optimization; parallel
architectures; parallel-vector loops; processor;
resource allocation; scheduled; scheduling; statement
migration; vector multiprocessors; vector processor
systems",
treatment = "P Practical",
}
@TechReport{Altwaijry:1995:PAT,
author = "H. Altwaijry and M. Flynn",
title = "Performance\slash area tradeoffs in {Booth}
multipliers",
type = "Technical Report",
number = "CSL-TR-95-684",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = nov,
year = "1995",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Anonymous:1995:FEF,
author = "Anonymous",
title = "Fraction eliminate floating-point multiply",
journal = j-EDN,
volume = "40",
number = "24",
pages = "88--??",
year = "1995",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "EDN",
}
@Article{Anonymous:1995:INM,
author = "Anonymous",
title = "{IBM}'s new {Model 3CT RS\slash 6000} workstation
provides the industry's best floating-point price\slash
performance numbers in the {US}\$35,000 to {US}\$50,000
price range",
journal = j-OPEN-SYSTEMS-TODAY,
volume = "??",
number = "169",
pages = "32--??",
month = feb,
year = "1995",
ISSN = "1061-0839",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Open Systems Today",
}
@Article{Anonymous:1995:MVW,
author = "Anonymous",
title = "Micro View --- What lessons can chip makers and their
customers take from the {Pentium} floating-point divide
flaw and the resultant tidal wave of publicity?",
journal = j-IEEE-MICRO,
volume = "15",
number = "2",
pages = "88--??",
month = mar # "\slash " # apr,
year = "1995",
CODEN = "IEMIDZ",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Anonymous:1995:PCH,
author = "Anonymous",
title = "Program converts hex to floating point",
journal = j-EDN,
volume = "40",
number = "15",
pages = "76--??",
year = "1995",
CODEN = "EDNSBH",
ISSN = "0012-7515, 0364-6637",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "EDN",
}
@InProceedings{Antelo:1995:RCR,
author = "Elisardo Antelo and Javier D. Bruguera and Julio
Villalba and Emilio L. Zapata",
title = "Redundant {CORDIC} Rotator Based on Parallel
Prediction",
crossref = "Knowles:1995:PSC",
pages = "172--179",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Antelo.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Bailey:1995:FBM,
author = "David H. Bailey",
title = "A {Fortran-90} Based Multiprecision System",
journal = j-TOMS,
volume = "21",
number = "4",
pages = "379--387",
month = dec,
year = "1995",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/212066.212075",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Apr 29 15:15:44 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also extension to complex arithmetic
\cite{Smith:1998:AMP}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p379-bailey/",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "arithmetic; Fortran 90; multiprecision",
subject = "D.3.2 [Programming Languages]: Language
Classifications -- Fortran 90; D.3.4 [Programming
Languages]: Processors; G.1.0 [Numerical Analysis]:
General; G.1.2 [Numerical Analysis]: Approximation",
}
@InProceedings{Bannon:1995:IAA,
author = "P. Bannon and J. Keller",
title = "Internal architecture of {Alpha 21164}
microprocessor",
crossref = "IEEE:1995:DPC",
pages = "79--87",
month = mar,
year = "1995",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Baron:1995:FPP,
author = "P. Baron and A. Joudon and F. Lugiez and M. Rouger",
title = "Floating Point Processor for Photomultiplier Tube
Signals",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "42",
number = "4",
pages = "750--752",
month = aug,
year = "1995",
CODEN = "IRNSAM",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
summary = "A fast digital readout system has been designed for
synchronous processing of the current signals delivered
by a 64-channel multichannel photomultiplier tube
(MCPMT) associated with fast scintillators. This mixed
analog digital full custom chip uses \ldots{}",
}
@Article{Bauer:1995:AEB,
author = "P. H. Bauer",
title = "Absolute Error Bounds for Block Floating-Point
Direct-Form Digital Filters",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "43",
number = "8",
pages = "1994--1996",
month = aug,
year = "1995",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "Provides an asymptotic response analysis of digital
filters, which are implemented in block floating-point
format. Using absolute bounds on the quantization
error, conditions for the existence of certain response
types and the corresponding bounds on \ldots{}",
}
@Article{Bauer:1995:ARE,
author = "P. H. Bauer",
title = "Absolute Response Error Bounds for Floating Point
Digital Filters in State Space Representation",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "42",
number = "9",
pages = "610--613",
month = sep,
year = "1995",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.466642",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "A deterministic study of the zero input asymptotic
behavior of second order state space digital filters
with floating point arithmetic is carried out. Using a
consecutive bound reduction method, asymptotic bounds
on the state response are derived. It \ldots{}",
}
@InProceedings{Baumhof:1995:NVV,
author = "Christoph Baumhof",
title = "A New {VLSI} Vector Arithmetic Coprocessor for the
{PC}",
crossref = "Knowles:1995:PSC",
pages = "210--215",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Baumhof.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Beaty:1995:EAS,
author = "Steven J. Beaty and Gearold R. Johnson",
title = "Effect of adding a scalar {D-cache} to the {Cray-4}
vector processor",
journal = j-IEEE-INT-CONF-ALG-ARCH-PAR-PROC,
volume = "1",
pages = "227--230",
year = "1995",
bibdate = "Mon Aug 26 10:51:12 MDT 1996",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 95TH0682-5.",
abstract = "In the past, vector supercomputers achieved high
performance with long arithmetic pipelines coupled with
fast scalar processors. Processor speed has increased
at a rate greater than memory speed. Indeed, current
vector processors have cycle times far faster than the
memories they are connected to. When compilers can
predict memory access patterns, they vectorize
computations and thereby hide the processor\slash
memory disparity. When memory access patterns are not
known until run-time, caches can pay large dividends.
This paper studies the effects of adding a scalar data
cache to a modern vector processor and shows some
encouraging results.",
acknowledgement = ack-nhfb,
affiliation = "Cray Computer Corp",
affiliationaddress = "Colorado Springs, CO, USA",
classification = "722.1; 722.4; 723.1; 723.2",
conference = "Proceedings of the IEEE 1st International Conference
on Algorithms and Architectures for Parallel
Processing. Part 1 (of 2)",
fjournal = "IEEE International Conference on Algorithms and
Architectures for Parallel Processing",
journalabr = "IEEE Int Conf Algorithms Archit Parall Process",
keywords = "Buffer storage; Cray memory hierarchy; Cray-4 vector
processor; Data processing; Hierarchical systems;
Program processors; Scalar D-cache; Supercomputers;
Systems analysis",
meetingaddress = "Brisbane, Aust",
meetingdate = "Apr 19--21 1995",
meetingdate2 = "04/19--21/95",
sponsor = "IEEE",
}
@InProceedings{Bederr:1995:AAE,
author = "H. Bederr and M. Nicolaidis and A. Guyot",
title = "Analytic Approach for Error Masking Elimination in
On-Line Multipliers",
crossref = "Knowles:1995:PSC",
pages = "30--37",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Bederr.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Bickerstaff:1995:PRA,
author = "K'Andrea C. Bickerstaff and Michael J. Schulte and
Earl E. {Swartzlander, Jr.}",
title = "Parallel reduced area multipliers",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "9",
number = "3",
pages = "181--191",
month = apr,
year = "1995",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/BF02407084",
ISSN = "0922-5773 (print), 1573-109X (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Mar 05 08:29:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://springerlink.metapress.com/content/761m0225754r4440/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@Article{Bierman:1995:FAI,
author = "Keith Bierman",
title = "{Fortran} access to {IEEE 754} exceptions",
journal = j-FORTRAN-FORUM,
volume = "14",
number = "3",
pages = "15--18",
month = sep,
year = "1995",
CODEN = "????",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Wed Feb 6 18:50:05 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "43",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@Article{Boley:1995:FPF,
author = "D. Boley and G. H. Golub and S. Makar and N. Saxena
and E. J. McCluskey",
title = "Floating Point Fault Tolerance with Backward Error
Assertions",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "2",
pages = "302--311",
month = feb,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.364541",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:26 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=364541",
abstract = "The paper introduces an assertion scheme based on the
backward error analysis for error detection in
algorithms that solve dense systems of linear
equations, Ax=b. Unlike previous methods, this backward
error assertion model is specifically designed to
operate in an environment of floating point arithmetic
subject to round-off errors, and it can be easily
instrumented in a Watchdog processor environment. The
complexity of verifying assertions is O(n/sup 2/),
compared to the O(n/sup 3/) complexity of algorithms
solving Ax=b. Unlike other proposed error detection
methods, this assertion model does not require any
encoding of the matrix A. Experimental results under
various error models are presented to validate the
effectiveness of this assertion scheme.",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Minnesota University,
Minneapolis, MN, USA",
ajournal = "IEEE Trans. Comput.",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity); C5230 (Digital arithmetic methods); C5470
(Performance evaluation and testing)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Assertion scheme; Backward error analysis; Backward
error assertions; Complexity; Dense systems; Error
detection; Error models; Floating point arithmetic;
Floating point fault tolerance; Linear equations;
Round-off errors; Watchdog processor environment",
summary = "The paper introduces an assertion scheme based on the
backward error analysis for error detection in
algorithms that solve dense systems of linear
equations, Ax=b. Unlike previous methods, this backward
error assertion model is specifically designed
\ldots{}",
thesaurus = "Computational complexity; Error analysis; Error
detection; Fault tolerant computing; Floating point
arithmetic; Linear algebra",
}
@Article{Bomar:1995:RNA,
author = "B. W. Bomar and L. M. Smith and R. D. Joseph",
title = "Roundoff Noise Analysis of State-Space Digital Filters
Implemented on Floating-Point Digital Signal
Processors",
journal = "Proceedings - IEEE International Symposium on Circuits
and Systems",
volume = "??",
number = "3",
pages = "III-2023",
year = "1995",
ISSN = "0271-4310",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Booker:1995:FER,
author = "Alan Booker",
title = "Floating-Point Emulation and Representation",
journal = j-EMBED-SYS-PROG,
volume = "8",
number = "9",
pages = "111--??",
year = "1995",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Embedded Systems Programming",
}
@Article{BrinchHansen:1995:LDA,
author = "Per {Brinch Hansen}",
title = "The Long Division Algorithm of {Linger}, {Mills} and
{Witt}",
journal = j-SPE,
volume = "25",
number = "1",
pages = "109--109",
month = jan,
year = "1995",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.4380250107",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat May 31 13:36:16 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/litprog.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
note = "See \cite{Linger:1979:SPT,BrinchHansen:1994:MLD}.",
abstract = "The long division algorithm of Linger, Mills and Witt
\cite{Linger:1979:SPT} is discussed and found to be
significantly slower than a recent algorithm developed
by the author.",
acknowledgement = ack-nhfb,
ajournal = "Softw. Pract. Exp.",
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "30 Oct 2006",
}
@Article{Burgess:1995:COT,
author = "N. Burgess and T. Williams",
title = "Choices of operand truncation in the {SRT} division
algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "7",
pages = "933--937",
month = jul,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.392852",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=392852",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Burnikel:1995:EGC,
author = "Christoph Burnikel and Jochen Konemann and Kurt
Mehlhorn and Stefan Naher and Stefan Schirra and
Christian Uhrig",
title = "Exact Geometric Computation in {LEDA}",
crossref = "ACM:1995:PEA",
pages = "C18--C19",
year = "1995",
bibdate = "Tue Nov 13 21:49:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Carreno:1995:IIF,
author = "Victor A. Carreno",
title = "Interpretation of {IEEE-854} floating-point standard
and definition in the {HOL} system",
type = "{NASA} technical memorandum",
number = "110189",
institution = pub-NASA,
address = pub-NASA:adr,
pages = "????",
year = "1995",
bibdate = "Thu Oct 24 14:19:35 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Shipping list no. 96-0366-M.",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; formalism; standards",
}
@InProceedings{Carreno:1995:SIF,
author = "Victor A. Carre{\~n}o and Paul S. Miner",
title = "Specification of the {IEEE-854} Floating-Point
Standard in {HOL} and {PVS}",
crossref = "Anonymous:1995:HEI",
year = "1995",
bibdate = "Wed Nov 24 09:09:34 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://shemesh.larc.nasa.gov/fm/ftp/larc/vac/hug95.ps",
acknowledgement = ack-mfc # " and " # ack-nhfb,
pagecount = "16",
}
@InProceedings{Chang:1995:REA,
author = "P. S. Chang and A. N. {Willson, Jr.}",
booktitle = "Conference Record of the Twenty-Ninth Asilomar
Conference on Signals, Systems and Computers, 1995",
title = "A roundoff error analysis of the normalized {LMS}
algorithm",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1337--1341",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper describes an analysis of the normalized LMS
algorithm under finite word-length effects. It is shown
that, using the averaging principle, it is possible to
derive a good approximation for the total MSE in
steady-state. Implementation \ldots{}",
}
@InProceedings{Chen:1995:UCA,
author = "San-Gee Chen and Chieh-Chih Li",
booktitle = "{IEEE} Signal Processing Society Workshop on {VLSI}
Signal Processing, {VIII, 1995}",
title = "A unified cellular array for multiplication, division
and square root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "533--541",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A unified fast, small-area processor capable of
executing multiplication, division and square-root
operations, all starting from MSD is proposed. Unlike
the existing designs which require both addition and
subtraction operations, and complicated \ldots{}",
}
@Article{Cheng:1995:PBS,
author = "Fuhua Cheng and G. W. Wasilkowski and Jiaye Wang and
Caiming Zhang and Wenping Wang",
title = "Parallel {B}-Spline Surface Interpolation on a
Mesh-Connected Processor Array",
journal = j-J-PAR-DIST-COMP,
volume = "24",
number = "2",
pages = "224--229",
day = "1",
month = feb,
year = "1995",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1995.1022",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:56 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1022/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1022/production/pdf",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation);
C4240C (Computational complexity); C4240P (Parallel
programming and algorithm theory)",
corpsource = "Department of Computer Science, Kentucky University,
Lexington, KY, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "algorithms; B-spline surface interpolation; bicubic
B-spline surface; Chebyshev approximation; Chebyshev
method; computational complexity; constant; control;
data points; finite precision; floating-point
arithmetic; interconnection networks; interpolation;
iterative methods; mesh-connected processor array;
multiprocessor; numerical stability; optimal; parallel;
parallel implementation; points; splines (mathematics);
time",
treatment = "T Theoretical or Mathematical",
}
@PhdThesis{Chesneaux:1995:LSL,
author = "Jean-Marie Chesneaux",
title = "L'arithm{\'e}tique stochastique et le logiciel
{CADNA}. ({French}) [{Stochastic} arithmetic and
{CADNA} software]",
type = "Habilitation {\`a} diriger des recherches",
school = "Universit{\'e} Pierre et Marie Curie",
address = "Paris, France",
pages = "????",
year = "1995",
bibdate = "Mon Mar 19 14:07:57 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Coe:1995:CAP,
author = "Tim Coe and Terje Mathisen and Cleve Moler and Vaughan
Pratt",
title = "Computational Aspects of the {Pentium} Affair",
journal = j-IEEE-COMPUT-SCI-ENG,
volume = "2",
number = "1",
pages = "18--30",
month = "Spring",
year = "1995",
CODEN = "ISCEE4",
ISSN = "1070-9924 (print), 1558-190X (electronic)",
ISSN-L = "1070-9924",
bibdate = "Sat Jan 9 08:57:23 MST 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.computer.org/cse/cs1998/c1018abs.htm",
abstract = "The Pentium affair has been widely publicized. It
started with an obscure defect in the floating-point
unit of Intel Corporation's flagship Pentium
microprocessor. This is the story of how the Pentium
floating-point division problem was discovered, and
what you need to know about the maths and computer
engineering involved before deciding whether to replace
the chip, install the workaround provided here, or do
nothing. The paper also discusses broader issues of
computational correctness.",
acknowledgement = ack-nhfb,
affiliation = "Vitesse Semicond. Corp., Camarillo, CA, USA",
classcodes = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
corpsource = "Vitesse Semicond. Corp., Camarillo, CA, USA",
fjournal = "IEEE Computational Science \& Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=99",
keywords = "computational aspects; computational correctness;
computer engineering; division problem; floating point
arithmetic; Floating-point division problem;
floating-point unit; Intel Corporation; microprocessor
chips; Pentium affair; Pentium microprocessor",
thesaurus = "Floating point arithmetic; Microprocessor chips",
treatment = "P Practical; T Theoretical or Mathematical",
}
@Article{Coe:1995:IPF,
author = "Tim Coe",
title = "Inside the {Pentium FDIV} Bug",
journal = j-DDJ,
volume = "20",
number = "4",
pages = "129--??",
month = apr,
year = "1995",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/documents/s=992/ddj9504l/;
http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "Intel Pentium divide flaw; Thomas R. Nicely",
}
@InProceedings{Coe:1995:ITS,
author = "Tim Coe and Ping Tak Peter Tang",
title = "It Takes Six Ones to Reach a Flaw",
crossref = "Knowles:1995:PSC",
pages = "140--148",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
note = "Also available as Chinese University of Hong Kong
technical report 95-5 (61), 1995.",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Coe.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12; Pentium divide flaw",
}
@Article{Crenshaw:1995:PTFa,
author = "Jack W. Crenshaw",
title = "Programmer's Toolbox: Floating-Point Math",
journal = j-EMBED-SYS-PROG,
volume = "8",
number = "11",
pages = "25--??",
year = "1995",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Embedded Systems Programming",
}
@Article{Crenshaw:1995:PTFb,
author = "Jack W. Crenshaw",
title = "Programmer's Toolbox: Floating-Point Math, Part 2",
journal = j-EMBED-SYS-PROG,
volume = "8",
number = "12",
pages = "29--??",
year = "1995",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Embedded Systems Programming",
}
@InProceedings{Cui:1995:GIFa,
author = "S. Cui and N. Burgess and M. Liebelt and K.
Eshraghian",
title = "A 32-bit {GaAs IEEE} floating point multiplier using
{Trailing-1}'s rounding algorithm",
crossref = "Jain:1995:PET",
pages = "246--252",
year = "1995",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Jain.pdf",
abstract = "The paper presents a GaAs 32-bit IEEE floating point
multiplier. A modified carry save array is used in
conjunction with Booth's algorithm to reduce the
partial product addition and interconnection. A special
rounding technique called Trailing-1's Predictor is
used to speed up the final addition and rounding. This
chip uses a new layout methodology for easy design
structure and improved GaAs technology layout density.
The combination of the fast arithmetic architecture and
compact layout style achieves 4ns multiplication time
with 3.5 W power dissipation at 75 degrees C. The area
is 2.43 mm by 3.77 mm (excluding pads) and uses 28000
transistors to give a density of 3056
transistors/mm/sup 2/ for 0.8 mu m GaAs technology. (11
Refs.)",
acknowledgement = ack-nhfb,
affiliation = "Department of Electr. and Electron. Eng., Adelaide
University, SA, Australia",
classification = "B1265B (Logic circuits); C5120 (Logic and switching
circuits); C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods)",
keywords = "3.5 W; 32 Bit; 32 Bit GaAs IEEE floating point
multiplier; 75 DegC; Booth algorithm; Compact layout
style; Easy design structure; Fast arithmetic
architecture; GaAs technology; Improved GaAs technology
layout density; Layout methodology; Modified carry save
array; Multiplication time; Partial product addition;
Power dissipation; Special rounding technique;
Trailing-1s rounding algorithm; Transistors",
numericalindex = "Word length 3.2E+01 bit; Power 3.5E+00 W;
Temperature 3.48E+02 K",
thesaurus = "Floating point arithmetic; Gallium arsenide;
Microprocessor chips; Multiplying circuits; Roundoff
errors; Societies",
}
@InProceedings{Cui:1995:GIFb,
author = "S. Cui and N. Burgess and M. Liebelt and K.
Eshraghian",
title = "A {GaAs} {IEEE} Floating Point Standard Single
Precision Multiplier",
crossref = "Knowles:1995:PSC",
pages = "91--97",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Cui.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Das:1995:IFC,
author = "D. Das and K. Mukhopadhyaya and B. P. Sinha",
title = "Implementation of four common functions on an {LNS}
co-processor",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "1",
pages = "155--161",
month = jan,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.367997",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "We propose a scheme for evaluating four commonly used
functions namely, (1) inverse trigonometric functions,
(2) trigonometric functions, (3) the exponential
function, and (4) the logarithmic function with the
help of a logarithmic number system (\ldots{})",
}
@Article{Daumas:1995:MRR,
author = "Marc Daumas and Christophe Mazenc and Xavier Merrheim
and Jean-Michel Muller",
title = "Modular range reduction: a new algorithm for fast and
accurate computation of the elementary functions",
journal = j-J-UCS,
volume = "1",
number = "3",
pages = "162--175",
day = "28",
month = mar,
year = "1995",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
MRclass = "68M07 (65D20 68Q20)",
MRnumber = "97b:68012",
bibdate = "Wed May 28 19:32:35 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.iicm.edu/jucs_1_3/modular_range_reduction",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
keywords = "range reduction",
}
@Article{Demmel:1995:CSB,
author = "James W. Demmel and Inderjit Dhillon and Huan Ren",
title = "On the correctness of some bisection-like parallel
eigenvalue algorithms in floating point arithmetic",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "3",
pages = "116--149",
year = "1995",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:29 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://etna.mcs.kent.edu/vol.3.1995/pp116-149.dir/pp116-149.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{DiClaudio:1995:FCR,
author = "E. D. {Di Claudio} and F. Piazza and G. Orlandi",
title = "Fast combinatorial {RNS} processors for {DSP}
applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "5",
pages = "624--633",
month = may,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.381948",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=381948",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Doman:1995:SAP,
author = "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
title = "A Set of {Ada} Packages for High Precision
Calculations",
journal = j-TOMS,
volume = "21",
number = "4",
pages = "416--431",
month = dec,
year = "1995",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/212066.212087",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Nov 14 09:57:55 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p416-doman/",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accuracy; Ada; arithmetic elementary-function
evaluation; floating-point; multiple-precision portable
software",
subject = "G.1.0 [Numerical Analysis]: General -- computer
arithmetic; G.1.2 [Numerical Analysis]: Approximation
-- elementary function approximation; G.4 [Mathematics
of Computing]: Mathematical Software -- algorithm
analysis; efficiency; portability",
}
@Article{Doran:1995:SCD,
author = "R. W. Doran",
title = "Special Cases of Division",
journal = j-J-UCS,
volume = "1",
number = "3",
pages = "176--194",
day = "28",
month = mar,
year = "1995",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
MRclass = "68M07 (68Q20)",
MRnumber = "97b:68013",
bibdate = "Wed May 28 19:32:35 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.iicm.edu/jucs_1_3/special_cases_of_division",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@InProceedings{Ercegovac:1995:SDC,
author = "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang",
title = "Sign Detection and Comparison Networks with a Small
Number of Transitions",
crossref = "Knowles:1995:PSC",
pages = "59--66",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ercegovac.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Espelid:1995:FPS,
author = "T. O. Espelid",
title = "On Floating-Point Summation",
journal = j-SIAM-REVIEW,
volume = "37",
number = "4",
pages = "603--607",
month = dec,
year = "1995",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1037130",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65Gxx (65Bxx)",
MRnumber = "1 368 391",
bibdate = "Sat Mar 29 09:55:35 MDT 2014",
bibsource = "Compendex database;
http://epubs.siam.org/toc/siread/37/4;
http://www.siam.org/journals/sirev/sirev374.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/27303.htm",
abstract = "In this paper we focus on some general error analysis
results in floating-point summation. We emphasize
analysis that is useful from both a scientific and a
teaching point of view.",
acknowledgement = ack-nhfb,
affiliation = "Univ of Bergen",
affiliationaddress = "Bergen, Norway",
classification = "721.1; 921.4; 921.6; C4110 (Error analysis in
numerical methods); C5230 (Digital arithmetic
methods)",
corpsource = "Department of Inf., Bergen University, Norway",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "accurate floating-point summation; algorithm sum;
algorithms; binary summation tree; digital arithmetic;
error analysis; floating-point arithmetic;
floating-point summation; number theory; numerical
analysis; ordering; root of the tree; rounding errors;
roundoff errors; set theory; trees (mathematics)",
onlinedate = "December 1995",
treatment = "T Theoretical or Mathematical",
}
@Article{Fateman:1995:FFP,
author = "Richard J. Fateman and Kevin A. Broughan and Diane K.
Willcock and Duane Rettig",
title = "Fast Floating Point Processing in {Common Lisp}",
journal = j-TOMS,
volume = "21",
number = "1",
pages = "26--62",
month = mar,
year = "1995",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/200979.200989",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 09 10:20:50 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See remark \cite{Reid:1996:RFF}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p26-fateman/",
acknowledgement = ack-nhfb # " and " # ack-rfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "C programming language; Common Lisp; compiler
optimization; floating-point arithmetic; Fortran; Lisp;
numerical algorithms; symbolic computation",
subject = "D.3.4 [Programming Languages]: Processors ---
compilers; interpreters; optimization; G.4 [Mathematics
of Computing]: Mathematical Software --- efficiency;
portability",
}
@InProceedings{Ferguson:1995:ECS,
author = "Warren E. {Ferguson, Jr.}",
title = "Exact Computation of a Sum or Difference with
Applications to Argument Reduction",
crossref = "Knowles:1995:PSC",
pages = "216--221",
year = "1995",
DOI = "https://doi.org/10.1109/ARITH.1995.465355",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ferguson.pdf",
abstract = "Results are presented that identify when the computed
value of a sum or difference is exact. The accuracy of
an argument reduction algorithm is analyzed using these
results. This analysis demonstrates that catastrophic
cancellation does not occur in this algorithm's
computation of the reduced argument.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; ARITH-12; range
reduction",
}
@Article{Figueroa:1995:WDR,
author = "Samuel A. Figueroa",
title = "When is Double Rounding Innocuous?",
journal = j-SIGNUM,
volume = "30",
number = "3",
pages = "21--26",
month = jul,
year = "1995",
CODEN = "SNEWD6",
DOI = "https://doi.org/10.1145/221332.221334",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:26 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.pdf",
abstract = "Double rounding is the phenomenon that occurs when the
result of an operation is rounded to fit some
intermediate destination, and then again when delivered
to its final destination. This can be a common
occurrence when using some floating-point arithmetic
engines which lack single precision registers: results
of operations are typically rounded to fit in a
register, whose width may be double precision or wider,
before being stored in some memory location possibly in
a format narrower than that of the registers. Examples
of such floating-point arithmetic engines include
Intel's x87 series and IBM's POWER architecture.
(Implementations of the latter are found in some IBM
workstations.)",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "https://dl.acm.org/loi/signum",
}
@TechReport{Flynn:1995:ADA,
author = "Michael J. Flynn and Stuart F. Oberman",
title = "An analysis of division algorithms and
implementations",
type = "Report",
number = "CSL-TR-95-675",
institution = "Stanford University",
address = "Stanford, CA, USA",
pages = "58",
month = jul,
year = "1995",
bibdate = "Wed Dec 13 08:55:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://searchworks.stanford.edu/view/4639530",
abstract = "Floating-point division is generally regarded as a low
frequency, high latency operation in typical
floating-point applications. However, the increasing
emphasis on high performance graphics and the
industry-wide usage of performance benchmarks forces
processor designers to pay close attention to all
aspects of floating-point computation. Many algorithms
are suitable for implementing division in hardware.
This paper presents four major classes of algorithms in
a unified framework, namely digit recurrence,
functional iteration, very high radix, and variable
latency. Digit recurrence algorithms, the most common
of which is SRT, use subtraction as the fundamental
operator, and they converge to a quotient linearly.
Division by functional iteration converges to a
quotient quadratically using multiplication. Very high
radix division algorithms are similar to digit
recurrence algorithms, but they incorporate
multiplication to reduce the latency. Variable latency
division algorithms reduce the average latency to form
the quotient. These algorithms are explained and
compared in this work. It is found that for low-cost
implementations where chip area must be minimized,
digit recurrence algorithms are suitable. An
implementation of division by functional iteration can
provide the lowest latency for typical multiplier
latencies. Variable latency algorithms show promise for
simultaneously minimizing average latency while also
minimizing area.",
acknowledgement = ack-nhfb,
}
@InProceedings{Flynn:1995:SPT,
author = "M. J. Flynn and K. Nowka and G. Bewick and E. Schwarz
and N. Quach",
title = "The {SNAP} Project: Towards Sub-Nanosecond
Arithmetic",
crossref = "Knowles:1995:PSC",
pages = "75--83",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "ftp://arith.stanford.edu/tr/snap_arith12.ps.Z;
http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Flynn.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Fried:1995:PON,
author = "Stephen S. Fried",
title = "{Pentium} Optimizations and Numeric Performance",
journal = j-DDJ,
volume = "20",
number = "1",
pages = "18--20, 22, 26--29",
month = jan,
year = "1995",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Sep 05 07:21:01 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "The Pentium is the first member of the Intel x86
family that requires RISC-style instruction scheduling
to achieve its full potential. Steve analyzes what this
means in terms of Pentium floating-point performance
and how you can get full throughput from a Pentium.",
acknowledgement = ack-nhfb,
affiliation = "Microway, Kingston, MA, USA",
classification = "C5130 (Microprocessor chips); C5230 (Digital
arithmetic methods); C5470 (Performance evaluation and
testing); C6150C (Compilers, interpreters and other
processors)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "Compilers; Floating-point performance; Full
throughput; Intel x86 family; Numeric performance;
Optimizations; Pentium; RISC-style instruction
scheduling; Tools",
thesaurus = "Floating point arithmetic; Microprocessor chips;
Optimisation; Performance evaluation; Program
compilers; Reduced instruction set computing",
}
@PhdThesis{Gluss:1995:DIA,
author = "Robert Joseph Gluss",
title = "Design and implementation of an asynchronous radix-$4$
pre-scaling floating-point divider",
type = "Thesis ({M.S.})",
school = "Department of Electrical and Computer Engineering,
University of California, Davis",
address = "Davis, CA, USA",
year = "1995",
LCCN = "LD781.D5j 1995 G587",
bibdate = "Thu Oct 24 14:19:35 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "dissertations, academic -- University of California,
Davis -- Electrical and Computer Engineering",
}
@InProceedings{Greenley:1995:UNG,
author = "D. Greenley and J. Bauman and D. Chang and Dennis Chen
and R. Eltejaein and P. Ferolito and P. Fu and Robert
B. Garner and D. Greenhill and H. Grewal and Kalon
Holdbrook and B. Kim and Leslie Kohn and H. Kwan and M.
Levitt and Guillermo Maturana and D. Mrazek and
Chitresh Narasimhaiah and Kevin Normoyle and N. Parveen
and P. Patel and A. Prabhu and Marc Tremblay and
Michelle Wong and L. Yang and Krishna Yarlagadda and
Robert K. Yu and Robert Yung and Gregory B. Zyner",
title = "{UltraSPARC}: the next generation superscalar 64-bit
{SPARC}",
crossref = "IEEE:1995:DPC",
pages = "442--451",
month = mar,
year = "1995",
DOI = "https://doi.org/10.1109/CMPCON.1995.512421",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "UltraSPARC is the first microprocessor from Sun
Microsystems' SPARC Technology Business to implement
the new 64-bit SPARC V9 architecture. ULtraSPARC is
equipped with unique multimedia capabilities and is
capable of 4-way superscalar instruction dispatch, with
an emphasis on maximal system efficiency and throughput
in the execution of complex, memory-intensive
applications. UltraSPARC maintains a strict binary
compatibility with the thousands of existing 32-bit
applications developed for other SPARC processors. This
paper describes the feature set and operation of
UltraSPARC.",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{Halfhill:1995:TBP,
author = "Tom R. Halfhill",
title = "The Truth Behind the {Pentium} Bug: How often do the
five empty cells in the {Pentium}'s {FPU} lookup table
spell miscalculation?",
journal = j-BYTE,
volume = "20",
number = "3",
pages = "163--??",
month = mar,
year = "1995",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Tue Jan 2 10:01:41 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
}
@InProceedings{Hamano:1995:DCA,
author = "Takafumi Hamano and Naofumi Takagi and Shuzo Yajima
and Franco P. Preparata",
title = "{$ O(n) $}-Depth Circuit Algorithm for Modular
Exponentiation",
crossref = "Knowles:1995:PSC",
pages = "188--192",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Hamano.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Harrison:1995:FPV,
author = "J. Harrison",
title = "Floating Point Verification in {HOL}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "??",
number = "971",
pages = "186--??",
year = "1995",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Hassler:1995:FET,
author = "Hannes Hassler and Naofumi Takagi",
title = "Function Evaluation by Table Look-up and Addition",
crossref = "Knowles:1995:PSC",
pages = "10--16",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Hassler.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@TechReport{Hauser:1995:HFE,
author = "John R. Hauser",
title = "Handling floating-point exceptions in numeric
programs",
type = "Report",
number = "UCB/CSD 95-870",
institution = "Computer Science Division (EECS), University of
California",
address = "Berkeley, CA, USA",
pages = "31",
month = mar,
year = "1995",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@MastersThesis{Helsley:1995:SZL,
author = "Harold David Helsley",
title = "A study of zero-input limit cycles in floating-point
digital signal processors",
type = "Thesis ({M.S.})",
school = "University of Tennessee, Knoxville",
address = "Knoxville, TN, USA",
pages = "vii + 65",
year = "1995",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Limit cycles.; Signal processing --- Digital
techniques.",
}
@InProceedings{Hiasat:1995:HSDa,
author = "A. A. Hiasat and H. S. Abdel-Aty-Zohdy",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '95}, 3 May 1995",
title = "A high-speed division algorithm for residue number
system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1996--1999",
year = "1995",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1995.523813",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new algorithm for one of the longstanding problems
in residue number system, namely division, is
presented. The algorithm is very simple. It approaches
the paper-and-pencil division procedure where the
quotient is selected to guarantee a non- \ldots{}",
}
@InProceedings{Hiasat:1995:HSDb,
author = "A. A. Hiasat and H. S. Abdel-Aty-Zohdy",
booktitle = "{IEEE} International Symposium on Circuits and
Systems, {ISCAS '95}, 3 May 1995",
title = "A high-speed division algorithm for residue number
system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1996--1999",
year = "1995",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1995.523813",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new algorithm for one of the longstanding problems
in residue number system, namely division, is
presented. The algorithm is very simple. It approaches
the paper-and-pencil division procedure where the
quotient is selected to guarantee a non- \ldots{}",
}
@Article{Hitz:1995:IDR,
author = "Markus A. Hitz and Erich Kaltofen",
title = "Integer division in residue number systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "8",
pages = "983--989",
month = aug,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.403714",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403714;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=9076",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue arithmetic; residue number system",
summary = "This contribution to the ongoing discussion of
division algorithm for residue number systems (RNS) is
based on Newton iteration for computing the reciprocal.
An extended RNS with twice the number of moduli
provides the range required for \ldots{}",
}
@InProceedings{Ho:1995:CFF,
author = "H. Ho and V. Szwarc and L. Desormeaux",
booktitle = "Proceedings of the Eighth Annual {IEEE} International
{ASIC} Conference and Exhibit, 1995",
title = "A comparison of {FIR} filter implementations based on
two's complement and residue number arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "35--38",
year = "1995",
CODEN = "????",
DOI = "https://doi.org/10.1109/ASIC.1995.580676",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Two FIR filter designs based on residue number
arithmetic (RNA) are presented and compared with a
conventional design based on two's complement
arithmetic (TCA). For the RNA based designs the
arithmetic operations are implemented by means of small
\ldots{}",
}
@MastersThesis{Ho:1995:FPI,
author = "Lei Ho",
title = "Floating point implementation for {Motorola HC6811C}:
{GNU C} cross-compiler",
type = "{Master}'s Thesis",
school = "Department of Electrical Engineering, Ryerson
Polytechnic University",
address = "Toronto, Ontario, Canada",
year = "1995",
bibdate = "Mon Apr 18 06:29:41 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxnote = "Check thesis type?? Ryerson library catalog does not
specify.",
}
@Article{Hobson:1995:EMR,
author = "R. F. Hobson and M. W. Fraser",
title = "An efficient maximum-redundancy radix-$8$ {SRT}
division and square-root method",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "30",
number = "1",
pages = "29--38",
month = jan,
year = "1995",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A new approach to integrating hardware multiplication,
division, and square-root is presented. We use a fully
integrated control path which simultaneously reduces
part of the redundant partial-remainder and performs a
truncated multiplication of the next quotient or
square-root digit by the divisor or square-root value.
A separate (parallel) full precision iterative
multiplier is used for partial remainder production.
Strategic details of a radix-8 implementation are
discussed. It is shown that a maximally redundant digit
set is a viable choice for high performance in this
case.",
acknowledgement = ack-nhfb,
affiliation = "Sch. of Computer Science, Simon Fraser University,
Burnaby, BC, Canada",
classification = "B1265B (Logic circuits); B2570D (CMOS integrated
circuits); C5230 (Digital arithmetic methods)",
fjournal = "IEEE Journal of Solid-State Circuits",
keywords = "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
floating point algorithm; Integrated control path;
Maximally redundant digit set; Maximum-redundancy
radix-8 SRT algorithm; Multiplication; Parallel
iterative multiplier; Partial remainder production;
Redundant partial-remainder; Square-root method; Table
lookup",
numericalindex = "Size 1.2E-06 m",
summary = "A new approach to integrating hardware multiplication,
division, and square-root is presented. We use a fully
integrated control path which simultaneously reduces
part of the redundant partial-remainder and performs a
truncated multiplication of the \ldots{}",
thesaurus = "Adders; CMOS digital integrated circuits; Digital
arithmetic; Dividing circuits; Floating point
arithmetic; Multiplying circuits",
}
@InProceedings{Houelle:1995:AFL,
author = "A. Houelle and H. Mehrez and N. Vaucher and L.
Montalvo and A. Guyot",
title = "Application of Fast Layout Synthesis Environment to
Dividers Evaluation",
crossref = "Knowles:1995:PSC",
pages = "67--74",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Houelle.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@TechReport{Hough:1995:EPD,
author = "David Hough",
title = "Effects of {Pentium} Division Flaw and its Software
Workaround",
type = "Report",
institution = "Sun Microsystems",
address = "Mountain View, CA 94043, USA",
pages = "22",
day = "28",
month = feb,
year = "1995",
bibdate = "Mon Dec 16 11:29:48 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.validlab.com/reports/pentium/",
abstract = "The infamous Intel Pentium floating-point division
flaw is seldom visible in the results of realistic
technical applications, nor does it perceptibly affect
performance. But some programs skillfully designed to
look for arithmetic flaws can find it. In contrast, the
expected harmless differences between 486 and Pentium
elementary transcendental functions, due to the
improved approximations in the latter, are often
evident in ordinary applications.\par
Intel and Cygnus published a recommended compiler
workaround that reduces the effect of the Pentium
division flaw to at most one unit per division, in the
least significant bit of extended precision. Intel has
also modified its math library product libm.a to avoid
the division flaw. The compiler and libm workarounds do
not affect results of CPU chips other than flawed
Pentium chips.\par
The two modifications to the compiler and libm avoid
any severe effects of the Pentium flaw, but sometimes
cause harmlessly different results in realistic
technical applications. The modifications degrade
performance of flawed CPU s by a median of 1\%, and
SPECfp92 ratios by about 9\%.",
acknowledgement = ack-nhfb,
keywords = "Pentium divide flaw",
}
@TechReport{Hough:1995:UVP,
author = "David Hough",
title = "{UCBTEST} vs. {Pentium}",
type = "Report",
institution = "Sun Microsystems",
address = "Mountain View, CA 94043, USA",
pages = "3",
day = "5",
month = mar,
year = "1995",
bibdate = "Mon Dec 16 11:40:24 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.validlab.com/reports/testing.pdf",
abstract = "University of California research into systematic
verification of computer arithmetic has been put into a
form in which anybody could in principle test any
computer arithmetic.\par
So it's exceedingly unlikely that another
microprocessor will come to market with bugs that
UCBTEST software might detect, or with uninitialized
entries in a divider's PLA. But to avoid the situation
of generals always fighting the last war, what can be
done to detect, or better prevent, the next arithmetic
flaw",
acknowledgement = ack-nhfb,
keywords = "Pentium divide flaw",
}
@InProceedings{Hunt:1995:APF,
author = "D. Hunt",
title = "Advanced performance features of the 64-bit
{PA-8000}",
crossref = "IEEE:1995:DPC",
pages = "123--128",
month = mar,
year = "1995",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@TechReport{Ito:1995:EIAa,
author = "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
title = "Efficient Initial Approximation Methods for Division
and Square Using a Multiply-Add Unit",
type = "SIG Notes",
number = "95-HPC-55-10",
institution = "IPSJ",
address = "????",
pages = "73--80",
month = mar,
year = "1995",
bibdate = "Wed Dec 13 10:53:57 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "I cannot find this online, so institution and address
are uncertain. Is this a journal article or technical
report?",
}
@InProceedings{Ito:1995:EIAb,
author = "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
title = "Efficient Initial Approximation and Fast Converging
Methods for Division and Square Root",
crossref = "Knowles:1995:PSC",
pages = "2--9",
month = jul,
year = "1995",
DOI = "https://doi.org/10.1109/arith.1995.465383",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ito.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-12",
summary = "Efficient initial approximations and fast converging
algorithms are important to achieve the desired
precision faster at lower hardware cost in
multiplicative division and square root. In this paper,
a new initial approximation method for division,
\ldots{}",
}
@InProceedings{Jain:1995:HSD,
author = "V. K. Jain and L. Lin",
title = "High-Speed Double Precision Computation of Nonlinear
Functions",
crossref = "Knowles:1995:PSC",
pages = "107--114",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Jang:1995:OSA,
author = "Ju-Wook Jang and Viktor K. Prasanna",
title = "An Optimal Sorting Algorithm on Reconfigurable Mesh",
journal = j-J-PAR-DIST-COMP,
volume = "25",
number = "1",
pages = "31--41",
day = "15",
month = feb,
year = "1995",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1995.1027",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:56 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1027/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1027/production/pdf",
acknowledgement = ack-nhfb,
classification = "C4240P (Parallel programming and algorithm theory);
C5220P (Parallel architecture); C6130 (Data handling
techniques)",
corpsource = "University of Southern California, Los Angeles, CA,
USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "architectures; arithmetic; bit model; computational
complexity; constant time; constant time algorithm;
lower bound; optimal sorting algorithm; parallel;
parallel algorithms; problems; reconfigurable
architecture; reconfigurable architectures;
reconfigurable mesh; sorting; VLSI",
treatment = "T Theoretical or Mathematical",
}
@Unpublished{Kahan:1995:TSD,
author = "W. Kahan",
title = "A Test for {SRT} Division",
year = "1995",
bibdate = "Mon Apr 25 05:50:41 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Lecture notes",
URL = "http://www.cs.berkeley.edu/~wkahan/srtest",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@Misc{Kahan:1995:USP,
author = "{Students of Prof.W.Kahan}",
title = "{UCBTEST}: a suite of programs for testing certain
difficult cases of {IEEE 754} floating-point
arithmetic",
howpublished = "World-Wide Web document",
day = "12",
month = mar,
year = "1995",
bibdate = "Wed May 26 07:29:55 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.netlib.org/fp/ucbtest.tgz",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
remark = "From the source code, students and authors credited
are (in alphabetical order) M. Alemi, D. Feenberg,
Warren Ferguson David G. Hough, David Gay, W. J. Cody,
R. Karpkinski, Z. A. Liu, S. Ma, Stephen Moshier, M.
Mueller, K. C. Ng, D. Priest, T. Quarles, T. Sumner, G.
Taylor, B. Toy, W. Waite, and B. Wichmann.",
}
@Article{Kaliski:1995:MIA,
author = "Burton S. {Kaliski, Jr.}",
title = "The {Montgomery} inverse and its applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "8",
pages = "1064--1065",
month = aug,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.403725",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403725",
abstract = "The Montgomery inverse of $b$ modulo $a$ is $ b^{-1}
2^n \bmod a $, where $n$ is the number of bits in $a$.
The right-shifting binary algorithm for modular
inversion is shown naturally to compute the new inverse
in fewer operations than the ordinary modular inverse.
The new inverse facilitates recent work by Ko{\c{c}} on
modular exponentiation and has other applications in
cryptography",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Kalliojarvi:1995:FWL,
author = "Kari Kallioj{\"a}rvi",
title = "Finite word length effects in floating-point and
block-floating-point digital signal processing
systems",
volume = "159",
type = "Avhandling (doktorgrad)",
school = "Tampereen teknillinen korkeakoulu",
address = "Tampere, Finland",
pages = "vii + 71 + 68",
year = "1995",
ISBN = "951-722-330-7",
ISBN-13 = "978-951-722-330-0",
bibdate = "Thu May 09 08:21:36 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Julkaisuja",
acknowledgement = ack-nhfb,
}
@Article{Ke:1995:SFQ,
author = "Qing Ke and M. J. Feldman",
title = "Single Flux Quantum Circuits Using the Residue Number
System",
journal = j-IEEE-TRANS-APPL-SUPERCOND,
volume = "5",
number = "2",
pages = "2988--2991",
month = jun,
year = "1995",
CODEN = "ITASE9",
DOI = "https://doi.org/10.1109/77.403220",
ISSN = "1051-8223 (print), 1558-2515 (electronic)",
ISSN-L = "1051-8223",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=9069",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Applied Superconductivity",
keywords = "residue arithmetic; residue number system (RNS)",
summary = "We have designed and developed superconducting single
flux quantum (SFQ) digital signal processing circuits
using the residue number system (RNS). RNS arithmetic
is a complete alternative to binary arithmetic for
performing digital computations, \ldots{}",
}
@InProceedings{Kistermann:1995:RWS,
author = "Friedrich Wilhelm Kistermann",
title = "{Die Rechentechnik um 1600 und Wilhelm Schickards
Rechenmaschine}. ({German}) [{The} calculating
technique of 1600 and {Wilhelm Schickard}'s
calculator]",
crossref = "Seck:1995:GWS",
pages = "241--272",
year = "1995",
bibdate = "Sat Jul 27 12:43:03 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@InProceedings{Knowles:1995:FSC,
author = "Simon Knowles and William H. McAllister",
title = "Foreword: {12th Symposium on Computer Arithmetic,
Assembly Rooms, Bath, England, July 19--21, 1995}",
crossref = "Knowles:1995:PSC",
pages = "ix--x",
year = "1995",
bibdate = "Sat Nov 17 12:02:52 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Koko:1995:FP,
author = "Boma Koko",
title = "Floating Point",
journal = j-COMPUT-AIDED-ENG,
volume = "14",
number = "10",
pages = "132--??",
year = "1995",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Kubota:1995:DRE,
author = "K. Kubota",
title = "On distribution of rounding errors generated in
additions and subtractions of floating-point numbers",
journal = "Transactions of the Japan Society for Industrial and
Applied Mathematics",
volume = "5",
number = "1",
pages = "37--46",
month = "????",
year = "1995",
ISSN = "0917-2246",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Analyzing the behaviour of rounding errors generated
in additions and subtractions of floating-point numbers
and regarding them as random variables, we propose a
slightly strange model for their distribution. The
model gives distributions which approximate the
observed generated relative errors more precisely than
the uniform distribution which is usually adopted in
probabilistic analysis of rounding errors.",
acknowledgement = ack-nhfb,
affiliation = "Fac. of Sci. and Eng., Chuo University, Tokyo, Japan",
classification = "C1140 (Probability and statistics); C4110 (Error
analysis in numerical methods); C5230 (Digital
arithmetic methods)",
keywords = "Additions; Distribution; Floating-point numbers;
Probabilistic analysis; Random variables; Relative
errors; Rounding errors; Subtractions; Uniform
distribution",
language = "Japanese",
pubcountry = "Japan",
thesaurus = "Error analysis; Floating point arithmetic;
Probability; Random processes",
}
@InProceedings{Kwan:1995:CII,
author = "Hercule Kwan and Robert Leonard {Nelson, Jr.} and Earl
E. {Swartzlander, Jr.}",
title = "Cascaded Implementation of an Iterative
Inverse-Square-Root Algorithm, with Overflow
Lookahead",
crossref = "Knowles:1995:PSC",
pages = "115--122",
year = "1995",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Kwan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
summary = "We present an unconventional method of computing the
inverse of the square root. It implements the
equivalent of two iterations of a well-known
multiplicative method to obtain 24-bit mantissa
accuracy. We implement each ``iteration'' as a
\ldots{}",
}
@InProceedings{Lang:1995:VHR,
author = "Tom{\'a}s Lang and Paolo Montuschi",
title = "Very-High Radix Combined Division and Square Root with
Prescaling and Selection by Rounding",
crossref = "Knowles:1995:PSC",
pages = "124--131",
year = "1995",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Lang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
summary = "An algorithm for square root with prescaling is
developed and combined with a similar scheme for
division. An implementation is described, evaluated and
compared with other combined div/sqrt \ldots{}",
}
@InProceedings{Leeser:1995:VSR,
author = "M. Leeser and J. O'Leary",
booktitle = "Proceedings of the {IEEE} International Conference on
Computer Design: {VLSI} in Computers and Processors,
{ICCD '95}",
title = "Verification of a subtractive radix-$2$ square root
algorithm and implementation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "526--531",
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Many modern microprocessors implement floating point
square root hardware using subtractive algorithms. Such
processors include the HP PA7200, the MIPS R4400, and
the Intel Pentium. The Intel Pentium division bug
highlights the importance of \ldots{}",
}
@InProceedings{Lehmann:1995:SLE,
author = "N. Joachim Lehmann",
title = "{Schickard und Leibniz als Erfinder von
rechenmaschinen}. ({German}) [{Schickard} and
{Leibniz}, the inventors of calculators]",
crossref = "Seck:1995:GWS",
pages = "273--286",
year = "1995",
bibdate = "Sat Jul 27 12:46:37 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Liu:1995:SRV,
author = "S.-I. Liu",
title = "Square-rooting and vector summation circuits using
current conveyors",
journal = "IEE Proceedings on Circuits, Devices and Systems [see
also IEE Proceedings G- Circuits, Devices and
Systems]",
volume = "142",
number = "4",
pages = "223--226",
month = aug,
year = "1995",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
summary = "New analogue squaring, square-rooting and vector
summation circuits using current conveyors (CCIIs) are
presented. They consist of MOS transistors biased in
the triode region, a buffered unity-gain inverting
amplifier, resistors and CCIIs. A general \ldots{}",
}
@Article{Louie:1995:VPS,
author = "Marianne E. Louie and Milo{\v{s}} D. Ercegovac",
title = "A Variable-Precision Square Root Implementation for
Field Programmable Gate Arrays",
journal = j-J-SUPERCOMPUTING,
volume = "9",
number = "3",
pages = "315--336",
month = sep,
year = "1995",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/BF01212874",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Wed Jul 6 11:13:09 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3;
http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315;
http://www.wkap.nl/oasis.htm/95692",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, California University,
Los Angeles, CA, USA",
classification = "C5120 (Logic and switching circuits); C5230 (Digital
arithmetic methods)",
corpsource = "Department of Computer Science, California University,
Los Angeles, CA, USA",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
keywords = "digital arithmetic; field programmable gate arrays;
square root; square root implementation;
variable-precision; Xilinx XC4010",
treatment = "P Practical",
}
@TechReport{Lozier:1995:EBL,
author = "Daniel W. Lozier and P. R. Turner",
title = "Error-Bounding in Level-Index Computer Arithmetic",
type = "Internal Report",
number = "NISTIR-5724",
institution = "National Bureau of Standards",
address = "Gaithersburg, MD, USA",
year = "1995",
bibdate = "Tue Nov 05 15:20:28 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.nist.gov/publications/error-bounding-level-index-computer-arithmetic",
acknowledgement = ack-nhfb,
}
@Article{Lynch:1995:HRL,
author = "Thomas Lynch and Michael J. Schulte",
title = "A High Radix On-line Arithmetic for Credible and
Accurate Computing",
journal = j-J-UCS,
volume = "1",
number = "7",
pages = "439--453",
day = "28",
month = jul,
year = "1995",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
MRclass = "68M07",
MRnumber = "1 403 706",
bibdate = "Wed May 28 19:32:35 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/a_high_radix_online_arithmetic",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@InProceedings{Lynch:1995:KTF,
author = "Tom Lynch and Ahmed Ahmed and Mike Schulte and Tom
Callaway and Robert Tisdale",
title = "The {K5} Transcendental Functions",
crossref = "Knowles:1995:PSC",
pages = "163--171",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf;
http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Lynch.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@InProceedings{Lyu:1995:RBB,
author = "Chung Nan Lyu and David W. Matula",
title = "Redundant Binary {Booth} Recoding",
crossref = "Knowles:1995:PSC",
pages = "50--58",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Chung.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Mandelbaum:1995:DUL,
author = "D. M. Mandelbaum",
title = "Division using a logarithmic-exponential transform to
form a short reciprocal",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "11",
pages = "1326--1330",
month = nov,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.475129",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=475129",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Martel:1995:DSO,
author = "Charles Martel and Vojin Oklobdzija and R. Ravi and
Paul F. Stelling",
title = "Design Strategies for Optimal Multiplier Circuits",
crossref = "Knowles:1995:PSC",
pages = "42--49",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Martel.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@InProceedings{Matsubara:1995:NBS,
author = "Gensoh Matsubara and Nobuhiro Ide and Haruyuki Tago
and Seigo Suzuki and Nobuyuki Goto",
title = "30-ns 55-b Shared Radix $2$ Division and Square Root
Using a Self-Timed Circuit",
crossref = "Knowles:1995:PSC",
pages = "98--105",
year = "1995",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Matsubara.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
summary = "A shared radix 2 division and square root
implementation using a self-timed circuit is presented.
The same execution time for division and square root is
achieved by using an on-the-fly digit decoding and a
root multiple generation technique. Most \ldots{}",
}
@Article{Meissner:1995:EAD,
author = "Loren P. Meissner",
title = "From the {Editor}: Allocatable Dummy Argument Arrays;
How Should {Fortran Standards} Describe Arithmetic? Are
External Procedures Obsolete?; When are Local Variables
Initialized in {F77} and {F90}?",
journal = j-FORTRAN-FORUM,
volume = "14",
number = "3",
pages = "1--3",
month = sep,
year = "1995",
CODEN = "????",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Thu Feb 07 06:54:12 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "43",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@Article{Metafas:1995:FAC,
author = "D. E. Metafas and C. E. Goutis",
title = "A Floating-Point Advanced {CORDIC} Processor",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "10",
number = "1",
pages = "53--65",
month = jun,
year = "1995",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/BF02407026",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, a novel architecture of a
floating-point digital signal processor is presented.
It introduces a single hardware structure with a full
set of elementary arithmetic functions which includes
sin, cos, tan, arctanh, circular rotation and
vectoring, sinh, cosh, tanh, arctanh, hyperbolic
rotation and vectoring, square root, logarithm,
exponential as well as addition, multiplication and
division. The architecture of the processor is based on
the COordinate Rotation DIgital Computer (CORDIC) and
the Convergence Computing Method (CCM) algorithms for
computing arithmetic functions and it is fully parallel
and pipelined. Its advanced functionality is achieved
without significant increase in hardware, in comparison
to ordinary CORDIC processor, and makes it an ideal
processing element in high speed multiprocessor
applications, e.g. real time Digital Signal Processing
(DSP) and computer graphics.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Michelucci:1995:ARD,
author = "D. Michelucci",
title = "An $ \epsilon $ Arithmetic for Removing Degeneracies",
crossref = "Knowles:1995:PSC",
pages = "230--238",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Michelucci.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@TechReport{Miner:1995:DIF,
author = "Paul S. Miner",
title = "Defining the {IEEE-854} floating-point standard in
{PVS}",
number = "110167",
institution = "National Aeronautics and Space Administration, Langley
Research Center; National Technical Information
Service, distributor",
address = "Hampton, VA, USA",
pages = "????",
year = "1995",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "NASA technical memorandum",
acknowledgement = ack-nhfb,
alttitle = "Defining the IEEE 854 floating point standard in PVS
Defining the IEEE eight hundred fifty-four floating
point standard in PVS",
govtdocnumber = "NAS 1.15:110167 0830-D (MF)",
keywords = "Floating point arithmetic.; Formalism.; Prototypes.;
Proving.",
remark = "Distributed to depository libraries in microfiche.
Shipping list no.: 96-0033-M. Microfiche. [Washington,
D.C.: National Aeronautics and Space Administration,
1995] 1 microfiche.",
}
@TechReport{Moler:1995:CCT,
author = "Cleve B. Moler",
title = "{Cleve}'s Corner: a Tale of Two Numbers: {With} the
{Pentium}, there is a very small chance of making a
very large error",
type = "Technical note",
institution = inst-MATHWORKS,
address = inst-MATHWORKS:adr,
month = "Winter",
year = "1995",
bibdate = "Thu Oct 24 07:16:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mathworks.com/company/newsletter/pdf/win95cleve.pdf",
acknowledgement = ack-nhfb,
keywords = "Matlab; Pentium FDIV divide flaw",
}
@Article{Moler:1995:TTN,
author = "Cleve B. Moler",
title = "A tale of two numbers",
journal = j-SIAM-NEWS,
volume = "28",
number = "1",
pages = "16--16",
day = "1",
month = jan,
year = "1995",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Wed Nov 13 07:16:43 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Discusses the Intel Pentium chip divide flaw.",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Article{Montuschi:1995:RRI,
author = "P. Montuschi and L. Ciminiera",
title = "A remark on {``Reducing iteration time when result
digit is zero for radix-$2$ SRT division and square
root with redundant remainders''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "1",
pages = "144--146",
month = jan,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.368000",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See \cite{Montuschi:1993:RIT}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=368000",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "In a previous paper by P. Montuschi and L. Ciminiera
(ibid., vol. 42, no.2 p239-246, Feb 1993), an
architecture for shared radix 2 division and square
root has been presented whose main characteristic is
the ability to avoid any addition/subtraction,
\ldots{}",
}
@InProceedings{Muller:1995:SLN,
author = "Jean-Michel Muller and Arnaud Tisserand and Alexandre
Scherbyna",
title = "Semi-Logarithmic Number Systems",
crossref = "Knowles:1995:PSC",
pages = "201--207",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Muller.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Nielsen:1995:MFD,
author = "Asger Munk Nielsen and Peter Kornerup",
title = "{MSB}-First Digit Serial Arithmetic",
journal = j-J-UCS,
volume = "1",
number = "7",
pages = "527--547",
day = "28",
month = jul,
year = "1995",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
MRclass = "68Mxx",
MRnumber = "1 403 711",
bibdate = "Wed May 28 19:32:35 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/jucs_1_7/msb_first_digit_serial",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@PhdThesis{Nowka:1995:HPC,
author = "Kevin Nowka",
title = "High Performance {CMOS} {VLSI} System Design Using
Wave Pipelining",
type = "Thesis ({Ph.D.})",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "????",
month = sep,
year = "1995",
bibdate = "Mon Dec 24 11:03:54 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Oberman:1995:DRC,
author = "S. F. Oberman and M. J. Flynn",
title = "On division and reciprocal caches",
type = "Technical Report",
number = "CSL-TR-95-666",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = apr,
year = "1995",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@Article{OGara:1995:SET,
author = "Linda O'Gara and Jeanne Adams and Walt Brainerd and
Vic Kelson and Craig Dedo and Keith Bierman and Jerry
Wagener and Richard Maine and Leonard J. Moss and James
H. Billen and Robert Corbett and Dick Hendrickson and
Jamie Shiers and David Levine and David L. Epstein and
John Reid and Lawrie Schonfelder and Kurt W. Hirchert
and Jens Helmers and William Behrman and A. C. Marshall
and William B. Clodius",
title = "Some Email threads: Is {Fortran 90} Succeeding?;
{Fortran} Market Acceptance; {Fortran--C}
Interoperability; {Fortran} Preprocessors or
Conditional Compilation: Is Standardization Needed?;
Floating Point Subsets of Enable; Pointers to
Procedures, or Procedure Names as Variables; Standard
Linear Algebra and Advanced Math Functions Modules; Re:
Allocatable arrays in structures; Restricted Module
Visibility",
journal = j-FORTRAN-FORUM,
volume = "14",
number = "1",
pages = "11--28",
month = mar,
year = "1995",
CODEN = "????",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Thu Feb 07 06:54:12 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "41",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@InProceedings{Ohi:1995:RCN,
author = "Y. Ohi and T. Aoki and T. Higuchi",
title = "Redundant Complex Number Systems",
crossref = "IEEE:1995:ISM",
pages = "14--??",
year = "1995",
DOI = "https://doi.org/10.1109/ISMVL.1995.513504",
bibdate = "Sat Aug 22 08:43:14 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents redundant complex number systems
(RCNSs)-new complex number representations for
high-speed arithmetic circuits. RCNS is a positional
number system that has a complex radix $ r_j $ and a
digit set $ \{ - \alpha, \ldots {}, 0, \ldots {},
\alpha \} $, where $ r \geq 2 $ and $ [(r^2 - 1) / 2] <
\alpha \leq r^2 - 1 $. The use of complex radix $ r_j $
allows additions and multiplications of complex numbers
to be done without treating real part and imaginary
part separately. Also the redundancy in the number
representation enables carry-free addition as well as
binary-tree multiple-operand addition. This paper
discusses the basic arithmetic algorithms of RCNSs and
their implementations.",
acknowledgement = ack-nhfb,
}
@Article{Ohkubo:1995:CBM,
author = "N. Ohkubo and M. Suzuki and T. Shinbo and T. Yamanaka
and A. Shimizu and K. Sasaki and Y. Nakagome",
title = "A 4.4ns {CMOS} $ 54 \times 54 $-b multiplier using
pass-transistor multiplexor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "SC-30",
number = "3",
pages = "251--257",
month = mar,
year = "1995",
CODEN = "IJSCBC",
DOI = "https://doi.org/10.1109/4.364439",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Mon Dec 24 10:23:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
xxpages = "294--305",
}
@Article{OLeary:1995:NRI,
author = "J. O'Leary and M. Leeser and J. Hickey and M.
Aagaard",
title = "Non-Restoring Integer Square Root: a Case Study in
Design by Principled Optimization",
journal = j-LECT-NOTES-COMP-SCI,
volume = "901",
pages = "52--??",
year = "1995",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat May 11 13:45:32 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Orup:1995:SQD,
author = "Holger Orup",
title = "Simplifying Quotient Determination in High-Radix
Modular Multiplication",
crossref = "Knowles:1995:PSC",
pages = "193--200",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Orup.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@InProceedings{Owens:1995:RNC,
author = "Robert M. Owens and Raminder S. Bajwa and Mary Jane
Irwin",
title = "Reducing the Number of Counters Needed for Integer
Multiplication",
crossref = "Knowles:1995:PSC",
pages = "38--41",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Owens.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Parker:1995:MUP,
author = "M. G. Parker and M. Benaissa",
title = "{$ \mathrm {GF}(p^m) $} multiplication using
polynomial residue number systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "42",
number = "11",
pages = "718--721",
month = nov,
year = "1995",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.475249",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=10018",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "$\mathrm{GF}(p^m)$ multiplication is computed in two
stages. First, the polynomial product is computed
modulus: a highly factorizable degree S polynomial,
$M(x)$, with $S \geq 2m - 1$. This enables the product
to be computed using a polynomial residue number
system. \ldots{}",
}
@Article{Popova:1995:FCI,
author = "E. Popova",
title = "On a Formally Correct Implementation of {IEEE}
Computer Arithmetic",
journal = j-J-UCS,
volume = "1",
number = "7",
pages = "560--??",
day = "28",
month = jul,
year = "1995",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Wed May 28 19:32:35 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.iicm.edu/jucs_1_7/on_a_formally_correct",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@Article{Posch:1995:MRRa,
author = "Karl C. Posch and Reinhard Posch",
title = "Modulo Reduction in Residue Number Systems",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "6",
number = "5",
pages = "449--454",
month = may,
year = "1995",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/71.382314",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8666",
acknowledgement = ack-nhfb,
classification = "721.1; 722.4; 723.1; 723.2; 921.6; C4240C
(Computational complexity); C4240P (Parallel
programming and algorithm theory); C5230 (Digital
arithmetic methods); C6110P (Parallel programming)",
corpsource = "Inst. for Appl. Inf. Process., Graz University of
Technol., Austria",
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
journalabr = "IEEE Trans Parallel Distrib Syst",
keywords = "Approximation theory; Carry free operations;
complexity; computational complexity; Computational
complexity; Computer arithmetic; Computer hardware;
Cryptography; cryptography; Digital arithmetic;
Distributed computer systems; distributed systems;
extremely long; integer arithmetic; Iterative methods;
Long integer arithmetic; Modulo reduction; modulo
reduction; number systems; Number theory; Parallel
algorithms; parallel algorithms; parallel
implementations; Parallel processing systems; residue
arithmetic; Residue number systems; residue number
systems",
summary = "Residue number systems provide a good means for
extremely long integer arithmetic. Their carry-free
operations make parallel implementations feasible. Some
applications involving very long integers, such as
public key encryption, rely heavily on \ldots{}",
treatment = "T Theoretical or Mathematical",
}
@Article{Posch:1995:MRRb,
author = "K. C. Posch and R. Posch",
title = "Modulo reduction in residue number systems",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "6",
number = "5",
pages = "449--454",
month = may,
year = "1995",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/71.382314",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8666",
acknowledgement = ack-nhfb,
affiliation = "Graz Univ of Technology",
affiliationaddress = "Graz, Austria",
classification = "721.1; 722.4; 723.1; 723.2; 921.6; C4240C
(Computational complexity); C4240P (Parallel
programming and algorithm theory); C5230 (Digital
arithmetic methods); C6110P (Parallel programming)",
corpsource = "Inst. for Appl. Inf. Process., Graz University of
Technol., Austria",
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
journalabr = "IEEE Trans Parallel Distrib Syst",
keywords = "Approximation theory; Carry free operations;
complexity; computational complexity; Computational
complexity; Computer arithmetic; Computer hardware;
Cryptography; cryptography; Digital arithmetic;
Distributed computer systems; distributed systems;
extremely long; integer arithmetic; Iterative methods;
Long integer arithmetic; Modulo reduction; modulo
reduction; number systems; Number theory; Parallel
algorithms; parallel algorithms; parallel
implementations; Parallel processing systems; residue;
Residue number systems; residue number systems",
summary = "Residue number systems provide a good means for
extremely long integer arithmetic. Their carry-free
operations make parallel implementations feasible. Some
applications involving very long integers, such as
public key encryption, rely heavily on \ldots{}",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Prabhu:1995:MRD,
author = "J. A. Prabhu and G. B. Zyner",
title = "{167 MHz} Radix-$8$ Divide and Square Root Using
Overlapped Radix-$2$ Stages",
crossref = "Knowles:1995:PSC",
pages = "155--162",
year = "1995",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
summary = "UltraSPARC's IEEE-754 compliant floating point divide
and square root implementation is presented. Three
overlapping stages of SRT radix-$2$ quotient selection
logic enable an effective radix-$8$ calculation at 167
MHz while only a single radix-$2$ \ldots{}",
}
@InProceedings{Prabhu:1995:MRF,
author = "J. Arjun Prabhu and Gregory B. Zyner",
title = "167 {MHz} Radix-8 floating point divide and square
root using overlapped radix-2 stages",
crossref = "Knowles:1995:PSC",
month = jul,
year = "1995",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Prabhu.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-12; UltraSPARC",
}
@Article{Pratt:1995:APB,
author = "V. Pratt",
title = "Anatomy of the {Pentium} Bug",
journal = j-LECT-NOTES-COMP-SCI,
volume = "915",
pages = "97--107",
year = "1995",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat May 11 13:45:32 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://boole.stanford.edu/pub/FDIV/anapent.ps.gz",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "Intel Pentium divide flaw; Thomas R. Nicely",
}
@Article{Price:1995:PFF,
author = "Dick Price",
title = "{Pentium FDIV} Flaw --- Lessons Learned",
journal = j-IEEE-MICRO,
volume = "15",
number = "2",
pages = "88, 86--87",
month = mar # "\slash " # apr,
year = "1995",
CODEN = "IEMIDZ",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
URL = "http://ieeexplore.ieee.org/iel1/40/8521/00372360.pdf",
abstract = "As the tidal wave of publicity surrounding the Pentium
floating-point divide bug subsides, questions about the
controversy's lasting impact linger. Intel's
competitors may rejoice at the industry giant's
technical and public relations missteps, but they too
must worry about damage done to customer confidence,
shuddering at the prospect of taking a similar public
pratfall. And consumers, justified or not, have new
reliability worries with every new product release.
Intel recently adopted a `no questions asked'
replacement policy for defective Pentium chips,
reversing its earlier stance. As part of a new
commitment to openness, Intel has posted a variety of
documents on its World Wide Web home page
(http://www.intel.com) describing the flaw, analysing
its severity, and providing replacement procedures.
Industry observers have pointed to the benefits that
will come from Intel's woes: more openness by
manufacturers, better understanding among consumers of
the problems facing chip makers, and greater emphasis
on testing. For chip makers and computer users alike,
it remains then to calculate the lessons learned.",
acknowledgement = ack-nhfb,
classcodes = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5470 (Performance evaluation
and testing); C5230 (Digital arithmetic methods)",
classification = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods); C5470 (Performance evaluation and testing)",
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "Chip makers; chip makers; circuit testing; computer
testing; Defective Pentium chips; defective Pentium
chips; floating point arithmetic; integrated; Intel;
Intel Pentium divide flaw; Pentium floating-point
divide bug; reliability; Reliability; replacement
procedures; Replacement procedures; Thomas R. Nicely",
thesaurus = "Computer testing; Floating point arithmetic;
Integrated circuit testing",
treatment = "G General Review",
}
@Article{Rogers:1995:UMP,
author = "John Rogers",
title = "Using the Multiple Precision Library",
journal = j-DDJ,
volume = "20",
number = "1",
pages = "36, 38, 40, 42, 86, 88--89",
month = jan,
year = "1995",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
UnCover database",
abstract = "Although most implementations of C boast 32-bit
integer arithmetic, many applications are beginning to
require higher precision. However, even the IEEE
double-precision floating-point format only gives 15
digits of precision. What is needed is a way to deal
with multiple-precision integers, independent of the
machine's word size. The multiple precision (MP)
integer library available with UNIX V7, UNIX SVR4,
4.3BSD, and other versions of UNIX provide infinite
precision signed integer operations for C programs. I
have also ported the GMP library to Windows NT. In this
article, I describe how to use the scantily documented
MP routines, along with providing sample code,
portability information, some MP helpers, and a few
other hints.",
acknowledgement = ack-nhfb,
classification = "C6110B (Software engineering techniques); C6140D
(High level languages)",
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "4.3BSD; C; C programs; GMP library; IEEE
double-precision floating-point format; Infinite
precision signed integer operations; Integer
arithmetic; MP routines; Multiple precision library;
Multiple-precision integers; Portability; UNIX; UNIX
SVR4; UNIX V7; Windows NT; Word size",
thesaurus = "C language; Software libraries; Software portability;
Subroutines; Unix",
}
@Article{Rubenking:1995:UNI,
author = "Neil J. Rubenking",
title = "User-to-User --- The natural imperfection of
floating-point calculations; customizing the {Windows}
95 boot process; providing a way for the user to exit",
journal = j-PC-MAGAZINE,
volume = "14",
number = "20",
pages = "293--??",
year = "1995",
CODEN = "PCMGEP",
ISSN = "0888-8507 (print), 1078-8085 (electronic)",
ISSN-L = "0888-8507",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "PC Magazine",
}
@Article{Sammut:1995:AUD,
author = "K. M. Sammut and S. R. Jones",
title = "Arithmetic unit design for neural accelerators: cost
performance issues",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "10",
pages = "1256--1260",
month = oct,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.467702",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=467702",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Sangwine:1995:CIT,
author = "S. J. Sangwine and D. A. Riach",
booktitle = "{Fifth International Conference on Image Processing
and its Applications: 4-6 July 1995: venue, Heriot-Watt
University, Edinburgh, UK}",
title = "Colour image thresholding at pixel rate using rational
arithmetic hardware",
publisher = pub-IEE,
address = pub-IEE:adr,
pages = "828--832",
year = "1995",
ISBN = "0-85296-642-3",
ISBN-13 = "978-0-85296-642-6",
LCCN = "A1632 .I553 1995",
bibdate = "Fri Nov 30 07:37:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Thresholding of images is a common precursor to many
object recognition or image analysis methods. Colours
images contain more information than monochrome images
of the same spatial resolution and in many applications
of colour image processing there will be a need for
thresholding. The paper presents a hardware
implementation and development of a technique published
by Pritchard et al. (1994). A brief review is given of
the rational arithmetic representation; the authors
then discuss the definition of colour purity, present a
description of the thresholding algorithm as
implemented in hardware and finally, give a block-level
description of the hardware implementation and some
results obtained",
acknowledgement = ack-nhfb,
}
@Article{Sanyal:1995:CAS,
author = "S. Sanyal",
title = "Computer Arithmetic Systems",
journal = j-COMP-J,
volume = "38",
number = "1",
pages = "79--79",
month = "????",
year = "1995",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/38.1.79",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:43 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/38/1.toc;
https://www.math.utah.edu/pub/tex/bib/compj1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/38/1/79.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@InProceedings{Sarma:1995:FBR,
author = "Debjit Das Sarma and David W. Matula",
title = "Faithful Bipartite {ROM} Reciprocal Tables",
crossref = "Knowles:1995:PSC",
pages = "17--29",
month = jul,
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Sarma.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-12",
xxnote = "Check: page 29 is missing from PDF file; is it
blank?",
xxpages = "17--28??",
}
@InProceedings{Schulte:1995:DAV,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "Design and applications for variable-precision,
interval arithmetic coprocessors",
crossref = "Kearfott:1996:AICa",
pages = "166--172",
year = "1995",
bibdate = "Tue Apr 07 16:25:50 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb # " and " # ack-jf,
}
@InProceedings{Schulte:1995:HDA,
author = "Michael J. Schulte and Eearl E. {Swartzlander, Jr.}",
title = "Hardware Design and Arithmetic Algorithms for a
Variable-Precision, Interval Arithmetic Coprocessor",
crossref = "Knowles:1995:PSC",
pages = "222--229",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://mesa.ece.wisc.edu/publications/cp_1995-03.pdf;
http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Schulte.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@InProceedings{Schulte:1995:PSI,
author = "Michael J. Schulte and Eearl E. {Swartzlander, Jr.}",
title = "A Processor for Staggered Interval Arithmetic",
crossref = "Cappello:1995:ICA",
pages = "104--112",
year = "1995",
bibdate = "Mon Oct 20 07:16:07 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1995-02.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schwarz:1995:RQC,
author = "E. M. Schwarz",
title = "Rounding for quadratically converging algorithms for
division and square root",
crossref = "Singh:1995:CRT",
volume = "1",
pages = "600--603",
month = oct,
year = "1995",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
summary = "Exactly rounded results are necessary for many
architectures such as IEEE 754 standard. For division
and square root, rounding is easy to perform if a
remainder is available. But for quadratically
converging algorithms, the remainder is not \ldots{}",
}
@InProceedings{Shirazi:1995:QAF,
author = "N. Shirazi and A. Walters and P. Athanas",
title = "Quantitative analysis of floating point arithmetic on
{FPGA} based custom computing machines",
crossref = "Athanas:1995:PIS",
pages = "155--162",
year = "1995",
DOI = "https://doi.org/10.1109/FPGA.1995.477421",
bibdate = "Sat Oct 9 13:02:18 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Many algorithms rely on floating point arithmetic for
the dynamic range of representations and require
millions of calculations per second. Such
computationally intensive algorithms are candidates for
acceleration using custom computing machines (CCMs)
being tailored for the application. Unfortunately,
floating point operators require excessive area (or
time) for conventional implementations. Instead, custom
formats, derived for individual applications, are
feasible on CCMs, and can be implemented on a fraction
of a single FPGA. Using higher-level languages, like
VHDL, facilitates the development of custom operators
without significantly impacting operator performance or
area. Properties, including area consumption and speed
of working arithmetic operator units used in real-time
applications, are discussed",
acknowledgement = ack-nhfb,
}
@TechReport{Sigvartsen:1995:TBF,
author = "Roy L. Sigvartsen and Roar Skogstr{\o}m",
title = "A test bench for floating point arithmetic",
type = "{FFI} rapport",
number = "95/04099",
institution = "Forsvarets forskningsinstitut",
address = "Kjeller, Norway",
pages = "54",
year = "1995",
bibdate = "Thu May 09 08:08:19 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@Book{Sites:1995:AAA,
author = "Richard L. Sites and Richard L. Witek",
title = "{Alpha AXP} Architecture Reference Manual",
publisher = pub-DP,
address = pub-DP:adr,
edition = "Second",
pages = "various",
year = "1995",
ISBN = "1-55558-145-5",
ISBN-13 = "978-1-55558-145-9",
LCCN = "QA76.9.A73A46 1995",
bibdate = "Thu Aug 07 13:41:17 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
price = "US\$52.95",
acknowledgement = ack-nhfb,
tableofcontents = "Foreword \\
Preface to the First Edition \\
Preface to the Second Edition \\
Part 1: Common Architecture (I) \\
1. Introduction (I) \\
1.1 The Alpha AXP Approach to RISC Architecture \\
1.2 Data Format Overview \\
1.3 Instruction Format Overview \\
1.4 Instruction Overview \\
1.5 Instruction Set Characteristics \\
1.6 Terminology and Conventions \\
2. Basic Architecture (I) \\
2.1 Addressing \\
2.2 Data Types \\
2.3 Big-endian Addressing Support \\
3. Instruction Formats (I) \\
3.1 Alpha AXP Registers \\
3.2 Notation \\
3.3 Instruction Formats \\
4. Instruction Descriptions (I) \\
4.1 Instruction Set Overview \\
4.2 Memory Integer Load/Store Instructions \\
4.3 Control Instructions \\
4.4 Integer Arithmetic Instructions \\
4.5 Logical and Shift Instructions \\
4.6 Byte-Manipulation Instructions \\
4.7 Floating-Point Instructions \\
4.8 Memory Format Floating-Point Instructions \\
4.9 Branch Format Floating-Point Instructions \\
4.10 Floating-Point Operate Format Instructions \\
4.11 Miscellaneous Instructions \\
4.12 VAX Compatibility Instructions \\
5. System Architecture and Programming Implications \\
5.1 Introduction \\
5.2 Physical Address Space Characteristics \\
5.3 Translation Buffers and Virtual Caches \\
5.4 Caches and Write Buffers \\
5.5 Data Sharing \\
5.6 Read/Write Ordering \\
5.7 Arithmetic Traps \\
6. Common PALcode Architecture (I) \\
6.1 PALcode \\
6.2 PALcode Instructions and Functions \\
6.3 PALcode Environment \\
6.4 Special Functions Required for PALcode \\
6.5 PALcode Effects on System Code \\
6.6 PALcode Replacement \\
6.7 Required PALcode Instructions \\
7. Console Subsystem Overview (I) \\
8. Input/Output Overview (I) \\
Specific Operating System PALcode Architecture (II) \\
Part 2: OpenVMS AXP Software (II-A) \\
1. Introduction to OpenVMS AXP (II-A) \\
1.1 Register Usage \\
2. OpenVMS AXP PALcode Instruction Descriptions (II-A)
\\
2.1 Unprivileged General OpenVMS AXP PALcode
Instructions \\
2.2 OpenVMS AXP Queue Data Types \\
2.3 Unprivileged OpenVMS AXP Queue PALcode Instructions
\\
2.4 Unprivileged VAX Compatibility PALcode Instructions
\\
2.5 Unprivileged PALcode Thread Instructions \\
2.6 Privileged PALcode Instructions \\
3. OpenVMS AXP Memory Management (II-A) \\
3.1 Introduction \\
3.2 Virtual Address Space \\
3.3 Physical Address Space \\
3.4 Memory Management Control \\
3.5 Page Table Entries \\
3.6 Memory Protection \\
3.7 Address Translation \\
3.8 Translation Buffer \\
3.9 Address Space Numbers \\
3.10 Memory Management Faults \\
4. OpenVMS AXP Process Structure (II-A) \\
4.1 Process Definition \\
4.2 Hardware Privileged Process Context \\
4.3 Asynchronous System Traps (AST) \\
4.4 Process Context Switching \\
5. OpenVMS AXP Internal Processor Registers (II-A) \\
5.1 Internal Processor Registers \\
5.2 Stack Pointer Internal Processor Registers \\
5.3 IPR Summary",
}
@Article{Siu:1995:TMP,
author = "Kai-Yeung Y. Siu and V. Roychowdhury and T. Kailath",
title = "Toward Massively Parallel Design of Multipliers",
journal = j-J-PAR-DIST-COMP,
volume = "24",
number = "1",
pages = "86--93",
month = jan,
year = "1995",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1995.1008",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:18:56 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1008/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1008/production/pdf",
acknowledgement = ack-nhfb,
classification = "C4210 (Formal logic); C4240C (Computational
complexity); C5110 (Logic elements); C5120 (Logic and
switching circuits); C5220P (Parallel architecture);
C5230 (Digital arithmetic methods)",
corpsource = "Department of Electr. and Comput. Eng., California
University, Irvine, CA, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "AND-OR circuits; arithmetic computation; asymptotic
time complexity; circuits; computation delays;
computational complexity; digital arithmetic; fan-in
threshold circuits; gates; hardware; logic; massively
parallel design; massively parallel high-speed
multipliers; multiplication; multipliers; multiplying;
parallel processing; parity; polynomial; speed;
symmetric functions; threshold; threshold elements;
unbounded fan-in/fan-out; VLSI technology",
treatment = "T Theoretical or Mathematical",
}
@Article{Sleijpen:1995:MCP,
author = "G{\`e}rard L. G. Sleijpen and Henk A. van der Vorst",
title = "Maintaining convergence properties of {BiCGstab}
methods in finite precision arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "10",
number = "3--4",
pages = "203--223",
month = oct,
year = "1995",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10 (65Y20)",
MRnumber = "MR1355732 (96g:65037)",
bibdate = "Sat Dec 31 06:28:14 2005",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); C4130 (Interpolation and
function approximation); C4140 (Linear algebra); C4240C
(Computational complexity)",
corpsource = "Math. Inst., Utrecht University, Netherlands",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Bi-CG coefficient accuracy; Bi-CG iteration
coefficients; Bi-CG process; BiCGstab methods;
computational complexity; conjugate gradient methods;
convergence of numerical methods; convergence property
maintenance; convergence speed; finite precision
arithmetic; hybrid methods; matrix algebra; rounding
errors; roundoff errors",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{Smith:1995:CFA,
author = "Roger Alan Smith",
title = "A Continued-Fraction Analysis of Trigonometric
Argument Reduction",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "11",
pages = "1348--1351",
month = nov,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.475133",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Dec 08 10:21:28 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The calculation of a trigonometric function of a large
argument x is effectively carried out by finding the
integer $N$ and $ 0 \leq \alpha < 1 $ such that $ x =
(N + \alpha) \pi / 4 $. This reduction modulo $ \pi / 4
$ makes it possible to calculate a trigonometric
function of a reduced argument, either $ \alpha \pi / 4
$ or $ (1 - \alpha) \pi / 4 $, which lies in the
interval $ (0, \pi / 4) $. Payne and Hanek [1]
described an efficient algorithm for computing $ \alpha
$ to a predetermined level of accuracy. They noted that
if $x$ differs only slightly from an integral multiple
$ \pi / 2 $, the reduction must be carried out quite
accurately to avoid loss of significance in the reduced
argument. We present a simple method using continued
fractions for determining, for all numbers $x$ for
which the greatest number of insignificant leading bits
occur. Applications are made IEEE single-precision and
double-precision formats and two extended- precision
formats.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "argument reduction; computer arithmetic; continued
fractions; nonlinear optimization; Payne/Hanek radian
reduction; range reduction; trigonometric functions",
}
@Article{Smith:1995:FTC,
author = "J. C. Smith and F. J. Taylor",
title = "A fault-tolerant {CEQRNS} processing element for
linear systolic array {DSP} applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "9",
pages = "1121--1130",
month = sep,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.464390",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=464390",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Soderquist:1995:APC,
author = "Peter Soderquist and Miriam Leeser",
title = "An Area\slash Performance Comparison of Subtractive
and Multiplicative Divide\slash Square Root
Implementations",
crossref = "Knowles:1995:PSC",
pages = "132--139",
month = jul,
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf",
acknowledgement = ack-sfo # " and " # ack-nhfb,
keywords = "ARITH-12",
}
@PhdThesis{Song:1995:RCT,
author = "Gi-Yong Song",
title = "Robust checksum test in algorithm-based fault
tolerance on {2-D} processor arrays",
type = "Thesis ({Ph.D.})",
school = "University of Southwestern Louisiana",
address = "Lafayette, LA, USA",
pages = "95",
year = "1995",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "error-correcting codes (information theory);
fault-tolerant computing; floating-point arithmetic;
floating-point testing",
}
@Article{Srinivas:1995:FRD,
author = "H. R. Srinivas and K. K. Parhi",
title = "A fast radix-4 division algorithm and its
architecture",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "6",
pages = "826--831",
month = jun,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.391179",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=391179",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Tatsaki:1995:ICB,
author = "A. Tatsaki and T. Stouraitis and C. Goutis",
title = "Image coder based on residue number system for
progressive transmission",
journal = j-ELECT-LETTERS,
volume = "31",
number = "6",
pages = "442--443",
month = mar,
year = "1995",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1109/12.403714",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8573",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A computationally efficient algorithm for image
compression and progressive transmission is presented.
A prime-factor discrete cosine transform (DCT) is
applied, where the coefficients are computed in three
groups and are residue represented by a \ldots{}",
}
@Article{Thimbleby:1995:NCW,
author = "Harold Thimbleby",
title = "A New Calculator and Why it is Necessary",
journal = j-COMP-J,
volume = "38",
number = "6",
pages = "418--433",
month = "????",
year = "1995",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/38.6.418",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:48:45 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/38/6.toc;
http://www3.oup.co.uk/computer_journal/Volume_38/Issue_06/Vol38_06.index.html;
https://www.math.utah.edu/pub/tex/bib/compj1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/38/6/418.full.pdf+html;
http://www3.oup.co.uk/computer_journal/Volume_38/Issue_06/Vol38_06.body.html#AbstractThimbleby",
acknowledgement = ack-nhfb,
classcodes = "C5430 (Microcomputers); C6180 (User interfaces)",
corpsource = "Department of Computer Science, Middlesex University,
London, UK",
email-1 = "[email protected]",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "conventional calculators; declarative design;
declarative system; design issues; electronic
calculators; interactive system; user interfaces",
treatment = "P Practical",
}
@Article{Thomas:1995:IFC,
author = "Jim Thomas and Jerome T. Coonen",
title = "An Introduction to Floating-Point {C} Extensions",
journal = j-CCCUJ,
volume = "13",
number = "1",
pages = "49--??",
month = jan,
year = "1995",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Fri Aug 30 16:52:23 MDT 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@InProceedings{Tsuji:1995:ASF,
author = "K. Tsuji",
title = "An Algorithm for Sum of Floating-Point Numbers without
Round-Off Error",
crossref = "Bainov:1995:PTI",
pages = "181--190",
year = "1995",
bibdate = "Sat Jun 02 08:14:13 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@TechReport{Turner:1995:PSI,
author = "P. R. Turner Daniel W. Lozier",
title = "Parallel and Serial Implementations of {SLI}
Arithmetic",
type = "Internal report",
number = "NISTIT-5660",
institution = "National Institute of Standards and Technology",
address = "Gaithersburg, MD, USA",
day = "1",
month = jun,
year = "1995",
bibdate = "Tue Nov 05 15:29:02 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Ueda:1995:DMA,
author = "T. Ueda",
title = "Decimal Multiplying Assembly and Multiply Module",
howpublished = "U.S. Patent number 5,379,245.",
month = jan,
year = "1995",
bibdate = "Fri Jun 24 20:43:45 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{VanDrunen:1995:ARA,
author = "R. VanDrunen and L. Spaanenburg and P. Lucassen and J.
A. G. Nijhuis",
title = "Arithmetic for Relative Accuracy",
crossref = "Knowles:1995:PSC",
pages = "208--209, 239--250",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_vanDrunen.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Vinnakota:1995:IMS,
author = "B. Vinnakota",
title = "Implementing multiplication with split read-only
memory",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "11",
pages = "1352--1356",
month = nov,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.475134",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=475134",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wang:1995:NDT,
author = "Zhongde Wang and G. A. Jullien and W. C. Miller",
title = "A new design technique for column compression
multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "8",
pages = "962--970",
month = aug,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.403712",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:01:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403712",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wei:1995:CNM,
author = "Belle W. Y. Wei and He Du and Honglu Chen",
title = "A Complex-Number Multiplier Using Radix-$4$ Digits",
crossref = "Knowles:1995:PSC",
pages = "84--90",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Wei.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Article{Williams:1995:SBA,
author = "T. Williams and N. Patkar and G. Shen",
title = "{SPARC64}: a 64-b 64-active-instruction
out-of-order-execution {MCM} processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "30",
number = "11",
pages = "1215--1226",
month = nov,
year = "1995",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@Article{Wong:1995:FEE,
author = "W. F. Wong and E. Goto",
title = "Fast evaluation of the elementary functions in single
precision",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "3",
pages = "453--457",
month = mar,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.372037",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Dec 14 11:25:18 MST 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we introduce a new method for the fast
evaluation of the elementary functions in single
precision based on the evaluation of truncated Taylor
series using a difference method. We assume the
availability of large and fast (at least for read
purposes) memory. We call this method the ATA
(Add-Table lookup-Add) method. As the name implies, the
hardware required for the method are adders (both two/
and multi/operand adders) and fast tables. For IEEE
single precision numbers our initial estimates indicate
that we can calculate the basic elementary functions,
namely reciprocal, square root, logarithm, exponential,
trigonometric and inverse trigonometric functions,
within the latency of two to four floating point
multiplies.",
acknowledgement = ack-nhfb,
affiliation = "Department of Inf. Syst. and Computer Science, Nat.
University of Singapore, Singapore",
ajournal = "IEEE Trans. Comput.",
classification = "C4110 (Error analysis in numerical methods); C5230
(Digital arithmetic methods)",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Difference method; Elementary functions; Fast
evaluation; Floating point multiplies; Inverse
trigonometric functions; Logarithm functions;
Reciprocal; Single precision; Square root; Truncated
Taylor series",
thesaurus = "Error analysis; Floating point arithmetic",
}
@Article{Wu:1995:SRM,
author = "Youfeng Wu",
title = "Strength Reduction of Multiplications by Integer
Constants",
journal = j-SIGPLAN,
volume = "30",
number = "2",
pages = "42--48",
month = feb,
year = "1995",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:17:00 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Ypma:1995:HDN,
author = "Tjalling J. Ypma",
title = "Historical Development of the {Newton--Raphson}
Method",
journal = j-SIAM-REVIEW,
volume = "37",
number = "4",
pages = "531--551",
month = dec,
year = "1995",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1037125",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "01A05 (65-03)",
MRnumber = "97b:01003",
MRreviewer = "M. Z. Nashed",
bibdate = "Sat Mar 29 09:55:35 MDT 2014",
bibsource = "Compendex database;
http://epubs.siam.org/toc/siread/37/4;
http://www.siam.org/journals/sirev/sirev374.htm;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/23425.htm;
http://link.aip.org/link/?SIR/37/531/1",
abstract = "This expository paper traces the development of the
Newton--Raphson method for solving nonlinear algebraic
equations through the extant notes, letters, and
publications of Isaac Newton, Joseph Raphson, and
Thomas Simpson. It is shown how Newton's formulation
differed from the iterative process of Raphson, and
that Simpson was the first to give a general
formulation, in terms of fluxional calculus, applicable
to nonpolynomial equations. Simpson's extension of the
method to systems of equations is exhibited.",
acknowledgement = ack-nhfb,
affiliation = "Western Washington Univ",
affiliationaddress = "Bellingham, WA, USA",
classification = "921.1; 921.2; 921.6",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "Algebra; Algorithms; Approximation theory;
Differentiation (calculus); Finite difference method;
Fluxional calculus; Isaac Newton; Iterative methods;
Joseph Raphson; Linearization; Newton--Raphson method;
Nonlinear algebraic equations; Nonlinear equations;
Nonpolynomial equation; Polynomials; Secant method;
Thomas Simpson",
onlinedate = "December 1995",
}
@InProceedings{Yu:1995:MRF,
author = "Robert K. Yu and Gregory B. Zyner",
title = "{167 MHz} Radix-$4$ Floating Point Multiplier",
crossref = "Knowles:1995:PSC",
pages = "149--154",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Yu.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12; UltraSPARC",
}
@Article{Zaytoun:1995:SFR,
author = "M. M. Zaytoun and T. J. Owens",
title = "State feedback robust to rounding errors",
journal = j-ELECT-LETTERS,
volume = "31",
number = "13",
pages = "1108--1109",
day = "22",
month = jun,
year = "1995",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 11:25:03 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "An algorithm for delivering a state feedback
controller that assigns desired distinct closed-loop
eigenvalues to the closed-loop system and is robust to
rounding errors in the elements of the controller is
\ldots{}",
}
@InProceedings{Zhou:1995:HSD,
author = "Feng Zhou and Peter Kornerup",
title = "High Speed {DCT}\slash {IDCT} Using a Pipelined
{CORDIC} Algorithm",
crossref = "Knowles:1995:PSC",
pages = "180--187",
year = "1995",
bibdate = "Mon May 20 06:05:24 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Feng.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@InProceedings{Ahrendt:1996:FHC,
author = "Timm Ahrendt",
title = "Fast High-Precision Computations of Complex Square
Roots",
crossref = "LakshmanYN:1996:IPI",
pages = "142--149",
year = "1996",
bibdate = "Thu Mar 12 08:43:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
acknowledgement = ack-nhfb,
keywords = "algebraic computation; algorithms; ISSAC; measurement;
SIGNUM; SIGSAM; symbolic computation",
subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
ALGEBRAIC MANIPULATION, Algorithms, Algebraic
algorithms. {\bf G.1.0} Mathematics of Computing,
NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
DEVICES, Models of Computation, Bounded-action devices.
{\bf G.1.5} Mathematics of Computing, NUMERICAL
ANALYSIS, Roots of Nonlinear Equations, Iterative
methods. {\bf G.1.2} Mathematics of Computing,
NUMERICAL ANALYSIS, Approximation.",
xxtitle = "Fast high-precision computation of complex square
roots",
}
@TechReport{Al-Twaijry:1996:OPR,
author = "H. Al-Twaijry and M. J. Flynn",
title = "Optimum placement and routing of multiplier partial
product trees",
type = "Technical report",
number = "CSL-TR-96-706",
institution = "Computer Systems Laboratory, Stanford University",
address = "Stanford, CA, USA",
month = sep,
year = "1996",
bibdate = "Mon Dec 24 10:13:01 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Alefeld:1996:EII,
author = "G. E. Alefeld and F. A. Potra and W. Voelker",
title = "Effective Improvements of the
Internal-{Newton}-Method",
crossref = "Alefeld:1996:SCV",
pages = "133--139",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Andraos:1996:FPU,
author = "S. Andraos",
booktitle = "{IEEE 39th} Midwest symposium on Circuits and Systems,
1996",
title = "Fixed point unsigned fractional representation in
residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "555--558",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1996.594239",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Representing fractions is one of the fundamental
problems in the Residue Number System (RNS) which is
considered an integer number system with no fractional
representation. This is one of its main drawbacks and
one of the main obstacles in its \ldots{}",
}
@MastersThesis{Angarai:1996:NRS,
author = "Vijayanand Jaganaathan Angarai",
title = "Number representation schemes for energy efficient
computer arithmetic",
type = "Thesis ({M.S.})",
school = "University of Texas at Dallas",
address = "Dallas, TX, USA",
pages = "ix + 57",
year = "1996",
bibdate = "Mon Mar 05 14:32:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Anonymous:1996:DC,
author = "Anonymous",
editor = "Barry Cipra and Paul Zorn",
booktitle = "What's Happening in the Mathematical Sciences",
title = "Divide and Conquer",
volume = "3",
publisher = pub-AMS,
address = pub-AMS:adr,
bookpages = "vi + 111",
pages = "39--47",
year = "1996",
ISBN = "0-8218-0355-7 (paperback)",
ISBN-13 = "978-0-8218-0355-4 (paperback)",
LCCN = "QA3 .C57 1996",
bibdate = "Thu Dec 08 16:31:52 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ams.org/samplings/math-history/divide.pdf",
acknowledgement = ack-nhfb,
keywords = "Pentium divide flaw",
}
@Article{Anonymous:1996:FPF,
author = "Anonymous",
title = "Floating Point --- Finding Electronic\slash Mechanical
Parts",
journal = j-COMPUT-AIDED-ENG,
volume = "15",
number = "1",
pages = "76--??",
year = "1996",
CODEN = "CCAEDJ",
ISSN = "0733-3536 (print), 2162-1365 (electronic)",
ISSN-L = "0733-3536",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer-aided engineering: CAE",
}
@Article{Anonymous:1996:IBT,
author = "Anonymous",
title = "Inquiry Board Traces {Ariane 5} Failure to Overflow
Error",
journal = j-SIAM-NEWS,
volume = "29",
number = "8",
pages = "1, 12, 13",
month = oct,
year = "1996",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Apr 28 18:48:53 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.siam.org/siamnews/general/ariane.htm",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Book{Anonymous:1996:SROa,
author = "Anonymous",
title = "The Square Root of 3 to one million digits",
volume = "628",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1996",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/3sqrt10.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
}
@Book{Anonymous:1996:SROb,
author = "Anonymous",
title = "The Square Root of 5 to one million digits",
volume = "629",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1996",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/5sqrt10.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
}
@Book{Anonymous:1996:SROc,
author = "Anonymous",
title = "The Square Root of 6 to one million digits",
volume = "630",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1996",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/6sqrt10.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
}
@Book{Anonymous:1996:SROd,
author = "Anonymous",
title = "The Square Root of 7 to one million digits",
volume = "631",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1996",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/7sqrt10.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
}
@Book{Anonymous:1996:SROe,
author = "Anonymous",
title = "The Square Root of 8 to one million digits",
volume = "632",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1996",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/8sqrt10.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
}
@Book{Anonymous:1996:SROf,
author = "Anonymous",
title = "The Square Root of 10 to one million digits",
volume = "635",
publisher = pub-PROJECT-GUTENBERG,
address = pub-PROJECT-GUTENBERG:adr,
year = "1996",
bibdate = "Sun Jan 24 10:00:27 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-PROJECT-GUTENBERG,
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/10srt10.zip",
acknowledgement = ack-nhfb # " and " # ack-st,
subject = "Mathematical constants.",
}
@InProceedings{Anuta:1996:BLA,
author = "M. A. Anuta and Daniel W. Lozier and N. Schabanel and
P. R. Turner",
title = "Basic Linear Algebra Operations in {SLI} Arithmetic",
crossref = "Bouge:1996:EPP",
pages = "193--202",
year = "1996",
DOI = "https://doi.org/10.1007/BFb0024702",
bibdate = "Fri Jul 09 07:17:24 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5811.ps.Z;
https://www.nist.gov/publications/basic-linear-algebra-operations-sli-arithmetic",
acknowledgement = ack-nhfb,
}
@Article{Anuta:1996:MMC,
author = "M. A. Anuta and Daniel W. Lozier and P. R. Turner",
title = "The {MasPar MP-1} as a Computer Arithmetic
Laboratory",
journal = j-J-RES-NATL-BUR-STAND,
volume = "101",
number = "2",
pages = "165--174",
month = mar # "\slash " # apr,
year = "1996",
CODEN = "JRNBAG",
DOI = "https://doi.org/10.6028/jres.101.018",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
bibdate = "Fri Jul 09 07:18:42 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4907584/",
abstract = "This paper is a blueprint for the use of a massively
parallel SIMD computer architecture for the simulation
of various forms of computer arithmetic. The particular
system used is a DEC/MasPar MP-1 with 4096 processors
in a square array. This architecture has many
advantages for such simulations due largely to the
simplicity of the individual processors. Arithmetic
operations can be spread across the processor array to
simulate a hardware chip. Alternatively they may be
performed on individual processors to allow simulation
of a massively parallel implementation of the
arithmetic. Compromises between these extremes permit
speed-area tradeoffs to be examined. The paper includes
a description of the architecture and its features. It
then summarizes some of the arithmetic systems which
have been, or are to be, implemented. The
implementation of the level-index and symmetric
level-index, LI and SLI, systems is described in some
detail. An extensive bibliography is included.",
acknowledgement = ack-nhfb,
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
keywords = "computer arithmetic, fixed-point and floating-point
arithmetic, logarithmic and level-index arithmetic,
residue number system arithmetic, serial and parallel
simulation of computer arithmetic",
}
@Article{Arioli:1996:REA,
author = "M. Arioli and C. Fassino",
title = "Roundoff error analysis of algorithms based on
{Krylov} subspace methods",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "2",
pages = "189--205",
month = jun,
year = "1996",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01731978",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F10 (15A23 65G05)",
MRnumber = "98e:65018",
MRreviewer = "Jean-Marie Chesneaux",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=189",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@InProceedings{Bajard:1996:NED,
author = "J.-C. Bajard and L.-S. Didier and Jean-Michel Muller",
booktitle = "Proceedings of International Conference on Application
Specific Systems, Architectures and Processors, 1996.
{ASAP 96}",
title = "A new {Euclidean} division algorithm for residue
number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "45--54",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1109/ASAP.1996.542800",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "We propose in this paper a new algorithm and
architecture for performing divisions in residue number
systems. Our algorithm is suitable for residue number
systems with large moduli, with the aim of manipulating
very large integers on a parallel \ldots{}",
}
@Article{Barber:1996:QAC,
author = "C. Bradford Barber and David P. Dobkin and Hannu
Huhdanpaa",
title = "The {Quickhull Algorithm} for Convex Hulls",
journal = j-TOMS,
volume = "22",
number = "4",
pages = "469--483",
month = dec,
year = "1996",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/235815.235821",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Nov 8 14:50:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/",
abstract = "The convex hull of a set of points is the smallest
convex set that contains the points. This article
presents a practical convex hull algorithm that
combines the two-dimensional Quickhull Algorithm with
the general-dimensional Beneath-Beyond Algorithm. It is
similar to the randomized, incremental algorithms for
convex hull and Delaunay triangulation. We provide
empirical evidence that the algorithm runs faster when
the input contains nonextreme points and that it uses
less memory. Computational geometry algorithms have
traditionally assumed that input sets are well behaved.
When an algorithm is implemented with floating-point
arithmetic, this assumption can lead to serious errors.
We briefly describe a solution to this problem when
computing the convex hull in two, three, or four
dimensions. The output is a set of ``thick'' facets
that contain all possible exact convex hulls of the
input. A variation is effective in five or more
dimensions.",
acknowledgement = ack-rfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms, reliability",
subject = "{\bf I.3.5}: Computing Methodologies, COMPUTER
GRAPHICS, Computational Geometry and Object Modeling,
Geometric algorithms, languages and systems.",
}
@InProceedings{Berlejung:1996:PSM,
author = "H. M. E. Berlejung",
title = "Processing Software Metrics in an Integrated
Development Environment for {Pascal-XSC}",
crossref = "Alefeld:1996:SCV",
pages = "79--83",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Berner:1996:PMV,
author = "S. Berner",
title = "A Parallel Method for Verified Global Optimization",
crossref = "Alefeld:1996:SCV",
pages = "200--206",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Blum:1996:RPD,
author = "Manuel Blum and H. Wasserman",
title = "Reflections on the {Pentium} Division Bug",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "4",
pages = "385--393",
month = apr,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.494097",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:10 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://http.cs.berkeley.edu/~blum/pentium.ps;
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=494097",
abstract = "We review the field of {\em result-checking\/} and
suggest that it be extended to a methodology for
enforcing hardware\slash software reliability. We
thereby formulate a vision for ``self-monitoring''
hardware\slash software whose reliability is augmented
through embedded suites of run-time correctness
checkers. In particular, we suggest that embedded
checkers and correctors may be employed to safeguard
against arithmetic errors such as that which has
bedeviled the Intel Pentium Microprocessor. We specify
checkers and correctors suitable for monitoring the
multiplication and division functionalities of an
arbitrary arithmetic processor and seamlessly
correcting erroneous output which may occur for any
reason during the lifetime of the chip.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Built-in testing; concurrent error detection; fault
tolerance; Pentium; reliability; result-checking;
verification",
}
@Article{Bockenfeld:1996:TNT,
author = "Don Bockenfeld",
title = "{TSQRT}: a New Trick for an Old Dog",
journal = j-CCCUJ,
volume = "14",
number = "3",
pages = "39--41",
month = mar,
year = "1996",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Sat Feb 10 08:57:37 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Implements a small table-driven square root function
in C, using exclusively integer operations.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@Article{Burger:1996:PFP,
author = "Robert G. Burger and R. Kent Dybvig",
title = "Printing Floating-Point Numbers Quickly and
Accurately",
journal = j-SIGPLAN,
volume = "31",
number = "5",
pages = "108--116",
month = may,
year = "1996",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/231379.231397",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Mon Feb 03 07:07:43 2003",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/231379/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This paper offers a significantly faster algorithm
than that of \cite{Steele:1990:HPF}, together with a
correctness proof and an implementation in Scheme. See
also
\cite{Clinger:1990:HRF,Abbott:1999:ASS,Steele:2004:RHP,Clinger:2004:RHR}.",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/231379/p108-burger/",
acknowledgement = ack-nhfb,
affiliation = "Department of Computer Science, Indiana University,
Bloomington, IN, USA",
annote = "Published as part of the Proceedings of PLDI'96.",
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "algorithms; design; theory",
subject = "{\bf I.3.3} Computing Methodologies, COMPUTER
GRAPHICS, Picture/Image Generation, Display algorithms.
{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf I.1.2} Computing Methodologies,
SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}
@TechReport{Burnikel:1996:HPF,
author = "Christoph Burnikel and Jochen K{\"o}nemann",
title = "High precision floating point numbers in {LEDA}",
type = "Report",
number = "MPI I 96 1 002",
institution = "Max-Planck-Institut f{\"u}r Informatik",
address = "Saarbr{\"u}cken, Germany",
pages = "7",
year = "1996",
bibdate = "Thu May 09 09:03:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Candev:1996:AIA,
author = "M. Candev",
title = "On the Application of an Interval Algorithm for Set
Inversion",
crossref = "Alefeld:1996:SCV",
pages = "140--146",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Cappuccino:1996:DDH,
author = "G. Cappuccino and P. Corsonello and G. Cocorullo",
title = "Design and demonstration of high throughput square
rooting circuit",
journal = j-ELECT-LETTERS,
volume = "32",
number = "5",
pages = "434",
month = "????",
year = "1996",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "Not \ldots{}",
}
@Article{Chaitin-Chatelin:1996:FPA,
author = "F. Chaitin-Chatelin",
title = "Is Finite Precision Arithmetic Useful For Physics?",
journal = j-J-UCS,
volume = "2",
number = "5",
pages = "380--??",
day = "28",
month = may,
year = "1996",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Wed May 28 19:32:35 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/is_finite_precision_arithmetic_useful_for_physics",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@Book{Chaitin-Chatelin:1996:LFP,
author = "Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie
Frayss{\'e}",
title = "Lectures on Finite Precision Computations",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xv + 235",
year = "1996",
ISBN = "0-89871-358-7",
ISBN-13 = "978-0-89871-358-9",
LCCN = "QA297 .C417 1996",
bibdate = "Wed Nov 16 14:38:30 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Software, environments, tools",
acknowledgement = ack-nhfb,
keywords = "Matlab",
subject = "numerical calculations; data processing; error
analysis (mathematics); toolbox PRECISE",
tableofcontents = "1. General Presentation \\
2. Computability in Finite Precision \\
3. Measures of Stability for Regular Problems \\
4. Computation in the Neighbourhood of a Singularity
\\
5. Arithmetic Quality of Reliable Algorithms \\
6. Numerical Stability in Finite Precision \\
7. Software Tools for Round-Off Error Analysis in
Algorithms \\
8. The Toolbox PRECISE for Computer Experimentation \\
9. Experiments with PRECISE \\
10. Robustness to Nonnormality \\
11. Qualitative Computing \\
12. More Numerical Illustrations with PRECISE \\
Annex: The Toolbox PRECISE for MATLAB.",
}
@Article{Chen:1996:VAC,
author = "Y.-A. Chen and E. Clarke and P.-H. Ho and Y. Hoskote
and T. Kam and M. Khaira and J. O. Leary and X. Zhao",
title = "Verification of All Circuits in a Floating-Point Unit
Using Word-Level Model Checking",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1166",
pages = "19--33",
year = "1996",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Jun 02 07:43:02 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Chesneaux:1996:CSS,
author = "J.-M. Chesneaux and B. Troff",
title = "Computational Stability Study Using the {CADNA}
Software Applied to the {Navier--Stokes} Solver
{PEGASE}",
crossref = "Alefeld:1996:SCV",
pages = "84--90",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Chren:1996:DPP,
author = "W. A. {Chren, Jr.} and C. H. Brogdon and D.
Andrevska",
booktitle = "{IEEE 39th} Midwest symposium on Circuits and Systems,
1996",
title = "Delay-power product simulation results for one-hot
residue number system arithmetic circuits",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "544--547",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1996.594237",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "We present Spice simulations which verify previous
analytical estimates of the delay-power product of
One-Hot Residue adders and multipliers. These
simulations show greater than a 50\% reduction in the
product below binary adders and an order of \ldots{}",
}
@InProceedings{Chren:1996:DSD,
author = "W. A. {Chren, Jr.}",
booktitle = "{IEEE} International Symposium on Circuits and
Systems. {ISCAS '96}, Connecting the World, 12--15 May
1996",
title = "Delta-sigma demodulator with large oversampling ratio
using the one-hot residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "473--476",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1996.541749",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A residue number system-based delta-sigma demodulator
is presented which demonstrates a significant
improvement in oversampling ratio in comparison with
equivalent binary designs. The second order design
employs a two-stage cascade architecture with
\ldots{}",
}
@InProceedings{Chren:1996:RDU,
author = "W. A. {Chren, Jr.} and C. H. Brogdon",
booktitle = "{IEEE 39th} Midwest symposium on Circuits and Systems,
1996",
title = "{RSA} decryption using the one-hot residue number
system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "551--554",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1996.594238",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The design of an RSA decryption circuit which uses the
One-Hot Residue Number System is presented. Large
modulus adders and multipliers are described which
reduce the area of previous (barrel shifter-based)
designs while preserving their low power \ldots{}",
}
@Article{Ciminiera:1996:CSM,
author = "L. Ciminiera and P. Montuschi",
title = "Carry-save multiplication schemes without final
addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "9",
pages = "1050--1055",
month = sep,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.537128",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:13 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537128",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Clarke:1996:VSD,
author = "E. M. Clarke and S. M. German and X. Zhao",
title = "Verifying the {SRT} division algorithm using theorem
proving techniques",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1102",
pages = "111--??",
year = "1996",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Sep 6 19:46:15 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Clarke:1996:WLS,
author = "E. M. Clarke and M. Khaira and X. Zhao",
title = "Word-level symbolic model checking: avoiding the
{Pentium FDIV} error",
crossref = "IEEE:1996:DAC",
pages = "645--648",
year = "1996",
bibdate = "Sat Jun 02 07:44:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/dac/240518/p645-clarke/p645-clarke.pdf;
http://www.acm.org/pubs/citations/proceedings/dac/240518/p645-clarke/;
http://www.acm.org/pubs/contents/proceedings/dac/240518/",
acknowledgement = ack-nhfb,
}
@InProceedings{Corliss:1996:VPE,
author = "G. F. Corliss and R. Rihm",
title = "Validating an {A} Priori Enclosure Using High-Order
{Taylor} Series",
crossref = "Alefeld:1996:SCV",
pages = "228--238",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Crenshaw:1996:PTF,
author = "Jack W. Crenshaw",
title = "Programmer's Toolbox: Floating-Point Math, Part 3",
journal = j-EMBED-SYS-PROG,
volume = "9",
number = "1",
pages = "19--??",
year = "1996",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Embedded Systems Programming",
}
@TechReport{Darcy:1996:FMF,
author = "Joseph D. Darcy and David Gay",
title = "{FLECKmarks}: Measuring Floating Point Performance
using a {FulL IEEE Compliant Arithmetic BenchmarK}",
type = "Technical report",
institution = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
month = dec,
year = "1996",
bibdate = "Mon Feb 18 12:25:24 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~darcy/Research/fleckmrk.pdf",
acknowledgement = ack-nhfb,
remark = "From the first author's home Web page: ``Errata: The
`subnormal' timings for x86 processors are incorrect;
they do not perform operations on subnormals at full
speed. However, what values are subnormals on the x86
are different than on other processors due to that
architecture's unusual floating-point register design.
On the x86, when a 64-bit double value is loaded into a
register, it has the 15 bit exponent of the 80-bit
double extended format instead of the 11 bit exponent
of the double format. Confusingly, this occurs even if
the processor's precision control is set to round to
double precision. The test programs in this project
used computations that would be subnormal in a pure
double format, not in double with extended exponent
range (non-zero subnormals in double with extended
exponent range would round to zero in pure double).
Operations on subnormals in double precision with
extended exponent range should take about 100 cycles on
the Pentium Pro and subsequent Intel x86
chips.\par
Thanks to David Scott of Intel for pointing out this
error.",
}
@InProceedings{Dimitrov:1996:NCD,
author = "V. Dimitrov and Saeid Sadeghi-Emamchaie and G. A.
Jullien and W. C. Miller",
title = "Near Canonic Double-Based Number System ({DBNS}) with
Applications in Digital Signal Processing",
crossref = "Luk:1996:PSC",
pages = "14--25",
year = "1996",
DOI = "https://doi.org/10.1117/12.255433",
bibdate = "Sat May 14 17:15:05 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://spie.org/x648.html?product_id=235316;
http://www.gbv.de/dms/bowker/toc/9780819422347",
acknowledgement = ack-nhfb,
keywords = "Double-Based Number System (DBNS)",
}
@InProceedings{Dimitrov:1996:RNS,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
booktitle = "{IEEE 39th} Midwest symposium on Circuits and Systems,
1996",
title = "A residue number system implementation of real
orthogonal transforms via approximation over a direct
product of quadratic number rings",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "533--536",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1996.594227",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Recent work has focused on doing residue computations
that are quantization within a dense ring of integers
in the real domain. The aims of the paper are to
provide and efficient algorithm for approximation of
the real input signal with arbitrarily \ldots{}",
}
@InProceedings{Dimitrova:1996:NAS,
author = "N. S. Dimitrova",
title = "On a Numerical Approach for Solving a Class of
Nonlinear Systems",
crossref = "Alefeld:1996:SCV",
pages = "147--153",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Djebbari:1996:GAS,
author = "A. Djebbari and S. A. Elahmar and M. F. Belbachir and
J. M. Rouvaen",
booktitle = "3rd International Conference on Signal Processing,
1996",
title = "Global asymptotic stability of normal digital filters
with rounding and two's complement truncation
quantization",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "154--157",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Normal form digital filters are investigated for limit
cycles due to both two's complement truncation and
rounding quantization. Conditions for existence are
derived. A method, based on an exhaustive search and
applicable to above types of \ldots{}",
}
@InProceedings{Dobner:1996:AAD,
author = "H.-J. Dobner and W. Klein",
title = "Application of Automatic Differentiation Techniques to
Circuit Simulation",
crossref = "Alefeld:1996:SCV",
pages = "329--333",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Dobronets:1996:PEE,
author = "B. S. Dobronets",
title = "A Posteriori Error Estimation for Partial Differential
Equations",
crossref = "Alefeld:1996:SCV",
pages = "239--244",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{El-Guibaly:1996:HSC,
author = "Fayez El-Guibaly and A. Sabaa",
title = "High-speed {CORDIC} algorithm",
crossref = "Luk:1996:PSC",
pages = "512--512",
year = "1996",
DOI = "https://doi.org/10.1117/12.255460",
bibdate = "Tue Jun 14 18:26:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Farag:1996:LPR,
author = "Emad N. Farag and M. Anwarul Hasan and Mohamed I.
Elmasry",
title = "Low-power radix 2 division algorithm with minimum
add\slash sub operations",
crossref = "Luk:1996:PSC",
pages = "39--511",
year = "1996",
DOI = "https://doi.org/10.1117/12.255450",
bibdate = "Tue Jun 14 18:26:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Feldstein:1996:OUM,
author = "Alan Feldstein and Peter R. Turner",
title = "Overflow and underflow in multiplication and
division",
journal = j-APPL-NUM-MATH,
volume = "21",
number = "3",
pages = "221--239",
day = "20",
month = aug,
year = "1996",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65Y99",
MRnumber = "97f:65086; 1 416 857",
bibdate = "Wed Jul 28 14:36:31 MDT 1999",
bibsource = "Compendex database;
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1996&volume=21&issue=3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1996&volume=21&issue=3&aid=692",
acknowledgement = ack-nhfb,
affiliation = "Arizona State Univ",
affiliationaddress = "AZ, USA",
classification = "721.1; 723.2; 921; 921.2; 921.6",
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
journalabr = "Appl Numer Math",
keywords = "Differential equations; Digital arithmetic; Division;
Floating point exponents; Floating point fractions;
Logarithmic distribution; Mathematical models;
Multiplication; Natural sciences computing; Overflow;
Underflow",
}
@Article{Fenn:1996:MDD,
author = "S. T. J. Fenn and M. Benaissa and D. Taylor",
title = "{$ \mathrm {GF}(2^m) $} multiplication and division
over the dual basis",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "3",
pages = "319--327",
month = mar,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.485570",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485570",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Flynn:1996:SPT,
author = "Michael J. Flynn and Stuart Oberman and Steve Fu and
Hesham Al-Twaijry and Kevin Nowka and Gary Bewick and
Eric Schwarz and Nhon Quach",
booktitle = "{NSF\slash MIPS} Conference on Experimental Research
on Computer Systems, June 1996",
title = "The {SNAP} Project: Towards Sub-Nanosecond
Arithmetic",
publisher = "????",
address = "????",
pages = "??--??",
year = "1996",
bibdate = "Mon Jul 18 17:18:49 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://arith.stanford.edu/tr/snap_nsf.ps.Z",
acknowledgement = ack-nhfb,
pagecount = "12",
}
@Article{Fortune:1996:SAY,
author = "Steven Fortune and Christopher J. {Van Wyk}",
title = "Static analysis yields efficient exact integer
arithmetic for computational geometry",
journal = j-TOG,
volume = "15",
number = "3",
pages = "223--248",
month = jul,
year = "1996",
CODEN = "ATGRDF",
ISSN = "0730-0301 (print), 1557-7368 (electronic)",
ISSN-L = "0730-0301",
bibdate = "Sat Aug 31 16:39:46 MDT 1996",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/0730-0301/230533.html",
abstract = "Geometric algorithms as usually described assuming
that arithmetic operations are performed exactly on
real numbers. A program implemented using a naive
substitution of floating-point arithmetic for real
arithmetic can fail, since geometric primitives depend
upon sign-evaluation and may not be reliable if
evaluated approximately. Geometric primitives are
reliable if evaluated exactly with integer arithmetic,
but this degrades performance since software
extended-precision arithmetic is required.\par
We describe static-analysis techniques that reduce the
performance cost of exact integer arithmetic used to
implement geometric algorithms. We have used the
techniques for a number of examples, including
line-segment intersection in two dimensions, Delaunay
triangulations, and a tree-dimensional boundary-based
polyhedral modeler. In general, the techniques are
appropriate for algorithms that use primitives of
relatively low algebraic total degree, e.g., those
involving flat objects (points, lines, planes) in two
or three dimensions. The techniques have been package
in a preprocessor for reasonably convenient use.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Graphics",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J778",
keywords = "algorithms; experimentation",
subject = "{\bf I.3.5}: Computing Methodologies, COMPUTER
GRAPHICS, Computational Geometry and Object Modeling,
Geometric algorithms, languages, and systems. {\bf
D.3.4}: Software, PROGRAMMING LANGUAGES, Processors,
Preprocessors. {\bf G.4}: Mathematics of Computing,
MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}:
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Reliability and robustness.",
}
@Article{Ganesan:1996:CSM,
author = "Ravikanth Ganesan and Kannan Govindarajan and Min-You
Wu",
title = "Comparing {SIMD} and {MIMD} Programming Modes",
journal = j-J-PAR-DIST-COMP,
volume = "35",
number = "1",
pages = "91--96",
day = "25",
month = may,
year = "1996",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1996.0071",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:19:00 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production/pdf",
acknowledgement = ack-nhfb,
classification = "C5220P (Parallel architecture); C6110P (Parallel
programming)",
corpsource = "Department of Computer Science, State University of
New York, Buffalo, NY, USA",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "application benchmarks; arithmetic operations; CM;
CM-5; communication; Connection Machine; Fortran;
message-passing Fortran; MIMD; parallel architectures;
parallel programming; performance evaluation;
programming modes; SIMD; software; synthetic
benchmarks; time",
treatment = "P Practical",
}
@InProceedings{Garg:1996:FTP,
author = "H. K. Garg and F. V. C. Mendis",
booktitle = "Conference Record of the Thirtieth Asilomar Conference
on Signals, Systems and Computers, 1996",
title = "On fault-tolerant polynomial residue number systems",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "206--209",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.1996.600858",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Fault-tolerant convolution techniques have been
described for polynomials defined over the fields of
complex and real numbers. Fault-tolerant convolution
schemes are derived for polynomials defined over finite
integer rings. A new algorithm for \ldots{}",
}
@InProceedings{Gibb:1996:FFI,
author = "S. Gibb and P. J. W. Graumann and Laurence E. Turner",
title = "{FIR} filter implementation using bit-serial
arithmetic and partial summation trees",
crossref = "Luk:1996:PSC",
pages = "63--74",
year = "1996",
DOI = "https://doi.org/10.1117/12.255462",
bibdate = "Tue Jun 14 18:26:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Goldberg:1996:CA,
author = "David Goldberg",
title = "Computer Arithmetic",
crossref = "Hennessy:1996:CAQ",
chapter = "A",
pages = "A-1--A-77",
year = "1996",
bibdate = "Mon May 20 10:05:22 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Goldstine:1996:ENI,
author = "H. H. Goldstine and A. Goldstine",
title = "The {Electronic Numerical Integrator and Computer}
({ENIAC})",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "18",
number = "1",
pages = "10--16",
month = "Spring",
year = "1996",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/85.476557",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Fri Nov 28 16:50:50 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Reprint of 1946 technical report and
\cite{Goldstine:1946:ENI}.",
URL = "http://ieeexplore.ieee.org/iel4/85/10202/00476557.pdf",
abstract = "It is our purpose in the succeeding pages to give a
brief description of the ENIAC and an indication of the
kinds of problems for which it can be used. This
general purpose electronic computing machine was
recently made public by the Army Ordnance Department
for which it was developed by the Moore School of
Electrical Engineering. The machine was developed
primarily for the purpose of calculating firing tables
for the armed forces. Its design is, however,
sufficiently general to permit the solution of a large
class of numerical problems which could hardly be
attempted by more conventional computing tools.\par
In order easily to obtain sufficient accuracy for
scientific computations, the ENIAC was designed as a
digital device. The equipment normally handles signed
10-digit numbers expressed in the decimal system. It
is, however, so constructed that operations with as
many as 20 digits are possible.\par
The machine is automatically sequenced in the sense
that all instructions needed to carry out a computation
are given to it before the computation commences. It
will be seen below how these instructions are given to
the machine.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Gudenberg:1996:HSI,
author = "J. W. Von Gudenberg",
title = "Hardware Support for Interval Arithmetic",
crossref = "Alefeld:1996:SCV",
pages = "32--37",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Book{Guedj:1996:EN,
author = "Denis Guedj",
title = "{L}'empire des nombres",
publisher = "Gallimard",
address = "Paris, France",
pages = "176",
year = "1996",
ISBN = "2-07-053373-5",
ISBN-13 = "978-2-07-053373-2",
LCCN = "????",
bibdate = "Sat Nov 29 06:57:01 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Gupta:1996:AAG,
author = "S. Gupta and J. Rajski and J. Tyszer",
title = "Arithmetic additive generators of pseudo-exhaustive
test patterns",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "8",
pages = "939--949",
month = aug,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.536236",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:13 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=536236",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Guyot:1996:STD,
author = "A. Guyot and M. Renaudin and B. El Hassan and V.
Levering",
booktitle = "Proceedings of the Ninth International Conference on
{VLSI} Design, 1996",
title = "Self timed division and square-root extraction",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "376--381",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper describes a self-timed integrated circuit
for division and square-root extraction. First it
concentrates on the development and the proof of a new
mathematical algorithm. Then the design methodology and
the architecture of a self-timed \ldots{}",
}
@Article{Haller:1996:AFP,
author = "G. M. Haller and D. R. Freytag",
title = "Analog floating-point {BiCMOS} sampling chip and
architecture of the {BaBar CsI} calorimeter front-end
electronics system at the {SLAC} {B}-factory",
journal = j-IEEE-TRANS-NUCL-SCI,
volume = "43",
number = "3",
pages = "1610--1614",
month = jun,
year = "1996",
CODEN = "IRNSAM",
ISSN = "0018-9499 (print), 1558-1578 (electronic)",
ISSN-L = "0018-9499",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Nuclear Science",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
summary = "The design and implementation of an analog
floating-point sampling integrated circuit for the
BaBar detector at the SLAC B-Factory is described. The
CARE (Custom Auto-Range Encoding) circuit is part of an
18-bit dynamic range sampling system with a \ldots{}",
}
@Book{Hamacher:1996:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Fourth",
pages = "xix + 555",
year = "1996",
ISBN = "0-07-025883-X",
ISBN-13 = "978-0-07-025883-9",
LCCN = "QA76.9.C643 H36 1996",
bibdate = "Sat May 18 14:24:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
}
@InProceedings{Hartwig:1996:RNA,
author = "F. Hartwig and A. Lacroix",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS '96}, `Connecting the World', 12--15
May 1996",
title = "Roundoff noise analysis on the basis of an improved
floating point error model",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "133--136",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Until now floating point roundoff analysis utilized
the assumption of statistical decorrelation between
roundoff error and internal signals subject to a signal
flow graph. A quantization within a signal flow graph
has been treated like a single \ldots{}",
}
@Article{Hauser:1996:HFE,
author = "John R. Hauser",
title = "Handling floating-point exceptions in numeric
programs",
journal = j-TOPLAS,
volume = "18",
number = "2",
pages = "139--174",
month = mar,
year = "1996",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/227699.227701",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Tue Aug 13 11:46:35 MDT 1996",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/toc/Abstracts/0164-0925/227701.html",
abstract = "There are a number of schemes for handling arithmetic
exceptions that can be used to improve the speed (or
alternatively the reliability) of numeric code.
Overflow and underflow are the most troublesome
exceptions, and depending on the context in which the
exception can occur, they may be addressed either: (1)
through a ``brute force'' reevaluation with extended
range, (2) by reevaluating using a technique known as
{\em scaling}, (3) by substituting an infinity or zero,
or (4) in the case of underflow, with gradual
underflow. In the first two of these cases, the
offending computation is simply reevaluated using a
safer but slower method. The latter two cases are
cheaper, more automated schemes that ideally are built
in as options within the computer system. Other
arithmetic exceptions can be handled with similar
methods. These and some other techniques are examined
with an eye toward determining the support programming
languages and computer systems ought to provide for
floating-point exception handling. It is argued that
the cheapest short-term solution would be to give full
support to most of the {\em required\/} (as opposed to
recommended) special features of the IEC/IEEE Standard
for Binary Floating-Point Arithmetic. An essential part
of this support would include standardized access from
high-level languages to the exception flags defined by
the standard. Some possibilities outside the IEEE
Standard are also considered, and a few thought on
possible better-structured support within programming
languages are discussed.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
keywords = "accurate floating-point summation; algorithms; design;
languages; performance; standardization",
subject = "{\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language
Constructs and Features, Control structures. {\bf
D.3.0}: Software, PROGRAMMING LANGUAGES, General,
Standards. {\bf G.1.0}: Mathematics of Computing,
NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
General, Numerical algorithms.",
}
@Book{Heck:1996:IM,
author = "Andr{\'e} Heck",
title = "Introduction to {Maple}",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xx + 699",
year = "1996",
DOI = "https://doi.org/10.1007/978-1-4684-0484-5",
ISBN = "0-387-94535-0 (hardcover), 1-4684-0484-9,
1-4684-0486-5",
ISBN-13 = "978-0-387-94535-4 (hardcover), 978-1-4684-0484-5,
978-1-4684-0486-9",
LCCN = "QA155.7.E4H43 1993",
MRclass = "65-01, 65B10, 65D18, 65Dxx, 65Fxx, 65Lxx, 68-01,
68N15, 68W30, 68NXX",
MRnumber = "MR1405611 (97c:68076)",
bibdate = "Tue Jun 06 17:57:02 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$39.00",
abstract = "The first edition of this book has been very well
received by the community. The new version 4 of Maple V
contains so many new mathematical features and
improvements in the user interface that Waterloo Maple
Inc. markets it as ``the Power Edition.'' These two
facts have made it necessary to write a second edition
within a short period of the first. I corrected
typographical errors, rephrased text, updated and
improved many examples, and added much new material.
Hardly any chapter has been left untouched.
Substantially changed or added sections and chapters
address the assume facility, I/O, approximation theory,
integration, composite data types, simplification,
graphics, differential equations, and matrix algebra.
Tables summarize features, command options, etc., and
constitute a quick reference. The enlarged index of the
book has been carefully compiled to make locating
search items quick and easy. Many new examples have
been included showing how to use Maple as a problem
solver, how to assist the system during computations,
and how to extend its built-in facilities. About the
Maple Version Used: The second edition of this book is
fully revised and updated to Maple V Release 4. More
precisely, the second edition of this book was produced
with Maple V Release 4, beta 3 on a SUN SPARCstation
20, Model 71. There should be hardly any difference
between this beta version and the final release; only
minor differences in the user interface are not
excluded.",
acknowledgement = ack-nhfb,
tableofcontents = "Preface to the Second Edition / v \\
Preface to the First Edition / ix \\
List of Tables / xix \\
1 Introduction to Computer Algebra / 1 \\
1.1 What is Computer Algebra? / 1 \\
1.2 Computer Algebra Systems / 2 \\
1.3 Some Properties of Computer Algebra Systems / 5 \\
1.4 Advantages of Computer Algebra / 11 \\
1.5 Limitations of Computer Algebra / 24 \\
1.6 Design of Maple / 30 \\
2 The First Steps: Calculus on Numbers / 35 \\
2.1 Getting Started / 35 \\
2.2 Getting Help / 38 \\
2.3 Integers and Rational Numbers / 44 \\
2.4 Irrational Numbers and Floating-Point Numbers / 48
\\
2.5 Algebraic Numbers / 54 \\
2.6 Complex Numbers / 59 \\
2.7 Exercises / 63 \\
3 Variables and Names / 65 \\
3.1 Assignment and Unassignment / 65 \\
3.2 Evaluation / 73 \\
3.3 Names of Variables / 77 \\
3.4 Basic Data Types / 82 \\
3.5 Attributes / 86 \\
3.6 Properties / 87 \\
3.7 Exercises / 92 \\
4 Getting Around with Maple / 95 \\
4.1 Maple Input and Output / 95 \\
4.2 The Maple Library / 101 \\
4.3 Reading and Writing Files / 105 \\
4.4 Importing and Exporting Numerical Data / 110 \\
4.5 Low-Level I/O / 113 \\
4.6 Code Generation / 123 \\
4.7 Changing Maple to Your Own Taste / 129 \\
4.8 Exercises / 133 \\
5 Polynomials and Rational Functions / 135 \\
5.1 Univariate Polynomials / 135 \\
5.2 Multivariate Polynomials / 140 \\
5.3 Rational Functions / 142 \\
5.4 Conversions / 144 \\
5.5 Exercises / 147 \\
6 Internal Data Representation and Substitution / 149
\\
6.1 Internal Representation of Polynomials / 149 \\
6.2 Generalized Rational Expressions / 155 \\
6.3 Substitution / 158 \\
6.4 Exercises / 170 \\
7 Manipulation of Polynomials and Rational Expressions
/ 173 \\
7.1 Expansion / 173 \\
7.2 Factorization / 176 \\
7.3 Canonical Form and Normal Form / 179 \\
7.4 Normalization / 181 \\
7.5 Collection / 183 \\
7.6 Sorting / 186 \\
7.7 Exercises / 186 \\
8 Functions / 189 \\
8.1 Mathematical Functions / 189 \\
8.2 Arrow Operators / 193 \\
8.3 Piecewise Defined Functions / 195 \\
8.4 Maple Procedures / 202 \\
8.5 Recursive Procedure Definitions / 204 \\
8.6 unapply / 209 \\
8.7 Operations on Functions / 210 \\
8.8 Anonymous Functions / 211 \\
8.9 Exercises / 212 \\
9 Differentiation / 213 \\
9.1 Symbolic Differentiation / 213 \\
9.2 Automatic Differentiation / 221 \\
9.3 Exercises / 224 \\
10 Integration and Summation / 227 \\
10.1 Indefinite Integration / 227 \\
10.2 Definite Integration / 236 \\
10.3 Numerical Integration / 241 \\
10.4 Integral Transforms / 242 \\
10.5 Assisting Maple's Integrator / 252 \\
10.6 Summation / 256 \\
10.7 Exercises / 261 \\
11 Series, Approximation, and Limits / 267 \\
11.1 Truncated Series / 267 \\
11.2 Approximation of Functions / 278 \\
11.3 Power Series / 285 \\
11.4 Limits / 288 \\
11.5 Exercises / 291 \\
12 Composite Data Types / 293 \\
12.1 Sequence / 293 \\
12.2 Set / 296 \\
12.3 List / 298 \\
12.4 Array / 304 \\
12.5 Table / 310 \\
12.6 Last Name Evaluation / 314 \\
12.7 Function Call / 317 \\
12.8 Conversion Between Composite Data Types / 319 \\
12.9 Exercises / 322 \\
13 The Assume Facility / 325 \\
13.1 The Need for an Assume Facility / 325 \\
13.2 Basics of assume / 329 \\
13.3 An Algebra of Properties / 332 \\
13.4 Implementation of assume / 335 \\
13.5 Exercises / 340 \\
13.6 Hierarchy of Properties / 340 \\
14 Simplification / 343 \\
14.1 Automatic Simplification / 344 \\
14.2 expand / 346 \\
14.3 combine / 353 \\
14.4 simplify / 358 \\
14.5 convert / 364 \\
14.6 Trigonometrie Simplification / 367 \\
14.7 Simplification w.r.t. Side Relations / 370 \\
14.8 Control Over Simplification / 374 \\
14.9 Defining Your Own Simplification Routines / 378
\\
14.10 Exercises / 383 \\
14.11 Simplification Chart / 385 \\
15 Graphics / 387 \\
15.1 Some Basic Two-Dimensional Plots / 389 \\
15.2 Options of plot / 393 \\
15.3 The Structure of Two-Dimensional Graphics / 406
\\
15.4 The plottools Package / 412 \\
15.5 Special Two-Dimensional Plots / 416 \\
15.6 Two-Dimensional Geometry / 429 \\
15.7 Plot Aliasing / 432 \\
15.8 A Common Mistake / 433 \\
15.9 Some Basic Three-Dimensional Plots / 434 \\
15.10 Options of plot3d / 436 \\
15.11 The Structure of Three-Dimensional Graphics / 444
\\
15.12 Special Three-Dimensional Plots / 449 \\
15.13 Data Plotting / 457 \\
15.14 Animation / 467 \\
15.15 List of Plot Options / 469 \\
15.16 Exercises / 475 \\
16 Solving Equations / 479 \\
16.1 Equations in One Unknown / 479 \\
16.2 Abbreviations in solve / 480 \\
16.3 Some Difficulties / 481 \\
16.4 Systems of Equations / 488 \\
16.5 The Gr{\"o}bner Basis Method / 499 \\
16.6 Inequalities / 505 \\
16.7 Numerical Solvers / 507 \\
16.8 Other Solvers in Maple / 509 \\
16.9 Exercises / 515 \\
17 Differential Equations / 519 \\
17.1 First Glance at ODEs / 519 \\
17.2 Analytic Solutions / 520 \\
17.3 Taylor Series Method / 532 \\
17.4 Power Series Method / 534 \\
17.5 Numerical Solutions / 536 \\
17.6 DEtools / 548 \\
17.7 Perturbation Methods / 555 \\
17.8 Partial Differential Equations / 567 \\
17.9 Lie Point Symmetries of PDEs / 569 \\
17.10 Exercises / 572 \\
18 Linear Algebra: The linaig Package / 575 \\
18.1 Loading the linaig Package / 575 \\
18.2 Creating New Vectors and Matrices / 576 \\
18.3 Vector and Matrix Arithmetic / 580 \\
18.4 Basic Matrix Functions / 584 \\
18.5 Structural Operations / 589 \\
18.6 Vector Operations / 592 \\
18.7 Standard Forms of Matrices / 592 \\
18.8 Exercises / 597 \\
19 Linear Algebra: Applications / 601 \\
19.1 Kinematics of the Stanford Manipulator / 601 \\
19.2 A Three-Compartment Model of Cadmium Transfer /
606 \\
19.3 Molecular-Orbital H{\"u}ckel Theory / 618 \\
19.4 Vector Analysis / 623 \\
19.5 Moore--Penrose Inverse / 631 \\
19.6 Exercises / 633 \\
References / 635 \\
Index / 651",
}
@Article{Hecker:1996:LGF,
author = "Chris Hecker",
title = "Let's get to the (floating) point",
journal = "Game Developer",
volume = "2",
number = "??",
pages = "19--24",
month = feb # "\slash " # mar,
year = "1996",
ISSN = "1073-922X",
bibdate = "Fri Jan 06 07:46:23 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "accurate floating-point summation; splitting of
floating-point numbers into high and low parts",
URL = "http://chrishecker.com/images/f/fb/Gdmfp.pdf;
https://www.gamasutra.com/php-bin/store.php?item_id=220&category=22&book=",
acknowledgement = ack-nhfb,
}
@InProceedings{Heikes:1996:DFP,
author = "Craig Heikes and Glenn Colon-Bonet",
title = "A Dual Floating Point Coprocessor with an {FMAC}
Architecture",
crossref = "Wuorinen:1996:DTP",
pages = "354--355",
year = "1996",
bibdate = "Fri Jun 24 10:49:14 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Heindl:1996:MVC,
author = "G. Heindl",
title = "A Method for Verified Computing of Inner and Outer
Approximations of the Interval Hull of a Tolerance
Polyhedron",
crossref = "Alefeld:1996:SCV",
pages = "207--213",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Heinrich:1996:AAF,
author = "Peter Heinrich",
title = "Algorithm Alley: a Fast Integer Square Root",
journal = j-DDJ,
volume = "21",
number = "4",
pages = "113--114, 130",
month = apr,
year = "1996",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Mon Sep 2 09:09:39 MDT 1996",
bibsource = "http://www.ddj.com/index/author/index.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Herzberger:1996:OCC,
author = "J. Herzberger",
title = "On the {$R$}-Order of Convergence of a Class of
Simultaneous Methods for the Inclusions of Polynomial
Roots",
crossref = "Alefeld:1996:SCV",
pages = "154--159",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@TechReport{Hickey:1996:FSP,
author = "Timothy J. Hickey and Qun Ju",
title = "Fast, Sound, and Precise Narrowing of the Exponential
Function",
type = "Technical report",
institution = "Computer Science Department, Brandeis University",
address = "Waltham, MA, USA 02254",
month = mar,
year = "1996",
bibdate = "Sat Nov 05 15:42:23 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
acknowledgement = ack-nhfb,
}
@Book{Higham:1996:ASN,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxviii + 688",
year = "1996",
ISBN = "0-89871-355-2 (paperback)",
ISBN-13 = "978-0-89871-355-8 (paperback)",
LCCN = "QA297.H53 1996",
MRclass = "65Fxx, 15-04, 65-02, 65G50",
bibdate = "Tue Jan 30 11:01:35 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$39.00",
URL = "http://www.ma.man.ac.uk/~higham/asna.html",
acknowledgement = ack-njh # " and " # ack-nhfb,
remark = "Typeset with \LaTeX2e.",
tableofcontents = "Principles of Finite Precision Computation \\
Relative Error and Significant Digits \\
Sources of Errors \\
Precision Versus Accuracy \\
Backward and Forward Errors \\
Conditioning \\
Cancellation \\
Solving a Quadratic Equation \\
Computing the Sample Variance \\
Solving Linear Equations \\
Accumulation of Rounding Errors \\
Instability Without Cancellation \\
Increasing the Precision \\
Cancellation of Rounding Errors \\
Rounding Errors Can Be Beneficial \\
Stability of an Algorithm Depends on the Problem \\
Rounding Errors Are Not Random \\
Designing Stable Algorithms \\
Misconceptions \\
Rounding Errors in Numerical Analysis \\
Floating Point Arithmetic \\
Floating Point Number System \\
Model of Arithmetic \\
IEEE Arithmetic \\
Aberrant Arithmetics \\
Exact Subtraction \\
Fused Multiply-Add Operation \\
Choice of Base and Distribution of Numbers \\
Statistical Distribution of Rounding Errors \\
Alternative Number Systems \\
Elementary Functions \\
Accuracy Tests \\
Inner and Outer Products \\
The Purpose of Rounding Error Analysis \\
Running Error Analysis \\
Notation for Error Analysis \\
Matrix Multiplication \\
Complex Arithmetic \\
Miscellany \\
Error Analysis Demystified \\
Other Approaches \\
Summation \\
Summation Methods \\
Error Analysis \\
Compensated Summation \\
Other Summation Methods \\
Statistical Estimates of Accuracy \\
Choice of Method \\
Polynomials \\
Horner's Method \\
Evaluating Derivatives \\
The Newton Form and Polynomial Interpolation \\
Matrix Polynomials \\
Norms \\
Vector Norms",
}
@Article{Hong:1996:NMM,
author = "Seong-Min Hong and Sang-Yeop Oh and Hyunsoo Yoon",
title = "New Modular Multiplication Algorithms for Fast Modular
Exponentiation",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1070",
pages = "166--??",
year = "1996",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Feb 4 12:02:22 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1070.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1070/10700166.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1070/10700166.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Hyvoenen:1996:SCE,
author = "E. Hyvoenen and S. De Pascale",
title = "Shared Computations for Efficient Interval Functions
Evaluation",
crossref = "Alefeld:1996:SCV",
pages = "38--44",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Inacio:1996:DDF,
author = "Christopher Inacio and Denise Ombres",
title = "The {DSP} decision: fixed point or floating?",
journal = j-IEEE-SPECTRUM,
volume = "33",
number = "9",
pages = "72--74",
month = sep,
year = "1996",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/6.535397",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Sep 01 16:15:25 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
}
@Article{ISO:1996:TRF,
author = "{ISO\slash IEC JTC1\slash SC22\slash WG5 --- N1231}",
title = "Technical report for floating-point exception
handling",
journal = j-FORTRAN-FORUM,
volume = "15",
number = "3",
pages = "1--28",
month = dec,
year = "1996",
CODEN = "????",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Wed Feb 6 18:50:06 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "7th October 1996.",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "47",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@Article{Ito:1996:SRI,
author = "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
title = "Square rooting by iterative multiply-additions",
journal = j-INFO-PROC-LETT,
volume = "60",
number = "5",
pages = "267--269",
day = "8",
month = dec,
year = "1996",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68M07",
MRnumber = "97i:68014",
bibdate = "Wed Nov 11 12:16:26 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C4130 (Interpolation and function approximation);
C5230 (Digital arithmetic methods)",
corpsource = "Department of Inf. Sci., Kyoto University, Japan",
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "computer arithmetic; convergence of numerical methods;
digital arithmetic; iterative methods; iterative
multiply-additions; linear converging ratio;
multiplicative methods; Newton--Raphson method;
read-only storage; ROM sizes; square root algorithm",
treatment = "T Theoretical or Mathematical",
}
@Article{Jayasuriya:1996:MAU,
author = "Kumara Jayasuriya",
title = "Multiprecision arithmetic using fast {Hartley}
transforms",
journal = j-APPL-MATH-COMP,
volume = "75",
number = "2--3",
pages = "239--251",
day = "15",
month = mar,
year = "1996",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/0096-3003(96)90067-3",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Nov 20 21:02:36 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0096300396900673",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Jessani:1996:FPU,
author = "R. M. Jessani and C. H. Olson",
title = "The floating point unit of the {PowerPC 603e}
microprocessor",
journal = j-IBM-JRD,
volume = "40",
number = "5",
pages = "559--566",
month = sep,
year = "1996",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Mar 25 14:26:59 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.almaden.ibm.com/journal/rd40-5.html#four",
abstract = "The IBM PowerPC 603e* floating-point unit (FPU) is an
on-chip functional unit to support IEEE 754 standard
single- and double-precision binary floating-point
arithmetic operations. The design objectives are to be
a low-cost, low-power, high-performance engine in a
single-chip superscalar microprocessor. Using less than
15 mm$^2$ of the available silicon area on the chip
(the size of the PowerPC 603e microprocessor is 98
mm$^2$) and operating at the peak clock frequency of
100 MHz, an average single-pumping multiply-add-fuse
instruction has one-cycle throughput and four-cycle
latency. An average double-pumping multiply-add-fuse
instruction has two-cycle throughput and five-cycle
latency. The estimated performance at 100 MHz is 105
against the SPECfp92** benchmark.",
acknowledgement = ack-nhfb,
classcodes = "B1265F (Microprocessors and microcomputers); C5130
(Microprocessor chips); C5230 (Digital arithmetic
methods)",
corpsource = "Somerset Design Center, Motorola Inc., Austin, TX,
USA",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "add-fuse instruction; design objectives; digital
arithmetic; double-pumping multiply-add-fuse; floating
point unit; functional unit; IEEE 754 standard;
instruction; microprocessor chips; on-chip; peak clock
frequency; PowerPC 603e microprocessor; silicon area;
single-pumping multiply-",
treatment = "A Application; P Practical",
xxlibnote = "Issue missing from UofUtah Marriott Library",
}
@InProceedings{Jullien:1996:VDS,
author = "Graham A. Jullien",
title = "{VLSI} Digital Signal Processing: Some Arithmetic
Issues",
crossref = "Luk:1996:PSC",
pages = "1--13",
year = "1996",
DOI = "https://doi.org/10.1117/12.255423",
bibdate = "Tue Jun 14 18:18:32 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.atips.ca/research/documents/ca/aa/1996_keynote.pdf",
acknowledgement = ack-nhfb,
remark = "Keynote address: VLSI Arithmetic and DSP
Implementations.",
}
@Misc{Kahan:1996:BEC,
author = "W. Kahan",
title = "The baleful effect of computer benchmarks upon applied
mathematics, physics, and chemistry",
howpublished = "World-Wide Web document.",
year = "1996",
bibdate = "Sat Apr 28 18:52:17 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/baleful.ps",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:1996:LNS,
author = "W. Kahan",
title = "Lecture notes on the status of {IEEE Standard 754} for
binary floating-point arithmetic",
howpublished = "World-Wide Web document.",
year = "1996",
bibdate = "Sat Apr 28 18:52:17 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps",
acknowledgement = ack-nhfb,
}
@Unpublished{Kahan:1996:WCY,
author = "W. Kahan",
key = "Kah96a",
title = "What can you learn about floating-point arithmetic in
one hour?",
institution = inst-BERKELEY-EECS,
address = inst-BERKELEY-EECS:adr,
pages = "23",
year = "1996",
bibdate = "Mon Apr 25 17:58:22 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Postscript version accessible electronically at
\path=http://http.cs.berkeley.edu/~wkahan/ieee754status=.",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/cs267fp.ps",
acknowledgement = ack-nhfb,
}
@Article{Kalantari:1996:HOI,
author = "B. Kalantari and I. Kalantari",
title = "High order iterative methods for approximating square
roots",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "2",
pages = "395--399",
month = jun,
year = "1996",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01731991",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D15 (65H99)",
MRnumber = "97k:65039",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Kalliojarvi:1996:REB,
author = "K. Kalliojarvi and J. Astola",
title = "Roundoff errors in block-floating-point systems",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "44",
number = "4",
pages = "783--790",
month = apr,
year = "1996",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "Block-floating-point representation is a special case
of floating-point representation, where several numbers
have a joint exponent term. In this paper, roundoff
errors in signal processing systems utilizing
block-floating-point representation are \ldots{}",
}
@Book{Kane:1996:PRA,
author = "Gerry Kane",
title = "{PA-RISC 2.0} Architecture",
publisher = pub-PHPTR,
address = pub-PHPTR:adr,
pages = "various",
year = "1996",
ISBN = "0-13-182734-0",
ISBN-13 = "978-0-13-182734-9",
LCCN = "QA76.8.H48K36 1996",
bibdate = "Tue Jan 09 12:34:37 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$34.40",
URL = "http://devresource.hp.com/devresource/Docs/Refs/PA2_0/index.html;
http://devresource.hp.com/devresource/Docs/Refs/PA2_0/updates/index.html",
abstract = "This is the authoritative definition of
Hewlett-Packard's 2.0 PA-RISC architecture, one of the
most mature and efficient RISC (Reduced Instruction Set
Computer) processor architectures in the industry.
PA-RISC is the foundation for machines proving
especially well-suited for such markets as high
performance graphics, mission critical transaction
processing, and emerging multimedia applications such
as interactive video services.",
acknowledgement = ack-nhfb,
keywords = "Hewlett--Packard computers; PA-RISC microprocessors",
tableofcontents = "1: Overview \\
2: Processing Resources \\
3: Addressing and Access Control \\
4: Control Flow \\
5: Interruptions \\
6: Instruction Set Overview \\
7: Instruction Descriptions \\
8: Floating-point Coprocessor \\
9: Floating-Point Instruction Set \\
10: Floating-Point Exceptions \\
11: Performance Monitor Coprocessor \\
B: Instruction Formats \\
C: Operation Codes \\
D: Conditions \\
E: Instruction Notation Control Structures \\
F: TLB and Cache Control \\
G: Memory Ordering Model \\
H: Address Formation Details \\
I: Programming Notes \\
PA-RISC 2 Instruction Completers and Pseudo-Ops",
}
@Article{Katti:1996:NRA,
author = "Rajendra S. Katti",
title = "A new residue arithmetic error correction scheme",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "1",
pages = "13--19",
month = jan,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.481482",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68M07",
MRnumber = "MR1372160 (96j:68011)",
bibdate = "Wed Jul 6 19:47:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=481482",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kearfott:1996:OPI,
author = "R. B. Kearfott and X. Shi",
title = "Optimal Preconditioners for Interval {Gauss--Seidel}
Methods",
crossref = "Alefeld:1996:SCV",
pages = "173--178",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Kearfott:1996:TNS,
author = "R. B. Kearfott",
title = "Treating Non-Smooth Functions as Smooth Functions in
Global Optimization and Nonlinear Systems Solvers",
crossref = "Alefeld:1996:SCV",
pages = "160--172",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Koeber:1996:IIF,
author = "M. Koeber",
title = "Inclusion of the Inverse of a Functions in $n$
Variables",
crossref = "Alefeld:1996:SCV",
pages = "179--185",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Kowaleski:1996:DEP,
author = "J. A. Kowaleski and G. M. Wolrich and T. C. Fischer
and R. J. Dupcak and P. L. Kroesen and T. Pham and A.
Olesin",
title = "A dual execution pipelined floating-point {CMOS}
processor",
crossref = "Wuorinen:1996:DTP",
pages = "358--359",
year = "1996",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-sfo # " and " # ack-nhfb,
}
@InProceedings{Kraemer:1996:CNI,
author = "W. Kraemer and S. Wedner",
title = "Computing Narrow Inclusions for {Cauchy} Principal
Value Integrals",
crossref = "Alefeld:1996:SCV",
pages = "45--51",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Kreinovich:1996:CCI,
author = "V. Kreinovich and A. Lakeyev and J. Rohn",
title = "Computational Complexity of Interval Algebraic
Problems: Some Are Feasible and Some Are
Computationally Intractable --- a Survey",
crossref = "Alefeld:1996:SCV",
pages = "293--306",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Ley:1996:PDU,
author = "Eduardo Ley",
title = "On the Peculiar Distribution of the {U.S.} Stock
Indexes' Digits",
journal = j-AMER-STAT,
volume = "50",
number = "4",
pages = "311--313",
month = nov,
year = "1996",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Mon Nov 14 15:09:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2684926",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@InProceedings{Li:1996:NNR,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the {IEEE} International Conference on
Computer Design: {VLSI} in Computers and Processors:
{ICCD '96}",
title = "A new non-restoring square root algorithm and its
{VLSI} implementations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "538--544",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We present a new non-restoring square root algorithm
that is very efficient to implement. The new algorithm
presented here has the following features unlike other
square root algorithms. First, the focus of the
``non-restoring'' is on the {\&} \ldots{}",
}
@TechReport{Lions:1996:AFF,
author = "Jacques-Louis Lions and Mauro Balduccini and Yvan
Choquer and Remy Hergott and Bernard Humbert and Eric
Lefort",
title = "{Ariane 5 Flight 501} failure, report by the {Inquiry
Board}",
type = "Technical Report",
institution = "European Space Agency",
address = "Paris, France",
year = "1996",
bibdate = "Sat Apr 01 07:39:11 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From the foreword: ``On 4 June 1996, the maiden flight
of the Ariane 5 launcher ended in a failure. Only about
40 seconds after initiation of the flight sequence, at
an altitude of about 3700 m, the launcher veered off
its flight path, broke up and exploded. Engineers from
the Ariane 5 project teams of CNES and Industry
immediately started to investigate the failure.'' From
the report: ``The internal SRI software exception was
caused during execution of a data conversion from
64-bit floating point to 16-bit signed integer value.
The floating point number which was converted had a
value greater than what could be represented by a
16-bit signed integer. This resulted in an Operand
Error. The data conversion instructions (in Ada code)
were not protected from causing an Operand Error,
although other conversions of comparable variables in
the same place in the code were protected.''",
URL = "http://sunnyday.mit.edu/accidents/Ariane5accidentreport.html",
acknowledgement = ack-nhfb,
remark = "Report of an arithmetic error that put an expensive
space missile off course, requiring its destruction in
the air. Presumably-reliable code in Ada adapted from
an earlier missile generated had not been updated for
the new design.",
}
@Article{Lo:1996:CBC,
author = "Jien-Chung Lo and S. Thanawastien and T. R. N. Rao",
title = "Correction to {``Berger Check Prediction for Array
Multipliers and Array Dividers''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "3",
pages = "383--383",
month = mar,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1996.485579",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:10 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See \cite{Lo:1993:BCP}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485579",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Louca:1996:IIS,
author = "L. Louca and T. A. Cook and W. H. Johnson",
title = "Implementation of {IEEE} single precision floating
point addition and multiplication on {FPGAs}",
crossref = "Pocek:1996:ISF",
pages = "107--116",
year = "1996",
DOI = "https://doi.org/10.1109/FPGA.1996.564761",
bibdate = "Sat Oct 9 12:52:57 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point operations are hard to implement on
FPGAs because of the complexity of their algorithms. On
the other hand, many scientific problems require
floating point arithmetic with high levels of accuracy
in their calculations. Therefore, we have explored FPGA
implementations of addition and multiplication for IEEE
single precision floating-point numbers. Customizations
were performed where this was possible in order to save
chip area, or get the most out of our prototype board.
The implementations tradeoff area and speed for
accuracy. The adder is a bit-parallel adder, and the
multiplier is a digit-serial multiplier. Prototypes
have been implemented on Altera FLEX8000s, and peak
rates of 7 MFlops for 32-bit addition and 2.3 MFlops
for 32-bit multiplication have been obtained.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lozier:1996:EBL,
author = "Daniel W. Lozier and P. R. Turner",
title = "Error-Bounding in Level-Index Computer Arithmetic",
crossref = "Alefeld:1996:NME",
pages = "138--145",
year = "1996",
bibdate = "Fri Jul 09 07:20:57 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://math.nist.gov/acmd/Staff/DLozier/publications/oldenburg95.ps.Z",
acknowledgement = ack-nhfb,
}
@InProceedings{Luther:1996:CAG,
author = "W. Luther and W. Otten",
title = "The Complex Arithmetic-Geometric Mean and
Multiple-Precision Matrix Functions",
crossref = "Alefeld:1996:SCV",
pages = "52--58",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{MacDonald:1996:NSS,
author = "D. A. MacDonald",
title = "A note on the summation of slowly convergent
alternating series",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "4",
pages = "766--774",
month = dec,
year = "1996",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01733790",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "40A25 (65B10 65B15)",
MRnumber = "98c:40001",
MRreviewer = "Vanna Zanelli",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=4&spage=766",
abstract = "The kth term of the infinite series $ \sum
\nolimits_{k = 0}^\infty {( - 1)^k [\ln (k + 2)]^{ -
0.1} } $ is larger than $ 0.5 $ whenever $ k < k_0 $,
where $ k_0 + 1 = e^{1024} $. To sum this series
correct to order $ 10^{-1} $ using direct summation
seems an impossible task, notwithstanding the power of
modern computers. This note will present an alternative
approach to those classical methods (the Euler
transformation is one) which can accurately sum such
series. The theory to be presented has the added
advantage of providing accurate bounds for the error in
the approximate result. The method used will be
Euler--Maclaurin summation, revitalised by computer
algebra.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point summation; Euler--Maclaurin
formula; slowly convergent alternating series;
summation",
}
@Article{Macpherson:1996:RAP,
author = "George W. Macpherson",
title = "A reusable {Ada} package for scientific dimensional
integrity",
journal = j-SIGADA-LETTERS,
volume = "16",
number = "3",
pages = "56--69",
month = may # "\slash " # jun,
year = "1996",
CODEN = "AALEE5",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Sat Aug 9 09:05:57 MDT 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
acknowledgement = ack-nhfb,
classcodes = "A0650M (Computing devices and techniques); A0620F
(Measurement units); C7320 (Physics and chemistry
computing); C6130 (Data handling techniques); C5230
(Digital arithmetic methods)",
corpsource = "CACI Inc.-Federal, Colorado Springs, CO, USA",
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
keywords = "Ada; Ada programming language; arithmetic operations;
ASSIGN function; checking; computational reliability;
data integrity; declaration; digital arithmetic;
entries; exponents; floating point numeric value;
fundamental physical units; generic package;
information hiding; integer; length; limited private;
mass; multiplication operation; numeric; operator;
overloading; PHYSICAL QUANTITY type; physics computing;
relational operations; reusability; reusable Ada
package; scientific dimensional integrity; software;
software modifiability; software packages; software
reliability; software reusability; strong typing;
symbol creation; time; types; units; units
(measurement); values; variables",
treatment = "P Practical",
}
@Article{Maeder:1996:MPLa,
author = "Roman E. Maeder",
title = "The {Mathematica} Programmer: Long Integers: Basic
Arithmetic and Data Types",
journal = j-MATHEMATICA-J,
volume = "6",
number = "2",
pages = "32--40",
month = "Spring",
year = "1996",
CODEN = "????",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
ISSN-L = "1047-5974",
bibdate = "Sat Nov 6 13:34:10 MDT 2010",
bibsource = "http://www.mathematica-journal.com/issue/v6i2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mathematica-journal.com/issue/v6i2/columns/maeder/index.html;
http://www.mathematica-journal.com/issue/v6i2/columns/maeder/maeder62.pdf",
abstract = "Long-integer arithmetic is a fundamental part of
symbolic computation. This article introduces the
fundamentals of long-integer calculations by
implementing a prototype system in Mathematica. Our
code is strictly procedural and could be translated
into C or assembler easily. The tools needed are arrays
that behave like arrays in procedural languages, as
well as tools for software testing and debugging.",
acknowledgement = ack-nhfb,
fjournal = "Mathematica Journal",
journal-URL = "http://www.mathematica-journal.com/",
}
@Article{Maeder:1996:MPLb,
author = "Roman E. Maeder",
title = "The {Mathematica} Programmer: Long Integers: Efficient
Algorithms",
journal = j-MATHEMATICA-J,
volume = "6",
number = "3",
pages = "37--43",
month = "Summer",
year = "1996",
CODEN = "????",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
ISSN-L = "1047-5974",
bibdate = "Sat Nov 6 13:34:12 MDT 2010",
bibsource = "http://www.mathematica-journal.com/issue/v6i3/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mathematica-journal.com/issue/v6i3/columns/maeder/contents/63maeder.pdf;
http://www.mathematica-journal.com/issue/v6i3/columns/maeder/index.html",
abstract = "This is the second part of an article on long-integer
arithmetic. It discusses the data type for long
integers and investigates a few asymptotically
efficient algorithms for multiplication and division.
We will not discuss all our code in detail, but point
out a few important ideas.",
acknowledgement = ack-nhfb,
fjournal = "Mathematica Journal",
journal-URL = "http://www.mathematica-journal.com/",
}
@Article{Makino:1996:MBF,
author = "H. Makino and H. Suzuki and H. Morinaka and Y. Nakase
and K. Mashiko and T. Sumi",
title = "A {286 MHz} 64-b floating point multiplier with
enhanced {CG} operation",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "31",
number = "4",
pages = "504--513",
month = apr,
year = "1996",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "This paper presents a high speed 64-b floating point
(FP) multiplier that has a useful function for computer
graphics (CG). The critical path delay is minimized by
using high speed logic gates and limiting the stage
number of series transmission gate \ldots{}",
}
@MastersThesis{Manickavasagam:1996:ATI,
author = "SenthilKumar Manickavasagam",
title = "``$ a + b $'' arithmetic: theory and implementation",
type = "Thesis ({M.S.})",
school = "Electrical Engineering and Computer Science, Ohio
University",
address = "Athens, OH, USA",
pages = "xi + 152",
year = "1996",
bibdate = "Mon Mar 05 14:33:56 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Manning:1996:FS,
author = "Evan Manning",
title = "Floating-point Summation",
journal = j-CCCUJ,
volume = "14",
number = "9",
pages = "51--??",
month = sep,
year = "1996",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Wed Nov 6 07:30:58 MST 1996",
bibsource = "http://www.cuj.com/cbklist.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
keywords = "accurate floating-point summation",
}
@InProceedings{Markov:1996:FIA,
author = "S. M. Markov",
title = "On the Foundations of Interval Arithmetic",
crossref = "Alefeld:1996:SCV",
pages = "307--313",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Mayer:1996:SEI,
author = "G. Mayer",
title = "Success in Epsilon-Inflation",
crossref = "Alefeld:1996:SCV",
pages = "98--104",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Mikov:1996:LSA,
author = "Alexander I. Mikov",
title = "Large-scale addition of machine real numbers:
{Accuracy} estimates",
journal = j-THEOR-COMP-SCI,
volume = "162",
number = "1",
pages = "151--170",
day = "05",
month = aug,
year = "1996",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Mon Jul 19 22:20:05 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_free/browse/browse.cgi?year=1996&volume=162&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tcs1995.bib",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_sub/browse/browse.cgi?year=1996&volume=162&issue=1&aid=2194",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Department of Computer Science, Perm State University,
Russia",
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975/",
keywords = "accuracy estimates; digital arithmetic; floating-point
arithmetic; large-scale addition; machine real numbers;
positive independent random variables; random
variables; real distribution interval; roundoff error",
pubcountry = "Netherlands",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Miner:1996:VIC,
author = "Paul S. Miner and James F. {Leathrum, Jr.}",
title = "Verification of {IEEE} Compliant Subtractive Division
Algorithms",
crossref = "Srivas:1996:FMC",
pages = "64--78",
year = "1996",
bibdate = "Wed Nov 24 12:01:07 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ece.odu.edu/~leathrum/Formal_Methods/computer_arithmetic/fmcad.ps",
acknowledgement = ack-nhfb,
remark = "fmcad.ps actually contains two separate versions of
this article, and must be split manually before
printing.",
}
@TechReport{Moler:1996:CCF,
author = "Cleve B. Moler",
title = "{Cleve}'s Corner: {Floating} points: {IEEE Standard}
unifies arithmetic model",
type = "Technical note",
institution = inst-MATHWORKS,
address = inst-MATHWORKS:adr,
pages = "3",
month = "Fall",
year = "1996",
bibdate = "Thu Oct 24 07:16:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mathworks.com/company/newsletter/pdf/Fall96Cleve.pdf",
acknowledgement = ack-nhfb,
keywords = "Matlab",
}
@InProceedings{Mraz:1996:ELB,
author = "F. Mraz",
title = "The Exact Lower Bound of Optimal Values in Interval
{LP}",
crossref = "Alefeld:1996:SCV",
pages = "214--220",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Mrozek:1996:IPC,
author = "M. Mrozek",
title = "Inheritable Properties and Computer Assisted Proofs in
Dynamics",
crossref = "Alefeld:1996:SCV",
pages = "245--257",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Muller:1996:CES,
author = "Michael M{\"u}ller and Christine R{\"u}b and Wolfgang
R{\"u}lling",
title = "A circuit for exact summation of floating-point
numbers",
journal = j-INFO-PROC-LETT,
volume = "57",
number = "3",
pages = "159--163",
day = "12",
month = feb,
year = "1996",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sat Nov 7 17:55:43 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "accurate floating-point summation",
}
@InProceedings{Muller:1996:TER,
author = "Jean-Michel Muller and A. Tisserand",
title = "Towards Exact Rounding of the Elementary Functions",
crossref = "Alefeld:1996:SCV",
pages = "59--71",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Nakao:1996:GEB,
author = "M. T. Nakao and N. Yamamoto and Y. Watanabe",
title = "Guaranteed Error Bounds for Finite Element Solutions
of the {Stokes} Problem",
crossref = "Alefeld:1996:SCV",
pages = "258--264",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Nonnenmacher:1996:LCS,
author = "A. Nonnenmacher and D. A. Mlynski",
title = "Liquid Crystal Simulation Using Automatic
Differentiation and Interval Arithmetic",
crossref = "Alefeld:1996:SCV",
pages = "334--340",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@PhdThesis{Oberman:1996:DIH,
author = "Stuart Franklin Oberman",
title = "Design Issues in High Performance Floating Point
Arithmetic Units",
type = "Thesis ({Ph.D.})",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "xiv + 151",
month = nov,
year = "1996",
bibdate = "Fri Mar 27 10:14:18 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://umunhum.stanford.edu/tr/oberman.nov96.thesis.ps.Z",
acknowledgement = ack-nhfb,
}
@TechReport{Oberman:1996:FIR,
author = "Stuart F. Oberman and Michael J. Flynn",
title = "Fast {IEEE} Rounding for Division by Functional
Iteration",
type = "Technical Report",
number = "CSL-TR-96-700",
institution = "Stanford University",
address = "Stanford, CA, USA",
pages = "v + 16",
month = jul,
year = "1996",
bibdate = "Sun Dec 10 13:50:59 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://i.stanford.edu/pub/cstr/reports/csl/tr/96/700/CSL-TR-96-700.pdf",
abstract = "A class of high performance division algorithms is
functional iteration. Division by functional iteration
uses multiplication as the fundamental operator. The
main advantage of division by functional iteration is
quadratic convergence to the quotient. However, unlike
non-restoring division algorithms such as SRT division,
functional iteration does not directly provide a final
remainder. This makes fast and exact rounding
difficult. This paper clarifies the methodology for
correct IEEE compliant rounding for
quadratically-converging division algorithms. It
proposes an extension to previously reported techniques
of using extended precision in the computation to
reduce the frequency of back multiplications required
to obtain the final remainder. Further, a technique
applicable to all IEEE rounding modes is presented
which replaces the final subtraction for remainder
computation with very simple combinational logic.",
acknowledgement = ack-nhfb,
keywords = "division, Goldschmidt's algorithm, IEEE rounding,
Newton--Raphson, variable latency",
}
@InProceedings{Oberman:1996:IDO,
author = "Stuart F. Oberman and Michael J. Flynn",
title = "Implementing Division and Other Floating-Point
Operations: a System Perspective",
crossref = "Alefeld:1996:SCV",
pages = "18--24",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "ftp://arith.stanford.edu/tr/scan_system.ps.Z",
acknowledgement = ack-nhfb,
summary = "Modern computer applications have increased in their
computation complexity in recent years. The
industry-wide usage of performance benchmarks, such as
SPECmarks forces processor designers to pay particular
attention to floating-point (FP) computation.
Furthermore, special purpose applications, such as high
performance graphics rendering systems, have placed
further demands on processors. The development of high
speed FP hardware is a requirement to meet these
increasing computation demands.",
}
@Article{Oberman:1996:RDL,
author = "S. F. Oberman and M. J. Flynn",
title = "Reducing division latency with reciprocal caches",
journal = j-RELIABLE-COMPUTING,
volume = "2",
number = "2",
pages = "147--153",
month = apr,
year = "1996",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Thu Apr 2 08:38:35 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://arith.stanford.edu/tr/scan_recip.ps.Z",
acknowledgement = ack-sfo # " and " # ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Oberman:1996:VLP,
author = "S. F. Oberman and M. J. Flynn",
title = "A Variable Latency Pipelined Floating-Point Adder",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1124",
pages = "183--192",
year = "1996",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Mar 27 10:07:13 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://arith.stanford.edu/tr/fpadd_euro.ps.Z",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Oklobdzija:1996:MSO,
author = "V. G. Oklobdzija and D. Villeger and S. S. Liu",
title = "A method for speed optimized partial product reduction
and generation of fast parallel multipliers using an
algorithmic approach",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "3",
pages = "294--306",
month = mar,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.485568",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485568",
acknowledgement = ack-sfo # " and " # ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Paar:1996:NAP,
author = "C. Paar",
title = "A new architecture for a parallel finite field
multiplier with low complexity based on composite
fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "7",
pages = "856--861",
month = jul,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.508323",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=508323",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Parhami:1996:CHS,
author = "B. Parhami and S. Kawahito and M. Ishida and T.
Nakamura and M. Kameyama and T. Higuchi",
title = "Comments on {``High-speed area-efficient multiplier
design using multiple-valued current-mode circuits''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "5",
pages = "637--639",
month = may,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.509918",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:11 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See \cite{Kawahito:1994:HSA}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509918",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Park:1996:OHW,
author = "Edwards Park",
title = "The Object at Hand: What a difference the {Difference
Engine} made: from {Charles Babbage}'s calculator
emerged today's computer",
journal = j-SMITHSONIAN,
volume = "26",
number = "11",
pages = "20--??",
day = "01",
month = feb,
year = "1996",
CODEN = "SMSNA5",
ISSN = "0037-7333 (print), 1930-5508 (electronic)",
ISSN-L = "0037-7333",
bibdate = "Fri Jun 21 14:38:22 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Smithsonian",
}
@Article{Park:1996:PAG,
author = "Taegeun Park",
title = "A Parallel Algorithm for Global Routing Using an
Associative Processor",
journal = j-J-PAR-DIST-COMP,
volume = "38",
number = "1",
pages = "51--62",
day = "10",
month = oct,
year = "1996",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1996.0128",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:19:01 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production/pdf",
acknowledgement = ack-nhfb,
classification = "C1180 (Optimisation techniques); C4240C
(Computational complexity); C4240P (Parallel
programming and algorithm theory); C5230 (Digital
arithmetic methods); C5340 (Associative storage)",
corpsource = "Design Lab., Hyundai Electron. Ind., Kyoungki, South
Korea",
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
keywords = "addressable storage; array; associative processing;
associative processor; benchmark problems;
computational complexity; content-; content-addressable
memory; control section; digital arithmetic; global
routing; layout process; matching; minimisation;
minimum-; multiple data device; O(d) complexity;
parallel algorithm; parallel algorithms; parallel
arithmetic; problem; processing elements; randomly
generated data; row logic; rudimentary logic;
search-oriented applications; selective; single
instruction; weight path",
treatment = "A Application; P Practical",
}
@InProceedings{Petunin:1996:UMI,
author = "D. Petunin and A. Semenov",
title = "The Use of Multi-Intervals in the {UniCalc} Solver",
crossref = "Alefeld:1996:SCV",
pages = "91--97",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Plum:1996:ETP,
author = "M. Plum",
title = "Enclosure for Two-Point Boundary Value Problems Near
Bifurcation Points",
crossref = "Alefeld:1996:SCV",
pages = "265--279",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Popova:1996:IOI,
author = "E. D. Popova",
title = "Interval operations involving {NaNs}",
journal = j-RELIABLE-COMPUTING,
volume = "2",
number = "2",
pages = "161--166",
month = jun,
year = "1996",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Feb 4 17:45:55 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Posch:1996:DRN,
author = "K. C. Posch and R. Posch",
title = "Division in residue number systems involving length
indicators",
journal = j-J-COMPUT-APPL-MATH,
volume = "66",
number = "1--2",
pages = "411--419",
day = "31",
month = jan,
year = "1996",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:27:48 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042795001646",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Price:1996:RA,
author = "David T. Price",
title = "Remark on {Algorithm 715}",
journal = j-TOMS,
volume = "22",
number = "2",
pages = "258--258",
month = jun,
year = "1996",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/229473.236186",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Cody:1993:ASE}",
URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p258-price/",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Rao:1996:NHS,
author = "Vishwas M. Rao and Behrouz Nowrouzian",
title = "Novel high-speed bit-parallel multiply accumulate
arithmetic architecture",
crossref = "Luk:1996:PSC",
pages = "26--38",
year = "1996",
DOI = "https://doi.org/10.1117/12.255442",
bibdate = "Tue Jun 14 18:26:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rao:1996:RTS,
author = "V. M. Rao and B. Nowrouzian",
booktitle = "Canadian Conference on Electrical and Computer
Engineering. 26--29 May 1996",
title = "Rounding techniques for signed binary arithmetic",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "294--297",
year = "1996",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper is concerned with the derivation of the
relationship that exists between the number truncation
in two's complement (TC) arithmetic and the
corresponding truncation in signed-binary (SB)
arithmetic. The resulting relationship is subsequently
exploited and applied to the development of a pair of
novel techniques for SB rounding. These techniques are
then translated into algorithm suitable for two-level
logic implementation. Finally, the resulting algorithms
are applied to the design and implementation of a
high-speed SB-kernel based TC multiply-accumulate
arithmetic architecture.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ratz:1996:BRS,
author = "D. Ratz",
title = "On Branching Rules in Second-Order Branch-and-Bound
Methods for Global Optimization",
crossref = "Alefeld:1996:SCV",
pages = "221--227",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Reid:1996:RFF,
author = "J. K. Reid",
title = "Remark on ``{Fast Floating-Point Processing in Common
Lisp}''",
journal = j-TOMS,
volume = "22",
number = "4",
pages = "496--497",
month = dec,
year = "1996",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/235815.235824",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 9 10:21:08 1999",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fateman:1995:FFP}.",
URL = "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p496-reid/",
abstract = "We explain why we feel that the comparison between
Common Lisp and Fortran in a recent article by Fateman
et al. in this journal is not entirely fair.",
acknowledgement = ack-nhfb # " and " # ack-rfb,
affiliation = "Rutherford Appleton Lab",
classification = "721.1; 723.1.1; 902.2; 921.6",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
journalabr = "ACM Trans Math Software",
keywords = "Common Lisp language; Control structures; Digital
arithmetic; Floating point computation; fortran
(programming language); Lisp (programming language);
Standards",
subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, General,
Standards. {\bf D.3.3}: Software, PROGRAMMING
LANGUAGES, Language Constructs and Features, Modules,
packages.",
}
@InProceedings{Rump:1996:DBR,
author = "Siegfried M. Rump",
title = "The Distance Between Regularity and Strong
Regularity",
crossref = "Alefeld:1996:SCV",
pages = "105--117",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Sarma:1996:HRT,
author = "D. Das Sarma and D. W. Matula",
title = "Hardware Reciprocal Table Compression\slash
Decompression Techniques",
crossref = "Alefeld:1996:SCV",
pages = "11--17",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@TechReport{Saunders:1996:TGF,
author = "Kevin Saunders",
title = "Third generation floating point {DSP} design",
type = "Report",
number = "800 XY/N-1",
institution = "University of Bristol. Department of Aerospace
Engineering",
address = "Bristol, UK",
year = "1996",
bibdate = "Thu May 09 08:52:59 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Schatzman:1996:ADF,
author = "James C. Schatzman",
title = "Accuracy of the discrete {Fourier} transform and the
fast {Fourier} transform",
journal = j-SIAM-J-SCI-COMP,
volume = "17",
number = "5",
pages = "1150--1166",
month = sep,
year = "1996",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827593247023",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65T20 (42A65 42C10 68Q25)",
MRnumber = "97e:65155",
bibdate = "Fri Dec 4 14:47:53 MST 1998",
bibsource = "http://epubs.siam.org/toc/sjoce3/17/5;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/24702",
acknowledgement = ack-nhfb,
ajournal = "SIAM J. Sci. Comput.",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
remark = "This article analyzes errors in computing
one-dimensional Fourier transforms, the fast way (FFT)
and the slow way. The author identifies two main causes
of accuracy loss in the computed transforms:
(1) inaccurate sine and cosine functions, and (2)
failure to use accurate summation methods, such as
Kahan's compensated summation.",
}
@InProceedings{Schulte:1996:HDI,
author = "M. J. Schulte and K. C. Bickerstaff and E. E.
{Swartzlander, Jr.}",
editor = "????",
booktitle = "Proceedings of the {II} Workshop on Computer
Arithmetic, Interval and Symbolic Computation, Recife,
Brazil, August, 1996",
title = "Hardware Designs for Interval Multiplication",
publisher = "????",
address = "????",
pages = "85--87",
year = "1996",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 04 10:51:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1996:PAS,
author = "M. J. Schulte and E. E. Swartzlander",
title = "A Processor for Accurate, Self-Validating Computing",
crossref = "Alefeld:1996:SCV",
pages = "25--31",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Schwandt:1996:GCI,
author = "H. Schwandt",
title = "Globally Convergent Iterative Domain Decomposition
Methods for the Parallel Solution of a Class of
Nonlinear Systems of Equations",
crossref = "Alefeld:1996:SCV",
pages = "280--286",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Schwarz:1996:HSA,
author = "Eric M. Schwarz and Michael J. Flynn",
title = "Hardware Starting Approximation Method and Its
Application to the Square Root Operation",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "12",
pages = "1356--1369",
month = dec,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.545966",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=545966",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "Quadratically converging algorithms for high-order
arithmetic operations typically are accelerated by a
starting approximation. The higher the precision of the
starting approximation, the less number of iterations
required for convergence. \ldots{}",
}
@Article{Sezgin:1996:SIR,
author = "F. Sezgin",
title = "Some improvements for a random number generator with
single-precision floating-point arithmetic",
journal = j-COMP-GEOSCI,
volume = "22",
number = "4",
publisher = "Elsevier Science",
pages = "453--455",
month = may,
year = "1996",
CODEN = "CGEODT, CGOSDN",
ISSN = "0098-3004 (print), 1873-7803 (electronic)",
ISSN-L = "0098-3004",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Computers and Geosciences",
pagecount = "3",
}
@InProceedings{Shary:1996:NAA,
author = "S. P. Shary",
title = "A New Approach to the Analysis of Static Systems Under
Internal Uncertainty",
crossref = "Alefeld:1996:SCV",
pages = "118--132",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@TechReport{Shewchuk:1996:APF,
author = "Jonathan Richard Shewchuk",
title = "Adaptive precision floating-point arithmetic and fast
robust geometric predicates",
type = "Report",
number = "CMU-CS-96-140",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
pages = "53",
year = "1996",
bibdate = "Fri Jan 06 11:59:17 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Exact computer arithmetic has a variety of uses
including, but not limited to, the robust
implementation of geometric algorithms. This report has
three purposes. The first is to offer fast
software-level algorithms for exact addition and
multiplication of arbitrary precision floating-point
values. The second is to propose a technique for
adaptive-precision arithmetic that can often speed
these algorithms when one wishes to perform
multiprecision calculations that do not always require
exact arithmetic, but must satisfy some error bound.
The third is to provide a practical demonstration of
these techniques, in the form of implementations of
several common geometric calculations whose required
degree of accuracy depends on their inputs. These
robust geometric predicates are adaptive; their running
time depends on the degree of uncertainty of the
result, and is usually small.\par
These algorithms work on computers whose floating-point
arithmetic uses radix two and exact rounding, including
machines complying with the IEEE 754 standard. The
inputs to the predicates may be arbitrary single or
double precision floating-point numbers. C code is
publicly available for the 2D and 3D orientation and
incircle tests, and robust Delaunay triangulation using
these tests. Timings of the implementations demonstrate
their effectiveness.",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; multiple-precision
arithmetic",
}
@InProceedings{Shewchuk:1996:RAF,
author = "Jonathan Richard Shewchuk",
booktitle = "{Proceedings of the 12th Annual ACM Symposium on
Computational Geometry}",
title = "Robust Adaptive Floating-Point Geometric Predicates",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "141--150",
year = "1996",
DOI = "https://doi.org/10.1145/237218.237337",
bibdate = "Sat May 1 15:33:15 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-predicates.ps",
acknowledgement = ack-nhfb,
}
@Article{Shewchuk:1996:TEQ,
author = "J. R. Shewchuk",
editor = "Ming C. Lin and Dinesh Manocha",
booktitle = "Applied Computational Geometry: Towards Geometric
Engineering",
title = "{Triangle}: Engineering a {$2$D} Quality Mesh
Generator and {Delaunay} Triangulator",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1148",
pages = "203--222",
year = "1996",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/BFb0014497",
ISBN = "3-540-61785-X (softcover), 3-540-70680-1 (e-book)",
ISBN-13 = "978-3-540-61785-3 (softcover), 978-3-540-70680-9
(e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Dec 21 09:47:26 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs1996b.bib",
URL = "https://link.springer.com/chapter/10.1007/BFb0014497",
acknowledgement = ack-nhfb,
book-URL = "https://link.springer.com/book/10.1007/BFb0014474",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "Delaunay triangulation; exact arithmetic; refinement
algorithm; refinement stage; roundoff error",
remark = "First ACM Workshop on Applied Computational
Geometry.",
}
@InProceedings{Shokin:1996:IPI,
author = "Y. I. Shokin",
title = "On Interval Problems, Interval Algorithms and Their
Computational Complexity",
crossref = "Alefeld:1996:SCV",
pages = "314--328",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Sinclair:1996:ORS,
author = "R. Sinclair",
title = "Optimization of reciprocals and square roots on the
{i860} microprocessor",
journal = j-INT-J-HIGH-SPEED-COMPUTING,
volume = "8",
number = "1",
pages = "57--64",
year = "1996",
CODEN = "IHSCEZ",
ISSN = "0129-0533",
bibdate = "Mon Feb 25 11:19:22 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Article1st database",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Speed Computing",
journal-URL = "http://www.worldscientific.com/worldscinet/ijhsc",
}
@Article{Singer:1996:EAP,
author = "Benjamin Singer and George Saon",
title = "An efficient algorithm for parallel integer
multiplication",
journal = j-J-NETW-COMPUT-APPL,
volume = "19",
number = "4",
pages = "415--418",
month = oct,
year = "1996",
CODEN = "JNCAF3",
ISSN = "1084-8045 (print), 1095-8592 (electronic)",
ISSN-L = "1084-8045",
bibdate = "Wed Jan 28 15:41:22 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jnetwcomputappl.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1084804596900296",
acknowledgement = ack-nhfb,
ajournal = "J. Netw. Comput. Appl.",
fjournal = "Journal of Network and Computer Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/10848045",
}
@Article{Soderquist:1996:AFT,
author = "Peter Soderquist and Miriam Leeser",
title = "Area and Performance Tradeoffs in Floating-Point
Divide and Square-Root Implementations",
journal = j-COMP-SURV,
volume = "28",
number = "3",
pages = "518--564",
month = sep,
year = "1996",
CODEN = "CMSVAN",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Wed Nov 13 06:52:01 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
}
@Article{Soderquist:1996:APT,
author = "Peter Soderquist and Miriam Leeser",
title = "Area and Performance Tradeoffs in Floating-Point
Divide and Square-Root Implementations",
journal = j-COMP-SURV,
volume = "28",
number = "3",
pages = "518--564",
month = sep,
year = "1996",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/243439.243481",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Thu Jun 19 09:54:32 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/surveys/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/surveys/1996-28-3/p518-soderquist/",
abstract = "Floating-point divide and square-root operations are
essential to many scientific and engineering
applications, and are required in all computer systems
that support the IEEE floating-point standard. Yet many
current microprocessors provide only weak support for
these operations. The latency and throughput of
division are typically far inferior to those of
floating-point addition and multiplication, and
square-root performance is often even lower. This
article argues the case for high-performance division
and square root. It also explains the algorithms and
implementations of the primary techniques, subtractive
and multiplicative methods, employed in microprocessor
floating-point units with their associated
area/performance tradeoffs. Case studies of
representative floating-point unit configurations are
presented, supported by simulation results using a
carefully selected benchmark, Givens rotation, to show
the dynamic performance impact of the various
implementation alternatives. The topology of the
implementation is found to be an important performance
factor. Multiplicative algorithms, such as the
Newton--Raphson method and Goldschmidt's algorithm, can
achieve low latencies. However, these implementations
serialize multiply, divide, and square root operations
through a single pipeline, which can lead to low
throughput. While this hardware sharing yields low size
requirements for baseline implementations,
lower-latency versions require many times more area.
For these reasons, multiplicative implementations are
best suited to cases where subtractive methods are
precluded by area constraints, and modest performance
on divide and square root operations is tolerable.
Subtractive algorithms, exemplified by radix-4 SRT and
radix-16 SRT, can be made to execute in parallel with
other floating-point operations.",
acknowledgement = ack-nhfb,
fjournal = "ACM Computing Surveys",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204",
keywords = "area and performance tradeoffs; arithmetic and logic
structures; computer arithmetic.; computer system
implementation; design studies. {\bf c.5.3}: computer
systems organization; design styles; division;
floating-point; FPU; general; microcomputers;
microprocessors. {\bf g.1.0}: mathematics of computing;
numerical analysis; parallel. {\bf c.4}: computer
systems organization; performance of systems; square
root; SRT; {\bf b.2.1}: hardware",
subject = "{\bf B.2.1}: Hardware, ARITHMETIC AND LOGIC
STRUCTURES, Design Styles, Parallel. {\bf C.4}:
Computer Systems Organization, PERFORMANCE OF SYSTEMS,
Design studies. {\bf C.5.3}: Computer Systems
Organization, COMPUTER SYSTEM IMPLEMENTATION,
Microcomputers, Microprocessors. {\bf G.1.0}:
Mathematics of Computing, NUMERICAL ANALYSIS, General,
Computer arithmetic.",
}
@InCollection{Steele:1996:EL,
author = "Guy L. {Steele Jr.} and Richard P. Gabriel",
title = "The evolution of {Lisp}",
crossref = "Bergin:1996:HPL",
pages = "233--330",
year = "1996",
bibdate = "Wed Jan 29 17:01:12 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "From \cite{Steele:2004:RHP}: ``In early 1971, he
[White] began to analyze the machine-language algorithm
used in the implementation of MacLisp (described in
this report) to convert PDP-10 floating-point numbers
into decimal notation.''",
}
@Book{Stewart:1996:ANA,
author = "G. W. (Gilbert W.) Stewart",
title = "Afternotes on numerical analysis: a series of lectures
on elementary numerical analysis presented at the
{University of Maryland at College Park} and recorded
after the fact",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "x + 200",
year = "1996",
DOI = "https://doi.org/10.1137/1.9781611971491",
ISBN = "0-89871-362-5 (paperback)",
ISBN-13 = "978-0-89871-362-6 (paperback)",
LCCN = "QA297 .S785 1996",
MRclass = "65-01",
MRnumber = "1372060",
bibdate = "Tue May 27 08:35:41 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0726/95047768-d.html;
http://www.loc.gov/catdir/enhancements/fy0726/95047768-t.html",
acknowledgement = ack-nhfb,
keywords = "numerical analysis",
subject = "Numerical analysis",
tableofcontents = "Part I. Nonlinear Equations \\
\\
Lecture 1. By the Dawn's Early Light \\
Interval Bisection \\
Relative Error \\
\\
Lecture 2. Newton's Method \\
Reciprocals and Square Roots \\
Local Convergence Analysis \\
Slow Death \\
\\
Lecture 3. A Quasi-Newton Method \\
Rates of Convergence \\
Iterating for a Fixed Point \\
Multiple Zeros \\
Ending with a Proposition \\
\\
Lecture 4. The Secant Method \\
Convergence \\
Rate of Convergence \\
Multipoint Methods \\
Muller's Method \\
The Linear-Fractional Method \\
\\
Lecture 5. A Hybrid Method \\
Errors, Accuracy, and Condition Numbers \\
\\
Part II. Computer Arithmetic: \\
\\
Lecture 6. Floating-Point Numbers \\
Overflow and Underflow \\
Rounding Error \\
Floating-point Arithmetic \\
\\
Lecture 7. Computing Sums \\
Backward Error Analysis \\
Perturbation Analysis \\
Cheap and Chippy Chopping \\
\\
Lecture 8. Cancellation \\
The Quadratic Equation \\
That Fatal Bit of Rounding Error \\
Envoi \\
\\
Part III. Linear Equations \\
\\
Lecture 9. Matrices, Vectors, and Scalars \\
Operations with Matrices \\
Rank-One Matrices \\
Partitioned Matrices \\
\\
Lecture 10. Theory of Linear Systems \\
Computational Generalities \\
Triangular Systems \\
Operation Counts \\
\\
Lecture 11. Memory Considerations \\
Row Oriented Algorithms \\
A Column Oriented Algorithm \\
General Observations on Row and Column Orientation \\
Basic Linear Algebra Subprograms \\
\\
Lecture 12. Positive Definite Matrices \\
The Cholesky Decomposition \\
Economics \\
\\
Lecture 13. Inner-Product Form of the Cholesky
Algorithm \\
Gaussian Elimination \\
\\
Lecture 14. Pivoting \\
BLAS \\
Upper Hessenberg and Tridiagonal Systems \\
\\
Lecture 15. Vector Norms \\
Matrix Norms \\
Relative Error \\
Sensitivity of Linear Systems \\
\\
Lecture 16. The Condition of Linear Systems \\
Artificial Ill Conditioning \\
Rounding Error and Gaussian Elimination \\
Comments on the Analysis \\
\\
Lecture 17. The Wonderful Residual: A Project \\
Introduction \\
More on Norms \\
The Wonderful Residual \\
Matrices with Known Condition \\
Invert and Multiply \\
Cramer's Rule \\
Submission \\
\\
Part IV. Polynomial Interpolation \\
\\
Lecture 18. Quadratic Interpolation \\
Shifting \\
Polynomial Interpolation \\
Lagrange Polynomials and Existence \\
Uniqueness \\
\\
Lecture 19. Synthetic Division \\
The Newton Form of the Interpolant \\
Evaluation \\
Existence \\
Divided Differences \\
\\
Lecture 20. Error in Interpolation \\
Error Bounds \\
Convergence \\
Chebyshev Points \\
\\
Part V. Numerical Integration and Differentiation \\
\\
Lecture 21. Numerical Integration \\
Change of Intervals \\
The Trapezoidal Rule \\
The Composite Trapezoidal Rule \\
Newton-Cotes Formulas \\
Undetermined Coefficients and Simpson's Rule \\
\\
Lecture 22. The Composite Simpson's Rule \\
Errors in Simpson's Rule \\
Weighting Functions \\
Gaussian Quadrature \\
\\
Lecture 23. The Setting \\
Orthogonal Polynomials \\
Existence \\
Zeros of Orthogonal Polynomials \\
Gaussian Quadrature \\
Error and Convergence \\
Examples \\
\\
Lecture 24. Numerical Differentiation and Integration
\\
Formulas From Power Series \\
Limitations \\
Bibliography",
}
@Article{Suzuki:1996:LZA,
author = "H. Suzuki and H. Morinaka and H. Makino and Y. Nakase
and K. Mashiko and T. Sumi",
title = "Leading-zero anticipatory logic for high-speed
floating point addition",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "31",
number = "8",
pages = "1157--1164",
month = aug,
year = "1996",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See comments \cite{Oklobdzija:1997:CLZ}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "This paper describes a new leading-zero anticipatory
(LZA) logic for high-speed floating-point addition
(FADD). This logic carries out the pre-decoding for
normalization concurrently with addition for the
significand. It also performs the shift operation
\ldots{}",
}
@MastersThesis{Tan:1996:MPF,
author = "Kien Beng Tan",
title = "A micro-power, floating point analog-to-digital
converter",
type = "Thesis ({M.S.})",
school = "Department of Electrical Engineering, University of
California, Los Angeles",
address = "Los Angeles, CA, USA",
pages = "????",
year = "1996",
bibdate = "Thu Oct 24 14:19:35 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "dissertations, academic -- UCLA -- Electrical
Engineering",
}
@InProceedings{Tatsaki:1996:AIC,
author = "A. Tatsaki",
booktitle = "Proceedings of the Third {IEEE} International
Conference on Electronics, Circuits, and Systems, 1996.
{ICECS 96}",
title = "An adaptive image coder based on residue number
system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "700--703",
year = "1996",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICECS.1996.584458",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "An efficient coder for adaptive lossy compression of
still images is presented. It is based on a
computational efficient extraction of the details of
image blocks. The Discrete Cosine Transform and an
efficient Lattice Vector Quantizer based on the
\ldots{}",
}
@MastersThesis{Trott:1996:AWL,
author = "Aaron Gregory Trott",
title = "The application of wavelets to lossless compression
and progressive transmission of floating point data in
three-dimensional curvilinear grids",
type = "{M.S.E.E.} thesis",
school = "Mississippi State University",
address = "Mississippi State, MS 39762, USA",
pages = "103",
year = "1996",
bibdate = "Fri Feb 1 09:20:32 MST 2013",
bibsource = "http://search.proquest.com/;
https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://search.proquest.com/docview/304273691",
acknowledgement = ack-nhfb,
advisor = "Robert J. Moorhead",
classification = "0538: Aerospace materials; 0544: Electrical
engineering",
dissertation-thesis-number = "1379238",
subject = "Electrical engineering; Aerospace materials",
}
@Misc{Urano:1996:MAN,
author = "M. Urano and T. Taniguchi",
title = "Method and apparatus for normalization of a floating
point binary number",
day = "30",
month = apr,
year = "1996",
bibdate = "Fri Nov 28 15:31:26 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,513,362.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Vassilladis:1996:ARA,
author = "S. Vassilladis and S. Contofana and K. Bertels",
title = "$2$-$1$ addition and related arithmetic operations
with threshold logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "45",
number = "9",
pages = "1062--1067",
month = sep,
year = "1996",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.537130",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 19:47:13 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537130",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Venners:1996:FPA,
author = "Bill Venners",
title = "Under the Hood: Floating-point arithmetic",
journal = j-JAVAWORLD,
volume = "1",
number = "9",
month = nov,
year = "1996",
CODEN = "????",
ISSN = "1091-8906",
bibdate = "Thu Aug 13 08:48:26 MDT 1998",
bibsource = "http://www.javaworld.com/javaworld/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.htm",
acknowledgement = ack-nhfb,
}
@Article{vonMatt:1996:RES,
author = "Urs {von Matt} and G. W. Stewart",
title = "Rounding errors in solving block {Hessenberg}
systems",
journal = j-MATH-COMPUT,
volume = "65",
number = "213",
pages = "115--135",
month = jan,
year = "1996",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F05 (65G05)",
MRnumber = "96e:65019",
MRreviewer = "Alfonso Laratta",
bibdate = "Fri Jul 16 10:38:30 MDT 1999",
bibsource = "http://www.ams.org/mcom/1996-65-213;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00667-9&u=/mcom/1996-65-213/",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
classcodes = "C4140 (Linear algebra); C1110 (Algebra); C4240
(Programming and algorithm theory)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algebra; algorithm; algorithm theory; block diagonally
dominant; block Hessenberg; block Hessenberg system;
divide and conquer methods; divide-and-conquer; linear;
linear system solution; linear systems; M-matrices;
matrices; matrix algebra; rounding error analysis;
rounding errors; solution; stable solution",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Vrahatis:1996:GBM,
author = "M. N. Vrahatis",
title = "A Generalized Bisection Method for Large and Imprecise
Problems",
crossref = "Alefeld:1996:SCV",
pages = "186--192",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Werner:1996:CIW,
author = "K. Werner",
title = "Calculations of the Inverse {Weierstrass} Functions in
an Arbitrary Machine Arithmetic",
crossref = "Alefeld:1996:SCV",
pages = "72--78",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@InProceedings{Wiethoff:1996:PAE,
author = "A. Wiethoff",
title = "A Parallel Algorithm for Enclosing All Zeros of a
Nonlinear System of Equations",
crossref = "Alefeld:1996:SCV",
pages = "193--199",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@Article{Williams:1996:TMF,
author = "K. B. Williams",
title = "Testing Math Functions: {When} requirements are tight,
we must carefully examine all potential sources of
error. {Make} sure your math library isn't the weak
link in the chain",
journal = j-CCCUJ,
volume = "14",
number = "12",
pages = "49--54, 58--65",
month = dec,
year = "1996",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Mon Apr 10 06:32:36 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Describes a package that extends the
Cody-Waite-Plauger work on the ELEFUNT package for the
testing of the elementary functions, including the
inverse hyperbolic functions, cube root, and Bessel
functions of the first and second kinds. The C++
package implements 192-bit extended precision versions
of all of the functions, so that accurate results are
available for comparison with the normal
double-precision results.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@InCollection{Zachary:1996:ESD,
author = "Joseph L. Zachary",
title = "{Eratosthenes}: Significant Digits and Interval
Arithmetic",
crossref = "Zachary:1996:ISP",
pages = "29--43",
year = "1996",
DOI = "https://doi.org/10.1007/978-1-4612-2366-5_3",
bibdate = "Sat Feb 16 15:23:11 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Zachary:1996:SHA,
author = "Joseph L. Zachary",
title = "Stairway to Heaven: Accumulation of Roundoff Error",
crossref = "Zachary:1996:ISP",
pages = "45--61",
year = "1996",
DOI = "https://doi.org/10.1007/978-1-4612-2366-5_4",
bibdate = "Sat Feb 16 15:30:56 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zgliczynski:1996:RVC,
author = "P. Zgliczynski",
title = "Rigorous Verification of Chaos in the {Roessler}
Equations",
crossref = "Alefeld:1996:SCV",
pages = "287--292",
year = "1996",
bibdate = "Mon May 20 06:32:10 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
}
@PhdThesis{Al-Twaijry:1997:APO,
author = "Hesham Abdulaziz Al-Twaijry",
title = "Area And Performance Optimized {CMOS} Multipliers",
type = "{Ph.D.} thesis",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "????",
month = aug,
year = "1997",
bibdate = "Mon Dec 24 10:02:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Allaart:1997:ISC,
author = "Pieter C. Allaart",
title = "An Invariant-Sum Characterization of {Benford's Law}",
journal = j-J-APPL-PROBAB,
volume = "34",
number = "1",
pages = "288--291",
month = mar,
year = "1997",
CODEN = "JPRBAM",
DOI = "https://doi.org/10.2307/3215195",
ISSN = "0021-9002 (print), 1475-6072 (electronic)",
ISSN-L = "0021-9002",
bibdate = "Fri Mar 30 11:25:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://links.jstor.org/sici?sici=0021-9002%28199703%2934%3A1%3C288%3AAICOBL%3E2.0.CO%3B2-S&size=LARGE",
abstract = "The accountant Nigrini remarked that in tables of data
distributed according to Benford's law, the sum of all
elements with first digit $ d (d = 1, 2, \cdots, 9) $
is approximately constant. In this note, a mathematical
formulation of Nigrini's observation is given and it is
shown that Benford's law is the unique probability
distribution such that the expected sum of all elements
with first digits $ d_1, \cdots, d_k $ is constant for
every fixed $k$.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Probability",
journal-URL = "http://www.jstor.org/journals/00219002.html;
http://projecteuclid.org/euclid.jap/",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@TechReport{Althaus:1997:MNF,
author = "Ernst Althaus and Kurt Mehlhorn",
title = "Maximum network flow with floating point arithmetic",
type = "Forschungsbericht",
number = "MPI-I-97-1-022",
institution = "Max-Planck-Institut f{\"u}r Informatik",
address = "Saarbr{\"u}cken, Germany",
pages = "5",
year = "1997",
ISSN = "0946-011X",
bibdate = "Thu May 09 08:55:36 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1997:BRPk,
author = "Anonymous",
title = "Book Review: {{\booktitle{Primes of the form $ x^2 + n
y^2 $: Fermat, class field theory, and complex
multiplication}}: David A. Cox. John Wiley \& Sons, New
York. (1989). 351 pages. \$49.95, \pounds 29.95}",
journal = j-COMPUT-MATH-APPL,
volume = "34",
number = "10",
pages = "141--141",
month = nov,
year = "1997",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:40 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122197902650",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Anonymous:1997:SIS,
author = "Anonymous",
title = "{SCAN-97} International Symposium on Scientific
Computing Computer Arithmetic and Validated Numerics",
journal = j-J-COMPUT-APPL-MATH,
volume = "81",
number = "2",
pages = "N13--N14",
day = "8",
month = jul,
year = "1997",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:36:02 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042797900741",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Aoki:1997:RCR,
author = "Takafumi Aoki and Hiroaki Amada and Tatsuo Higuchi",
title = "Real\slash Complex Reconfigurable Arithmetic Using
Redundant Complex Number Systems",
crossref = "Lang:1997:ISC",
pages = "200--207",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Aoki.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Arnold:1997:ACT,
author = "Mark G. Arnold and Thomas A. Bailey and John R. Cowles
and Mark D. Winkel",
title = "Arithmetic Co-Transformations in the Real and Complex
Logarithmic Number Systems",
crossref = "Lang:1997:ISC",
pages = "190--199",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Arnold.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Atkinson-Barr:1997:LEP,
author = "Martin Atkinson-Barr",
title = "Letter to the {Editor}: {Pentium II} Math Bug",
journal = j-DDJ,
volume = "22",
number = "10",
pages = "10--10",
month = oct,
year = "1997",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Nov 8 14:50:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Identifies himself as the ``Mr. X'' cited in
\cite{Collins:1997:IPI}, and provides more the
background on the discovery of the Pentium FIST
(floating-point to integer store) instruction.",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Avnaim:1997:ESD,
author = "Francis Avnaim and Jean-Daniel Boissonnat and Olivier
Devillers and Franco P. Preparata and Mariette Yvinec",
title = "Evaluating Signs of Determinants Using
Single-Precision Arithmetic",
journal = j-ALGORITHMICA,
volume = "17",
number = "2",
pages = "111--132",
month = feb,
year = "1997",
CODEN = "ALGOEJ",
ISSN = "0178-4617 (print), 1432-0541 (electronic)",
ISSN-L = "0178-4617",
MRclass = "65Y25 (65F99 68U05)",
MRnumber = "MR1425729 (97k:65311)",
MRreviewer = "Luiz Henrique de Figueiredo",
bibdate = "Fri Jan 6 11:38:07 MST 2006",
bibsource = "dblp-journals-algorithmica.bib;
http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica17.html#AvnaimBDPY97;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0178-4617&volume=17&issue=2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica;
MathSciNet database",
URL = "http://www.springerlink.com/link.asp?id=nlr883hde9w2av31;
http://www.springerlink.com/openurl.asp?genre=article&eissn=1432-0541&volume=17&issue=2&spage=111;
http://www.springerlink.com/openurl.asp?genre=article&issn=0178-4617&volume=17&issue=2&spage=111",
abstract = "We propose a method to evaluate signs of $ 2 \times 2
$ and $ 3 \times 3 $ determinants with $b$-bit integer
entries using only $b$ and $ (b + 1) $-bit arithmetic
respectively. This algorithm has numerous applications
in geometric computation and provides a general and
practical approach to robustness. The algorithm has
been implemented and experimental results show that it
slows down the computing time by only a small factor
with respect to floating-point calculation.",
acknowledgement = ack-nhfb,
fjournal = "Algorithmica. An International Journal in Computer
Science",
journal-URL = "http://link.springer.com/journal/453",
keywords = "exact arithmetic; floating-point arithmetic",
oldlabel = "AvnaimBDPY97",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/algorithmica/AvnaimBDPY97",
}
@InProceedings{Bajard:1997:RMM,
author = "Jean-Claude Bajard and Laurent-St{\'e}phane Didier and
Peter Kornerup",
title = "An {RNS Montgomery} Modular Multiplication Algorithm",
crossref = "Lang:1997:ISC",
pages = "234--239",
year = "1997",
bibdate = "Wed Nov 14 18:54:27 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A revised version published in IEEE Transactions on
Computers, Vol.46(7), July 1998",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Bajard.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Baker:1997:LEP,
author = "Louis Baker",
title = "Letter to the {Editor}: {Pentium II} Math Bug",
journal = j-DDJ,
volume = "22",
number = "10",
pages = "10--10",
month = oct,
year = "1997",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Nov 8 14:50:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Comments on the Ariane 5 missile failure mentioned in
\cite{Collins:1997:IPI}.",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@InProceedings{Beaumont-Smith:1997:GBA,
author = "Andrew Beaumont-Smith and Neil Burgess",
title = "A {GaAs} 32-Bit Adder",
crossref = "Lang:1997:ISC",
pages = "10--17",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Beaumont_Smith.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Blackford:1997:PEN,
author = "L. S. Blackford and A. Cleary and A. Petitet and R. C.
Whaley and J. Demmel and I. Dhillon and H. Ren and K.
Stanley and J. Dongarra and S. Hammarling",
title = "Practical Experience in the Numerical Dangers of
Heterogeneous Computing",
journal = j-TOMS,
volume = "23",
number = "2",
pages = "133--147",
month = jun,
year = "1997",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/264029.264030",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Nov 8 14:50:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p133-blackford/",
abstract = "Special challenges exist in writing reliable numerical
library software for heterogeneous computing
environments. Although a lot of software for
distributed-memory parallel computers has been written,
porting this software to a network of workstations
requires careful consideration. The symptoms of
heterogeneous computing failures can range from
erroneous results without warning to deadlock. Some of
the problems are straightforward to solve, but for
others the solutions are not so obvious, or incur an
unacceptable overhead. Making software robust on
heterogeneous systems often requires additional
communication. We describe and illustrate the problems
encountered during the development of ScaLAPACK and the
NAG Numerical PVM Library. Where possible, we suggest
ways to avoid potential pitfalls, or if that is not
possible, we recommend that the software not be used on
heterogeneous networks.",
acknowledgement = ack-rfb # " and " # ack-kr,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "distributed-memory systems, floating-point arithmetic,
heterogeneous processor networks, message passing,
numerical software, reliability",
subject = "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
Concurrent Programming, Distributed programming. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic. {\bf G.1.0} Mathematics
of Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms.",
}
@Article{Blinn:1997:JBC,
author = "James F. Blinn",
title = "{Jim Blinn}'s Corner: Floating-Point Tricks",
journal = j-IEEE-CGA,
volume = "17",
number = "4",
pages = "80--84",
month = jul # "\slash " # aug,
year = "1997",
CODEN = "ICGADZ",
DOI = "https://doi.org/10.1109/38.595279",
ISSN = "0272-1716 (print), 1558-1756 (electronic)",
ISSN-L = "0272-1716",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Discusses use of IEEE 754 single-precision
floating-point bit patterns as integers for
implementations of fast, but low-accuracy, functions
useful in computer graphics.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Computer Graphics and Applications",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/cga",
summary = "The author discusses IEEE floating point
representation that stores numbers in what amounts to
scientific notation. He considers the sign bit, the
logarithm function, function approximations, errors and
refinements \ldots{}",
}
@Article{Bomar:1997:RNA,
author = "B. W. Bomar and L. M. Smith and R. D. Joseph",
title = "Roundoff noise analysis of state-space digital filters
implemented on floating-point digital signal
processors",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "44",
number = "11",
pages = "952--955",
month = nov,
year = "1997",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.644048",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "An expression is obtained for the output
floating-point roundoff noise variance of a general
Nth-order state-space digital filter with zero-mean
white noise input signal. This expression is then
simplified for the case there the filter is implemented
\ldots{}",
}
@Article{Bshouty:1997:TBA,
author = "Nader H. Bshouty and Yishay Mansour and Baruch
Schieber and Prasoon Tiwari",
title = "A tight bound for approximating the square root",
journal = j-INFO-PROC-LETT,
volume = "63",
number = "4",
pages = "211--213",
day = "10",
month = sep,
year = "1997",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68Q25 (65B15 68Q40)",
MRnumber = "1 477 306",
bibdate = "Sat Nov 7 17:55:54 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@InProceedings{Burgess:1997:SUR,
author = "Neil Burgess",
title = "Scaled and unscaled residue number system to binary
conversion techniques using the core function",
crossref = "Lang:1997:ISC",
pages = "250--257",
year = "1997",
DOI = "https://doi.org/10.1109/ARITH.1997.614902",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Burgess.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13; residue arithmetic; residue number system",
summary = "The paper presents related techniques for converting a
residue number system (RNS) number to binary, with and
without scaling, that use the core function. The
techniques remove the difficulties associated with
conversion procedures based on the \ldots{}",
}
@InProceedings{Callaway:1997:PDC,
author = "Thomas K. Callaway and Earl E. {Swartzlander, Jr.}",
title = "Power-Delay Characteristics of {CMOS} Multipliers",
crossref = "Lang:1997:ISC",
pages = "26--33",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Callaway.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Cao:1997:HPH,
author = "Jun Cao and Belle W. Y. Wei",
title = "High-Performance Hardware for Function Generation",
crossref = "Lang:1997:ISC",
pages = "184--189",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cao.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Cena:1997:QCA,
author = "Gianluca Cena and Paolo Montuschi and Luigi Ciminiera
and Andrea Sanna",
title = "A {Q}-Coder Algorithm with Carry Free Addition",
crossref = "Lang:1997:ISC",
pages = "282",
year = "1997",
bibdate = "Sat Nov 17 12:22:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cena.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@TechReport{Chen:1997:PEG,
author = "Yirng-An Chen and Randal E. Bryant",
title = "{PBHD}: an efficient graph representation for floating
point circuit verification",
type = "Report",
number = "CMU-CS-97-134",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
year = "1997",
bibdate = "Thu May 09 08:39:56 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Collins:1997:IPI,
author = "Robert C. Collins",
title = "Inside the {Pentium II} Math Bug",
journal = j-DDJ,
volume = "22",
number = "8",
pages = "52, 55--57",
month = aug,
year = "1997",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Sat Mar 07 08:27:48 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See letters
\cite{Atkinson-Barr:1997:LEP,Baker:1997:LEP}.",
abstract = "Two days before Intel's biggest processor announcement
in years, a math bug in the Pentium Pro and Pentium II
came to light. Robert takes you inside the Dan-0411
flag erratum,' and tells how the story unfolded.",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Compagner:1997:RER,
author = "A. Compagner and A. S. Berdnikov and S. B. Turtia and
A. Larionov",
title = "Rounding errors in random number generators",
journal = j-COMP-PHYS-COMM,
volume = "106",
number = "3",
pages = "207--218",
month = nov,
year = "1997",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(97)00070-2",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Dec 29 21:19:40 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465597000702",
abstract = "The deviations of the cumulative distribution function
from the uniform one for the pseudorandom floating
point values produced by integer arithmetics are
discussed. It is shown that the conversion from fixed
point values into floating point values introduces
specific artefacts even when the integer arithmetics
guarantees ideal uniformity. Two type of defects are
considered: the appearance of the value 1.0 among
pseudorandom values, and the sharp jumps of uniformity
at the level of discreteness which corresponds to the
computer representation of the floating point values.
The non-uniformity at small level of discreteness can
be neglected in most cases, but the appearance of the
parasitic value 1.0 where nobody expects it can be very
dangerous if special precautions are not taken by the
user. Both defects are demonstrated using the random
number generator from the system library of the
Microsoft Power Station Fortran 1.0.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Cuyt:1997:FPV,
author = "A. Cuyt",
title = "Floating-point versus Symbolic Computations in the
{QD}-algorithm",
journal = j-J-SYMBOLIC-COMP,
volume = "24",
number = "6",
publisher = "Academic Press, Harcourt Place, 32 Jamestown Road,
London, NW1 7BY, U.K.",
pages = "695--703",
month = dec,
year = "1997",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
pagecount = "9",
}
@Article{Daumas:1997:VRD,
author = "M. Daumas and D. W. Matula",
title = "Validated roundings of dot products by sticky
accumulation",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "5",
pages = "623--629",
month = may,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.589241",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589241",
abstract = "The dot product operation is very prevalent in
scientific computation and has therefore been
incorporated as a primitive operation in some
languages. The implementation of the dot product
operation by a sequence of IEEE standard
multiplications and additions does not prevent a
substantial accumulation of the round-off errors or
warn the user about a catastrophic cancellation. We
present the design of a double precision dot product
operation employing sticky accumulation, where the
final rounded result is validated by raising a new
exception flag if the result incurred catastrophic
cancellation. Sticky accumulation can be implemented in
a pipeline or parallel environment to sustain double
precision with an extended control of the error. Our
design allows that, in the absence of catastrophic
cancellation, one ulp accuracy is guaranteed",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "floating-point arithmetic",
}
@InProceedings{Dimitrov:1997:AME,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
title = "Algorithms for Multi-Exponentiation Based on Complex
Arithmetic",
crossref = "Lang:1997:ISC",
pages = "208--217",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_algorithms.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Dimitrov:1997:ERN,
author = "V. Dimitrov and G. A. Jullien and W. C. Miller",
booktitle = "Proceedings of the 40th Midwest Symposium on Circuits
and Systems, 1997",
title = "{Eisenstein} residue number system with applications
to {DSP}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "675--678",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1997.662165",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new approach for processing complex numbers has been
proposed, Basically, it is aimed at the implementation
of radix-3 FFTs, but it can be used in any situation
where the requirement to process Eisenstein integers
arises, The comparison between \ldots{}",
}
@InProceedings{Dimitrov:1997:TAD,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
title = "Theory and Applications for a Double-Base Number
System",
crossref = "Lang:1997:ISC",
pages = "44--53",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_theory.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Doring:1997:DAL,
author = "Andreas D{\"o}ring and Wolfgang J. Paul",
title = "Decimal adjustment of long numbers in constant time",
journal = j-INFO-PROC-LETT,
volume = "62",
number = "3",
pages = "161--163",
day = "4",
month = jun,
year = "1997",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
MRclass = "68M07 (68M20)",
MRnumber = "1 453 700",
bibdate = "Sat Nov 7 17:55:52 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "decimal floating-point arithmetic",
}
@Article{Drmac:1997:IJR,
author = "Zlatko Drma{\v{c}}",
title = "Implementation of {Jacobi} Rotations for Accurate
Singular Value Computation in Floating Point
Arithmetic",
journal = j-SIAM-J-SCI-COMP,
volume = "18",
number = "4",
pages = "1200--1222",
month = jul,
year = "1997",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827594265095",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15 (65G10)",
MRnumber = "98e:65027; 1 453 565",
MRreviewer = "Ljiljana Petkovi{\'c}",
bibdate = "Fri Dec 4 14:47:53 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/18/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/26509",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{Drolshagen:1997:PES,
author = "A. Drolshagen and H. Henkelmann and W. Anheier",
booktitle = "{IEEE} International Conference on
Application-Specific Systems, Architectures and
Processors, Proceedings, 14--16 July 1997",
title = "Processor elements for the standard cell
implementation of residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "116--123",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1109/ASAP.1997.606818",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this article processor elements for the effective
implementation of standard cell circuits based on
residue number systems (RNS) are presented. Two new
processors are proposed helping to reduce the hardware
requirements of the implementations. \ldots{}",
}
@Manual{EC:1997:IER,
author = "{European Commission}",
title = "The Introduction of the Euro and the Rounding of
Currency Amounts",
organization = "European Commission Directorate General II Economic
and Financial Affairs",
address = "Brussels, Belgium",
pages = "29",
year = "1997",
bibdate = "Fri Nov 28 11:18:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Edelman:1997:MPD,
author = "Alan Edelman",
title = "The Mathematics of the {Pentium} Division Bug",
journal = j-SIAM-REVIEW,
volume = "39",
number = "1",
pages = "54--67",
month = mar,
year = "1997",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/S0036144595293959",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "68M07",
MRnumber = "1 439 485",
bibdate = "Sat Mar 29 09:55:47 MDT 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/39/1;
http://epubs.siam.org/toc/siread/39/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/29395;
http://www-math.mit.edu/~edelman/homepage/papers/pentiumbug.pdf;
http://www.siam.org/journals/sirev/sirev391.htm",
abstract = "Despite all of the publicity surrounding the Pentium
bug of 1994, the mathematical details of the bug are
poorly understood. We discuss these details and supply
a new proof of the Coe--Tang result that the at-risk
divisors have six consecutive ones in positions 5
through 10. Also, we prove that the worst-case absolute
error for arguments in $ [1, 2) $ is on the order of
1e-5.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "Intel Pentium divide flaw; Thomas R. Nicely",
onlinedate = "January 1997",
}
@InProceedings{Even:1997:DIC,
author = "Guy Even and Wolfgang Paul",
title = "On the Design of {IEEE} Compliant Floating Point
Units",
crossref = "Lang:1997:ISC",
pages = "54--63",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Even.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
remark = "Cited in \cite{Mueller:2000:CAC}.",
}
@Article{Fitzpatrick:1997:EBE,
author = "P. Fitzpatrick",
title = "Extending backward error assertions to tolerance of
large errors in floating point computations",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "4",
pages = "505--510",
month = apr,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.588072",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588072",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "The use of backward error assertions combined with
iterative refinement has been suggested for the
correction of small fault induced errors in the
floating point solution of linear systems. We extend
this to the correction of large errors, typically
\ldots{}",
}
@InProceedings{Frougny:1997:FAS,
author = "Christiane Frougny",
title = "On-the-Fly Algorithms and Sequential Machines",
crossref = "Lang:1997:ISC",
pages = "260--265",
year = "1997",
bibdate = "Wed Nov 14 18:57:13 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Frougny.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Garber:1997:NBB,
author = "Lee Garber",
title = "News Briefs: Binary Version Could Bring {VRML} into
the Mainstream. {FCC} Jumps Into {Internet} Fray.
{Java} and Floating-Point Math. {Intel} to Design
{NDRAM}. Battle over Net Telephony. Vendors Seek Fast
Modems. {US} Permits Export of Strong Encryption.
{E}-commerce Nears \$1 Billion. Chasing the Blue Light.
Personal {E}-mail Use Will Soar",
journal = j-COMPUTER,
volume = "30",
number = "4",
pages = "25--27",
month = apr,
year = "1997",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Tue May 06 16:51:53 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Garjanov:1997:CRE,
author = "A. E. Garjanov",
booktitle = "Proceedings of the 1st International Conference on
Control of Oscillations and Chaos, 1997",
title = "Controlled round-off error oscillations for initial
value problem numerical solution",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "333--334",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A new methodology of a computer simulation is desired
for the accumulated round-off error elimination to be
possible. It is well known that the propagation of
round-off error in the numerical integration of
differential equations may be crucial \ldots{}",
}
@Article{Giachetti:1997:PRF,
author = "Ronald E. Giachetti and Robert E. Young",
title = "A Parametric Representation of Fuzzy Numbers and Their
Arithmetic Operators",
journal = j-FUZZY-SETS-SYSTEMS,
volume = "92",
number = "2",
pages = "??--??",
day = "1",
month = sep,
year = "1997",
CODEN = "FSSYD8",
ISSN = "0165-0114 (print), 1872-6801 (electronic)",
ISSN-L = "0165-0114",
bibdate = "Tue Nov 05 15:22:41 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.nist.gov/publications/parametric-representation-fuzzy-numbers-and-their-arithmetic-operators",
abstract = "Direct implementation of extended arithmetic operators
on fuzzy numbers is computationally complex.
Implementation of the extension principle is equivalent
to solving a nonlinear programming problem. To overcome
this difficulty many applications limit the membership
functions to certain shapes, usually either triangular
fuzzy numbers (TFN) or trapezoidal fuzzy numbers
(TrFN). Then calculation of the extended operators can
be performed on the parameters defining the fuzzy
numbers, thus making the calculations trivial.
Unfortunately the TFN shape is not closed under
multiplication and division. The result of these
operators is a polynomial membership function and the
triangular shape only approximates the actual
result.The linear approximation can be quite poor and
may lead to incorrect results when used in engineering
applications. We analyze this problem and propose six
parameters which define parameterized fuzzy numbers
(PFN), of which TFNs are a special case. We provide the
methods for performing fuzzy arithmetic and show that
the PFN representation is closed under the arithmetic
operations. The new representation in conjunction with
the arithmetic operators obeys many of the same
arithmetic properties as TFNs. The new method has
better accuracy and similar computational speed to
using TFNs and appears to have benefits when used in
engineering applications.",
acknowledgement = ack-nhfb,
fjournal = "Fuzzy Sets and Systems",
journal-URL = "http://www.sciencedirect.com/science/journal/01650114",
keywords = "arithmetic approximations; Fuzzy arithmetic;
membership functions; triangular fuzzy numbers",
}
@Misc{Gosling:1997:ENC,
author = "James A. Gosling",
title = "The Evolution of Numerical Computing in {Java}",
howpublished = "World Wide Web document.",
year = "1997",
bibdate = "Mon May 06 17:11:19 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://java.sun.com/people/jag/FP.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Grosse:1997:RI,
author = "Eric Grosse",
title = "Real {Inferno}",
crossref = "Boisvert:1997:QNS",
pages = "270--279",
year = "1997",
bibdate = "Tue Jul 21 11:18:48 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://cm.bell-labs.com/inferno/real.ps",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``the language Limbo
adopted accurate base conversion as one of its
improvements over C (p. 271 of this article)''.",
}
@Book{Guedj:1997:NUL,
author = "Denis Guedj",
title = "Numbers: The Universal Language",
publisher = "Harry N. Abrams, Inc.",
address = "New York, NY, USA",
pages = "175",
year = "1997",
ISBN = "0-8109-2845-0",
ISBN-13 = "978-0-8109-2845-9",
LCCN = "QA141.G8413 1997",
bibdate = "Fri Nov 28 17:05:12 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from the French edition
\cite{Guedj:1996:EN} by Lory Frankel.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Hagihara:1997:FPD,
author = "Y. Hagihara and S. Inui and F. Okamoto and M. Nishida
and T. Nakamura and H. Yamada",
title = "Floating-point datapaths with online built-in self
speed test",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "32",
number = "3",
pages = "444--449",
month = mar,
year = "1997",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "This paper describes floating-point (FP) datapaths
developed for graphics and simulation applications. The
datapaths are fabricated using 0.35 $\mu$m CMOS
technology and embedded in a 125 MHz, 291 MFLOPS vector
pipelined processor for use in supercomputers
\ldots{}",
}
@Book{Hanson:1997:CII,
author = "David R. Hanson",
title = "{C} Interfaces and Implementations: Techniques for
Creating Reusable Software",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xvii + 519",
year = "1997",
ISBN = "0-201-49841-3",
ISBN-13 = "978-0-201-49841-7",
LCCN = "QA76.73.C15H37 1997",
bibdate = "Fri Feb 27 16:08:11 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/litprog.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Addison-Wesley Professional Computing Series",
URL = "http://www.cs.princeton.edu/software/cii/",
acknowledgement = ack-nhfb,
subject = "C (Computer program language); Computer software;
Reusability; Literate Programming",
tableofcontents = "1. Introduction \\
2. Interfaces and Implementations \\
3. Atoms \\
4. Exceptions and Assertions \\
5. Memory Management \\
6. More Memory Management \\
7. Lists \\
8. Tables \\
9. Sets \\
10. Dynamic Arrays \\
11. Sequences \\
12. Rings \\
13. Bit Vectors \\
14. Formatting \\
15. Low-Level Strings \\
16. High-Level Strings \\
17. Extended-Precision Arithmetic \\
18. Arbitrary-Precision Arithmetic \\
19. Multiple-Precision Arithmetic \\
20. Threads",
}
@TechReport{Hanson:1997:ECR,
author = "Kenton L. Hanson",
title = "Economical Correctly Rounded Binary Decimal
Conversion",
type = "Report",
number = "??",
institution = "????",
address = "????",
day = "19",
month = dec,
year = "1997",
bibdate = "Sat May 07 09:46:31 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Cited in \cite[p. 134, reference 4]{Hack:2004:IPR},
and reported there to be now inaccessible. Further
queries in May 2022 to four search engines fail to find
this document, or its institution and address.",
acknowledgement = ack-nhfb,
}
@Misc{Hanson:1997:MAD,
author = "Kenton L. Hanson",
title = "Method and apparatus for determining a precision of an
intermediate arithmetic for converting values between a
first numeric format and a second numeric format",
howpublished = "US Patent 5652862",
day = "29",
month = jul,
year = "1997",
bibdate = "Thu Oct 14 14:54:45 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentgenius.com/patent/5652862.html",
abstract = "A method and apparatus for efficient allocation of
temporary storage for performing accurate and correct
numeric base conversions on a computer system is
provided. Numeric base conversions are common because
computers operate in binary whereas the values that are
input into computers are based on a decimal system. A
common source of error occurs when converted values are
rounded. The intermediate arithmetic used to perform
the conversion requires greater precision than the
target floating point format. It is known that to
always insure correctly rounded results, an extremely
high precision intermediate arithmetic may be used.
However, in many case this is a waste of system memory.
To efficiently allocate system memory to this task, the
most difficult rounding case is determined. The
precision needed to correctly round the most difficult
case is then derived. This information is then stored
and subsequently used to allocate an efficient amount
of storage whenever a numeric base conversion is to
take place.",
acknowledgement = ack-nhfb,
remark = "Patent held by Apple Computer, Inc., Cupertino, CA,
USA.",
}
@InProceedings{Harris:1997:SDA,
author = "David L. Harris and Stuart F. Oberman and Mark A.
Horowitz",
title = "{SRT} Division Architectures and Implementations",
crossref = "Lang:1997:ISC",
pages = "18--25",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "ftp://arith.stanford.edu/tr/srtcircuits.ps.Z;
http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Harris.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@TechReport{Harrison:1997:FPV,
author = "John Robert Harrison",
title = "Floating point verification in {HOL Light}: the
exponential function",
type = "Technical Report",
number = "428",
institution = "University of Cambridge Computer Laboratory",
address = "Cambridge, UK",
pages = "ii + 110",
month = jun,
year = "1997",
LCCN = "QA76.9.A96 H367 1997",
bibdate = "Thu Oct 24 14:30:40 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cl.cam.ac.uk/users/jrh/papers/tang.ps.gz",
acknowledgement = ack-nhfb,
keywords = "automatic theorem proving; floating-point arithmetic;
proof theory",
}
@InProceedings{Harrison:1997:VAP,
author = "John Harrison",
editor = "Elsa L. Gunter and Amy Felty",
booktitle = "Theorem Proving in Higher Order Logics: {10th
International Conference, TPHOLs'97, Murray Hill, NJ,
USA, August 19--22, 1997, Proceedings}",
title = "Verifying the accuracy of polynomial approximations in
{HOL}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "137--152",
year = "1997",
DOI = "https://doi.org/10.1007/BFb0028391",
ISBN = "3-540-63379-0 (print), 3-540-69526-5 (electronic)",
ISBN-13 = "978-3-540-63379-2 (print), 978-3-540-69526-4
(electronic)",
LCCN = "QA76.9.A96 I577 1997",
bibdate = "Tue May 07 16:45:16 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0028381",
}
@Article{Hasan:1997:DA,
author = "M. A. Hasan",
title = "Division-and-accumulation over {$ \mathrm {GF}(2^m)
$}",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "6",
pages = "705--708",
month = jun,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.600829",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=600829",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hekstra:1997:FRL,
author = "Gerber J. Hekstra and Ed F. A. Deprettere",
title = "Fast Rotations: Low-Cost Arithmetic Methods for
Orthonormal Rotation",
crossref = "Lang:1997:ISC",
pages = "116--125",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hekstra.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Hiasat:1997:DIR,
author = "Ahmad A. Hiasat and Hoda S. Abdel-Aty-Zohdy",
title = "Design and Implementation of an {RNS} Division
Algorithm",
crossref = "Lang:1997:ISC",
pages = "240--249",
year = "1997",
bibdate = "Wed Nov 14 18:57:54 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hiasat.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13; residue number system",
}
@MastersThesis{Hix:1997:CTV,
author = "Robert W. Hix",
title = "A comparison of two {VHDL} design environments for
{FPGA}-based computer arithmetic",
type = "Thesis ({M.S.})",
school = "Tennessee Technological University",
address = "Cookeville, TN, USA",
pages = "x + 301",
year = "1997",
bibdate = "Mon Mar 05 14:38:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Holmes:1997:CAP,
author = "W. Neville Holmes",
title = "Composite Arithmetic: Proposal for a New Standard",
journal = j-COMPUTER,
volume = "30",
number = "3",
pages = "65--73",
month = mar,
year = "1997",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri May 9 17:30:55 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsdf.ps;
ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsrf.ps;
ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dssf.ps",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Department of Comput., Tasmania University,
Launceston, Tas., Australia",
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "composite arithmetic; digital arithmetic; exact
numbers; extended arithmetic; floating point
arithmetic; formatting scheme; general computation;
general-purpose arithmetic standard; inexact numbers;
number display; number format; number storage;
reliability; stability; standards",
treatment = "P Practical",
}
@Article{Irmay:1997:RBZ,
author = "Shragga Irmay",
title = "The relationship between {Zipf}'s law and the
distribution of first digits",
journal = j-J-APPL-STAT,
volume = "24",
number = "4",
pages = "383--393",
day = "1",
month = aug,
year = "1997",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
MRclass = "62E15",
MRnumber = "98h:62015",
bibdate = "Sat Apr 13 11:27:31 MDT 2002",
bibsource = "http://www.catchword.co.uk/titles/carfax/02664763/;
http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.catchword.co.uk/cgi-bin/cgi?ini=carfax&body=linker&reqidx=/catchword/carfax/13600532/v24n4/s2/p383",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
keywords = "Benford's Law; Zipf's Law",
xxpages = "383--394",
}
@Article{Ito:1997:EIA,
author = "M. Ito and N. Takagi and S. Yajima",
title = "Efficient initial approximation for multiplicative
division and square root by a multiplication with
operand modification",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "4",
pages = "495--498",
month = apr,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.588066",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "An efficient initial approximation method for
multiplicative division and square root is proposed. It
is a modification of the piecewise linear
approximation. The multiplication and the addition
required for the linear approximation are replaced by
\ldots{}",
}
@Misc{Kahan:1997:JNL,
author = "W. Kahan",
title = "The {John von Neumann} lecture at the {SIAM} 45th
annual meeting",
howpublished = "World-Wide Web document.",
year = "1997",
bibdate = "Sat Apr 28 18:52:17 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/SIAMjvnl.ps",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:1997:LNS,
author = "W. Kahan",
title = "Lecture Notes on the Status of {IEEE Standard 754 for
Binary Floating-Point Arithmetic}",
howpublished = "World-Wide Web document",
pages = "30",
day = "1",
month = oct,
year = "1997",
bibdate = "Mon Apr 25 17:54:35 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF",
acknowledgement = ack-nhfb,
}
@TechReport{Kahan:1997:RDI,
author = "W. Kahan and Melody Y. Ivory",
title = "Roundoff Degrades an Idealized Cantilever",
type = "Technical report",
institution = "Department of Mathematics and Department of Electrical
Engineering and Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "11",
day = "3",
month = jul,
year = "1997",
bibdate = "Fri May 03 12:15:09 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/Cantilever.pdf;
http://www.cs.berkeley.edu/~wkahan/Cantilever.ps",
acknowledgement = ack-nhfb,
}
@Article{Kako:1997:PEF,
author = "Fujio Kako and Tateaki Sasaki",
title = "Proposal of {``Effective} Floating-Point Number'' for
Approximate Algebraic Computation",
journal = j-SIGSAM,
volume = "31",
number = "3",
pages = "31--31",
month = sep,
year = "1997",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Wed Dec 17 07:49:58 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Poster abstract only. Discusses fuzzy and interval
floating-point arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Kapur:1997:MVA,
author = "Deepak Kapur and M. Subramaniam",
title = "Mechanizing Verification of Arithmetic Circuits: {SRT}
Division",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1346",
pages = "103--??",
year = "1997",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:51:29 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1346.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1346/13460103.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1346/13460103.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Karp:1997:HPD,
author = "Alan H. Karp and Peter Markstein",
title = "High-Precision Division and Square Root",
journal = j-TOMS,
volume = "23",
number = "4",
pages = "561--589",
month = dec,
year = "1997",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/279232.279237",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Nov 8 14:50:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
abstract = "We present division and square root algorithms for
calculation with more bits than are handled by the
floating-point hardware. These algorithms avoid the
need to multiply two high-precision numbers, speeding
up the last iteration by as much as a factor of 10. We
also show how to produce the floating-point number
closest to the exact result with relatively few
additional operations.",
accepted = "June 1997",
acknowledgement = ack-rfb # " and " # ack-kr,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms, performance, division, quad precision,
square root.",
subject = "G.1.0 [Numerical Analysis]: General -- computer
arithmetic. G.4 [Mathematics of Computing]:
Mathematical Software.",
}
@Book{Khinchin:1997:CF,
author = "Aleksandr Iakovlevich Khinchin",
title = "Continued fractions",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xi + 95",
year = "1997",
ISBN = "0-486-69630-8 (paperback)",
ISBN-13 = "978-0-486-69630-0 (paperback)",
LCCN = "QA295 .K513 1997",
bibdate = "Fri Nov 30 06:55:53 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/description/dover032/97008056.html;
http://www.loc.gov/catdir/toc/dover031/97008056.html",
acknowledgement = ack-nhfb,
author-dates = "1894--1959",
remark = "Translated from the Russian by Scripta Technica, Inc.
Originally published: Chicago : University of Chicago
Press, 1964. Edited by Herbert Eagle.",
}
@InProceedings{King:1997:DDT,
author = "E. J. King and E. E. {Swartzlander, Jr.}",
title = "Data-Dependent Truncation Scheme for Parallel
Multipliers",
crossref = "Fargues:1997:CRT",
pages = "1178--1182",
year = "1997",
bibdate = "Fri Jun 24 20:50:14 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Kinoshita:1997:RAE,
author = "Eisuke Kinoshita and Ki-Ja Lee",
title = "A Residue Arithmetic Extension for Reliable Scientific
Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "2",
pages = "129--138",
month = feb,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.565587",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "65G10 (65Y99)",
MRnumber = "MR1434396 (97j:65080)",
bibdate = "Wed Jul 6 10:06:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565587",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Koc:1997:FSE,
author = "{\c{C}}. K. Ko{\c{c}} and T. Acar",
title = "Fast Software Exponentiation in {$ \mathrm {GF}(2^k)
$}",
crossref = "Lang:1997:ISC",
pages = "225--231",
year = "1997",
bibdate = "Sat Nov 17 12:22:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Koc.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Kramer:1997:PWC,
author = "Walter Kr{\"a}mer",
title = "A Priori Worst-Case Error Bounds for Floating-Point
Computations",
crossref = "Lang:1997:ISC",
pages = "64--73",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Kramer.pdf",
acknowledgement = ack-nhfb,
author-dates = "1952--2014",
keywords = "ARITH-13",
}
@Article{Kravchenko:1997:AEP,
author = "Yu. P. Kravchenko and M. A. Liberman",
title = "On the Application of Extended Precision Arithmetic to
Quantum Mechanical Calculations",
journal = j-IJQC,
volume = "62",
number = "6",
pages = "593--601",
month = "????",
year = "1997",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/(SICI)1097-461X(1997)62:6<593::AID-QUA3>3.0.CO;2-R",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Tue Oct 4 06:59:08 MDT 2011",
bibsource = "Compendex database;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42544;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42544&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Quantum Chem.",
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
journalabr = "Int J Quant Chem",
onlinedate = "6 Dec 1998",
}
@InProceedings{Lang:1997:CVA,
author = "Tom{\'a}s Lang and Elisardo Antelo",
title = "{CORDIC} Vectoring with Arbitrary Target Value",
crossref = "Lang:1997:ISC",
pages = "108--115",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Lang:1997:FIS,
author = "Tom{\'a}s Lang and Jean-Michel Muller and Naofumi
Takagi",
title = "Foreword: {13th IEEE Symposium on Computer Arithmetic,
July 6--9, 1997, Asilomar, California, USA}",
crossref = "Lang:1997:ISC",
pages = "viii--viii",
year = "1997",
bibdate = "Sat Nov 17 12:22:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Lee:1997:SSA,
author = "Choong Ho Lee and M. Kawamata and T. Higuchi",
booktitle = "Proceedings of 1997 {IEEE} International Symposium on
Circuits and Systems: {ISCAS '97}, 9--12 June 1997",
title = "State-space approach to roundoff error analysis of
fractal image coding",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1341--1344",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Roundoff error due to iterative computation with
finite wordlength degrades the quality of decoded
images in fractal image coding that employs a
deterministic iterated function system. This paper
presents a state-space approach to roundoff error
\ldots{}",
}
@InProceedings{Lee:1997:VDA,
author = "Inseop Lee and W. K. Jenkins",
booktitle = "Proceedings of the 40th Midwest Symposium on Circuits
and Systems, 1997",
title = "{VLSI} design for an adaptive equalizer using a
residue number system architecture for magnetic
channels",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "782--785",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.1997.662191",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents the design of an experimental ASIC
for an all-digital adaptive equalizer for magnetic
channels. The equalizer design, which is based on an
RNS chip architecture, is presented at a system level,
with particular attention to \ldots{}",
}
@InProceedings{Lefevre:1997:TCR,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
Tisserand",
title = "Towards Correctly Rounded Transcendentals",
crossref = "Lang:1997:ISC",
pages = "132--139",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lefevre.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13; correct rounding; floating-point
arithmetic",
summary = "The Table Maker's Dilemma is the problem of always
getting exactly rounded results when computing the
elementary functions. After a brief presentation of
this problem, we present new developments that helped
us to solve this problem for the double \ldots{}",
}
@InProceedings{LeLann:1997:AAF,
author = "G{\'e}rard {Le Lann}",
booktitle = "{Proceedings of the International Conference and
Workshop on Engineering of Computer-Based Systems}",
title = "An Analysis of the {Ariane 5 Flight 501} Failure --- A
System Engineering Perspective",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "339--346",
year = "1997",
DOI = "https://doi.org/10.1109/ECBS.1997.581900",
bibdate = "Sat Apr 01 08:29:32 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From the article: ``The SRI S/W exception was raised
during a conversion from a 64-bit floating point number
F to a 16-bit signed integer number. F had a value
greater than what can be represented by a 16-bit signed
integer, which caused an Operand Error (data conversion
--- in Ada code --- was not protected, for the reason
that a maximum workload target of 80\% had been set for
the SRI computer). \ldots{} The value of BH was much
higher than expected because the early part of the
trajectory of Ariane 5 differs from that of Ariane 4,
which results in considerably higher horizontal
velocity values.''",
URL = "http://ieeexplore.ieee.org/document/581900/",
acknowledgement = ack-nhfb,
remark = "Report of an arithmetic error that put an expensive
space missile off course, requiring its destruction in
the air. Presumably-reliable code in Ada adapted from
an earlier missile generated had not been updated for
the new design.",
}
@InProceedings{Li:1997:ISP,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the 5th Annual {IEEE} Symposium on
{FPGAs} for Custom Computing Machines, 16--18 April
1997",
title = "Implementation of single precision floating point
square root on {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "226--232",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The square root operation is hard to implement on
FPGAs because of the complexity of the algorithms. In
this paper, we present a non-restoring square root
algorithm and two very simple single precision floating
point square root implementations \ldots{}",
}
@InProceedings{Li:1997:PAI,
author = "Yamin Li and Wanming Chu",
booktitle = "Proceedings of the 1997 {IEEE} International
Conference on Computer Design: {VLSI} in Computers and
Processors: {ICCD '97}",
title = "Parallel-array implementations of a non-restoring
square root algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "690--695",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "In this paper we present a parallel-array
implementation of a new non-restoring square root
algorithm (PASQRT). The carry-save adder (CSA) is used
in the parallel array. The PASQRT has several features
unlike other implementations. First, it does \ldots{}",
}
@Article{Lin:1997:DOA,
author = "Ming-Bo Lin and A. Y. Oruc",
title = "The design of an optoelectronic arithmetic processor
based on permutation networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "2",
pages = "142--153",
month = feb,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.565589",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565589",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Lin:1997:HSN,
author = "Lei Lin",
title = "High-speed nonlinear computer arithmetic: algorithms,
{VLSI} design, and accuracy prediction",
type = "Thesis ({Ph.D.})",
school = "University of South Florida",
address = "Tampa, FL, USA",
pages = "xv + 204",
year = "1997",
bibdate = "Mon Mar 05 14:36:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Lu:1997:SMK,
author = "Chung-Chin Lu",
title = "A search of minimal key functions for normal basis
multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "5",
pages = "588--592",
month = may,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.589230",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589230",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lutz:1997:HAF,
author = "David R. Lutz and D. N. Jayasimha",
title = "The Half-Adder Form and Early Branch Condition
Resolution",
crossref = "Lang:1997:ISC",
pages = "266--273",
year = "1997",
bibdate = "Sat Nov 17 12:22:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lutz.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Matsubara:1997:LPZ,
author = "G. Matsubara and N. Ide",
booktitle = "Proceedings of the Third International Symposium on
Advanced Research in Asynchronous Circuits and Systems,
7--10 April 1997",
title = "A low power zero-overhead self-timed division and
square root unit combining a single-rail static circuit
with a dual-rail dynamic circuit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "198--209",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An asynchronous pipeline scheme that combines a low
power static circuit with a high-speed dual-rail
dynamic circuit is proposed. The scheme utilizes a
dual-rail circuit only in the critical path of an SRT
division and square root calculation unit. \ldots{}",
}
@InProceedings{Matula:1997:PPF,
author = "David W. Matula and Asger Munk Nielsen",
title = "Pipelined Packet-Forwarding Floating Point: {I}.
Foundations and a Rounder",
crossref = "Lang:1997:ISC",
pages = "140--147",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Matula.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
summary = "The paper presents the foundations for a packet
forwarding floating point format and the design of a
rounder ensuring compatibility between packet
forwarding format and the standard binary IEEE 754
floating point format. The packet forwarding format
\ldots{}",
}
@Article{McClain:1997:EC,
author = "Dylan Loeb McClain",
title = "The Evolution of the Calculator",
journal = j-NY-TIMES,
volume = "??",
number = "??",
pages = "D3--D3",
day = "1",
month = sep,
year = "1997",
CODEN = "NYTIAO",
ISSN = "0362-4331 (print), 1542-667X, 1553-8095",
ISSN-L = "0362-4331",
bibdate = "Sat Aug 17 16:58:52 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://search.proquest.com/docview/109786292",
acknowledgement = ack-nhfb,
fjournal = "New York Times",
journal-URL = "http://www.nytimes.com/",
keywords = "Charles Babbage: Difference Engine",
}
@Article{Michelucci:1997:LA,
author = "D. Michelucci and J.-M. Moreau",
title = "Lazy arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "9",
pages = "961--975",
month = sep,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.620478",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=620478",
abstract = "Finite-precision leads to many problems in geometric
methods from CAD or Computational Geometry. Until now,
using exact rational arithmetic was a simple, yet much
too slow, solution to be of any practical use in
real-scale applications. A recent optimization-the lazy
rational arithmetic-seems promising: It defers exact
computations until they become either unnecessary (in
most cases) or unavoidable; in such a context, only
indispensable computations are performed exactly, that
is, those without which any given decision cannot be
reached safely using only floating-point arithmetic.
This paper takes stock of the lazy arithmetic paradigm:
principles, functionalities and limits, speed, possible
variants and extensions, difficulties, problems solved
or left unresolved",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Mizukami:1997:AFP,
author = "Etsuko Mizukami",
title = "The Accuracy of Floating Point Summations for
{CG}-Like Methods",
type = "{Master's Thesis}",
school = "Department of Computer Science, Indiana
University-Bloomington",
address = "Bloomington, IN, USA",
pages = "v + 55",
year = "1997",
bibdate = "Tue Nov 22 07:27:31 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also issued as Technical report 486.",
URL = "ftp://ftp.cs.indiana.edu/pub/techreports/TR486.pdf;
ftp://ftp.cs.indiana.edu/pub/techreports/TR486.ps;
ftp://ftp.cs.indiana.edu/pub/techreports/TR486.ps.Z;
http://www.cs.indiana.edu/cgi-bin/techreports/TRNNN.cgi?trnum=TR486",
abstract = "It is well known that different ordering of summations
in floating point arithmetic can give different sums
due to rounding error. This dissertation reviews
classic analytic error bounds. A new accurate algorithm
is explained thoroughly along with its analytic error
bound. These summation algorithms were implemented as
dotproducts in an iterative solver to determine which
summation ordering is more accurate in practice.
Another issue is the relationship between dotproduct
accuracy and the convergence of iterative solvers.
Analysis and experiments indicate there are two primary
sources of errors, and show which summation methods are
better for reducing these errors. Results also indicate
little correlation between dotproduct accuracy and
numbers of iterations required by a solver, within a
wide range of accuracies.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{MRaihi:1997:XFO,
author = "David M'Ra{\"\i}hi and David Naccache and Jacques
Stern and Serge Vaudenay",
title = "{XMX}: a Firmware-Oriented Block Cipher Based on
Modular Multiplications",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1267",
pages = "166--??",
year = "1997",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:51:07 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1267.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1267/12670166.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1267/12670166.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Mukherjee:1997:DTM,
author = "N. Mukherjee and J. Rajski and J. Tyszer",
title = "Design of testable multipliers for fixed-width data
paths",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "7",
pages = "795--810",
month = jul,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.599900",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=599900",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Muller:1997:EFA,
author = "Jean-Michel Muller",
title = "Elementary Functions: Algorithms and Implementation",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xv + 204",
year = "1997",
ISBN = "0-8176-3990-X",
ISBN-13 = "978-0-8176-3990-7",
LCCN = "QA331.M866 1997",
bibdate = "Fri Jul 25 12:00:55 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$59.95",
URL = "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X;
http://www.ens-lyon.fr/~jmmuller/book_functions.html",
abstract = "The elementary functions (sine, cosine, tan,
exponentials, and logarithms) are the most commonly
used mathematical functions in science and engineering.
Computing these functions quickly and accurately is a
major goal in computer arithmetic. This new book gives
the concepts and background necessary to understand and
build algorithms for computing these functions,
presenting and structuring the algorithms
(hardware-oriented as well as software-oriented), and
discusses issues related to the accurate floating-point
implementation. The purpose is not to give ``cookbook
recipes'' that allow one to implement some given
function, but to provide the reader with the knowledge
that is necessary to build, or adapt, algorithms to
their specific computing environment. The book provides
an up-to-date presentation of the information needed to
understand and accurately use mathematical functions
and algorithms in computational work and design.
Graduates, professionals and researchers in scientific
computing, software engineering and computer
engineering will find the book a useful reference and
resource.",
acknowledgement = ack-nhfb,
shorttableofcontents = "1: Introduction \\
2: Computer arithmetic \\
I: Algorithms based on polynomial approximation and/or
table lookup \\
3: Polynomial approximations \\
4: Table-based methods \\
II: Shift-and-Add algorithms \\
5: Shift-and-Add algorithms 6: The CORDIC algorithm \\
7: Other shift-and-add algorithms \\
III: Range reduction, final rounding and exceptions \\
8: Range reduction \\
9: Final rounding \\
10: Miscellaneous",
tableofcontents = "1 Introduction / 1 \\
2 Computer Arithmetic / 9 \\
2.1 Floating-Point Arithmetic / 9 \\
2.1.1 Floating-point formats / 9 \\
2.1.2 Rounding modes / 10 \\
2.1.3 Subnormal numbers and exceptions / 12 \\
2.1.4 ULPs / 13 \\
2.1.5 Testing your computational environment / 13 \\
2.2 Redundant Number Systems / 13 \\
2.2.1 Signed-digit number systems / 14 \\
2.2.2 Radix-2 redundant number systems / 15 \\
I Algorithms Based on Polynomial Approximation and/or
Table Lookup / 19 \\
3 Polynomial Approximations / 21 \\
3.1 Least Squares Polynomial Approximations / 22 \\
3.1.1 Legendre polynomials / 23 \\
3.1.2 Chebyshev polynomials / 23 \\
3.1.3 Jacobi polynomials / 23 \\
3.2 Least Maximum Approximations / 24 \\
3.3 Speed of Convergence / 31 \\
3.4 Rational Approximations / 34 \\
3.5 Actual Computation / 38 \\
3.6 Example: the Cyrix FastMath Processor / 41 \\
3.7 Algorithms and Architectures / 43 \\
3.7.1 The E-Method / 45 \\
3.7.2 Estrin's Method / 47 \\
3.8 Miscellaneous / 47 \\
4 Table-Based Methods / 51 \\
4.1 Introduction / 51 \\
4.2 Table-Driven Algorithms / 53 \\
4.2.1 Tang's algorithm for $\exp(x)$ in IEEE
floating-point arithmetic / 55 \\
4.2.2 $\ln(x)$ on $[1,2]$ / 57 \\
4.2.3 $\sin(x)$ on $[0,\pi/4]$ / 58 \\
4.3 Gal's Accurate Tables Method / 58 \\
4.4 Methods Requiring Specialized Hardware / 62 \\
4.4.1 Wong and Goto, logarithm / 62 \\
4.4.2 Wong and Goto, exponential / 65 \\
II Shift-and-Add Algorithms / 69 \\
5 Shift-and-Add algorithms / 71 \\
5.1 The Restoring and Nonrestoring Algorithms / 73 \\
5.2 Simple Algorithms for Exponentials and Logarithms /
77 \\
5.2.1 The restoring algorithm for exponentials / 77 \\
5.2.2 The restoring algorithm for logarithms / 79 \\
5.3 Faster Algorithms / 81 \\
5.3.1 Faster computation of exponentials / 81 \\
5.3.2 Faster computation of logarithms / 87 \\
5.4 Baker's Predictive Algorithm / 90 \\
5.5 Bibliographic notes / 98 \\
6 The CORDIC Algorithm / 101 \\
6.1 Introduction / 101 \\
6.2 The Conventional Iteration / 101 \\
6.3 Scale Factor Compensation / 107 \\
6.4 CORDIC With Redundant Number Systems / 109 \\
6.4.1 Signed-digit implementation / 111 \\
6.4.2 Carry-save implementation / 111 \\
6.4.3 The variable scale factor problem / 112 \\
6.5 The Double Rotation Method / 112 \\
6.6 Branching CORDIC / 115 \\
6.7 Differential CORDIC / 118 \\
6.8 Computation of $\cos^{-1}$ and $\sin^{-1}$ / 122
\\
6.9 Variations on CORDIC / 124 \\
7 Other Shift-and-Add Algorithms / 127 \\
7.1 High-Radix Algorithms / 127 \\
7.1.1 Ercegovac's radix-16 algorithms / 127 \\
7.2 The BKM Algorithm / 131 \\
7.2.1 The BKM iteration / 133 \\
7.2.2 Computation of the exponential function (E-mode)
/ 133 \\
7.2.3 Computation of the logarithm function (L-mode) /
137 \\
7.2.4 Application to the computation of elementary
functions / 138 \\
III Range Reduction, Final Rounding and Exceptions /
141 \\
8 Range Reduction / 143 \\
8.1 Introduction / 143 \\
8.2 Cody and Waite's Method for Range Reduction / 148
\\
8.3 Worst Cases for Range Reduction / 149 \\
8.3.1 A few basic notions on continued fractions / 149
\\
8.3.2 Finding worst cases using continued fractions /
151 \\
8.4 The Payne and Hanek Algorithm / 154 \\
8.5 The Modular Algorithm / 158 \\
8.5.1 Fixed-point reduction / 158 \\
8.5.2 Floating-point reduction / 161 \\
8.5.3 Architectures for Modular Reduction / 161 \\
9 Final Rounding / 163 \\
9.1 Introduction / 163 \\
9.2 Monotonicity / 164 \\
9.3 Exact Rounding: Presentation of the Problem / 165
\\
9.4 Some Experiments / 168 \\
9.5 A ``Probabilistic'' Approach / 168 \\
9.6 Upper Bounds on $m$ / 171 \\
9.6.1 Frequency of failures / 173 \\
9.6.2 Computing with one million bits / 173 \\
10 Miscellaneous / 175 \\
10.1 Exceptions / 175 \\
10.1.1 NaNs / 176 \\
10.1.2 Exact results / 177 \\
10.2 Notes on $x^y$ / 178 \\
10.3 Multiple Precision / 180",
}
@InProceedings{Nielsen:1997:PPF,
author = "Asger Munk Nielsen and David Matula and C. Lyu and Guy
Even",
title = "Pipelined Packet-Forwarding Floating Point: {II}. An
Adder",
crossref = "Lang:1997:ISC",
pages = "148--155",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Nielsen_Matula.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Nielsen:1997:RRR,
author = "Asger Munk Nielsen and Peter Kornerup",
title = "On Radix Representation of Rings",
crossref = "Lang:1997:ISC",
pages = "34--43",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Nielsen.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Oberman:1997:DAI,
author = "S. F. Oberman and M. J. Flynn",
title = "Division Algorithms and Implementations",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "8",
pages = "833--854",
month = aug,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.609274",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "ftp://arith.stanford.edu/tr/divalgo_TOC.pdf;
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=609274",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Oberman:1997:DID,
author = "S. F. Oberman and M. J. Flynn",
title = "Design Issues in Division and Other Floating-Point
Operations",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "2",
pages = "154--161",
month = feb,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.565590",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "ftp://arith.stanford.edu/tr/desissues_TOC.pdf;
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565590",
abstract = "Floating-point division is generally regarded as a low
frequency, high latency operation in typical
floating-point applications. However, in the worst
case, a high latency hardware floating-point divider
can contribute an additional 0.50 CPI to a system
executing SPECfp92 applications. This paper presents
the system performance impact of floating-point
division latency for varying instruction issue rates.
It also examines the performance implications of shared
multiplication hardware, shared square root, on-the-fly
rounding and conversion, and fused functional units.
Using a system level study as a basis, it is shown how
typical floating-point applications can guide the
designer in making implementation decisions and
trade-offs.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "Floating-point division is generally regarded as a low
frequency, high latency operation in typical
floating-point applications. However, in the worst
case, a high latency hardware floating-point divider
can contribute an additional 0.50 CPI to a \ldots{}",
}
@InProceedings{Oberman:1997:SPD,
author = "Stuart F. Oberman and Hesham Al-Twaijry and Michael J.
Flynn",
title = "The {SNAP} Project: Design of Floating Point
Arithmetic Units",
crossref = "Lang:1997:ISC",
pages = "156--165",
year = "1997",
DOI = "https://doi.org/10.1109/ARITH.1997.614891",
bibdate = "Mon May 27 09:39:18 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "ftp://arith.stanford.edu/tr/snap13.ps.Z;
http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Oberman.pdf",
abstract = "In recent years computer applications have increased
in their computational complexity. The industry wide
usage of performance benchmarks, such as SPECmarks, and
the popularity of 3D graphics applications forces
processor designers to pay particular attention to
implementation of the floating point unit, or FPU. The
paper presents results of the Stanford subnanosecond
arithmetic processor (SNAP) research effort in the
design of hardware for floating point addition,
multiplication and division. We show that one cycle FP
addition is achievable 32\% of the time using a
variable latency algorithm. For multiplication, a
binary tree is often inferior to a Wallace tree
designed using an algorithmic layout approach for
contemporary feature sizes (0.3 $ \mu $ m). Further, in
most cases two bit Booth encoding of the multiplier is
preferable to non Booth encoding for partial product
generation. It appears that for division, optimum area
performance is achieved using functional iteration, and
we present two techniques to further reduce average
division latency.",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
remark = "Pages 166--167 left blank.",
}
@Article{Oklobdzija:1997:CLZ,
author = "V. Oklobdzija and H. Suzuki and H. Morinaka and H.
Makino and Y. Nakase and K. Mashiko and T. Sumi",
title = "Comments on {``Leading-zero anticipatory logic for
high-speed floating point addition''} [with reply]",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "32",
number = "2",
pages = "292--292",
month = feb,
year = "1997",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Suzuki:1996:LZA}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "For original article see H. Suzuki, H. Morinaka, H.
Makino, Y. Nakase, K. Mashiko and T. Sumi, ibid.,
vol.31, pp.1157-69 (Aug. 1996). I have read with a
great interest the article by H. Suzuki et al. I am
familiar with their work, and I found their \ldots{}",
}
@Article{Paar:1997:FAA,
author = "Christof Paar and Pedro Soria-Rodriguez",
title = "Fast Arithmetic Architectures for Public-Key
Algorithms over {Galois} Fields {{\em GF\/}$ ((2^n)^m)
$}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1233",
pages = "363--??",
year = "1997",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Feb 4 12:02:26 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1233.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1233/12330363.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1233/12330363.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Parker:1997:MAU,
author = "M. G. Parker and M. Benaissa",
title = "Modular arithmetic using low order redundant bases",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "5",
pages = "611--616",
month = may,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.589237",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:22 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589237",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Parker:1997:MCAa,
author = "Douglass Stott Parker",
title = "{Monte Carlo} arithmetic: exploiting randomness in
floating-point arithmetic",
number = "CSD 970002",
institution = "Department of Computer Science, University of
California, Los Angeles",
address = "Los Angeles, CA, USA",
pages = "86",
year = "1997",
LCCN = "QA75.5 .R46 no.970002 1997",
bibdate = "Thu Oct 24 14:31:00 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.ucla.edu/~stott/mca/CSD-970002.ps.gz",
acknowledgement = ack-nhfb,
}
@TechReport{Parker:1997:MCAb,
author = "Douglass Stott Parker and Paul R. Eggert and Brad
Pierce",
title = "{Monte Carlo} arithmetic: a framework for the
statistical analysis of roundoff error",
type = "Technical report",
number = "CSD-970014",
institution = "Computer Science Department, University of California,
Los Angeles",
address = "Los Angeles, CA 90095-1596, USA",
pages = "23",
day = "30",
month = mar,
year = "1997",
bibdate = "Sun Jun 17 18:24:01 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://fmdb.cs.ucla.edu/treports/970014.pdf;
https://pdfs.semanticscholar.org/b728/afdb230aa1869f79bdc21ff7a6252d3be9ab.pdf",
acknowledgement = ack-nhfb,
keywords = "ANSI\slash IEEE floating-point standards;
floating-point arithmetic; floating-point rounding;
Monte Carlo methods; random rounding; roundoff error;
significance arithmetic",
}
@PhdThesis{Pierce:1997:ARF,
author = "Brad Pierce",
title = "Applications of randomization to floating-point
arithmetic and to linear systems solution",
type = "Thesis ({Ph.D.})",
school = "Department of Computer Science, University of
California, Los Angeles",
address = "Los Angeles, CA, USA",
year = "1997",
bibdate = "Thu Oct 24 14:19:35 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "dissertations, academic -- UCLA -- Computer Science",
}
@InProceedings{Priest:1997:FTD,
author = "Douglas M. Priest",
title = "Fast Table-Driven Algorithms for Interval Elementary
Functions",
crossref = "Lang:1997:ISC",
pages = "168--174",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Priest.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Rederlechner:1997:NCP,
author = "B. Rederlechner and J. Keller",
title = "A Note on Correctness Proofs for Overflow Detection
Logic in Adders for $d$-th Complement Numbers",
journal = j-J-UCS,
volume = "3",
number = "10",
pages = "1121--1125",
day = "28",
month = oct,
year = "1997",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Wed Mar 4 15:32:49 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://medoc.springer.de:8000/jucs/jucs_3_10/a_note_on_correctness",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@Misc{Reppy:1997:EAH,
author = "John H. Reppy and others",
title = "The {Standard ML} Basis Library",
howpublished = "World-Wide Web document",
month = oct,
year = "1997",
bibdate = "Wed Jan 29 16:52:50 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "To be published in/as \cite{Gansner:2003:SMB}.",
URL = "http://cm.bell-labs.com/cm/cs/what/smlnj/doc/basis/pages/real.html",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "From \cite{Steele:2004:RHP}: ``toDecimal should
produce only as many digits as are necessary for
fromDecimal to convert back to the same number, i.e.,
for any Normal or SubNormal real value r, we have:
fromDecimal (toDecimal r) = r \ldots{} Algorithms for
accurately and efficiently converting between binary
and decimal real representations are readily available,
e.g., see the technical report \cite{Gay:1990:CRB}.''",
}
@InProceedings{Rice:1997:MDB,
author = "Eric Rice and Richard Hughey",
title = "Multiprecision Division on an 8-Bit Processor",
crossref = "Lang:1997:ISC",
pages = "74--81",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Rice.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Sanz-Gonzalez:1997:TBR,
author = "J. L. Sanz-Gonzalez",
booktitle = "Acoustics, Speech, and Signal Processing, 1997.
{ICASSP-97., 1997} {IEEE} International Conference on.
21--24 April 1997",
title = "Tradeoff between roundoff and overflow errors in
digital filter realizations",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2189--2192",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper is concerned with a linked analysis of
overflow and roundoff errors in fixed-point digital
filter realizations. Upper bounds for the overflow
error power are obtained, having considered the
saturation quantizer characteristics. Also, \ldots{}",
}
@InProceedings{Sarma:1997:FIR,
author = "Debjit Das Sarma and David W. Matula",
title = "Faithful Interpolation in Reciprocal Tables",
crossref = "Lang:1997:ISC",
pages = "82--91",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Sarma.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@InProceedings{Schulte:1997:AFA,
author = "M. J. Schulte and James E. Stine",
title = "Accurate Function Approximations by Symmetric Table
Lookup and Addition",
crossref = "Thiele:1997:IIC",
pages = "144--153",
year = "1997",
bibdate = "Sun Mar 04 10:55:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1997:HSR,
author = "M. J. Schulte and J. E. Stine and K. E. Wires",
title = "High-Speed Reciprocal Approximations",
crossref = "Fargues:1997:CRT",
pages = "1183--1187",
year = "1997",
bibdate = "Sun Mar 04 10:53:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1997-03.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1997:SBT,
author = "Michael J. Schulte and James E. Stine",
title = "Symmetric Bipartite Tables for Accurate Function
Approximation",
crossref = "Lang:1997:ISC",
pages = "175--183",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf;
http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Schulte.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Schwarz:1997:CFP,
author = "E. M. Schwarz and L. Sigal and T. J. McPherson",
title = "{CMOS} floating-point unit for the {S/390 Parallel
Enterprise Server G4}",
journal = j-IBM-JRD,
volume = "41",
number = "4/5",
pages = "475--488",
month = "????",
year = "1997",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Mon Feb 12 08:10:59 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.almaden.ibm.com/journal/rd/414/schwarz.html",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@InProceedings{Schwarz:1997:RCM,
author = "Eric M. Schwarz and Robert M. {Averill III} and Leon
J. Sigal",
title = "A Radix-8 {CMOS S/390} Multiplier",
crossref = "Lang:1997:ISC",
pages = "2--9",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Schwarz.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Shewchuk:1997:APF,
author = "Jonathan Richard Shewchuk",
title = "Adaptive precision floating-point arithmetic and fast
robust geometric predicates",
journal = j-DISCRETE-COMPUT-GEOM,
volume = "18",
number = "3",
pages = "305--363",
year = "1997",
CODEN = "DCGEER",
DOI = "https://doi.org/10.1007/PL00009321",
ISSN = "0179-5376 (print), 1432-0444 (electronic)",
ISSN-L = "0179-5376",
bibdate = "Sat Apr 28 19:08:39 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.cmu.edu/~quake/robust.html",
acknowledgement = ack-nhfb,
fjournal = "Discrete and Computational Geometry",
journal-URL = "http://link.springer.com/journal/454",
keywords = "accurate floating-point summation",
}
@Article{Soderquist:1997:DSR,
author = "Peter Soderquist and Miriam Leeser",
title = "Division and Square Root: Choosing the Right
Implementation: Exploring the major design choices for
microprocessor implementations of floating-point
division and square root",
journal = j-IEEE-MICRO,
volume = "17",
number = "4",
pages = "56--66",
month = jul # "\slash " # aug,
year = "1997",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/40.612224",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Dec 14 06:08:58 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Science Citation Index database (1980--2000)",
URL = "http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Solinas:1997:IAA,
author = "Jerome A. Solinas",
title = "An Improved Algorithm for Arithmetic on a Family of
Elliptic Curves",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1294",
pages = "357--??",
year = "1997",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:51:15 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1294.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1294/12940357.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1294/12940357.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Srinivas:1997:RDR,
author = "H. R. Srinivas and K. K. Parhi and L. A. Montalvo",
title = "Radix $2$ division with over-redundant quotient
selection",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "1",
pages = "85--92",
month = jan,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.559806",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=559806",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Stan:1997:SUC,
author = "Mircea R. Stan",
title = "Synchronous Up\slash Down Counter with Clock Period
Independent of Counter Size",
crossref = "Lang:1997:ISC",
pages = "274--281",
year = "1997",
bibdate = "Sat Nov 17 12:22:42 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Stankovic:1997:ASM,
author = "M. Stankovi{\'c} and J. Madi{\'c} and P.
Stanimirovi{\'c}",
title = "Addition, subtraction and multiplication of sequences
of fractions by means of residue arithmetic and
mathematical spectra",
journal = "Math. Balkanica (N.S.)",
volume = "11",
number = "1--2",
pages = "11--23",
year = "1997",
ISSN = "0205-3217",
MRclass = "11Y55 (11A67 68R99)",
MRnumber = "MR1606580 (98m:11141)",
MRreviewer = "Marc Del{\'e}glise",
bibdate = "Thu Nov 8 14:50:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematica Balkanica. New Series",
}
@InProceedings{Stelling:1997:IMA,
author = "Paul F. Stelling and Voji. G. Oklobdzija",
title = "Implementing Multiply-Accumulate Operation In
Multiplication Time",
crossref = "Lang:1997:ISC",
pages = "99--107",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stelling.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Strzebonski:1997:CFC,
author = "Adam Wojciech Strzebo{\'n}ski",
title = "Computing in the Field of Complex Algebraic Numbers",
journal = j-J-SYMBOLIC-COMP,
volume = "24",
number = "6",
pages = "647--656",
month = dec,
year = "1997",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "68Q40",
MRnumber = "98h:68125",
bibdate = "Tue Nov 10 06:53:22 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171/",
}
@InProceedings{Szabo:1997:REAa,
author = "T. Szabo and G. Horvath",
booktitle = "Acoustics, Speech, and Signal Processing, 1997.
{ICASSP-97., 1997} {IEEE} International Conference on.
21--24 April 1997",
title = "A roundoff error analysis of the {Oja}'s subspace
rule",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3297--3300",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper deals with the effects of finite precision
data representation and arithmetic in principal
component analysis (PCA) networks. PCA or Karhunen
Loeve transform (KLT) is a statistical method that
determines an optimal linear transformation \ldots{}",
}
@InProceedings{Szabo:1997:REAb,
author = "T. Szabo and G. Horvath",
booktitle = "Instrumentation and Measurement Technology Conference,
1997. {IMTC/97}. Proceedings. 'Sensing, Processing,
Networking'., {IEEE. 19--21} May 1997",
title = "Roundoff error analysis of the {PCA} networks",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "263--268",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper deals with some of the effects of finite
precision data representation and arithmetics in
principal component analysis (PCA) neural networks. The
PCA networks are single layer linear neural networks
that use some versions of Oja's \ldots{}",
}
@Misc{Taborn:1997:DSM,
author = "M. P. Taborn and S. M. Burchfiel and D. T. Matheny",
title = "Denormalization system and method of operation",
day = "8",
month = jul,
year = "1997",
bibdate = "Fri Nov 28 15:28:39 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,646,875.",
acknowledgement = ack-nhfb,
}
@InProceedings{Takagi:1997:GPO,
author = "Naofumi Takagi",
title = "Generating a Power of an Operand by a Table Look-Up
and a Multiplication",
crossref = "Lang:1997:ISC",
pages = "126--131",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Takagi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Manual{TI:1997:TUG,
title = "{TMS320C3x} User's Guide",
organization = "Texas Instruments",
address = "Post Office box 655303, Dallas, TX 75265, USA",
year = "1997",
bibdate = "Wed Nov 24 09:20:17 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www-s.ti.com/sc/psheets/spru031e/spru031e.pdf;
http://www-s.ti.com/sc/psheets/spru031f/spru031f.pdf",
acknowledgement = ack-nhfb,
keywords = "digital signal processor (DSP)",
remark = "No longer accessible at the first URL. A 2004 edition
is at the second URL.",
}
@InProceedings{Tomabechi:1997:WOD,
author = "N. Tomabechi",
booktitle = "Proceedings of 1997 {IEEE} International Symposium on
Circuits and Systems, {ISCAS '97}, 9--12 June 1997",
title = "{WSI} oriented design for noise-tolerant systems based
on the residue number system",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2733--2736",
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1997.612890",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents a design method for noise-tolerant
WSI systems in which the features of the residue number
system and multiple clock pulses are effectively
combined. The analysis shows that the reliability of
the presented system is greatly \ldots{}",
}
@Article{Tsai:1997:FPR,
author = "Chimin Tsai",
title = "Floating-point roundoff noises of first- and
second-order sections in parallel form digital
filters",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "44",
number = "9",
pages = "774--779",
month = sep,
year = "1997",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.625021",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "Assuming wide-sense stationary white noise input, we
investigated the floating-point roundoff noises of
first- and second order digital subfilters. For
first-order subfilters, the roundoff noise of parallel
form 3P realization is invariably smaller \ldots{}",
}
@InProceedings{Turner:1997:FFR,
author = "Peter R. Turner",
title = "Fraction-Free {RNS} Algorithms for Solving Linear
Systems",
crossref = "Lang:1997:ISC",
pages = "218--224",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Turner.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Book{Ueberhuber:1997:NCM,
author = "Christoph W. Ueberhuber",
title = "Numerical Computation: Methods, Software, and
Analysis",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 474 (vol. 1), xvi + 495 (vol. 2)",
year = "1997",
DOI = "https://doi.org/10.1007/978-3-642-59118-1",
ISBN = "3-540-62058-3 (vol. 1: softcover), 3-540-62057-5 (vol.
2: softcover), 3-642-59118-3 (e-book)",
ISBN-13 = "978-3-540-62058-7 (vol. 1: softcover),
978-3-540-62057-0 (vol. 2: softcover),
978-3-642-59118-1 (e-book)",
LCCN = "QA297 .U2413 1997",
bibdate = "Thu Oct 28 15:17:48 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
price = "US\$44.95 (vol. 1), US\$49.95 (vol. 2)",
abstract = "This book is the first part of a modern, two-volume
introduction to numerical computation, which strongly
emphasizes software aspects. It can serve as a textbook
for courses on numerical analysis, particularly for
engineers. The book can also be used as a reference
book and it includes an extensive bibliography. The
author is a well-known specialist in numerical analysis
who was involved in the creation of the software
package QUADPACK.",
acknowledgement = ack-nhfb,
tableofcontents = "1 Scientific Modeling \\
1.1 Reality Versus Model \\
1.2 The Model Subject and the Model \\
1.3 The Model Subject and Reality \\
1.4 Model Building \\
2 Fundamental Principles of Numerical Methods \\
2.1 From Application Problems to their Numerical
Solution \\
2.2 Numerical Problems \\
2.3 Types of Errors in Numerics \\
2.4 The Condition of Mathematical Problems \\
2.5 The Condition of Application Problems \\
2.6 The Mathematical Elements of Condition Estimation
\\
2.7 Validation of Numerical Computations \\
3 Computers for Numerical Data Processing \\
3.1 Processors \\
3.2 Memory \\
3.3 Performance Quantification \\
3.4 Analytical Performance Assessment \\
3.5 Empirical Performance Assessment \\
4 Numerical Data and Numerical Operations \\
4.1 Mathematical Data \\
4.2 Numerical Data on Computers \\
4.3 Operations on Numerical Data \\
4.4 Number Systems on Computers \\
4.5 Structure of Floating-Point Systems \\
4.6 Standardization of Floating-Point Number Systems
\\
4.7 Arithmetics for Floating-Point Systems \\
4.8 Inquiry Functions and Manipulation of Numbers in
Fortran 90 \\
4.9 Operations with Algebraic Data \\
4.10 Operations with Arrays \\
4.11 Operations with Analytic Data \\
5 Numerical Algorithms \\
5.1 The Intuitive Notion of an Algorithm \\
5.2 Properties of Algorithms \\
5.3 Existence of Algorithms \\
5.4 Practical Solvability of Problems \\
5.5 Complexity of Algorithms \\
5.6 Representation of Algorithms \\
5.7 Influence of Rounding Errors on Numerical
Algorithms \\
5.8 Case Study: Floating-Point Summation \\
6 Numerical Programs \\
6.1 The Quality of Numerical Programs \\
6.2 Reasons for Poor Efficiency \\
6.3 The Measurement of Performance Indices \\
6.4 Performance Optimization \\
6.5 Architecture Independent Optimizations \\
6.6 Loop Optimizations \\
6.7 Blocked Memory Access \\
6.8 Case Study: Multiplication of Matrices \\
7 Available Numerical Software \\
7.1 The Cost of Software \\
7.2 Sources of Numerical Software \\
7.3 Software and the Internet \\
7.4 Interactive Multifunctional Systems \\
7.5 Problem Solving Environments \\
7.6 Case Study: Software for Elliptic PDEs \\
8 Using Approximation in Mathematical Model Building
\\
8.1 Analytic Models \\
8.2 Information and Data \\
8.3 Discrete Approximation \\
8.4 Function Approximation \\
8.5 Choosing a Model Function \\
8.6 Choice of the Distance Function \\
8.7 Transformation of the Problem \\
9 Interpolation \\
9.1 Interpolation Problems \\
9.2 Mathematical Foundations \\
9.3 Univariate Polynomial Interpolation \\
9.4 Univariate, Piecewise, Polynomial Interpolation \\
9.5 Polynomial Splines \\
9.6 B-Splines \\
9.7 Cubic Spline Interpolation \\
9.8 Splines Without Undesirable Oscillations \\
9.9 Multivariate Interpolation \\
9.10 Multivariate Polynomial Interpolation \\
9.11 Multivariate (Sub-) Spline Interpolation \\
9.12 Related Problems and Methods \\
Glossary of Notation \\
Author Index",
}
@Article{Verschaeren:1997:NPF,
author = "Dennis Verschaeren and Annie Cuyt and Brigitte
Verdonk",
title = "On the Need for Predictable Floating-Point Arithmetic
in the Programming Languages {Fortran 90} and {C\slash
C++}",
journal = j-SIGPLAN,
volume = "32",
number = "3",
pages = "57--64",
month = mar,
year = "1997",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:17:30 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@InProceedings{Walter:1997:EUD,
author = "Colin D. Walter",
title = "Exponentiation using Division Chains",
crossref = "Lang:1997:ISC",
pages = "92--98",
year = "1997",
bibdate = "Mon May 20 05:45:32 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Walter.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
}
@Article{Walter:1997:STT,
author = "C. D. Walter",
title = "Space\slash time trade-offs for higher radix modular
multiplication using repeated addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "46",
number = "2",
pages = "139--141",
month = feb,
year = "1997",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.565588",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:06:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565588",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wilkes:1997:AE,
author = "M. V. Wilkes",
title = "Arithmetic on the {EDSAC}",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "19",
number = "1",
pages = "13--15",
month = jan # "\slash " # mar,
year = "1997",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/85.560726",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Thu Jul 12 08:14:44 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
URL = "http://ieeexplore.ieee.org/iel4/85/12228/00560726.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Ann. Hist. Comput.",
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}
@Article{Williams:1997:IPC,
author = "C. Williams",
title = "{Intel}'s {Pentium} chip crisis: an ethical analysis",
journal = j-IEEE-TRANS-PROF-COMMUN,
volume = "40",
number = "1",
pages = "13--19",
month = mar,
year = "1997",
CODEN = "IEPCBU",
DOI = "https://doi.org/10.1109/47.557513",
ISSN = "0361-1434 (print), 1558-1500 (electronic)",
ISSN-L = "0361-1434",
bibdate = "Sat Dec 18 11:57:01 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransprofcommun.bib",
abstract = "In October 1994 a mathematics professor informed the
Intel Corporation that its Pentium chip had a flaw
which caused mathematical errors. Intel's response to
the professor and its customers created a backlash of
anger and a public relations crisis. By analyzing
Intel's actions using the work of two relevant ethical
philosophies, the article shows that some of the
company's errors in public relations were also ethical
errors. However, it also points out that Intel has made
improvements which will help it avoid future problems
and which could set an ethical precedent for the
semiconductor industry.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Professional Communication",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=47",
keywords = "Pentium divide flaw; Thomas Nicely",
}
@Article{Woehr:1997:CWK,
author = "Jack Woehr",
title = "A Conversation with {William Kahan}: How important is
numerical accuracy?",
journal = j-DDJ,
volume = "22",
number = "11",
pages = "18--20, 22, 24, 26, 30, 32",
month = nov,
year = "1997",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Fri Nov 28 17:28:03 MST 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Kahan, the father of the IEEE 754 floating-point
standard, talks about floating-point arithmetic issues,
and numerical deficiencies in Java.",
abstract = "Noted mathematician and computer scientist William
Kahan has played a central role in everything from the
design of the 8087 math coprocessor to defining the
ANSI\slash IEEE Standard for binary floating-point
arithmetic. He takes time out of his schedule to talk
with us about the current state of numeric computing.",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Xue:1997:DPK,
author = "Jinyun Xue and Ruth Davis",
title = "A Derivation and Proof of {Knuth}'s Binary to Decimal
Conversion Program",
journal = j-SOFTW-CONCEPTS-TOOLS,
volume = "18",
number = "4",
pages = "149--156",
year = "1997",
CODEN = "SCOTE5",
ISSN = "0945-8115 (print), 1432-2188 (electronic)",
ISSN-L = "0945-8115",
bibdate = "Sat Jan 6 12:49:28 2024",
bibsource = "dblp computer science bibliography; https://dblp.org;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/structprogram.bib",
acknowledgement = ack-nhfb,
biburl = "https://dblp.org/rec/journals/stp/XueD97.bib",
dblp-id = "DBLP:journals/stp/XueD97",
fjournal = "Software---Concepts and Tools",
journal-URL = "https://link.springer.com/journal/378",
timestamp = "Fri Apr 11 09:35:40 2025",
}
@InProceedings{Zeng:1997:REA,
author = "Bing Zeng",
booktitle = "Proceedings of 1997 {IEEE} International Symposium on
Circuits and Systems: {ISCAS '97}, 9--12 June 1997",
title = "Roundoff error analysis of floating-point paraunitary
filter banks realized in lattice structure",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2405--2408",
year = "1997",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Floating-point roundoff noise characteristics of
two-channel paraunitary filter banks realized in
lattice structure are studied in detail in this paper.
Under the assumption that all quantization errors are
independent WSS white noise with zero-mean, \ldots{}",
}
@Article{Aberbour:1998:PMF,
author = "M. Aberbour and A. Houelle and H. Mehrez and N.
Vaucher and A. Guyot",
title = "On portable macrocell {FPU} generators for division
and square root operators complying to the full
{IEEE-754} standard",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "6",
number = "1",
pages = "114--121",
month = mar,
year = "1998",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/92.661253",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
summary = "In this paper, we investigate the design of macrocell
generators of division and square root floating-point
operators. The number representation used in our
operators is the IEEE-754-1985 standard for binary
floating-point numbers. The design and \ldots{}",
}
@Book{Aberth:1998:PNM,
author = "Oliver Aberth",
title = "Precise numerical methods using {C++}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiv + 238",
year = "1998",
ISBN = "0-12-041750-2",
ISBN-13 = "978-0-12-041750-6",
LCCN = "QA76.73.C153 A32 1998",
bibdate = "Wed Nov 3 09:30:14 MST 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Contents: I. Introduction -- II. Various Arithmetics
-- III. Solvable Problems and Nonsolvable Problems --
IV. Computing Derivatives and Integrals -- V. Finding
Zeros of Real Functions -- VI. Finding Zeros of
Polynomials and Other Analytic Functions -- VII.
Problems of Linear Algebra -- VIII. Optimization
Problems -- IX. Numerical Solution of Ordinary
Differential Equations -- X. The C++ System for Precise
Computation.",
price = "US\$59.95",
acknowledgement = ack-nhfb,
keywords = "C (computer program language); numerical analysis --
data processing",
}
@Article{Al-Twaijry:1998:SPB,
author = "H. A. Al-Twaijry and S. F. Oberman and S. T. Fu and M.
J. Flynn",
title = "The {SNAP} Project: Building Validated Floating
Point",
journal = j-J-UCS,
volume = "4",
number = "2",
pages = "99--109",
day = "28",
month = feb,
year = "1998",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Wed Mar 4 15:32:49 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://medoc.springer.de:8000/jucs/jucs_4_2/the_snap_project_building;
http://www.jucs.org/jucs_4_2/the_snap_project_building/Al_twaijry_H_A.pdf",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@Article{Al-Twaijry:1998:TSE,
author = "H. A. Al-Twaijry and M. J. Flynn",
title = "Technology scaling effects on multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "11",
pages = "1201--1215",
month = nov,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.736430",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736430",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Althaus:1998:MNF,
author = "Ernst Althaus and Kurt Mehlhorn",
title = "Maximum network flow with floating point arithmetic",
journal = j-INFO-PROC-LETT,
volume = "66",
number = "3",
pages = "109--113",
day = "15",
month = may,
year = "1998",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sat Nov 7 17:55:59 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/
2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Anonymous:1998:ANO,
author = "Anonymous",
title = "Announcements: New Official {Fortran} Technical
Reports; Working Group 5 Documents; {OpenGL} {Fortran
95} Bindings; {MPI} Module Provides Enhanced {Fortran}
Support; Variable Precision Arithmetic; {Fortran}
Information Sites; New {Fortran} Compiler Versions from
{Lahey} and {Fujitsu}; Downloadable Advanced {Fortran}
Textbook; {Fortran} Engineering Textbook",
journal = j-FORTRAN-FORUM,
volume = "17",
number = "3",
pages = "1--2",
month = dec,
year = "1998",
CODEN = "????",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Thu Feb 07 13:34:54 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "53",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@Article{Anonymous:1998:PIS,
author = "Anonymous",
title = "Papers from the {13th IEEE Symposium on Computer
Arithmetic}",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "7",
pages = "721--721",
month = jul,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1998.709371",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709371",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Antelo:1998:CVH,
author = "E. Antelo and T. Lang and J. D. Bruguera",
title = "Computation of $ \sqrt {(x / d)} $ in a very high
radix combined division\slash square-root unit with
scaling and selection by rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "2",
pages = "152--161",
month = feb,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.663761",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A very-high radix digit-recurrence algorithm for the
operation {\surd}(x/d) is developed, with residual
scaling and digit selection by rounding. This is an
extension of the division and square-root algorithms
presented previously, and for which a \ldots{}",
}
@Book{Appel:1998:MCI,
author = "Andrew W. Appel",
title = "Modern Compiler Implementation in {ML}",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "x + 538",
year = "1998",
DOI = "https://doi.org/10.1017/CBO9780511811449",
ISBN = "0-521-58274-1, 0-521-60764-7 (paperback)",
ISBN-13 = "978-0-521-58274-2, 978-0-521-60764-3 (paperback)",
LCCN = "QA76.76.C65 A675 1998",
bibdate = "Sat Apr 1 07:46:22 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://proquest.safaribooksonline.com/9781107263826;
http://www.loc.gov/catdir/description/cam028/97031091.html;
http://www.loc.gov/catdir/toc/cam023/97031091.html",
abstract = "This new, expanded textbook describes all phases of a
modern compiler: lexical analysis, parsing, abstract
syntax, semantic actions, intermediate representations,
instruction selection via tree matching, dataflow
analysis, graph-coloring register allocation, and
runtime systems. It includes good coverage of current
techniques in code generation and register allocation,
as well as functional and object-oriented languages,
that are missing from most books. In addition, more
advanced chapters are now included so that it can be
used as the basis for two-semester or graduate course.
The most accepted and successful techniques are
described in a concise way, rather than as an
exhaustive catalog of every possible variant. Detailed
descriptions of the interfaces between modules of a
compiler are illustrated with actual C header files.
The first part of the book, Fundamentals of
Compilation, is suitable for a one-semester first
course in compiler design. The second part, Advanced
Topics, which includes the advanced chapters, covers
the compilation of object-oriented and functional
languages, garbage collection, loop optimizations, SSA
form, loop scheduling, and optimization for
cache-memory hierarchies.",
acknowledgement = ack-nhfb,
author-dates = "1960--",
subject = "ML (Computer program language); Compilers (Computer
programs); Compilers (Computer programs); ML (Computer
program language); Compiler",
tableofcontents = "Part I. Fundamentals of Compilation: \\
1. Introduction \\
2. Lexical analysis \\
3. Parsing \\
4. Abstract syntax \\
5. Semantic analysis \\
6. Activation records \\
7. Translation to intermediate code \\
8. Basic blocks and traces \\
9. Instruction selection \\
10. Liveness analysis \\
11. Register allocation \\
12. Putting it all together \\
Part II. Advanced Topics: \\
13. Garbage collection \\
14. Object-oriented languages \\
15. Functional programming languages \\
16. Polymorphic types \\
17. Dataflow analysis \\
18. Loop optimizations \\
19. Static single-assignment form \\
20. Pipelining and scheduling \\
21. The memory hierarchy",
}
@Article{Arnold:1998:ACT,
author = "M. G. Arnold and T. A. Bailey and J. R. Cowles and M.
D. Winkel",
title = "Arithmetic co-transformations in the real and complex
logarithmic number systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "7",
pages = "777--786",
month = jul,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.709377",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709377",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bailey:1998:OEF,
author = "Daniel V. Bailey and Christof Paar",
title = "Optimal Extension Fields for Fast Arithmetic in
Public-Key Algorithms",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1462",
pages = "472--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:52:43 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1462.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1462/14620472.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1462/14620472.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Bajard:1998:NED,
author = "Jean-Claude Bajard and Laurent-St{\'e}phane Didier and
Jean-Michel Muller",
title = "A New {Euclidean} Division Algorithm for Residue
Number Systems",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "19",
number = "2",
pages = "167--178",
month = jul,
year = "1998",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1008065819322",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
abstract = "We propose a new algorithm and architecture for
performing divisions in residue number systems (RNS).
Our algorithm is suitable for RNS with large moduli,
with the aim of manipulating very large integers on a
parallel computer or a special-purpose architecture.
The two basic features of our algorithm are the use of
a high-radix division method, and the use of a
floating-point arithmetic that should run in parallel
with the modular arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
keywords = "residue number systems (RNS)",
pagecount = "12",
}
@Article{Bajard:1998:RMM,
author = "J.-C. Bajard and L.-S. Didier and P. Kornerup",
title = "An {RNS} {Montgomery} modular multiplication
algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "7",
pages = "766--776",
month = jul,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.709376",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709376",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Bhardwaj:1998:RRN,
author = "M. Bhardwaj and B. Ljusanin",
booktitle = "Conference Record of the Thirty-Second Asilomar
Conference on Signals, Systems {\&} Computers, 1998",
title = "The {Renaissance} --- a residue number system based
vector co-processor for {DSP} dominated embedded
{ASICs}",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "202--207",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.1998.750854",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper reports our ongoing investigation of a new
paradigm to realize high performance DSP architectures
suitable for embedded ASICs. The reasons for the
significant gap between achievable MAC bandwidth and
that delivered by current embedded DSP \ldots{}",
}
@Misc{Bjorksten:1998:FFP,
author = "A. A. Bjorksten and J. D. G. Mikan and M. S.
Schmookler",
title = "Fast floating point results alignment apparatus",
day = "9",
month = jun,
year = "1998",
bibdate = "Fri Nov 28 15:36:39 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,764,549.",
acknowledgement = ack-nhfb,
}
@Misc{Briggs:1998:DFP,
author = "Keith Briggs",
title = "Doubledouble floating point arithmetic",
howpublished = "World-Wide Web document.",
institution = "Department of Plant Sciences, University of
Cambridge",
address = "Downing Street, Cambridge CB2 3EA, UK",
year = "1998",
bibdate = "Wed Nov 24 08:26:24 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://web.archive.org/web/20000520034826/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
http://web.archive.org/web/20000815202251/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
http://web.archive.org/web/20001207115000/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
http://web.archive.org/web/20010204072400/http://web.archive.org/web/20010204072400/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.tgz;
http://web.archive.org/web/20010204072400/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html",
acknowledgement = ack-nhfb,
remark = "Author no longer at Cambridge, and Web page gone;
however, www.archive.org has saved it (see the second
URL)",
}
@InProceedings{Bronnimann:1998:IAY,
author = "Herv{\'e} Br{\"o}nnimann and Christoph Burnikel and
Sylvain Pion",
booktitle = "Proc. 14th Annu. {ACM} Sympos. Comput. Geom. (1998)",
title = "Interval arithmetic yields efficient dynamic filters
for computational geometry",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "165--174",
year = "1998",
bibdate = "Fri Jan 6 11:53:51 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "citeseer.csail.mit.edu/onnimann98interval.html",
abstract = "We discuss floating-point filters as a means of
restricting the precision needed for arithmetic
operations while still computing the exact result. We
show that interval techniques can be used to speed up
the exact evaluation of geometric predicates and
describe an efficient implementation of interval
arithmetic that is strongly influenced by the rounding
modes of the widely used IEEE 754 standard. Using this
approach we engineer an efficient floating-point filter
for the computation of the sign of a determinant that
works for arbitrary dimensions. We validate our
approach experimentally, comparing it with other
static, dynamic and semi-static filters.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chang:1998:HPD,
author = "Yun-Nan Chang and Keshab K. Parhi",
title = "High-Performance Digit-Serial Complex-Number
Multiplier-Accumulator",
crossref = "IEEE:1998:IIC",
pages = "211--??",
year = "1998",
DOI = "https://doi.org/10.1109/ICCD.1998.727050",
bibdate = "Sat Aug 22 08:31:58 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a fast highly regular digit-serial
complex-number multiplier-accumulator (CMAC)
architecture which is well suited for VLSI
implementations. This paper makes two contributions.
First, several complex-number representation schemes
are discussed. It is shown that the real-imaginary
alternate (RIA) scheme is the best among all
representation schemes and the prior designs of CMACs
based on the radix-(2j) Redundant Complex Number System
(RCNS) are not efficient with respect to hardware
complexity and processing speed. Second, digit-serial
CMAC architectures which can be pipelined at fine-grain
level to increase the throughput rate are designed
based on carry-save configuration.",
acknowledgement = ack-nhfb,
keywords = "complex-number; digit-serial multiplier; redundant
arithmetic",
}
@Misc{Chatterjee:1998:MMP,
author = "Siddhardtha Chatterjee",
title = "{MPFUN++}: a multiple precision floating point
computation package in {C++}",
howpublished = "World Wide Web document.",
year = "1998",
bibdate = "Thu Nov 25 10:08:42 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.unc.edu/Research/HARPOON/mpfun++/",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:1998:PCL,
author = "Chichyang Chen and Chih-Huan Yang",
booktitle = "Proceedings International Conference on Computer
Design: {VLSI} in Computers and Processors: {ICCD
'98}",
title = "Pipelined computation of {LNS} addition\slash
subtraction with very small lookup tables",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "292--297",
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Logarithmic number system (LNS) has the advantages of
regular data flow high speed, and high precision.
However, the development of LNS arithmetic is hindered
by the large size of the lookup tables used in LNS
addition/subtraction, since the size is \ldots{}",
}
@TechReport{Chen:1998:VFP,
author = "Yirng-An Chen and Randal E. Bryant",
title = "Verification of floating-point adders",
type = "Report",
number = "CMU-CS-98-121",
institution = "Department of Computer Science, Carnegie-Mellon
University",
address = "Pittsburgh, PA, USA",
year = "1998",
bibdate = "Thu May 09 08:44:02 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Cheon:1998:TEA,
author = "Jung Hee Cheon and S. M. Park and S. W. Park and D.
Kim",
title = "Two efficient algorithms for arithmetic of elliptic
curves using {Frobenius} map",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1431",
pages = "195--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Thu Oct 31 17:36:21 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Chren:1998:OHR,
author = "W. A. Chren",
title = "One-Hot Residue Coding for Low Delay Power Product
{CMOS} Design",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "45",
number = "3",
pages = "303--313",
month = mar,
year = "1998",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Jun 24 18:14:56 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
}
@Article{Citron:1998:AMM,
author = "Daniel Citron and Dror Feitelson and Larry Rudolph",
title = "Accelerating Multi-Media processing by Implementing
Memoing in Multiplication and Division Units",
journal = j-SIGPLAN,
volume = "33",
number = "11",
pages = "252--261",
month = nov,
year = "1998",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat May 1 15:51:26 MDT 1999",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/asplos/291069/p252-citron/",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "design; measurement; performance; theory",
remark = "This paper shows how memoing of multiply and divide
units in a 32-entry four-way set associative memo cache
can produces cache hit ratios of 0.11 for
floating-point multiply, and 0.16 for floating-point
divide on the Perfect benchmarks. For SPEC95, the
corresponding results are 0.20 and 0.17. For a
multimedia benchmark, the figures are 0.39 and 0.47,
and for integer multiply 0.59. Current architectures
require 2 to 5 cycles for pipelined floating-point
multiply (one result per clock, in the best case), but
22 to 40 cycles for floating-point division (not
pipelined). Such a cache would require about 1KB of
on-chip memory, which is currently feasible, since
several architectures offer on-chip caches of up to
64KB, and could offer significant speedups for
division.",
subject = "{\bf H.5.1} Information Systems, INFORMATION
INTERFACES AND PRESENTATION, Multimedia Information
Systems. {\bf H.5.2} Information Systems, INFORMATION
INTERFACES AND PRESENTATION, User Interfaces. {\bf
B.3.2} Hardware, MEMORY STRUCTURES, Design Styles,
Cache memories.",
}
@Article{Collins:1998:PFB,
author = "Robert R. Collins",
title = "The {Pentium F00F} Bug",
journal = j-DDJ,
volume = "23",
number = "5",
pages = "62, 64--66",
month = may,
year = "1998",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Sat Jun 05 14:14:22 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/dr-dobbs.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ddj.com/ftp/1998/1998_05/f00fbug.txt;
http://www.ddj.com/ftp/1998/1998_05/f00fbug.zip",
abstract = "When x86 processors encounter an invalid instruction
and the processor is supposed to generate an invalid
opcode exception. If this mechanism fails and however
and the program can bring the system down -- and that's
what happens with the F00F bug. Additional resources
include F00FBUG.TXT (listings) and f00fbug.zip (source
code).",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
}
@Article{Cornea-Hasegan:1998:PIC,
author = "Marius Cornea-Hasegan",
title = "Proving the {IEEE} Correctness of Iterative
Floating-Point Square Root, Divide, and Remainder
Algorithms",
journal = j-INTEL-TECH-J,
volume = "Q2",
pages = "11",
year = "1998",
bibdate = "Fri Jun 01 06:02:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://developer.intel.com/technology/itj/q21998/articles/art_3.htm;
http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf",
acknowledgement = ack-nhfb,
}
@Article{Crenshaw:1998:ISR,
author = "Jack W. Crenshaw",
title = "Integer Square Roots",
journal = j-EMBED-SYS-PROG,
volume = "11",
number = "2",
pages = "15--32",
month = feb,
year = "1998",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Fri Nov 28 16:31:58 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.embedded.com/98/9802fe2.htm",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Embedded Systems Programming",
}
@TechReport{Darcy:1998:APE,
author = "Joseph D. Darcy and William Kahan",
title = "Analysis of {{\em Proposal for Extension to Java
Floating Point Semantics, Revision 1}}",
institution = "{Java Grande Numerics Working Group}",
pages = "18",
day = "7",
month = aug,
year = "1998",
bibdate = "Mon May 06 09:08:27 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sonic.net/~jddarcy/Research/jgrande.pdf",
acknowledgement = ack-nhfb,
}
@MastersThesis{Darcy:1998:BAI,
author = "Joseph D. Darcy",
title = "{Borneo 1.0}: adding {IEEE 754} floating point support
to {Java}",
type = "{Master of Science, Plan II}",
school = "University of California, Berkeley, Dept. of
Electrical Engineering and Computer Sciences",
address = "Berkeley, CA, USA",
pages = "131",
year = "1998",
LCCN = "T7.49.1998 D27",
bibdate = "Mon May 06 09:01:22 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sonic.net/~jddarcy/Borneo/borneo.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Darcy:1998:EJF,
author = "Joseph D. Darcy",
title = "Evolving {Java}'s Floating Point Support: The Good,
The Bad, and the Ugly",
crossref = "MacKay:1998:PCT",
pages = "??--??",
year = "1998",
bibdate = "Mon May 06 09:11:13 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "31 slides.",
URL = "http://www.sonic.net/~jddarcy/Research/cascon.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Darcy:1998:WRI,
author = "Joseph D. Darcy",
title = "Writing robust {IEEE} recommended functions in ``100
Pure {Java\TM}''",
type = "Report",
number = "UCB/CSD-98-1009",
institution = "University of California, Berkeley. Computer Science
Division",
address = "Berkeley, CA, USA",
month = aug,
year = "1998",
bibdate = "Mon May 06 09:03:35 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://sunsite.berkeley.edu/Dienst/UI/2.0/Describe/ncstrl.ucb/CSD-98-1009",
acknowledgement = ack-nhfb,
}
@InProceedings{Daumas:1998:ELM,
author = "Marc Daumas",
editor = "????",
booktitle = "Architecture and Arithmetic Support for Multimedia,
Dagstuhl, Germany",
title = "Expansions: lightweight multiple precision
arithmetic",
publisher = "????",
address = "????",
pages = "14--??",
year = "1998",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Nov 24 07:59:30 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Dimitrov:1998:AME,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
title = "An algorithm for modular exponentiation",
journal = j-INFO-PROC-LETT,
volume = "66",
number = "3",
pages = "155--159",
day = "15",
month = may,
year = "1998",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Sat Nov 7 17:55:59 MST 1998",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Dimitrov:1998:FRR,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
title = "A fast and robust {RNS} algorithm for evaluating signs
of determinants",
journal = j-COMPUT-MATH-APPL,
volume = "35",
number = "8",
pages = "9--14",
month = apr,
year = "1998",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:48 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122198000418",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Dimitrov:1998:RNS,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
title = "A residue number system implementation of real
orthogonal transforms",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "46",
number = "3",
pages = "563--570",
month = mar,
year = "1998",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.661325",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=14431",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "Previous work has focused on performing residue
computations that are quantized within a dense ring of
integers in the real domain. The aims of this paper are
to provide an efficient algorithm for the approximation
of real input signals, with \ldots{}",
}
@Article{Drolet:1998:NRE,
author = "G. Drolet",
title = "A new representation of elements of finite fields {$
\mathrm {GF}(2^m) $} yielding small complexity
arithmetic circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "9",
pages = "938--946",
month = sep,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.713313",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713313",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Drolshagen:1998:RNA,
author = "A. Drolshagen and C. C. Sekhar and W. Anheier",
booktitle = "Eleventh International Conference on {VLSI} Design,
1998. Proceedings",
title = "A residue number arithmetic based circuit for
pipelined computation of autocorrelation coefficients
of speech signal",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "122--127",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICVD.1998.646589",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents a new design for module
multipliers suitable for moduli that are not
necessarily prime. The design avoids the need for
building special purpose look-up tables. An RNS
arithmetic based autocorrelator circuit that uses a
large \ldots{}",
}
@InProceedings{Dunay:1998:DFP,
author = "Rezso Dunay and Istvan Kollar and Bernard Widrow",
title = "Dithering for Floating-Point Number Representation",
crossref = "Holub:1998:ILW",
pages = "0--1--9--12",
year = "1998",
bibdate = "Thu Sep 11 07:08:34 2003",
bibsource = "http://measure.feld.cvut.cz/dithering98/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://citeseer.nj.nec.com/cache/papers/cs/1878/ftp:zSzzSzftp.mit.bme.huzSzpubzSzstaffzSzkollarzSzpaperszSzditherws.ps.gz/dunay98dithering.ps.gz;
http://citeseer.nj.nec.com/dunay98dithering.html",
abstract = "Dithering is widely used for decreasing the bias in
fixed-point quantization and rounding. Since
floating-point digital signal processors (DSP's) and
floating-point arithmetic are becoming widely used, it
is timely to investigate the necessity and
possibilities of dithering for floating-point numbers.
The paper introduces a simple model of dithers for
floating-point, and discusses its practical use.",
acknowledgement = ack-nhfb,
keywords = "digital signal processor; Dither; DSP; floating-point;
quantization; roundoff",
}
@TechReport{ECDG:1998:IER,
author = "{European Commission Directorate General II}",
title = "The Introduction of the Euro and the Rounding of
Currency Amounts",
type = "{II/28/99-EN Euro Papers}",
number = "22",
institution = "European Commission",
pages = "32",
month = mar,
year = "1998",
bibdate = "Wed Nov 24 12:56:20 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "DGII/C-4-SP(99) European Commission.",
acknowledgement = ack-nhfb,
}
@Article{Emiris:1998:MAL,
author = "Ioannis Z. Emiris and Victor Y. Pan and Yanqiang Yu",
title = "Modular arithmetic for linear algebra computations in
the real field",
journal = j-J-SYMBOLIC-COMP,
volume = "26",
number = "1",
pages = "71--87",
month = jul,
year = "1998",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1006/jsco.1998.0201",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
MRclass = "15-XX (68Q40)",
MRnumber = "1 633 585",
bibdate = "Tue Nov 10 06:41:20 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171/",
keywords = "accurate floating-point summation; floating-point
arithmetic",
}
@InProceedings{Ercegovac:1998:BSO,
author = "M. Ercegovac and D. Kirovski and G. Mustafa and M.
Potkonjak",
booktitle = "Proceedings of the 1998 {IEEE} International
Conference on Acoustics, Speech, and Signal Processing,
1998: {ICASSP '98}, 12--15 May 1998",
title = "Behavioral synthesis optimization using multiple
precision arithmetic",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3113--3116",
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Modern image and video processing applications are
characterized by a unique combination of arithmetic and
computational features: fixed point arithmetic, a
variety of short data types, high degree of
instruction-level parallelism, strict timing \ldots{}",
}
@InProceedings{Fiore:1998:LR,
author = "P. D. Fiore",
booktitle = "{IEEE} Workshop on Signal Processing Systems, 1988:
{SIPS 98}",
title = "Lazy rounding",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "449--458",
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Intermediate results in digital signal processing
(DSP) hardware frequently must be truncated or rounded
to maintain reasonable wordlengths. Noise and bias are
introduced into the signal due to these operations. For
the addition operation, we \ldots{}",
}
@InProceedings{Garcia:1998:PHC,
author = "A. Garcia and U. Meyer-Baese and F. Taylor",
booktitle = "Proceedings of the 1998 {IEEE} International
Conference on Acoustics, Speech, and Signal Processing,
{ICASSP 98}, 12--15 May 1998",
title = "Pipelined Hogenauer {CIC} filters using
field-programmable logic and residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3085--3088",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICASSP.1998.678178",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Field-programmable logic (FPL) is on the verge of
revolutionizing digital signal processing (DSP) in the
manner that programmable DSP microprocessors did nearly
two decades ago. While FPL densities and performance
have steadily improved to the point \ldots{}",
}
@Article{Gordon:1998:CLF,
author = "Robert Gordon",
title = "A Calculated Look at Fixed-Point Arithmetic",
journal = j-EMBED-SYS-PROG,
volume = "11",
number = "4",
pages = "72--78",
month = apr,
year = "1998",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Fri Nov 28 16:54:07 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Embedded Systems Programming",
}
@PhdThesis{Grisoni-Busca:1998:LPF,
author = "Louisa Grisoni-Busca",
title = "Low power floating point {A/D} converters for audio
signals",
type = "Dissertation",
school = "Univ. Neuch{\^a}tel",
address = "Neuch{\^a}tel, Switzerland",
pages = "xii + 136",
year = "1998",
bibdate = "Thu May 09 09:08:18 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Grushin:1998:CMA,
author = "A. I. Grushin and E. S. Vlasenko",
title = "Computer methods and apparatus for eliminating leading
non-significant digits in floating point computations",
day = "24",
month = may,
year = "1998",
bibdate = "Fri Nov 28 15:34:04 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,732,007.",
acknowledgement = ack-nhfb,
}
@Article{Guo:1998:SAI,
author = "Jyh-Huei Guo and Chin-Liang Wang",
title = "Systolic array implementation of {Euclid}'s algorithm
for inversion and division in {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "10",
pages = "1161--1167",
month = oct,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.729800",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=729800",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hars:1998:FCC,
author = "L. Hars",
title = "Fast Calculation of Common Mathematical Functions with
Floating-Point {DSPs}",
crossref = "Anonymous:1998:PNI",
pages = "521--525",
year = "1998",
bibdate = "Sat Jun 02 08:32:02 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Heckmann:1998:ABI,
author = "Reinhold Heckmann",
title = "The Appearance of Big Integers in Exact Real
Arithmetic Based on Linear Fractional Transformations",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1378",
pages = "172--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:51:46 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1378.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1378/13780172.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1378/13780172.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Hill:1998:FDP,
author = "Theodore P. Hill",
title = "The First Digit Phenomenon",
journal = j-AM-SCI,
volume = "86",
number = "4",
pages = "358--363",
month = jul # "\slash " # aug,
year = "1998",
CODEN = "AMSCAC",
DOI = "https://doi.org/10.1511/1998.4.358",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Sat Dec 10 11:54:49 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf;
http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf",
abstract = "A century ago, Simon Newcomb observed an unexpected
pattern in the first digits of logarithm tables: The
digit $1$ is significantly more likely to occur than
$2$, $2$ than $3$, and so on. More than a half-century
later, Frank Benford rediscovered the first-digit
phenomenon and found that it applied to many tables of
numerical data, including the stock market, census
statistics and accounting figures. New mathematical
insights establish the empirical law developed by
Newcomb and Benford as part of modern probability
theory, and recent applications include testing of
mathematical models, design of computers and detection
of fraud in accounting.",
acknowledgement = ack-nhfb,
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@InProceedings{Huertgen:1998:TFP,
author = "F. Huertgen and H. Meyr and M. Willems",
title = "Transformation of Floating-Point into Fixed-Point
Algorithms by Interpolation Applying a Statistical
Approach",
crossref = "Anonymous:1998:PNI",
pages = "630--634",
year = "1998",
bibdate = "Sat Jun 02 08:29:37 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hussein:1998:LPA,
author = "A. E. Hussein and M. A. Hasan and M. I. Elmasry",
booktitle = "{IEEE} Canadian Conference on Electrical and Computer
Engineering, 24--28 May 1998",
title = "A low power algorithm for division in residue number
system ({RNS})",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "205--208",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1109/CCECE.1998.682718",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new algorithm for computing division in residue
number system (RNS) is presented. The algorithm imposes
no restrictions on the dividend and the divisor (except
zero divisor), and requires no initial quotient
estimation. It eliminates the need for \ldots{}",
}
@InCollection{IBM:1998:DAI,
author = "{IBM}",
booktitle = "{ESA\slash 390} Principles of Operation",
title = "Decimal Arithmetic Instructions",
chapter = "8",
publisher = pub-IBM,
address = pub-IBM:adr,
year = "1998",
bibdate = "Fri Nov 28 17:57:22 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The decimal instructions of this chapter perform
arithmetic and editing operations on decimal data.
Additional operations on decimal data are provided by
several of the instructions in Chapter 7, ``General
Instructions''. Decimal operands always reside in
storage, and all decimal instructions use the SS
instruction format. Decimal operands occupy storage
fields that can start on any byte boundary.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Book{IEC:1998:IITa,
author = "{IEC}",
title = "{ISO\slash IEC\slash TR2 15580 (1998-12)}: Information
technology --- Programming languages --- {Fortran} ---
Floating-point exception handling",
publisher = pub-IEC,
address = pub-IEC:adr,
pages = "27",
year = "1998",
bibdate = "Mon Apr 24 06:32:09 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$56.00",
URL = "http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=023454",
acknowledgement = ack-nhfb,
}
@Book{ISO:1998:IITc,
author = "{International Organization for Standardization}",
title = "{ISO\slash IEC TR 15580:1998}: {Information}
technology --- {Programming} languages --- {Fortran}
--- {Floating-point} exception handling",
publisher = pub-ISO,
address = pub-ISO:adr,
pages = "27",
year = "1998",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Dec 12 06:45:58 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Available in English only.",
price = "CHF 104; US\$72.00",
URL = "http://webstore.ansi.org/ansidocstore/product.asp?sku=ISO%2FIEC+TR+15580%3A1998;
http://www.iso.ch/cate/d28230.html",
acknowledgement = ack-nhfb,
pricecode = "N",
}
@Article{Jessani:1998:CSD,
author = "R. M. Jessani and M. Putrino",
title = "Comparison of Single- and Dual-Pass Multiply-Add Fused
Floating-Point Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "9",
pages = "927--937",
month = sep,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.713312",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713312",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "alignment shifter; Booth encoding; floating-point
unit; multiply array; multiply-add fused; sign
encoding",
summary = "Low power, low cost, and high performance factors
dictate the design of many microprocessors targeted to
the low power computing market. The floating point unit
occupies a significant percentage of the silicon area
in a microprocessor due its wide data bandwidth (for
double-precision computations) and the area occupied by
the multiply array. For microprocessors designed for
portable products, the design-size of the
floating-point unit plays an important role in the low
cost factor driven by reduced chip area. Some
microprocessors have multiply-add fused floating-point
units with a reduced multiply array, requiring two
passes through the array for operations involving
double-precision multiplies. This paper discusses the
design complexities around the dual-pass multiply array
and its effect on area and performance. Floating-point
unit areas and their associated multiply array areas
are compared for a single- and dual-pass implementation
in a given technology (PowerPC 604e and PowerPC 603e
microprocessors, respectively).",
}
@TechReport{Kahan:1998:HJFa,
author = "W. Kahan and Joseph D. Darcy",
title = "How {Java}'s Floating-Point Hurts Everyone
Everywhere",
type = "Technical Report",
institution = "Department of Mathematics and Department of Electrical
Engineering and Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "80",
day = "18",
month = jun,
year = "1998",
bibdate = "Sat Sep 12 18:53:11 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf;
http://www.cs.berkeley.edu/~wkahan/JAVAhurt.ps",
acknowledgement = ack-nhfb,
remark = "The authors deliver a biting criticism of Java for its
failure to use the 80-bit temporary real format on
Intel x86 architectures, failure to use multiply-add
instructions when available, and failure to compute
float subexpressions in double precision.",
}
@InProceedings{Kahan:1998:HJFb,
author = "William Kahan",
title = "How {Java}'s Floating-Point Hurts Everyone
Everywhere",
crossref = "ACM:1998:AWJ",
pages = "??--??",
year = "1998",
bibdate = "Sat Dec 01 07:55:27 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.ucsb.edu/conferences/java98/papers/javahurt.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Kahan:1998:IPE,
author = "W. Kahan",
title = "The Improbability of Probabilistic Error Analyses for
Numerical Computations",
institution = "Department of Mathematics and Department of Electrical
Engineering and Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
pages = "34",
day = "10",
month = jun,
year = "1998",
bibdate = "Fri May 03 12:30:29 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/improber.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kelsey:1998:RRA,
author = "Richard Kelsey and William Clinger and Jonathan Rees",
title = "Revised$^5$ Report on the Algorithmic Language
{Scheme}",
journal = j-SIGPLAN,
volume = "33",
number = "9",
pages = "26--76",
month = sep,
year = "1998",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Sep 15 17:01:28 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With H. Abelson, N. I. {Adams, IV}, D. H. Bartley, G.
Brooks, R. K. Dybvig, D. P. Friedman, R. Halstead, C.
Hanson, C. T. Haynes, E. Kohlbecker, D. Oxley, K. M.
Pitman, G. J. Rozas, G. L. {Steele Jr.}, G. J. Sussman,
and M. Wand.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "decimal floating-point arithmetic",
remark = "From \cite{Steele:2004:RHP}: ``the result [of a
binary-to-decimal conversion] is expressed using the
minimum number of digits\ldots{}''",
}
@Article{Kiranon:1998:SRV,
author = "W. Kiranon and N. Kumprasert",
title = "Square-rooting and vector summation circuits using
current conveyors",
journal = "Circuits, Devices and Systems, IEE Proceedings [see
also IEE Proceedings G- Circuits, Devices and
Systems]",
volume = "145",
number = "2",
pages = "139",
month = apr,
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
summary = "Recently, Lui [1995] presented a square-rooting
circuit using CCII, MOS transistors and a buffered
unity-gain inverting amplifier. It is interesting since
it finds various applications as described in his
paper. However, an error occurred in the \ldots{}",
}
@Book{Knuth:1998:SA,
author = "Donald E. Knuth",
title = "Seminumerical Algorithms",
volume = "2",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Third",
pages = "xiii + 762",
year = "1998",
ISBN = "0-201-89684-2",
ISBN-13 = "978-0-201-89684-8",
LCCN = "QA76.6 .K64 1997",
bibdate = "Fri Jul 11 15:41:22 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/css.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
note = "See section 4.2.4V, The Fraction Parts, pages
254--262, for a discussion of Benford's Law.",
price = "US\$52.75",
series = "The Art of Computer Programming",
acknowledgement = ack-nhfb,
remark = "Knuth comments on page 255: ``The fact that the
leading digits tend to be small makes the most obvious
techniques of ``average error'' estimation for floating
point calculations invalid. The relative error due to
rounding is usually a little more than expected.",
tableofcontents = "3: Random Numbers / 1 \\
3.1. Introduction / 1 \\
3.2. Generating Uniform Random Numbers / 10 \\
3.2.1. The Linear Congruential Method / 10 \\
3.2 1.1. Choice of modulus / 12 \\
3.2.1.2 Choice of multiplier / 16 \\
3.2.1.3. Potency / 23 \\
3.2.2. Other Methods / 26 \\
3.3. Statistical Tests / 41 \\
3.3.1. General Test Procedures for Studying Random Data
/ 41 \\
3.3.2. Empirical Tests / 61 \\
*3.3.3. Theoretical Tests / 80 \\
3.3.4. The Spectral Test / 93 \\
3.4. Other Types of Random Quantities / 119 \\
3.4 1. Numerical Distributions / 119 \\
3.4.2. Random Sampling and Shuffling / 142 \\
*3.5. What Is a Random Sequence? / 149 \\
3.6. Summary / 184 \\
4: Arithmetic / 194 \\
4.1. Positional Number Systems / 195 \\
4.2. Floating Point Arithmetic / 214 \\
4.2.1. Single-Precision Calculations / 214 \\
4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
*4.2.3. Double-Precision Calculations / 246 \\
4.2.4. Distribution of Floating Point Numbers / 253 \\
4.3 Multiple Precision Arithmetic / 265 \\
4.3.1. The Classical Algorithms / 265 \\
*4.3.2. Modular Arithmetic / 284 \\
*4.3.3. How Fast Can We Multiply? / 294 \\
4.4. Radix Conversion / 319 \\
4.5. Rational Arithmetic / 330 \\
4.5.1. Fractions / 330 \\
4.5.2. The Greatest Common Divisor / 333 \\
*4.5.3. Analysis of Euclid's Algorithm / 356 \\
4.5.4. Factoring into Primes / 379 \\
4.6. Polynomial Arithmetic / 418 \\
4.6.1. Division of Polynomials / 420 \\
*4.6.2. Factorization of Polynomials / 439 \\
4.6.3. Evaluation of Powers / 461 \\
4.6.4. Evaluation of Polynomials / 485 \\
*4.7. Manipulation of Power Series / 525 \\
Answers to Exercises / 538 \\
Appendix A: Tables of Numerical Quantities / 726 \\
1. Fundamental Constants (decimal) / 726 \\
2; Fundamental Constants ( octal) / 727 \\
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
Numbers / 728 \\
Appendix B: Index to Notations / 730 \\
Index and Glossary / 735",
}
@Article{Koc:1998:LCB,
author = "C. K. Koc and B. Sunar",
title = "Low-complexity bit-parallel canonical and normal basis
multipliers for a class of finite fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "3",
pages = "353--356",
month = mar,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.660172",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660172",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kramer:1998:PWC,
author = "W. Kramer",
title = "A priori worst case error bounds for floating-point
computations",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "7",
pages = "750--756",
month = jul,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.709374",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
note = "See \cite{Tang:1992:TDI}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
abstract = "A new technique for the a priori calculation of
rigorous error bounds for floating-point computations
is introduced. The theorems given in the paper combined
with interval arithmetic lead to the implementation of
reliable software routines, which enable the user to
compute the desired error bounds automatically by a
suitable computer program. As a prominent example, a
table-lookup algorithm for calculating the function $
{\rm exp}(x) - 1 $ that has been published by P. T. P.
Tang (1992) is analyzed using these new tools. The
result shows the high quality of the new approach",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kuhlmann:1998:FLP,
author = "M. Kuhlmann and K. K. Parhi",
booktitle = "Proceedings of the 1998 International Conference on
Computer Design: {VLSI} in Computers and Processors.
{ICCD '98}",
title = "Fast low-power shared division and square-root
architecture",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "128--135",
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper addresses a fast low-power implementation
of a shared division and square-root architecture. Two
approaches are considered in this paper; these include
the SRT (Sweeney, Robertson and Tocher) approach which
does not require prescaling and \ldots{}",
}
@Article{Labrosse:1998:FPA,
author = "Jean J. Labrosse",
title = "Fixed-Point Arithmetic for Embedded Systems",
journal = j-CCCUJ,
volume = "16",
number = "2",
pages = "??--??",
month = feb,
year = "1998",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Tue May 14 18:09:14 MDT 2002",
bibsource = "http://www.cuj.com/articles/1998/9802/9802toc.htm?topic=articles;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Fixed-point arithmetic is fast: you just have to worry
more about overflow and significance loss.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@Article{Langer:1998:CFP,
author = "Steven H. Langer and Paul F. Dubois",
title = "A comparison of the floating-point performance of
current computers",
journal = j-COMPUT-PHYS,
volume = "12",
number = "4",
pages = "338--??",
month = jul,
year = "1998",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.168693",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:46:15 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://aip.scitation.org/doi/10.1063/1.168693",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
}
@Article{Langlois:1998:RBR,
author = "Ph. Langlois and F. Nativel",
title = "Reduction and bounding of the rounding error in
floating-point arithmetic",
journal = j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
volume = "327",
number = "??",
pages = "781--786",
year = "1998",
CODEN = "CASMEI",
ISSN = "0249-6291",
bibdate = "Thu May 27 07:37:54 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des
Sciences. S{\'e}rie I. Math{\'e}matique",
journal-URL = "http://www.sciencedirect.com/science/journal/1631073X",
}
@InProceedings{Lee:1998:DRN,
author = "I. Lee and W. K. Jenkins",
booktitle = "Proceedings of the 8th Great Lakes Symposium on {VLSI,
1998}",
title = "The design of residue number system arithmetic units
for a {VLSI} adaptive equalizer",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "179--184",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1109/GLSV.1998.665222",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents the design details of an
experimental ASIC for an all-digital adaptive
equalizer. In this design, the LMS algorithm is chosen
because of its simplicity. The adaptive equalizer
design, which is based on an RNS architecture,
\ldots{}",
}
@Article{Lefevre:1998:TCR,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
Tisserand",
title = "Toward correctly rounded transcendentals",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "11",
pages = "1235--1243",
month = nov,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.736435",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "The Table Maker's Dilemma is the problem of always
getting correctly rounded results when computing the
elementary functions. After a brief presentation of
this problem, we present new developments that have
helped us to solve this problem for the
double-precision exponential function in a small
domain. These new results show that this problem can be
solved, at least for the double-precision format, for
the most usual functions.",
}
@InProceedings{Ligon:1998:REP,
author = "W. B. {Ligon III} and S. McMillan and G. Monn and K.
Schoonover and F. Stivers and K. D. Underwood",
title = "A re-evaluation of the practicality of floating-point
operations on {FPGAs}",
crossref = "Pocek:1998:PIS",
pages = "206--215",
year = "1998",
DOI = "https://doi.org/10.1109/FPGA.1998.707898",
bibdate = "Sat Oct 9 12:51:26 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The use of reconfigurable hardware to perform high
precision operations such as IEEE floating point
operations has been limited in the past by FPGA
resources. We discuss the implementation of IEEE single
precision floating-point multiplication and addition.
Then, we assess the practical implications of using
these operations in the Xilinx 4000 series FPGAs
considering densities available now and scheduled for
the near future. For each operation, we present space
requirements and performance information. This is
followed by a discussion of an algorithm, matrix
multiplication, based on these operations, which
achieves performance comparable to conventional
microprocessors. Algorithm implementation options and
their performance implications are discussed and
corresponding measured results are given",
acknowledgement = ack-nhfb,
}
@Misc{LPT:1998:SC,
author = "{Log Point Technologies}",
title = "Soft {CoProcessor}",
howpublished = "World-Wide Web document.",
month = jun,
year = "1998",
bibdate = "Tue Jun 16 13:12:58 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This product provides software emulation of a
logarithmic floating-point representation. Programming
support is provided by a drop-in module for the GNU C
compiler, {\tt gcc}, and user-callable library support
is available for several commercial compilers.",
URL = "http://www.logpoint.com/;
http://www.logpoint.com/prelimi.htm",
acknowledgement = ack-nhfb,
}
@Article{Ma:1998:SAM,
author = "Yutai Ma",
title = "A simplified architecture for modulo $ (2^n + 1) $
multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "3",
pages = "333--337",
month = mar,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.660169",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660169",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{McCullough:1998:ARS,
author = "B. D. McCullough",
title = "Assessing the Reliability of Statistical Software:
{Part I}",
journal = j-AMER-STAT,
volume = "52",
number = "4",
pages = "358--366",
month = nov,
year = "1998",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 14:51:25 MST 2012",
bibsource = "http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326502;
https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2685442",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Mohan:1998:EFC,
author = "P. V. Ananda Mohan",
title = "Evaluation of fast conversion techniques for
binary-residue number systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
volume = "45",
number = "10",
pages = "1107--1109",
month = oct,
year = "1998",
CODEN = "ITCAEX",
DOI = "https://doi.org/10.1109/81.728866",
ISSN = "????",
ISSN-L = "1057-7122",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=15711",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I:
Fundamental Theory and Applications",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
keywords = "residue arithmetic; residue number system",
summary = "Vinnakota and Rao's RNS-to-binary converter proposed
recently (see ibid., vol. CAS-41, p. 927-9, 1994) for
the moduli set {2 n -1, 2 n and 2 n +1} is shown to be
a simple modification of the well-known Mixed Radix
\ldots{}",
}
@Article{Montalvo:1998:NST,
author = "L. A. Montalvo and K. K. Parhi and A. Guyot",
title = "New {Svoboda--Tung} division",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "9",
pages = "1014--1020",
month = sep,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.713319",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713319",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Moore:1998:MCP,
author = "J. S. Moore and T. W. Lynch and M. Kaufmann",
title = "A mechanically checked proof of the {AMD5 K 86{\TM}}
floating-point division program",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "9",
pages = "913--926",
month = sep,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.713311",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713311",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "We report on the successful application of a
mechanical theorem prover to the problem of verifying
the division microcode program used on the AMD5$_K$ 86
microprocessor. The division algorithm is an iterative
shift and subtract type. It was \ldots{}",
}
@InProceedings{Murabayashi:1998:WBP,
author = "F. Murabayashi and T. Yamauchi and R. Yamagata and T.
Shimizu",
title = "A {400MHz} 160-Word $ \times $ 64-Bit 14-Port
Floating-point Register File Macrocell for a
Superscalar {RISC} Processor",
crossref = "Huijsing:1998:EPE",
pages = "440--443",
year = "1998",
bibdate = "Sat Jun 02 08:21:00 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Naffziger:1998:MAB,
author = "S. D. Naffziger and R. G. Beraha",
title = "Method and apparatus for bounding alignment shifts to
enable at speed denormalized result generation in an
{FMAC}",
day = "26",
month = may,
year = "1998",
bibdate = "Fri Nov 28 15:35:29 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,757,687.",
acknowledgement = ack-nhfb,
}
@Article{Nguyen:1998:MLS,
author = "Phong Nguyen",
title = "A {Montgomery}-Like Square Root for the Number Field
Sieve",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1423",
pages = "151--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:52:18 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Oberman:1998:ATK,
author = "Stuart Oberman and Fred Weber and Norbert Juffa and
Greg Favor",
title = "{AMD 3DNow!} Technology and the {K6-2}
Microprocessor",
crossref = "IEEE:1998:HCC",
pages = "245--254",
year = "1998",
bibdate = "Mon Jan 08 17:02:55 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Oberman:1998:MCS,
author = "S. F. Oberman and M. J. Flynn",
title = "Minimizing the Complexity of {SRT} Tables",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "6",
number = "1",
pages = "141--149",
month = "????",
year = "1998",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/92.661256",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Fri Mar 27 09:56:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@Article{Oberman:1998:RML,
author = "S. F. Oberman and M. J. Flynn",
title = "Reducing the mean latency of floating-point addition",
journal = j-THEOR-COMP-SCI,
volume = "196",
number = "1-2",
pages = "201--214",
day = "6",
month = apr,
year = "1998",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed May 27 07:21:35 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
classification = "C5230 (Digital arithmetic methods)",
corpsource = "Comput. Syst. Lab., Stanford University, CA, USA",
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "adders; floating point arithmetic; floating-point
adder; floating-point addition; maximum throughput;
mean addition latency; mean latency; microprocessors;
shift-add-shift-round data flow; single-cycle
throughput",
pubcountry = "Netherlands",
treatment = "P Practical",
}
@Article{Paar:1998:EMA,
author = "C. Paar and P. Fleischmann and P. Roeise",
title = "Efficient multiplier architectures for {Galois} fields
{$ \mathrm {GF}(2^{4n}) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "2",
pages = "162--170",
month = feb,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.663762",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663762",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Paul:1998:CBR,
author = "W. J. Paul and P.-M. Seidel",
title = "On the complexity of {Booth} recoding",
crossref = "Chesneaux:1998:PCR",
pages = "199--218",
year = "1998",
bibdate = "Tue Mar 13 10:23:30 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Mueller:2000:CAC}.",
}
@Article{Paulus:1998:CRI,
author = "Sachar Paulus and Andreas Stein",
title = "Comparing Real and Imaginary Arithmetics for Divisor
Class Groups of Hyperelliptic Curves",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1423",
pages = "576--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:52:18 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230576.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1423/14230576.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@TechReport{Pena:1998:CDI,
author = "J. Pena",
title = "Computing the Distance to Infeasibility: Theoretical
and Practical Issues",
type = "Technical Report",
institution = "Center for Applied Mathematics, Cornell University",
address = "Ithaca, NY, USA",
year = "1998",
bibdate = "Tue Nov 22 06:34:32 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@InProceedings{Peuto:1998:ITM,
author = "Bernard L. Peuto and Leonard J. Shustek",
title = "An Instruction Timing Model of {CPU} Performance",
crossref = "Sohi:1998:YIS",
pages = "152--163",
year = "1998",
bibdate = "Fri Nov 28 18:36:16 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A model of high-performance computers is derived from
instruction timing formulas, with compensation for
pipeline and cache memory effects. The model is used to
predict the performance of the IBM 370/168 and the
Amdahl 470 V/6 on specific programs, and the results
are verified by comparison with actual performance.
Data collected about program behavior is combined with
the performance analysis to highlight some of the
problems with high-performance implementations of such
architectures.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Book{Rajski:1998:ABS,
author = "Janusz Rajski and Jerzy Tyszer",
title = "Arithmetic built-in self-test for embedded systems",
publisher = pub-PHPTR,
address = pub-PHPTR:adr,
pages = "xii + 268",
year = "1998",
ISBN = "0-13-756438-4",
ISBN-13 = "978-0-13-756438-5",
LCCN = "TK7895.E42 R35 1998",
bibdate = "Mon Dec 24 09:18:51 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
keywords = "BIST (Built-In Self Test); DFT (Design for
Testability); floating-point testing",
subject = "Embedded computer systems; Testing; Computer
firmware",
tableofcontents = "1. Built-In Self-Test. Introduction. Design for
Testability. Generation of Test Vectors. Compaction of
Test Responses. BIST Schemes for Random Logic. BIST for
Memory Arrays\\
2. Generation of Test Vectors. Additive Generators of
Exhaustive Patterns. Other Generation Schemes.
Two-Dimensional Generators\\
3. Test-Response Compaction. Binary Adders. 1's
Complement Adders. Rotate-Carry Adders. Cascaded
Compaction Scheme\\
4. Fault Diagnosis. Analytical Model. Experimental
Validation. The Quality of Diagnostic Resolution. Fault
Diagnosis in Scan-Based Designs\\
5. BIST of Data-Path Kernel. Testing of ALU. Testing of
the MAC Unit. Testing of the Microcontroller\\
6. Fault Grading. Fault Simulation Framework.
Functional Fault Simulation. Experimental Results\\
7. High-Level Synthesis. Implementation-Dependent Fault
Grading. Synthesis Steps. Simulation Results\\
8. ABIST at Work. Testing of Random Logic. Memory
Testing. Digital Integrators. Leaking Integrators\\
9. Epilog\\
A. Tables of Generators\\
B. Assembly Language\\
Bibliography\\
Index",
}
@Article{Rivolo:1998:CDR,
author = "M. T. Rivolo and A. Simi",
title = "Il Calcolo delle Radici Quadrate e Cubiche in {Italia}
da {Fibonacci} a {Bombelli}. ({Italian}) [{The}
calculation of square and cube roots in {Italy} from
{Fibonacci} to {Bombelli}]",
journal = j-ARCH-HIST-EXACT-SCI,
volume = "52",
number = "2",
pages = "161--193",
month = feb,
year = "1998",
CODEN = "AHESAN",
DOI = "https://doi.org/10.1007/s004070050015",
ISSN = "0003-9519 (print), 1432-0657 (electronic)",
ISSN-L = "0003-9519",
MRclass = "01A35 (01A40)",
MRnumber = "1610136 (99d:01015)",
MRreviewer = "Massimo Galuzzi",
bibdate = "Fri Feb 4 21:50:33 MST 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161",
acknowledgement = ack-nhfb,
fjournal = "Archive for History of Exact Sciences",
journal-URL = "http://link.springer.com/journal/407",
language = "Italian",
MRtitle = "The computation of square and cube roots in {Italy}
from {Fibonacci} to {Bombelli}",
}
@Misc{Russinoff:1998:MCPa,
author = "D. M. Russinoff",
title = "A mechanically-checked proof of {IEEE} compliance of a
register-transfer-level specification of the {AMD K7}
floating-point division and square root instructions",
howpublished = "World-Wide Web document.",
year = "1998",
bibdate = "Fri Nov 29 09:41:27 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See journal article \cite{Russinoff:1998:MCPb}.",
URL = "http://www.onr.com/user/russ/david/k7-div-sqrt.html",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Mueller:2000:CAC}.",
}
@Article{Russinoff:1998:MCPb,
author = "David M. Russinoff",
title = "A mechanically checked proof of {IEEE} compliance of
the floating point multiplication, division and square
root algorithms of the {AMD-K7{\TM}} processor",
journal = j-LMS-J-COMPUT-MATH,
volume = "1",
pages = "148--200",
year = "1998",
CODEN = "????",
ISSN = "1461-1570",
MRclass = "68M07 (65Y99 68T15)",
MRnumber = "99m:68015",
MRreviewer = "J. Michel Muller",
bibdate = "Wed Nov 24 09:19:02 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Appendices A and B available to subscribers
electronically
(http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and
http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)",
URL = "http://www.lms.ac.uk/jcm/1/lms1998-001/;
http://www.onr.com/user/russ/david/k7-div-sqrt.ps",
acknowledgement = ack-nhfb,
fjournal = "LMS Journal of Computation and Mathematics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=JCM",
}
@InProceedings{Sasaki:1998:ACE,
author = "Tateaki Sasaki and Satoshi Yamaguchi",
title = "An analysis of cancellation error in multivariate
{Hensel} construction with floating-point number
arithmetic",
crossref = "Gloor:1998:IPI",
pages = "1--8",
year = "1998",
bibdate = "Wed Sep 16 17:16:31 1998",
bibsource = "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/proceedings/issac/281508/p1-sasaki/",
acknowledgement = ack-nhfb,
}
@Article{Sasaki:1998:CEM,
author = "Tateaki Sasaki and Tomoyuki Sato",
title = "Cancellation Errors in Multivariate Resultant
Computation with Floating-point Numbers",
journal = j-SIGSAM,
volume = "32",
number = "4",
pages = "13--20",
month = dec,
year = "1998",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Wed Apr 14 15:21:10 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
issue = "126",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Sastry:1998:EIF,
author = "S. Subramanya Sastry and Subbarao Palacharla and James
E. Smith",
title = "Exploiting Idle Floating-Point Resources for Integer
Execution",
journal = j-SIGPLAN,
volume = "33",
number = "5",
pages = "118--129",
month = may,
year = "1998",
CODEN = "SINODQ",
ISBN = "0-89791-987-4",
ISBN-13 = "978-0-89791-987-6",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:17:47 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/pldi/277650/index.html;
http://www.cs.virginia.edu/pldi98/program.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/277650/p118-sastry/",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "algorithms; performance",
remark = "Published as part of the Proceedings of PLDI'98.",
subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
Processors, Compilers. {\bf D.3.4} Software,
PROGRAMMING LANGUAGES, Processors, Optimization. {\bf
G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
General, Computer arithmetic.",
}
@InProceedings{Seidel:1998:HHL,
author = "P.-M. Seidel",
title = "How to half [sic] the latency of {IEEE} compliant
floating-point multiplication",
crossref = "IEEE:1998:IOM",
pages = "329--332",
year = "1998",
bibdate = "Fri Jun 24 20:55:14 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Seidel:1998:HSR,
author = "P.-M. (Peter-Michael) Seidel",
booktitle = "Proceedings of the 3rd Conference on Real Numbers and
Computers {(RNC3)}, Paris, April 1998",
title = "High-Speed Redundant Reciprocal Approximation",
publisher = "????",
address = "????",
pages = "219--229",
year = "1998",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Jun 25 07:46:25 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Severance:1998:IOM,
author = "C. Severance",
title = "An interview with the old man of floating-point:
Reminiscences elicited from {William Kahan}",
howpublished = "World-Wide Web document.",
year = "1998",
bibdate = "Sat Apr 28 19:05:42 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A shortened version appears in
\cite{Severance:1998:SII}.",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html",
acknowledgement = ack-nhfb,
}
@Article{Severance:1998:SII,
author = "Charles Severance",
title = "Standards: {IEEE 754}: An Interview with {William
Kahan}",
journal = j-COMPUTER,
volume = "31",
number = "3",
pages = "114--115",
month = mar,
year = "1998",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Wed Mar 4 10:07:59 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://pdf.computer.org/co/books/co1998/pdf/r3114.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Simons:1998:IFP,
author = "N. R. S. Simons and G. E. Bridges and B. Ghosh and M.
Cuhaci",
booktitle = "1998. {IEEE} Antennas and Propagation Society
International Symposium. 21--26 June 1998",
title = "Investigation of floating-point round-off errors
within time-domain electromagnetic field computations",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "260--263",
year = "1998",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:04 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We present an investigation of floating-point
round-off errors within time-domain electromagnetic
field computations. Our eventual goal is to determine
the minimal computational requirements for the
successful implementation of algorithms for \ldots{}",
}
@InProceedings{Skavantzos:1998:ERW,
author = "A. Skavantzos",
booktitle = "Proceedings of the 8th Great Lakes Symposium on {VLSI,
1998}",
title = "An efficient residue to weighted converter for a new
residue number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "185--191",
year = "1998",
CODEN = "????",
DOI = "https://doi.org/10.1109/GLSV.1998.665223",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The Residue Number System (RNS) is an integer system
appropriate far implementing fast digital signal
processors since it can support parallel, carry-free,
high-speed arithmetic. In this paper a new RNS system
and an efficient implementation of its \ldots{}",
}
@Misc{Slabodkin:1998:SGL,
author = "G. Slabodkin",
title = "Software glitches leave {Navy Smart Ship} dead in the
water",
howpublished = "Web site",
day = "31",
month = jul,
year = "1998",
bibdate = "Mon Aug 26 11:13:26 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.rose-hulman.edu/class/cs/csse442/current/hw/homework6-story.pdf",
acknowledgement = ack-nhfb,
keywords = "Aegis missile cruiser USS Yorktown",
}
@Article{Smith:1998:AMP,
author = "David M. Smith",
title = "{Algorithm 786}: Multiple-Precision Complex Arithmetic
and Functions",
journal = j-TOMS,
volume = "24",
number = "4",
pages = "359--367",
month = dec,
year = "1998",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/293686.293687",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Mar 09 10:09:51 1999",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also
\cite{Bailey:1995:FBM,Brent:1978:AMF,Brent:1979:RMF,Brent:1980:AIB}.",
URL = "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p359-smith/",
abstract = "The article describes a collection of Fortran routines
for multiple-precision complex arithmetic and
elementary functions. The package provides good
exception handling, flexible input and output, trace
features, and results that are almost always correctly
rounded. For best efficiency on different machines, the
user can change the arithmetic type used to represent
the multiple-precision numbers.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; correct rounding; floating-point
arithmetic; performance; reliability",
subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL
ANALYSIS, General, Computer arithmetic. {\bf G.1.2}
Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation, Elementary function approximation. {\bf
G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
Algorithm design and analysis. {\bf G.4} Mathematics of
Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}
Mathematics of Computing, MATHEMATICAL SOFTWARE,
Portability**.",
}
@Article{Stelling:1998:OCP,
author = "P. F. Stelling and C. U. Martel and V. G. Oklobdzija
and R. Ravi",
title = "Optimal circuits for parallel multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "3",
pages = "273--285",
month = mar,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.660163",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660163",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Stine:1998:CIFa,
author = "J. E. Stine and M. J. Schulte",
title = "A Combined Interval and Floating Point Divider",
crossref = "Matthews:1998:CRT",
pages = "218--222",
year = "1998",
bibdate = "Sun Mar 04 10:59:12 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1998-02.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Stine:1998:CIFb,
author = "J. E. Stine and M. J. Schulte",
title = "A Combined Interval and Floating Point Multiplier",
crossref = "IEEE:1998:PGL",
pages = "208--213",
year = "1998",
bibdate = "Sun Mar 04 10:59:12 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1998-01.pdf",
acknowledgement = ack-nhfb,
}
@Article{Takagi:1998:PTL,
author = "N. Takagi",
title = "Powering by a table look-up and a multiplication with
operand modification",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "11",
pages = "1216--1222",
month = nov,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.736432",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736432",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Takashi:1998:FPN,
author = "Y. Takashi",
title = "Floating Point Number Format with Number System with
Base of 1000",
journal = j-IBM-TDB,
volume = "01-98",
pages = "609--610",
month = jan,
year = "1998",
CODEN = "IBMTAA",
ISSN = "0018-8689",
bibdate = "Fri Nov 28 19:29:01 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Disclosed is a use number system with a base of 1000
instead of 2 at the mantissa part of a floating point
number. The unit is 10 bit. Each 10 bit keeps the value
between 0 and 1000. This format is superior to Binary
Coded Decimal (BCD) because it can keep more decimal
numbers in the same size. This format is superior to
binary because 1000 is 100 times of 10, and it makes no
difference when converted to/from human's decimal
format.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "IBM Technical Disclosure Bulletin",
}
@Article{Thorup:1998:FIS,
author = "M. Thorup",
title = "Floats, Integers, and Single Source Shortest Paths",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1373",
pages = "14--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 28 08:51:33 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Ulman:1998:HPF,
author = "Zenon D. Ulman and Maciej Czyzak",
title = "Highly parallel, fast scaling of numbers in
nonredundant residue arithmetic",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "46",
number = "2",
pages = "487--496",
year = "1998",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
MRclass = "94A12 (11A67 65Y10 68W35)",
MRnumber = "MR1664521 (2000c:94006)",
MRreviewer = "Behrooz Parhami",
bibdate = "Thu Nov 8 14:50:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}
@Article{Upton:1998:RH,
author = "Graham Upton",
title = "Rounding halves",
journal = j-J-APPL-STAT,
volume = "25",
number = "6",
pages = "811--816",
day = "1",
month = dec,
year = "1998",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Sat Apr 13 11:27:32 MDT 2002",
bibsource = "http://www.carfax.co.uk/jas-con.htm;
http://www.catchword.co.uk/titles/carfax/02664763/;
http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.catchword.co.uk/cgi-bin/cgi?ini=carfax&body=linker&reqidx=/catchword/carfax/13600532/v25n6/s9/p811",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Vogt:1998:FPP,
author = "Christopher J. Vogt",
title = "Floating Point Performance of {Common Lisp}",
journal = j-SIGPLAN,
volume = "33",
number = "9",
pages = "103--107",
month = sep,
year = "1998",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:17:51 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Walter:1998:EUD,
author = "C. D. Walter",
title = "Exponentiation using division chains",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "7",
pages = "757--765",
month = jul,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.709375",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709375",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Walters:1998:SFF,
author = "A. Walters and P. Athanas",
title = "A scaleable {FIR} filter using 32-bit floating-point
complex arithmetic on a configurable computing
machine",
crossref = "Pocek:1998:PIS",
pages = "333--334",
year = "1998",
DOI = "https://doi.org/10.1109/FPGA.1998.707941",
bibdate = "Sat Oct 09 15:44:51 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents an approach for implementing a
scalable high-performance digital filter using the
WILDFORCE configurable computing platform. Although not
designed specifically for signal processing,
configurable computing platforms offer more flexibility
for algorithms than application-specific hardware,
which is often needed for instances when factors such
as environment or product volume dictate alterations in
computing. The added flexibility enables users to
construct deep pipelines to exploit properties of
specific computations. In this paper, wide 32-bit
floating-point arithmetic operators have been
implemented which provide compatibility with hosts
machines. The filter achieves 160 MFLOPs on a single
WILDFORCE configurable computing platform.",
acknowledgement = ack-nhfb,
}
@InProceedings{Wei:1998:RAC,
author = "Shugang Wei and Kensuke Shimizu",
title = "Residue Arithmetic Circuits Based on Signed-Digit
Multi-Valued Arithmetic Circuits",
crossref = "Sasao:1998:ISM",
pages = "276--281",
year = "1998",
DOI = "https://doi.org/10.1109/ISMVL.1998.679470",
MRclass = "68M07",
MRnumber = "MR1676993",
bibdate = "Fri Jun 24 19:50:29 2005",
bibsource = "http://www.informatik.uni-trier.de/~ley/db/conf/ismvl/ismvl1998.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/dl/proceedings/ismvl/1998/8371/00/83710276.pdf",
abstract = "Multiple-valued residue arithmetic circuits using
integers $ 4^p $ and $ 4^p \pm 1 $ as moduli of residue
number system (RNS) are presented. Conventional residue
arithmetic circuits have been designed using binary
number arithmetic system, but the carry propagation
arises which limits the speed of arithmetic operations
in residue modules. In this paper, a radix-4
signed-digit(SD) number system is introduced, and the
compact SD adder based on the multiple-valued
current-mode circuits is applied for the implementation
of high-speed and compact residue arithmetic circuits.
The modulo $m$ addition, $ m = 4^p $ or $ m = 4^p \pm 1
$, can be performed by an SD adder or an
end-around-carry SD adder with the multiple-valued
circuits and the addition time is independent of the
word length of operands. Modulo $m$ multiplier can be
compactly constructed using a binary modulo $m$ SD
adder tree based on the multiple-valued addition
circuits, and the modulo m multiplication can be
performed in a time proportional to $ \log_2 p $.",
acknowledgement = ack-nhfb,
}
@Article{Weiss:1998:FPM,
author = "S. Weiss and A. Goldstein",
title = "Floating point micropipeline performance",
journal = j-J-SYST-ARCH,
volume = "45",
number = "1",
pages = "15--29",
month = oct,
year = "1998",
CODEN = "JSARFB",
ISSN = "1383-7621 (print), 1873-6165 (electronic)",
ISSN-L = "1383-7621",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Journal of Systems Architecture",
pagecount = "15",
}
@Article{Wu:1998:LCB,
author = "Huapeng Wu and M. A. Hasan",
title = "Low complexity bit-parallel multipliers for a class of
finite fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "8",
pages = "883--887",
month = aug,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.707588",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=707588",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wu:1998:NLC,
author = "H. Wu and M. A. Hasan and I. F. Blake",
title = "New low-complexity bit-parallel finite field
multipliers using weakly dual bases",
journal = j-IEEE-TRANS-COMPUT,
volume = "47",
number = "11",
pages = "1223--1234",
month = nov,
year = "1998",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.736433",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 09:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736433",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Abbott:1999:ASS,
author = "P. H. Abbott and D. G. Brush and C. W. {Clark III} and
C. J. Crone and J. R. Ehrman and G. W. Ewart and C. A.
Goodrich and M. Hack and J. S. Kapernick and B. J.
Minchau and W. C. Shepard and R. M. {Smith, Sr.} and R.
Tallman and S. Walkowiak and A. Watanabe and W. R.
White",
title = "Architecture and software support in {IBM S/390
Parallel Enterprise Servers} for {IEEE} Floating-Point
arithmetic",
journal = j-IBM-JRD,
volume = "43",
number = "5/6",
pages = "723--760",
month = sep # "\slash " # nov,
year = "1999",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.435.0723",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Mon Feb 03 07:08:45 2003",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
note = "Besides important history of the development of the
S/360 floating-point architecture, this paper has a
good description of IBM's algorithm for exact
decimal-to-binary conversion, complementing earlier
ones
\cite{Steele:1990:HPF,Clinger:1990:HRF,Knuth:1990:SPW,Burger:1996:PFP,Steele:2004:RHP}.",
URL = "http://www.research.ibm.com/journal/rd/435/abbott.html",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Agarwal:1999:SAM,
author = "Rames C. Agarwal and Fred G. Gustavson and Martin S.
Schmookler",
title = "Series Approximation Methods for Divide and Square
Root in the {Power3\TM{}} Processor",
crossref = "Koren:1999:ISC",
pages = "116--123",
year = "1999",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-144.pdf;
http://euler.ecs.umass.edu/paper/final/paper-144.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Agarwal.pdf",
abstract = "The Power3 processor is a 64-bit implementation of the
PowerPC\TM{} architecture and is the successor to the
Power2\TM{} processor for workstations and servers
which require high performance floating point
capability. The previous processors used
Newton--Raphson algorithms for their implementations of
divide and square root. The Power3 processor has a
longer pipeline latency, which would substantially
increase the latency for these instructions. Instead,
new algorithms based on power series approximations
were developed which provide significantly better
performance than the Newton- Raphson algorithm for this
processor. This paper describes the algorithms, and
then shows how both the series based algorithms and the
Newton--Raphson algorithms are affected by pipeline
length. For the Power3, the power series algorithms
reduce the divide latency by over 20\% and the square
root latency by 35\%.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Ait-Ameur:1999:RRE,
author = "Y. Ait-Ameur",
title = "Refinement of rational end-points real numbers by
means of floating-point numbers",
journal = j-SCI-COMPUT-PROGRAM,
volume = "33",
number = "2",
publisher = "Elsevier Science",
pages = "133--162",
month = feb,
year = "1999",
CODEN = "SCPGD4",
ISSN = "0167-6423 (print), 1872-7964 (electronic)",
ISSN-L = "0167-6423",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Science of Computer Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/01676423",
pagecount = "30",
}
@Article{Allender:1999:BDA,
author = "Eric Allender and Andris Ambainis and David A. Mix
Barrington and Samir Datta and Huong L{\^e}Thanh",
title = "Bounded Depth Arithmetic Circuits: Counting and
Closure",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1644",
pages = "149--??",
year = "1999",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:54:23 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1644.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1644/16440149.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1644/16440149.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Anderson:1999:DAF,
author = "I. J. Anderson",
title = "A Distillation Algorithm for Floating-Point
Summation",
journal = j-SIAM-J-SCI-COMP,
volume = "20",
number = "5",
pages = "1797--1806",
month = sep,
year = "1999",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827596314200",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Sat Jul 17 19:14:38 MDT 1999",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/20/5;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31420",
abstract = "The addition of two or more floating-point numbers is
fundamental to numerical computations. This paper
describes an efficient ``distillation'' style algorithm
which produces a precise sum by exploiting the natural
accuracy of compensated cancellation. The algorithm is
applicable to all sets of data but is particularly
appropriate for ill-conditioned data, where standard
methods fail due to the accumulation of rounding error
and its subsequent exposure by cancellation. The method
uses only standard floating-point arithmetic and does
not rely on the radix used by the arithmetic model, the
architecture of specific machines, or the use of
accumulators.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation",
}
@Misc{Anonymous:1999:SLH,
author = "Anonymous",
title = "Standard libraries for the {Haskell 98} programming
language",
howpublished = "World-Wide Web document",
month = feb,
year = "1999",
bibdate = "Wed Jan 29 16:42:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.haskell.org/definition/haskell98-library.pdf",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``a comment that appears
in the code for the function floatToDigits in the
Haskell 98 library [p. 14 of this article] says that
the code is based on Burger and Dybvig's work
\cite{Burger:1996:PFP}.",
}
@InProceedings{Antelo:1999:VRC,
author = "Elisardo Antelo and Tom{\'a}s Lang and Javier D.
Bruguera",
title = "Very-High Radix {CORDIC} Vectoring with Scalings and
Selection by Rounding",
crossref = "Koren:1999:ISC",
pages = "204--213",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-154.pdf;
http://euler.ecs.umass.edu/paper/final/paper-154.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Antelo.pdf",
abstract = "A very-high radix algorithm and implementation for
circular CORDIC in vectoring mode is presented. As for
division, to simplify the selection function, the
operands are pre-scaled. However, in the CORDIC
algorithm the coordinate x varies during the execution
so several scalings might be needed; we show that two
scalings are sufficient. Moreover, the compensation of
the variable scale factor is done by computing the
logarithm of the scale factor and performing the
compensation by an exponential. Estimations of the
delay for 32-bit precision show a speed up of about two
with respect to the radix-4 case with redundant
addition. This speed up is obtained at the cost of an
increase in the hardware complexity, which is moderate
for the pipelined implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
summary = "A very-high radix algorithm and implementation for
circular CORDIC in vectoring mode is presented. As for
division, to simplify the selection function, the
operands are pre-scaled. However in the CORDIC
algorithm the coordinate x varies during the \ldots{}",
}
@InProceedings{Aoki:1999:RCA,
author = "Takafumi Aoki and Ken-ichi Hoshi and Tatsuo Higuchi",
title = "Redundant Complex Arithmetic and Its Application to
Complex Multiplier Design",
crossref = "IEEE:1999:PII",
pages = "200--207",
year = "1999",
DOI = "https://doi.org/10.1109/ISMVL.1999.779717",
bibdate = "Sat Aug 22 08:46:40 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a class of complex number
representations called Redundant Complex Number Systems
(RCNSs), which are useful for designing VLSI signal
processors with complex arithmetic capability. A
redundant complex: number system is defined as an
imaginary-radix number system having a redundant
integer digit set. This makes possible the construction
of high-speed complex arithmetic circuits: examples
include a complex-number parallel adder with no carry
propagation chain, and a complex-number multiplier
using fast binary-tree addition structure. This paper
also presents the experimental fabrication of the
RCNS-based complex multiplier in 0.5 $ \mu $ m CMOS
technology",
acknowledgement = ack-nhfb,
}
@Article{Bach:1999:NTS,
author = "E. Bach and K. Huber",
title = "Note on taking square-roots modulo {$N$}",
journal = j-IEEE-TRANS-INF-THEORY,
volume = "45",
number = "2",
pages = "807--809",
month = mar,
year = "1999",
CODEN = "IETTAW",
DOI = "https://doi.org/10.1109/18.749034",
ISSN = "0018-9448 (print), 1557-9654 (electronic)",
ISSN-L = "0018-9448",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Information Theory",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
summary = "In this article it is shown how Gauss' (1981) famous
cyclotomic sum formula can be used for extracting
square-roots modulo \ldots{}",
}
@InProceedings{Batten:1999:IBO,
author = "D. Batten and S. Jinturkar and J. Glossner and M.
Schulte and R. Peri and P. D'arcy",
editor = "????",
booktitle = "Proceedings of the International Conference on Signal
Processing Applications and Technologies, Orlando,
Florida, November, 1999",
title = "Interactions Between Optimizations and a New Type of
{DSP} Intrinsic Function",
publisher = "????",
address = "????",
year = "1999",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 04 11:05:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Shortened version in \cite{Batten:1999:IFB}.",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf",
acknowledgement = ack-nhfb,
}
@Article{Batten:1999:IFB,
author = "D. Batten and P. D'arcy",
title = "Intrinsic Functions Boost Compilers",
journal = "Electrical Engineering Times",
volume = "1085",
pages = "104--104",
month = nov,
year = "1999",
bibdate = "Sun Mar 04 11:06:22 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Beaumont-Smith:1999:RLI,
author = "A. Beaumont-Smith and N. Burgess and S. Lefrere and C.
C. Lim",
title = "Reduced Latency {IEEE} Floating-Point Standard Adder
Architectures",
crossref = "Koren:1999:ISC",
pages = "35--43",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-163.pdf;
http://euler.ecs.umass.edu/paper/final/paper-163.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Beaumont_Smith.pdf",
abstract = "The design and implementation of a double precision
floating-point IEEE-754 standard adder is described
which uses ``flagged prefix addition'' to merge
rounding with the significand addition. The
floating-point adder is implemented in $ 0.5 \mu $ m
CMOS, measures $ 1.8 $ mm$^2$, has a 3-cycle latency
and implements all rounding modes. A modified version
of this floating-point adder can perform accumulation
in 2-cycles with a small amount of extra hardware for
use in a parallel processor node. This is achieved by
feeding back the previous un-normalised but correctly
rounded result together with the normalisation
distance. A 2-cycle latency floating-point adder
architecture with potentially the same cycle time that
also employs flagged prefix addition is described. It
also incorporates a fast prediction scheme for the true
subtraction of significands with an exponent difference
of 1, with one less adder.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic; correct rounding;
floating-point arithmetic",
}
@Misc{Benschop:1999:MML,
author = "Nico Fritz Benschop",
title = "Multiplier for the multiplication of at least two
figures in an original format",
howpublished = "US Patent number 5,923,888.",
day = "13",
month = jul,
year = "1999",
bibdate = "Fri Jun 24 15:16:03 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US5923888A",
abstract = "The invention relates to a multiplier for the
multiplication of at least two figures in an original
format. Each of said figures is fed to a first
converter for conversion of each of said figures in the
product of a first binary number representing a power
of 2, and a second binary number representing a signed
power of 3, the exponents of the powers of 2 of the
concerning figures being fed to a first adder and the
exponents of the powers of 3 of the concerning figures
being fed to a second adder, whereby the combined
respective outputs of the first adder and the second
adder represent the multiplied value of said figures,
and the resulting powers of 2 and 3 as available at the
outputs of the first and second adder being fed to a
second converter for conversion of the multiplied value
into the original format.",
acknowledgement = ack-nhfb,
remark = "Patent filed 15 December 1997, granted 13 July 1999,
expected expiration on 15 December 2017.",
}
@InProceedings{Bhardwaj:1999:RCM,
author = "M. Bhardwaj and T. Srikanthan and C. T. Clarke",
title = "A Reverse Converter for the $4$-Moduli Superset $ \{
2^n - 1 $, $ 2^n $, $ 2^n + 1 $, $ 2^(n + 1) + 1 \} $",
crossref = "Koren:1999:ISC",
pages = "168--175",
year = "1999",
DOI = "https://doi.org/10.1109/ARITH.1999.762842",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-137.pdf;
http://euler.ecs.umass.edu/paper/final/paper-137.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Bhardwaj.pdf",
abstract = "The authors propose an extension to the popular $ \{
2^n - 1, 2^n, 2^n + 1 \} $ moduli set by adding a
fourth modulus $ 2^{n + 1} + 1 $. This extension leads
to higher parallelism while keeping the forward
conversion and modular arithmetic units simple. The
main challenge of efficient reverse conversion is met
by three techniques described for the first time.
Firstly, we reverse convert linear combinations of
moduli hence reducing the number of non-zero bits in
the Booth encoded multiplicands from $n$ to merely 2.
Secondly, it is shown that division by 3, if introduced
at the right stage, can be implemented very efficiently
and can, in turn, reduce the cost of the converter. To
implement VLSI efficient modulo reduction, we propose
two techniques-multiple split tables (MST) and a
modified division algorithm (MDA). It is shown that the
MST can reduce exponential ROM requirements to
quadratic ROM requirements while the MDA can reduce
these further to linear requirements. As a result of
these innovations, the proposed reverse converter uses
simple shift and add operations and needs a lookup with
only 6 entries. The delay of the converter is
approximately $ 10 n + 13 $ full adder delays and the
area cost is quadratic in $n$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{Bhardwaj:1999:VCA,
author = "M. Bhardwaj and T. Srikanthan and C. T. Clarke",
title = "{VLSI} Costs of Arithmetic Parallelism: a Residue
Reverse Conversion Perspective",
crossref = "Koren:1999:ISC",
pages = "176--185",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-138.pdf;
http://euler.ecs.umass.edu/paper/final/paper-138.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Bhardwaj_VLSI.pdf",
abstract = "This paper reports how VLSI cost metrics (area, delay,
power) of residue reverse converters scale with the
cardinality and dynamic range of moduli sets. The study
uses CMAC reverse converters, reported previously by
the authors to be the most efficient known to date in
terms of area and delay. In all, 134 reverse converters
with dynamic ranges from 32 to 120 bits and set
cardinalities ranging from 4 to 20 are actually
constructed and analyzed. It is seen that area, delay
and power costs are cardinality insensitive once the
cardinality exceeds a threshold (usually between five
to eight). For cardinalities beyond this threshold,
conversion costs are essentially dynamic range
dependent. This insensitivity is explained in detail by
noting the counterbalancing effects of the various
sub-units of a CMAC reverse converter. Since practical
implementations of RNS usually employ cardinalities
beyond the abovementioned thresholds, the significance
of this study is its conclusion that increasing the set
cardinality in most implementations will have a
marginal, if any, effect on VLSI reverse conversion
costs.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{Blum:1999:MME,
author = "Thomas Blum and Christoph Paar",
title = "{Montgomery} Modular Exponentiation on Reconfigurable
Hardware",
crossref = "Koren:1999:ISC",
pages = "70--77",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-133.pdf;
http://euler.ecs.umass.edu/paper/final/paper-133.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Blum.pdf",
abstract = "It is widely recognized that security issues will play
a crucial role in the majority of future computer and
communication systems. Central tools for achieving
system security are cryptographic algorithms. For
performance as well as for physical security reasons,
it is often advantageous to realize cryptographic
algorithms in hardware. In order to overcome the
well-known drawback of reduced flexibility that is
associated with traditional ASIC solutions, this
contribution proposes arithmetic architectures which
are optimized for modern field programmable gate arrays
(FPGAs). The proposed architectures perform modular
exponentiation with very long integers. This operation
is at the heart of many practical public-key algorithms
such as RSA and discrete logarithm schemes. We combine
the Montgomery modular multiplication algorithm with a
new systolic array design, which is capable of
processing a variable number of bits per array cell.
The designs are flexible, allowing any choice of
operand and modulus.\par
Unlike previous approaches, we systematically implement
and compare several variants of our new architecture
for different bit lengths. We provide absolute area and
timing measures for each architecture. The results
allow conclusions about the feasibility and time-space
trade-offs of our architecture for implementation on
Xilinx XC4000 series FPGAs. As a major practical result
we show that it is possible to implement modular
exponentiation at secure bit lengths on a single
commercially available FPGA.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@TechReport{Boldo:1999:CRE,
author = "Sylvie Boldo",
title = "Calcul rapide et exact de fonctions
{\'e}l{\'e}mentaires en pr{\'e}cision arbitraire par la
moyenne arithm{\'e}tico-g{\'e}om{\'e}trique. ({French})
[Rapid and exact computation of elementary functions in
arbitrary precision by the arithmetic-geometric mean]",
type = "Report",
institution = "INRIA, Projet Spaces, LORIA, Campus Scientifique",
address = "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
France",
pages = "29",
year = "1999",
bibdate = "Tue Nov 23 11:00:03 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Under the direction of Paul Zimmermann.",
URL = "http://perso.ens-lyon.fr/sylvie.boldo/doc/mpfr.ps",
acknowledgement = ack-nhfb,
language = "French",
}
@InProceedings{Brent:1999:CAP,
author = "Richard P. Brent",
title = "Computer Arithmetic --- a Programmer's Perspective",
crossref = "Koren:1999:ISC",
pages = "2--2",
year = "1999",
bibdate = "Wed Jan 20 09:38:39 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/brentr.pdf;
http://euler.ecs.umass.edu/paper/final/brentr.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Brent.pdf",
abstract = "Advances in computer hardware often have little impact
until they become accessible to programmers using
high-level languages. For example, the IEEE
floating-point arithmetic standard provides various
rounding modes and exceptions, but it is difficult or
impossible to take advantage of these from most
high-level languages, so the full capabilities of
IEEE-compatible hardware are seldom used. When they are
used by writing in machine or assembly language, there
is a high cost in program development and testing time,
lack of portability, and difficulty of software
maintenance.\par
In this talk we discuss several areas in which computer
hardware, especially arithmetic hardware, can or should
significantly influence programming language design.
These include: vector units, floating-point exception
handling, floating-point rounding modes, high/extended
precision registers/arithmetic, and use of unusual
number systems. Relevant application areas include
interval arithmetic, high-precision integer arithmetic
for computer algebra and cryptography, and testing of
hardware by comparison with software simulations.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14",
remark = "Abstract only: no text of the paper available.",
}
@Article{Bronnimann:1999:SDR,
author = "Herve Bronnimann and Ioannis Z. Emiris and Victor Y.
Pan and Sylvain Pion",
title = "Sign determination in residue number systems",
journal = j-THEOR-COMP-SCI,
volume = "210",
number = "1",
pages = "173--197",
day = "06",
month = jan,
year = "1999",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Mon Jul 19 22:22:18 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_free/browse/browse.cgi?year=1999&volume=210&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.com/cas/tree/store/tcs/sub/1999/210/1/2931.pdf",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@InProceedings{Bui:1999:DSI,
author = "H. Bui and S. Tahar",
booktitle = "1999 {IEEE} Canadian Conference on Electrical and
Computer Engineering, 9--12 May 1999",
title = "Design and synthesis of an {IEEE-754} exponential
function",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "450--455",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 17:14:11 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We have designed a floating-point exponential function
using the table-driven method. The algorithm was first
implemented using sequential VHDL and later translated
to Concurrent Verilog. The main part of the work
consisted of creating modules that \ldots{}",
}
@InProceedings{Burgess:1999:EIR,
author = "N. Burgess and S. Knowles",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "Efficient implementation of rounding units",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1489--1493",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper shows how IEEE 754 floating-point standard
compliant rounding may be merged with carry-propagate
addition in high-performance FPU designs. The paper
considers addition/subtraction, multiplication and
divide/square root operations and \ldots{}",
}
@InProceedings{Burgess:1999:FIS,
author = "Neil Burgess and Luigi Ciminiera",
title = "{Fifteenth IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "Koren:1999:ISC",
pages = "ix--ix",
year = "1999",
bibdate = "Sat Nov 17 21:53:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-14",
}
@Article{Cappuccino:1999:HSS,
author = "G. Cappuccino and G. Cocorullo and P. Corsonello and
S. Perri",
title = "High speed self-timed pipelined datapath for square
rooting",
journal = "Circuits, Devices and Systems, IEE Proceedings [see
also IEE Proceedings G- Circuits, Devices and
Systems]",
volume = "146",
number = "1",
pages = "16--22",
month = feb,
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The authors describe a new high-performance self-timed
circuit for asynchronous square rooting. The new
architecture is based on a modified nonrestoring
algorithm. An asynchronous pipelined cellular array
without auxiliary system for the \ldots{}",
}
@Article{Chren:1999:DSM,
author = "W. A. {Chren, Jr.}",
title = "Delta-sigma modulator with large {OSR} using the
one-hot residue number system",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "46",
number = "8",
pages = "1002--1008",
month = aug,
year = "1999",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.782041",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=16972",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "A digital delta-sigma modulator using the one-hot
residue number system (OHRNS) is presented. It exhibits
a large oversampling ratio (OSR) in comparison with
equivalent binary designs. Its second-order
architecture employs a two-stage cascade \ldots{}",
}
@Article{Christensen:1999:BFP,
author = "E. L. Christensen",
title = "Block floating point for radar data",
journal = j-IEEE-TRANS-AEROSP-ELECTRON-SYST,
volume = "35",
number = "1",
pages = "308--318",
month = jan,
year = "1999",
CODEN = "IEARAX",
ISSN = "0018-9251 (print), 1557-9603 (electronic)",
ISSN-L = "0018-9251",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Aerospace and Electronic
Systems",
summary = "Integer, floating point, and block floating point
(BFP) data formats are analyzed and compared in order
to establish the mathematical tools for selection of an
optimal format which fulfils the demands of high
resolution radar (SAR) data to large \ldots{}",
}
@Article{Chung:1999:RAC,
author = "Sei-Jong Chung",
title = "Recursive algorithm with {C++} program for
floating-point arithmetic",
journal = j-SIGCSE,
volume = "31",
number = "2",
pages = "28--30",
month = jun,
year = "1999",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/571535.571562",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sat Nov 17 16:56:38 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
abstract = "Floating point Arithmetic is a topic included in
virtually all textbooks for Computer Systems (CS 3:
ACM's Curriculum Recommendation) or for Computer
Organization (CS 4: ACM's Curriculum Recommendation).
This paper presents a mathematical optimization model
for the topic. The problem of converting real (float)
numbers into binary equivalents is first modeled as a
Zero-One Integer Programming problem. Then, a Recursive
Algorithm is formulated for Floating-Point Formats.
Computer programs are written in both C and C++ for a
32-bit floating-point format, using the recursive
algorithm. [The computer programs are available at the
email \ldots{}.]",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@Article{Cilio:1999:FPF,
author = "A. Cilio and H. Corporaal",
title = "Floating Point to Fixed Point Conversion of {C} Code",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1575",
pages = "229--243",
year = "1999",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 14 06:09:05 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs1999a.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "CC; compiler construction; ETAPS; software",
}
@Article{Clarke:1999:VSD,
author = "Edmund M. Clarke and Steven M. German and Xudong
Zhao",
title = "Verifying the {SRT} Division Algorithm Using Theorem
Proving Techniques",
journal = j-FORM-METHODS-SYST-DES,
volume = "14",
number = "1",
pages = "7--44",
month = jan,
year = "1999",
CODEN = "FMSDE6",
ISSN = "0925-9856 (print), 1572-8102 (electronic)",
ISSN-L = "0925-9856",
bibdate = "Sat Jun 02 09:21:29 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Special issue on arithmetic circuits.",
URL = "http://www.wkap.nl/jrnltoc.htm/0925-9856;
http://www.wkap.nl/oasis.htm/194806",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
journal-URL = "https://dl.acm.org/loi/fmsd",
}
@Article{Clouser:1999:MSF,
author = "J. Clouser and M. Matson and R. Badeau and R. Dupcak
and S. Samudrala and R. Allmon and N. Fairbanks",
title = "A {600-MHz} superscalar floating-point processor",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "34",
number = "7",
pages = "1026--1029",
month = jul,
year = "1999",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "The floating-point unit of a 600-MHz, out-of order,
superscalar RISC Alpha microprocessor is described. The
unit achieves 59 SpecFP95 and can transfer register
data at up to 9.6 GB/s. It has two independent
pipelines for multiply and add/subtract \ldots{}",
}
@InProceedings{Coleman:1999:BLA,
author = "J. N. Coleman and E. I. Chester",
title = "A $ 32 $-Bit Logarithmic Arithmetic Unit and Its
Performance Compared to Floating-Point",
crossref = "Koren:1999:ISC",
pages = "142--151",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-160.pdf;
http://euler.ecs.umass.edu/paper/final/paper-160.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Coleman.pdf",
abstract = "As an alternative to floating-point, several papers
have proposed the use of a logarithmic number system,
in which a real number is represented as a fixed-point
logarithm. Multiplication and division therefore
proceed in minimal time with no rounding error.
However, the system can only offer an overall advantage
if addition and subtraction can be performed with speed
and accuracy at least equal to that of floating-point,
but these operations require the interpolation of a
non-linear function which has hitherto been either
time-consuming or inaccurate. We present a procedure by
which additions and subtractions can be performed
rapidly and accurately, and show that these operations
are thereby competitive with their floating-point
equivalents. We then show that the average performance
of the logarithmic system exceeds floating-point, in
terms of both speed and accuracy.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Collavizza:1999:CPC,
author = "H. Collavizza and F. Delobel and M. Rueher",
title = "Comparing Partial Consistencies",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "213--228",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@TechReport{Connors:1999:SOF,
author = "Daniel A. Connors and Yoji Yamada and Wen-mei W. Hwu",
title = "A Software-Oriented Floating-Point Format for
Enhancing Automotive Control Systems",
type = "Report",
institution = "Department of Electrical and Computer Engineering, The
Coordinated Science Laboratory, University of
Illinois",
address = "Urbana, IL 61801, USA",
day = "11",
month = aug,
year = "1999",
bibdate = "Thu Jun 09 18:01:33 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Updated version of paper presented at the {\em
Workshop on Compiler and Architecture Support for
Embedded Computing Systems (CASES98), December,
1998}.",
URL = "http://rogue.colorado.edu/draco/papers/case-98-float.pd",
acknowledgement = ack-nhfb,
remark = "Describes an embedded system with 32-bit floating
point with a 24-bit significand, 5-bit signed exponent
in excess-15 base-8 representation, with a single zero,
no hidden bit, no NaN, no Infinity, and no
subnormals.",
}
@Article{Constales:1999:PSS,
author = "Denis Constales",
title = "Problems and Solutions: Solutions: 10568. Subtracting
Square Roots Repeatedly",
journal = j-AMER-MATH-MONTHLY,
volume = "106",
number = "2",
pages = "167--167",
month = feb,
year = "1999",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Wed Dec 29 06:14:39 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
xxnote = "See problem \cite{Knuth:1997:xxx}",
}
@Article{Conway:1999:FCM,
author = "R. Conway and J. Nelson",
title = "Fast converter for 3 moduli {RNS} using new property
of {CRT}",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "8",
pages = "852--860",
month = aug,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.795127",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:46:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=795127",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Cornea-Hasegan:1999:CPO,
author = "Marius A. Cornea-Hasegan and Roger A. Golliver and
Peter Markstein",
title = "Correctness proofs outline for {Newton--Raphson} based
floating-point divide and square root algorithms",
crossref = "Koren:1999:ISC",
pages = "96--105",
year = "1999",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-121.pdf;
http://euler.ecs.umass.edu/paper/final/paper-121.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Cornea_Hasegan.pdf",
abstract = "This paper describes a study of a class of algorithms
for the floating-point divide and square root
operations, based on the Newton--Raphson iterative
method. The two main goals were:\par
(1) Proving the IEEE correctness of these iterative
floating-point algorithms, i.e. compliance with the
IEEE-754 standard for binary floating-point operations
[1]. The focus was on software driven iterative
algorithms, instead of the hardware based
implementations that dominated until now.\par
(2) Identifying the special cases of operands that
require software assistance due to possible overflow,
underflow, or loss of precision of intermediate
results.\par
This study was initiated in an attempt to prove the
IEEE correctness for a class of divide and square root
algorithms based on the Newton--Raphson iterative
methods. As more insight into the inner workings of
these algorithms was gained, it became obvious that a
formal study and proof were necessary in order to
achieve the desired objectives. The result is a
complete and rigorous proof of IEEE correctness for
floating-point divide and square root algorithms based
on the Newton--Raphson iterative method. Even more, the
method used in proving the IEEE correctness of the
square root algorithm is applicable in principle to any
iterative algorithm, not only based on the
Newton--Raphson method. Conditions requiring Software
Assistance (SWA) were also determined, and were used to
identify cases when alternate algorithms are needed to
generate correct results. Overall, this is one
important step toward flawless implementation of these
floating-point operations based on software
implementations.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
summary = "This paper describes a study of a class of algorithms
for the floating-point divide and square root
operations, based on the Newton--Raphson iterative
method. The two main goals were. (1) Proving the IEEE
correctness of these iterative floating-point
\ldots{}",
}
@Article{Cornea-Hasegan:1999:IFP,
author = "Marius Cornea-Hasegan and Bob Norin",
title = "{IA-64} Floating-Point Operations and the {IEEE}
Standard for Binary Floating-Point Arithmetic",
journal = j-INTEL-TECH-J,
volume = "Q4",
pages = "16",
day = "22",
month = nov,
year = "1999",
ISSN = "1535-766X",
bibdate = "Fri Jun 01 06:02:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intel-tech-j.bib",
URL = "http://developer.intel.com/technology/itj/q41999/articles/art_6.htm;
http://developer.intel.com/technology/itj/q41999/pdf/ia64fpbf.pdf;
http://gec.di.uminho.pt/discip/minf/ac0203/icca03/ia64fpbf1.pdf",
acknowledgement = ack-nhfb,
}
@Article{Corsonello:1999:HPS,
author = "P. Corsonello and S. Perri",
title = "High performance square rooting circuit using hybrid
radix-$2$ adders",
journal = j-ELECT-LETTERS,
volume = "35",
number = "3",
pages = "185--186",
day = "4",
month = feb,
year = "1999",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "A new high performance bit parallel architecture for
computing square roots is proposed. The architecture
implements a non-restoring algorithm and is structured
as a pipelined cellular array. To improve the
performance, hybrid radix-$2$ adders are \ldots{}",
}
@TechReport{Crandall:1999:VIM,
author = "Richard E. Crandall and Jason Klivington",
title = "Vector implementation of multiprecision arithmetic",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "11",
day = "25",
month = oct,
year = "1999",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://images.apple.com/acg/pdf/G4multiprecision.pdf",
acknowledgement = ack-nhfb,
}
@Article{Cucker:1999:CED,
author = "Felipe Cucker and Steve Smale",
title = "Complexity estimates depending on condition and
round-off error",
journal = j-J-ACM,
volume = "46",
number = "1",
pages = "113--184",
month = jan,
year = "1999",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Tue May 25 18:51:21 MDT 1999",
bibsource = "http://www.acm.org/pubs/contents/journals/jacm/1999-46/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org:80/pubs/citations/journals/jacm/1999-46-1/p113-cucker/",
abstract = "This paper has two agendas. One is to develop the
foundations of round-off in computation. The other is
to describe an algorithm for deciding feasibility for
polynomial systems of equations and inequalities
together with its complexity analysis and its round-off
properties. Each role reinforces the other.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
keywords = "algorithms; theory",
subject = "{\bf F.2.1} Theory of Computation, ANALYSIS OF
ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
and Problems. {\bf G.1.5} Mathematics of Computing,
NUMERICAL ANALYSIS, Roots of Nonlinear Equations.",
}
@TechReport{Cuyt:1999:UR,
author = "Annie Cuyt and Peter Kuterna and Brigitte Verdonk and
Dennis Verschaeren",
title = "Underflow revisited",
type = "Technical report",
institution = "University of Antwerp (UIA)",
address = "Antwerp, Belgium",
year = "1999",
bibdate = "Mon Feb 25 12:26:10 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://wins.uia.ac.be/pub/preprints/99/underflow.ps",
acknowledgement = ack-nhfb,
}
@InProceedings{Darcy:1999:JEF,
author = "J. D. Darcy",
editor = "Robert F. Enenkel",
booktitle = "{CASCON 1998} Workshop Report, Numerical Computing:
Compiler and Library Support",
title = "{Java}'s evolving floating-point support: The good,
the bad, and the ugly",
publisher = "IBM Center for Advanced Studies",
address = "Toronto, ON, Canada",
pages = "2--10",
year = "1999",
bibdate = "Sun May 28 18:36:17 2006",
bibsource = "https://www-927.ibm.com/ibm/cas/publications/TR-74.165/TR-74.165.shtml;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Technical report TR-74.165-n.",
URL = "https://www-927.ibm.com/ibm/cas/publications/TR-74.165/n/numcomp6.pdf",
acknowledgement = ack-nhfb,
}
@Article{Daumas:1999:DFP,
author = "M. Daumas and C. Finot",
title = "Division of Floating Point Expansions with an
Application to the Computation of a Determinant",
journal = j-J-UCS,
volume = "5",
number = "6",
pages = "323--??",
day = "28",
month = jun,
year = "1999",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Thu Oct 12 14:21:59 MDT 2000",
bibsource = "http://www.jucs.org/jucs;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/jucs_5_6/division_of_floating_point",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@InProceedings{Daumas:1999:MFP,
author = "Marc Daumas",
title = "Multiplications of Floating Point Expansions",
crossref = "Koren:1999:ISC",
pages = "250--257",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-102.pdf;
http://euler.ecs.umass.edu/paper/final/paper-102.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Daumas.pdf",
abstract = "In modern computers, the floating point unit is the
part of the processor delivering the highest computing
power and getting most attention from the design team.
Performance of any multiple precision application will
be dramatically enhanced by adequate use of floating
point expansions. We present in this work three
multiplication algorithms faster and more integrated
than the stepwise algorithm proposed earlier. We have
tested these new algorithms on an application that
computes the determinant of a matrix. In the absence of
overflow or underflow, the process is error free and
possibly more efficient than its integer based
counterpart.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Denise:1999:URG,
author = "A. Denise and P. Zimmermann",
title = "Uniform random generation of decomposable structures
using floating-point arithmetic",
journal = j-THEOR-COMP-SCI,
volume = "218",
number = "2",
publisher = "Elsevier Science",
pages = "233--248",
day = "26",
month = may,
year = "1999",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
pagecount = "16",
}
@Article{Dimitrov:1999:TAD,
author = "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
title = "Theory and Applications for a Double-Base Number
System",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "10",
pages = "1098--1106",
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.805158",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Nov 14 18:56:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Dimitrova:1999:VCF,
author = "N. S. Dimitrova and S. M. Markov",
title = "Verified Computation of Fast Decreasing Polynomials",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "229--240",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@Misc{Dyke-Lewis:1999:MAP,
author = "M. D. V. Dyke-Lewis and W. Meeker",
title = "Method and Apparatus for performing fast floating
point operations",
day = "12",
month = oct,
year = "1999",
bibdate = "Fri Nov 28 15:17:46 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,966,085.",
acknowledgement = ack-nhfb,
}
@Article{Dyllong:1999:ADC,
author = "E. Dyllong and W. Luther and W. Otten",
title = "An Accurate Distance-Calculation Algorithm for Convex
Polyhedra",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "241--253",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@Manual{ECDG:1999:IER,
author = "{European Commission Directorate General II}",
title = "The Introduction of the Euro and the Rounding of
Currency Amounts",
organization = "European Commission Directorate General II Economic
and Financial Affairs",
address = "Brussels, Belgium",
pages = "32",
month = feb,
year = "1999",
bibdate = "Fri Nov 28 11:18:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "II/28/99-EN Euro Papers No. 22. Earlier edition dated
March 1998.",
acknowledgement = ack-nhfb,
}
@Article{Edalat:1999:NIE,
author = "A. Edalat and M. Krznaric",
title = "Numerical Integration with Exact Real Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1644",
pages = "90--??",
year = "1999",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Sep 13 16:57:02 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs1999b.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@TechReport{Ercegovac:1999:IGD,
author = "Milo{\v{s}} D. Ercegovac and Laurent Imbert and David
W. Matula and Jean-Michel Muller and Guoheng Wei",
title = "Improving {Goldschmidt} Division, Square Root, and
Square Root Reciprocal",
type = "Research Report",
number = "99-41",
institution = "Laboratoire de l'Informatique du Parall{\'e}lisme",
address = "Lyon, France",
pages = "ii + 17",
month = sep,
year = "1999",
bibdate = "Mon Dec 11 07:53:15 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/inria-00072909/file/RR1999-41.pdf",
abstract = "The aim of this paper is to accelerate division,
square root and square root reciprocal computations,
when Goldschmidt method is used on a pipelined
multiplier. This is done by replacing the last
iteration by the addition of a correcting term that can
be looked up during the early iterations. We describe
several variants of the Goldschmidt algorithm assuming
4-cycle pipelined multiplier and discuss obtained
number of cycles and error achieved. Extensions to
other than 4-cycle multipliers are given",
acknowledgement = ack-nhfb,
keywords = "Computer Arithmetic; Convergence division; Division;
Goldschmidt iteration; Square root; Square root
reciprocal",
}
@InProceedings{Ercegovac:1999:LPB,
author = "M. Ercegovac and D. Kirovski and M. Potkonjak",
booktitle = "Proceedings of the 36th Design Automation Conference,
21--25 June 1999",
title = "Low-power behavioral synthesis optimization using
multiple precision arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "568--573",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Many modern multimedia applications such as image and
video processing are characterized by a unique
combination of arithmetic and computational features:
fixed-point arithmetic, a variety of short data types,
high degree of instruction-level \ldots{}",
}
@InProceedings{Even:1999:CTR,
author = "Guy Even and Peter-M. Seidel",
title = "A Comparison of Three Rounding Algorithms for {IEEE}
Floating-Point Multiplication",
crossref = "Koren:1999:ISC",
pages = "225--232",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-100.pdf;
http://euler.ecs.umass.edu/paper/final/paper-100.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Even.pdf",
abstract = "A new IEEE compliant floating-point rounding algorithm
for computing the rounded product from a carry-save
representation of the product is presented. The new
rounding algorithm is compared with the rounding
algorithms of Yu and Zyner [23] and of Quach et al.
[18]. For each rounding algorithm, a logical
description and a block diagram is given and the
latency is analyzed.\par
We conclude that the new rounding algorithm is the
fastest rounding algorithm, provided that an injection
(which depends only on the rounding mode and the sign)
can be added in during the reduction of the partial
products into a carry-save encoded digit string. In
double precision the latency of the new rounding
algorithm is 12 logic levels compared to 14 logic
levels in the algorithm of Quach et al., and 16 logic
levels in the algorithm of Yu and Zyner.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{Eweda:1999:REA,
author = "E. Eweda and W. M. Younis and S. H. El-Ramly",
booktitle = "Proceedings of the Sixteenth National Radio Science
Conference 1999: {NRSC '99}",
title = "Roundoff error analysis of the tracking performance of
the block {LMS} algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "C30/1--C30/9",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The paper is concerned with analyzing the roundoff
error effect on the tracking performance of the block
least mean square (BLMS) algorithm when used in the
adaptive identification of a time-varying plant.
Rounding quantization is assumed. \ldots{}",
}
@Article{Farid:1999:RCA,
author = "T. Farid and D. Zerbino",
title = "Realization of Complex Arithmetic on Cellular
Automata",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1662",
pages = "479--??",
year = "1999",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Sep 13 16:57:02 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs1999b.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Fateman:1999:SEN,
author = "Richard J. Fateman",
title = "Symbolic execution and {NaNs}: diagnostic tools for
tracking scientific computation",
journal = j-SIGSAM,
volume = "33",
number = "3",
pages = "25--26",
month = sep,
year = "1999",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Fri Feb 8 18:27:06 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@InProceedings{Fernandez:1999:NID,
author = "P. G. Fernandez and A. Garcia and J. Ramirez and L.
Parrilla and A. Lloris",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "A new implementation of the discrete cosine transform
in the residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1302--1306",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.1999.831917",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A field-programmable logic (FPL) implementation of a
discrete cosine transform (DCT) based on the residue
number system (RNS) is presented. Compared with a
binary distributed arithmetic implementation, the
presented architecture provides \ldots{}",
}
@Article{Fiore:1999:PMU,
author = "P. D. Fiore",
title = "Parallel multiplication using fast sorting networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "6",
pages = "640--645",
month = jun,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.773800",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:46:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=773800",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Flynn:1999:FDA,
author = "Patrick Hung and Hossam Fahmy and Oskar Mencer and
Michael J. Flynn",
editor = "{IEEE}",
booktitle = "Asilomar Conference on Signals, Systems, and
Computers, California, Nov. 1999",
title = "Fast Division Algorithm with a Small Lookup Table",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "??--??",
year = "1999",
bibdate = "Mon Jul 18 17:26:03 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://arith.stanford.edu/tr/asil99div.ps.gz",
abstract = "This paper presents a new division algorithm, which
requires two multiplication operations and a single
lookup in a small table. The division algorithm takes
two steps. The table lookup and the first
multiplication are processed concurrently in the first
step, and the second multiplication is executed in the
next step. This divider uses a single multiplier and a
lookup table with $ 2^m(2 m + 1) $ bits to produce $ 2
m $-bit results that are guaranteed correct to one ulp.
By using a multiplier and a KB lookup table, the basic
algorithm generates a 24-bit result in two cycles.",
acknowledgement = ack-nhfb,
pagecount = "4",
}
@InProceedings{Freking:1999:MMM,
author = "W. L. Freking and K. K. Parhi",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "{Montgomery} modular multiplication and exponentiation
in the residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1312--1316",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.1999.831919",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Modular exponentiation and its constituent operation,
modular multiplication, are fundamental to numerous
public-key cryptography schemes including RSA.
Efficient hardware implementations via ASIC or
coprocessor approaches are essential to high-
\ldots{}",
}
@Article{Frommer:1999:VEB,
author = "A. Frommer and A. Weinberg",
title = "Verified Error Bounds for Linear Systems Through the
{Lanczos} Process",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "255--267",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@Article{Garcia:1999:LSS,
author = "A. Garcia and A. Lloris",
title = "A look-up scheme for scaling in the {RNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "7",
pages = "748--751",
month = jul,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.780883",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:46:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=780883",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gay:1999:SAF,
author = "David M. Gay and Eric Grosse",
title = "Self-adapting {Fortran 77} Machine Constants: Comment
on {Algorithm 528}",
journal = j-TOMS,
volume = "25",
number = "1",
pages = "123--126",
month = mar,
year = "1999",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/305658.305711",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Oct 20 12:38:08 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fox:1978:AFP}.",
URL = "http://cm.bell-labs.com/who/ehg/mach/d1mach.ps;
http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gay:1999:SAF;
http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMScitation?Fox:1978:AFP;
http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p123-gay/",
abstract = "This note discusses user dissatisfaction with the need
to uncomment data statements in Algorithm 528, comments
on alternative approaches tried by the community, and
proposes a solution that is both automatic and safe.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "algorithms; d1mach; languages; machine environment
parameters",
subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
Classifications, FORTRAN 77. {\bf G.1.0} Mathematics of
Computing, NUMERICAL ANALYSIS, General, Computer
arithmetic.",
}
@Article{German:1999:ISI,
author = "Steven M. German",
title = "Introduction to the Special Issue on Verification of
Arithmetic Hardware",
journal = j-FORM-METHODS-SYST-DES,
volume = "14",
number = "1",
pages = "5--6",
month = jan,
year = "1999",
CODEN = "FMSDE6",
ISSN = "0925-9856 (print), 1572-8102 (electronic)",
ISSN-L = "0925-9856",
bibdate = "Sat Jun 02 09:20:18 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.wkap.nl/jrnltoc.htm/0925-9856;
http://www.wkap.nl/oasis.htm/194805",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
journal-URL = "https://dl.acm.org/loi/fmsd",
}
@InProceedings{Gerwig:1999:FPU,
author = "Guenter Gerwig and Michael Kroener",
title = "Floating-Point Unit in Standard Cell Design with $ 116
$ bit Wide Dataflow",
crossref = "Koren:1999:ISC",
pages = "266--273",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-132.pdf;
http://euler.ecs.umass.edu/paper/final/paper-132.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Gerwig.pdf",
abstract = "The floating-point unit of a S/390 CMOS microprocessor
is described. It contains a 116 bit fraction dataflow
for addition and subtraction and a 64 bit-wide
multiplier. Besides the register array, there are no
other dataflow macros used; it is fully designed with
standard cell books and is placed flat with a timing
driven placement algorithm. This design method allows
more `irregular' structures than usually found in
custom designs.\par
An overview of the floating-point unit is given and
some interesting design items are shown: a 120 bit-wide
true-complement adder with precounting of leading zero
digits, a signed multiplier with bit-optimized Wallace
tree, intensive forwarding in source equal target cases
and the checking method.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Gizopoulos:1999:EBS,
author = "D. Gizopoulos and A. Paschalis and Y. Zorian",
title = "An effective built-in self-test scheme for parallel
multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "9",
pages = "936--950",
month = sep,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.795222",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:46:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=795222",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Gorshtein:1999:MAM,
author = "V. Y. Gorshtein and V. T. Khlobystov",
title = "Multiplication apparatus and methods which generate a
shift amount by which the product of the significands
is shifted for normalization or denormalization",
day = "5",
month = oct,
year = "1999",
bibdate = "Fri Nov 28 15:32:30 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,963,461.",
acknowledgement = ack-nhfb,
}
@Article{Gueron:1999:FFP,
author = "Shay Gueron",
title = "Flying in a floating (point) world",
journal = "International Journal of Computers for Mathematical
Learning",
volume = "4",
number = "2--3",
pages = "225--234",
month = may,
year = "1999",
DOI = "https://doi.org/10.1023/A:1009818429410",
ISSN = "1382-3892 (print), 1573-1766 (electronic)",
ISSN-L = "1382-3892",
bibdate = "Wed Jul 01 15:36:52 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/content/j071k8608t578153/",
acknowledgement = ack-nhfb,
journal-URL = "https://link.springer.com/journal/10758",
}
@InProceedings{Gustavson:1999:FMA,
author = "Fred G. Gustavson and Jos{\'e} E. Moreira and Robert
F. Enenk",
editor = "????",
booktitle = "{CASCON '99}: Proceedings of the 1999 Conference of
the Centre for Advanced Studies on Collaborative
Research. November 8--11, 1999, Mississauga, Ontario,
Canada",
title = "The fused multiply-add instruction leads to algorithms
for extended-precision floating point: applications to
{Java} and high-performance computing",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "4",
year = "1999",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Nov 26 15:40:34 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Dedicated to Cleve Moler on his 60th birthday.",
acknowledgement = ack-nhfb,
}
@Misc{Handlogten:1999:MAP,
author = "G. H. Handlogten",
title = "Method and apparatus to perform pipelined
denormalization of floating-point results",
day = "24",
month = aug,
year = "1999",
bibdate = "Fri Nov 28 15:37:38 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,943,249.",
acknowledgement = ack-nhfb,
}
@Article{Harrison:1999:CTF,
author = "John Harrison and Ted Kubaska and Shane Story and Ping
Tak Peter Tang",
title = "The Computation of Transcendental Functions on the
{IA-64} Architecture",
journal = j-INTEL-TECH-J,
volume = "Q4",
pages = "7",
day = "22",
month = nov,
year = "1999",
bibdate = "Fri Jun 01 06:02:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://developer.intel.com/technology/itj/q41999/articles/art_5.htm;
http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf",
acknowledgement = ack-nhfb,
}
@Article{Harrison:1999:MCT,
author = "John Harrison",
title = "A Machine-Checked Theory of Floating Point
Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1690",
pages = "113--130",
year = "1999",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/3-540-48256-3_9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Jun 5 10:53:14 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cl.cam.ac.uk/users/jrh/papers/fparith.html",
acknowledgement = ack-jh,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Hayashi:1999:SRR,
author = "Takao Hayashi",
title = "A set of rules for the root-extraction prescribed by
the sixteenth-century {Indian} mathematicians,
{N{\=\i}laka{\d{n}}{\d{t}}ha Somastuvan} and
{{\'S}a{\.n}kara V{\=a}riyar}",
journal = j-HIST-SCI-2,
volume = "9",
number = "2",
pages = "135--153",
month = nov,
year = "1999",
CODEN = "HISCDU",
ISSN = "0285-4821",
ISSN-L = "0285-4821",
MRclass = "01A32",
MRnumber = "1762168",
MRreviewer = "A. I. Volodarski{\u\i}",
bibdate = "Sat Oct 6 17:22:25 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/histscijpn.bib",
acknowledgement = ack-nhfb,
fjournal = "Historia Scientiarum. Second Series. International
Journal of the History of Science Society of Japan",
journal-URL = "http://hssj.info/",
}
@Article{Heindl:1999:RIH,
author = "G. Heindl",
title = "A Representation of the Interval Hull of a Tolerance
Polyhedron Describing Inclusions of Function Values and
Slopes",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "269--278",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@Article{Hiasat:1999:SCV,
author = "Ahmad A. Hiasat and Hoda Abdel-Aty-Zohdy",
title = "Semi-Custom {VLSI} Design and Implementation of a New
Efficient {RNS} Division Algorithm",
journal = j-COMP-J,
volume = "42",
number = "3",
pages = "232--240",
month = "????",
year = "1999",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Sep 2 06:09:59 MDT 1999",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_42/Issue_03/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_42/Issue_03/420232.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_42/Issue_03/pdf/420232.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@MastersThesis{Hirn:1999:GBI,
author = "Ulrich Hirn",
title = "{Groebner} bases implementation using modular and
floating point arithmetic",
type = "{Dipl.-Arb.}",
school = "Technische Universit{\"a}t Graz",
address = "Graz, Austria",
pages = "87",
year = "1999",
bibdate = "Thu May 09 09:37:46 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hormigo:1999:ISC,
author = "J. Hormigo and J. Villalba and E. L. Zapata",
title = "Interval Sine and Cosine Functions Computation Based
on Variable Precision {CORDIC} Algorithm",
crossref = "Koren:1999:ISC",
pages = "186--193",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-128.pdf;
http://euler.ecs.umass.edu/paper/final/paper-128.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Hormigo.pdf",
abstract = "In this paper we design a CORDIC architecture for
variable-precision, and a new algorithm is proposed to
perform the interval sine and cosine functions. This
system allows us to specify the precision to perform
the sine and cosine functions, and control the accuracy
of the result, in such a way that recomputation of
inaccurate results can be carried out with higher
precision. An important reduction in the number of
iterations is obtained by taking advantage of the
differential angle, and the number of cycles per
iteration is reduced by avoiding the additions of the
leading all zero words. As a consequence, the
computation time of the interval function evaluation
obtained is close to that of a point function
evaluation. The problem of the large table of angles
and the scale factor compensation involved in a high
precision CORDIC has been solved efficiently.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{Hung:1999:FDA,
author = "P. Hung and H. Fahmy and O. Mencer and M. J. Flynn",
title = "Fast division algorithm with a small lookup table",
crossref = "Matthews:1999:CRT",
volume = "2",
pages = "1465--1468",
year = "1999",
DOI = "https://doi.org/10.1109/ACSSC.1999.831992",
bibdate = "Sat Oct 9 12:45:46 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a new division algorithm, which
requires two multiplication operations and a single
lookup in a small table. The division algorithm takes
two steps. The table lookup and the first
multiplication are processed concurrently in the first
step, and the second multiplication is executed in the
next step. This divider uses a single multiplier and a
lookup table with $ 2 m (2 m + 1) $ bits to produce $2$
$m$-bit results that are guaranteed correct to one ulp.
By using a multiplier and a 12.5 KB lookup table, the
basic algorithm generates a 24-bit result in two
cycles",
acknowledgement = ack-nhfb,
}
@InProceedings{Hyogo:1999:LVF,
author = "A. Hyogo and Y. Fukutomi and K. Sekine",
booktitle = "Proceedings of the 1999 {IEEE} International Symposium
on Circuits and Systems: {ISCAS '99}, 2 June 1999",
title = "Low voltage four-quadrant analog multiplier using
square-root circuit based on {CMOS} pair",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "274--277",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We proposed a square-root circuit based on CMOS pairs.
In this paper, we propose a low voltage four-quadrant
analog multiplier using the square-root circuit. Also
we confirmed this operation by PSpice \ldots{}",
}
@InProceedings{Ide:1999:GFP,
author = "N. Ide and M. Hirano and Y. Endo and S. Yoshioka and
H. Murakami and A. Kunimatsu and T. Sato and T. Kamei
and T. Okada and M. Suzuoki",
title = "{2.44 GFLOPS 300MHz} floating-point vector processing
unit for high performance {$3$D} graphics computing",
crossref = "Hosticka:1999:EPE",
pages = "106--109",
year = "1999",
bibdate = "Sat Jun 02 08:23:03 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Iordache:1999:ARS,
author = "Cristina Iordache and David W. Matula",
title = "Analysis of Reciprocal and Square Root Reciprocal
Instructions in the {AMD K6-2} Implementation of
{3DNow!}",
journal = j-ELECT-NOTES-THEOR-COMP-SCI,
volume = "24",
pages = "34--62",
month = apr,
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1016/S1571-0661(05)80621-8",
ISSN = "1571-0661",
ISSN-L = "1571-0661",
bibdate = "Fri Jun 24 20:23:13 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Reciprocal and root reciprocal functions at ``half''
and IEEE single precision formats are specified in the
AMD 3DNow! instruction set. Implementations in the
recently released AMD K6-2 microprocessor are analyzed
herein by exhaustive computation and timing loops to
ascertain the accuracy and monotonicity properties of
the output and throughput\slash latency cycle counts.
Periodicities in stepwise function output were observed
and employed to construct an underlying bipartite table
that can serve as the core of the respective reciprocal
function outputs. The recommended RISC instruction
macros generated single precision reciprocals and root
reciprocals accurate to a unit in the last place.
However, the root reciprocal functions failed to
satisfy the desirable monotonicity property typically
implemented as an industry standard for elementary
functions on x86 floating point units. Reasons for the
failure are provided and an adjusted table is shown to
satisfy the monotonicity standard. Results are
summarized in Table 1 and described in the body of this
report.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Notes in Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/15710661",
}
@InProceedings{Iordache:1999:IPR,
author = "Cristina Iordache and David W. Matula",
title = "On Infinitely Precise Rounding for Division, Square
Root, Reciprocal and Square Root Reciprocal",
crossref = "Koren:1999:ISC",
pages = "233--240",
year = "1999",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-164.pdf;
http://euler.ecs.umass.edu/paper/final/paper-164.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Iordache.pdf",
abstract = "Quotients, reciprocals, square roots and square root
reciprocals all have the property that infinitely
precise p-bit rounded results for p-bit input operands
can be obtained from approximate results of bounded
accuracy. We investigate lower bounds on the number of
bits of an approximation accurate to a unit in the last
place sufficient to guarantee that correct round and
sticky bits can be determined. Known lower bounds for
quotients and square roots are given and/or sharpened,
and a new lower bound for root reciprocals is proved.
Specifically for reciprocals, quotients and square
roots, tight bounds of order $ 2 p + O(1) $ are
presented. For infinitely precise rounding of the root
reciprocal a lower bound can be found at $ 3 p + O(1)
$, but exhaustive testing for small sizes of the
operand suggests that in practice $ (2 + \epsilon)p $
for small $ \epsilon $ is usually sufficient.
Algorithms can be designed for obtaining the round and
sticky bits based on the bit pattern of an
approximation computed to the required accuracy. We
show that some improvement of the known lower bound for
reciprocals and division is achievable at the cost of
somewhat more complex hardware for rounding. Tests for
the exactness of the quotient and square root are also
provided.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic; correct rounding;
floating-point arithmetic",
summary = "Quotients, reciprocals, square roots and square root
reciprocals all have the property that infinitely
precise p-bit rounded results for p-bit input operands
can be obtained from approximate results of bounded
accuracy. We investigate lower bounds \ldots{}",
}
@Article{Jamieson:1999:NRF,
author = "M. J. Jamieson",
title = "Notes: On rational function approximations to square
roots",
journal = j-AMER-MATH-MONTHLY,
volume = "106",
number = "1",
pages = "50--52",
month = jan,
year = "1999",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11Yxx",
MRnumber = "1 674 202",
bibdate = "Tue Jun 22 10:29:34 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Jamieson:1999:RFA,
author = "M. J. Jamieson",
title = "On rational function approximations to square roots",
journal = j-AMER-MATH-MONTHLY,
volume = "106",
number = "1",
pages = "50--52",
year = "1999",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "11Yxx",
MRnumber = "1 674 202",
bibdate = "Tue Jun 22 10:29:34 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@InProceedings{Jeong:1999:CPT,
author = "Cheol-Ho Jeong and Woo-Chan Park and Tack-Don Dan and
Shin-Dug Kim",
title = "Cost\slash performance Trade-off in Floating-point
Unit Design for {$3$D} Geometry Processor",
crossref = "IEEE:1999:AAF",
pages = "104--107",
year = "1999",
DOI = "https://doi.org/10.1109/APASIC.1999.824039",
bibdate = "Fri Jun 24 12:18:17 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Jones:1999:BAT,
author = "Douglas W. Jones",
title = "{BCD} Arithmetic, a tutorial",
howpublished = "Web tutorial.",
year = "1999",
bibdate = "Tue Jan 22 07:13:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://homepage.cs.uiowa.edu/~jones/bcd/bcd.html",
acknowledgement = ack-nhfb,
}
@Misc{Jones:1999:BDC,
author = "Douglas W. Jones",
title = "Binary to Decimal Conversion in Limited Precision",
howpublished = "Web tutorial.",
year = "1999",
bibdate = "Tue Jan 22 07:13:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://homepage.cs.uiowa.edu/~jones/bcd/decimal.html",
acknowledgement = ack-nhfb,
}
@Misc{Jones:1999:MDT,
author = "Douglas W. Jones",
title = "Modulus without Division, a tutorial",
howpublished = "Web tutorial.",
year = "1999",
bibdate = "Tue Jan 22 07:13:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://homepage.cs.uiowa.edu/~jones/bcd/mod.shtml",
acknowledgement = ack-nhfb,
}
@Misc{Jones:1999:RMT,
author = "Douglas W. Jones",
title = "Reciprocal Multiplication, a tutorial",
howpublished = "Web tutorial.",
year = "1999",
bibdate = "Tue Jan 22 07:13:24 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://homepage.cs.uiowa.edu/~jones/bcd/divide.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Jullien:1999:HDP,
author = "G. A. Jullien and V. S. Dimitrov and B. Li and W. C.
Miller and A. Lee and M. Ahmadi",
editor = "{IEEE}",
booktitle = "{Proceedings of the 1999 IEEE International Symposium
on Circuits and Systems: ISCAS '99, May 30--June 2
1999, Orlando, Florida}",
title = "A Hybrid {DBNS} Processor for {DSP} Computation",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "liv + 565",
pages = "5--8",
year = "1999",
DOI = "https://doi.org/10.1109/ISCAS.1999.777792",
ISBN = "0-7803-5471-0 (softbound), 0-7803-5472-9 (casebound),
0-7803-5473-7 (microfiche)",
ISBN-13 = "978-0-7803-5471-5 (softbound), 978-0-7803-5472-2
(casebound), 978-0-7803-5473-9 (microfiche)",
LCCN = "TK7801 .I22 1999",
bibdate = "Sat May 14 17:21:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 99CH36349.",
acknowledgement = ack-nhfb,
keywords = "Double-Based Number System (DBNS)",
}
@Misc{Kahan:1999:SRD,
author = "W. Kahan",
title = "Square Root Without Division",
howpublished = "World-Wide Web document",
pages = "3",
day = "23",
month = feb,
year = "1999",
bibdate = "Mon Apr 25 18:01:49 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kaplan:1999:JVA,
author = "Bonnie Kaplan",
title = "{John V. Atanasoff} (1903--1995) interview: {August
10, 1972}",
journal = "Computer Oral History Collection, Smithsonian
Institution Press",
year = "1999",
bibdate = "Fri Aug 08 08:33:46 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Article No. 17.",
abstract = "The conversation begins with Atanasoff's method of
adding and counting---an idea he conceived of while in
a honky-tonk bar in Illinois in 1937. This concept of
addition was to be performed by logic and not by
successive inching of a dial. Atanasoff further remarks
that his interest in electronic computation began by
thinking along the Eccles-Jordan lines. The
Eccles-Jordan circuit was used for part of the
operation and intended to do successive impulses.
Further comments about the Eccles-Jordan circuitry are
made. The use of vacuum tubes in Atanasoff's machine
was prompted be economy. Vacuum tube circuits were fast
enough to solve the sums of all digits and thus
economize on time and material. The use of base two for
arithmetic was employed because it was simpler. The use
of dual triodes (6F8G and then ultimately the 6C8G) in
the circuitry was also based on economy--original cost
and space. The difference between these two tubes is
discussed. Comments on the machines ability to do
subtraction using [Comptu's?] complements. Atanasoff
decided to use the complements in the memory in order
to subtract. This use of complements was not original
to Atanasoff. Atanasoff explains his use of lower base
numbers opposed to larger. The simplest way of storing
numbers up to 25 is by coding them into numbers
probably with a base of two. Numbers associated with
the base of two were associated with a simpler logical
system. While Atanasoff experimented with larger base
numbers, he found them to unsatisfactory. Atanasoff
discussed his decision to use base two with George
Gross and William Mercer who did the calculations which
were needed for the base ten- base two conversion
table. While doing the conversions on the machine, the
addition was automatically carried out in the computing
machine. Atanasoff explains the concept of a floating
grid. This type of grid implied that it did not have a
bias resistor to the ground, it was not connected.
Normal grids in vacuum tubes are connected to the
ground. Another of Atanasoff's addition to the machine
was the use of a dielectric sheet to record the base
two numbers. The dielectric had difficulty working
since Atanasoff could never find a satisfactory paper
on which to record the readings. Atanasoff discusses
his desire to have worked for IBM despite the rebuffs
he had received over the years. He notes that he wanted
to be more in the mainstream of the development of
computers with funding, and the possibilities of
research. IBM seemed to provide the best possible
future for computing. This transcript concludes with
several miscellaneous questions based on the court
transcripts from the litigation Honeywell vs.
Sperry-Rand. Individuals mentioned include: Ernest
Anderson, Clifford Berry, George Gross, James Elder,
Norman Fulmer, and Hazeltine.",
acknowledgement = ack-nhfb,
}
@Book{Kaplan:1999:NNH,
author = "Robert Kaplan",
title = "The Nothing That Is: a Natural History of Zero",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xii + 225",
year = "1999",
ISBN = "0-19-512842-7",
ISBN-13 = "978-0-19-512842-0",
LCCN = "QA141 .K36 1999",
bibdate = "Mon Dec 06 16:15:22 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$22.00",
acknowledgement = ack-nhfb,
}
@InProceedings{Karamcheti:1999:CLR,
author = "V. Karamcheti and C. Li and I. Pechtchanski and C.
Yap",
title = "A core library for robust numerical and geometric
libraries",
crossref = "ACM:1999:PFA",
pages = "351--359",
year = "1999",
bibdate = "Sat Apr 28 18:58:05 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.nyu.edu/exact",
acknowledgement = ack-nhfb,
}
@Article{Kern:1999:FVH,
author = "Christoph Kern and Mark R. Greenstreet",
title = "Formal verification in hardware design: a survey",
journal = j-TODAES,
volume = "4",
number = "2",
pages = "123--193",
month = apr,
year = "1999",
CODEN = "ATASFO",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Fri Jul 27 10:05:33 MDT 2001",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/articles/journals/todaes/1999-4-2/p123-kern/p123-kern.pdf;
http://www.acm.org/pubs/citations/journals/todaes/1999-4-2/p123-kern/",
abstract = "In recent years, formal methods have emerged as an
alternative approach to ensuring the quality and
correctness of hardware designs, overcoming some of the
limitations of traditional validation techniques such
as simulation and testing.\par
There are two main aspects to the application of formal
methods in a design process: the formal framework used
to specify desired properties of a design and the
verification techniques and tools used to reason about
the relationship between a specification and a
corresponding implementation. We survey a variety of
frameworks and techniques proposed in the literature
and applied to actual designs. The specification
frameworks we describe include temporal logics,
predicate logic, abstraction and refinement, as well as
containment between -regular languages. The
verification techniques presented include model
checking, automata-theoretic techniques, automated
theorem proving, and approaches that integrate the
above methods.\par
In order to provide insight into the scope and
limitations of currently available techniques, we
present a selection of case studies where formal
methods were applied to industrial-scale designs, such
as microprocessors, floating-point hardware, protocols,
memory subsystems, and communications hardware.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Design Automation of Electronic
Systems (TODAES)",
generalterms = "Design; Verification",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J776",
keywords = "case studies; formal methods; formal verification;
hardware verification; language containment; model
checking; survey; theorem proving",
subject = "General Literature --- Introductory and Survey (A.1);
Hardware --- Integrated Circuits --- Design Aids
(B.7.2): {\bf Verification}",
}
@InProceedings{Knowles:1999:FA,
author = "Simon Knowles",
title = "A Family of Adders",
crossref = "Koren:1999:ISC",
pages = "30--34",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-168.pdf;
http://euler.ecs.umass.edu/paper/final/paper-168.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Knowles.pdf",
abstract = "Binary carry-propagating addition can be efficiently
expressed as a prefix computation. Several examples of
adders based on such a formulation have been published,
and efficient implementations are numerous. Chief among
the known constructions are those of Kogge \& Stone and
Ladner \& Fischer. In this work we show that these are
end cases of a large family of addition structures, all
of which share the attractive property of minimum
logical depth. The intermediate structures allow
trade-offs between the amount of internal wiring and
the fanout of intermediate nodes, and can thus usually
achieve a more attractive combination of speed and
area/power cost than either of the known end-cases.
Rules for the construction of such adders are given, as
are examples of realistic 32b designs implemented in an
industrial 0u25 CMOS process.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{Koren:1999:FIS,
author = "Israel Koren and Peter Kornerup",
title = "{Fourteenth IEEE Symposium on Computer Arithmetic}:
Foreword",
crossref = "Koren:1999:ISC",
pages = "viii--viii",
year = "1999",
bibdate = "Sat Nov 17 21:53:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-14",
}
@Misc{Koren:1999:ITS,
author = "Israel Koren and Peter Kornerup",
title = "{IEEE TC} Special Issue on Computer Arithmetic ---
{May} 2000",
howpublished = "World-Wide Web document.",
year = "1999",
bibdate = "Wed Jan 20 10:00:59 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ecs.umass.edu/ece/koren/sp-issue/",
acknowledgement = ack-nhfb,
}
@InProceedings{Kornerup:1999:NSC,
author = "Peter Kornerup",
title = "Necessary and Sufficient Conditions for Parallel,
Constant Time Conversion and Addition",
crossref = "Koren:1999:ISC",
pages = "152--157",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-103.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Kornerup.pdf",
abstract = "This note presents necessary and sufficient conditions
for parallel and constant time conversions from one
digit-set into another, and thus also for constant time
addition. In the integer domain it is generally
believed that such conversion and addition is possible
if the target digit-set is redundant and complete. This
is also the case when the digit-set is a contiguous set
of integers. However, when this is not the case then
such conversion and addition in the integer domain is
not possible in general, and when more general rings
are considered, the same problem may be present.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Krick:1999:AN,
author = "T. Krick and L. M. Pardo and M. Sombra",
title = "Arithmetic {Nullstellens{\"a}tze}",
journal = j-SIGSAM,
volume = "33",
number = "3",
pages = "17--17",
month = sep,
year = "1999",
CODEN = "SIGSBZ",
ISSN = "0163-5824 (print), 1557-9492 (electronic)",
ISSN-L = "0163-5824",
bibdate = "Fri Feb 8 18:27:06 MST 2002",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIGSAM Bulletin",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Lang:1999:VHR,
author = "T. Lang and P. Montuschi",
title = "Very high radix square root with prescaling and
rounding and a combined division\slash square root
unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "8",
pages = "827--841",
month = aug,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.795124",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:46:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=795124",
abstract = "An algorithm for square root with prescaling and
selection by rounding is developed and combined with a
similar scheme for division. Since division is usually
more frequent than square root, the main concern of the
combined implementation is to maintain the low
execution time of division, while accepting a somewhat
larger execution time for square root. The algorithm is
presented in detail, including the mathematical
development of bounds for the first square-root digit
and for the scaling factor. The proposed implementation
is described, evaluated and compared with other
combined div/sqrt units. The comparisons show that the
proposed scheme potentially produces a significant
speed-up for division, whereas, for square root, the
speed-up is small",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "An algorithm for square root with prescaling and
selection by rounding is developed and combined with a
similar scheme for division. Since division is usually
more frequent than square root, the main concern of the
combined implementation is to \ldots{}",
}
@Article{Langlois:1999:WAL,
author = "Ph. Langlois and F. Nativel",
title = "When automatic linear correction of rounding errors is
exact",
journal = j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
volume = "328",
number = "??",
pages = "543--548",
year = "1999",
CODEN = "CASMEI",
ISSN = "0249-6291",
bibdate = "Thu May 27 07:37:54 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See erratum, p. 829, in same volume.",
acknowledgement = ack-nhfb,
fjournal = "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des
Sciences. S{\'e}rie I. Math{\'e}matique",
journal-URL = "http://www.sciencedirect.com/science/journal/1631073X",
}
@Article{Lee:1999:EFS,
author = "Sung-Woo Lee and Hyun-Sung Kim and Jung-Joon Kim and
Tae-Geun Kim and Kee-Young Yoo",
title = "Efficient Fixed-Size Systolic Arrays for the Modular
Multiplication",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1627",
pages = "442--??",
year = "1999",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:54:14 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1627.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1627/16270442.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1627/16270442.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Lee:1999:NAD,
author = "Chang-Hyi Lee and Jong-In Lim",
title = "A New Aspect of Dual Basis for Efficient Field
Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1560",
pages = "12--28",
year = "1999",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:53:42 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1560.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1560/15600012.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1560/15600012.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "PKC; public key cryptography",
}
@InProceedings{Lee:1999:STS,
author = "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and
Seung-Ho Hwang",
booktitle = "6th International Conference on {VLSI} and {CAD}:
{ICVC '99}",
title = "Self-timed shared division and square-root
implementation using full redundant signed digit
numbers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "541--544",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A radix-$2$ square root implementation for self-timed
dividers using redundant signed-digit (RSD) adders is
presented. In this method, two self-timed RSD adder
stages are used for each result bit selection. A very
efficient and simple result bit \ldots{}",
}
@InCollection{Lefevre:1999:ACL,
author = "V. Lef{\`e}vre",
title = "An Algorithm That Computes a Lower Bound on the
Distance Between a Segment and {$ \mathbb {Z}^2 $}",
crossref = "Csendes:1999:DRC",
pages = "203--212",
year = "1999",
bibdate = "Fri Jun 24 12:41:23 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lewis:1999:CLN,
author = "David Lewis",
title = "Complex Logarithmic Number System Arithmetic Using
High-Radix Redundant {CORDIC} Algorithms",
crossref = "Koren:1999:ISC",
pages = "194--203",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-135.pdf;
http://euler.ecs.umass.edu/paper/final/paper-135.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Lewis.pdf",
abstract = "This paper describes the application of high radix
redundant CORDIC algorithms to complex logarithmic
number system arithmetic. It shows that a CLNS addition
can be performed with approximately the same hardware
as a high-radix CORDIC operation. A design example
comparable to single precision floating point has been
designed and simulated.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Misc{Liao:1999:SDR,
author = "Yuyun Liao and Tom M. Hameenanttila and David B.
Roberts",
howpublished = "US Patent 6,611,856B1",
day = "23",
month = dec,
year = "1999",
bibdate = "Thu Oct 17 12:11:10 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US6611856B1",
abstract = "A multiply-accumulate unit, or MAC, may achieve high
throughput. The MAC need not use redundant hardware,
such as multiple Wallace trees, or pipelining logic,
yet may perform Wallace tree and carry look-ahead adder
functions simultaneously for different operations.",
acknowledgement = ack-nhfb,
remark = "Patent filed 23 December 1999, priority claimed from
British patent GB0407413A of 4 December 2000, granted
26 August 2003 to Intel Corporation, expected
expiration 23 December 2019.",
}
@InProceedings{Liew:1999:SDR,
author = "T. H. Liew and L.-L. Yang and L. Hanzo",
booktitle = "{VTC 1999} --- Fall. {IEEE} {VTS 50th} Vehicular
Technology Conference",
title = "Soft-decision redundant residue number system based
error correction coding",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2546--2550",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/VETECF.1999.800245",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Soft-decision-based redundant residue number system
(RRNS)-assisted error control coding is proposed and
its performance is evaluated. An RRNS(n,k) code is a
maximum-minimum distance block code, exhibiting
identical distance properties to Reed- \ldots{}",
}
@InProceedings{Lopez:1999:IPF,
author = "D. Lopez and J. Llosa and E. Ayguade and M. Valero",
title = "Impact on performance of fused multiply-add units in
aggressive {VLIW} architectures",
crossref = "Shiratori:1999:PIC",
pages = "22--29",
year = "1999",
DOI = "https://doi.org/10.1109/ICPP.1999.797384",
bibdate = "Sun Feb 20 09:51:00 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Loops are the main time consuming part of programs
based on floating point computations. The performance
of the loops is limited either by recurrences in the
computation or by the resources offered by the
architecture. Several general-purpose superscalar
microprocessors have been implemented with multiply-add
fused floating-point units, that reduces the latency of
the combined operation and the number of resources
used. This paper analyses the influence of these two
factors in the instruction-level parallelism
exploitable from loops executed on a broad set of
future aggressive processor configurations. The
estimation of implementation costs (area and cycle
time) enables a fair comparison of these configurations
in terms of final performance and implementation
feasibility. The paper performs technological
projection for the next years in order to foresee the
possible implementable alternatives. From this study we
conclude that multiply-add fused units may have a deep
impact in raising the performance of future processor
architectures with a reasonable increase in cost.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lue:1999:ADE,
author = "Jeng-Jong J. Lue and Dhananjay S. Phatak",
title = "Area $ \times $ Delay ({$ A \cdot T $}) Efficient
Multipliers Based on an Intermediate Hybrid
Signed-Digit ({HSD-1}) Representation",
crossref = "Koren:1999:ISC",
pages = "216--224",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-159.pdf;
http://euler.ecs.umass.edu/paper/final/paper-159.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Lue.pdf",
abstract = "Intermediate Signed Digit (SD) representation can
facilitate fast and compact VLSI implementations of
partial product accumulation trees. It achieves a
reduction ratio of 2:1 at every level and also leads to
more regular layouts. Its disadvantage is that the
number of bit lines that need to routed can be high.
This can lead to a significant area overhead especially
at smaller feature sizes where the wire/interconnect
area and delay can be dominant.\par
A Hybrid Signed Digit (HSD) representation lets some of
the digits be unsigned bits, thereby reducing the
number of bit lines. By arbitrarily varying the
positions of and distances between consecutive signed
digits, this representation can trade off latency for
area and offers a continuum of choices between the
two's complement representation on the one hand and
fully Signed Digit (FSD or simply SD) representation on
the other.\par
In this paper, we illustrate an $ A \cdot T $ (area $
\times $ delay) efficient multiplier based on the HSD?1
representation which is one of the many possible HSD
formats, wherein every alternate digit is signed and
the rest are unsigned (ordinary) bits. It is seen that
multipliers based on HSD?1 format require more
transistors than those based on FSD format. However,
they require fewer bit lines to be routed, which
substantially reduces the interconnect area; thereby
leading to a reduction in the total VLSI area and a
lower $ A \cdot T $ product. The design reaffirms that
the interconnect area can be significant especially at
small feature sizes.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{Mahesh:1999:IAE,
author = "M. N. Mahesh and S. Gupta and M. Mehendale",
booktitle = "Twelfth International Conference on {VLSI} Design,
1999. Proceedings",
title = "Improving area efficiency of residue number system
based implementation of {DSP} algorithms",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "340--345",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICVD.1999.745179",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue Number System based applications involve
modulo-arithmetic which is typically implemented using
look-up-tables (LUTs) for a small value of modulus. In
this paper we present a data coding technique to
minimize the area of these LUTs when \ldots{}",
}
@Article{McCullough:1999:ARS,
author = "B. D. McCullough",
title = "Assessing the Reliability of Statistical Software:
{Part II}",
journal = j-AMER-STAT,
volume = "53",
number = "2",
pages = "149--159",
month = may,
year = "1999",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jan 27 14:51:25 MST 2012",
bibsource = "http://www.amstat.org/publications/tas/toc_99.html;
http://www.jstor.org/journals/00031305.html;
http://www.jstor.org/stable/i326504;
https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.amstat.org/publications/tas/mccull.pdf;
http://www.jstor.org/stable/2685736",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{McCullough:1999:NRE,
author = "B. D. McCullough and H. D. Vinod",
title = "The Numerical Reliability of Econometric Software",
journal = j-J-ECON-LIT,
volume = "37",
number = "2",
pages = "633--665",
month = jun,
year = "1999",
CODEN = "JECLB3",
DOI = "https://doi.org/10.1257/jel.37.2.633",
ISSN = "0022-0515 (print), 1547-1101 (electronic)",
ISSN-L = "0022-0515",
bibdate = "Thu Oct 17 05:56:48 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.jstor.org/stable/2565215;
https://www.aeaweb.org/articles?id=10.1257/jel.37.2.633",
abstract = "Numerous examples show that some econometric software
packages contain serious flaws, and that users cannot
safely assume that their software is accurate. A brief
survey of the fundamentals of computer arithmetic
discusses the sources of numerical error and emphasizes
that computer arithmetic is not at all like
pencil-and-paper arithmetic. Both users and developers
of econometrics software should first pay attention to
accuracy, and only later consider user-friendliness.
Details are provided for assessing the accuracy of
basic estimation routines, statistical distributions,
and random number generators. More accuracy benchmarks
are needed, especially for specialized econometric
procedures.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Economic Literature",
journal-URL = "https://www.aeaweb.org/journals/jel/issues",
remark = "This paper discusses the effect of both floating-point
arithmetic and random-number generators on econometric
computations.",
}
@InProceedings{Montuschi:1999:BVH,
author = "Paolo Montuschi and Tom{\'a}s Lang",
title = "Boosting Very High Radix Division with Prescaling and
Selection by Rounding",
crossref = "Koren:1999:ISC",
pages = "52--59",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-150.pdf;
http://euler.ecs.umass.edu/paper/final/paper-150.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Montuschi.pdf",
abstract = "An extension of the very-high radix division with
prescaling and selection by rounding is presented. This
extension consists in increasing the effective radix of
the implementation by obtaining a few additional bits
of the quotient per iteration, without increasing the
complexity of the unit to obtain the prescaling factor
nor the delay of an iteration. As a consequence, for
some values of the effective radix, it permits an
implementation with a smaller area and the same
execution time than the original scheme. Estimations
are given for 54-bit and 114-bit quotients.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Muller:1999:FRT,
author = "Jean-Michel Muller",
title = "A Few Results on Table-Based Methods",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "279--288",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@Article{Muroi:1999:ESR,
author = "Kazuo Muroi",
title = "Extraction of square roots in {Babylonian}
mathematics",
journal = j-HIST-SCI-2,
volume = "9",
number = "2",
pages = "127--133",
month = nov,
year = "1999",
CODEN = "HISCDU",
ISSN = "0285-4821",
ISSN-L = "0285-4821",
MRclass = "01A17",
MRnumber = "1762167",
MRreviewer = "Bruno Poizat",
bibdate = "Sat Oct 6 17:22:25 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/histscijpn.bib",
acknowledgement = ack-nhfb,
fjournal = "Historia Scientiarum. Second Series. International
Journal of the History of Science Society of Japan",
journal-URL = "http://hssj.info/",
}
@InProceedings{Nannarelli:1999:LPDa,
author = "Alberto Nannarelli and Tomas Lang",
title = "Low-Power Division: Comparison among Implementations
of Radix $4$, $8$ and $ 16 $",
crossref = "Koren:1999:ISC",
pages = "60--69",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-158.pdf;
http://euler.ecs.umass.edu/paper/final/paper-158.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Nannarelli.pdf",
abstract = "Although division is less frequent than addition and
multiplication, because of its longer latency it
dissipates a substantial part of the energy in
floating-point units. In this paper we explore the
relation between the radix and the energy dissipated.
Previous work has been done on radix-4 and radix-8
division. Here we extend this study to a radix-16
scheme with two overlapped radix-4 stages and compare
the latency, area, and energy of the three
implementations.\par
Results show that by applying the low-power techniques
the energy dissipation is reduced from 30\% to 40\%,
with respect to the standard implementation. An
additional 20\% reduction can be obtained using a dual
voltage. Moreover, the energy dissipated to complete
the division is roughly the same for the three radices.
However, the power dissipation, proportional to the
average current, increases with the radix. If reducing
the energy is the priority, for the same latency
radix-16 with dual voltage produces the smallest energy
dissipation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Nannarelli:1999:LPDb,
author = "A. Nannarelli and T. Lang",
title = "Low-Power Divider",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "1",
pages = "2--14",
month = jan,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.743407",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:46:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=743407",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Nannarelli:1999:LPR,
author = "Alberto Nannarelli and Tomas Lang",
booktitle = "{(ICCD '99)} International Conference on Computer
Design",
title = "Low-power radix-$4$ combined division and square
root",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "236--242",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Because of the similarities in the algorithm it is
quite common to implement division and square root in
the same unit. The purpose of this work is to implement
a low-power combined radix-$4$ division and square root
floating-point double precision \ldots{}",
}
@Article{Nedialkov:1999:IHO,
author = "N. S. Nedialkov and K. R. Jackson",
title = "An Interval Hermite-Obreschkoff Method for Computing
Rigorous Bounds on the Solution of an Initial Value
Problem for an Ordinary Differential Equation",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "289--310",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@InProceedings{Northrop:1999:GM,
author = "G. Northrop and R. Averill and K. Barkley and S. Carey
and Y. Chan and Y. H. Chan and M. Check and D. Hoffman
and W. Huott and B. Krumm and C. Krygowski and J.
Liptay and M. Mayo and T. McNamara and T. McPherson and
E. Schwarz and L. Sigal and T. Slegel and C. Webb and
D. Webber and P. Williams",
title = "{600MHz G5 S/390} Microprocessor",
crossref = "Wuorinen:1999:IIS",
pages = "??--??",
year = "1999",
bibdate = "Mon Jan 08 08:40:27 2001",
bibsource = "http://www.sscs.org/digests/1999/DATA/05_2.pdf;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
pagecount = "9",
}
@InProceedings{Oberman:1999:FPD,
author = "Stuart F. Oberman",
title = "Floating point division and square root algorithms and
implementation in the {AMD-K7{\TM}} microprocessor",
crossref = "Koren:1999:ISC",
pages = "106--115",
year = "1999",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-139.pdf;
http://euler.ecs.umass.edu/paper/final/paper-139.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Oberman.pdf",
abstract = "This paper presents the AMD-K7 IEEE 754 and x87
compliant floating point division and square root
algorithms and implementation. The AMD-K7 processor
employs an iterative implementation of a series
expansion to converge quadratically to the quotient and
square root. Highly accurate initial approximations and
a high performance shared floating point multiplier
assist in achieving low division and square root
latencies at high operating frequencies. A novel
time-sharing technique allows independent floating
point multiplication operations to proceed while
division or square root computation is in progress.
Exact IEEE 754 rounding for all rounding modes and
target precisions has been verified by conventional
directed and random testing procedures, along with the
formulation of a mechanically-checked formal proof
using the ACL2 theorem prover.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
summary = "This paper presents the AMD-K7 IEEE 754 and $\times$87
compliant floating point division and square root
algorithms and implementation. The AMD-K7 processor
employs an iterative implementation of a series
expansion to converge quadratically to the \ldots{}",
}
@Article{OLeary:1999:FVI,
author = "John O'Leary and Xudong Zhao and Rob Gerth and
Carl-Johan H. Seger",
title = "Formally Verifying {IEEE} Compliance of Floating-Point
Hardware",
journal = j-INTEL-TECH-J,
volume = "Q1",
pages = "10",
day = "17",
month = feb,
year = "1999",
bibdate = "Fri Jun 01 06:02:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://developer.intel.com/technology/itj/q11999/articles/art_5.htm;
http://developer.intel.com/technology/itj/q11999/pdf/floating_point.pdf",
acknowledgement = ack-nhfb,
}
@Article{Paar:1999:FAP,
author = "C. Paar and P. Fleischmann and P. Soria-Rodriguez",
title = "Fast arithmetic for public-key algorithms in {Galois}
fields with composite exponents",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "10",
pages = "1025--1034",
month = oct,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.805153",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 08:46:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=805153",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Paliouras:1999:MAR,
author = "V. Paliouras and T. Stouraitis",
title = "Multifunction Architectures for {RNS} Processors",
journal = j-IEEE-TRANS-CIRCUITS-SYST,
volume = "46",
number = "8",
pages = "1041--1054",
month = aug,
year = "1999",
CODEN = "ICSYBT",
ISSN = "0098-4094 (print), 1558-1276 (electronic)",
ISSN-L = "0098-4094",
bibdate = "Fri Jun 24 18:26:56 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems",
keywords = "Residue Number System (RNS)",
}
@InProceedings{Paliouras:1999:NHR,
author = "V. Paliouras and T. Stouraitis",
booktitle = "{ISCAS '99}. Proceedings of the 1999 {IEEE}
International Symposium on Circuits and Systems, 2 June
1999",
title = "Novel high-radix residue number system multipliers and
adders",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "451--454",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1999.777911",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Radix-r modulo r n multipliers and adders are
introduced in this paper. The proposed architectures
are shown to require several times less area than
previously reported architectures, for particular
moduli of operation. The proposed \ldots{}",
}
@InProceedings{Parhami:1999:ALT,
author = "B. Parhami",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "Analysis of the lookup table size for square-rooting",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1327--1330",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Convergence methods are widely used for division,
reciprocation, and square-rooting. With such methods,
it is common to use an initial table lookup step for
obtaining an approximate result that leads to faster
convergence. In the case of division \ldots{}",
}
@Article{Park:1999:FPM,
author = "W.-C. Park and T.-D. Han and S.-D. Kim and S.-B.
Yang",
title = "A floating point multiplier performing {IEEE} rounding
and addition in parallel",
journal = j-J-SYST-ARCH,
volume = "45",
number = "14",
pages = "1195--1207",
month = jul,
year = "1999",
CODEN = "JSARFB",
ISSN = "1383-7621 (print), 1873-6165 (electronic)",
ISSN-L = "1383-7621",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Journal of Systems Architecture",
pagecount = "13",
}
@Misc{Parker:1999:SPA,
author = "D. Stott Parker",
title = "A semi-portable {ANSI} {C} implementation of {Monte
Carlo} floating-point arithmetic",
howpublished = "World-Wide Web document.",
year = "1999",
bibdate = "Mon Aug 25 15:08:02 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.ucla.edu/~stott/mca/MCAdemo.c",
acknowledgement = ack-nhfb,
}
@InProceedings{Parks:1999:NTT,
author = "Michael Parks",
title = "Number-Theoretic Test Generation for Directed
Rounding",
crossref = "Koren:1999:ISC",
pages = "241--249",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-131.pdf;
http://euler.ecs.umass.edu/paper/final/paper-131.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Parks.pdf",
abstract = "We present methods to generate systematically the
hardest test cases for multiplication, division, and
square root subject to directed rounding, essentially
extending previous work on number-theoretic
floating-point testing to rounding modes other than
to-nearest. The algorithms focus upon the rounding
boundaries of the modes truncate, to-minus-infinity,
and to-infinity, and programs based on them require
little beyond exact arithmetic in the working precision
to create billions of edge cases. We will show that the
amount of work required to calculate trial
multiplicands pays off in the form of free extra tests
due to an interconnection among the operations
considered herein. Although these tests do not replace
proofs of correctness, they can be used to gain a high
degree of confidence that the accuracy requirements as
mandated by IEEE Standard 754 have been satisfied.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic; correct rounding;
floating-point arithmetic; floating-point testing",
summary = "We present methods to generate systematically the
hardest test cases for multiplication, division, and
square root subject to directed rounding, essentially
extending previous work on number-theoretic floating
point testing to rounding modes other \ldots{}",
}
@InProceedings{Phatak:1999:IVE,
author = "Dhananjay S. Phatak and I. Koren",
title = "Intermediate Variable Encodings that Enable
Multiplexor-Based Implementations of Two Operand
Addition",
crossref = "Koren:1999:ISC",
pages = "22--29",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-149.pdf;
http://euler.ecs.umass.edu/paper/final/paper-149.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Phatak.pdf",
abstract = "In two operand addition, bit-wise intermediate
variables such as the ``propagate'' and ``generate''
terms are defined \slash evaluated first. Basic carry
propagation recursion is then expressed in terms of
these variables and is ``unrolled'' to obtain a tree
structure for fast execution. In CMOS VLSI technology,
multiplexors are fast and efficient to implement.
Hence, we investigate in this paper all possible
two-bit encodings for the intermediate variables and
identify the ones that enable multiplexor-based
implementations. Some of these encodings enable further
simplification of the multiplexor-based realizations.
Our analysis also shows that adopting an intermediate
signed-digit representation simply amounts to selecting
one of the possible encodings. Thus, there is no
inherent advantage to the use of intermediate
signed-digit representations in a two operand addition.
Finally, we extend our analysis to the generalized
look-ahead-recursions proposed by Doran.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Ralev:1999:RBF,
author = "K. R. Ralev and P. H. Bauer",
title = "Realization of block floating-point digital filters
and application to block implementations",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "47",
number = "4",
pages = "1076--1086",
month = apr,
year = "1999",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "Realization issues of block floating-point (BFP)
filters such as complexity, roundoff noise, and absence
of limit cycles are analyzed. Several new results are
established. Under certain conditions, BFP filters
perform better than fixed-point filters \ldots{}",
}
@Article{Ruess:1999:MVS,
author = "Harald Ruess and Natarajan Shankar and Mandayam K.
Srivas",
title = "Modular Verification of {SRT} Division",
journal = j-FORM-METHODS-SYST-DES,
volume = "14",
number = "1",
pages = "45--73",
month = jan,
year = "1999",
CODEN = "FMSDE6",
ISSN = "0925-9856 (print), 1572-8102 (electronic)",
ISSN-L = "0925-9856",
bibdate = "Sat Jun 02 09:22:39 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Special issue on arithmetic circuits.",
URL = "http://www.wkap.nl/jrnltoc.htm/0925-9856;
http://www.wkap.nl/oasis.htm/194807",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
journal-URL = "https://dl.acm.org/loi/fmsd",
}
@Article{Rugina:1999:APD,
author = "Radu Rugina and Martin Rinard",
title = "Automatic parallelization of divide and conquer
algorithms",
journal = j-SIGPLAN,
volume = "34",
number = "8",
pages = "72--83",
month = aug,
year = "1999",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:18:06 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/ppopp/301104/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/proceedings/ppopp/301104/p72-rugina/",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@InProceedings{Rump:1999:IIL,
author = "Siegfried M. Rump",
title = "{INTLAB--INTerval LABoratory}",
crossref = "Csendes:1999:DRC",
pages = "77--104",
year = "1999",
bibdate = "Tue Nov 22 06:39:33 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; interval
arithmetic",
}
@Article{Russinoff:1999:MCP,
author = "David M. Russinoff",
title = "A mechanically checked proof of correctness of the
{AMD K5} floating point square root microcode",
journal = j-FORM-METHODS-SYST-DES,
volume = "14",
number = "1",
pages = "75--125",
month = jan,
year = "1999",
CODEN = "FMSDE6",
DOI = "https://doi.org/10.1023/A:1008669628911",
ISSN = "0925-9856 (print), 1572-8102 (electronic)",
ISSN-L = "0925-9856",
bibdate = "Sat Jun 02 07:51:51 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Special issue on arithmetic circuits.",
URL = "http://www.wkap.nl/jrnltoc.htm/0925-9856;
http://www.wkap.nl/oasis.htm/194808;
https://dl.acm.org/doi/abs/10.1023/A:1008669628911",
abstract = "We present a rigorous mathematical proof of the
correctness of the floating point square root
instruction of the AMD K5 microprocessor. The
instruction is represented as a program in a formal
language that was designed for this purpose, based on
the K5 microcode and the architecture of its FPU. We
prove a statement of its correctness that corresponds
directly with the IEEE Standard. We also derive an
equivalent formulation, expressed in terms of rational
arithmetic, which has been encoded as a formula in the
ACL2 logic and mechanically verified with the ACL2
prover. Finally, we describe a microcode modification
that was implemented as a result of this analysis in
order to ensure the correctness of the instruction.",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
journal-URL = "https://dl.acm.org/loi/fmsd",
}
@InProceedings{Saed:1999:ASA,
author = "Aryan Saed and Majid Ahmadi and Graham A. Jullien",
title = "Arithmetic with Signed Analog Digits",
crossref = "Koren:1999:ISC",
pages = "134--141",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-140.pdf;
http://euler.ecs.umass.edu/paper/final/paper-140.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Saed.pdf",
abstract = "This paper presents mathematical foundations of the
Overlap Resolution Number System (ORNS) which is based
on signed Continuous Valued Digits (CVD's). ORNS is a
redundant Number System employing residue arithmetic.
In contrast to the implementation of arithmetic by
binary or multiple-valued logic circuits, arithmetic
operations in this novel number system are performed by
analog digit manipulation circuitry. The redundancy in
an ensemble of Continuous Valued Digits that comprises
a number provides tolerance to implementation
imprecisions. Processing with these analog digits is
performed by carry-free arithmetic structures with
systematic circuit level redundancy.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{SanGregory:1999:FLP,
author = "Samuel L. SanGregory and Charles Brothers and David
Gallagher and Raymond Siferd",
editor = "{IEEE}",
booktitle = "{Proceedings of 1999 Midwest Symposium on Circuits and
Systems: August 8--12, 1999, Corbett Center, New Mexico
State University, Las Cruces, New Mexico}",
title = "A Fast, Low-Power Logarithm Approximation with {CMOS
VLSI} Implementation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xl + 1150 (two volumes)",
pages = "388--391",
year = "1999",
DOI = "https://doi.org/10.1109/MWSCAS.1999.867287",
ISBN = "0-7803-5491-5 (softbound), 0-7803-5492-3 (casebound),
0-7803-5493-1 (microfiche)",
ISBN-13 = "978-0-7803-5491-3 (softbound), 978-0-7803-5492-0
(casebound), 978-0-7803-5493-7 (microfiche)",
LCCN = "TK3226 .M531 42nd 1999",
bibdate = "Wed Dec 20 07:16:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://digitalcommons.cedarville.edu/engineering_and_computer_science_presentations/13",
abstract = "A new technique and CMOS VLSI implementation for
computing approximate logarithms (base 2 and 10) for
binary integers is presented. The approximation is
performed using only combinational logic and requires
no multiplications. Additionally, as implemented, a ROM
of only $ N \times \log_2 (N) $ bits is used to convert
$N$ bit integers. The maximum error of the
approximation is 1.5\% when the input value is 3, and
decays exponentially to less than 0.5\% for input
values greater than 25.",
acknowledgement = ack-nhfb,
}
@InProceedings{Scherer:1999:OTW,
author = "Alisa Scherer and Michael Golden and Norbert Juffa and
Stephan Meier and Stuart Oberman and Hamid Partovi and
Fred Weber",
title = "An Out-of-Order Three-Way Superscalar Multimedia
Floating-Point Unit",
crossref = "Wuorinen:1999:IIS",
pages = "??--??",
year = "1999",
bibdate = "Mon Jan 08 08:35:15 2001",
bibsource = "http://www.sscs.org/digests/1999/DATA/05_5.pdf;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "AMD-K7 floating-point unit",
pagecount = "10",
remark = "The AMD-K7 floating-point unit is implemented as an
out-of-order coprocessor responsible for executing all
x86 FPU, MMX, and AMD 3DNow! instructions.",
}
@InProceedings{Schmookler:1999:LPH,
author = "Martin S. Schmookler and Michael Putrino and Charles
Roth and Mukesh Sharma and Anh Mather and Jon Tyler and
Huy Van Nguyen and Mydung N. Pham and Jeff Lent",
title = "A Low-Power, High-Speed Implementation of a
{PowerPC[TM]} Microprocessor Vector Extension",
crossref = "Koren:1999:ISC",
pages = "12--21",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-145.pdf;
http://euler.ecs.umass.edu/paper/final/paper-145.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Schmookler.pdf",
abstract = "The AltiVec{\TM} technology is an extension to the
PowerPC architecture{\TM} which provides new
computational and storage operations for handling
vectors of various data lengths and data types. The
first implementation using this technology is a low
cost, low power processor based on the acclaimed
PowerPC 750{\TM} microprocessor. This paper describes
the microarchitecture and design of the vector
arithmetic unit of this implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Schulte:1999:AEF,
author = "M. Schulte and J. Stine",
title = "Approximating Elementary Functions with Symmetric
Bipartite Tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "8",
pages = "842--847",
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.795125",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 20:20:58 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Schulte:1999:CSI,
author = "M. J. Schulte and A. Akkas and V. Zelov and J. C.
Burley",
booktitle = "Proceedings of {16th IEEE Instrumentation and
Measurement Technology Conference, Venice, Italy, May,
1999}",
title = "Compiler Support for Interval Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1189--1193",
year = "1999",
bibdate = "Fri Jun 11 05:44:37 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://home.ku.edu.tr/~ahakkas/publications/comp-supp.pdf;
http://mesa.ece.wisc.edu/publications/cp_1999-04.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1999:ESO,
author = "M. J. Schulte and K. E. Wires",
title = "Efficient Second Order Approximations for Reciprocals
and Square Roots",
crossref = "Luk:1999:PSA",
volume = "3807",
pages = "10--18",
year = "1999",
bibdate = "Sun Mar 04 11:10:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schulte:1999:HSI,
author = "Michael J. Schulte and Kent E. Wires",
title = "High-Speed Inverse Square Roots",
crossref = "Koren:1999:ISC",
pages = "124--131",
year = "1999",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-109.pdf;
http://euler.ecs.umass.edu/paper/final/paper-109.ps;
http://mesa.ece.wisc.edu/publications/cp_1999-03.pdf;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Schulte.pdf",
abstract = "Inverse square roots are used in several digital
signal processing, multimedia, and scientific computing
applications. This paper presents a high-speed method
for computing inverse square roots. This method uses a
table lookup, operand modification, and multiplication
to obtain an initial approximation to the inverse
square root. This is followed by a modified
Newton--Raphson iteration, consisting of one square,
one multiply-complement, and one multiply-add
operation. The initial approximation and
Newton--Raphson iteration employ specialized hardware
to reduce the delay, area, and power dissipation.
Application of this method is illustrated through the
design of an inverse square root unit for operands in
the IEEE single precision format. An implementation of
this unit with a 4-layer metal, 2.5 Volt, 0.25 micron
CMOS standard cell library has a cycle time of 6.7 ns,
an area of 0.41 mm$^2$, a latency of five cycles, and a
throughput of one result per cycle.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
summary = "Inverse square roots are used in several digital
signal processing, multimedia, and scientific computing
applications. This paper presents a high-speed method
for computing inverse square roots. This method uses a
table lookup, operand modification, \ldots{}",
}
@InProceedings{Schulte:1999:IEG,
author = "M. J. Schulte and V. A. Zelov and A. Akkas and J. C.
Burley",
title = "The interval-enhanced {GNU Fortran} compiler",
crossref = "Csendes:1999:DRC",
pages = "311--322",
year = "1999",
bibdate = "Wed Jan 29 16:56:25 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-12.pdf",
acknowledgement = ack-nhfb,
remark = "From \cite{Steele:2004:RHP}: ``A recent extension of
the GNU Fortran compiler makes use of accurate
conversion techniques.''",
}
@InProceedings{Schulte:1999:RPD,
author = "M. J. Schulte and J. G. Jansen and J. E. Stine",
title = "Reduced Power Dissipation Through Truncated
Multiplication",
crossref = "Piuri:1999:IAV",
pages = "61--69",
year = "1999",
bibdate = "Sun Mar 04 11:16:43 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-01.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Schwarz:1999:GFPa,
author = "Eric M. Schwarz and Ronald M. Smith and Christopher A.
Krygowski",
title = "The {S/390 G5} Floating Point Unit Supporting Hex and
Binary Architectures",
crossref = "Koren:1999:ISC",
pages = "258--265",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://computer.org/proceedings/arith/0116/0116toc.htm;
http://euler.ecs.umass.edu/paper/final/paper-112.pdf;
http://euler.ecs.umass.edu/paper/final/paper-112.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Schwarz.pdf",
abstract = "The first high performance floating point unit to
support both IBM 360 hexadecimal based floating point
architecture and the IEEE 754 Standard binary floating
point architecture is described. The S/390 G5 floating
point unit supports the new S/390 architecture which
includes hexadecimal based short, long, and extended
precision formats and IEEE 754 standard single, double,
and quad formats. This floating point unit is part of
the microprocessor chip on the S/390 G5 mainframe
computer introduced in 1998 and generally available at
500 MHz speeds. The S/390 G5 represents the current
state of the art in CISC processor design. This paper
describes the S/390 architecture enhancements, the
internal format of the FPU, and the modifications to
the FPU dataflow.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Schwarz:1999:GFPb,
author = "E. M. Schwarz and C. A. Krygowski",
title = "The {S/390 G5} floating-point unit",
journal = j-IBM-JRD,
volume = "43",
number = "5/6",
pages = "707--721",
month = sep # "\slash " # nov,
year = "1999",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.435.0707",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Wed Apr 19 18:58:23 MDT 2000",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
URL = "http://www.research.ibm.com/journal/rd/435/schwarz.html",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}
@Misc{Schwarz:1999:MSE,
author = "E. M. Schwarz and B. Giamei and C. Krygowski and M.
Check and J. Liptay",
title = "Method and system for executing denormalized numbers",
day = "11",
month = may,
year = "1999",
bibdate = "Fri Nov 28 15:29:52 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent No. 5,903,479.",
acknowledgement = ack-nhfb,
}
@Article{Seidel:1999:HSR,
author = "Peter-Michael Seidel",
title = "High-Speed Redundant Reciprocal Approximation",
journal = j-INTEGRATION-VLSI-J,
volume = "28",
number = "1",
pages = "1--12",
month = sep,
year = "1999",
CODEN = "IVJODL",
DOI = "https://doi.org/10.1016/S0167-9260(99)00008-5",
ISSN = "0167-9260 (print), 1872-7522 (electronic)",
ISSN-L = "0167-9260",
bibdate = "Fri Jun 24 20:25:43 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a fast implementation for
reciprocal approximation, that can compute a redundant
reciprocal of a normalized number with a precision of $
2^-28 $ in roughly 16--17 logic levels. Moreover, a
less accurate, but much cheaper implementation is
proposed. The redundant representation of the
reciprocal can directly be fed into a common Booth
multiplier. This allows to implement IEEE
floating-point division with correct rounding in all
rounding modes with a latency of 7 clock cycles in
double precision and 4 clock cycles in single
precision. We also consider fast redundant compressions
from carry-save representations to redundant
Booth-digit representations.",
acknowledgement = ack-nhfb,
fjournal = "Integration, the VLSI journal",
keywords = "Booth recoding; correct rounding; floating-point
arithmetic; Multiplicative division; Reciprocal
approximation; Redundant compression",
}
@Article{Shary:1999:OEG,
author = "S. P. Shary",
title = "Outer Estimation of Generalized Solution Sets to
Interval Linear Systems",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "323--335",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@InProceedings{Skavantzos:1999:GMR,
author = "A. Skavantzos and T. Stouraitis",
booktitle = "{ISCAS '99}. Proceedings of the 1999 {IEEE}
International Symposium on Circuits and Systems, 2 June
1999",
title = "Grouped-moduli residue number systems for fast signal
processing",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "478--483",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.1999.778887",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper a new class of multi-moduli residue
number systems (RNS) and their efficient
RNS-to-weighted converters are presented. The new RNS
systems are based on sets consisting of two groups of
moduli with the moduli-product within one group
\ldots{}",
}
@Article{Skavantzos:1999:IIT,
author = "A. Skavantzos and M. Abdallah",
title = "Implementation issues of the two-level residue number
system with pairs of conjugate moduli",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "47",
number = "3",
pages = "826--838",
month = mar,
year = "1999",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/78.747787",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=16138",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
keywords = "residue arithmetic; residue number system",
summary = "One of the most important considerations when
designing residue number systems (RNSs) is the choice
of the moduli set; this is due to the fact that the
dynamic range of the system, its speed, as well as its
hardware complexity, depend on both the \ldots{}",
}
@InProceedings{Skavantzos:1999:NER,
author = "A. Skavantzos and Y. Wang",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "New efficient {RNS}-to-weighted decoders for
conjugate-pair-moduli residue number systems",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1345--1350",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.1999.831926",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "New efficient residue-to-weighted converters for
multi-moduli residue number systems (RNS) based on sets
{2 n1 -1, 2 n1 +1, 2 n2 -1, 2 n2 +1, {\ldots}, 2 nL -1,
2 nL +1} are presented. The \ldots{}",
}
@Article{Skeel:1999:SIF,
author = "R. D. Skeel",
title = "Symplectic integration with floating-point arithmetic
and other approximations",
journal = j-APPL-NUM-MATH,
volume = "29",
number = "1",
publisher = "Elsevier Science",
pages = "3--18",
month = jan,
year = "1999",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
pagecount = "16",
}
@Article{Stine:1999:STA,
author = "J. E. Stine and M. J. Schulte",
title = "The Symmetric Table Addition Method for Accurate
Function Approximation",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "21",
number = "2",
pages = "167--177",
month = jun,
year = "1999",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1008004523235",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sun Mar 04 11:02:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf",
abstract = "This paper presents a high-speed method for computing
elementary functions using parallel table lookups and
multi-operand addition. Increasing the number of tables
and inputs to the multi-operand adder significantly
reduces the amount of memory required. Symmetry and
leading zeros in the table coefficients are used to
reduce the amount of memory even further. This method
has a closed-form solution for the table entries and
can be applied to any differentiable function. For
24-bit operands, it requires two to three orders of
magn",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Story:1999:NAI,
author = "Shane Story and Ping Tak Peter Tang",
title = "New Algorithms for Improved Transcendental Functions
on {IA-64}",
crossref = "Koren:1999:ISC",
pages = "4--11",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-118.pdf;
http://euler.ecs.umass.edu/paper/final/paper-118.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Story.pdf",
abstract = "The IA-64 architecture provides new opportunities and
challenges for implementing an improved set of
transcendental functions. Using several novel
polynomial-based table-driven techniques, we are able
to provide new algorithms for the transcendental
functions. Major improvements include an accuracy level
of about 0.6 ulps (units in the last place) and forward
trigonometric functions that have a period of $ 2 \pi
$. The accuracy enhancements are achieved at improved
speed, yet without an increase in the table size. In
this paper, we highlight the key IA-64 architectural
features that influenced our designs and explain the
main ideas used in our new algorithms.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@Article{Strzebonski:1999:RPD,
author = "A. Strzebonski",
title = "A Real Polynomial Decision Algorithm Using
Arbitrary-Precision Floating Point Arithmetic",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "337--346",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@Article{Sunar:1999:MMA,
author = "B. Sunar and {\c{C}}. K. Ko{\c{c}}",
title = "{Mastrovito} multiplier for all trinomials",
journal = j-IEEE-TRANS-COMPUT,
volume = "48",
number = "5",
pages = "522--527",
month = may,
year = "1999",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.769434",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 21:18:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Sutherland:1999:LEDk,
author = "Ivan Sutherland and Bob Sproull and David Harris",
title = "Logical Effort: Designing Fast {CMOS} Circuits",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xv + 239",
year = "1999",
ISBN = "1-55860-557-6",
ISBN-13 = "978-1-55860-557-2",
LCCN = "TK7871.99.M44 S88 1999",
bibdate = "Thu Sep 21 17:07:13 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "circuiti elettronici CMOS; circuiti integrati CMOS;
circuiti logici; CMOS (Circuit int{\'e}gr{\'e});
CMOS-Schaltung; Complementary; Conception et
construction; Delay faults (Semiconductors); Design and
construction; Dispositifs logiques; Logic design; Logic
devices; Logischer Entwurf; Metal oxide semiconductors,
Complementary; Metal oxide semiconductors; MOS
compl{\'e}mentaires; Pannes temporelles
(Semi-conducteurs); Progettazione Schaltungsentwurf;
Semiconductores; Structure logique; Transistores MOS
complementarios",
tableofcontents = "1. The Method of Logical Effort \\
2. Design Examples \\
3. Deriving the Method of Logical Effort \\
4. Calculating the Logical Effort of Gates \\
5. Calibrating the Model \\
6. Asymmetric Logic Gates \\
7. Unequal Rising and Falling Delays \\
8. Circuit Families \\
9. Forks of Amplifiers \\
10. Branches and Interconnect \\
11. Wide Structures \\
12. Conclusions \\
App. A. Cast of Characters \\
App. B. Reference Process Parameters \\
App. C. Solutions to Selected Exercises",
}
@Article{Suzuoki:1999:MBC,
author = "M. Suzuoki and K. Kutaragi and T. Hiroi and H. Magoshi
and S. Okamoto and M. Oka and A. Ohba and Y. Yamamoto
and M. Furuhashi and M. Tanaka and T. Yutaka and T.
Okada and M. Nagamatsu and Y. Urakawa and M. Funyu and
A. Kunimatsu and H. Goto and K. Hashimoto and N. Ide
and H. Murakami and Y. Ohtaguro and A. Aono",
title = "A microprocessor with a 128-bit {CPU}, ten
floating-point {MAC}'s, four floating-point dividers,
and an {MPEG-2} decoder",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "34",
number = "11",
pages = "1608--1618",
month = nov,
year = "1999",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A 250-MHz microprocessor intended for home computer
entertainment consists of a CPU core with 128-b
multimedia extensions, two single-instruction,
multiple-data (SIMD) very long instruction word (VLIW)
vector processors containing ten floating-point
\ldots{}",
}
@InProceedings{Swartzlander:1999:TMA,
author = "E. E. {Swartzlander, Jr.}",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "Truncated multiplication with approximate rounding",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1480--1483",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "In many signal processing applications it is desirable
to maintain constant word size through the basic
arithmetic operations of add, subtract, multiply and
divide. Of these operations, multiply is the biggest
concern as multiplying two n-bit data \ldots{}",
}
@InProceedings{Takagi:1999:DRA,
author = "Naofumi Takagi and Seiji Kuwahara",
title = "Digit-Recurrence Algorithm for Computing {Euclidean}
Norm of a {$3$-D} Vector",
crossref = "Koren:1999:ISC",
pages = "86--95",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-142.pdf;
http://euler.ecs.umass.edu/paper/final/paper-142.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Takagi.pdf",
abstract = "A digit-recurrence algorithm for computing the
Euclidean norm of a 3-dimensional vector is proposed.
Starting from the vector component with the highest
order of magnitude as the initial value of partial
result, correcting-digits produced by the recurrence
are added to it step by step. Partial products of the
squares of the other two components are added to the
residual, step by step. The addition\slash subtractions
in the recurrence are performed without carry\slash
borrow propagation by the use of a redundant
representation of the residual. An extension of the
on-the-fly conversion algorithm is used for updating
the partial result. Different specific versions of the
algorithm are possible, depending on the radix, the
redundancy factor of the correcting-digit set, the type
of representation of the residual, and the
correcting-digit selection function.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{Tanskanen:1999:REF,
author = "J. M. A. Tanskanen and V. S. Dimitrov",
booktitle = "Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999",
title = "Round-off error free fixed-point design of polynomial
{FIR} predictors",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1317--1321",
year = "1999",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We present a novel method for designing polynomial FIR
predictors for fixed-point environments. Our method
yields filters that perform exact prediction of
polynomial signals even with short coefficient word
lengths. Under ordinary coefficient \ldots{}",
}
@InProceedings{Tenca:1999:DHR,
author = "Alexandre F. Tenca and Milo{\v{s}} D. Ercegovac",
title = "On the Design of High-Radix On-Line Division for Long
Precision",
crossref = "Koren:1999:ISC",
pages = "44--51",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-143.pdf;
http://euler.ecs.umass.edu/paper/final/paper-143.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Tenca.pdf",
abstract = "We present a design of a high-radix on-line division
suitable for long precision computations. The proposed
scheme uses a quotient-digit selection function based
on the residual rounding and scaling of the operands.
The bounds on the number of cycles and the cycle time
for radix $ 2^k $ and $n$-bit precision are obtained in
terms of full-adder delays. The speedup with respect to
radix 2 is greater than 3.3 for $ k \geq 6 $ and $ n
\geq 64 $. The cost increases as a function of the
radix. For the case $ r = 64 $ and $ n = 64 $, the
increase in area with respect to $ r = 2 $ is about 6.6
times plus a $ 512 \times 10 $-bit table. The proposed
scheme has been designed and verified using VHDL and a
$ 1.2 \mu $ m CMOS standard gate technology from MOSIS
library.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@InProceedings{Thompson:1999:BPF,
author = "D. U. Thompson and B. A. Wooley",
title = "A 15-bit Pipelined Floating-Point {A/D} Converter",
crossref = "Hosticka:1999:EPE",
pages = "170--173",
year = "1999",
bibdate = "Sat Jun 02 08:23:03 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Tisseur:1999:NMF,
author = "F. Tisseur",
title = "{Newton}'s method in floating point arithmetic and
iterative refinement of generalized eigenvalue
problems",
type = "Numerical analysis report",
number = "346-XY/N-1",
institution = "Manchester Centre for Computational Mathematics",
address = "Manchester, UK",
month = aug,
year = "1999",
bibdate = "Thu May 09 08:58:00 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Tropp:1999:HAI,
author = "Henry S. Tropp",
title = "{Howard Aiken} interview: {February 26--27, 1973}",
journal = "Computer Oral History Collection, Smithsonian
Institution Press",
year = "1999",
bibdate = "Thu Aug 07 19:21:30 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Article No. 1.",
abstract = "Howard Hathaway Aiken was born in 1900. He earned an
undergraduate degree in electrical engineering from the
University of Wisconsin in 1923, a Masters in Physics
from Harvard in 1937, and his Ph.d in Physics from
Harvard in 1939. He was the designer and developer of
the first large-scale operating relay calculator in the
United States. Aiken begins with a discussion of
problems associated with mechanical computation while
writing his thesis. He comments on Leslie John Comrie
and his contributions to computational techniques and
discusses his proposal for the MARK I and IBM's
agreement and involvement in 1939, to build the
machine. Aiken comments on his choice to design MARK I
as an electronic device. He was motivated by money
because digital counters made with vacuum tubes would
have involved thousands of parts which would have been
expensive. Aiken comments on early discussions with IBM
about what kind of machine would eventually be built
and their funding of the machine. He recalls learning
that IBM could not divide and how he invented the
technique of dividing by computing by reciprocals in
response to this problem. Because of what Aiken
introduced, the divider became a standard technique in
IBM's technical machine design thereafter. The MARK I
machine never did any computations for IBM, but rather
split its computing time between a project for the Navy
and for Harvard. Ultimately, Aiken's MARK machines were
used by several other government agencies. He comments
on his tenure on the National Academy of Sciences
Commission and he discusses the other individuals on
the committee---John von Neumann, George Stibitz, and
John Curtiss---to name a few. Curtiss promoted the idea
of starting an association for people interested in
computing machines, which Aiken was opposed to. Curtiss
ultimately founded the Association for Computing
Machinery which Aiken never joined. The conferences
Aiken held at Harvard University beginning in 1946 were
solely his doing. He selected the participants and
topics to be discussed. These conferences/lectures
were, according to Aiken, essential to getting the
field of computing ahead at that time. He comments at
length on his work outside of the United States,
specifically in Europe, and the individuals with whom
he worked. Because of Aiken's work at Harvard with
MARK, he had a steady stream of foreign researchers who
came to work with his machine. He discusses at length
the chronology of his four large scale calculators:
MARK I, II, III and IV. MARK II was built for the Naval
Proving Ground at Dahlgren and implemented in 1950.
Aiken would then proceed to design MARK III almost at
the same time, 1948 to 1950, and later MARK IV from
1950 to 1952. There was an overlap in the construction
and conceptual periods for all the MARK machines. After
all of Aiken's MARK machines were built, he felt his
effort with computers was completed too and that
competing with the industry would not be wise.\par
The second portion of this interview was conducted on
February 27, 1973, and begins with a discussion of
Aiken's method of division using the Newton-Raffson
rule. Comments include subsequent machines, problems
and users, historical digressions, elaboration on
specific computing techniques, documentation regarding
miscellaneous people and events, and some biographical
background information. Those mentioned frequently
include: Leon Chaffee, Leslie John Comrie, Donald
Menzel, Ted Brown, Harlow Shapley, J.G. Phillips, E.B.
Huntington, Ted Kimball, George Stibitz, Dick Bloch,
Norbert Wiener, and Grace Murray Hopper.",
acknowledgement = ack-nhfb,
}
@Article{Tropp:1999:NRI,
author = "Henry S. Tropp and Jean Sammett",
title = "{Nat Rochester} interview: {July 24, 1973}",
journal = "Computer Oral History Collection, Smithsonian
Institution Press",
year = "1999",
bibdate = "Thu Aug 07 18:47:37 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Article No. 75.",
abstract = "Rochester studied electrical engineering at the
Massachusetts Institute of Technology (MIT) and was
working in acoustics at the outset of World War II.
During the war, he worked on radar at the MIT Radiation
Laboratory and at Sylvania, building equipment for the
Radiation Laboratory. After the war, he worked on the
arithmetic unit for Whirlwind and on cryptanalysis
equipment for the national Security Agency (NSA). In
1948, feeling that computers would be a ``major
thing,'' he went to IBM where he urged their
development. His work on a study of the significance of
magnetic tape lead to the IBM 700 series. He discusses
assembly programming, the switches from card to tape
and from decimal to binary systems, the seesawing of
the relative reliability of software and hardware, and
the advantages and disadvantages of system
compatibility. Special mention is made of: the 1946
summer school program at the University of
Pennsylvania; the 1947 Aberdeen meeting; and the
meeting called by Tom Watson, Jr., at which the
decision was made to go ahead with the 700 series, thus
making a commitment to computers. Jean Sammett sat in
on the interview. Among those often mentioned are John
von Neumann, Ralph Palmer, Werner Buchholz, Cuthbert
Hurd, and Steve Dunwell.",
acknowledgement = ack-nhfb,
}
@InProceedings{Tsuji:1999:REO,
author = "K. Tsuji",
title = "Round-off error of optimal control problems in
floating-point number systems",
crossref = "Begehr:1999:PSI",
pages = "929--944",
year = "1999",
bibdate = "Sat Jun 02 08:12:11 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Walter:1999:MTI,
author = "Colin D. Walter",
title = "Moduli for Testing Implementations of the {RSA}
Cryptosystem",
crossref = "Koren:1999:ISC",
pages = "78--85",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-130.pdf;
http://euler.ecs.umass.edu/paper/final/paper-130.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Walter.pdf",
abstract = "Comprehensive testing of any implementation of the RSA
cryptosystem requires the use of a number of moduli
with specific properties. It is shown how to generate a
sufficient variety of these to enable testing which
will justify high confidence in the correctness of both
the design and the operation of hardware
implementations. The tests avoid the necessity of
another implementation for comparison. Many of these
moduli are also suitable for testing software
implementations. Furthermore, the methods apply equally
well to other similar modular arithmetic based
cryptosystems which use exponentiation, such as
Diffie-Helman key exchange.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic; correctness;
cryptography; implementation validation benchmark.; RSA
modulus; testing; verification",
}
@Article{Watanabe:1999:NVM,
author = "Y. Watanabe and N. Yamamoto and M. T. Nakao",
title = "A Numerical Verification Method of Solutions for the
{Navier--Stokes} Equations",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "347--357",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Mon May 20 06:37:48 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@InProceedings{Wires:1999:CUT,
author = "K. E. Wires and M. J. Schulte and L. P. Marquette and
P. I. Balzola",
title = "Combined Unsigned and Two's Complement Squarers",
crossref = "Matthews:1999:CRT",
pages = "1215--1219",
year = "1999",
bibdate = "Sun Mar 04 11:08:58 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-06.pdf",
acknowledgement = ack-nhfb,
}
@Article{Wong:1999:OFP,
author = "W. F. Wong",
title = "Optimizing floating point operations in {Scheme}",
journal = j-COMP-LANGS,
volume = "25",
number = "2",
pages = "89--112",
month = jul,
year = "1999",
CODEN = "COLADA",
ISSN = "0096-0551 (print), 1873-6742 (electronic)",
ISSN-L = "0096-0551",
bibdate = "Thu Oct 12 10:20:10 MDT 2000",
bibsource = "http://www.elsevier.com/locate/complang;
https://www.math.utah.edu/pub/tex/bib/complngs.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.nl/gej-ng/10/15/18/28/27/26/abstract.html;
http://www.elsevier.nl/gej-ng/10/15/18/28/27/26/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computer Languages",
journal-URL = "http://www.sciencedirect.com/science/journal/00960551",
}
@InProceedings{Yadav:1999:PSF,
author = "N. Yadav and M. J. Schulte and J. Glossner",
title = "Parallel Saturating Fractional Arithmetic Units",
crossref = "Mazumder:1999:NGL",
pages = "214--217",
year = "1999",
bibdate = "Sun Mar 04 11:15:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_1999-02.pdf",
acknowledgement = ack-nhfb,
}
@Article{Yang:1999:CIS,
author = "D. X. D. Yang and A. E. Gamal and B. Fowler and H.
Tian",
title = "A 640$ \times $512 {CMOS} image sensor with ultrawide
dynamic range floating-point pixel-level {ADC}",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "34",
number = "12",
pages = "1821--1834",
month = dec,
year = "1999",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "Analysis results demonstrate that multiple sampling
can achieve consistently higher signal-to-noise ratio
at equal or higher dynamic range than using other image
sensor dynamic range enhancement schemes such as well
capacity adjusting. Implementing \ldots{}",
}
@Article{Yang:1999:RNSa,
author = "Lie-Liang Yang and L. Hanzo",
title = "Residue number system arithmetic assisted {$M$}-ary
modulation",
journal = j-IEEE-COMMUN-LET,
volume = "3",
number = "2",
pages = "28--30",
month = feb,
year = "1999",
CODEN = "ICLEF6",
DOI = "https://doi.org/10.1109/4234.749352",
ISSN = "????",
ISSN-L = "1089-7798",
bibdate = "Fri Nov 9 11:38:58 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=16186",
acknowledgement = ack-nhfb,
fjournal = "IEEE Communications Letters",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
keywords = "residue arithmetic; residue number system",
summary = "A residue number system based M-ary modem is proposed
and its performance is evaluated over Gaussian
channels. When one or two redundant moduli are
employed, a signal-to-noise ratio gain of 1.2-2 dB was
achieved for a 16-ary, 32-ary and 37-ary modem,
\ldots{}",
}
@InProceedings{Yang:1999:RNSb,
author = "Lie-Liang Yang and L. Hanzo",
booktitle = "{IEEE 49th} Vehicular Technology Conference, 16--20
May 1999",
title = "Residue number system based multiple code {DS-CDMA}
systems",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1450--1454",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/VETEC.1999.780587",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A novel multi-code direct-sequence code division
multiple-access (DS-CDMA) system based on the so-called
residue number system (RNS) or the redundant residue
number system (RRNS) is proposed. Concatenated codes
employing RNS product codes (RNS-PC) \ldots{}",
}
@InProceedings{Yang:1999:RST,
author = "Lie-Liang Yang and L. Hanzo",
booktitle = "{IEEE 49th} Vehicular Technology Conference. 16--20
May 1999",
title = "Ratio statistic test assisted residue number system
based parallel communication schemes",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "894--898",
year = "1999",
CODEN = "????",
DOI = "https://doi.org/10.1109/VETEC.1999.780477",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A residue number system (RNS) based parallel
communication system is proposed and its performance is
evaluated using non-coherent demodulation. Diversity
reception techniques with equal gain combining (EGC) or
selection combining (SC) are considered \ldots{}",
}
@Misc{Yap:1999:REI,
author = "C. Yap and K. Ouchi",
title = "{Real/Expr}: Implementation of Exact Computation",
howpublished = "Web site",
day = "22",
month = jan,
year = "1999",
bibdate = "Tue Oct 22 06:22:39 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://cs.nyu.edu/exact/realexpr/",
acknowledgement = ack-nhfb,
}
@InProceedings{Yuan:1999:FPA,
author = "J. Yuan and J. Piper",
title = "Floating-Point Analog-To-Digital Converter",
crossref = "IEEE:1999:IPI",
pages = "1385--1388",
year = "1999",
bibdate = "Sat Jun 02 08:19:08 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zimmermann:1999:EVI,
author = "Reto Zimmermann",
title = "Efficient {VLSI} Implementation of Modulo $ (2^n \pm
1) $ Addition and Multiplication",
crossref = "Koren:1999:ISC",
pages = "158--167",
year = "1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://euler.ecs.umass.edu/paper/final/paper-127.pdf;
http://euler.ecs.umass.edu/paper/final/paper-127.ps;
http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Zimmermann.pdf",
abstract = "New VLSI circuit architectures for addition and
multiplication modulo $ (2 n - 1) $ and $ (2 n + 1) $
are proposed that allow the implementation of highly
efficient combinational and pipelined circuits for
modular arithmetic. It is shown that the
parallel-prefix adder architecture is well suited to
realize fast end-around-carry adders used for modulo
addition. Existing modulo multiplier architectures are
improved for higher speed and regularity. These allow
the use of common multiplier speedup techniques like
Wallace tree addition and Booth recoding, resulting in
the fastest known modulo multipliers. Finally, a
high-performance modulo multiplier-adder for the IDEA
block cipher is presented. The resulting circuits are
compared qualitatively and quantitatively, i.e., in a
standard cell technology, with existing solutions and
ordinary integer adders and multipliers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-14; computer arithmetic",
}
@TechReport{Zimmermann:1999:KSR,
author = "Paul Zimmermann",
title = "{Karatsuba} Square Root",
type = "Research Report",
number = "3805",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "8",
year = "1999",
bibdate = "Sun Sep 10 08:56:48 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz;
http://www.inria.fr/rrrt/rr-3805.html",
abstract = "We exhibit an algorithm to compute the square-root
with remainder of a $n$-word number in $ 3 / 2 $ word
operations, where $ K(n) $ is the number of words
operations to multiply two $n$-word numbers using
Karatsuba's algorithm. If the remainder is not needed,
the cost can be reduced to $ K(n) $ on average. This
algorithm can be used for floating-point or polynomial
computations too; although not optimal asymptotically,
its simplicity gives a wide range of use, from about 50
to 1,000,000 digits, as shown by computer
experiments.",
acknowledgement = ack-nhfb,
}
@Article{Ziv:1999:SUR,
author = "Abraham Ziv",
title = "Sharp {ULP} rounding error bound for the hypotenuse
function",
journal = j-MATH-COMPUT,
volume = "68",
number = "227",
pages = "1143--1148",
month = jul,
year = "1999",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri Jul 16 10:39:05 MDT 1999",
bibsource = "http://www.ams.org/mcom/1999-68-227;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-01103-5&u=/mcom/1999-68-227/",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Periodical{FPS:19xx:R,
author = "{Floating Point Systems, Inc.Users Group Meeting}",
key = "FPS",
title = "Record",
publisher = "Floating Point Systems",
address = "Portland, OR, USA",
pages = "various",
year = "19xx",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
alttitle = "Record (Floating Point Systems, Inc. Users Group.
Meeting) ARRAY (Organization). Conference.
Proceedings",
keywords = "Array processors --- Congresses; Parallel processing
(Electronic computers) --- Congresses",
}
@Manual{Intel:19xx:IAP,
author = "{Intel}",
title = "{Intel 8231A} Arithmetic Processing Unit",
organization = "Intel Corp",
address = "San Jose, CA, USA",
year = "19xx",
bibdate = "Thu Oct 14 15:14:43 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From the datasheet (p. 3-5): ``The mantissa is
expressed as a 24-bit (fractional) value; the exponent
is expressed as a two's complement 7-bit value having
the range $ - 64 $ to $ + 63 $. The most significant
bit is the sign of the mantissa ($0$ = positive, $1$ =
negative), for a total of 32 bits. The binary point is
assumed to be [to] the left of the most significant
mantissa bit (bit 23). All floating-point data values
must be normalized. Bit 23 must be equal to 1, except
for the value zero, which is represented by all zeros.
The range of values that can be represented in this
format is $ \pm (2.7 \time 10^{-10} \ldots {} 9.2
\times 10^{18}) $ and zero.''",
URL = "http://www.datasheetarchive.com/pdf-datasheets/Datasheets-14/DSA-276911.html",
acknowledgement = ack-nhfb,
remark = "Undated processor datasheet.",
}
@Article{Anonymous:2000:BRCd,
author = "Anonymous",
title = "Book Review: {{\booktitle{Computer arithmetic:
Algorithms and hardware designs}}: By Behrooz Parhami.
Oxford University Press, New York. (2000). 490 pages.
\$85.00}",
journal = j-COMPUT-MATH-APPL,
volume = "39",
number = "3--4",
pages = "264--264",
month = feb,
year = "2000",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:06 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122100900518",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Anonymous:2000:BRCg,
author = "Anonymous",
title = "Book Review: {{\booktitle{Computer arithmetic:
Algorithms and hardware designs}}: By Behrooz Parhami.
Oxford University Press, New York. (2000). 490 pages.
\$85.00}",
journal = j-COMPUT-MATH-APPL,
volume = "39",
number = "7--8",
pages = "266--266",
month = apr,
year = "2000",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:08 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122100902955",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Antelo:2000:VHR,
author = "E. Antelo and T. Lang and J. D. Bruguera",
title = "Very-High Radix Circular {CORDIC}: Vectoring and
Unified Rotation\slash Vectoring",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "727--739",
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863043",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:47:55 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@Misc{Arnold:2000:EAS,
author = "D. Arnold",
title = "The Explosion of the {Ariane 5}. {Some} disasters
attributable to bad numerical computing",
howpublished = "Web site.",
day = "23",
month = aug,
year = "2000",
bibdate = "Mon Aug 26 11:10:55 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www-users.math.umn.edu/~arnold/disasters/ariane.html",
acknowledgement = ack-nhfb,
}
@PhdThesis{Baidas:2000:HLF,
author = "Zaher A. Baidas",
title = "High-level floating-point synthesis",
type = "Thesis ({Ph.D.})",
school = "University of Southampton, Department of Electronics
and Computer Science",
address = "Southampton, UK",
pages = "327",
year = "2000",
bibdate = "Thu May 09 08:47:14 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Batten:2000:NAD,
author = "D. Batten and S. Jinturkar and J. Glossner and M.
Schulte and P. D'arcy",
title = "A New Approach to {DSP} Intrinsic Functions",
crossref = "Sprague:2000:PAH",
pages = "2892--2901",
year = "2000",
bibdate = "Sun Mar 04 11:18:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf",
acknowledgement = ack-nhfb,
}
@Article{Becker:2000:JSE,
author = "Pete Becker",
title = "The Journeyman's Shop: Error in Floating-Point
Calculations",
journal = j-CCCUJ,
volume = "18",
number = "7",
pages = "73--??",
month = jul,
year = "2000",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Tue May 14 18:09:27 MDT 2002",
bibsource = "http://www.cuj.com/articles/2000/0007/0007toc.htm?topic=articles;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "And you thought error, accuracy, precision, and
significance were pretty synonymous.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@Article{Becker:2000:JSF,
author = "Pete Becker",
title = "The Journeyman's Shop: Floating-Point Basics",
journal = j-CCCUJ,
volume = "18",
number = "6",
pages = "??--??",
month = jun,
year = "2000",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Tue May 14 18:09:26 MDT 2002",
bibsource = "http://www.cuj.com/articles/2000/0006/0006toc.htm?topic=articles;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "You can't overcome a fear of floating-point arithmetic
--- or complacency about it --- until you understand
what's going on.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@Article{Becker:2000:JST,
author = "Pete Becker",
title = "The Journeyman's Shop: Trap Handlers, Sticky Bits, and
Floating-Point Comparisons",
journal = j-CCCUJ,
volume = "18",
number = "12",
pages = "54--??",
month = dec,
year = "2000",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Tue May 14 18:09:29 MDT 2002",
bibsource = "http://www.cuj.com/articles/2000/0012/0012toc.htm?topic=articles;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Pete wraps up his series on practical floating-point
math.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@Article{Becker:2000:JSWb,
author = "Pete Becker",
title = "The Journeyman's Shop: When Bad Things Happen to Good
Numbers",
journal = j-CCCUJ,
volume = "18",
number = "10",
pages = "54--??",
month = oct,
year = "2000",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Tue May 14 18:09:28 MDT 2002",
bibsource = "http://www.cuj.com/articles/2000/0010/0010toc.htm?topic=articles;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "It takes a lot of preparation to write really robust
floating-point code.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@Article{Bertossi:2000:RNS,
author = "A. A. Bertossi and A. Mei",
title = "A residue number system on reconfigurable mesh with
applications to prefix sums and approximate string
matching",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "11",
number = "11",
pages = "1186--1199",
month = nov,
year = "2000",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/71.888638",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=19224",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
keywords = "residue arithmetic; residue number system",
summary = "Several new number representations based on a residue
number system are presented which use the smallest
prime numbers as moduli and are suited for parallel
computations on a reconfigurable mesh architecture. The
bit model of linear reconfigurable \ldots{}",
}
@TechReport{Boldo:2000:QDP,
author = "Sylvie Boldo",
title = "Quad double precision specification and proofs about
the addition",
type = "Traineeship report -- {MIM2}",
institution = "University of California, Berkeley, and {\'E}cole
Normale Sup{\'e}rieure de Lyon",
address = "Berkeley, CA, USA and 69364 Lyon Cedex 07, France",
pages = "51",
month = jun # "\slash " # aug,
year = "2000",
bibdate = "Tue Nov 23 10:59:46 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Under the direction of Jonathan Shewchuk.",
URL = "http://perso.ens-lyon.fr/sylvie.boldo/doc/qd.ps",
acknowledgement = ack-nhfb,
}
@Article{Brooks:2000:VBC,
author = "David Brooks and Margaret Martonosi",
title = "Value-based clock gating and operation packing:
dynamic strategies for improving processor power and
performance",
journal = j-TOCS,
volume = "18",
number = "2",
pages = "89--126",
month = may,
year = "2000",
CODEN = "ACSYEC",
ISSN = "0734-2071 (print), 1557-7333 (electronic)",
ISSN-L = "0734-2071",
bibdate = "Tue Sep 26 07:54:31 MDT 2000",
bibsource = "http://www.acm.org/pubs/contents/journals/tocs/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/tocs/2000-18-2/p89-brooks/",
abstract = "The large address space needs of many current
applications have pushed processor designs toward
64-bit word widths. Although full 64-bit addresses and
operations are indeed sometimes needed, arithmetic
operations on much smaller quantities are still more
common. In fact, another instruction set trend has been
the introduction of instructions geared toward subword
operations on 16-bit quantities. For examples, most
major processors now include instruction set support
for multimedia operations allowing parallel execution
of several subword operations in the same ALU. This
article presents our observations demonstrating that
operations on ``narrow-width'' quantities are common
not only in multimedia codes, but also in more general
workloads. In fact, across the SPECint95 benchmarks,
over half the integer operation executions require 16
bits or less. Based on this data, we propose two
hardware mechanisms that dynamically recognize and
capitalize on these narrow-width operations. The first,
power-oriented optimization reduces processor power
consumption by using operand-value-based clock gating
to turn off portions of arithmetic units that will be
unused by narrow-width operations. This optimization
results in a 45\%--60\% reduction in the integer unit's
power consumption for the SPECint95 and MediaBench
benchmark suites. Applying this optimization to
SPECfp95 benchmarks results in slightly smaller power
reductions, but still seems warranted. These reductions
in integer unit power consumption equate to a 5\%--10\%
full-chip power savings. Our second,
performance-oriented optimization improves processor
performance by packing together narrow-width operations
so that they share a single arithmetic unit.
Conceptually similar to a dynamic form of MMX, this
optimization offers speedups of 4.3\%--6.2\% for
SPECint95 and 8.0\%--10.4\% for
MediaBench.\par
Overall, these optimizations highlight an increasing
opportunity for value-based optimizations to improve
both power and performance in current
microprocessors.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Computer Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J774",
subject = "Hardware --- Arithmetic and Logic Structures (B.2);
Computer Systems Organization --- Processor
Architectures --- Single Data Stream Architectures
(C.1.1): {\bf RISC/CISC, VLIW architectures}",
}
@InProceedings{Cardarilli:2000:RPD,
author = "G. C. Cardarilli and A. Nannarelli and M. Re",
booktitle = "Proceedings of the 43rd {IEEE} Midwest Symposium on
Circuits and Systems, 2000",
title = "Reducing power dissipation in {FIR} filters using the
residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "320--323",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.2000.951651",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The aim of this work is to reduce the power dissipated
in high order finite impulse response (FIR) filters,
while maintaining the delay unchanged. We compare in
terms of performance, area, and power dissipation the
implementation of a traditional \ldots{}",
}
@Article{Chen:2000:PCV,
author = "Chichyang Chen and Rui-Lin Chen and Chih-Huan Yang",
title = "Pipelined Computation of Very Large Word-Length {LNS}
Addition\slash Subtraction with Polynomial Hardware
Cost",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "716--726",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863041",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
summary = "A novel pipelined method is proposed to compute the
addition/subtraction in very large word-length
logarithmic number system (LNS) arithmetic.
Digit-parallel additive-normalization and digit on-line
multiplicative-normalization methods are adopted
\ldots{}",
}
@Article{Cheng:2000:STC,
author = "F.-C. Cheng and S. H. Unger and M. Theobald",
title = "Self-Timed Carry-Lookahead Adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "659--672",
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863035",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:47:55 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@TechReport{Cheng:2000:TID,
author = "Y.-T. Cheng",
title = "{TMS320C60000} integer division",
type = "Application Report",
number = "SPRA707",
institution = "Texas Instruments",
address = "Post Office box 655303, Dallas, TX 75265, USA",
month = oct,
year = "2000",
bibdate = "Fri Sep 22 16:24:20 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.ti.com/lit/an/spra707/spra707.pdf",
acknowledgement = ack-nhfb,
}
@Article{Cherri:2000:PCC,
author = "A. K. Cherri and M. S. Alam",
title = "Parallel computation of complex elementary functions
using quaternary signed-digit arithmetic",
journal = "Optics and Laser Technology",
volume = "32",
number = "6",
publisher = "Elsevier Science",
pages = "391--399",
year = "2000",
CODEN = "????",
ISSN = "0030-3992",
bibdate = "Sat Dec 7 09:21:28 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
pagecount = "9",
}
@InProceedings{Chu:2000:CPT,
author = "Wanming Chu and Yamin Li",
booktitle = "{ACAC 2000}: 5th Australasian Computer Architecture
Conference",
title = "Cost\slash performance tradeoff of $n$-select square
root implementations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "9--16",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Hardware square-root units require large numbers of
gates even for iterative implementations. In this paper
we present four low-cost high-performance
fully-pipelined n-select implementations (nS-Root)
based on a non-restoring-remainder square root
\ldots{}",
}
@Article{Coleman:2000:AEL,
author = "J. N. Coleman and E. I. Chester and C. I. Softley and
J. Kadlec",
title = "Arithmetic on the {European Logarithmic
Microprocessor}",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "702--715",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863040",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
OCLC Proceedings database",
note = "See corrections \cite{Coleman:2000:CAE}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863040",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@Article{Coleman:2000:CAE,
author = "J. N. Coleman and E. I. Chester and C. I. Softley and
J. Kadlec",
title = "Corrections to {``Arithmetic on the European
Logarithmic Microprocessor''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "10",
pages = "1152--1152",
month = oct,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2000.888057",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:26 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
note = "See \cite{Coleman:2000:AEL}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=888057",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Collins:2000:MFP,
author = "George E. Collins and Werner Krandick",
title = "Multiprecision floating point addition",
crossref = "Traverso:2000:IAU",
pages = "71--77",
year = "2000",
bibdate = "Tue Apr 17 09:15:54 MDT 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/issac/345542/p71-collins/p71-collins.pdf;
http://www.acm.org/pubs/citations/proceedings/issac/345542/p71-collins/",
acknowledgement = ack-nhfb,
keywords = "FSUM; interval arithmetic; LEDA; MPADD; MPFUN;
polynomial root finding",
}
@InProceedings{Constantinides:2000:MPR,
author = "G. A. Constantinides and P. Y. K. Cheung and W. Luk",
booktitle = "{IEEE} Symposium on Field-Programmable Custom
Computing Machines, 17--19 April 2000",
title = "Multiple precision for resource minimization",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "307--308",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Presents the Synoptix high-level synthesis and
precision optimization system for FPGAs. Given abstract
specifications in the form of infinite-precision signal
flow graphs and a set of error constraints, Synoptix
creates hardware descriptions of \ldots{}",
}
@InProceedings{Cornea:2000:IDR,
author = "M. Cornea and C. Iordache and J. Harrison and P.
Markstein",
editor = "????",
booktitle = "{Fourth conference on Real numbers and Computers,
Schlo{\ss} Dagstuhl, April 2000}",
title = "Integer divide and remainder operations in the {IA-64}
architecture",
publisher = "????",
address = "????",
pages = "??--??",
year = "2000",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Sep 22 16:50:51 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.imada.sdu.dk/kornerup/RNC4/papers/p17.ps",
acknowledgement = ack-nhfb,
remark = "I cannot yet find this online.",
}
@Article{Corsonello:2000:PCB,
author = "P. Corsonello and S. Perri and G. Cocorullo",
title = "Performance comparison between static and dynamic
{CMOS} logic implementations of a pipelined
square-rooting circuit",
journal = "Circuits, Devices and Systems, IEE Proceedings [see
also IEE Proceedings G- Circuits, Devices and
Systems]",
volume = "147",
number = "6",
pages = "347--355",
month = dec,
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Pipelined cellular array implementations of arithmetic
circuits are usually adopted to obtain high throughput
at reasonable cost. The circuit design style used to
implement the array greatly influences both performance
and cost. The designer has to \ldots{}",
}
@InProceedings{DAmora:2000:RPD,
author = "A. D'Amora and A. Nannarelli and M. Re and G. C.
Cardarilli",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "Reducing power dissipation in complex digital filters
by using the quadratic residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "879--883",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.2000.910639",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper compares in terms of performance, area and
power dissipation, a complex FIR filter realized in the
traditional two's complement system with a Quadratic
Residue Number System (QRNS) based one. The resulting
implementations, designed to \ldots{}",
}
@InProceedings{Daumas:2000:EIT,
author = "Marc Daumas and Claire Moreau-Finot",
editor = "????",
booktitle = "Real Numbers and Computers, Dagstuhl, Germany, 2000",
title = "Exponential: implementation trade-offs for hundred bit
precision",
publisher = "????",
address = "????",
pages = "61--74",
year = "2000",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Nov 24 12:44:20 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Delves:2000:MUI,
author = "L. M. Delves",
title = "Making Use of {IEEE} Arithmetic Facilities",
journal = j-FORTRAN-FORUM,
volume = "19",
number = "3",
pages = "9--12",
month = dec,
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1145/570899.570902",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Wed Jun 18 16:26:21 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "59",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@Article{Drmac:2000:AQS,
author = "Zlatko Drma{\v{c}} and Elizabeth R. Jessup",
title = "On accurate quotient singular value computation in
floating-point arithmetic",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "3",
pages = "853--873",
year = "2000",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (65G20)",
MRnumber = "MR1799528 (2001j:65062)",
MRreviewer = "Fabio Di Benedetto",
bibdate = "Thu Nov 8 19:32:13 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Ercegovac:2000:IGD,
author = "Milo{\v{s}} D. Ercegovac and Laurent Imbert and David
W. Matula and Jean-Michel Muller and Guoheng Wei",
title = "Improving {Goldschmidt} Division, Square Root, and
Square Root Reciprocal",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "759--763",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863046",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863046",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14; correct rounding; floating-point
arithmetic",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
remark-2 = "From the first column: ``These methods do not directly
produce the remainder and correct rounding (as required
by the IEEE-754 standard [8]) requires extra quotient
digits. According to [7], roughly twice as many digits
of intermediate result are needed as in the final
result unless the iterations are performed using a
fused multiply-accumulate operator [1].''",
summary = "The aim of this paper is to accelerate division,
square root, and square root reciprocal computations
when the Goldschmidt method is used on a pipelined
multiplier. This is done by replacing the last
iteration by the addition of a correcting term that can
be looked up during the early iterations. We describe
several variants of the Goldschmidt algorithm, assuming
4-cycle pipelined multiplier, and discuss obtained
number of cycles and error achieved. Extensions to
other than 4-cycle multipliers are given. If we call
$G_m$ the Goldschmidt algorithm with $m$ iterations,
our variants allow us to reach an accuracy that is
between that of $G_3$ and that of $G_4$, with a number
of cycles equal to that of $G_3$.",
}
@Article{Ercegovac:2000:RSR,
author = "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang and
Jean-Michel Muller and Arnaud Tisserand",
title = "Reciprocation, Square Root, Inverse Square Root, and
Some Elementary Functions Using Small Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "628--637",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863031",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68M07 (65B15)",
MRnumber = "MR1783602 (2001e:68016)",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863031",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
summary = "This paper deals with the computation of reciprocals,
square roots, inverse square roots, and some elementary
functions using small tables, small multipliers, and,
for some functions, a final ``large'' (almost
full-length) multiplication. \ldots{}",
}
@InProceedings{Eskritt:2000:DDF,
author = "J. Eskritt and R. Muscedere and G. A. Jullien and V.
S. Dimitrov and W. C. Miller",
editor = "Magdy A. Bayoumi and Eby G. Friedman",
booktitle = "{SiPS 2000: 2000 IEEE Workshop on Signal Processing
Systems: design and implementation: 11--13 October
2000: Lafayette, Louisiana}",
title = "A 2-Digit {DBNS} Filter Architecture",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xv + 836",
pages = "447--456",
year = "2000",
DOI = "https://doi.org/10.1109/SIPS.2000.886743",
ISBN = "0-7803-6488-0",
ISBN-13 = "978-0-7803-6488-2",
LCCN = "TK7874 .S58 2000",
bibdate = "Sat May 14 17:26:55 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Double-Based Number System (DBNS)",
}
@Article{Even:2000:CTR,
author = "G. Even and P.-M. Seidel",
title = "A Comparison of Three Rounding Algorithms for {IEEE}
Floating-Point Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "638--650",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863033",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863033",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
summary = "A new IEEE compliant floating-point rounding algorithm
for computing the rounded product from a carry-save
representation of the product is presented. The new
rounding algorithm is compared with the rounding
algorithms of Yu and Zyner (1995) and of \ldots{}",
}
@Article{Even:2000:DIC,
author = "G. Even and W. J. Paul",
title = "On the design of {IEEE} compliant floating point
units",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "5",
pages = "398--413",
month = may,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.859536",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
MRclass = "68M07",
MRnumber = "MR1764655",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=859536",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "Engineering design methodology recommends designing a
system as follows: Start with an unambiguous
specification, partition the system into blocks,
specify the functionality of each block, design each
block separately, and glue the blocks together.
\ldots{}",
}
@Article{Even:2000:DPI,
author = "G. Even and S. M. Mueller and P.-M. Seidel",
title = "A dual precision {IEEE} floating-point multiplier",
journal = j-INTEGRATION-VLSI-J,
volume = "29",
number = "2",
publisher = "Elsevier Science",
pages = "167--180",
month = sep,
year = "2000",
CODEN = "IVJODL",
ISSN = "0167-9260 (print), 1872-7522 (electronic)",
ISSN-L = "0167-9260",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Integration, the VLSI journal",
pagecount = "14",
}
@InProceedings{Ferguson:2000:IRM,
author = "M. I. Ferguson and M. D. Ercegovac",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "The {IEEE} rounding for multiplier with redundant
operands",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1334--1338",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We present a design for a multiplier with redundant
operands which conforms to the IEEE-754 floating-point
standard. The design consists of a multiplier core and
a rounding unit which conforms to the rounding modes
specified by the IEEE standard and \ldots{}",
}
@InProceedings{Fernandez:2000:FRB,
author = "Pedro G. Fern{\'a}ndez and Anton{\'\i}o Garc{\'\i}a
and Javier Ram{\'\i}rez and Luis Parrilla and
Anton{\'\i}o Lloris",
title = "Fast {RNS}-based {DCT} Computation with Fewer
Multiplication Stages",
crossref = "Anonymous:2000:DPX",
pages = "276--281",
year = "2000",
bibdate = "Fri Jun 24 18:22:06 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ditec.ugr.es/~grios/papers/dcis00_dct.pdf",
acknowledgement = ack-nhfb,
keywords = "Discrete Cosine Transform (DCT); Residue Number System
(RNS)",
}
@Article{Fey:2000:DPA,
author = "Dietmar Fey and Marko Degenkolb",
title = "Digit Pipelined Arithmetic for {$3$-D} Massively
Parallel Optoelectronic Circuits",
journal = j-J-SUPERCOMPUTING,
volume = "16",
number = "3",
pages = "177--196",
month = jul,
year = "2000",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1023/A:1008160925753",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Wed Jul 6 12:13:14 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=16&issue=3;
http://www.wkap.nl/issuetoc.htm/0920-8542+16+3+2000;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=16&issue=3&spage=177;
http://www.wkap.nl/oasis.htm/262637",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@PhdThesis{FigueroadelCid:2000:RFF,
author = "Samuel {Figueroa del Cid}",
title = "A Rigorous Framework for Fully Supporting the {IEEE
Standard} for Floating-Point Arithmetic in High-Level
Programming Languages",
type = "{Ph.D.} Thesis",
school = "Department of Computer Science, New York University",
address = "New York, NY, USA",
pages = "345",
month = jan,
year = "2000",
ISBN = "0-599-59894-8",
ISBN-13 = "978-0-599-59894-2",
bibdate = "Fri Oct 25 17:16:24 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.nyu.edu/csweb/Research/theses.html;
http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.html;
http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.pdf;
http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.ps.gz;
http://wwwlib.umi.com/dissertations/fullcit/9956669;
http://wwwlib.umi.com/dissertations/preview/9956669",
abstract = "Processors conforming to the IEEE Standard for
Floating-Point Arithmetic have been commonplace for
some years, and now several programming languages seem
to support or conform to this standard, from hereon
referred to as ``the IEEE Standard.'' For example, The
Java Language Specification by Gosling, Joy, and
Steele, which defines the Java language, frequently
mentions the IEEE Standard. Indeed, Java, as do other
languages, supports some of the features of the IEEE
Standard, including a couple floating-point data
formats, and even requires (in section 4.2.4
``Floating-Point Operations'' of the aforementioned
book) that ``operators on floating-point numbers behave
exactly as specified by IEEE 754.'' Arguing that the
support current languages offer is not enough, this
thesis establishes clear criteria for what it means to
fully support the IEEE Standard in a programming
language. Each aspect of the IEEE Standard is examined
in detail from the point of view of how various
arithmetic engines implement that aspect of the IEEE
Standard, how different languages (and implementations
thereof) support it, and what the range of options are
in supporting that aspect. Practical recommendations
are then offered (particularly, but not exclusively,
for Ada and Java), taking, for example, programmer
convenience and impact on performance into
consideration. A detailed model specification following
these recommendations is provided for the Ada language.
In addition, a variety of issues related to the
floating-point aspects of programming languages are
discussed, so as to serve as a more complete guide to
language designers. One such issue is floating-point
expression evaluation schemes, and, more specifically,
whether bit-for-bit identical results are actually
achievable on a variety of platforms that conform to
the IEEE Standard, as the Java language promises.
Closely tied to this issue is that of double rounding,
which occurs when a (possibly intermediate) result is
rounded more than once before subsequent use or before
being delivered to its final destination. So this
thesis discusses when double rounding makes a
difference, how it can be avoided, and what the
performance impact is in avoiding it.",
acknowledgement = ack-nhfb,
keywords = "double rounding",
tableofcontents = "List of Tables / vii \\
1 Introduction / 1 \\
1.1 The IEEE Standard for Floating-Point Arithmetic / 1
\\
1.2 What does it mean to support the IEEE Standard? / 2
\\
1.3 Considerations in deciding how to support the IEEE
Standard in high-level languages / 2 \\
1.4 Prior Related Work / 3 \\
2 What Does It Mean to Support the IEEE Standard? / 5
\\
3 Supporting Data Formats in High-Level Languages / 9
\\
3.1 IEEE Standard requirements in regards to data
formats / 9 \\
3.2 Hardware facilities supporting data formats / 10
\\
3.3 Making data formats available in high-level
languages / 11 \\
3.4 Associating floating-point literals with data
formats / 13 \\
3.5 Other issues related to numeric literals / 13 \\
3.6 Issues related to mixed-language programming / 14
\\
3.7 What support exists in high-level languages / 15
\\
3.7.1 Traditional language designs / 15 \\
3.7.2 Implementations of traditional languages / 16 \\
3.7.3 Extensions to traditional languages / 16 \\
3.7.4 New language designs / 17 \\
3.8 What support should exist in high-level languages /
17 \\
4 Supporting Rounding Modes in High-Level Languages /
21 \\
4.1 IEEE Standard requirements in regards to rounding
modes / 21 \\
4.2 Hardware facilities for accessing rounding modes /
22 \\
4.2.1 Processors with dynamic rounding modes / 22 \\
4.2.2 Processors with static rounding modes / 24 \\
4.3 Making rounding modes available in high-level
languages / 25 \\
4.4 Handling static evaluation and numeric literals /
27 \\
4.5 Issues related to mixed-language programming / 29
\\
4.6 What support exists in high-level languages / 30
\\
4.6.1 Existing language designs / 30 \\
4.6.2 Compilers for existing languages / 30 \\
4.6.3 Extensions to existing languages / 30 \\
4.6.4 New language designs / 31 \\
4.7 Why having more than one rounding mode available is
useful / 32 \\
4.8 What support should exist in high-level languages /
33 \\
5 Supporting Precision Modes in High-Level Languages /
35 \\
5.1 IEEE Standard requirements in regards to precision
modes / 35 \\
5.2 Hardware facilities for accessing precision modes /
36 \\
5.2.1 Processors with dynamic precision modes / 36 \\
5.2.2 Processors with static precision modes / 36 \\
5.2.3 Processors without precision modes / 38 \\
5.3 Different ways of making precision modes available
in a high-level language / 39 \\
5.4 Handling static evaluation and numeric literals /
39 \\
5.5 Issues related to mixed-language programming / 39
\\
5.6 What support exists in high-level languages / 39
\\
5.6.1 Compilers for existing languages / 39 \\
5.6.2 Extensions to existing languages / 39 \\
5.6.3 Experimental language designs / 40 \\
5.7 Why it is useful to be able to change the precision
mode / 41 \\
5.8 Why compiler support is required in order to avoid
double rounding / 42 \\
5.9 What support should exist in high-level languages /
43 \\
6 Double Rounding / 47 \\
6.1 Why double rounding can be undesirable / 48 \\
6.2 When is double rounding innocuous? / 50 \\
6.2.1 Addition / 51 \\
6.2.2 Subtraction / 52 \\
6.2.3 Multiplication / 53 \\
6.2.4 Division / 54 \\
6.2.5 Square root / 55 \\
6.2.6 Additional comments / 57 \\
6.3 On avoiding double rounding / 58 \\
6.4 Practical ways of avoiding double rounding / 60 \\
7 Supporting the Standard Operations in High-Level
Languages / 63 \\
7.1 IEEE Standard requirements in regards to operations
/ 63 \\
7.2 How different architectures implement these
operations / 66 \\
7.2.1 CISC architectures / 66 \\
7.2.2 RISC architectures / 68 \\
7.2.3 How different architectures implement comparison
/ 69 \\
7.3 Making the standard operations available in
high-level languages / 70 \\
7.4 Handling static evaluation / 72 \\
7.5 What support exists in high-level languages / 72
\\
7.5.1 Existing language designs / 72 \\
7.5.2 Compilers for existing languages / 74 \\
7.5.3 Extensions to existing languages / 74 \\
7.5.4 New language designs / 75 \\
7.6 What support should exist in high-level languages /
76 \\
8 Supporting Exceptional Situations in High-Level
Languages / 79 \\
8.1 IEEE Standard requirements in regards to special
computational situations / 79 \\
8.2 Different architectures' support for exceptional
situations / 81 \\
8.2.1 CISC architectures / 81 \\
8.2.2 RISC architectures / 84 \\
8.2.3 How different architectures distinguish between
signaling and quiet NaNs / 87 \\
8.2.4 How different architectures detect underflow / 88
\\
8.3 Handling special computational situations in
high-level languages / 89 \\
8.3.1 Ways of representing special values / 89 \\
8.3.2 Handling static evaluation and numeric literals /
90 \\
8.3.3 Supporting arithmetic involving special
computational situations / 91 \\
8.3.4 Ways of allowing access to status flags / 92 \\
8.3.5 Ways of managing the status flags / 93 \\
8.3.6 Facilities for exception handling / 95 \\
8.4 Issues related to mixed-language programming / 96
\\
8.5 What support exists in high-level languages / 97
\\
8.5.1 Existing language designs / 97 \\
8.5.2 Compilers for existing languages / 98 \\
8.5.3 Extensions to existing languages / 98 \\
8.5.4 New language designs / 99 \\
8.6 What support should exist in high-level languages /
100 \\
9 Floating-Point Expression Evaluation Schemes / 105
\\
9.1 Predictable expression evaluation schemes / 106 \\
9.2 Advantages and disadvantages of various evaluation
schemes / 106 \\
9.3 Bit-for-bit identical results and the IEEE Standard
/ 108 \\
9.3.1 Optional and implementation defined features of
the IEEE Standard / 108 \\
9.3.2 Are bit-for-bit identical results achievable in
Java? / 110 \\
10 Supporting the IEEE Standard in Ada and Java / 113
\\
10.1 Ada / 114 \\
10.1.1 Data formats / 114 \\
10.1.2 Rounding and rounding precision modes / 114 \\
10.1.3 Operations / 114 \\
10.1.4 Exceptional situations / 115 \\
10.1.5 Expression evaluation / 117 \\
10.1.6 Pragmas related to floating-point arithmetic /
117 \\
10.2 Java / 118 \\
10.2.1 Data formats / 118 \\
10.2.2 Rounding and (rounding) precision modes / 119
\\
10.2.3 Operations / 120 \\
10.2.4 Exceptional situations / 120 \\
11 Conclusion / 123 \\
11.1 How well current languages support the IEEE
Standard / 123 \\
11.2 Related unfinished work and open issues / 126 \\
A Supporting the IEEE Standard in Ada / 127 \\
A.1 The Package Standard FP Arithmetic / 127 \\
A.1.1 Data Formats / 130 \\
A.1.2 Operations of Floating-Point Types / 131 \\
A.1.3 Rounding Modes / 132 \\
A.1.4 Status Flags / 132 \\
A.1.5 Trap Handlers / 132 \\
A.2 Floating-Point Operations / 132 \\
A.2.1 The Package Generic FP Operations / 132 \\
A.2.2 Required Functions and Predicates / 136 \\
A.2.3 Recommended Functions and Predicate / 138 \\
A.3 Model of Floating-Point Arithmetic / 138 \\
A.3.1 Floating-Point Evaluation Format / 139 \\
A.3.2 Exception Handling / 139 \\
A.4 Pragmas Related to Floating-Point Arithmetic / 144
\\
A.4.1 Pragmas Related to the Accuracy of Results / 144
\\
A.4.2 Pragmas Related to Rounding Modes / 146 \\
A.4.3 Other Pragmas / 148 \\
Bibliography / 151",
}
@InProceedings{Freking:2000:MMR,
author = "W. L. Freking and K. K. Parhi",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "Modular multiplication in the residue number system
with application to massively-parallel public-key
cryptography systems",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1339--1343",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.2000.911210",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Modular multiplication is a fundamental operation in
many public-key cryptography systems including RSA.
Residue number system (RNS) implementation of modular
multiplication has been of recent interest due to
inherent RNS properties of \ldots{}",
}
@PhdThesis{Fu:2000:CPO,
author = "Steve Fu",
title = "Cost Performance Optimizations of Microprocessors",
type = "{Ph.D.} Thesis",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "????",
year = "2000",
bibdate = "Mon Dec 24 11:02:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Gallagher:2000:FTN,
author = "W. L. Gallagher and E. E. {Swartzlander, Jr.}",
title = "Fault-tolerant {Newton--Raphson} and {Goldschmidt}
dividers using time shared {TMR}",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "6",
pages = "588--595",
month = jun,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.862218",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=862218",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Gay:2000:SAC,
author = "David M. Gay",
title = "Symbolic-Algebraic Computations in a Modeling Language
for Mathematical Programming",
type = "Technical Report",
number = "00-3-02",
institution = "Computing Sciences Research Center, Bell
Laboratories",
address = "Murray Hill, NJ, USA",
month = jul,
year = "2000",
bibdate = "Wed Jan 29 16:34:27 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "correct rounding; decimal floating-point arithmetic",
remark = "From \cite{Steele:2004:RHP}: ``AMPL and its solver
interface library use correctly rounded binary-decimal
conversions, which is now possible on all machines
where AMPL has run other than old Cray machines.''",
}
@InProceedings{Goldovsky:2000:DIL,
author = "A. Goldovsky and B. Patel and M. Schulte and R.
Kolagotla and H. Srinivas and G. Burns",
title = "Design and Implementation of a $ 16 $ by $ 16 $ Low
Power Two's Complement Multiplier",
crossref = "IEEE:2000:IGP",
pages = "345--348",
year = "2000",
bibdate = "Sun Mar 04 11:22:03 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-03.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Groza:2000:FPA,
author = "V. Groza",
title = "Floating-Point Analog-to-Digital Converters with
Predictive Auto-Ranging",
crossref = "IEEE:2000:IPI",
pages = "759--762",
year = "2000",
bibdate = "Sat Jun 02 08:27:44 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Hanrot:2000:ML,
author = "Guillaume Hanrot and Vincent Lef{\`e}vre and Patrick
P{\'e}lissier and Paul Zimmermann and Sylvie Boldo and
David Daney and Mathieu Dutour and Emmanuel Jeandel and
Laurent Fousse and Fabrice Rouillier and Kevin Ryde",
title = "The {MPFR} Library",
howpublished = "World-Wide Web software project archive.",
year = "2000",
bibdate = "Fri Jun 24 14:53:37 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mpfr.org/",
abstract = "The MPFR library is a C library for multiple-precision
floating-point computations with exact rounding (also
called correct rounding). It is based on the GMP
multiple-precision library.\par
The main goal of MPFR is to provide a library for
multiple-precision floating-point computation which is
both efficient and has a well-defined semantics. It
copies the good ideas from the ANSI/IEEE-754 standard
for double-precision floating-point arithmetic (53-bit
mantissa).",
acknowledgement = ack-nhfb,
}
@TechReport{Hanrot:2000:SDS,
author = "Guillaume Hanrot and Michel Quercia and Paul
Zimmermann",
title = "Speeding up the division and square root of power
series",
type = "Research Report",
number = "3973",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "23",
day = "17",
month = jul,
year = "2000",
ISSN = "0249-6399",
bibdate = "Sun Sep 10 08:52:54 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3973.ps.gz",
abstract = "We present new algorithms for the inverse, quotient,
or square root of power series. The key trick is a new
algorithm RecursiveMiddleProduct or RMP computing the
$n$ middle coefficients of a $ 2 n \times n $ product
in essentially the same number of operations $ K(n) $
than a full $ n \times n $ product with Karatsuba's
method. This improves previous work of Mulders, Karp
and Markstein, Burnikel and Ziegler. These results
apply both to series, polynomials, and multiple
precision floating-point numbers.",
acknowledgement = ack-nhfb,
keywords = "division; Karatsuba's algorithm; Newton method; square
root",
}
@Article{Harrison:2000:FPV,
author = "John Harrison",
title = "Floating Point Verification in {HOL Light}: The
Exponential Function",
journal = j-FORM-METHODS-SYST-DES,
volume = "16",
number = "3",
pages = "271--305",
year = "2000",
CODEN = "FMSDE6",
ISSN = "0925-9856 (print), 1572-8102 (electronic)",
ISSN-L = "0925-9856",
bibdate = "Thu May 09 09:43:30 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since they often embody compact but mathematically
sophisticated algorithms, operations for computing the
common transcendental functions in floating point
arithmetic seem good targets for formal verification
using a mechanical theorem prover. We discuss some of
the general issues that arise in verifications of this
class, and then present a machine-checked verification
of an algorithm for computing the exponential function
in IEEE-754 standard binary floating point arithmetic.
We confirm (indeed strengthen) the main result of a
previousl published error analysis, though we uncover a
minor error in the hand proof and are forced to
confront several subtle issues that might easily be
overlooked informally. The development described here
includes, apart from the proof itself, a formalization
of IEEE arithmetic, a mathematical semantics for the
programming language in which the algorithm is
expressed, and the body of pure mathematics needed. All
this is developed logically from first principles using
the HOL Light prover, which guarantees strict adherence
to simple rules of inference while allowing the user to
perform proofs using higher-level derived rules.",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
journal-URL = "https://dl.acm.org/loi/fmsd",
}
@Article{Harrison:2000:FVF,
author = "John Harrison",
title = "Formal Verification of Floating Point Trigonometric
Functions",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1954",
pages = "217--233",
year = "2000",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:08:55 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1954.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1954/19540217.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1954/19540217.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Harrison:2000:FVI,
author = "John Harrison",
editor = "Mark Aagaard and John Harrison",
booktitle = "Theorem Proving in Higher Order Logics: {13th
International Conference, TPHOLs 2000 Portland, OR,
USA, August 14-18, 2000 Proceedings}",
title = "Formal Verification of {IA-64} Division Algorithms",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xi + 533",
pages = "233--251",
year = "2000",
CODEN = "1869",
DOI = "https://doi.org/10.1007/3-540-44659-1_15",
ISBN = "3-540-44659-1 (e-book), 3-540-67863-8 (paper)",
ISBN-13 = "978-3-540-44659-0 (e-book), 978-3-540-67863-2
(paper)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.9.A96 T655 2000",
bibdate = "Fri Sep 22 16:31:35 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/3-540-44659-1",
}
@TechReport{Harrison:2000:HOM,
author = "John Harrison and Ted Kubaska and Bob Norin and Shane
Story and Ping Tak Peter Tang",
title = "Highly Optimized Mathematical Functions for the
{IA-64} Architectures",
type = "Technical report",
number = "245410-002",
institution = "Intel Corporation",
address = "San Jose, CA, USA",
month = apr,
year = "2000",
bibdate = "Sat Jun 02 11:04:28 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://download.intel.com/design/IA-64/Downloads/libm.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Hasan:2000:FPI,
author = "M. A. Hasan and A. A. Hasan and S. Rahman",
booktitle = "Proceedings of the 39th {IEEE} Conference on Decision
and Control",
title = "Fixed point iterations for computing square roots and
the matrix sign function of complex matrices",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "4253--4258",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The purpose of this work has been the development of
new set of rational iterations for computing square
roots and the matrix sign function of complex matrices.
Given any positive integer r{\&}ges;2, we presented a
systematic way of deriving rth order \ldots{}",
}
@Article{Hasan:2000:LTB,
author = "M. A. Hasan",
title = "Look-Up Table-Based Large Finite Field Multiplication
in Memory Constrained Cryptosystems",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "749--758",
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863045",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:47:55 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@InProceedings{Hassibi:2000:ESR,
author = "B. Hassibi",
booktitle = "Proceedings. 2000 {IEEE} International Conference on
Acoustics, Speech, and Signal Processing: {ICASSP '00},
5--9 June 2000",
title = "An efficient square-root algorithm for {BLAST}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II737--II740",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Bell Labs Layered Space-Time (BLAST) is a scheme for
transmitting information over a rich-scattering
wireless environment using multiple receive and
transmit antennas. The main computational bottleneck in
the BLAST algorithm is a ``nulling and \ldots{}",
}
@InProceedings{Hassibi:2000:FSR,
author = "B. Hassibi",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "A fast square-root implementation for {BLAST}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1255--1259",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Bell Labs Layered Space-Time (BLAST) is a scheme for
transmitting information over a rich-scattering
wireless environment using multiple receive and
transmit antennas. The main computational bottleneck in
the BLAST algorithm is a ``nulling and \ldots{}",
}
@InProceedings{He:2000:UAA,
author = "Yun He and Chris H. Q. Ding",
title = "Using accurate arithmetics to improve numerical
reproducibility and stability in parallel
applications",
crossref = "Reynders:2000:IPI",
pages = "225--234",
year = "2000",
DOI = "https://doi.org/10.1145/335231.335253",
bibdate = "Sat Feb 8 18:35:50 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/335231.335253",
abstract = "Numerical reproducibility and stability of large scale
scientific simulations, especially climate modeling, on
distributed memory parallel computers are becoming
critical issues. In particular, global summation of
distributed arrays is most susceptible to rounding
errors, and their propagation and accumulation cause
uncertainty in final simulation results. We analyzed
several accurate summation methods and found that two
methods are particularly effective to improve (ensure)
reproducibility and stability: Kahan's self-compensated
summation and Bailey's double-double precision
summation. We provide an MPI operator MPLSUMDD to work
with MPI collective operations to ensure a scalable
implementation on large number of processors. The final
methods are particularly simple to adopt in practical
codes.",
acknowledgement = ack-nhfb,
}
@Article{Hiasat:2000:NES,
author = "A. A. Hiasat",
title = "New efficient structure for a modular multiplier for
{RNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "2",
pages = "170--174",
month = feb,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.833113",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=833113",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Hida:2000:QDA,
author = "Yozo Hida and Xiaoye S. Li and David H. Bailey",
title = "Quad-Double Arithmetic: Algorithms, Implementation,
and Application",
type = "Technical report",
number = "LBNL-46996",
institution = "Lawrence Berkeley National Laboratory",
address = "1 Cycloton Rd, Berkeley, CA 94720",
pages = "28",
day = "30",
month = oct,
year = "2000",
bibdate = "Wed Nov 24 08:18:07 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~yozo/papers/LBNL-46996.ps.gz",
acknowledgement = ack-nhfb,
}
@Article{Higuchi:2000:FAA,
author = "Akira Higuchi and Naofumi Takagi",
title = "A fast addition algorithm for elliptic curve
arithmetic in {$ {\rm GF}(2 n) $} using projective
coordinates",
journal = j-INFO-PROC-LETT,
volume = "76",
number = "3",
pages = "101--103",
day = "15",
month = dec,
year = "2000",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Apr 18 07:11:20 MDT 2001",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.nl/gej-ng/10/23/20/67/27/25/abstract.html;
http://www.elsevier.nl/gej-ng/10/23/20/67/27/25/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@InProceedings{Hormigo:2000:HAVa,
author = "J. Hormigo and J. Villalba and M. Schulte",
editor = "????",
booktitle = "Proceedings of the 4th Conference on Real Numbers and
Computers, Dagstuhl, Germany, April, 2000",
title = "A Hardware Algorithm for Variable-Precision Division",
publisher = "????",
address = "????",
pages = "104--112",
year = "2000",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 04 11:20:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-02.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Hormigo:2000:HAVb,
author = "J. Hormigo and J. Villalba and M. Schulte",
title = "A Hardware Algorithm for Variable-Precision
Logarithm",
crossref = "Swartzlander:2000:IIC",
pages = "215--224",
year = "2000",
bibdate = "Sun Mar 04 11:20:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-04.pdf",
acknowledgement = ack-nhfb,
}
@Article{Ide:2000:GMF,
author = "Nobuhiro Ide and Masashi Hirano and Yukio Endo and
Shin ichi Yoshioka and Hiroaki Murakami and Atsushi
Kunimatsu and Toshinori Sato and Takayuki Kamei and
Toyoshi Okada and Masakazu Suzuoki",
title = "{2.44 GFLOPS 300-MHz} Floating-Point Vector-Processing
Unit for High-Performance {$3$-D} Graphics Computing",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "35",
number = "7",
pages = "1025--1033",
month = jul,
year = "2000",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.hwswworld.com/downloads/a7/1025ide.pdf",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A vector unit for high-performance three-dimensional
graphics computing has been developed. We implement
four floating-point multiply-accumulate units, which
execute multiply-add operations with one throughput;
one floating-point divide/square root \ldots{}",
}
@Book{Ifrah:2000:UHN,
author = "Georges Ifrah",
title = "The Universal History of Numbers from Prehistory to
the Invention of the Computer",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xxii + 633",
year = "2000",
ISBN = "0-471-37568-3",
ISBN-13 = "978-0-471-37568-5",
LCCN = "QA141.I3713 2000",
bibdate = "Mon Dec 06 16:02:33 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Translated from the French edition, {\em Histoire
universelle des chiffres}, by David Bellos, E. F.
Harding, Sophie Wood, and Ian Monk.",
price = "US\$39.95",
acknowledgement = ack-nhfb,
}
@InProceedings{Imajo:2000:CSB,
author = "Tetsuji Imajo and Tatsuki Miyake and Shinobu Sato and
Toshiyuki Ito and Daisuke Yokotsuka and Yoshihide
Tsujihata and Shunsuke Uemura",
title = "{COBOL Script}: a Business-Oriented Scripting
Language",
crossref = "IEEE:2000:EPI",
pages = "231--??",
year = "2000",
bibdate = "Thu Aug 07 17:50:59 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes COBOL Script, a Web-oriented
script language developed by Hitachi. COBOL Script
includes the following features: (1) The language
specifications, which consist of functions required for
Web computing, are a subset of COBOL85, the most
frequently used programming language in business
information systems. (2) COBOL Script supports decimal
arithmetic functions that have the same precision as in
standard COBOL85 on mainframe computers. (3) Efficient
implementation was based on analysis of the pros and
cons of the COBOL processing system. Using COBOL
Script, users can: (1) Process applications requiring
high precision, such as account-related applications,
over the Web. (2) Use a test debugger and a Coverage
Function with COBOL Script for large-scale development
projects. (3) Use Japanese in programs. (4) Achieve
good run-time performance.",
acknowledgement = ack-nhfb,
keywords = "account-related applications; business information
systems; business-oriented scripting language; COBOL;
COBOL processing system; COBOL Script; COBOL85; decimal
arithmetic functions; decimal floating-point
arithmetic; language specifications; large-scale
development projects; test debugger; Web computing;
Web-oriented script language",
}
@Misc{Intel:2000:DSR,
author = "{Intel}",
title = "Divide, Square Root, and Remainder Algorithms for the
{Itanium} Architecture",
howpublished = "Intel Software Development Products",
month = jul,
year = "2000",
bibdate = "Fri Sep 22 17:06:23 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://studylib.net/doc/7921762/divide--square-root-and-remainder-algorithms-for-the-ia-64",
acknowledgement = ack-nhfb,
}
@Manual{Intel:2000:IPF,
title = "{Itanium} Processor Floating-point Software Assistance
and Floating-point Exception Handling",
number = "245415-001",
organization = pub-INTEL,
address = pub-INTEL:adr,
month = jan,
year = "2000",
bibdate = "Tue Nov 18 16:18:52 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://cache-www.intel.com/cd/00/00/21/92/219290_fpswa_software.pdf",
acknowledgement = ack-nhfb,
}
@Misc{ISO:2000:FSI,
author = "{ISO/IEC JTC1/SC22/WG5}",
title = "Information technology --- Programming languages ---
{Fortran} -- Floating-point exception handing (draft)",
howpublished = "World-Wide Web document.",
edition = "Second",
day = "19",
month = jan,
year = "2000",
bibdate = "Thu May 09 10:24:52 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.nag.co.uk/sc22wg5/N1351-N1400/N1378.pdf",
acknowledgement = ack-nhfb,
}
@Article{Joye:2000:OLR,
author = "M. Joye and S.-M. Yen",
title = "Optimal Left-to-Right Binary Signed-Digit Recoding",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "740--748",
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863044",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:47:55 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@Misc{Kahan:2000:MAA,
author = "W. Kahan",
title = "Miscalculating Area and Angles of a Needle-like
Triangle",
howpublished = "World-Wide Web lecture notes for introductory
numerical analysis classes.",
day = "24",
month = mar,
year = "2000",
bibdate = "Fri Jul 15 12:30:24 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/Triangle.pdf",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic",
}
@TechReport{Kahan:2000:MVM,
author = "W. Kahan",
title = "Marketing versus Mathematics and other Ruminations on
the design of floating-point arithmetic",
howpublished = "World-Wide Web document.",
institution = "Mathematics Department and Electrical Engineering and
Computer Science Department, University of California,
Berkeley",
address = "Berkeley, CA, USA",
pages = "48",
day = "27",
month = aug,
year = "2000",
bibdate = "Fri May 03 12:19:56 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/MktgMath.pdf;
http://www.cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:2000:RDFa,
author = "W. Kahan",
title = "Ruminations on the Design of Floating-Point
Arithmetic",
howpublished = "World-Wide Web document",
pages = "29",
day = "25",
month = apr,
year = "2000",
bibdate = "Sat Mar 03 18:19:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Kahan:2000:RDFb,
author = "W. Kahan",
title = "Marketing versus Mathematics and other Ruminations on
the design of floating-point arithmetic",
howpublished = "World-Wide Web document.",
institution = "Mathematics Department and Electrical Engineering and
Computer Science Department, University of California,
Berkeley",
address = "Berkeley, CA, USA",
pages = "48",
day = "27",
month = aug,
year = "2000",
bibdate = "Fri May 03 12:19:56 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/MktgMath.pdf;
http://www.cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kalampoukas:2000:HSP,
author = "L. Kalampoukas and D. Nikolos and C. Efstathiou and H.
T. Vergos and J. Kalamatianos",
title = "High-Speed Parallel-Prefix Modulo $ 2^{n - 1} $
Adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "673--680",
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863036",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon May 20 06:47:55 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@Article{Kao:2000:LTA,
author = "Ming-Yang Kao and Jie Wang",
title = "Linear-Time Approximation Algorithms for Computing
Numerical Summation with Provably Small Errors",
journal = j-SIAM-J-COMPUT,
volume = "29",
number = "5",
pages = "1568--1576",
month = oct,
year = "2000",
CODEN = "SMJCAT",
DOI = "https://doi.org/10.1137/S0097539798341594",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Fri Oct 27 06:28:34 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/29/5;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/34159",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{Kapur:2000:UIP,
author = "Deepak Kapur and Mahadevan Subramaniam",
title = "Using an induction prover for verifying arithmetic
circuits",
journal = j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
volume = "3",
number = "1",
pages = "32--65",
month = sep,
year = "2000",
CODEN = "????",
ISSN = "1433-2779 (print), 1433-2787 (electronic)",
ISSN-L = "1433-2779",
bibdate = "Tue Nov 23 15:01:40 MST 2004",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1433-2779;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal on Software Tools for Technology
Transfer: STTT",
journal-URL = "http://link.springer.com/journal/10009",
}
@Article{Kawamura:2000:CRA,
author = "Shinichi Kawamura and Masanobu Koike and Fumihiko Sano
and Atsushi Shimbo",
title = "{Cox-Rower} Architecture for Fast Parallel
{Montgomery} Multiplication",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1807",
pages = "523--??",
year = "2000",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Feb 1 09:16:29 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1807.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1807/18070523.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1807/18070523.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Keller:2000:ARR,
author = "T. Keller and T. H. Liew and Lajos Hanzo",
title = "Adaptive redundant residue number system coded
multicarrier modulation",
journal = j-IEEE-J-SEL-AREAS-COMMUN,
volume = "18",
number = "11",
pages = "2292--2301",
month = nov,
year = "2000",
CODEN = "ISACEM",
DOI = "https://doi.org/10.1109/49.895034",
ISSN = "0733-8716 (print), 1558-0008 (electronic)",
ISSN-L = "0733-8716",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=19376",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal on Selected Areas in Communications",
keywords = "residue arithmetic; residue number system",
summary = "The novel class of nonbinary maximum minimum distance
redundant residue number system (RRNS) codes is invoked
in the context of adaptively RRNS coded,
symbol-by-symbol adaptive multicarrier modulation, in
order to combat the effects of frequency- \ldots{}",
}
@Article{Kim:2000:PSA,
author = "Hyun-Sung Kim and Sung-Woo Lee and Kee-Young Yoo",
title = "Partitioned systolic architecture for modular
multiplication in {GF} (2 { m })",
journal = j-INFO-PROC-LETT,
volume = "76",
number = "3",
pages = "135--139",
day = "15",
month = dec,
year = "2000",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Apr 18 07:11:20 MDT 2001",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.nl/gej-ng/10/23/20/67/27/30/abstract.html;
http://www.elsevier.nl/gej-ng/10/23/20/67/27/30/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Kobayashi:2000:HBF,
author = "Shiro Kobayashi and Gerhard P. Fettweis",
title = "A Hierarchical Block-Floating-Point Arithmetic",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "24",
number = "1",
pages = "19--30",
month = feb,
year = "2000",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1008110410087",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
abstract = "In order to give an answer to a question of the
arithmetic in future DSP architectures for mobile
communication applications, the signal processing
quality of different arithmetic representations has
been studied. Based on the result, a new approach for
implementing block-floating-point arithmetic is
proposed. This approach intends to preserve the
least-significant-bits (LSBs) to improve signal
processing quality. The preservation of LSBs is
automatically and perfectly done by hardware. Several
simulation results show that the proposed
block-floating-point implementation provides improved
SNRs over conventional block-floating-point
implementations. For the same number of bits in the
memory for each representation, the SNRs better than
floating-point are also observed. For multiple datapath
DSPs, this implementation also requires significantly
less hardware complexity than floating-point.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
pagecount = "12",
}
@Article{Koren:2000:GEI,
author = "Israel Koren and Peter Kornerup",
title = "{Guest Editors}' Introduction: Special Issue on
Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "625--627",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2000.863030",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863030",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "From the article: ``The papers included in this
special issue were selected from 56 manuscripts
submitted in response to the call for papers.
Submissions were also solicited from the authors of
papers presented at the 14th Symposium on Computer
Arithmetic (ARITH-14), held in Adelaide, Australia, on
April 14--16 1999. This symposium was the most recent
in a series of biannual events whose proceedings have
provided a wealth of much cited and often seminal
papers. As a result of the review process, 14 papers
were selected to be included in this special issue.
Four of these papers are extensions of papers presented
at ARITH-14, some are further descendents of such
papers and the rest have originated from the open call
for papers.''",
}
@TechReport{Krishnan:2000:PEM,
author = "S. Krishnan and M. Foskey and T. Culver and J. Keyser
and D. Manocha",
title = "{Precise}: Efficient multiprecision evaluation of
algebraic roots and predicates for reliable geometric
computations",
type = "Technical Report",
number = "TR00 008",
institution = "Department of Computer Science, University of North
Carolina",
address = "Chapel Hill, NC, USA",
year = "2000",
bibdate = "Mon Oct 21 18:00:02 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://citeseer.nj.nec.com/krishnan00precise.html",
acknowledgement = ack-nhfb,
}
@Article{Kum:2000:ACO,
author = "Ki-Il Kum and Jiyang Kang and Wonyong Sung",
title = "{AUTOSCALER} for {C}: an optimizing floating-point to
integer {C} program converter for fixed-point digital
signal processors",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "47",
number = "9",
pages = "840--848",
month = sep,
year = "2000",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.868453",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
summary = "A translator which converts C-based floating-point
digital signal processing programs to optimized integer
C versions is developed for convenient programming and
efficient use of fixed-point digital signal processors
(DSPs). It not only converts data \ldots{}",
}
@Article{Lee:2000:LSM,
author = "Keon-Jik Lee and Kee-Young Yoo",
title = "Linear systolic multiplier\slash squarer for fast
exponentiation",
journal = j-INFO-PROC-LETT,
volume = "76",
number = "3",
pages = "105--111",
day = "15",
month = dec,
year = "2000",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Wed Apr 18 07:11:20 MDT 2001",
bibsource = "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.nl/gej-ng/10/23/20/67/27/26/abstract.html;
http://www.elsevier.nl/gej-ng/10/23/20/67/27/26/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Leemis:2000:SDS,
author = "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L.
Evans",
title = "Survival Distributions Satisfying {Benford}'s Law",
journal = j-AMER-STAT,
volume = "54",
number = "4",
pages = "236--??",
month = nov,
year = "2000",
CODEN = "ASTAAJ",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Fri Jul 20 11:18:01 MDT 2001",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.amstat.org/publications/tas/Leemis.htm",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@InProceedings{Lefevre:2000:CRF,
author = "V. D. Lefevre and Jean-Michel Muller",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "Correctly rounded functions for better arithmetic",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "875--878",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The IEEE 754 standard for floating-point arithmetic
requires that the four arithmetic operations and the
square root should be correctly rounded. This has
improved the accuracy, reliability and portability of
numerical software. Unfortunately, such \ldots{}",
}
@PhdThesis{Lefevre:2000:MAP,
author = "Vincent Lef{\`e}vre",
title = "Moyens arithm{\'e}tiques pour un calcul fiable.
({French}) [{Arithmetic} means for reliable
calculation]",
type = "{Ph.D.} dissertation",
school = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "Lyon, France",
pages = "148",
year = "2000",
bibdate = "Fri Sep 22 16:11:21 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.theses.fr/2000ENSL0142",
acknowledgement = ack-nhfb,
advisor = "Jean-Michel Muller",
}
@InProceedings{Liew:2000:IDR,
author = "T. H. Liew and L.-L. Yang and L. Hanzo",
booktitle = "{VTC 2000-Spring} Tokyo, {IEEE 51st} Vehicular
Technology Conference Proceedings, 15--18 May 2000",
title = "Iterative decoding of redundant residue number system
codes",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "576--580",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/VETECS.2000.851523",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Turbo decoded redundant residue number system (RRNS)
codes are proposed and their performance is evaluated.
An RRNS (n,k) code is a maximum-minimum distance block
code, exhibiting identical distance properties to
Reed--Solomon (RS) codes. Hence their \ldots{}",
}
@Article{Lin:2000:NBP,
author = "Rong Lin and James L. Schwing",
title = "A Non-binary Parallel Arithmetic Architecture",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1800",
pages = "149--??",
year = "2000",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/3-540-45591-4_19",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Feb 1 09:16:18 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1800.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1800/18000149.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1800/18000149.pdf",
abstract = "In this paper we present a novel parallel arithmetic
architecture using an efficient non-binary logic
scheme. We show that by using parallel broadcasting (or
domino propagating) state signals, on short
reconfigurable buses equipped with a type of switches,
called GP (generate-propagate) shift switches, several
arithmetic operations can be carried out efficiently.
We extend a recently proposed shift switching mechanism
by letting the switch array automatically generate a
semaphore to indicate the end of each domino process.
This reduces the complexity of the architecture and
improves the performance significantly.",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Lopez:2000:HSS,
author = "Julio L{\'o}pez and Ricardo Dahab",
title = "High-Speed Software Multiplication in $ \mathbb
{f}_{2^m} $",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1977",
pages = "203--??",
year = "2000",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:08:57 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1977.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1977/19770203.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1977/19770203.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Luo:2000:API,
author = "Z. Luo and M. Martonosi",
title = "Accelerating pipelined integer and floating-point
accumulations in configurable hardware with delayed
addition techniques",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "3",
pages = "208--218",
month = mar,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.841125",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=841125",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "The speed of arithmetic calculations in configurable
hardware is limited by carry propagation, even with the
dedicated hardware found in recent FPGAs. This paper
proposes and evaluates an approach called delayed
addition that reduces the carry-propagation \ldots{}",
}
@TechReport{Maclaren:2000:IEH,
author = "Nick Maclaren",
title = "{IEEE 754} Error Handling and Programming Languages",
type = "Report",
institution = "Cambridge University",
address = "Cambridge, UK",
pages = "15",
month = mar,
year = "2000",
bibdate = "Wed Nov 10 08:10:24 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://grouper.ieee.org/groups/1788/email/pdfmPSi1DgZZf.pdf",
abstract = "IEEE 754-1985 introduced order to a particularly
chaotic area and, in general, it has been very
successful, though experts disagree about which of its
properties are merits. Hindsight shows several areas
where some unfortunate decisions were taken, but few of
the problems were predicted at the time.",
acknowledgement = ack-nhfb,
keywords = "exception handling; IEEE 754 arithmetic; Infinity;
quiet NaN; signaling NaN; signed zero; traps",
remark = "The author reviews the good and bad points of IEEE 754
arithmetic. He is particularly critical of the
inconsistencies in hardware and programming languages
in the handling of quiet and signaling NaN, real and
complex Infinity, signed zero, and failure of NaNs to
propagate in certain C99 functions. He has a clear
discussion of five distinct uses of NaN, and how they
ought to behave differently in numerical operations and
function calls. He also laments the unreliability of
{\tt errno}, exception handling, and traps,
particularly across platforms and code libraries.",
}
@InProceedings{Madhukumar:2000:DPR,
author = "A. S. Madhukumar and F. Chin",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "Design and performance of residue number system based
multicarrier {CDMA} in frequency-selective {Rayleigh}
fading channels",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "884--888",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.2000.910640",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper is concerned with a new method to enhance
the bandwidth efficiency of an MC-CDMA system by using
a residue number based representation for information
symbols. The residues are mapped into a set of
orthogonal sequences and are transmitted \ldots{}",
}
@InProceedings{Madhukumar:2000:PRN,
author = "A. S. Madhukumar and F. Chin",
booktitle = "{IEEE} {VTS-Fall} {VTC 2000}. 52nd Vehicular
Technology Conference, 2000",
title = "Performance of a residue number system based
{DS--CDMA} system over bursty communication channels",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2433--2440",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/VETECF.2000.883300",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper is concerned with the performance of a
residue number system (RNS) based direct-sequence CDMA
system over bursty communication channels. Concatenated
codes employing redundant RNS as inner codes and
convolution codes as outer codes are \ldots{}",
}
@InProceedings{Madhukumar:2000:RNS,
author = "A. S. Madhukumar and F. Chin and A. B. Premkumar",
booktitle = "Proceedings of the 43rd {IEEE} Midwest Symposium on
Circuits and Systems 2000",
title = "Residue number system based multicarrier {CDMA} for
broadband mobile communication systems",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "536--539",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.2000.952812",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper is concerned with a new method to enhance
the bandwidth efficiency of an MC-CDMA system by using
a residue number based representation for information
symbols. The residues are mapped into a set of
orthogonal sequences and are transmitted \ldots{}",
}
@InProceedings{Mahesh:2000:LPR,
author = "M. N. Mahesh and M. Mehendale",
booktitle = "Thirteenth International Conference on {VLSI} Design,
2000",
title = "Low power realization of residue number system based
{FIR} filters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "30--33",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICVD.2000.812580",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper, we present algorithmic and
architectural transforms for low power realization of
Residue Number System (RNS) based FIR filters. These
transforms have been systematically derived so as to
achieve power reduction by voltage scaling, \ldots{}",
}
@Book{Markstein:2000:IEF,
author = "Peter Markstein",
title = "{IA-64} and Elementary Functions: Speed and
Precision",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xix + 298",
year = "2000",
ISBN = "0-13-018348-2",
ISBN-13 = "978-0-13-018348-4",
LCCN = "QA76.9.A73 M365 2000",
bibdate = "Fri Jan 5 08:00:52 MST 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib;
University of California MELVYL catalog.",
series = "Hewlett--Packard professional books",
URL = "http://www.markstein.org/",
acknowledgement = ack-nhfb,
keywords = "correct rounding; floating-point arithmetic; IA-64
(computer architecture)",
remark = "Besides recipes for accurate computation of elementary
functions, this book also contains algorithms for the
correctly-rounded computation of floating-point
division and square-root, and of integer division,
starting from low-precision reciprocal approximations.
There is also a wealth of information on the tradeoffs
between integer and floating-point instruction use in a
pipelined parallel architecture.",
tableofcontents = "IA-64 Architecture \\
New Architecture Objectives \\
VLIW \\
Memory Enhancements \\
Software Pipelining \\
Floating Point Enhancements \\
Summary \\
IA-64 Instructions And Registers \\
Instructions \\
Register Sets \\
Accessing Memory \\
Assembly Language \\
Problems \\
Increasing Instruction Level Parallelism \\
Branching \\
Speculation \\
Problems \\
Floating Point Architecture \\
Floating Point Status Register \\
Precision \\
Fused Multiply-Add \\
Division and Square Root Assists \\
Floating Comparisons \\
Communication between Floating Point and General
Purpose Registers \\
Fixed Point Multiplication \\
SIMD Arithmetic \\
Problems \\
Programming For IA-64 \\
Compiler Options \\
Pragmas \\
Floating Point Data Types \\
In-Line Assembly \\
The fenv.h Header \\
Extended Examples \\
Quad Precision \\
Problems \\
Computation of Elementary Functions \\
Mathematical Preliminaries \\
Floating Point \\
Approximation and Error Analysis \\
The Exclusion Theorem \\
Ulps \\
Problems \\
Approximation Of Functions \\
Taylor Series \\
Lagrangian Interpolation \\
Chebychev Approximation \\
Remez Approximation \\
Practical Considerations \\
Function Evaluation \\
Table Construction \\
Problems \\
Division \\
Approximations for the Reciprocal \\
Computing the Quotient \\
Division Using Only Final Precision Results \\
Fast Variants of Division \\
Remainder \\
Integer Division \\
An Implementation of Division \\
Problems \\
Square Root \\
Approximations \\
Rounding the Square Root \\
Computing the Square Root \\
Calculating the Reciprocal Square Root \\
An Implementation of Square Root \\
Problems \\
Exponential Functions \\
Definitions and Formulas \\
Argument Reduction \\
Error Containment \\
Computing the Exponential \\
The Function expm \\
Problems \\
Logarithmic Functions \\
General Relations \\
Argument Reductions \\
Error Analysis \\
The Function log1p \\
Computing the Logarithm \\
Problems \\
The Power Function \\
Definition \\
Single Precision \\
Double Precision \\
Double-Extended Precision \\
Quad Precision \\
Computing the Power Function \\
Problems \\
Trigonometric Functions \\
Formulas and Identities \\
Argument Reduction \\
Error Analysis \\
Computing the Trigonometric Functions \\
Problems \\
Inverse Sine And Cosine \\
Definitions and Formulas \\
Argument Reduction \\
Error Analysis \\
Computing the arcsin \\
Problems \\
Inverse Tangent Functions \\
Definitions and Formulas \\
Argument Reduction \\
Error Analysis \\
Computing the arctan \\
Problems \\
Hyperbolic Functions \\
Definitions and Formulas \\
Argument Reduction \\
Error Analysis \\
Computing the Hyperbolic Functions \\
Problems \\
Inverse Hyperbolic Functions \\
Definitions and Formulas. arcsinh. arccosh. arctanh \\
Problems \\
Odds And Ends \\
Correctly Rounded Functions \\
Monotonicity \\
Alternative Algorithms \\
Testing \\
New Architectural Directions \\
Problems \\
In-Line Assembly \\
Solutions To Problems \\
Bibliography \\
Subject Index",
}
@Article{Maryska:2000:SCR,
author = "J. Maryska and M. Rozlozn{\'\i}k and M. Tuma",
title = "{Schur} complement reduction in the mixed-hybrid
approximation of {Darcy}'s law: rounding error
analysis",
journal = j-J-COMPUT-APPL-MATH,
volume = "117",
number = "2",
pages = "159--173",
day = "15",
month = may,
year = "2000",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:43:35 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042799003441",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{McKenzie:2000:ACP,
author = "Pierre McKenzie and Heribert Vollmer and Klaus W.
Wagner",
title = "Arithmetic Circuits and Polynomial Replacement
Systems",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1974",
pages = "164--??",
year = "2000",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Feb 1 09:17:23 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1974.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1974/19740164.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1974/19740164.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@PhdThesis{Mencer:2000:RAU,
author = "Oskar Mencer",
title = "Rational Arithmetic Units in Computer Systems",
type = "{Ph.D.} Thesis",
school = "Department of Electrical Engineering, Stanford
University",
address = "Stanford, CA, USA",
pages = "????",
month = jan,
year = "2000",
bibdate = "Mon Dec 24 11:05:19 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Moreira:2000:FMJ,
author = "Jos{\'e} E. Moreira and Samuel P. Midkiff and Manish
Gupta",
title = "From flop to megaflops: {Java} for technical
computing",
journal = j-TOPLAS,
volume = "22",
number = "2",
pages = "265--295",
month = mar,
year = "2000",
CODEN = "ATPSDT",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Tue Sep 26 10:12:58 MDT 2000",
bibsource = "http://www.acm.org/pubs/contents/journals/toplas/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/citations/journals/toplas/2000-22-2/p265-moreira/",
abstract = "Although there has been some experimentation with Java
as a language for numerically intensive computing,
there is a perception by many that the language is
unsuited for such work because of performance
deficiencies. In this article we show how optimizing
array bounds checks and null pointer checks creates
loop nests on which aggressive optimizations can be
used. Applying these optimizations by hand to a simple
matrix-multiply test case leads to Java-compliant
programs whose performance is in excess of 500 Mflops
on a four-processor 332MHz RS/6000 model F50 computer.
We also report in this article the effect that various
optimizations have on the performance of six
floating-point-intensive benchmarks. Through these
optimizations we have been able to achieve with Java at
least 80\% of the peak Fortran performance on the same
benchmarks. Since all of these optimizations can be
automated, we conclude that Java will soon be a serious
contender for numerically intensive computing.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
keywords = "arrays; compilers; Java",
subject = "Software --- Programming Languages --- Processors
(D.3.4): {\bf Compilers}; Software --- Programming
Languages --- Processors (D.3.4): {\bf Run-time
environments}; Software --- Programming Techniques ---
Concurrent Programming (D.1.3): {\bf Parallel
programming}; Software --- Programming Languages ---
Language Classifications (D.3.2): {\bf Java}",
}
@Book{Mueller:2000:CAC,
author = "Silvia M. Mueller and Wolfgang J. Paul",
title = "Computer Architecture: Complexity and Correctness",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 553",
year = "2000",
ISBN = "3-540-67481-0",
ISBN-13 = "978-3-540-67481-8",
LCCN = "QA76.9.A73 M845 2000",
bibdate = "Mon Mar 05 18:45:52 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
URL = "http://www-wjp.cs.uni-sb.de/info/papers/#books",
abstract = "\booktitle{Computer Architecture: Complexity and
Correctness} develops, at the gate level, the complete
design of a pipelined RISC processor with delayed
branch, forwarding, hardware interlock, precise
maskable nested interrupts, caches, and a fully
IEEE-compliant floating point unit. In contrast to
other design approaches applied in practice and unlike
other textbooks available, the designs presented here
are modular, clean and complete up to the construction
of entire complex machines. The authors systematically
basing their approach on rigorous mathematical
formalisms allows for rigorous correctness proofs,
accurate hardware cost determination, and performance
evaluation as well as, generally speaking, for coverage
of a broad variety of relevant issues within a
reasonable number of pages. The book is written as a
text for classes on computer architecture and related
topics and will serve as source of reference for
professionals in hardware design. Numerous
illustrations, examples, exercises, and a subject index
support the reader in accessing the material
presented.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; DLX; floating-point arithmetic; IEEE
754; RISC",
libnote = "Not yet in my library.",
remark = "This book is about the design of the DLX (MIPS
derivative) processor, at the circuit level. As such,
it lacks the broad view of Hennessy \& Patterson's
books, but by considering actual gate implementation
costs, it is able to provide precise details of
implementation tradeoffs, in particular, on cache size
and design, and on why memory on chip is expensive (in
number of gates) [although the recent work by David
Patterson's group at UC/Berkeley on the Vector IRAM
processor is putting about 16MB RAM on chip, to make a
system-on-a-chip suitable for embedded devices, like
the 0.5B cell phones that will be manufactured in
2001].\par
The book includes mathematical correctness proofs of
all circuits, and automated verification of these
proofs is in progress.\par
From p. 10: ``\ldots{} All C programs associated with
the designs in this book are accessible at the our web
site.'' [see the URL field in this entry].\par
Chapter 7 ``IEEE Floating Point Standard and Theory of
Rounding'' has a good survey of the IEEE 754 Standard,
and its implications at the hardware level.\par
Chapter 8 ``Floating Point Algorithms and Data Paths'',
and Chapter 9 ``Pipelined DLX Machine with
Floating-Point Core'', examine the hardware
implementation of IEEE 754 arithmetic.\par
Chapter 9 makes very brief mention of the design issues
for fast interval arithmetic.",
tableofcontents = "1: Introduction \\
2: Basics \\
2.1: Hardware Model \\
2.2: Number Representations and Basic Circuits \\
2.3: Basic Circuits \\
2.4: Arithmetic Circuits \\
2.5: Multipliers \\
2.6: Control Automata \\
3: A Sequential DLX Design \\
3.1: Instruction Set Architecture \\
3.2: High Level Data Paths \\
3.3: Environments \\
3.4: Sequential Control \\
3.5: Hardware Cost and Cycle Time \\
4: Basic Pipelining \\
4.1: Delayed Branch and Delayed PC \\
4.2: Prepared Sequential Machines \\
4.3: Pipelining as a Transformation \\
4.4: Result Forwarding \\
4.5: Hardware Interlock \\
4.6: Cost Performance Analysis \\
5: Interrupt Handling \\
5.1: Attempting a Rigorous Treatment of Interrupts \\
5.2: Extended Instruction Set Architecture",
}
@Article{Mulders:2000:SMD,
author = "Thom Mulders",
title = "On short multiplications and divisions",
journal = j-APPL-ALGEBRA-ENG-COMMUN-COMPUT,
volume = "11",
number = "1",
pages = "69--88",
month = aug,
year = "2000",
CODEN = "AAECEW",
DOI = "https://doi.org/10.1007/s002000000037",
ISSN = "0938-1279 (print), 1432-0622 (electronic)",
ISSN-L = "0938-1279",
MRclass = "68W30",
MRnumber = "MR1817699 (2001m:68187)",
bibdate = "Thu Nov 8 14:50:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See note \cite{Hanrot:2002:LNM}.",
acknowledgement = ack-nhfb,
fjournal = "Applicable Algebra in Engineering, Communication and
Computing",
}
@Article{Nielsen:2000:ICF,
author = "Asger Munk Nielsen and David W. Matula and Chung Nan
Lyu and Guy Even",
title = "An {IEEE} compliant floating-point adder that conforms
with the pipeline packet-forwarding paradigm",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "1",
pages = "33--47",
month = jan,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.822562",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:23 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=822562",
abstract = "This paper presents a floating-point addition
algorithm and adder pipeline design employing a packet
forwarding pipeline paradigm. The packet forwarding
format and the proposed algorithms constitute a new
paradigm for handling data hazards in deeply pipelined
floating-point pipelines. The addition and rounding
algorithms employ a four stage execution phase pipeline
with each stage suitable for implementation in a short
clock period, assuming about 15 logic levels per cycle.
The first two cycles are related to addition proper and
are the focus of this paper. The last two cycles
perform the rounding and have been covered in a paper
by D. W. Matula and A. M. Nielsen (1997). The addition
algorithm accepts one operand in a standard binary
floating-point formal at the start of cycle one. The
second operand is represented in the packet forwarding
floating-point format: namely, it is divided into four
parts: the sign bit, the exponent string, the principal
part of the significant, and the carry-round packet.
The first three parts of the second operand are input
at the start of cycle one and the carry-round packet is
input at the start of cycle two. The result is output
in two formats that both represent the rounded result
as required by the IEEE 754 standard. The result is
output in the packet forwarding floating-point format
at the end of cycles two and three to allow forwarding
with an effective latency of two cycles. The result is
also format at the end of cycle four for retirement to
a register. The packet forwarding result is thus
available with an effective two cycle latency for
forwarding to the start of the adder pipeline or to a
cooperating multiplier pipeline accepting a packet
forwarding operand. The effective latency of the
proposed design is two cycles for successive dependent
operations while perceiving IEEE 754 binary
floating-point compatibility.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "This paper presents a floating-point addition
algorithm and adder pipeline design employing a packet
forwarding pipeline paradigm. The packet forwarding
format and the proposed algorithms constitute a new
paradigm for handling data hazards in deeply \ldots{}",
}
@Article{Oh:2000:ENB,
author = "Sangho Oh and Chang Han Kim and Jongin Lim and Dong
Hyeon Cheon",
title = "Efficient normal basis multipliers in composite
fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "10",
pages = "1133--1138",
month = oct,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.888054",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:26 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=888054",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Paliouras:2000:FPP,
author = "Vassilis Paliouras and Konstantina Karagianni and
Thanos Stouraitis",
title = "A floating-point processor for fast and accurate
sine\slash cosine evaluation",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "47",
number = "5",
pages = "441--451",
month = may,
year = "2000",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.842112",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "0.7 micron; Approximation algorithms; CMOS digital
integrated circuits; CMOS process technology;
computational complexity; Computer architecture;
coprocessors; digital signal processing chips; DSP
chip; error analysis; fast cosine evaluation; fast sine
evaluation; Fixed-point arithmetic; fixed-point
arithmetic; floating point arithmetic; floating-point
arithmetic; floating-point processor; Hardware;
Interleaved codes; interpolation; Interpolation;
mathematics computing; memory architecture; Memory
architecture; memory interleaving scheme; memory size
reduction; Partitioning algorithms; performance
evaluation; Polynomials; polynomials; roundoff error
bounds; roundoff errors; second order polynomial
interpolation; second-order Horner polynomial;
trigonometric functions; Very large scale integration;
VLSI; VLSI architecture",
summary = "A VLSI architecture for fast and accurate
floating-point sine/cosine evaluation is presented,
combining floating-point and simple fixed-point
arithmetic. The algorithm implemented by the
architecture is based on second order polynomial
interpolation \ldots{}",
}
@InProceedings{Paliouras:2000:HRR,
author = "V. Paliouras and T. Stouraitis",
booktitle = "The 7th {IEEE} International Conference on
Electronics, Circuits and Systems, 2000. {ICECS 2000}",
title = "High-radix residue number system forward and inverse
converters",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "858--861",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICECS.2000.913011",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Novel radix-r modulo-r n forward and inverse
converters for residue number system (RNS)-based
processors are introduced in this paper. The proposed
circuits convert conventional radix-2 data to
high-radix residues and vice-versa with low \ldots{}",
}
@Article{Paliouras:2000:NHR,
author = "V. Paliouras and T. Stouraitis",
title = "Novel high-radix residue number system architectures",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "47",
number = "10",
pages = "1059--1073",
month = oct,
year = "2000",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.877147",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=18987",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "residue arithmetic; residue number system",
summary = "Novel radix-r modulo-r n arithmetic units for residue
number system (RNS)-based architectures are introduced
in this paper. The proposed circuits are shown to
require several times less area than previously
reported architectures for \ldots{}",
}
@MastersThesis{Papakonstantinou:2000:IUF,
author = "Alexandros Papakonstantinou",
title = "Implementations of units for floating point
arithmetic",
type = "Thesis ({M.Sc.})",
school = "Department of Electrical and Electronic Engineering,
Imperial College, London",
address = "London, UK",
year = "2000",
bibdate = "Thu May 09 08:42:09 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Parhami:2000:CAA,
author = "Behrooz Parhami",
title = "Computer Arithmetic: Algorithms and Hardware Designs",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xx + 490",
year = "2000",
ISBN = "0-19-512583-5 (hardcover), 3-540-04907-X (print),
3-540-36246-0 (e-book)",
ISBN-13 = "978-0-19-512583-2 (hardcover), 978-3-540-04907-4
(print), 978-3-540-36246-3 (e-book)",
LCCN = "QA76.9.C62P37 1999",
bibdate = "Sat Jun 17 12:26:40 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$85.00",
abstract = "The field of digital computer architecture has grown
explosively in the past two decades. Through a steady
stream of experimental research, tool-building efforts,
and theoretical studies, the design of an
instruction-set architecture has been transformed into
one of the most quantitative branches of computer
technology. However, this explosive growth has led to
unprecedented hardware complexity and almost
intolerable development costs. The challenge faxing
current and future computer designers is to institute
simplicity where we now have complexity; to use
fundamental theories being developed in this area to
gain performance and ease-of-use benefits from simpler
circuits; to understand the interplay between
technological capabilities/limitations and sound
architectural decisions. Computer arithmetic plays a
key role in the computer designers' quest for
user-friendliness, compactness, simplicity, high
performance, low cost, and low power. Parhami's
Computer Architecture emphasizes both the underlying
theory and actual hardware designs. and links computer
arithmetic to other subfields of computing. It is the
first computer arithmetic book to cover all topics
important for a balanced and complete view of the
field. IT will be accompanied by an instructor's
manual, with problem solutions and enlarged versions of
the figures/charts, suitable for reproduction as
transparencies. This is a textbook for senior/graduate
level courses in departments of computer science and
electrical and computer engineering. The course is
commonly called Computer Arithmetic. Students wishing
to enroll will usually have taken courses in computer
organization and advanced digital design before
enrolling. Computer Arithmetic is a sub-field of
digital computer organization. It deals with the
hardware realization of arithmetic functions to support
various computer architectures, as well as arithmetic
algorithms for firmware or software implementations. A
major thrust of digital computer arithmetic is the
design of hardware algorithms and circuits to enhance
the speed of numeric operations. Thus much of what is
presented in this book complements the architectural
and algorithmic speedup techniques studied in the
context of high performance computer architecture and
parallel processing.",
acknowledgement = ack-nhfb,
tableofcontents = "Part I: Number Representation \\
1: Numbers and Arithmetic \\
2: Representing Signed Numbers \\
3: Redundant Number Systems \\
4: Residue Number Systems \\
Part II: Addition/Subtraction \\
5: Basic Addition and Counting \\
6: Carry-Lookahead Adders \\
7: Variations in Fast Adders \\
8: Multioperand Addition \\
Part III: Multiplication \\
9: Basic Multiplication Schemes \\
10: High-Radix Multipliers \\
11: Tree and Array Multipliers \\
12: Variations in Multipliers \\
Part IV: Division \\
13: Basic Division Schemes \\
14: High-Radix Dividers \\
15: Variations in Dividers \\
16: Division by Convergence \\
Part V: Real Arithmetic \\
17: Floating-Point Representations \\
18: Floating-Point Operations \\
19: Errors and Error Control",
}
@InProceedings{Parhami:2000:PER,
author = "B. Parhami",
booktitle = "Conference Record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers, 2000",
title = "On producing exactly rounded results in digit-serial
on-line arithmetic",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "889--893",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The input and output of an on-line computation
involving redundant numbers must generally be
compatible with standard nonredundant formats. When
rounding of a result is required in the last
computation step, the process can be combined with
on-the- \ldots{}",
}
@InProceedings{Park:2000:ESR,
author = "Woo-Chan Park and Tack-Don Han and Shin-Dug Kim",
booktitle = "Proceedings of the Second {IEEE} Asia Pacific
Conference on {ASICs 2000}: {AP-ASIC 2000}",
title = "Efficient simultaneous rounding method removing
sticky-bit from critical path for floating point
addition",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "223--226",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Processing flow of the conventional floating point
addition/subtraction operation consists of several
steps, i.e., alignment, addition/subtraction,
normalization, and rounding stages in this order. A
floating adder/subtractor performing addition/
\ldots{}",
}
@TechReport{Parker:2000:MCAa,
author = "D. Stott Parker and Brad Pierce and Paul R. Eggert",
title = "{Monte Carlo} arithmetic: a framework for the
statistical analysis of roundoff error",
number = "CSD 970014",
institution = "Department of Computer Science, University of
California, Los Angeles",
address = "Los Angeles, CA, USA",
pages = "18",
month = mar,
year = "2000",
LCCN = "QA75.5 .R46 no.970002 1997",
bibdate = "Mon Aug 25 15:03:13 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.ucla.edu/~stott/mca/CSD-970014.ps.gz",
acknowledgement = ack-nhfb,
}
@Article{Parker:2000:MCAb,
author = "D. Stott Parker and Brad Pierce and Paul R. Eggert",
title = "{Monte Carlo} Arithmetic: How to Gamble with Floating
Point and Win",
journal = j-COMPUT-SCI-ENG,
volume = "2",
number = "4",
pages = "58--68",
month = jul # "\slash " # aug,
year = "2000",
CODEN = "CSENFA",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/cs/books/cs2000/pdf/c4058.pdf;
http://www.computer.org/cse/cs1999/c4058abs.htm",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
summary = "How sensitive to rounding errors are the results
generated from a particular code running on a
particular machine applied to a particular input? Monte
Carlo arithmetic illustrates the potential for tools to
support new kinds of a posteriori round-off analysis.",
}
@Article{Parks:2000:NTT,
author = "M. Parks",
title = "Number-Theoretic Test Generation for Directed
Rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "651--658",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863034",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863034",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14; floating-point testing",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
summary = "We present methods to systematically generate the
hardest test cases for multiplication, division, and
square root subject to directed rounding, essentially
extending previous work on number-theoretic
floating-point testing to rounding modes other than
to-nearest. The algorithms focus upon the rounding
boundaries of the modes truncate, to-minus-infinity,
and to-infinity, and programs based on them require
little beyond exact arithmetic in the working precision
to create billions of edge cases. We will show that the
amount of work required to calculate trial
multiplicands pays off in the form of free extra tests
due to an interconnection among the operations
considered herein. Although these tests do not replace
proofs of correctness, they can be used to gain a high
degree of confidence that the accuracy requirements as
mandated by IEEE Standard 754 have been satisfied.",
}
@Article{Philippsen:2000:CNJ,
author = "Michael Philippsen and Edwin G{\"u}nthner",
title = "Complex numbers for {Java}",
journal = j-CPE,
volume = "12",
number = "6",
pages = "477--491",
month = may,
year = "2000",
CODEN = "CPEXEI",
DOI = "https://doi.org/10.1002/1096-9128(200005)12:6<477::AID-CPE486>3.0.CO;2-W",
ISSN = "1040-3108 (print), 1096-9128 (electronic)",
ISSN-L = "1040-3108",
bibdate = "Sun Oct 29 16:57:06 MST 2000",
bibsource = "http://www.interscience.wiley.com/jpages/1040-3108;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract/72515730/START;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=72515730&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
fjournal = "Concurrency, practice and experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-0634/issues",
}
@Article{Pillai:2000:LPA,
author = "R. V. Pillai and D. Al-Khalili and A. J. Al-Khalili",
title = "Low Power Architecture for Floating-Point {MAC}
Fusion",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "147",
pages = "288--296",
year = "2000",
CODEN = "ICDTEA",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Fri Jun 24 10:52:39 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
}
@InProceedings{Ploog:2000:MPB,
author = "H. Ploog and D. Timmermann",
booktitle = "Proceedings of the 2000 International Conference on
Computer Design",
title = "On multiple precision based {Montgomery}
multiplication without precomputation of {$ N'_0 = -
N_0^{-1} \bmod W $}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "589--590",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An efficient implementation of modular exponentiation,
i.e., the main building block of many public key
cryptographic devices, is achieved by algorithmic
optimization of the Montgomery modular multiplication
algorithm based on multiple precision \ldots{}",
}
@Book{Poitras:2000:EHF,
author = "Geoffrey Poitras",
title = "The Early History of Financial Economics, 1478--1776:
from Commercial Arithmetic to Life Annuities and Joint
Stocks",
publisher = "Edward Elgar",
address = "Cheltenham, UK",
pages = "x + 522",
year = "2000",
ISBN = "1-84064-455-9",
ISBN-13 = "978-1-84064-455-5",
LCCN = "HG101 .P65 2000",
bibdate = "Sat Aug 12 14:42:20 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Geoffrey Poitras provides an exhaustive account of the
early development of the subject and, in so doing,
provides a sound basis for the study of modern
financial economics.",
acknowledgement = ack-nhfb,
author-dates = "1954--",
subject = "Finance; History; Economics; Business mathematics;
Life annuities; Stocks; Finances; Histoire;
{\'E}conomie politique; Math{\'e}matiques
financi{\`e}res; Rentes viag{\`e}res; Actions (Titres
de soci{\'e}t{\'e}); Business mathematics; Economics;
Finance; Life annuities; Stocks; Finanzierungstheorie;
Finanzwirtschaft; Finanzwissenschaft; Kredittheorie;
Financi{\"e}n.",
tableofcontents = "1: Introduction \\
2: History of Commerce and Finance \\
3: The Scholastic Analysis of Usury and Other Subjects
\\
4: The Evolution of Commercial Arithmetic \\
5: Simple Interest and Compound Interest \\
6: The Valuation of Life Annuities \\
7: Foreign Exchange and the Bill Market \\
8: The Analysis of Joint Stocks \\
9: Development of Derivative Securities \\
10: Manias, Manipulations and Institutional Failures
\\
11: English Debates over Interest Rates and Public
Credit \\
12: Maritime Insurance, Life Insurance and Other
Subjects \\
13: Some Speculative Conclusions",
}
@InProceedings{Premkumar:2000:CLB,
author = "A. B. Premkumar and M. Bhardwaj",
booktitle = "The 2000 {IEEE} International Symposium on Circuits
and Systems, Proceedings, {ISCAS 2000} Geneva, 28--31
May 2000",
title = "Combinatorial logic based forward converters in
residue number systems",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "317--320",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2000.857428",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The Residue Number System (RNS) offers unlimited
opportunities for high performance arithmetic provided
efficient forward and reverse converters could be
constructed for the moduli set at hand. All forward
conversion proposals to date, require some \ldots{}",
}
@InProceedings{Ramirez:2000:NAC,
author = "J. Ramirez and A. Garcia and P. G. Fernandez and L.
Parrilla and A. Lloris",
booktitle = "Proceedings, {ISCAS 2000} Geneva, The 2000 {IEEE}
International Symposium on Circuits and Systems, 28--31
May 2000",
title = "A new architecture to compute the discrete cosine
transform using the quadratic residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "321--324",
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2000.857429",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A new methodology to compute the N-point DCT (Discrete
Cosine Transform) in the QRNS (Quadratic Residue Number
System) is presented, with a significant improvement in
complexity and speed compared to the corresponding
binary version. This reduction \ldots{}",
}
@Article{Reyhani-Masoleh:2000:ENB,
author = "A. Reyhani-Masoleh and M. A. Hasan",
title = "On Efficient Normal Basis Multiplication",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1977",
pages = "213--??",
year = "2000",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:08:57 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1977.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1977/19770213.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1977/19770213.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Russinoff:2000:CSF,
author = "David M. Russinoff",
title = "A Case Study in Formal Verification of
Register-Transfer Logic with {ACL2}: The Floating Point
Adder of the {AMD Athlon} Processor",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1954",
pages = "3--36",
year = "2000",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Thu Sep 12 09:02:10 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1954.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1954/19540003.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1954/19540003.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Savas:2000:MMI,
author = "E. Savas and {\c{C}}. K. Ko{\c{c}}",
title = "The {Montgomery} Modular Inverse---Revisited",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "763--766",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863048",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863048",
abstract = "We modify an algorithm given by Kaliski to compute the
Montgomery inverse of an integer modulo a prime number.
We also give a new definition of the Montgomery
inverse, and introduce efficient algorithms for
computing the classical modular inverse, the
Kaliski-Montgomery inverse, and the new Montgomery
inverse. The proposed algorithms are suitable for
software implementations on general-purpose
microprocessors",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@InProceedings{Schulte:2000:CUT,
author = "M. Schulte and M. Gok and P. Balzola and R. Brocato",
title = "Combined Unsigned and Two's Complement Saturating
Multipliers",
crossref = "Luk:2000:PSA",
pages = "185--196",
year = "2000",
bibdate = "Sun Mar 04 11:31:05 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-05.pdf",
acknowledgement = ack-nhfb,
}
@Article{Schulte:2000:FVP,
author = "M. J. Schulte and E. E. {Swartzlander, Jr.}",
title = "A Family of Variable-Precision, Interval Arithmetic
Processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "5",
pages = "387--398",
month = may,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.859535",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=859535;
http://mesa.ece.wisc.edu/publications/cp_2000-09.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Schulte:2000:IMO,
author = "M. J. Schulte and P. I. Balzola and A. Akkas and R. W.
Brocato",
title = "Integer Multiplication with Overflow Detection or
Saturation",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "681--691",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863038",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
OCLC Proceedings database",
URL = "http://home.ku.edu.tr/~ahakkas/publications/overflow.pdf;
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863038;
http://mesa.ece.wisc.edu/publications/cp_2000-08.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@InProceedings{Schulte:2000:PSM,
author = "M. J. Schulte and P. I. Balzola and J. Ruan and J.
Glossner",
title = "Parallel Saturating Multioperand Adders",
crossref = "ACM:2000:PIC",
pages = "172--179",
year = "2000",
DOI = "https://doi.org/10.1145/354880.354904",
bibdate = "Sun Mar 04 11:32:39 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-06.pdf",
acknowledgement = ack-nhfb,
}
@PhdThesis{Seidel:2000:DIC,
author = "Peter-Michael Seidel",
title = "On the Design of {IEEE} Compliant Floating-point Units
and their Quantitative Analysis",
type = "{Ph.D.} thesis",
school = "Computer Science Department, University of Saarland",
address = "Saarbr{\"u}cken, Germany",
pages = "xii + 188",
year = "2000",
bibdate = "Tue Mar 13 10:27:30 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Mueller:2000:CAC}.",
}
@Book{Seife:2000:ZBD,
author = "Charles Seife",
title = "Zero: The Biography of a Dangerous Idea",
publisher = pub-VIKING,
address = pub-VIKING:adr,
pages = "vi + 248",
year = "2000",
ISBN = "0-670-88457-X, 0-14-029647-6 (paperback)",
ISBN-13 = "978-0-670-88457-5, 978-0-14-029647-1 (paperback)",
LCCN = "QA141 .S45 2000",
bibdate = "Fri Nov 28 19:15:01 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Article{Sleijpen:2000:DER,
author = "Gerard L. G. Sleijpen and Henk A. van der Vorst and
Jan Modersitzki",
title = "Differences in the Effects of Rounding Errors in
{Krylov} Solvers for Symmetric Indefinite Linear
Systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "3",
pages = "726--751 (electronic)",
year = "2000",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479897323087",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10 (65N12)",
MRnumber = "MR1785632 (2001j:65058)",
MRreviewer = "Larisa V. Maslovskaya",
bibdate = "Sat Dec 31 06:28:14 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib;
MathSciNet database",
URL = "http://epubs.siam.org/sam-bin/dbq/article/32308;
http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Swider:2000:FPR,
author = "Zbigniew {\'S}wider",
title = "Floating-point roundoff errors of second-order
state-space digital filters",
journal = "Systems Sci.",
volume = "26",
number = "1",
pages = "67--81",
year = "2000",
CODEN = "SYSCDP",
ISSN = "0137-1223",
MRclass = "93E11 (65G20)",
MRnumber = "MR1787396",
bibdate = "Thu Nov 8 19:32:19 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Wroc\l aw University of Technology. Systems Science",
keywords = "rounding errors",
}
@InProceedings{Takahashi:2000:IMP,
author = "D. Takahashi",
booktitle = "Proceedings of the 2000 International Workshops on
Parallel Processing",
title = "Implementation of multiple-precision parallel division
and square root on distributed-memory parallel
computers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "229--235",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We present efficient parallel algorithms for
multiple-precision division and square root operation
of more than several million decimal digits on
distributed-memory parallel computers. It is well known
that multiple-precision division and square \ldots{}",
}
@Article{Talahmeh:2000:ADR,
author = "S. Talahmeh and P. Siy",
title = "Arithmetic division in {RNS} using {Galois Field
GF($p$) }",
journal = j-COMPUT-MATH-APPL,
volume = "39",
number = "5--6",
pages = "227--238",
month = mar,
year = "2000",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/S0898-1221(00)00056-0",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Nov 18 09:47:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper develops an enhanced algorithm for the
arithmetic division problem in the Residue Number
System. The proposed algorithm is based on Galois Field
Theory GF($p$). Mapping the arithmetic division problem
over the Galois Field GF($p$) eliminates many of the
limitations of existing algorithms. The advantage of
the proposed algorithm is that it has no restriction on
the dividend and the divisor, no mixed radix
conversion, no quotient estimation before division, no
reciprocal estimation of the divisor, and no based
extension operation.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Tchoumatchenko:2000:FBS,
author = "V. Tchoumatchenko and T. Vassileva and P. Gurov",
booktitle = "Proceedings of the 22nd {EUROMICRO} Conference
{EUROMICRO 96}. 'Beyond 2000: Hardware and Software
Design Strategies'",
title = "A {FPGA} based square-root coprocessor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "520--525",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We present an FPGA implementation of a non-restoring
integer square-root algorithm, that uses estimates for
result-digit selection and radix-$2$ redundant addition
in recurrence. On-the-fly conversion of the
result-digit and signed-digit adder/ \ldots{}",
}
@Article{Thimbleby:2000:CNB,
author = "Harold Thimbleby",
title = "Calculators are needlessly bad",
journal = "International Journal of Human-Computer Studies",
volume = "52",
number = "6",
pages = "1031--1069",
month = jun,
year = "2000",
CODEN = "????",
DOI = "https://doi.org/10.1006/ijhc.1999.0341",
ISSN = "????",
bibdate = "Mon Jan 14 21:51:22 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1071581999903415",
acknowledgement = ack-nhfb,
keywords = "Charles Babbage",
}
@InProceedings{Tommiska:2000:AEI,
author = "M. T. Tommiska",
booktitle = "Proceedings of the 2000 Third {IEEE} International
Caracas Conference on Devices, Circuits and Systems,
15--17 March 2000",
title = "Area-efficient implementation of a fast square root
algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "S18/1--S18/4",
year = "2000",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An area-efficient implementation of a fast-converging
square-root algorithm is presented. The design of
special arithmetic operations differs in many ways from
the traditional tasks that digital designers are used
to, and the role of \ldots{}",
}
@Article{Tong:2000:RPO,
author = "J. Y. F. Tong and D. Nagle and R. A. Rutenbar",
title = "Reducing power by optimizing the necessary
precision\slash range of floating-point arithmetic",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "8",
number = "3",
pages = "273--286",
month = jun,
year = "2000",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/92.845894",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
summary = "Low-power systems often find the power cost of
floating-point (FP) hardware prohibitively expensive.
This paper explores ways of reducing FP power
consumption by minimizing the bitwidth representation
of FP data. Analysis of several FP programs that
\ldots{}",
}
@InProceedings{Tsuji:2000:REO,
author = "Kumiko Tsuji",
booktitle = "Proceedings of the Second {ISAAC} Congress, Vol. 2
(Fukuoka, 1999)",
title = "Round-off error of optimal control problems in
floating-point number systems",
volume = "8",
publisher = "Kluwer Acad. Publ.",
address = "Dordrecht",
pages = "929--944",
year = "2000",
MRclass = "49M30 (65G50)",
MRnumber = "MR1940881",
bibdate = "Thu Nov 8 19:32:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Int. Soc. Anal. Appl. Comput.",
acknowledgement = ack-nhfb,
keywords = "rounding errors",
}
@Article{vanderKolk:2000:FPV,
author = "K. J. van der Kolk and J. A. Lee and E. F. A.
Deprettere",
title = "A Floating Point Vectoring Algorithm Based on Fast
Rotations",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "25",
number = "2",
pages = "125--139",
month = jun,
year = "2000",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1008166822333",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Thu May 09 09:46:25 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The idea of approximate rotations has been introduced
by J. G{\"o}tze and G. Hekstra. G. Hekstra and E.
Deprettere extended the concept to orthogonal fast
rotations and formalized the concept by providing a
fast rotation theory. In this theory, the emphasis has
been on fast rotation, whereas fast rotation-based
vectorization has only been considered in an
approximating sense in examples published by J.
G{\"o}tze and G. Hekstra. The formalization of fast
rotation-based vectorization is the subject of this
paper. The few known approximate fast vectorization
algorithms are special cases of the generic fast
rotation-based vectorization algorithm proposed in this
paper.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@Article{Wang:2000:NSA,
author = "Chin-Liang Wang and Jyh-Huei Guo",
title = "New systolic arrays for {$ C + A B^2 $}, inversion,
and division in {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "10",
pages = "1120--1125",
month = oct,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.888047",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:26 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=888047",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wires:2000:VCT,
author = "K. E. Wires and M. J. Schulte and J. E. Stine",
title = "Variable-Correction Truncated Floating Point
Multipliers",
crossref = "Matthews:2000:CRT",
pages = "1344--1348",
year = "2000",
bibdate = "Sun Mar 04 11:34:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2000-07.pdf",
acknowledgement = ack-nhfb,
}
@Article{Yang:2000:EPG,
author = "Chia-Lin Yang and B. Sano and A. R. Lebeck",
title = "Exploiting parallelism in geometry processing with
general purpose processors and floating-point {SIMD}
instructions",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "9",
pages = "934--946",
month = sep,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.869324",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:25 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=869324",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "Three-dimensional (3D) graphics applications have
become very important workloads running on today's
computer systems. A cost-effective graphics solution is
to perform geometry processing of 3D graphics on the
host CPU and have specialized hardware \ldots{}",
}
@Article{Yeh:2000:HSB,
author = "Wen-Chang Yeh and Chein-Wei Jen",
title = "High-Speed {Booth} Encoded Parallel Multiplier
Design",
journal = j-IEEE-TRANS-COMPUT,
volume = "49",
number = "7",
pages = "692--701",
month = jul,
year = "2000",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.863039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:35:24 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
OCLC Proceedings database",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863039",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-14",
remark = "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}
@TechReport{Zimmermann:2000:PGF,
author = "Paul Zimmermann",
title = "A proof of {GMP} fast division and square root
implementations",
type = "Technical report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "14",
month = sep,
year = "2000",
bibdate = "Sun Sep 10 08:48:46 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz",
abstract = "This short note gives a detailed correctness proof of
fast (i.e., subquadratic) versions of the GNU MP {\tt
mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions,
together with complete GMP code. The {\tt
mpn\_bz\_divrem\_n} function divides (with remainder) a
number of $ 2 n $ limbs by a divisor of $n$ limbs in $
2 K(n) $, where $ K(n) $ is the time spent in a $ (n
\times n) $ multiplication, using the
Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm.
The {\tt mpn\_sqrtrem} computes the square root and the
remainder of a number of $ 2 n $ limbs (square root and
remainder have about $n$ limbs each) in time $ 3 K(n) /
2 $; it uses Karatsuba Square Root.",
acknowledgement = ack-nhfb,
}
@Article{Akishita:2001:FSS,
author = "Toru Akishita",
title = "Fast Simultaneous Scalar Multiplication on Elliptic
Curve with {Montgomery} Form",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2259",
pages = "255--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:44 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590255.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2259/22590255.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@PhdThesis{Akkas:2001:ISE,
author = "Ahmet Akkas",
title = "Instruction set enhancements for reliable
computations",
type = "{Ph.D.} Thesis",
school = "Lehigh University",
address = "Bethlehem, PA, USA",
pages = "159",
year = "2001",
ISBN = "0-493-49369-7",
ISBN-13 = "978-0-493-49369-5",
bibdate = "Fri Oct 25 17:09:55 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://wwwlib.umi.com/dissertations/fullcit/3036247;
http://wwwlib.umi.com/dissertations/preview/3036247",
abstract = "Although there have been significant advances in VLSI
technology and numerical computing, floating-point
computations still suffer from undetected errors due to
rounding and catastrophic cancellation. Fast computers
let programmers write numerically intensive programs,
but computed results can be far from the true results
due to the accumulation of errors in arithmetic
operations. Therefore, accurate and reliable
computations have become more important. Interval
arithmetic is one technique for accurate and reliable
computing. With interval arithmetic, each data value is
represented by two floating-point numbers which
correspond to the endpoints of an interval, such that
the true result is guaranteed to lie on this interval.
Since interval arithmetic represents ranges of numbers,
it also provides the ability to solve problems that
cannot be efficiently solved using floating-point
arithmetic. Although interval arithmetic provides an
efficient method for monitoring and controlling errors
in floating-point computations, it is not yet used
widely because it is not sufficiently fast. This
dissertation investigates instruction set enhancements
for interval arithmetic. Existing interval arithmetic
programs are examined to determine bottlenecks in
interval computations. Then, a variety of instruction
set enhancements are pro posed to overcome these
bottlenecks. The efficiency of the proposed
enhancements are evaluated using an interval-enhanced
compiler and a superscalar processor simulator.
Hardware modifications to support these enhancements
are evaluated, and a novel design for a combined
Interval and Floating-point Comparator is presented.
This dissertation also investigates instruction set
enhancements for extended precision arithmetic. In
particular, instruction set support for quadruple
precision arithmetic is examined. Hardware
modifications needed to support quadruple precision
arithmetic on superscalar processor is evaluated to
determine which extensions can be most efficiently
incorporated into superscalar processor designs.
Furthermore, a technique for performing parallel double
precision multiplication using quadruple precision
hardware is proposed.",
acknowledgement = ack-nhfb,
}
@Book{Alefeld:2001:SAM,
editor = "G{\"o}tz Alefeld and Ji{\v{r}}i Rohn and Siegfried
Rump and Tetsuro Yamamoto",
title = "Symbolic algebraic methods and verification methods",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 266",
year = "2001",
ISBN = "3-211-83593-8",
ISBN-13 = "978-3-211-83593-7",
LCCN = "QA76.9.M35 S92 2001",
bibdate = "Thu May 09 07:34:15 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$69.95",
series = "Springer mathematics",
URL = "http://www.springer-ny.com/detail.tpl?cart=10209516271260963&isbn=3211835938",
acknowledgement = ack-nhfb,
contents = "\begin{itemize}
\item Introduction (G. Alefeld, J. Rohn, S. Rump, T.
Yamamoto).
\item Topological Concepts for Hierarchies of
Variables, Types and Controls (R. Albrecht).
\item Modifications of the Oettli-Prager Theorem with
Application to the Eigenvalue Problem (G. Alefeld, V.
Kreinovich, G. Mayer).
\item Symbolic-Numeric Algorithms for Polynomials: Some
Recent Results (R. Corless).
\item Symbolic-Numeric QD-Algorithms with Applications
in Function Theory and Linear Algebra (A. Cuyt).
\item On the Isoefficiency of the Parallel Descartes
Method (Th. Decker, W. Krandick).
\item Matrix Methods for Solving Algebraic Systems (I.
Z. Emiris).
\item A Feasibility Result for Interval Gaussian
Elimination Relying on Graph Structure (A.
Frommer).
\item Solution of Systems of Polynomial Equations by
Using Bernstein Expansion (J. Garloff, A. P.
Smith).
\item Symbolic-Algebraic Computations in Modeling
Language for Mathematical Programming (D. M.
Gay).
\item Translation of Taylor Series into LFT Expansions
(R. Heckmann).
\item Quasi Convex-Concave Extensions (Chr.
Jansson).
\item Rewriting, Induction and Decision Procedures: A
Case Study of Presburger Arithmetic (D. Kapur).
\item Derivative-Based Subdivision in Multi-dimensional
Verified Gaussian Quadrature (B. Lang).
\item On the Shape of the Fixed Points of
$\overline{A}f\overline{U}(\overline{A}x\overline{U}) =
\overline{A}A\overline{U}\overline{A}x\overline{U} +
\overline{A}b\overline{U}$ (G. Mayer, I. Warnke).
\item Exact Computation with leda real --- Theory and
Geometric Applications (K. Mehlhorn, St.
Schirra).
\item Numerical Verification Method for Solutions of
Nonlinear Hyperbolic Equations (T. Minamoto).
\item Geometric Series Bounds for the Local Errors of
Taylor Methods for Linear $n$-th-Order ODEs (M.
Neher).
\item Save Numerical Error Bounds for Solutions of
Nonlinear Elliptic Boundary Value Problems (M.
Plum).
\item Fast Verification Algorithms in MATLAB (S.
Rump).
\item The Linear Complementarity Problem with Interval
Data (U. Sch{\"a}fer).
\item Some Numerical Methods for Nonlinear Least
Squares Problems (St. Shakhno).
\item A New Insight of the Shortley--Weller
Approximation for Dirichlet Problems (T.
Yamamoto).
\item How Orthogonality is Lost in Krylov Methods
(\ldots{})
\end{itemize}",
keywords = "Computer arithmetic; Floating-point arithmetic;
Numerical calculations--Verification",
remark = "From the publisher: ``The usual `implementation' of
real numbers as floating point numbers on existing
computers has the well-known disadvantage that most of
the real numbers are not exactly representable in
floating point. Also the four basic arithmetic
operations can usually not be performed exactly. During
the last years research in different areas has been
intensified in order to overcome these problems. ({\em
LEDA-Library}, by K. Mehlhorn et al., {\em Exact
arithmetic with real numbers}, by A. Edalat et al.,
Symbolic algebraic methods, verification methods). The
latest development is the combination of
symbolic-algebraic methods and verification methods to
so-called hybrid methods. This book contains a
collection of worked out talks on these subjects given
during a Dagstuhl seminar at the Forschungszentrum fuer
Informatik, Schlo{\ss} Dagstuhl, Germany, presenting
the state of the art.''",
}
@InProceedings{Ammar:2001:SIC,
author = "A. Ammar and A. Al Kabbany and M. Youssef and A.
Amam",
booktitle = "{NRSC 2001}, Proceedings of the Eighteenth National
Radio Science Conference, 27--29 March 2001",
title = "A secure image coding scheme using residue number
system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "399--405",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/NRSC.2001.929397",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A secure image coding scheme using the residue number
system (RNS) is presented and tested. The proposed
scheme can be also used as the base for a full security
multiple access image communication system. Using RNS
with multiple look-up tables for \ldots{}",
}
@Article{Aoki:2001:ECA,
author = "Kazumaro Aoki and Fumitaka Hoshino and Tetsutaro
Kobayashi and Hiroaki Oguro",
title = "Elliptic Curve Arithmetic Using {SIMD}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2200",
pages = "235--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:06:44 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000235.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2200/22000235.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Armando:2001:PEM,
author = "A. Armando and S. Ranise",
title = "A Practical Extension Mechanism for Decision
Procedures: the Case Study of Universal {Presburger}
Arithmetic",
journal = j-J-UCS,
volume = "7",
number = "2",
pages = "124--??",
day = "28",
month = feb,
year = "2001",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Wed Feb 20 07:23:08 MST 2002",
bibsource = "http://www.jucs.org/jucs;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/jucs_7_2/a_practical_extension_mechanism",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@InProceedings{Arnold:2001:ACL,
author = "M. Arnold and T. Bailey and J. Cowles and C. Walter",
booktitle = "2001 {IEEE} Workshop on Signal Processing Systems",
title = "Analysis of complex {LNS} {FFTs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "58--69",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The complex-logarithmic number system (CLNS), which
represents each complex point in log/polar coordinates,
may be practical to implement the fast Fourier
transform (FFT). The roots of unity needed by the FFT
have exact representations in CLNS and \ldots{}",
}
@InProceedings{Arnold:2001:DFL,
author = "M. G. Arnold",
booktitle = "Proceedings of the Euromicro Symposium on Digital
Systems, Design, 2001",
title = "Design of a faithful {LNS} interpolator",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "336--345",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A design is given for a quadratic interpolator needed
by the logarithmic number system (LNS). Unlike previous
LNS designs that have attempted to produce results
consistently better than a floating-paint
representation of the same word size (32 bits),
\ldots{}",
}
@InProceedings{Arnold:2001:PLA,
author = "M. G. Arnold",
booktitle = "Proceedings of the {IEEE} Computer Society Workshop on
{VLSI, 19--20} April 2001",
title = "A pipelined {LNS} {ALU}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "155--161",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A new ALU design is proposed that is more economical
than a conventional Logarithmic Number System (LNS) ALU
for pipelined multiply-accumulate applications (such as
FIR filters). A novel interpolator that accepts both
positive and negative arguments \ldots{}",
}
@InProceedings{Arnold:2001:SMQ,
author = "M. G. Arnold and M. D. Winkel",
title = "A Single-Multiplier Quadratic Interpolator for {LNS}
Arithmetic",
crossref = "IEEE:2001:PII",
pages = "178--183",
year = "2001",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "logarithmic number system (LNS)",
summary = "Linear interpolation requires a single multiplication
but is significantly less accurate than quadratic
interpolation. The latter requires two multiplications.
Two novel quadratic interpolation schemes are shown
that approximate the functions \ldots{}",
}
@InProceedings{Arnold:2001:UFR,
author = "Mark G. Arnold and Colin Walter",
title = "Unrestricted Faithful Rounding is Good Enough for Some
{LNS} Applications",
crossref = "Burgess:2001:ISC",
pages = "237--246",
year = "2001",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Arnold.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
summary = "We propose to relax the restricted form of faithful
rounding used in prior 32 bit logarithmic number system
(LNS) implementations. Unrestricted faithful rounding
yields three- to six-fold savings in VLSI ROM size (or
four- to six-fold savings in \ldots{}).",
}
@Article{Atlamazoglou:2001:ALP,
author = "P. E. Atlamazoglou and H. T. Anastassiu and D. I.
Kaklamani",
title = "Application of literate-programming principles for the
description of a {FORTRAN 90} extension to quaternion
arithmetic",
journal = j-IEEE-APM,
volume = "43",
number = "4",
pages = "104--114",
month = aug,
year = "2001",
CODEN = "IAPMEZ",
DOI = "https://doi.org/10.1109/74.951564",
ISSN = "1045-9243 (print), 1558-4143 (electronic)",
ISSN-L = "1045-9243",
bibdate = "Mon Jul 5 14:39:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In an effort to effectively annotate and document a
FORTRAN 90 module that extends the language's
mathematical capabilities to the performance of
quaternion operations, the literate-programming
paradigm is adopted. The basic principles of this
paradigm are discussed through a short introduction to
the features of a specific literate-programming system
known as FWEB. This system is then employed for the
efficient presentation of the FORTRAN 90 quaternion
arithmetic module",
acknowledgement = ack-nhfb,
fjournal = "IEEE Antennas and Propagation Magazine",
}
@Article{Baidas:2001:FPB,
author = "Z. Baidas and A. D. Brown and A. C. Williams",
title = "Floating-point behavioral synthesis",
journal = j-IEEE-TRANS-CAD-ICS,
volume = "20",
number = "7",
pages = "828--839",
month = jul,
year = "2001",
CODEN = "ITCSDI",
ISSN = "0278-0070 (print), 1937-4151 (electronic)",
ISSN-L = "0278-0070",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computer-Aided Design of
Integrated Circuits and Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=43",
summary = "Traditionally, the data processed by a synthesized
digital design is fixed (occasionally variable) width
integer, and the functional units available are
concomitantly simple ladders, subtractors, multipliers,
multiplexers, and so on. The aims of \ldots{}",
}
@InProceedings{Bajard:2001:MMB,
author = "Jean-Claude Bajard and Laurent-Stephane Didier and
Peter Kornerup",
title = "Modular Multiplication and Base Extensions in Residue
Number Systems",
crossref = "Burgess:2001:ISC",
pages = "59--65",
year = "2001",
DOI = "https://doi.org/10.1109/ARITH.2001.930104",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bajard.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15; residue arithmetic; residue number system",
summary = "We present a new RNS modular multiplication for very
large operands. The algorithm is based on Montgomery's
(1985) method adapted to residue arithmetic. By
choosing the moduli of the RNS system reasonably large,
an effect corresponding to a \ldots{}",
}
@InProceedings{Balzola:2001:DAP,
author = "P. I. Balzola and M. J. Schulte and J. Ruan and J.
Glossner and E. Hokenek",
title = "Design Alternatives for Parallel Saturating
Multioperand Adders",
crossref = "IEEE:2001:PII",
pages = "172--177",
year = "2001",
bibdate = "Sun Mar 04 11:43:43 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2001-06.pdf",
acknowledgement = ack-nhfb,
}
@InCollection{Barraud:2001:SAR,
author = "Alain Barraud and Suzanne Lesecq and Nicolai
Christov",
booktitle = "Numerical analysis and its applications (Rousse,
2000)",
title = "From sensitivity analysis to random floating point
arithmetics---application to {Sylvester} equations",
volume = "1988",
publisher = pub-SV,
address = pub-SV:adr,
pages = "35--41",
year = "2001",
MRclass = "65F35 (93B40)",
MRnumber = "MR1938402",
bibdate = "Thu Nov 8 19:16:07 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
}
@Article{Bashagha:2001:NRS,
author = "A. E. Bashagha",
title = "Novel radix-$2$ $k$ square root module",
journal = "Circuits, Devices and Systems, IEE Proceedings [see
also IEE Proceedings G- Circuits, Devices and
Systems]",
volume = "148",
number = "4",
pages = "190--196",
month = aug,
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The conventional two's complement radix-$2$ k square
root algorithm requires a set of 2 k full precision
comparisons to generate all the 2 k possible values of
the partial remainder. The correct remainder is the
minimum \ldots{}",
}
@InProceedings{Beaumont-Smith:2001:PPA,
author = "Andrew Beaumont-Smith and Cheng-Chew Lim",
title = "Parallel Prefix Adder Design",
crossref = "Burgess:2001:ISC",
pages = "218--228",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Beaumont_Smith.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Misc{Beebe:2001:IFP,
author = "Nelson H. F. Beebe",
title = "{IEEE 754} floating-point test software",
howpublished = "World-Wide Web document.",
pages = "17",
day = "1",
month = dec,
year = "2001",
bibdate = "Sat Dec 01 16:34:39 2001",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.math.utah.edu/~beebe/software/ieee/",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@Article{Berg:2001:FVV,
author = "Christoph Berg and Christian Jacobi",
title = "Formal Verification of the {VAMP} Floating Point
Unit",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2144",
pages = "325--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:47 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2144.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2144/21440325.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2144/21440325.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Bickerstaff:2001:ACC,
author = "K'Andrea C. Bickerstaff and Earl E. {Swartzlander,
Jr.} and Michael J. Schulte",
title = "Analysis of Column Compression Multipliers",
crossref = "Burgess:2001:ISC",
pages = "33--39",
year = "2001",
bibdate = "Fri May 3 13:52:01 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://mesa.ece.wisc.edu/publications/cp_2001-02.pdf;
http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bickerstaff.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Blanck:2001:ERA,
author = "Jens Blanck",
title = "Exact Real Arithmetic Systems: Results of
Competition",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2064",
pages = "389--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:04:19 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640389.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2064/20640389.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Blum:2001:HRM,
author = "T. Blum and C. Paar",
title = "High-radix {Montgomery} modular exponentiation on
reconfigurable hardware",
journal = j-IEEE-TRANS-COMPUT,
volume = "50",
number = "7",
pages = "759--764",
month = jul,
year = "2001",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.936241",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 6 10:36:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=936241",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@MastersThesis{Boldo:2001:FAP,
author = "Sylvie Boldo",
title = "Formalisation, am{\'e}lioration et preuves
d'algorithmes en arithm{\'e}tique flottante. ({French})
[Formalization, improvement, and proofs of algorithms
in floating-point arithmetic]",
type = "{Master}'s thesis",
school = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "ix + 42",
day = "27",
month = jun,
year = "2001",
bibdate = "Tue Nov 23 09:48:04 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also issued as Report DEA No. 2001-03.",
URL = "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/DEA/DEA2001/DEA2001-03.ps.Z",
acknowledgement = ack-nhfb,
language = "French",
}
@InProceedings{Boldo:2001:MVT,
author = "Sylvie Boldo and Marc Daumas",
title = "A mechanically validated technique for extending the
available precision",
crossref = "Matthews:2001:CRT",
pages = "1299--1303",
year = "2001",
bibdate = "Tue Nov 23 10:22:31 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://perso.ens-lyon.fr/marc.daumas/SoftArith/BolDau01b.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Boldo:2001:PIA,
author = "Sylvie Boldo and Marc Daumas",
editor = "????",
booktitle = "{ASTI '2001\slash} {SYMPA 7}: 7{\`e}me Symposium en
Architectures Nouvelles de Machines, La Villette,
Paris, 24--27 avril, 2001",
title = "Performances d'implantations de l'addition en
pr{\'e}cision quad-double sur diff{\'e}rentes machines.
({French}) [Performance of implantations of quad-double
precision on different machines]",
publisher = "????",
address = "????",
pages = "??--??",
year = "2001",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Nov 23 10:28:39 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.laria.u-picardie.fr/~cerin/paris2001.html",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Breyer:2001:NGE,
author = "Laird Breyer and Gareth O. Roberts and Jeffrey S.
Rosenthal",
title = "A note on geometric ergodicity and floating-point
roundoff error",
journal = j-STAT-PROB-LETT,
volume = "53",
number = "2",
publisher = "Elsevier Science",
pages = "123--127",
day = "1",
month = jun,
year = "2001",
CODEN = "SPLTDC",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
MRclass = "60J10 (65C40)",
MRnumber = "MR1843871 (2002f:60138)",
MRreviewer = "Denis Talay",
bibdate = "Fri Nov 8 05:39:32 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
pagecount = "5",
}
@Misc{Briggs:2001:XER,
author = "Keith Briggs and Yannis Smaragdakis",
title = "{XR} --- Exact Real Arithmetic",
howpublished = "World-Wide Web document and software package.",
day = "01",
month = mar,
year = "2001",
bibdate = "Sat Apr 28 10:07:59 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From the overview: ``This is an implementation of
exact (or constructive) real arithmetic, as an
alternative to multiple-precision floating-point
(MPFP). An important distinction is that in MPFP one
sets the precision before starting a computation, and
then one cannot be sure of the final result. Interval
arithmetic is an improvement on this, but still not an
ideal solution because if the final interval is larger
than desired, there is no simple way to restart the
computation at higher precision. By contrast, in XR no
precision level is set in advance, and no computation
takes place until a final request takes place for some
output. Despite this, programming with XR is no
different from MPFP, except for the declaration of
critical variables as type `XR'.\par
The main aim is to produce a usably efficient
implementation, which can be easily interfaced with
existing C++ code. This contrasts with previous
implementations in functional languages (Haskell,
Miranda etc.), which, although theoretically important,
seem to be rather too slow for real use.\par
This code is designed as an add-on to Victor Shoup's
arbitrary-precision arithmetic package NTL, and
implements a new type XR, to complement NTL's ZZ and RR
integer and real types.",
URL = "http://www.btexact.com/people/briggsk2/XR.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Bruguera:2001:URC,
author = "Javier D. Bruguera and Tom{\'a}s Lang",
title = "Using the Reverse-Carry Approach for Double-Datapath
Floating-Point Addition",
crossref = "Burgess:2001:ISC",
pages = "203--210",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bruguera.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Bryant:2001:VAC,
author = "Randal E. Bryant and Yirng-An Chen",
title = "Verification of arithmetic circuits using binary
moment diagrams",
journal = j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
volume = "3",
number = "2",
pages = "137--155",
month = may,
year = "2001",
CODEN = "????",
ISSN = "1433-2779 (print), 1433-2787 (electronic)",
ISSN-L = "1433-2779",
bibdate = "Tue Nov 23 15:01:40 MST 2004",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1433-2779;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal on Software Tools for Technology
Transfer: STTT",
journal-URL = "http://link.springer.com/journal/10009",
}
@InProceedings{Burgess:2001:DIR,
author = "N. Burgess and C. Hinds",
booktitle = "Conference Record of the Thirty-Fifth Asilomar
Conference on Signals, Systems and Computers, 2001",
title = "Design issues in radix-$4$ {SRT} square root {\&}
divide unit",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1646--1650",
year = "2001",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper introduces a number of design issues not
covered in the open literature that arose during the
design of a radix-$4$ SRT divide/square root unit for a
vector processing chip. These include compression of
the partial remainder's m.s.b.'s, \ldots{}",
}
@InProceedings{Busaba:2001:IZD,
author = "Fadi Y. Busaba and Christopher A. Krygowski and Wen H.
Li and Eric M. Schwarz and Steven R. Carlough",
title = "The {IBM z900} Decimal Arithmetic Unit",
crossref = "Matthews:2001:CRT",
volume = "2",
pages = "1335--1339",
year = "2001",
DOI = "https://doi.org/10.1109/ACSSC.2001.987708",
bibdate = "Fri Nov 28 16:15:49 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "As the cost for adding functions to a processor
continues to decline, processor designs are including
many additional features. An example of this trend is
the appearance of graphics engines and compression
engines on midrange and even low end microprocessors.
One area that has the potential to capture chip real
estate is the decimal arithmetic engine because of its
importance in financial and business applications.
Studies show that 55\% of the numeric data stored on
commercial databases are in decimal format. Although
decimal arithmetic is supported in many software
languages it is not yet available on many
microprocessors. This paper details the decimal
arithmetic engine in the recently announced z900
microprocessor.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Cao:2001:HPA,
author = "Jun Cao and Belle W. Y. Wei and Jie Cheng",
title = "High-Performance Architectures for Elementary Function
Generation",
crossref = "Burgess:2001:ISC",
pages = "136--144",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Cao.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@InProceedings{Chen:2001:ADF,
author = "Chichyang Chen and Liang-An Chen and Jih-Ren Cheng",
title = "Architectural Design of a Fast Floating-Point
Multiplication-Add Fused Unit Using Signed-Digit
Addition",
crossref = "IEEE:2001:PES",
pages = "346--353",
year = "2001",
DOI = "https://doi.org/10.1109/DSD.2001.952324",
bibdate = "Fri Jun 24 10:45:22 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Signed digit (SD) addition is applied to the design of
a new floating-point (FLP) multiplication-add fused
(MAF) unit. This adoption, together with the proposed
two-step normalization method, can reduce the
three-word-length addition that is required in the
conventional FLP MAF unit to two-word-length addition.
Furthermore, the sign reversion of the intermediate
mantissa that requires three-word-length carry
propagation in the conventional MAF unit is replaced by
only single-word sign detection. These two improvements
can enhance the speed and cost of the MAF unit
significantly. With the use of the SD addition, the
circuit of the unit can be designed in a more regular
and simple manner, which is a property that is desired
in VLSI design. The proposed FLP MAF unit has been
designed and simulated by using Verilog hardware
description language. The functions of the deigned unit
are verified to be correct.",
acknowledgement = ack-nhfb,
}
@Article{Coppersmith:2001:FSS,
author = "Don Coppersmith",
title = "Finding Small Solutions to Small Degree Polynomials",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2146",
pages = "20--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:49 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2146.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2146/21460020.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2146/21460020.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@TechReport{Cowlishaw:2001:DAJ,
author = "Mike Cowlishaw",
title = "Decimal Arithmetic for {\tt java.math}: {JSR 13}
Public Review Draft",
type = "Technical Report",
number = "Version 1.33",
institution = "IBM UK Laboratories",
address = "Hursley, UK",
pages = "iii + 60",
day = "16",
month = jul,
year = "2001",
bibdate = "Fri May 20 14:37:16 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www2.hursley.ibm.com/jsr13/jsr13spec.pdf",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "Describes a proposal for arbitrary-precision decimal
floating-point arithmetic in Java.",
}
@InProceedings{Cowlishaw:2001:DFP,
author = "Michael F. Cowlishaw and Eric M. Schwarz and Ronald M.
Smith and Charles F. Webb",
title = "A Decimal Floating-Point Specification",
crossref = "Burgess:2001:ISC",
pages = "147--154",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Cowlishaw.pdf;
http://www2.hursley.ibm.com/decimal/arith15-foils.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15; decimal floating-point arithmetic",
}
@Misc{Cuyt:2001:ARI,
author = "A. Cuyt and P. Kuterna and B. Verdonk and J.
Vervloet",
title = "{Arithmos}: a reliable integrated computational
environment",
howpublished = "World Wide Web document.",
year = "2001",
bibdate = "Wed Nov 24 07:50:59 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://win-www.uia.ac.be/u/cant/arithmos/index.html",
acknowledgement = ack-nhfb,
}
@Article{Cuyt:2001:REC,
author = "Annie Cuyt and Brigitte Verdonk and S. Becuwe and
Peter Kuterna",
title = "A Remarkable Example of Catastrophic Cancellation
Unraveled",
journal = j-COMPUTING,
volume = "66",
number = "3",
pages = "309--320",
year = "2001",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65-04 65G10 65Y99",
bibdate = "Thu Jul 12 05:20:09 MDT 2001",
bibsource = "http://link.springer-ny.com/link/service/journals/00607/tocs/t1066003.htm;
http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/journals/00607/bibs/1066003/10660309.htm;
http://link.springer-ny.com/link/service/journals/00607/papers/1066003/10660309.pdf",
abstract = "In this paper we reinvestigate a well-known expression
first published in [7], which is often used to
illustrate catastrophic cancellation as well as the
fact that identical output in different precisions does
not imply reliability. The purpose of revisiting this
expression is twofold. First, we show in Section 2 that
the effect of the cancellation is very different on
different IEEE 754 compliant platforms, and we unravel
the underlying (hardware) reasons which are unknown to
many numerical analysts. Besides illustrating
cancellation, this expression also counters the common
misbelief among many numerical analysts that a same
program will deliver identical results on all IEEE
conforming systems. Second, in Section 3 we use,
illustrate and comment upon the cross-platform
didactical tool Arithmetic Explorer developed at the
University of Antwerp, by means of which we performed
the bit level analysis of the expression evaluation
under investigation on the different machines. We
believe that this tool, which is freely available from
the authors, can be of use to all of us teaching a
first numerical analysis course.",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Misc{Darcy:2001:BLH,
author = "Joseph D. Darcy",
title = "{Borneo} Language Homepage",
howpublished = "World Wide Web site.",
year = "2001",
bibdate = "Mon May 06 09:06:04 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jddarcy.org/Borneo",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; IEEE 754; Java",
}
@Misc{Darcy:2001:DLS,
author = "Joseph D. Darcy",
title = "Designing Language Support for {IEEE 754}",
howpublished = "IEEE 754 Revision Committee meeting, October 18,
2001.",
year = "2001",
bibdate = "Mon May 06 09:16:52 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "50 slides.",
URL = "http://grouper.ieee.org/groups/754/meeting-materials/2001-10-18-langdesign.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Darcy:2001:WEU,
author = "Joseph D. Darcy",
title = "What Everybody Using the {Java\TM} Programming
Language Should Know About Floating-Point Arithmetic",
crossref = "Anonymous:2001:JJ",
pages = "??--??",
year = "2001",
bibdate = "Mon May 06 09:14:05 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "51 slides.",
URL = "http://java.sun.com/people/darcy/JavaOne/2001/1789darcy.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Daumas:2001:CVP,
author = "Marc Daumas and Claire Moreau-Finot and Laurent
Thery",
title = "Computer validated proofs of a toolset for adaptable
arithmetic",
type = "Research report",
number = "4095",
institution = "Institut National de Recherche en Informatique et en
Automatique",
address = "Le Chesnay, France",
year = "2001",
bibdate = "Wed Nov 24 10:50:24 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Daumas:2001:GLF,
author = "Marc Daumas and Laurence Rideau and Laurent
Th{\'e}ry",
title = "A Generic Library for Floating-Point Numbers and Its
Application to Exact Computing",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2152",
pages = "169--184",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRclass = "68T15 (65G50)",
MRnumber = "MR1907603",
bibdate = "Sat Feb 2 13:05:56 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2152.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2152/21520169.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2152/21520169.pdf;
https://hal.archives-ouvertes.fr/hal-00157285",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{deDinechin:2001:SIM,
author = "Florent de Dinechin and Arnaud Tisserand",
title = "Some Improvements on Multipartite Table Methods",
crossref = "Burgess:2001:ISC",
pages = "128--135",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Dinechin.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@TechReport{Defour:2001:CREa,
author = "David Defour and Florent de Dinechin and Jean-Michel
Muller",
title = "Correctly rounded exponential function in double
precision arithmetic",
type = "Rapport de recherche",
number = "RR-4231",
institution = "INRIA Rhone-Alpes",
address = "ZIRST, 655 Avenue de l'Europe, Montbonnot, 38334 Saint
Ismier cedex, France",
month = jul,
year = "2001",
bibdate = "Sat Jun 25 11:10:46 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4231.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4231.ps.gz;
http://www.inria.fr/rrrt/rr-4231.html",
abstract = "We present an algorithm for implementing correctly
rounded exponentials in double-precision floating point
arithmetic. This algorithm is based on floating-point
operations in the widespread IEEE-754 standard, and is
therefore more efficient than those using
multiprecision arithmetic, while being fully portable.
It requires a table of reasonable size and IEEE-754
double precision multiplications and additions. In a
preliminary implementation, the overhead due to correct
rounding is a 2.3 times slowdown when compared to the
standard library function.",
acknowledgement = ack-nhfb,
}
@InProceedings{Defour:2001:CREb,
author = "David Defour and Florida de Dinechin and Jean-Michel
Muller",
title = "Correctly rounded exponential function in double
precision arithmetic",
crossref = "Luk:2001:ASP",
pages = "156--167",
year = "2001",
bibdate = "Fri Jun 24 14:43:41 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bookstore.spie.org/index.cfm?fuseaction=DetailPaper&ProductId=448644&coden=PSISDG",
abstract = "We present an algorithm for implementing correctly
rounded exponentials in double-precision floating point
arithmetic. This algorithm is based on floating-point
operations in the widespread EEE-754 standard, and is
therefore more efficient than those using
multiprecision arithmetic, while being fully portable.
It requires a table of reasonable size and IEEE-754
double precision multiplications and additions. In a
preliminary implementation, the overhead due to correct
rounding is a 6 times slowdown when compared to the
standard library function.",
acknowledgement = ack-nhfb,
}
@TechReport{Defour:2001:NRRa,
author = "David Defour and Peter Kornerup and Jean-Michel Muller
and Nathalie Revol",
title = "A new range reduction algorithm",
type = "Research Report",
number = "{LIP RR 2001-33, INRIA RR-4267}",
institution = "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "Lyon, France",
pages = "13",
year = "2001",
bibdate = "Sat Jun 25 08:52:06 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2001/RR2001-33.ps.Z;
ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4267.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4267.ps.gz;
http://www.inria.fr/rrrt/rr-4267.html",
abstract = "Range reduction is a key point for getting accurate
elementary function routines. We introduce a new
algorithm that is fast for input arguments belonging to
the most common domains, yet accurate over the full
double precision range.",
acknowledgement = ack-nhfb,
keywords = "range reduction",
}
@InProceedings{Defour:2001:NRRb,
author = "David Defour and Peter Kornerup and Jean-Michel Muller
and Nathalie Revol",
title = "A new range reduction algorithm",
crossref = "Matthews:2001:CRT",
pages = "??--??",
year = "2001",
bibdate = "Fri Jun 24 12:12:10 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.imada.sdu.dk/~kornerup/papers/RR2.pdf",
abstract = "Range reduction is a key point for getting accurate
elementary function routines. We introduce a new
algorithm that is fast for input arguments belonging to
the most common domains, yet accurate over the full
double precision range.",
acknowledgement = ack-nhfb,
keywords = "range reduction",
pagecount = "11",
}
@InProceedings{DelRe:2001:IDF,
author = "A. {Del Re} and A. Nannarelli and M. Re",
booktitle = "Conference Record of the Thirty-Fifth Asilomar
Conference on Signals, Systems and Computers, 2001",
title = "Implementation of digital filters in carry-save
residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1309--1313",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.2001.987702",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this work, we present the implementation of a
finite impulse response (FIR) filter in the residue
number system (RNS), in which we use a carry-save
scheme in the binary representation of the residues to
speed-up modular additions. We compare the \ldots{}",
}
@Unpublished{Demmel:2001:CAF,
author = "J. Demmel and Ben Diament and W. Kahan and Plamen Koev
and Ming Gu and Stan Eisenstat and Ivan Slapni{\v{c}}ar
and Kresimir Veseli{\'c} and Zlatko Drma{\v{c}}",
title = "The Complexity of Accurate Floating Point Computation
and Symbolic Computing, or, Can we do Numerical Linear
Algebra In Polynomial Time?",
pages = "31",
year = "2001",
bibdate = "Mon Apr 25 06:47:21 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Lecture slides",
URL = "http://www.cs.berkeley.edu/~demmel/ISSAC2001_2.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Dhong:2001:ACR,
author = "Sang Hoo Dhong and Harm Peter Hofstee and Christian
Jacobi and Silvia Melitta Mueller and Hwa-Joon Oh",
title = "Apparatus for controlling rounding modes in single
instruction multiple data ({SIMD}) floating-point
units",
howpublished = "US Patent 7447725",
day = "04",
month = dec,
year = "2001",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7444367/fulltext.html",
abstract = "An apparatus for controlling rounding modes in a
single instruction multiple data (SIMD) floating-point
unit is disclosed. The SIMD floating-point unit
includes a floating-point status-and-control register
(FPSCR) having a first rounding mode bit field and a
second rounding mode bit field. The SIMD floating-point
unit also includes means for generating a first slice
and a second slice. During a floating-point operation,
the SIMD floating-point unit concurrently performs a
first rounding operation on the first slice and a
second rounding operation on the second slice according
to a bit in the first rounding mode bit field and a bit
in the second rounding mode bit field within the FPSCR,
respectively.",
acknowledgement = ack-nhfb,
}
@Misc{Dickinson:2001:IRB,
author = "Patrick Dickinson",
title = "Instant Replay: Building a Game Engine with
Reproducible Behavior",
howpublished = "Web site",
day = "13",
month = jul,
year = "2001",
bibdate = "Mon Dec 04 07:04:15 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.gamedeveloper.com/design/instant-replay-building-a-game-engine-with-reproducible-behavior#close-modal",
acknowledgement = ack-nhfb,
remark = "Comments on problems of rerunning games on different
platforms where floating-point issues produce differing
outcomes, See also \cite{Fiedler:2010:GGF}.",
}
@InProceedings{Dimitrov:2001:UMD,
author = "V. S. Dimitrov and J. Eskritt and L. Imbert and G. A.
Jullien and W. C. Miller",
title = "The Use of the Multi-Dimensional Logarithmic Number
System in {DSP} Applications",
crossref = "Burgess:2001:ISC",
pages = "247--256",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Dimitrov.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Drmac:2001:AQS,
author = "Zlatko Drmac and Elizabeth R. Jessup",
title = "On Accurate Quotient Singular Value Computation in
Floating-Point Arithmetic",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "3",
pages = "853--873",
month = jul,
year = "2001",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Wed Oct 23 08:36:30 MDT 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31054",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Fernandez:2001:IOD,
author = "P. G. Fernandez and J. Ramirez and A. Garcia and L.
Parrilla and A. Lloris",
booktitle = "The 8th {IEEE} International Conference on
Electronics, Circuits and Systems, {ICECS 2001}",
title = "Implementation of the one dimensional discrete cosine
transform using the residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "433--436",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICECS.2001.957772",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper shows the implementation of the one
dimensional discrete cosine transform (1D-DCT) based on
the residue number system (RNS). The 1D-DCT has been
derived by,the application of a previously developed
scaled fast cosine transform (FCT) \ldots{}",
}
@PhdThesis{Finot-Moreau:2001:PAU,
author = "Claire Finot-Moreau",
title = "Preuves et algorithmes utilisant l'arithm{\'e}tique
flottante normalis{\'e}e {IEEE}",
type = "{Ph.D.} thesis",
school = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "Lyon, France",
month = jul,
year = "2001",
bibdate = "Sat Apr 01 08:46:03 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Flynn:2001:ACA,
author = "Michael J. Flynn and Stuart F. Oberman",
title = "Advanced computer arithmetic design",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 325",
year = "2001",
ISBN = "0-471-41209-0",
ISBN-13 = "978-0-471-41209-0",
LCCN = "TK7895.A65 F59 2001",
bibdate = "Tue May 07 05:20:32 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From the preface: ``The book is not written as a
textbook, but rather, it is written with computer
designers and researchers in mind. Therefore its focus
is on {\em design}, not on other aspects of computer
arithmetic, such as number systems, representation, or
precision.'' Chapter 12, Rational Arithmetic, treats
the application of continued fractions to the
computation of elementary functions.",
tableofcontents = "Preface \\
Acknowledgments \\
Notation \\
1. Integer Addition \\
2. Floating-Point Addition \\
3. Multiplication with Partially Redundant Multiples
\\
4. Multiplier Topologies \\
5. Technology Scaling Effects on Multipliers \\
6. Design Issues in Division \\
7. Minimizing the Complexity of SRT Tables \\
8. Very High-Radix Division \\
9. Using a Multiplier for Function Approximation \\
10. FUPA [Floating-point unit-cost performance analysis
metric] \\
11. High-Speed Clocking Using Wave Pipelining \\
12. Rational Arithmetic \\
Bibliography \\
Index",
}
@Article{Galan-Simon:2001:MLD,
author = "F. Javier Gal{\'a}n-Sim{\'o}n and Edgar
Mart{\'\i}nez-Moro and Juan G. Tena-Ayuso",
title = "Majority-Logic-Decodable Cyclic Arithmetic-Modular
{AN}-Codes in $1$, $2$, and {$L$} Steps",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2260",
pages = "128--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:45 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2260.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2260/22600128.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2260/22600128.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Gallant:2001:FPM,
author = "Robert P. Gallant and Robert J. Lambert and Scott A.
Vanstone",
title = "Faster Point Multiplication on Elliptic Curves with
Efficient Endomorphisms",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2139",
pages = "190--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:41 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2139.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2139/21390190.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2139/21390190.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Gelbukh:2001:ZHL,
author = "Alexander Gelbukh and Grigori Sidorov",
title = "{Zipf} and {Heaps Laws}' Coefficients Depend on
Language",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2004",
pages = "332--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:03:22 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Gil:2001:SAT,
author = "Joseph (Yossi) Gil",
title = "Subtyping arithmetical types",
journal = j-SIGPLAN,
volume = "36",
number = "3",
pages = "276--289",
month = mar,
year = "2001",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sun Dec 14 09:18:23 MST 2003",
bibsource = "http://portal.acm.org/;
http://www.acm.org/pubs/contents/proceedings/series/popl/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acm.org/pubs/articles/proceedings/plan/360204/p276-gil/p276-gil.pdf;
http://www.acm.org/pubs/citations/proceedings/plan/360204/p276-gil/",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@InProceedings{Gok:2001:EIM,
author = "M. Gok and M. J. Schulte and P. I. Balzola",
title = "Efficient Integer Multiplication Overflow Detection
Circuits",
crossref = "Matthews:2001:CRT",
pages = "1661--1665",
year = "2001",
bibdate = "Sun Mar 04 11:45:08 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2001-07.pdf",
acknowledgement = ack-nhfb,
}
@Article{Goubault:2001:SAP,
author = "Eric Goubault",
title = "Static Analyses of the Precision of Floating-Point
Operations",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2126",
pages = "234--259",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRnumber = "MR2051233",
bibdate = "Sat Feb 2 13:05:28 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2126.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2126/21260234.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2126/21260234.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Gowland:2001:SEA,
author = "Paul Gowland and David Lester",
title = "A Survey of Exact Arithmetic Implementations",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2064",
pages = "30--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:04:19 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640030.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2064/20640030.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Grossschadl:2001:BSU,
author = "J. Gro{\ss}sch{\"a}dl",
title = "A Bit-Serial Unified Multiplier Architecture for
Finite Fields {GF$ (p) $} and {GF$ (2^m) $}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2162",
pages = "202--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:06:06 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620202.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2162/21620202.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Groza:2001:HRF,
author = "V. Z. Groza",
title = "High-resolution floating-point {ADC}",
journal = j-IEEE-TRANS-INSTRUM-MEAS,
volume = "50",
number = "6",
pages = "1822--1829",
month = dec,
year = "2001",
CODEN = "IEIMAO",
ISSN = "0018-9456 (print), 1557-9662 (electronic)",
ISSN-L = "0018-9456",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Instrumentation and Measurement",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19",
summary = "Floating-point analog-to-digital converters (FP-ADC)
are used for acquiring signals within a high dynamic
range. The quantization range of FP-ADCs is several
orders of magnitude higher than that of a fixed-point
analog-to-digital converter (ADC). \ldots{}",
}
@Article{Gunther:2001:SAK,
author = "Christian G{\"u}nther and Tanja Lange and Andreas
Stein",
title = "Speeding up the Arithmetic on {Koblitz} Curves of
Genus Two",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2012",
pages = "106--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:03:30 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2012.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2012/20120106.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2012/20120106.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Hasan:2001:ECM,
author = "M. A. Hasan",
title = "Efficient Computation of Multiplicative Inverses for
Cryptographic Applications",
crossref = "Burgess:2001:ISC",
pages = "66--72",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Hasan.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Hayes:2001:TB,
author = "Brian Hayes",
title = "Third Base",
journal = j-AM-SCI,
volume = "89",
number = "6",
pages = "490--495",
month = nov # "\slash " # dec,
year = "2001",
CODEN = "AMSCAC",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Tue Nov 08 08:06:17 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.americanscientist.org/content/AMSCI/AMSCI/ArticleAltFormat/20035214317_146.pdf",
abstract = "People count by tens and machines count by twos that
pretty much sums up the way we do arithmetic on this
planet. But there are countless other ways to count.
Here I want to offer three cheers for base 3, the
ternary system. The numerals in this sequence beginning
0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101 are not as
widely known or widely used as their decimal and binary
cousins, but they have charms all their own. They are
the Goldilocks choice among numbering systems: When
base 2 is too small and base 10 is too big, base 3 is
just right.",
acknowledgement = ack-nhfb,
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
keywords = "ternary arithmetic",
}
@Article{He:2001:UAA,
author = "Yun He and Chris H. Q. Ding",
title = "Using Accurate Arithmetics to Improve Numerical
Reproducibility and Stability in Parallel
Applications",
journal = j-J-SUPERCOMPUTING,
volume = "18",
number = "3",
pages = "259--277",
month = mar,
year = "2001",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1023/A:1008153532043",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Wed Jul 6 12:13:17 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=18&issue=3;
http://www.wkap.nl/issuetoc.htm/0920-8542+18+3+2001;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=18&issue=3&spage=259;
http://www.wkap.nl/oasis.htm/323815",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Hesse:2001:DUT,
author = "William Hesse",
title = "Division Is in Uniform {TC$^0$}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2076",
pages = "104--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Feb 1 09:17:25 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2076.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2076/20760104.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2076/20760104.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Hida:2001:AQD,
author = "Yozo Hida and Xiaoye S. Li and David H. Bailey",
title = "Algorithms for Quad-Double Precision Floating Point
Arithmetic",
crossref = "Burgess:2001:ISC",
pages = "155--162",
year = "2001",
DOI = "https://doi.org/10.1109/ARITH.2001.930115",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Hida.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@TechReport{Hlavacs:2001:IAN,
author = "H. Hlavacs and C. W. Ueberhuber",
title = "Improving the Accuracy of Numerical Integration",
type = "Technical report",
number = "TR 2001-06",
institution = "Aurora: Advanced Models, Applications and Software
Systems for High Performance Computing",
address = "European Centre for Parallel Computing at Vienna
Nordbergstra{\ss}e 15/C/3, A-1090 Vienna, Austria",
pages = "i + 14",
year = "2001",
bibdate = "Tue Nov 22 06:22:21 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.vcpc.univie.ac.at/projects/aurora/reports/auroratr2001-06.ps.gz;
http://citeseer.ist.psu.edu/hlavacs01improving.html",
abstract = "In this report, a method for reducing the effect of
round-off errors occurring in one-dimensional
integration is presented. The new method, applicable to
uneven integrand functions, is based on an extended
version of Kahan--Babuska summation.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Book{Hsu:2001:CAS,
author = "John Y. Hsu",
title = "Computer Architecture: Software Aspects, Coding,
Hardware",
publisher = pub-CRC,
address = pub-CRC:adr,
pages = "427",
year = "2001",
ISBN = "0-8493-1026-1, 1-351-83604-8, 1-4200-4110-X (e-book)",
ISBN-13 = "978-0-8493-1026-3, 978-1-351-83604-3,
978-1-4200-4110-1 (e-book)",
LCCN = "A76.9.A73 H758 2001",
bibdate = "Fri Jan 19 15:47:59 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/java2000.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib;
https://www.math.utah.edu/pub/tex/bib/virtual-machines.bib;
https://www.math.utah.edu/pub/tex/bib/visual-instruction-set.bib",
price = "US\$89.95, UK\pounds 59.99",
abstract = "With the new developments in computer architecture,
fairly recent publications can quickly become outdated.
Computer Architecture: Software Aspects, Coding, and
Hardware takes a modern approach. This comprehensive,
practical text provides that critical understanding of
a central processor by clearly detailing fundamentals,
and cutting edge design features. With its balanced
software/hardware perspective and its description of
Pentium processors, the book allows readers to acquire
practical PC software experience. The text presents a
foundation-level set of ideas, design concepts, and
applications that fully meet the requirements of
computer organization and architecture courses. The
book features a ``bottom up'' computer design approach,
based upon the author's thirty years experience in both
academe and industry. By combining computer engineering
with electrical engineering, the author describes how
logic circuits are designed in a CPU. The extensive
coverage of a microprogrammed CPU and new processor
design features gives the insight of current computer
development. Computer Architecture: Software Aspects,
Coding, and Hardware presents a comprehensive review of
the subject, from beginner to advanced levels. Topics
include: * Two's complement numbers * Integer overflow
* Exponent overflow and underflow * Looping *
Addressing modes * Indexing * Subroutine linking * I/O
structures * Memory mapped I/O * Cycle stealing *
Interrupts * Multitasking * Microprogrammed CPU *
Multiplication tree * Instruction queue * Multimedia
instructions * Instruction cache * Virtual memory *
Data cache * Alpha chip * Interprocessor communications
* Branch prediction * Speculative loading * Register
stack * JAVA virtual machine * Stack machine
principles.",
acknowledgement = ack-nhfb,
keywords = "Compaq/DEC Alpha; floating-point arithmetic; Intel
x86; Java Virtual Machine; multimedia instructions;
Pentium",
libnote = "Not yet in my library.",
tableofcontents = "Number Systems \\
Basic Computer Principles \\
Assembly Language Principles \\
Computer Architecture--General Features \\
Microprogrammed CPU Design \\
Superscalar Machine Principles \\
Vector and Multiple-Processor Machines \\
Processor Design Case Studies \\
Stack Machine Principles",
}
@Article{Hur:2001:GRO,
author = "Namhyun Hur and James H. Davenport",
title = "A Generic Root Operation for Exact Real Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2064",
pages = "82--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:04:19 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640082.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2064/20640082.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Book{ISO:2001:IIIc,
author = "{ISO}",
title = "{ISO\slash IEC 10967-2}: {Information} technology ---
{Language} independent arithmetic --- {Part} 2:
{Elementary} numerical functions",
publisher = pub-ISO,
address = pub-ISO:adr,
pages = "x + 177",
day = "15",
month = aug,
year = "2001",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 15 11:09:44 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://standards.iso.org/ittf/PubliclyAvailableStandards/c024427_ISO_IEC_10967-2_2001(E).zip;
http://www.iso.ch/cate/d24427.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Jacobi:2001:FVT,
author = "Christian Jacobi",
title = "Formal verification of a theory of {IEEE} rounding",
crossref = "Boulton:2001:TPH",
pages = "239--254",
year = "2001",
bibdate = "Wed Nov 24 11:55:24 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatics.ed.ac.uk/publications/online/0046/b239.pdf",
acknowledgement = ack-nhfb,
}
@Article{Jamil:2001:CBN,
author = "T. Jamil",
title = "The complex binary number system",
journal = j-IEEE-POT,
volume = "20",
number = "5",
pages = "39--41",
month = dec,
year = "2001",
CODEN = "IEPTDF",
DOI = "https://doi.org/10.1109/45.983342",
ISSN = "0278-6648 (print), 1558-1772 (electronic)",
ISSN-L = "0278-6648",
bibdate = "Sat Dec 04 10:43:52 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Conversion algorithms and arithmetic procedures for a
$ ( - 1 + j) $-base binary number allow a given complex
number to be represented as one unit. This should
simplify the operations involving complex numbers in
today's microprocessors. With the division process
secure, we can implement the usual algorithms for
calculating functions and processes such as logarithms,
exponentials and trigonometric functions Currently,
work is underway to write Java applets for the
algorithms. We are planning to design an arithmetic
unit based on the new binary system which will then be
implemented using field programmable gate arrays",
acknowledgement = ack-nhfb,
fjournal = "IEEE Potentials",
}
@InProceedings{Jeong:2001:OIO,
author = "Cheol-Ho Jeong and Woo-Chan Park and Tack-Don Han and
Sang-Woo Kim and Moon-Key Lee",
title = "In-Order Issue Out-of-Order Execution Floating-Point
Coprocessor for {CalmRISC32}",
crossref = "Burgess:2001:ISC",
pages = "195--202",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Jeong.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@TechReport{Kahan:2001:NSF,
author = "W. Kahan",
title = "Names for Standardized Floating-Point Formats",
institution = "Mathematics Department and Electrical Engineering and
Computer Science Department, University of California,
Berkeley",
address = "Berkeley, CA, USA",
pages = "4",
day = "17",
month = may,
year = "2001",
bibdate = "Fri May 03 12:23:25 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/Names.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:2001:SFP,
author = "W. Kahan",
title = "{SRTEST}: a {Fortran} program to test any {SRT}
divider's logic for quotient-digit selection",
howpublished = "World-Wide Web document",
day = "6",
month = aug,
year = "2001",
bibdate = "Mon Apr 25 17:47:53 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/srtest/",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@TechReport{Kahan:2001:WVT,
author = "W. Kahan",
title = "What has the Volume of a Tetrahedron to do with
Computer Programming Languages?",
institution = "Department of Mathematics and Department of Electrical
Engineering and Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
day = "20",
month = apr,
year = "2001",
bibdate = "Fri May 03 13:36:17 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/VtetLang.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kaivola:2001:PEL,
author = "Roope Kaivola and Katherine Kohatsu",
title = "Proof Engineering in the Large: Formal Verification of
{Pentium\reg4} Floating-Point Divider",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2144",
pages = "196--211",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:47 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2144.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2144/21440196.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2144/21440196.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Kao:2001:MRE,
author = "Ming-Yang Kao and Jie Wang",
title = "Minimizing roundoff errors of prefix sums via dynamic
construction of {Huffman} trees",
journal = j-THEOR-COMP-SCI,
volume = "262",
number = "1--2",
pages = "101--115",
day = "6",
month = jul,
year = "2001",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Jul 25 18:49:25 MDT 2001",
bibsource = "http://www.elsevier.com/locate/issn/03043975;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.nl/gej-ng/10/41/16/204/21/26/abstract.html;
http://www.elsevier.nl/gej-ng/10/41/16/204/21/26/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "accurate floating-point summation",
}
@Article{Khachatrian:2001:FMI,
author = "Gurgen H. Khachatrian and Melsik K. Kuregian and Karen
R. Ispiryan and James L. Massey",
title = "Fast Multiplication of Integers for Public-Key
Applications",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2259",
pages = "245--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:44 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590245.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2259/22590245.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Kim:2001:AEE,
author = "Hyun-Sung Kim and Kee-Young Yoo",
title = "Area Efficient Exponentiation Using Modular
Multiplier\slash Squarer in {GF$ (2^m) $}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2108",
pages = "262--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:08 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2108.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2108/21080262.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2108/21080262.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{King:2001:IIE,
author = "Brian King",
title = "An Improved Implementation of Elliptic Curves over
{GF} (2) when Using Projective Point Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2259",
pages = "134--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:44 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590134.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2259/22590134.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Kistermann:2001:CHU,
author = "Friedrich W. Kistermann",
title = "Calculators: How to Use the {Schickard} Calculator",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "23",
number = "1",
pages = "80--85",
month = jan # "\slash " # mar,
year = "2001",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/85.929917",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Thu Jul 12 06:23:02 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
URL = "http://dlib.computer.org/an/books/an2001/pdf/a1080.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Ann. Hist. Comput.",
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}
@InProceedings{Knowles:2001:FA,
author = "Simon Knowles",
title = "A Family of Adders",
crossref = "Burgess:2001:ISC",
pages = "277--284",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Knowles.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@InProceedings{Koc-Sahan:2001:STA,
author = "N. Koc-Sahan and J. Schlessman and M. J. Schulte",
title = "Symmetric Table Addition Methods for Neural Network
Approximations",
crossref = "Luk:2001:ASP",
pages = "126--133",
year = "2001",
bibdate = "Sun Mar 04 11:40:20 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2001-03.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kosaraju:2001:MAM,
author = "S. Rao Kosaraju",
title = "Mesh Algorithms for Multiplication and Division",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2228",
pages = "17--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:14 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2228.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2228/22280017.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2228/22280017.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Koy:2001:SLRb,
author = "Henrik Koy and Claus Peter Schnorr",
title = "Segment {LLL}-Reduction with Floating Point
Orthogonalization",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2146",
pages = "81--96",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRclass = "11H55 (11Y16)",
MRnumber = "MR1903889 (2003f:11096)",
bibdate = "Sat Feb 2 13:05:49 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2146.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2146/21460081.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2146/21460081.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Kramer:2001:AFE,
author = "Walter Kr{\"a}mer and Armin Bantle",
title = "Automatic forward error analysis for floating point
algorithms",
journal = j-RELIABLE-COMPUTING,
volume = "7",
number = "4",
pages = "321--340",
year = "2001",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
MRclass = "65G40 (65G50)",
MRnumber = "MR1843023 (2002d:65046)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "1952--2014 (WK)",
fjournal = "Reliable Computing. An International Journal Devoted
to Reliable Mathematical Computations Based on Finite
Representations and Guaranteed Accuracy",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Kreinovich:2001:INB,
author = "Vladik Kreinovich",
title = "{Itanium}'s New Basic Operation of Fused Multiply-Add:
Theoretical Explanation and Theoretical Challenge",
journal = j-SIGACT,
volume = "32",
number = "1",
pages = "115--117",
year = "2001",
CODEN = "SIGNDM",
ISSN = "0163-5700 (print), 1943-5827 (electronic)",
ISSN-L = "0163-5700",
bibdate = "Sat Dec 06 15:20:39 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.utep.edu/vladik/2000/tr00-42.pdf;
http://www.cs.utep.edu/vladik/2000/tr00-42.ps.gz",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGACT News",
issue = "118",
journal-URL = "http://dl.acm.org/citation.cfm?id=J697",
}
@InProceedings{Krishnan:2001:PEM,
author = "Shankar Krishnan and Mark Foskey and Tim Culver and
John Keyser and Dinesh Manocha",
title = "{PRECISE}: efficient multiprecision evaluation of
algebraic roots and predicates for reliable geometric
computation",
crossref = "ACM:2001:PSA",
pages = "274--283",
year = "2001",
DOI = "https://doi.org/10.1145/378583.378693",
bibdate = "Fri Jan 06 07:53:04 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Many geometric problems like generalized Voronoi
diagrams, medial axis computations and boundary
evaluation involve computation and manipulation of
non-linear algebraic primitives like curves and
surfaces. The algorithms designed for these problems
make decisions based on signs of geometric predicates
or on the roots of polynomials characterizing the
problem. The reliability of the algorithm depends on
the accurate evaluation of these signs and roots. In
this paper, we present a {\em naive precision-driven
computational model\/} to perform these computations
reliably and demonstrate its effectiveness on a certain
class of problems like sign of determinants with
rational entries, boundary evaluation and curve
arrangements. We also present a novel algorithm to
compute all the roots of a univariate polynomial to any
desired accuracy. The computational model along with
the underlying number representation, precision-driven
arithmetic and all the algorithms are implemented as
part of a stand-alone software library, PRECISE.",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; interval arithmetic;
multiple-precision arithmetic; PRECISE",
}
@InProceedings{Lang:2001:BRZ,
author = "Tom{\'a}s Lang and Jean-Michel Muller",
title = "Bounds on Runs of Zeros and Ones for Algebraic
Functions",
crossref = "Burgess:2001:ISC",
pages = "13--22",
year = "2001",
bibdate = "Fri May 3 13:52:01 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lang.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@InProceedings{Lang:2001:CRR,
author = "Tom{\'a}s Lang and Elisardo Antelo",
title = "Correctly Rounded Reciprocal Square-Root by Digit
Recurrence and Radix-$4$ Implementation",
crossref = "Burgess:2001:ISC",
pages = "83--93",
year = "2001",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lang_Antelo.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15; correct rounding; floating-point
arithmetic",
summary = "We present a reciprocal square-root algorithm by digit
recurrence and selection by a staircase function, and
the radix-$4$ implementation. As similar algorithms for
division and square-root, the results are obtained
correctly rounded in a \ldots{}",
}
@Article{Langlois:2001:ALC,
author = "Philippe Langlois",
title = "Automatic Linear Correction of Rounding Errors",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "3",
pages = "515--539",
month = jun,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021919329342",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=515",
abstract = "A new automatic method to correct the first-order
effect of floating point rounding errors on the result
of a numerical algorithm is presented. A correcting
term and a confidence threshold are computed using
algorithmic differentiation, computation of elementary
rounding error and running error analysis. Algorithms
for which the accuracy of the result is not affected by
higher order terms are identified. The correction is
applied to the final result or to sensitive
intermediate results to improve the accuracy of the
computed result and\slash or the stability of the
algorithm.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "automatic error analysis; correct rounding;
floating-point arithmetic; rounding errors",
}
@InProceedings{Laurent:2001:UFV,
author = "O. Laurent and P. Michel and V. Wiels",
title = "Using formal verification techniques to reduce
simulation and test effort",
crossref = "Oliveira:2001:FFM",
pages = "465--477",
year = "2001",
DOI = "https://doi.org/10.1007/3-540-45251-6_27",
bibdate = "Wed Nov 24 11:58:06 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.de/link/service/series/0558/papers/2021/20210465.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Lee:2001:BPS,
author = "Chiou-Yng Lee and Erl-Huei Lu and Jau-Yien Lee",
title = "Bit-Parallel Systolic Modular Multipliers for a Class
of {$ \mathrm {GF}(2^m) $}",
crossref = "Burgess:2001:ISC",
pages = "51--58",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Chiou_Yng.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@InProceedings{Lee:2001:CAP,
author = "Ruby B. Lee",
title = "Computer Arithmetic --- a Processor Architect's
Perspective",
crossref = "Burgess:2001:ISC",
pages = "3--4",
year = "2001",
bibdate = "Fri May 3 13:52:01 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lee.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Lee:2001:DLS,
author = "Won-Ho Lee and Keon-Jik Lee and Kee-Young Yoo",
title = "Design of a linear systolic array for computing
modular multiplication and squaring in {$ {\bf GF}(2^m)
$}",
journal = j-COMPUT-MATH-APPL,
volume = "42",
number = "1--2",
pages = "231--240",
month = jul,
year = "2001",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S089812210100147X",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Lefevre:2001:WCC,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller",
title = "Worst Cases for Correct Rounding of the Elementary
Functions in Double Precision",
crossref = "Burgess:2001:ISC",
pages = "111--118",
year = "2001",
DOI = "https://doi.org/10.1109/ARITH.2001.930110",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lefevre.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15; correct rounding; floating-point
arithmetic",
summary = "We give the results of a four-year search for the
worst cases for correct rounding of the major
elementary functions in double precision. These results
allow the design of reasonably fast routines that will
compute these functions with correct \ldots{}",
}
@Article{Lemieux:2001:FPM,
author = "Joe Lemieux",
title = "Fixed-Point Math in {C}",
journal = j-EMBED-SYS-PROG,
volume = "14",
number = "1",
pages = "??--??",
month = apr,
year = "2001",
CODEN = "EYPRE4",
ISSN = "1040-3272",
bibdate = "Fri Nov 28 18:24:03 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.embedded.com/story/OEG20010311S0022",
abstract = "Floating-point arithmetic can be expensive if you're
using an integer-only processor. But floating-point
values can be manipulated as integers, as a less
expensive alternative.",
acknowledgement = ack-mfc # " and " # ack-nhfb,
fjournal = "Embedded Systems Programming",
}
@Article{Leone:2001:NLC,
author = "M. Leone",
title = "A New Low Complexity Parallel Multiplier for a Class
of Finite Fields",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2162",
pages = "160--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:06:06 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620160.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2162/21620160.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Lester:2001:ECF,
author = "David Lester",
title = "Effective Continued Fractions",
crossref = "Burgess:2001:ISC",
pages = "163--172",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lester.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@TechReport{Li:2001:LLF,
author = "Ren-Cang Li and Peter Markstein and Jon P. Okada and
James W. Thomas",
title = "The {\tt libm} library and floating-point arithmetic
for {HP-UX} on {Itanium}",
type = "Technical report",
institution = "Hewlett--Packard Company",
address = "Palo Alto, CA, USA",
pages = "??",
month = apr,
year = "2001",
bibdate = "Fri Jun 24 20:12:09 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
acknowledgement = ack-nhfb,
}
@Article{Li:2001:PMM,
author = "Keqin Li and V. Y. Pan",
title = "Parallel matrix multiplication on a linear array with
a reconfigurable pipelined bus system",
journal = j-IEEE-TRANS-COMPUT,
volume = "50",
number = "5",
pages = "519--525",
month = may,
year = "2001",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.926164",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:03:10 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=926164",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lippert:2001:HSM,
author = "Th. Lippert and N. Petkov and P. Palazzari and K.
Schilling",
title = "Hyper-systolic matrix multiplication",
journal = j-PARALLEL-COMPUTING,
volume = "27",
number = "6",
pages = "737--759",
month = may,
year = "2001",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Wed Jul 18 06:31:15 MDT 2001",
bibsource = "http://www.elsevier.com/locate/issn/01678191;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/abstract.html;
http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@InProceedings{Madhukumar:2001:EMH,
author = "A. S. Madhukumar and F. Chin",
booktitle = "12th {IEEE} International Symposium on Personal,
Indoor and Mobile Radio Communications, 2001",
title = "An efficient method for high-rate data transmission
using residue number system based {DS--CDMA}",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "C-1--C-5",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/PIMRC.2001.965450",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents an advanced architecture for a
residue number system (RNS) based CDMA system for
high-rate data transmission by combining RNS
representation, PSK/QAM modulation and orthogonal
modulation. The proposed system uses a lesser
\ldots{}",
}
@InProceedings{Madhukumar:2001:IBE,
author = "A. S. Madhukumar and F. Chin",
booktitle = "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
Technology Conference",
title = "Improving bandwidth efficiency for a residue number
system based {DS--CDMA} system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "247--251",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/VTC.2001.956595",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents a new method to improve bandwidth
efficiency of RNS based CDMA system by combining RNS
representation, PSK/QAM modulation and orthogonal
modulation. Using the proposed method significantly
reduces the computational complexity of \ldots{}",
}
@InProceedings{Madhukumar:2001:IIR,
author = "A. S. Madhukumar and F. Chin",
booktitle = "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
Technology Conference",
title = "Incorporating incremental redundancy and link
adaptation in communication systems using residue
number systems",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2272--2276",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/VTC.2001.957150",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper explores the use of redundant residue
number systems to incorporate incremental redundancy in
a communication system. By exploiting this property
further, one can design an appropriate coding scheme
for transmission at the currently \ldots{}",
}
@InProceedings{Matula:2001:ITL,
author = "David W. Matula",
title = "Improved Table Lookup Algorithms for Postscaled
Division",
crossref = "Burgess:2001:ISC",
pages = "101--110",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Matula.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@InProceedings{McFearin:2001:GAH,
author = "Lee D. McFearin and David W. Matula",
title = "Generation and Analysis of Hard to Round Cases for
Binary Floating Point Division",
crossref = "Burgess:2001:ISC",
pages = "119--127",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_McFearin.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
summary = "We investigate two sets of hard to round p$\times$p
bit fractions arising from division of a normalized p
bit floating point dividend by a normalized p bit
floating point divisor. These sets are characterized by
the p$\times$p bit fraction's quotient \ldots{}",
}
@Article{Michel:2001:SCF,
author = "Claude Michel and Michel Rueher and Yahia Lebbah",
title = "Solving Constraints over Floating-Point Numbers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2239",
pages = "524--538",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRclass = "90C08 (65G30 68T20)",
MRnumber = "MR1904621",
bibdate = "Sat Feb 2 13:07:24 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2239.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2239/22390524.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2239/22390524.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@PhdThesis{Mobley:2001:ICW,
author = "Byron Paul Mobley",
title = "The ingenuity of common workmen: and the invention of
the computer",
type = "{Ph.D.} thesis",
school = "Department of History, Iowa State University",
address = "Ames, IA, USA",
pages = "301",
year = "2001",
ISBN = "0-493-46949-4",
ISBN-13 = "978-0-493-46949-2",
bibdate = "Thu Nov 18 11:31:13 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Since World War II, state support for scientific
research has been assumed crucial to technological and
economic progress. Governments accordingly spent
tremendous sums to that end. Nothing epitomizes the
alleged fruits of that involvement better than the
electronic digital computer. The first such computer
has been widely reputed to be the ENIAC, financed by
the U.S. Army for the war but finished afterwards.
Vastly improved computers followed, initially paid for
in good share by the Federal Government of the United
States, but with the private sector then dominating,
both in development and use, and computers are of major
significance. Despite the supposed success of
public-supported science, evidence is that computers
would have evolved much the same without it but at less
expense. Indeed, the foundations of modern computer
theory and technology were articulated before World War
II, both as a tool of applied mathematics and for
information processing, and the computer was itself on
the cusp of reality. Contrary to popular understanding,
the ENIAC actually represented a movement backwards and
a dead end.\par
Rather, modern computation derived more directly, for
example, from the prewar work of John Vincent Atanasoff
and Clifford Berry, a physics professor and graduate
student, respectively, at Iowa State College (now
University) in Ames, Iowa. They built the Atanasoff
Berry Computer (ABC), which, although special purpose
and inexpensive, heralded the efficient and elegant
design of modern computers. Moreover, while no one
foresaw commercialization of computers based on the
ungainly and costly ENIAC, the commercial possibilities
of the ABC were immediately evident, although
unrealized due to war. Evidence indicates, furthermore,
that the private sector was willing and able to develop
computers beyond the ABC and could have done so more
effectively than government, to the most sophisticated
machines. A full and inclusive history of computers
suggests that Adam Smith, the eighteenth century
Scottish philosopher, had it right. He believed that
minimal and aloof government best served society, and
that the inherent genius of citizens was itself enough
to ensure the general prosperity.",
acknowledgement = ack-nhfb,
keywords = "ABC (Atanasoff-Berry Computer); ENIAC (Electronic
Numerical Integrator and Computer)",
}
@Article{Moller:2001:SEC,
author = "Bodo M{\"o}ller",
title = "Securing Elliptic Curve Point Multiplication against
Side-Channel Attacks",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2200",
pages = "324--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:06:44 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000324.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2200/22000324.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Montuschi:2001:BVH,
author = "P. Montuschi and T. Lang",
title = "Boosting very-high radix division with prescaling and
selection by rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "50",
number = "1",
pages = "13--27",
month = jan,
year = "2001",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.902750",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:03:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902750",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "An extension of the very-high radix division with
prescaling and selection by rounding is presented. This
extension consists of increasing the effective radix of
the implementation by obtaining a few additional bits
of the quotient per iteration, \ldots{}",
}
@Article{Morioka:2001:TEV,
author = "Sumio Morioka and Yasunao Katayama and Toshiyuki
Yamane",
title = "Towards Efficient Verification of Arithmetic
Algorithms over {Galois} Fields {$ G F(2^m) $}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2102",
pages = "465--477",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:02 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2102.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2102/21020465.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2102/21020465.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{MRaihi:2001:ACR,
author = "David M'Ra{\"\i}hi and David Naccache and Michael
Tunstall",
title = "Asymmetric Currency Rounding",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1962",
pages = "192--201",
year = "2001",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/3-540-45472-1",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:02:55 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1962.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1962/19620192.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1962/19620192.pdf",
abstract = "The euro was introduced on the first of January 1999
as a common currency in fourteen European nations. EC
regulations are fundamentally different from usual
banking practices for they forbid fees when converting
national currencies to euros (fees would otherwise
deter users from adopting the euro); this creates a
unique fraud context where money can be made by taking
advantage of the EC's official rounding rules. This
paper proposes a public-key-based protection against
such attacks. In our scheme, the parties conducting a
transaction can not predict whether the rounding will
cause loss or gain while the expected statistical
difference between an amount and its euro-equivalent
decreases exponentially as the number of transactions
increases.",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Muller:2001:IEA,
author = "Norbert Th. M{\"u}ller",
title = "The {iRRAM}: Exact Arithmetic in {C++}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2064",
pages = "222--252",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:04:19 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640222.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2064/20640222.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Naini:2001:GHS,
author = "Ajay Naini and Atul Dhablania and Warren James and
Debjit Das Sarma",
title = "{1-GHz HAL SPARC64\reg{}} Dual Floating Point Unit
with {RAS} Features",
crossref = "Burgess:2001:ISC",
pages = "173--183",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Naini.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Nakamura:2001:AAA,
author = "Yoshimasa Nakamura",
title = "Algorithms associated with arithmetic, geometric and
harmonic means and integrable systems",
journal = j-J-COMPUT-APPL-MATH,
volume = "131",
number = "1--2",
pages = "161--174",
day = "1",
month = jun,
year = "2001",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00316-2",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65P40 (37N30 39A10)",
MRnumber = "1835710",
bibdate = "Sat Feb 25 12:45:18 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/agm.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700003162",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Nannarelli:2001:TBR,
author = "A. Nannarelli and M. Re and G. C. Cardarilli",
booktitle = "{ISCAS 2001}, The 2001 {IEEE} International Symposium
on Circuits and Systems, 6--9 May 2001",
title = "Tradeoffs between residue number system and
traditional {FIR} filters",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "305--308",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2001.921068",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this work, a study on the implementation of FIR
filters in the Residue Number System (RNS) is carried
out. For different configurations, RNS filters are
compared with filters realized in the traditional two's
complement system (TCS) in terms of \ldots{}",
}
@Article{Ning:2001:ESI,
author = "Peng Ning and Yiqun Lisa Yin",
title = "Efficient Software Implementation for Finite Field
Multiplication in Normal Basis",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2229",
pages = "177--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:15 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290177.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2229/22290177.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Nozaki:2001:IRA,
author = "H. Nozaki and M. Motoyama and A. Shimbo and S.
Kawamura",
title = "Implementation of {RSA} Algorithm Based on {RNS
Montgomery} Multiplication",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2162",
pages = "364--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:06:06 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620364.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2162/21620364.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Oishi:2001:FEM,
author = "Shin'ichi Oishi",
title = "Fast enclosure of matrix eigenvalues and singular
values via rounding mode controlled computation",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "324",
number = "1--3",
pages = "133--146",
day = "15",
month = feb,
year = "2001",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Mar 19 19:03:24 MST 2001",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Okeya:2001:EEC,
author = "K. Okeya and K. Sakurai",
title = "Efficient Elliptic Curve Cryptosystems from a Scalar
Multiplication Algorithm with Recovery of the
$y$-Coordinate on a {Montgomery}-Form Elliptic Curve",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2162",
pages = "126--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:06:06 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620126.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2162/21620126.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Book{Overton:2001:NCI,
author = "Michael L. Overton",
title = "Numerical Computing with {IEEE} Floating Point
Arithmetic, Including One Theorem, One Rule of Thumb,
and One Hundred and One Exercises",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiv + 104",
year = "2001",
ISBN = "0-89871-482-6 (hardcover), 0-89871-571-7 (paperback),
0-89871-807-4 (ebook)",
ISBN-13 = "978-0-89871-482-1 (hardcover), 978-0-89871-571-2
(print), 978-0-89871-807-2 (e-book)",
LCCN = "QA76.9.M35 O94 2001",
MRclass = "65-02 (65G30 68M07 68N99)",
MRnumber = "MR1828597 (2003b:65002)",
MRreviewer = "Jesse L. Barlow",
bibdate = "Fri Apr 27 16:50:46 2001",
bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
price = "US\$40.00",
URL = "http://www.cs.nyu.edu/cs/faculty/overton/book/;
http://www.siam.org/catalog/mcc07/ot76.htm",
abstract = "Are you familiar with the IEEE floating point
arithmetic standard? Would you like to understand it
better? This book gives a broad overview of numerical
computing, in a historical context, with a special
focus on the IEEE standard for binary floating point
arithmetic. Key ideas are developed step by step,
taking the reader from floating point representation,
correctly rounded arithmetic, and the IEEE philosophy
on exceptions, to an understanding of the crucial
concepts of conditioning and stability, explained in a
simple yet rigorous context. It gives technical details
that are not readily available elsewhere and includes
challenging exercises that go beyond the topics covered
in the text. Numerical Computing with IEEE Floating
Point Arithmetic provides an easily accessible yet
detailed discussion of IEEE Std 754-1985, arguably the
most important standard in the computer industry. The
result of an unprecedented cooperation between academic
computer scientists and the cutting edge of industry,
it is supported by virtually every modern computer.
Other topics include the floating point architecture of
the Intel microprocessors and a discussion of
programming language support for the standard.",
acknowledgement = ack-nhfb,
tableofcontents = "1: Introduction \\
2: The real numbers \\
3: Computer representation of numbers \\
4: IEEE floating point representation \\
5: Rounding \\
6: Correctly rounded floating point operations \\
7: Exceptions \\
8: The Intel microprocessors \\
9: Programming languages \\
10: Floating point in C \\
11: Cancellation \\
12: Conditioning of problems \\
13: Stability of algorithms \\
14: Conclusion",
}
@InProceedings{Paliouras:2001:LPP,
author = "V. Paliouras and T. Stouraitis",
title = "Low-Power Properties of the Logarithmic Number
System",
crossref = "Burgess:2001:ISC",
pages = "229--236",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Paliouras.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Park:2001:ADI,
author = "Young-Ho Park and Sangtae Jeong and Chang Han Kim and
Jongin Lim",
title = "An Alternate Decomposition of an Integer for Faster
Point Multiplication on Certain Elliptic Curves",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2274",
pages = "323--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:07 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740323.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2274/22740323.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Park:2001:IMM,
author = "Young-Ho Park and Sangho Oh and Sangjin Lee and Jongin
Lim and Maenghee Sung",
title = "An Improved Method of Multiplication on Certain
Elliptic Curves",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2274",
pages = "310--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:07 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740310.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2274/22740310.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Phillips:2001:MMM,
author = "B. Phillips",
booktitle = "Conference Record of the Thirty-Fifth Asilomar
Conference on Signals, Systems and Computers, 2001",
title = "Modular multiplication in the {Montgomery} residue
number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1637--1640",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.2001.987762",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper considers the evaluation of long wordlength
modular products. An algorithm is described in which
long wordlength (e.g. 1024-bit) integers are
represented by short-wordlength (e.g. 32-bit)
Montgomery (1985) residues. Long integer modular
\ldots{}",
}
@Article{Phillips:2001:MRN,
author = "B. J. Phillips",
title = "{Montgomery} residue number systems",
journal = j-ELECT-LETTERS,
volume = "37",
number = "21",
pages = "1286--1287",
day = "11",
month = oct,
year = "2001",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:20010852",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=20889",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "The Montgomery residue number system (MRNS) for long
word-length arithmetic is introduced. MRNS, a
modification of the residue number system (RNS),
represents a long integer as a set of smaller
Montgomery residues. Long integer addition, subtraction
\ldots{}",
}
@InProceedings{Phillips:2001:OSL,
author = "Braden Phillips",
title = "Optimised Squaring of Long Integers Using Precomputed
Partial Products",
crossref = "Burgess:2001:ISC",
pages = "73--82",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Phillips.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Pietronero:2001:EUD,
author = "L. Pietronero and E. Tosatti and V. Tosatti and A.
Vespignani",
title = "Explaining the uneven distribution of numbers in
nature: the laws of {Benford} and {Zipf}",
journal = j-PHYSICA-A,
volume = "293",
number = "??",
pages = "297--304",
month = "????",
year = "2001",
CODEN = "PHYADX",
DOI = "https://doi.org/10.1016/S0378-4371(00)00633-6",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Thu Feb 15 16:36:18 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The distribution of first digits in numbers series
obtained from very different origins shows a marked
asymmetry in favor of small digits that goes under the
name of Benford's law. We analyze in detail this
property for different data sets and give a general
explanation for the origin of the Benford's law in
terms of multiplicative processes. We show that this
law can be also generalized to series of numbers
generated from more complex systems like the catalogs
of seismic activity. Finally, we derive a relation
between the generalized Benford's law and the popular
Zipf's law which characterize the rank order statistics
and has been extensively applied to many problems
ranging from city population to linguistics.",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Pillai:2001:LPA,
author = "R. V. K. Pillai and D. Al-Khalili and A. J. Al-Khalili
and S. Y. A. Shah",
title = "A Low Power Approach to Floating Point Adder Design
for {DSP} Applications",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "27",
number = "3",
pages = "195--213",
month = mar,
year = "2001",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1008140025773",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Thu May 09 09:49:01 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The demand for high performance, low power floating
point adder cores has been on the rise during the
recent years particularly for DSP applications. In this
paper, we present a new architecture for a low power,
IEEE compatible, floating point adder, that is fast and
has low latency. The functional partitioning of the
adder into three distinct, clock gated data paths
allows activity reduction. The switching activity
function of the proposed adder is represented as a
three state FSM. During any given operation cycle, only
one of the data paths is active, during which time, the
logic assertion status of the circuit nodes of the
other data paths are held at their previous states.
Critical path delay and latency are reduced by
incorporating speculative rounding and pseudo leading
zero anticipatory logic as well as data path
simplifications. In contrast to conventional high speed
floating point adders that use leading zero
anticipatory logic, the proposed scheme offers a worst
case power reduction of 50\%.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Pineiro:2001:FPC,
author = "J. A. Pi{\~n}eiro and J. D. Bruguera and J.-M.
Muller",
title = "Faithful Powering Computation Using Table Look-Up and
a Fused Accumulation Tree",
crossref = "Burgess:2001:ISC",
pages = "40--50",
year = "2001",
bibdate = "Fri May 3 13:52:01 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Pineiro.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
xxnote = "Check pages: one reference has 40--47??",
}
@InProceedings{Rajagopal:2001:LAD,
author = "Sridhar Rajagopal and Joseph R. Cavallaro",
title = "On-Line Arithmetic for Detection in Digital
Communication Receivers",
crossref = "Burgess:2001:ISC",
pages = "257--265",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Rajagopal.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Book{Ralston:2001:FCN,
author = "Anthony Ralston and Philip Rabinowitz",
title = "A first course in numerical analysis",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "Second",
pages = "xviii + 556 + 50",
year = "2001",
ISBN = "0-486-41454-X (paperback)",
ISBN-13 = "978-0-486-41454-6 (paperback)",
LCCN = "QA297 .R3 2001",
bibdate = "Fri Aug 20 10:13:32 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/description/dover032/00064343.html;
http://www.loc.gov/catdir/toc/dover031/00064343.html",
acknowledgement = ack-nhfb,
remark = "This Dover edition, first published in 2001, is an
unabridged, slightly corrected republication of the
second edition of the work originally published in
\cite{Ralston:1965:FC} and issued in a revised second
edition in \cite{Ralston:1978:FCN}.",
subject = "Numerical analysis",
}
@InProceedings{Rejeb:2001:IDR,
author = "B. Rejeb and H. Henkelmann and W. Anheier",
booktitle = "The 8th {IEEE} International Conference on
Electronics, Circuits and Systems, {ICECS 2001}",
title = "Integer division in residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "259--262",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICECS.2001.957729",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Division, sign detection and number comparison are the
more difficult operations in residue number systems
(RNS). These shortcomings limited most RNS
implementations to additions, subtractions and
multiplications. In this paper, a high level \ldots{}",
}
@Article{Reyhani-Masoleh:2001:FNB,
author = "Arash Reyhani-Masoleh and M. Anwar Hasan",
title = "Fast Normal Basis Multiplication Using General Purpose
Processors",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2259",
pages = "230--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:44 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590230.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2259/22590230.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Rinfret:2001:BSI,
author = "Denis Rinfret and Patrick O'Neil and Elizabeth
O'Neil",
title = "Bit-sliced index arithmetic",
journal = j-SIGMOD,
volume = "30",
number = "2",
pages = "47--57",
month = jun,
year = "2001",
CODEN = "SRECD8",
ISSN = "0163-5808 (print), 1943-5835 (electronic)",
ISSN-L = "0163-5808",
bibdate = "Mon Jan 12 08:46:06 MST 2004",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGMOD Record",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J689",
}
@Article{Ring:2001:MPA,
author = "Michael C. Ring",
title = "{MAPM}, {A} Portable Arbitrary Precision Math Library
in {C}",
journal = j-CCCUJ,
volume = "19",
number = "11",
pages = "??--??",
month = nov,
year = "2001",
CODEN = "CCUJEX",
ISSN = "1075-2838",
bibdate = "Tue May 14 18:09:34 MDT 2002",
bibsource = "http://www.cuj.com/articles/2001/0111/0111toc.htm?topic=articles;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Frustrated by the finiteness of fixed-size arithmetic?
This math library gives you the precision you need.",
acknowledgement = ack-nhfb,
fjournal = "C/C++ Users Journal",
}
@Article{Rudra:2001:ERE,
author = "A. Rudra and P. K. Dubey and C. S. Jutla and V. Kumar
and J. R. Rao and P. Rohatgi",
title = "Efficient {Rijndael} Encryption Implementation with
Composite Field Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2162",
pages = "171--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:06:06 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620171.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2162/21620171.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Rugina:2001:RUD,
author = "Radu Rugina and Martin Rinard",
title = "Recursion Unrolling for Divide and Conquer Programs",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2017",
pages = "34--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:03:35 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2017.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2017/20170034.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2017/20170034.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Rump:2001:RPS,
author = "Siegfried M. Rump",
title = "Rigorous and Portable Standard Functions",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "3",
pages = "540--562",
month = jun,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021971313412",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540",
abstract = "Today's floating point implementations of elementary
transcendental functions are usually very accurate.
However, with few exceptions, the actual accuracy is
not known. In the present paper we describe a rigorous,
accurate, fast and portable implementation of the
elementary standard functions based on some existing
approximate standard functions. The scheme is outlined
for IEEE 754, but not difficult to adapt to other
floating point formats. A Matlab implementation is
available on the net. Accuracy of the proposed
algorithms can be rigorously estimated. As an example
we prove that the relative accuracy of the exponential
function is better than 2.07 eps in a slightly reduced
argument range (eps denoting the relative rounding
error unit). Otherwise, extensive computational tests
suggest for all elementary functions and all suitable
arguments an accuracy better than about 3 eps.",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "elementary functions; floating-point arithmetic",
}
@Article{Sakai:2001:PMS,
author = "Yasuyuki Sakai and Kouichi Sakurai",
title = "On the Power of Multidoubling in Speeding Up Elliptic
Scalar Multiplication",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2259",
pages = "268--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:44 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590268.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2259/22590268.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Savas:2001:SUM,
author = "Erkay Savas and Alexandre F. Tenca and {\c{C}}etin K.
Ko{\c{c}}",
title = "A Scalable and Unified Multiplier Architecture for
Finite Fields {GF}$ (p) $ and {GF}$ (2 m) $",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1965",
pages = "277--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:02:57 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650277.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1965/19650277.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Schmookler:2001:LZA,
author = "Martin S. Schmookler and Kevin J. Nowka",
title = "Leading Zero Anticipation and Detection --- a
Comparison of Methods",
crossref = "Burgess:2001:ISC",
pages = "7--12",
year = "2001",
DOI = "https://doi.org/10.1109/ARITH.2001.930098",
bibdate = "Fri May 3 13:52:01 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Schmookler.pdf",
abstract = "Design of the leading zero anticipator (LZA) or
detector (LZD) is pivotal to the normalization of
results for addition and fused multiplication-addition
in high-performance floating point processors. This
paper formalizes the analysis and describes some
alternative organizations and implementations from the
known art. It shows how choices made in the design are
often dependent on the overall design of the addition
unit, on how subtraction is handled when the exponents
are the same, and on how it detects and corrects for
the possible one-bit error of the LZA.",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Schonfelder:2001:VPA,
author = "J. L. Schonfelder",
title = "Variable Precision Arithmetic: a {Fortran 95} Module",
journal = j-FORTRAN-FORUM,
volume = "20",
number = "3",
pages = "2--11",
month = dec,
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1145/570822.570823",
ISSN = "1061-7264 (print), 1931-1311 (electronic)",
ISSN-L = "1061-7264",
bibdate = "Wed Jun 18 16:26:45 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes the design and development of a
software package supporting variable precision
arithmetic as a semantic extension to the core FORTRAN
language. The working precision of the arithmetic
supported by this package can be dynamically and
arbitrarily variable. The facility exploits the
data-abstraction capabilities of Fortran 95 and allows
the operations to be used elementally with array
operands as well as with scalars. The number system is
defined in such a way as to be closed under all of the
basic operations of normal arithmetic; no
program-terminating numerical exceptions can occur.
Precision loss situations like underflow and overflow
are handled by defining special value representations
that preserve as much of the numeric information as is
practical and the operation semantics are defined so
that these exceptional values propagate as appropriate
to reflect this loss of information. The number system
uses an essentially conventional variable precision
floating-point representation. Where operations can be
performed exactly within the currently-set working
precision limit, the excess trailing zero digits are
not stored, nor do they take part in future operations.
This is both economical in storage and improves
efficiency. By judiciously managing the working
precision, arithmetic operations that are potentially
exact can be performed exactly.",
acknowledgement = ack-nhfb,
fjournal = "ACM Fortran Forum",
issue = "62",
journal-URL = "http://portal.acm.org/toc.cfm?id=J286",
}
@InProceedings{Seidel:2001:BMR,
author = "Peter-Michael Seidel and Lee D. McFearin and David W.
Matula",
title = "Binary Multiplication Radix-$ 32 $ and Radix-$ 256 $",
crossref = "Burgess:2001:ISC",
pages = "23--32",
year = "2001",
bibdate = "Fri May 3 13:52:01 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Seidel.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@InProceedings{Seidel:2001:DFI,
author = "Peter-Michael Seidel and Guy Even",
title = "On the Design of Fast {IEEE} Floating-Point Adders",
crossref = "Burgess:2001:ISC",
pages = "184--194",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Seidel_Even.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@InProceedings{Seidel:2001:EAB,
author = "Peter-Michael Seidel",
title = "Exact arithmetic based on floating-point numbers",
crossref = "Kraemer:2001:SCV",
pages = "123--??",
year = "2001",
bibdate = "Wed Nov 24 10:53:43 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Smith:2001:AFS,
author = "David M. Smith",
title = "{Algorithm 814}: {Fortran 90} software for
floating-point multiple precision arithmetic, gamma and
related functions",
journal = j-TOMS,
volume = "27",
number = "4",
pages = "377--387",
month = dec,
year = "2001",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/504210.504211",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Mar 13 08:49:29 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A collection of Fortran 90 routines for evaluating the
Gamma function and related functions using the FM
multiple-precision arithmetic package.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Misc{Steele:2001:SMFa,
author = "Guy L. {Steele Jr.}",
title = "System and method for floating-point computation",
howpublished = "US Patent 6327604",
day = "04",
month = dec,
year = "2001",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/6327604/fulltext.html",
abstract = "A system is disclosed for performing floating point
computation in connection with numbers in a base
floating point representation (such as the
representation defined in IEEE Std. 754) that defines a
plurality of formats, including a normalized format and
a de-normalized format, using a common floating point
representation that defines a unitary normalized
format. The system includes a base to common
representation converter, a processor and a common to
base representation converter. The base to common
representation converter converts numbers from the base
floating point representation to the common floating
point representation, so that all numbers involved in a
computation will be expressed in the unitary normalized
format. The processor is configured to perform a
mathematical operation of at least one predetermined
type in connection with the converted numbers generated
by the base to common representation converter to
generate a floating point result in the common
representation. The common to base representation
converter converts numbers from the common floating
point representation selectively to either the
normalized or de-normalized format of the base
representation.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2001:SMFb,
author = "Guy L. {Steele Jr.}",
title = "System and method for floating-point computation",
howpublished = "US Patent 6289365",
day = "11",
month = sep,
year = "2001",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/6289365/fulltext.html",
abstract = "A system is disclosed for performing floating point
computation in connection with numbers in a base
floating point representation (such as the
representation defined in IEEE Std. 754) that defines a
plurality of formats, including a normalized format and
a de-normalized format, using a common floating point
representation that defines a unitary normalized
format. The system includes a base to common
representation converter, a processor and a common to
base representation converter. The base to common
representation converter converts numbers from the base
floating point representation to the common floating
point representation, so that all numbers involved in a
computation will be expressed in the unitary normalized
format. The processor is configured to perform a
mathematical operation of at least one predetermined
type in connection with the converted numbers generated
by the base to common representation converter to
generate a floating point result in the common
representation. The common to base representation
converter converts numbers from the common floating
point representation selectively to either the
normalized or denormalized format of the base
representation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Stine:2001:CIH,
author = "J. E. Stine and M. J. Schulte",
title = "A Case for Interval Hardware on Superscalar
Processors",
crossref = "Kraemer:2001:SCV",
pages = "53--68",
year = "2001",
bibdate = "Tue Nov 25 12:33:34 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic",
}
@PhdThesis{Stine:2001:DIA,
author = "James Edward {Stine, Jr.}",
title = "Design issues for accurate and reliable arithmetic",
type = "{Ph.D.} Thesis",
school = "Lehigh University",
address = "Bethlehem, PA, USA",
year = "2001",
bibdate = "Fri Oct 25 17:18:13 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://wwwlib.umi.com/dissertations/fullcit/9995540;
http://wwwlib.umi.com/dissertations/preview/9995540",
abstract = "The use of floating-point data types in high-level
languages is prevalent in many of today's scientific
applications. However, the approximation of real
numbers by finite precision floating-point numbers can
produce inaccurate results due to round off error and
catastrophic cancellation. Interval arithmetic provides
a method for monitoring errors in numerical
computations, and can provide solutions to problems
that cannot be efficiently solved with traditional
floating point arithmetic. Although several software
tools for interval arithmetic have been developed,
these tools have severe performance limitations due to
a lack of hardware support for interval arithmetic.
This dissertation investigates the design, development,
and evaluation of hardware and instruction set support
for interval arithmetic. In contrast to previous
research, which employed dedicated functional units and
coprocessors for interval arithmetic, this research
focuses on the integration of interval arithmetic
support with traditional IEEE floating point hardware.
Novel algorithms and hardware designs for interval
arithmetic are developed, and methods for adding
interval arithmetic instructions to the instruction set
architectures of conventional processors are presented.
To evaluate the cost and performance of this approach,
hardware designs with support for interval arithmetic
have been realized using VHDL and synthesized with the
Leonardo/Spectrum tool set from Exemplar. These designs
are compared to conventional floating point units in
terms of area and delay. Simulations of interval
benchmarks both with and without interval hardware
support are performed using an interval-enhanced
version of the SimpleScalar tool suite and GNU's gcc
compiler. The results of these simulations indicate
that the proposed hardware support for interval
arithmetic improves the execution time of interval
operations by a factor 6.3 to 14.9.",
acknowledgement = ack-nhfb,
}
@InProceedings{Stoffel:2001:VIM,
author = "Dominik Stoffel and Wolfgang Kunz",
title = "Verification of integer multipliers on the arithmetic
bit level",
crossref = "IEEE:2001:IPI",
pages = "183--189",
year = "2001",
bibdate = "Fri Aug 08 08:59:39 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the most severe short-comings of currently
available equivalence checkers is their inability to
verify integer multipliers. In this paper, we present a
bit level reverse-engineering technique that can be
integrated into standard equivalence checking flows. We
propose a Boolean mapping algorithm that extracts a
network of half adders from the gate netlist of an
addition circuit. Once the arithmetic bit level
representation of the circuit is obtained, equivalence
checking can be performed using simple arithmetic
operations. Experimental results show the promise of
our approach.",
acknowledgement = ack-nhfb,
}
@Article{Sun:2001:NSM,
author = "Fangyu Sun and Peter Kosmol",
title = "A new simultaneous method of fourth order for finding
complex zeros in circular interval arithmetic",
journal = j-J-COMPUT-APPL-MATH,
volume = "130",
number = "1--2",
pages = "293--307",
day = "1",
month = may,
year = "2001",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:18 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042799003751",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Sunar:2001:EON,
author = "B. Sunar and C. K. Koc",
title = "An efficient optimal normal basis type {II}
multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "50",
number = "1",
pages = "83--87",
month = jan,
year = "2001",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.902754",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:03:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902754",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Takagi:2001:HAC,
author = "Naofumi Takagi",
title = "A Hardware Algorithm for Computing Reciprocal Square
Root",
crossref = "Burgess:2001:ISC",
pages = "94--100",
year = "2001",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Takagi.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
summary = "A hardware algorithm for computing the reciprocal
square root which appears frequently in multimedia and
graphics applications is proposed. The reciprocal
square root is computed by iteration of
carry-propagation-free additions, shifts, and
\ldots{}",
}
@Article{Tasche:2001:WAC,
author = "Manfred Tasche and Hansmartin Zeuner",
title = "Worst and average case roundoff error analysis for
{FFT}",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "3",
pages = "563--581",
month = jun,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021923430250",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=563",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Fast Fourier Transform (FFT); floating-point
arithmetic; rounding errors",
}
@InProceedings{Tenca:2001:DRL,
author = "Alexandre F. Tenca and Syed Ubaid Hussaini",
title = "A Design of Radix-$2$ On-Line Division Using {LSA}
Organization",
crossref = "Burgess:2001:ISC",
pages = "266--276",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Tenca.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Tenca:2001:HRD,
author = "A. F. Tenca and G. Todorov and {\c{C}}.K. Ko{\c{c}}",
title = "High-Radix Design of a Scalable Modular Multiplier",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2162",
pages = "185--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:06:06 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620185.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2162/21620185.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Thompson:2001:BPC,
author = "D. U. Thompson and B. A. Wooley",
title = "A 15-b pipelined {CMOS} floating-point {A/D}
converter",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "36",
number = "2",
pages = "299--303",
month = feb,
year = "2001",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "A floating-point approach can be used to extend the
dynamic range of analog-to-digital (A/D) converters in
applications where large signals need not be encoded
with a precision greater than that required for small
signals. Owing to the nonuniform nature \ldots{}",
}
@Manual{TI:2001:TTPa,
title = "{TI-89\slash TI-92 Plus Sierra C} Assembler Reference
Manual, Beta Version .02",
organization = "Texas Instruments",
address = "Post Office box 655303, Dallas, TX 75265, USA",
pages = "322",
year = "2001",
bibdate = "Thu Nov 25 09:44:52 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Manual{TI:2001:TTPb,
title = "{TI-89\slash TI-92 Plus} Developers Guide, Beta
Version .02",
organization = "Texas Instruments",
address = "Post Office box 655303, Dallas, TX 75265, USA",
pages = "1356",
year = "2001",
bibdate = "Thu Nov 25 09:44:52 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Tisseur:2001:NMF,
author = "Fran{\c{c}}oise Tisseur",
title = "{Newton}'s Method in Floating Point Arithmetic and
Iterative Refinement of Generalized Eigenvalue
Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "4",
pages = "1038--1057",
month = "????",
year = "2001",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479899359837",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (65F35)",
MRnumber = "MR1824056 (2002b:65061)",
MRreviewer = "Raffaella Pavani",
bibdate = "Tue Feb 11 14:17:49 MST 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2001",
}
@Article{Trichina:2001:SAM,
author = "Elena Trichina and Alex Tiountchik",
title = "Scalable Algorithm for {Montgomery} Multiplication and
Its Implementation on the Coarse-Grain Reconfigurable
Chip",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2020",
pages = "235--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:03:38 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2020.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2020/20200235.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2020/20200235.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Um:2001:OAC,
author = "Junhyung Um and Taewhan Kim",
title = "An optimal allocation of carry-save-adders in
arithmetic circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "50",
number = "3",
pages = "215--233",
month = mar,
year = "2001",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.910813",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:03:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=910813",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Verdonk:2001:PRIa,
author = "Brigitte Verdonk and Annie Cuyt and Dennis
Verschaeren",
title = "A precision- and range-independent tool for testing
floating-point arithmetic {I}: {Basic} operations,
square root, and remainder",
journal = j-TOMS,
volume = "27",
number = "1",
pages = "92--118",
month = mar,
year = "2001",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/382043.382404",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.win.ua.ac.be/~cant/ieeecc754.html",
abstract = "This paper introduces a precision- and
range-independent tool for testing the compliance of
hardware or software implementations of
(multiprecision) floating-point arithmetic with the
principles of the IEEE standards 754 and 854. The tool
consists of a driver program, offering many options to
test only specific aspects of the IEEE standards, and a
large set of test vectors, encoded in a
precision-independent syntax to allow the testing of
basic and extended hardware formats as well as
multiprecision floating-point implementations. The
suite of test vectors stems on one hand from the
integration and fully precision- and range-independent
generalization of existing hardware test sets, and on
the other hand from the systematic testing of exact
rounding for all combinations of round and sticky bits
that can occur. The former constitutes only 50\% of the
resulting test set. In the latter we especially focus
on hard-to-round cases. In addition, the test suite
implicitly tests properties of floating-point
operations, following the idea of Paranoia, and it
reports which of the three IEEE-compliant underflow
mechanisms is used by the floating-point implementation
under consideration. We also check whether that
underflow mechanism is used consistently. The tool is
backward compatible with the UCBTEST package and with
Coonen's test syntax.",
accepted = "23 February 2001",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "arithmetic; floating-point testing; IEEE
floating-point standard; multiprecision; validation;
Verification",
subject = "Primary Classification: G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
arithmetic\\
Additional Classification: D. Software D.3 PROGRAMMING
LANGUAGES D.3.0 General Subjects: Standards",
}
@Article{Verdonk:2001:PRIb,
author = "Brigitte Verdonk and Annie Cuyt and Dennis
Verschaeren",
title = "A precision- and range-independent tool for testing
floating-point arithmetic {II}: conversions",
journal = j-TOMS,
volume = "27",
number = "1",
pages = "119--140",
month = mar,
year = "2001",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/382043.382405",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 6 16:43:42 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://www.win.ua.ac.be/~cant/ieeecc754.html",
abstract = "The IEEE 754 and 854 standards for floating-point
arithmetic are essentially a specification of a
programming environment, encompassing aspects from
computer hardware, operating systems and compilers to
programming languages (see especially section 8). Part
I and II of this paper together describe a tool to test
floating-point implementations of arbitrary precision
and exponent range (hardware as well as software) for
compliance with the principles outlined in the IEEE
standards. The tool consists of a driver program,
together with a very large set of test vectors encoded
in a precision independent syntax.\par
In Part I we have covered the testing of the basic
operations +, -, $ \times $, /, the square root and
remainder functions. In Part II we describe the
extension of the test tool to deal with conversions
between floating-point formats, conversions between
floating-point and integer formats, the rounding of
floating-point numbers to integral values and last but
not least binary-decimal conversions. Conversions can
now be tested from a floating-point format of arbitrary
precision and exponent range to another arbitrary
smaller (larger) floating-point format as well as to
and from fixed hardware integer formats. Conversions
between the bases 2 and 10 can be tested for a number
of precisions ranging from single (24 bits), double (53
bits), long double or extended (64 bits) to quadruple
(113 bits) precision and a proper multiprecision (240
bits) format.\par
We conclude Part II with some applications of our test
tool and report on the results of testing various
floating-point implementations, meaning various
language-compiler-hardware combinations as well as
multiprecision libraries.",
accepted = "23 February 2001",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "decimal floating-point arithmetic; floating-point
testing",
}
@InProceedings{Vergos:2001:HSP,
author = "H. T. Vergos and C. Efstathiou and D. Nikolos",
title = "High Speed Parallel-Prefix Modulo $ 2^{n + 1} $ Adders
for Diminished-One Operands",
crossref = "Burgess:2001:ISC",
pages = "211--217",
year = "2001",
bibdate = "Fri May 3 13:58:18 MDT 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
OCLC Proceedings database",
URL = "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Vergos.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
}
@Article{Visavakul:2001:DSS,
author = "Chakkapas Visavakul and Peter Y. K. Cheung and Wayne
Luk",
title = "A Digit-Serial Structure for Reconfigurable
Multipliers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2147",
pages = "565--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:49 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470565.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2147/21470565.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Walter:2001:DIH,
author = "Colin D. Walter",
title = "Data Integrity in Hardware for Modular Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1965",
pages = "204--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:02:57 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650204.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1965/19650204.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Walter:2001:PBM,
author = "Colin D. Walter",
title = "Precise Bounds for {Montgomery} Modular Multiplication
and Some Potentially Insecure {RSA} Moduli",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2271",
pages = "30--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:06 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2271.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2271/22710030.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2271/22710030.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Walters:2001:CUT,
author = "E. G. Walters and J. Schlessman and M. J. Schulte",
title = "Combined Unsigned and Two's Complement Hybrid
Squarers",
crossref = "Matthews:2001:CRT",
pages = "861--866",
year = "2001",
bibdate = "Sun Mar 04 11:46:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2001-08.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Wang:2001:LPF,
author = "Wei Wang and M. N. S. Swamy and M. O. Ahmad",
booktitle = "{MWSCAS 2001}, Proceedings of the 44th {IEEE 2001}
Midwest Symposium on Circuits and Systems",
title = "Low power {FIR} filter {FPGA} implementation based on
distributed arithmetic and residue number system",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "102--105",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.2001.986125",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper, several low power techniques are
proposed for the FPGA implementation of a distributed
arithmetic and residue number system-based FIR filter.
Two algorithms are proposed to reduce the size of the
residue-to-binary converter, which is \ldots{}",
}
@InProceedings{Wires:2001:FRR,
author = "K. E. Wires and M. J. Schulte and D. McCarley",
title = "{FPGA} Resource Reduction Through Truncated
Multiplication",
crossref = "Brebner:2001:FLA",
pages = "574--583",
year = "2001",
DOI = "https://doi.org/10.1007/3-540-44687-7_59",
bibdate = "Sun Mar 04 11:42:02 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2001-04.pdf",
acknowledgement = ack-nhfb,
}
@Article{Wirthlin:2001:ECC,
author = "Michael J. Wirthlin and Brian McMurtrey",
title = "Efficient Constant Coefficient Multiplication Using
Advanced {FPGA} Architectures",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2147",
pages = "555--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:49 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470555.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2147/21470555.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Wright:2001:EFP,
author = "Stephen J. Wright",
title = "Effects of Finite-Precision Arithmetic on
Interior-Point Methods for Nonlinear Programming",
journal = j-SIAM-J-OPT,
volume = "12",
number = "1",
pages = "36--78",
month = may # "\slash " # oct,
year = "2001",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/S1052623498347438",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "90C51 (90C30 90C33)",
MRnumber = "MR1870586 (2002j:90107)",
MRreviewer = "Levent Tun{\c{c}}el",
bibdate = "Sat Oct 4 12:16:05 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/12/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
MathSciNet database",
URL = "http://epubs.siam.org/sam-bin/dbq/article/34743",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
}
@Article{Wu:2001:MMSa,
author = "Huapeng Wu",
title = "{Montgomery} Multiplier and Squarer in {GF$ (2^m) $}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1965",
pages = "264--276",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:02:57 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650264.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1965/19650264.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Yamauchi:2001:AOO,
author = "Tsukasa Yamauchi and Shogo Nakaya and Takeshi Inuo and
Nobuki Kajihara",
title = "Arithmetic Operation Oriented Reconfigurable Chip:
{RHW}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2147",
pages = "618--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:05:49 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470618.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2147/21470618.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Yang:2001:MDD,
author = "Lie-Liang Yang and L. Hanzo",
booktitle = "{ICC 2001}. {IEEE} International Conference on
Communications. 11--14 June 2001",
title = "Minimum-distance decoding of redundant residue number
system codes",
volume = "10",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2975--2979",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICC.2001.937218",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this contribution the conventional error-detection
and error-correction algorithms used for RRNS codes are
improved and unified in the context of a so-called
projection-based `minimum-distance decoding' algorithm,
which can efficiently detect or \ldots{}",
}
@InProceedings{Yang:2001:RRN,
author = "Lie-Liang Yang and L. Hanzo",
booktitle = "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
Technology Conference",
title = "Redundant residue number system based error correction
codes",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1472--1476",
year = "2001",
CODEN = "????",
DOI = "https://doi.org/10.1109/VTC.2001.956442",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper residue number system (RNS) arithmetic
and redundant residue number system (RRNS) based codes
as well as their properties are reviewed. We propose a
number of applications for RRNS codes and demonstrate
how RRNS codes can be employed \ldots{}",
}
@Article{Yeh:2001:RAO,
author = "Thomas Y. Yeh and Hong Wang",
title = "Redundant Arithmetic Optimizations (Research Note)",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1900",
pages = "984--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:02:44 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t1900.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/1900/19000984.htm;
http://link.springer-ny.com/link/service/series/0558/papers/1900/19000984.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Yu:2001:DID,
author = "Sungwook Yu and E. E. {Swartzlander, Jr.}",
title = "{DCT} implementation with distributed arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "50",
number = "9",
pages = "985--991",
month = sep,
year = "2001",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.954513",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 10:03:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=954513",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Zhang:2001:FSM,
author = "Fangguo Zhang and Futai Zhang and Yumin Wang",
title = "Fast Scalar Multiplication on the {Jacobian} of a
Family of Hyperelliptic Curves",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2229",
pages = "74--??",
year = "2001",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Feb 2 13:07:15 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290074.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2229/22290074.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Zhang:2001:NCP,
author = "Hong Zhang",
title = "Numerical condition of polynomials in different
forms",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "12",
pages = "66--87",
year = "2001",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:29 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/etna.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://etna.mcs.kent.edu/vol.12.2001/pp66-87.dir/pp66-87.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@InProceedings{Zheng:2001:ARE,
author = "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
title = "The application of redundant encoding in iterative
implementation of division and square root",
crossref = "Tang:2001:ICA",
pages = "603--606",
year = "2001",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "The purpose of this paper is to discuss the speed
improvement in division and square root computation
with small area penalty. The digit recurrence SRT
algorithm and functional iteration Newton--Raphson
algorithm are generally used in modern \ldots{}",
}
@Article{Zielke:2001:GLL,
author = "G. Zielke and V. Drygalla",
title = "{Genaue L{\"o}sung Linearer Gleichungssysteme}.
({German}) [Exact solution of linear sets of
equations]",
journal = j-GAMM-MIT,
volume = "26",
number = "??",
pages = "7--107",
year = "2001",
CODEN = "????",
ISSN = "0936-7195",
bibdate = "Tue Nov 22 06:49:35 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Mitteilungen der Gesellschaft f{\"u}r Angewandte
Mathematik und Mechanik",
keywords = "accurate floating-point summation",
language = "German",
}
@TechReport{Zimmermann:2001:AAC,
author = "Paul Zimmermann",
title = "De l'algorithmique {\`a} l'arithm{\'e}tique via le
calcul formel. ({French}) [{From} algorithmics to
arithmetic via symbolic calculation]",
type = "Technical report",
institution = "D{\'e}partement de formation doctorale en
informatique. {\'E}cole doctorale IAEM Lorraine, UFR
STMIA",
address = "B{\^a}timent A, Technop{\^o}le de Nancy-Brabois, 615
rue du jardin botanique, F-54602 Villers-l{\`e}s-Nancy
Cedex, France",
pages = "43",
month = nov,
year = "2001",
bibdate = "Sun Sep 10 08:37:41 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/hdr.ps.gz",
abstract = "This document presents my research contributions from
1988 to 2001, performed first at INRIA Rocquencourt
within the Algo project (1988 to 1992), then at INRIA
Lorraine and LORIA within the projects Eur{\'e}ca
(1993-1997), PolKA (1998-2000), and Spaces (2001).
Three main periods can be roughly distinguished: from
1988 to 1992 where my research focused on analysis of
algorithms and random generation, from 1993 to 1997
where I worked on computer algebra and related
algorithms, finally from 1998 to 2001 where I was
interested in arbitrary precision floating-point
arithmetic with well-defined semantics.",
acknowledgement = ack-nhfb,
language = "French",
remark = "Habilitation {\`a} diriger des recherches",
}
@TechReport{Zimmermann:2001:APA,
author = "Paul Zimmermann",
title = "Arithm{\'e}tique en pr{\'e}cision arbitraire.
({French}) [Arbitrary-precision arithmetic]",
type = "Research Report",
number = "4272",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "25",
day = "29",
month = sep,
year = "2001",
ISSN = "0249-6399",
bibdate = "Sun Sep 10 08:43:26 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/RR4272.ps.gz",
abstract = "This paper surveys the available algorithms for
integer or floating-point arbitrary precision
calculations. After a brief discussion about possible
memory representations, known algorithms for
multiplication, division, square root, greatest common
divisor, input and output, are presented, together with
their complexity and usage. For each operation, we
present the naive algorithm, the asymptotically optimal
one, and also intermediate ``divide and conquer''
algorithms, which often are very useful. For
floating-points computations, some general-purpose
methods are presented for algebraic, elementary,
hypergeometric and special functions.",
acknowledgement = ack-nhfb,
language = "French",
}
@Misc{Ziv:2001:APM,
author = "Abraham Ziv and Moshe Olshansky and Ealan Henis and
Anna Reitman",
title = "Accurate Portable Mathematical Library ({IBM
APMathLib})",
howpublished = "World-Wide Web document",
publisher = pub-IBM,
address = pub-IBM:adr,
day = "20",
month = dec,
year = "2001",
bibdate = "Wed Nov 24 08:06:54 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
http://oss.software.ibm.com/mathlib/",
acknowledgement = ack-nhfb,
}
@Article{Agarwal:2002:FPN,
author = "R. C. Agarwal and R. F. Enenkel and F. G. Gustavson
and A. Kothari and M. Zubair",
title = "Fast pseudorandom-number generators with modulus $ 2^k
$ or $ 2^{k - 1} $ using fused multiply--add",
journal = j-IBM-JRD,
volume = "46",
number = "1",
pages = "97--116",
month = jan,
year = "2002",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.461.0097",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Mon Mar 18 17:27:08 MST 2002",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/461/agarwal.html;
http://www.research.ibm.com/journal/rd/461/agarwal.pdf",
abstract = "Many numerically intensive computations done in a
scientific computing environment require uniformly
distributed pseudorandom numbers in the range $ (0, 1)
$ and $ ( - 1, 1) $. For multiplicative congruential
generators with modulus $ 2^k $, $ k \leq 52 $, and
period $ 2^k - 2 $, we show that the cost per random
number for these two distributions is 3 and 3.125
multiply-adds on RS/6000 processors. Our code, on the
IBM POWER2 Model 590, produces more than 40 million
uniformly distributed pseudorandom numbers per second
for both ranges $ (0, 1) $ and $ ( - 1, 1) $.
Additionally, our code sustains the 40 million per
second rate for data out of cache. The Numerical
Aerodynamic Simulation (NAS) parallel benchmarks use a
linear congruential generator with modulus 246. Our
result is about 50 times faster than the generic
implementation given in the benchmarks. The
extra-accuracy fused multiply-add instruction of
RS/6000 machines combined with a few algorithmic
innovations gives rise to the 50-fold increase. If IEEE
64-bit arithmetic is used with our Fortran code on
POWER and PowerPC architectures, the results we obtain
are bit-wise identical to the generic algorithms. The
paper gives several illustrations of a general
technique called the Algorithm and Architecture
approach. We demonstrate herein that
programmer-controlled unrolling of loops is equivalent
to ``customized vectorization of RISC-type code.''
Customized vectorization is more powerful than ordinary
vectorization, and it is only possible on RISC-type
machines. We illustrate its use to show that RS/6000
processors can compute the distribution $ ( - 1, 1) $
at the rate of 3.125 multiply-adds. We also specify a
linear congruential generator that is related to the
multiplicative congruential generator referred to
above. It has a full period of 2k, where 2k is the
modulus. The cost per random number [in the range $ (0,
1) $ ] for this generator is four multiply-adds on
RS/6000 processors. Our code, on the IBM POWER2 Model
590, for this generator produces more than 30 million
uniformly distributed pseudorandom numbers per second
for the range $ (0, 1) $. We show that this generator
is ``embarrassingly parallel,'' or EP. Using the
Algorithm and Architecture approach, we describe a new
concept called ``generalized unrolling.'' Finally, we
present a multiplicative congruential generator for
which the modulus is not a power of $2$. Such a
generator, as well as one with modulus $ 2^k $, is
selectable as the generator used in the RANDOM_NUMBER
intrinsic function of IBM XL Fortran and XL High
Performance Fortran. All of the generators reported
here are EP. Using an IBM SP2 machine with 250 wide
nodes, it is possible to compute more than ten billion
uniform random numbers in a second.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
ordernumber = "G322-0230",
}
@Article{Akbarpour:2002:FCS,
author = "Behzad Akbarpour and Abdelkader Dekdouk and
Sofi{\`e}ne Tahar",
title = "Formalization of Cadence {SPW} Fixed-Point Arithmetic
in {HOL}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2335",
pages = "185--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:38 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2335.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2335/23350185.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2335/23350185.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Akkas:2002:CIF,
author = "A. Akkas",
booktitle = "{IEEE 13th} International Conference on
Application-specific Systems, Architectures, and
Processors, San Jose, {USA}, July, 2002",
title = "A Combined Interval and Floating-point
Comparator\slash Selector",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "208--217",
year = "2002",
bibdate = "Fri Jun 11 05:39:44 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://home.ku.edu.tr/~ahakkas/publications/comparator.pdf",
acknowledgement = ack-nhfb,
}
@PhdThesis{Akkas:2002:ISE,
author = "Ahmet Akkas",
title = "Instruction Set Enhancements for Reliable
Computations",
type = "{Ph.D.} Thesis",
school = "Lehigh University",
address = "Bethlehem, PA, USA",
pages = "159",
year = "2002",
bibdate = "Tue Nov 25 12:43:51 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3036247",
abstract = "Although there have been significant advances in VLSI
technology and numerical computing, floating-point
computations still suffer from undetected errors due to
rounding and catastrophic cancellation. Fast computers
let programmers write numerically intensive programs,
but computed results can be far from the true results
due to the accumulation of errors in arithmetic
operations. Therefore, accurate and reliable
computations have become more important.\par
Interval arithmetic is one technique for accurate and
reliable computing. With interval arithmetic, each data
value is represented by two floating-point numbers
which correspond to the endpoints of an interval, such
that the true result is guaranteed to lie on this
interval. Since interval arithmetic represents ranges
of numbers, it also provides the ability to solve
problems that cannot be efficiently solved using
floating-point arithmetic. Although interval arithmetic
provides an efficient method for monitoring and
controlling errors in floating-point computations, it
is not yet used widely because it is not sufficiently
fast.\par
This dissertation investigates instruction set
enhancements for interval arithmetic. Existing interval
arithmetic programs are examined to determine
bottlenecks in interval computations. Then, a variety
of instruction set enhancements are proposed to
overcome these bottlenecks. The efficiency of the
proposed enhancements are evaluated using an
interval-enhanced compiler and a superscalar processor
simulator. Hardware modifications to support these
enhancements are evaluated, and a novel design for a
combined Interval and Floating-point Comparator is
presented.\par
This dissertation also investigates instruction set
enhancements for extended precision arithmetic. In
particular, instruction set support for quadruple
precision arithmetic is examined. Hardware
modifications needed to support quadruple precision
arithmetic on superscalar processor is evaluated to
determine which extensions can be most efficiently
incorporated into superscalar processor designs.
Furthermore, a technique for performing parallel double
precision multiplication using quadruple precision
hardware is proposed.",
acknowledgement = ack-nhfb,
advisor = "Michael J. Schulte",
remark = "Dissertation Abstracts International, Volume: 62-12,
Section: B, page: 5799.",
}
@Article{Alvarez:2002:IRF,
author = "C. Alvarez and J. Corbal and E. Salami and M. Valero",
title = "Initial Results on Fuzzy Floating Point Computation
for Multimedia Processors",
journal = j-IEEE-COMPUT-ARCHIT-LETT,
volume = "1",
number = "1",
pages = "1--1",
month = jan,
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1109/L-CA.2002.6",
ISSN = "1556-6056 (print), 1556-6064 (electronic)",
ISSN-L = "1556-6056",
bibdate = "Fri Jun 21 05:49:19 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib",
abstract = "During the recent years the market of mid low end
portable systems such as PDAs or mobile digital phones
have experimented a revolution in both selling volume
and features as handheld devices incorporate Multimedia
applications. This fact brings to an increase in the
computational demands of the devices while still having
the limitation of power and energy consumption.
Instruction memoization is a promising technique to
help alleviate the problem of power consumption of
expensive functional units such as the floating point
one. Unfortunately this technique could be energy
inefficient for low end systems due to the additional
power consumption of the relatively big tables
required. In this paper we present a novel way of
understanding multimedia floating point operations
based on the fuzzy computation paradigm losses in the
computation precision may exchange performance for
negligible errors in the output. Exploiting the
implicit characteristics of media FP computation we
propose a new technique called fuzzy memoization. Fuzzy
memoization expands the capabilities of classic
memoization by attaching entries with similar inputs to
the same output. We present a case of study for a SH
like processor and report good performance and power
delay improvements with feasible hardware
requirements",
acknowledgement = ack-nhfb,
fjournal = "IEEE Computer Architecture Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208",
keywords = "Delay; Energy consumption; Fuzzy systems; Handheld
computers; Joining processes; Mobile computing;
Multimedia systems; Performance loss; Personal digital
assistants; Portable computers",
}
@Article{Anonymous:2002:AIVf,
author = "Anonymous",
title = "Author index volume 279 (2002)",
journal = j-THEOR-COMP-SCI,
volume = "279",
number = "1-2",
pages = "97",
month = may,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:08:56 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@TechReport{Anonymous:2002:OFP,
author = "Anonymous",
title = "{OpenVMS} floating-point arithmetic on the {Itanium}
architecture",
institution = inst-HP,
address = inst-HP:adr,
month = sep,
year = "2002",
bibdate = "Tue Nov 18 15:23:17 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://sysdoc.doors.ch/HP/openvms_ipf_floating_point_wp.pdf",
acknowledgement = ack-nhfb,
}
@Manual{ARM:2002:VVF,
title = "{VFP9-S} Vector Floating-point Coprocessor (r0p2)
Technical Reference Manual",
organization = "ARM Limited",
address = "Sunnyvale, CA, USA",
pages = "xvi + 156",
year = "2002",
bibdate = "Fri May 27 17:59:08 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.arm.com/pdfs/VFP-S_Vector_Floating_Point_Tech_Manual.pdf",
acknowledgement = ack-nhfb,
remark = "From the manual, p. 1-7: ``The FMAC family of
instructions (FMAC, FNMAC, FMSC, and FNMSC) perform a
chained multiply and accumulate operation. The product
is computed, rounded according to the specified
rounding mode and destination precision, and checked
for exceptions before the accumulate operation is
performed. The accumulate operation is also rounded
according to the specified rounding mode and
destination precision, and checked for exceptions. The
final result is identical to the equivalent sequence of
operations executed in sequence.''\par
From p. 1-12: ``For instance, the VFP9-S coprocessor
does not process subnormal input values directly. To
provide correct handling of subnormal inputs according
to the IEEE 754 standard, a trap is made to support
code to process the operation. Using the support code
for processing this operation can require hundreds of
cycles.''\par
From p. 2-2: ``The VFP9-S register file contains
thirty-two 32-bit registers organized in four banks.
Each register can store either a single-precision
floating-point number or an integer.''\par
From p. 3-5: ``Any SNaN passed as input to an operation
causes an Invalid Operation exception, which is passed
to a user trap handler, if present. If a user trap
handler is not present, then a default QNaN is
created.''\par
From p. 3-7: ``In Flush-to-Zero mode, results that are
tiny before rounding, as described in the IEEE 754
standard, are flushed to a positive zero, and the UFC
flag, FPSCR[3], is set. Support code is not involved.
\ldots{} When the VFP9-S coprocessor is not in
Flush-to-Zero mode, any operation with a risk of
producing a tiny result, as described in the IEEE 754
standard, bounces to support code. If the operation
does not produce a tiny result, it returns the computed
result, and the UFC flag, FPSCR[3], is not set. The IXC
flag, FPSCR[4], is set if the operation is inexact. If
the operation produces a tiny result, the result is a
subnormal or zero value, and the UFC flag, FPSCR[3], is
set.",
}
@InProceedings{Arnold:2002:AOS,
author = "M. G. Arnold",
booktitle = "2002 {IEEE} Workshop on Multimedia Signal Processing",
title = "Avoiding oddification to simplify {MPEG}-1 decoding
with {LNS}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "125--129",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Low-precision logarithmic number system (LNS)
arithmetic can reduce the power consumption for MPEG
decoding compared to conventional fixed-point
techniques. Although this introduces small numeric
errors, which violate the IEEE-1180 standard for the
\ldots{}",
}
@InProceedings{Arnold:2002:ICL,
author = "M. G. Arnold",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS 2002}, 26--29 May 2002",
title = "Improved cotransformation for {LNS} subtraction",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-752--II-755",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Two co-transformations have been proposed previously
to avoid interpolation difficulties for logarithmic
subtraction: Arnold's and Coleman's. We show these two
are closely related, but that Arnold's is considerably
more accurate in the worst case. \ldots{}",
}
@PhdThesis{Arnold:2002:LNS,
author = "Mark Gordon Arnold",
title = "Logarithmic Number Systems for {MPEG} and Multimedia
Applications",
type = "{Ph.D.} thesis",
school = "University of Manchester",
address = "Manchester, UK",
pages = "xiv + 358",
month = apr,
year = "2002",
bibdate = "Fri Dec 01 07:16:52 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.proquest.com/pqdtglobal/docview/2780144113",
acknowledgement = ack-nhfb,
advisor = "Colin Donald Walter",
}
@InProceedings{Arnold:2002:RPC,
author = "Mark G. Arnold",
title = "Reduced Power Consumption for {MPEG} Decoding with
{LNS}",
crossref = "Schulte:2002:PII",
pages = "65--75",
year = "2002",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "LNS (logarithmic number system)",
summary = "By reducing the accuracy of the logarithmic number
system (LNS) it is possible to achieve lower power
consumption for multimedia applications, such as MPEG,
without significantly lowering the visual quality of
the output. An LNS wordsize of 8 to 10 \ldots{}",
}
@TechReport{Bailey:2002:AAP,
author = "David H. Bailey and Yozo Hida and Xiaoye S. Li and
Brandon Thompson",
title = "{ARPREC}: An arbitrary precision computation package",
type = "Technical Report",
number = "LBNL-53651",
institution = "Lawrence Berkeley National Laboratory",
address = "Berkeley, CA, USA",
month = sep,
year = "2002",
DOI = "https://doi.org/10.2172/817634",
bibdate = "Fri Jan 31 15:28:44 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://pubarchive.lbl.gov/islandora/object/ir:121949",
acknowledgement = ack-nhfb,
}
@InProceedings{Bailey:2002:HPC,
author = "David H. Bailey and David Broadhurst and Yozo Hida and
Xiaoye S. Li and Brandon Thompson",
title = "High Performance Computing Meets Experimental
Mathematics",
crossref = "IEEE:2002:STI",
pages = "??--??",
year = "2002",
bibdate = "Wed Nov 26 07:34:20 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sc-2002.org/paperpdfs/pap.pap124.pdf",
abstract = "In this paper we describe some novel applications of
high performance computing in a discipline now known as
experimental mathematics. The paper reviews some recent
published work, and then presents some new results that
have not yet appeared in the literature. A key
technique involved in this research is the PSLQ integer
relation algorithm (recently named one of ten
algorithms of the century by Computing in Science and
Engineering). This algorithm permits one to recognize a
numeric constant in terms of the formula that it
satisfies. We present a variant of PSLQ that is
well-suited for parallel computation, and give several
examples of new mathematical results that we have found
using it. Two of these computations were performed on
highly parallel computers, since they are not feasible
on conventional systems. We also describe a new
software package for performing arbitrary precision
arithmetic, which is required in this research.",
acknowledgement = ack-nhfb,
}
@Article{Barrio:2002:REB,
author = "Roberto Barrio",
title = "Rounding error bounds for the {Clenshaw} and
{Forsythe} algorithms for the evaluation of orthogonal
polynomial series",
journal = j-J-COMPUT-APPL-MATH,
volume = "138",
number = "2",
pages = "185--204",
day = "15",
month = jan,
year = "2002",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:23 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270100382X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Belanovic:2002:LPF,
author = "Pavle Belanovic and Miriam Leeser",
title = "A Library of Parameterized Floating-Point Modules and
Their Use",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2438",
pages = "657--666",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380657.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2438/24380657.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Bertot:2002:PGS,
author = "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
title = "A Proof of {GMP} Square Root",
journal = j-J-AUTOM-REASON,
volume = "29",
number = "3--4",
pages = "225--252",
month = sep,
year = "2002",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1023/A:1021987403425",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Sat Feb 08 08:59:09 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "https://link.springer.com/article/10.1023/A:1021987403425",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
keywords = "GNU Multiple Precision library",
}
@Article{Beuchat:2002:SMB,
author = "Jean-Luc Beuchat and Arnaud Tisserand",
title = "Small Multiplier-Based Multiplication and Division
Operators for Virtex-{II} Devices",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2438",
pages = "513--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380513.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2438/24380513.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Blackford:2002:USB,
author = "L. Susan Blackford and James Demmel and Jack Dongarra
and Iain Duff and Sven Hammarling and Greg Henry and
Michael Heroux and Linda Kaufman and Andrew Lumsdaine
and Antoine Petitet and Roldan Pozo and Karin Remington
and R. Clint Whaley",
title = "An updated set of {Basic Linear Algebra Subprograms
(BLAS)}",
journal = j-TOMS,
volume = "28",
number = "2",
pages = "135--151",
month = jun,
year = "2002",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/567806.567807",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 9 11:16:50 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "This paper expands the specification of a set of
kernel routines for linear algebra, historically called
the Basic Linear Algebra Subprograms and commonly known
as the BLAS.\par
Numerical linear algebra, particularly the solution of
linear systems of equations, linear least squares
problems, eigenvalue problems and singular value
problems, is fundamental to most calculations in
scientific computing, and is often the computationally
intense part of such calculations. Designers of
computer programs involving linear algebraic operations
have frequently chosen to implement certain low level
operations, such as the dot product or the matrix
vector product, as separate subprograms. This may be
observed both in many published codes and in codes
written for specific applications at many computer
installations.\par
A major aim of the standards defined in this paper is
to enable linear algebra libraries (both public domain
and commercial) to interoperate efficiently, reliably
and easily.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Boldo:2002:FRF,
author = "Sylvie Boldo and Marc Daumas",
booktitle = "10th {IMACS-GAMM} International Symposium on
Scientific Computing, Computer Arithmetic and Validated
Numerics, {SCAN-2002}, September 24--27, Paris,
France",
title = "Faithful rounding without fused multiply and
accumulate",
publisher = "????",
address = "????",
bookpages = "????",
pages = "??--??",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Nov 23 10:31:01 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://scan2002.lip6.fr/abstracts/boldo.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Boldo:2002:IAO,
author = "Sylvie Boldo",
title = "Introduction {\`a} l'arithm{\`e}tique des ordinateurs.
({French}) [Introduction to computer arithmetic]",
howpublished = "World-Wide Web document",
publisher = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
year = "2002",
bibdate = "Tue Nov 23 10:51:50 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Presented in 2002 at the ``Forum des jeunes
math{\`e}maticiennes et des jeunes
informaticiennes''.",
URL = "http://perso.ens-lyon.fr/sylvie.boldo/doc/FetM.ps",
acknowledgement = ack-nhfb,
language = "French",
}
@TechReport{Boldo:2002:NSC,
author = "Sylvie Boldo and Marc Daumas",
title = "Necessary and sufficient conditions for exact floating
point operations",
type = "Research Report",
number = "2002-44",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
month = nov,
year = "2002",
bibdate = "Tue Nov 23 10:54:25 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4644.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Boldo:2002:PSVa,
author = "Sylvie Boldo and Marc Daumas",
title = "Properties of the Subtraction Valid for any Floating
Point System",
type = "Research Report",
number = "2002-23",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
month = jun,
year = "2002",
bibdate = "Tue Nov 23 11:08:31 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2002/RR2002-23.ps.gz;
ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4473.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Boldo:2002:PSVb,
author = "Sylvie Boldo and Marc Daumas",
editor = "Rance Cleaveland and Hubert Garavel",
booktitle = "7th International {ERCIM} Workshop on Formal Methods
for Industrial Critical Systems {(FMICS 02)}:
University of M{\'a}laga, Spain July 12--13, 2002",
title = "Properties of the Subtraction Valid for any Floating
Point System",
publisher = "Universidad de M{\'a}laga, Spain",
address = "M{\'a}laga, Spain",
bookpages = "v + 217",
pages = "137--149",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Nov 23 10:14:59 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Available as Technical Report ITI-2002-5, Dpto. de
Lenguajes y Ciencias de la Computaci{\'o}n, Universidad
de M{\'a}laga, Spain",
URL = "http://www.inrialpes.fr/vasy/fmics/workshop-7/proceedings.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Cardarilli:2002:RNS,
author = "G. C. Cardarilli and A. Del Re and A. Nannarelli and
M. Re",
booktitle = "{ISCAS 2002}, {IEEE} International Symposium on
Circuits and Systems, 26--29 May 2002",
title = "Residue number system reconfigurable datapath",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-756--II-759",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2002.1011463",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper we describe a possible approach to
implement a reconfigurable datapath for digital signal
processing. The datapath should be programmable in
terms of dynamic range, type and sequence of
operations. We chose to implement it in the \ldots{}",
}
@Article{Chesneaux:2002:FRN,
author = "Jean-Marie Chesneaux and Christiane Frougny and
Jean-Michel Muller",
title = "Foreword: Real Numbers",
journal = j-THEOR-COMP-SCI,
volume = "279",
number = "1-2",
pages = "1--2",
month = may,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:08:56 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Chiricescu:2002:MM,
author = "Silviu Chiricescu and Michael Schuette and Robin
Glinton and Herman Schmit",
title = "Morphable Multipliers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2438",
pages = "647--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380647.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2438/24380647.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Chotin:2002:FPU,
author = "R. Chotin and H. Mehrez",
booktitle = "9th International Conference on Electronics, Circuits
and Systems, 2002",
title = "A floating-point unit using stochastic arithmetic
compliant with the {IEEE-754} standard",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "603--606",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 17:14:11 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "In this paper, we present CESTAC, a method to control
round-off errors in floating-point scientific
computation, based on stochastic arithmetic. The real
time use of this method suffers from a bottleneck of
software calculations. This paper gives a \ldots{}",
}
@Article{Col:2002:ALC,
author = "Marie-Andr{\'e}e Jacob-Da Col",
title = "About local configurations in arithmetic planes",
journal = j-THEOR-COMP-SCI,
volume = "283",
number = "1",
pages = "183--201",
month = jun,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:08:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@InProceedings{Conway:2002:NOH,
author = "Richard Conway and Thomas Conway and John Nelson",
title = "New One-Hot {RNS} Structures for High-Speed Signal
Processing",
crossref = "Luk:2002:PSA",
pages = "381--392",
year = "2002",
bibdate = "Fri Jun 24 18:17:01 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bookstore.spie.org/index.cfm?fuseaction=DetailPaper&ProductId=452053",
abstract = "New efficient structures using the one-hot residue
number system (OHRNS) are presented. Normally the RNS
uses a binary representation for the residues, though
recently there has been renewed interest in the OHRNS,
which uses a simple, but novel representation for the
residues. The basic component of the OHRNS is the
barrel shifter, making the OHRNS suitable for very high
speed applications. The first of the new structures
presented reduces the power dissipation in OHRNS adder
trees. A modification to the normal barrel shifter is
proposed, which reduces the power dissipated by as much
as 30\%. This improvement is obtained through the use
of the modified barrel shifter and the appropriate
connection of active-low and active-high stages. This
overall power reduction offers the possibility of using
the OHRNS in place of a typical full adder based tree
in high speed DSP applications. A new storage register
for one-hot representations is detailed, which
overcomes the problem of having to use a large number
of registers. A new architecture is presented for fast
OHRNS sign detection. Sign detection is complex and
slow to perform in the RNS. A mixed radix conversion
(MRC) is typically used for sign detection in the
OHRNS. The new sign detection architecture is based on
a new property of the Chinese Remainder Theorem (CRT)
and is significantly faster than the MRC approach for
large moduli sets. Simulation results using SPICE are
detailed for the new structures.",
acknowledgement = ack-nhfb,
keywords = "One-Hot Residue Number System (OHRNS); Residue Number
System (RNS)",
}
@Article{Conway:2002:SRI,
author = "T. Conway",
title = "Static register implementation for one hot residue
number systems",
journal = j-ELECT-LETTERS,
volume = "38",
number = "2",
pages = "63--64",
day = "17",
month = jan,
year = "2002",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:20020050",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=21138",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keywords = "residue arithmetic; residue number system",
summary = "A method of implementing static registers for one-hot
residue number systems is described. The method
overcomes the high power dissipation problems
associated with conventional flip-flops and clock
distribution. The proposed design relies on the low
\ldots{}",
}
@Book{Cornea:2002:SCI,
author = "Marius Cornea and John Harrison and Ping Tak Peter
Tang",
title = "Scientific computing on {Itanium}-based systems",
publisher = pub-INTEL,
address = pub-INTEL:adr,
pages = "xvii + 406",
year = "2002",
ISBN = "0-9712887-7-1",
ISBN-13 = "978-0-9712887-7-5",
LCCN = "QA76.8.I83 C67 2002",
bibdate = "Sat Dec 06 15:02:26 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$69.95",
URL = "http://www.intel.com/intelpress/sum_scientific.htm",
abstract = "Written for professionals who need to write, port, or
maintain reliable, accurate, and efficient numerical
software for the Itanium architecture, Scientific
Computing on Itanium-based Systems shows you how to
construct key numerical infrastructure and application
programs.\par
This book describes the crucial techniques required for
stability and reliability in developing numerical
kernels and applications. Through numerous tested
examples, the authors explain how you can get the most
from the 64-bit architecture. This combination of
explanation with example helps you to make difficult
computations more easily and to increase the
performance of your numerical software.\par
This book provides examples to solve problems
encountered in scientific and engineering computations,
such as:\par
* Polynomial evaluation\\
* Complex arithmetic\\
* Quad-precision arithmetic\\
* Software pipelining, to include register rotation and
modulo-scheduled loop support\\
* SIMD instructions\\
* Interval arithmetic\\
* Fast-Fourier Transformation (FFT) algorithms\\
* Numerical linear algebra and basic linear algebra
subprograms(BLAS)\\
* Vector Math Library (VML)\\
* Cryptography",
acknowledgement = ack-nhfb,
}
@Article{Cowlishaw:2002:DPD,
author = "Michael F. Cowlishaw",
title = "Densely Packed Decimal Encoding",
journal = j-IEE-PROC-COMPUT-DIGIT-TECH,
volume = "149",
number = "3",
pages = "102--104",
year = "2002",
CODEN = "ICDTEA",
DOI = "https://doi.org/10.1049/ip-cdt:20020407",
ISSN = "1350-2387 (print), 1359-7027 (electronic)",
ISSN-L = "1350-2387",
bibdate = "Fri Jun 07 11:08:45 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEE Proceedings. Computers and Digital Techniques",
keywords = "decimal floating-point arithmetic",
}
@Misc{Cowlishaw:2002:TB,
author = "M. F. Cowlishaw",
title = "The `telco' benchmark",
howpublished = "World-Wide Web document.",
institution = "IBM Hursley Laboratory",
address = "Hursley, UK",
pages = "3",
year = "2002",
bibdate = "Fri Nov 28 11:14:02 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www2.hursley.ibm.com/decimal/telco.html",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@TechReport{Crandall:2002:OPF,
author = "R. E. Crandall and J. Papadopoulos",
title = "Octuple-precision floating point on {Apple G4}",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "8",
day = "8",
month = may,
year = "2002",
bibdate = "Tue Mar 19 09:06:09 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://images.apple.com/acg/pdf/oct3a.pdf",
acknowledgement = ack-nhfb,
}
@Article{Daumas:2002:ASN,
author = "Marc Daumas and Philippe Langlois",
title = "Additive symmetries: the non-negative case",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "143--157",
month = nov,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:15:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@InProceedings{deDinechin:2002:MTJ,
author = "Florent de Dinechin and J{\'e}r{\'e}mie Detrey",
title = "Multipartite Tables in {JBits} for the Evaluation of
Functions on {FPGA}'s",
crossref = "IEEE:2002:IRA",
pages = "154--160",
year = "2002",
bibdate = "Fri Jun 24 20:27:42 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Arenaire/News/JBits/",
abstract = "This paper presents the implementation, on Virtex
FPGAs, of a core generator for arbitrary numeric
functions in fixed-point format. The cores use the
state-of-theart multipartite table method, which allows
input and output precisions in the range of 8 to 24
bits on current Virtex chips. The implementation uses
the JBits API to embed elaborate optimisation
techniques in the description of the hardware.",
acknowledgement = ack-nhfb,
}
@TechReport{Defour:2002:SCSa,
author = "David Defour and Florent de Dinechin",
title = "Software Carry-Save for Fast Multiple-Precision
Algorithms",
type = "Research Report",
number = "2002-08",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "12",
month = feb,
year = "2002",
bibdate = "Wed Nov 24 07:47:53 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2002/RR2002-08.ps.gz;
http://www.ens-lyon.fr/LIP/Arenaire/Ware/SCSLib/",
acknowledgement = ack-nhfb,
}
@InProceedings{Defour:2002:SCSb,
author = "David Defour and Florent de Dinechin",
title = "Software Carry-Save for Fast Multiple-Precision
Algorithms",
crossref = "Cohen:2002:MSP",
pages = "29--39",
year = "2002",
bibdate = "Fri Jun 24 19:59:47 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxbooktitle = "35th International Congress of Mathematical Software,
Beijing, China, 2002",
xxnote = "Check: 1st or 35th congress??",
}
@InProceedings{Demmel:2002:AEA,
author = "J. Demmel and P. Koev",
title = "Accurate and Efficient Algorithms for Floating Point
Computation",
crossref = "Li:2002:PIC",
pages = "16",
year = "2002",
bibdate = "Mon Apr 25 07:13:09 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://math.mit.edu/~plamen/files/ICIAM_main.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Demmel:2002:AFP,
author = "James Demmel and Yozo Hida",
title = "Accurate floating-point summation",
type = "Report",
institution = "Computer Science Division and Mathematics Department,
University of California, Berkeley",
address = "Berkeley, CA, USA",
day = "8",
month = may,
year = "2002",
bibdate = "Wed May 08 15:15:07 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~demmel/AccurateSummation.pdf;
http://www.cs.berkeley.edu/~demmel/AccurateSummation.ps",
abstract = "We present and analyze several simple algorithms for
accurately summing $n$ floating point numbers $ S =
\sum_{i = 1}^n s_i $ independent of how much
cancellation occurs in the sum. Let $f$ be the number
of significant bits in the $ s_i $. We assume a
register is available with $ F > f $ significant bits.
Then assuming that (1) $ n \leq \floor {2^{F - f} / (1
- 2^{-f})} + 1 $, (2) rounding is to nearest, (3) no
overflow occurs, and (4) all underflow is gradual,then
simply summing the $ s_i $ in decreasing order of
magnitude yields $S$ rounded to within just over 1.5
units in its last place. If $ S = 0 $, then it is
computed exactly. If we increase $n$ slightly to $
\floor {2^{F - f} / (1 - 2^{-f})} + 3 $ then all
accuracy can be lost. This result extends work of
Priest and others who considered double precision only
$ (F \geq 2 f) $. We apply this result to the floating
point formats in the (proposed revision of the) IEEE
floating point standard. For example, a dot product of
IEEE single precision vectors $ \sum_{i = 1}^n x_i \dot
{}y_i $ computed using double precision and sorting is
guaranteed correct to nearly $ 1.5 $ ulps as long as $
n \leq 33 $. If double extended is used $n$ can be as
large as $ 65537 $. We also show how sorting may be
avoided while retaining accuracy.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@InCollection{Demmel:2002:CAF,
author = "J. Demmel and Plamen Koev and Ben Diament",
title = "The Complexity of Accurate Floating Point
Computation",
crossref = "Li:2002:PIC",
volume = "III (1--3)",
year = "2002",
MRclass = "65G30 (65Y20)",
MRnumber = "MR1957571 (2004b:65060)",
bibdate = "Mon Apr 25 06:44:54 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~demmel/ICM_final.pdf;
http://www.fernuni-hagen.de/MATHPHYS/veselic/abstracts/abs_demmel.html",
abstract = "We consider the complexity of accurately evaluating
floating point expressions, by which we mean getting
some guaranteed relative accuracy, and identify a class
of expressions where this can be done in polynomial
time in the size of the expression and data. We also
have a simple expression not in this class for which we
have strong evidence that it cannot be evaluated
accurately in polynomial time. We extend these results
to the accurate computations of certain matrix
computations including inverses, LU decompositions, and
the SVD.\par
If time permits, we will also present a recent result
where we show that the complexity of approximate
condition estimation is as large as ``verifying''
matrix multiplication. Together with the
widely-believed conjecture that verifying that A*B=0
cannot be done more cheaply than by multiplying A*B,
this implies that all fast condition estimators in
widespread use have counterexamples, i.e. matrices for
which their estimates are arbitrarily wrong.",
acknowledgement = ack-nhfb,
pagecount = "10",
remark = "Also presented at the Householder Symposium on
Numerical Linear Algebra June 17--21, 2002 Peebles
Hotel Hydro, Scotland, and the IV International
Workshop on Accurate Solution of Eigenvalue Problems
Split, Croatia, June 24--27, 2002.",
}
@TechReport{Devillers:2002:FPE,
author = "Olivier Devillers and Philippe Guigue",
title = "Finite Precision Elementary Geometric Constructions",
type = "Technical report",
number = "RR 4559",
institution = "Unit{\'e} de recherche INRIA Sophia Antipolis",
address = "2004, route des Lucioles, BP 93, 06902 Sophia
Antipolis C{\'e}dex, France",
pages = "17",
month = sep,
year = "2002",
bibdate = "Tue Nov 13 21:54:25 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www-sop.inria.fr/rapports/sophia/RR-4559.html",
abstract = "In this paper we propose a new approach for the robust
computation of the nearest integer lattice points of
some specific geometric constructions (intersection of
two planar segments, circumcenter of a planar triangle
and of a spatial tetrahedron). Given that the data and
the final results of the geometric constructions are
stored using single precision floating point
representation (typically fixed size integers), the
proposed algorithms first perform the geometric
construction in IEEE double precision floating point
arithmetic, the rounding error is estimated, and only
if the error estimation indicates that the result of
the floating point computation may be wrong, the
computation is repeated with exact arithmetic. The
basic advantage is that exact computations are in most
cases avoided, thus reducing both the storage and the
required computation time.",
acknowledgement = ack-nhfb,
keywords = "computational geometry; Floating point filter;
robustness, floating point arithmetic",
}
@InProceedings{Dido:2002:FFP,
author = "J. Dido and N. Geraudie and L. Loiseau and O. Payeur
and Y. Savaria and D. Poirier",
title = "A flexible floating-point format for optimizing
data-paths and operators in {FPGA} based {DSPs}",
crossref = "Trimberger:2002:FTA",
pages = "50--55",
year = "2002",
DOI = "https://doi.org/10.1145/503048.503056",
bibdate = "Sat Oct 9 12:34:43 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Video signal processing requires complex algorithms
performing many basic operations on a video stream. To
perform these calculations in real-time in a FPGA, we
must use innovative structures to meet speed
requirements while managing complexity. As part of a
project aiming at the development of a video noise
reducer, we developed an optimized processing stream
that required some floating-point calculations. This
paper presents the rationale for developing a
floating-point unit, justifies the data representation
used, its implementation in a Xilinx VirtexE FPGA and
reports the performance we obtained. A divider using
this representation is also presented, with its
implementation and performances in the same FPGA.",
acknowledgement = ack-nhfb,
}
@Article{Elia:2002:ISC,
author = "M. Elia and M. Leone",
title = "On the inherent space complexity of fast parallel
multipliers for {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "3",
pages = "346--351",
month = mar,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.990131",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 09:41:49 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=990131",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Erle:2002:PSD,
author = "Mark A. Erle and Michael J. Schulte and J. G.
Linebarger",
title = "Potential Speedup with Decimal Floating-Point
Hardware",
crossref = "Matthews:2002:PTS",
pages = "1073--1077",
year = "2002",
bibdate = "Thu Mar 24 13:47:20 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2002-05.pdf",
abstract = "This paper addresses the potential speedup achieved by
using decimal floating-point hardware, instead of
software routines, on a high-performance superscalar
architecture. Software routines were written to perform
decimal addition, subtraction, multiplication, and
division. Cycle counts were then measured for each
instruction using the Simplescalar simulator. After
this, new hardware algorithms were developed, existing
hardware algorithms were analyzed, and cycle counts
were estimated for the same set of instructions using
specialized decimal floating-point hardware. This data
was then used to show the potential speedup obtained
for programs with different instruction mixes and a
recently developed benchmark.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Etiemble:2002:CAH,
author = "Daniel Etiemble",
title = "Computer arithmetic and hardware: ``off the shelf''
microprocessors versus ``custom hardware''",
journal = j-THEOR-COMP-SCI,
volume = "279",
number = "1--2",
pages = "3--27",
month = may,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:08:56 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper discusses the relationship between computer
arithmetic and hardware implementation. First, we
examine the impact of computer arithmetic on the
overall performance of today's microprocessors. By
comparing their evolution over the last 10 years, we
show that the performance of arithmetic operators is
far less critical than the performance of the memory
hierarchy or the branch predictors. We then discuss the
potential for improvement in arithmetic performance,
both for pipelined and non-pipelined operations. We
then examine the possible impact of new technologies,
such as MMX technology or asynchronous control of
microprocessors, on computer arithmetic. Finally, we
show that programmable logic devices now permit a
cost-effective implementation of specific arithmetic
number representations, such as serial arithmetic or
logarithmic representations.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Gaffar:2002:ACF,
author = "Altaf Abdul Gaffar and Wayne Luk and Peter Y. K.
Cheung and Nabeel Shirazi and James Hwang",
title = "Automating Customisation of Floating-Point Designs",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2438",
pages = "523--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380523.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2438/24380523.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Galbraith:2002:ASC,
author = "S. D. Galbraith and S. M. Paulus and N. P. Smart",
title = "Arithmetic on superelliptic curves",
journal = j-MATH-COMPUT,
volume = "71",
number = "237",
pages = "393--405",
month = jan,
year = "2002",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Thu Jan 31 06:16:28 MST 2002",
bibsource = "http://www.ams.org/mcom/2002-71-237;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-00-01297-7;
http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.dvi;
http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.pdf;
http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.ps;
http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.tex",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Garcia:2002:CBB,
author = "E. Garcia and M. J. Schulte",
title = "A Combined 16-Bit Binary and Dual {Galois} Field
Multiplier",
crossref = "IEEE:2002:IWS",
pages = "63--68",
year = "2002",
bibdate = "Sun Mar 04 17:49:09 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2002-04.pdf",
acknowledgement = ack-nhfb,
}
@Article{Geiselmann:2002:NRE,
author = "W. Geiselmann and J. Muller-Quade and R. Steinwandt",
title = "On {``A new representation of elements of finite
fields $ \mathrm {GF}(2^m) $ yielding small complexity
arithmetic circuits''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "12",
pages = "1460--1461",
month = dec,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2002.1146713",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 09:42:01 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1146713",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Glossner:2002:JED,
author = "C. John Glossner and Michael Schulte and Stamatis
Vassiliadis",
title = "A {Java}-Enabled {DSP}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2268",
pages = "307--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:05 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2268.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2268/22680307.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2268/22680307.pdf;
http://mesa.ece.wisc.edu/publications/cp_2002-01.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InCollection{Goldberg:2002:CA,
author = "David Goldberg",
title = "Computer Arithmetic",
crossref = "Hennessy:2002:CAQ",
chapter = "H",
pages = "H-1--H-74",
year = "2002",
bibdate = "Fri May 31 16:10:43 2002",
bibsource = "http://www.mkp.com/CA3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The complete Appendix H is not in the printed book; it
is available only at the book's Web site:
\path=http://www.mkp.com/CA3=.",
URL = "http://books.elsevier.com/companions/1558605967/appendices/1558605967-appendix-h.pdf",
acknowledgement = ack-nhfb,
}
@Article{Gonzalez:2002:NME,
author = "Daniel Gonz{\'a}lez and Antonio Garc{\'\i}a and Graham
A. Jullien and Javier Ram{\'\i}rez and Luis Parrilla
and Antonio Lloris",
title = "A New Methodology for Efficient Synchronization of
{RNS}-Based {VLSI} Systems",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2451",
pages = "188--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:32 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2451.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2451/24510188.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2451/24510188.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Gottwald:2002:NBL,
author = "G. A. Gottwald and M. Nicol",
title = "On the nature of {Benford's Law}",
journal = j-PHYSICA-A,
volume = "303",
number = "??",
pages = "387--396",
month = "????",
year = "2002",
CODEN = "PHYADX",
ISSN = "0378-4371 (print), 1873-2119 (electronic)",
ISSN-L = "0378-4371",
bibdate = "Thu Feb 15 16:32:55 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Physica A. Statistical Mechanics and its
Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/03784371",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Goubault:2002:APF,
author = "Eric Goubault and Matthieu Martel and Sylvie Putot",
title = "Asserting the Precision of Floating-Point
Computations: a Simple Abstract Interpreter",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2305",
pages = "209--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:22 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2305.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2305/23050209.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2305/23050209.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Guo:2002:RIB,
author = "Linfeng Guo and Yan Meng",
title = "Round-up of integer bit allocation",
journal = j-ELECT-LETTERS,
volume = "38",
number = "10",
pages = "466--467",
day = "9",
month = may,
year = "2002",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "A non-iterative algorithm is presented for the
round-up procedure of integer bit allocation. The
round-up algorithm will give the optimum result without
the disadvantages of the traditional iterative
\ldots{}",
}
@Book{Hamacher:2002:CO,
author = "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
Zaky",
title = "Computer organization",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
edition = "Fifth",
pages = "xx + 805",
year = "2002",
ISBN = "0-07-232086-9",
ISBN-13 = "978-0-07-232086-2",
LCCN = "QA76.9.C643 .H36 2002",
bibdate = "Sat May 18 14:24:11 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "McGraw-Hill series in computer organization and
architecture",
acknowledgement = ack-nhfb,
}
@Article{Hanrot:2002:DRF,
author = "G. Hanrot and J. Rivat and G. Tenenbaum and P.
Zimmermann",
title = "Density results on floating-point invertible numbers",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "135--141",
month = nov,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:15:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@TechReport{Hanrot:2002:LNM,
author = "G. Hanrot and P. Zimmermann",
title = "A long note on {Mulders}' short product",
type = "Technical Report",
number = "RR-4654",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "12",
month = nov,
year = "2002",
bibdate = "Sun Sep 10 08:17:26 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Mulders:2000:SMD}",
abstract = "The short product of two power series is the
meaningful part of the product of these objects, i.e.,
$ \sum_{i + j < n} a_i b_j x^{i + j} $. In [2], Mulders
gives an algorithm to compute a short product faster
than the full product in the case of Karatsuba's
multiplication [1]. This algorithm work by selecting a
cutoff point $k$ and performing a full $ k \times k $
product and two $ (n - k) \times (n - k) $ short
products recursively. Mulders also gives an
heuristically optimal cutoff point $ \beta n $. In this
paper, we determine the optimal cutoff point in
Mulders' algorithm. We also give a slightly more
general description of Mulders' method.",
acknowledgement = ack-nhfb,
}
@Article{Heckmann:2002:CLF,
author = "Reinhold Heckmann",
title = "Contractivity of linear fractional transformations",
journal = j-THEOR-COMP-SCI,
volume = "279",
number = "1-2",
pages = "65--82",
month = may,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:08:56 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Helms:2002:IPM,
author = "D. Helms and E. Schmidt and A. Schulz and A.
Stammermann and W. Nebel",
title = "An Improved Power Macro-Model for Arithmetic Datapath
Components",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2451",
pages = "16--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:32 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2451.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2451/24510016.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2451/24510016.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Hertling:2002:LBR,
author = "Peter Hertling",
title = "A lower bound for range enclosure in interval
arithmetic",
journal = j-THEOR-COMP-SCI,
volume = "279",
number = "1-2",
pages = "83--95",
month = may,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:08:56 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Hiasat:2002:HSR,
author = "A. A. Hiasat",
title = "High-speed and reduced-area modular adder structures
for {RNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "1",
pages = "84--89",
month = jan,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.980018",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 09:41:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=980018",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Higham:2002:ASN,
author = "Nicholas J. Higham",
title = "Accuracy and Stability of Numerical Algorithms",
publisher = pub-SIAM,
address = pub-SIAM:adr,
edition = "Second",
pages = "xxx + 680",
year = "2002",
DOI = "https://doi.org/10.1137/1.9780898718027",
ISBN = "0-89871-521-0 (hardcover), 0-89871-802-3 (e-book)",
ISBN-13 = "978-0-89871-521-7 (hardcover), 978-0-89871-802-7
(e-book)",
LCCN = "QA297 .H53 2002",
MRclass = "65G50 (65-02)",
MRnumber = "MR1927606 (2003g:65064)",
bibdate = "Wed Oct 30 14:20:02 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
abstract = "\booktitle{Accuracy and Stability of Numerical
Algorithms} gives a thorough, up-to-date treatment of
the behavior of numerical algorithms in finite
precision arithmetic. It combines algorithmic
derivations, perturbation theory, and rounding error
analysis, all enlivened by historical perspective and
informative quotations. This second edition expands and
updates the coverage of the first edition (1996) and
includes numerous improvements to the original
material. Two new chapters treat symmetric indefinite
systems and skew-symmetric systems, and nonlinear
systems and Newton's method. Twelve new sections
include coverage of additional error bounds for
Gaussian elimination, rank revealing $ L U $
factorizations, weighted and constrained least squares
problems, and the fused multiply-add operation found on
some modern computer architectures.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
tableofcontents = "List of Figures \\
List of Tables \\
Preface to Second Edition \\
Preface to First Edition \\
About the Dedication \\
1: Principles of Finite Precision Computation \\
2: Floating Point Arithmetic \\
3: Basics \\
4: Summation \\
5: Polynomials \\
6: Norms \\
7: Perturbation Theory for Linear Systems \\
8: Triangular Systems \\
9: $ L U $ Factorization and Linear Equations \\
10: Cholesky Factorization \\
11: Symmetric Indefinite and Skew-Symmetric Systems \\
12: Iterative Refinement \\
13: Block LU Factorization \\
14: Matrix Inversion \\
15: Condition Number Estimation \\
16: The Sylvester Equation \\
17: Stationary Iterative Methods \\
18: Matrix Powers \\
19: QR Factorization \\
20: The Least Squares Problem \\
21: Underdetermined Systems \\
22: Vandermonde Systems \\
23: Fast Matrix Multiplication \\
24: The Fast Fourier Transform and Applications \\
25: Nonlinear Systems and Newton's Method \\
26: Automatic Error Analysis \\
27: Software Issues in Floating Point Arithmetic \\
28: A Gallery of Test Matrices \\
Appendix A: Solutions to Problems \\
Appendix B: Acquiring Software \\
Appendix C: Program Libraries \\
Appendix D: The Matrix Computation Toolbox \\
Bibliography \\
Name Index \\
Subject Index",
}
@Article{Hitchcock:2002:NEC,
author = "Yvonne Hitchcock and Paul Montague",
title = "A New Elliptic Curve Scalar Multiplication Algorithm
to Resist Simple Power Analysis",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2384",
pages = "214--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:02 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2384.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2384/23840214.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2384/23840214.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Hoenninger:2002:FPD,
author = "J. C. {Hoenninger III} and L. E. Crooks and M.
Arakawa",
title = "A floating-point digital receiver for {MRI}",
journal = j-IEEE-TRANS-BIOMED-ENG,
volume = "49",
number = "7",
pages = "689--693",
month = jul,
year = "2002",
CODEN = "IEBEAX",
ISSN = "0018-9294 (print), 1558-2531 (electronic)",
ISSN-L = "0018-9294",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Biomedical Engineering",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10",
summary = "A magnetic resonance imaging (MRI) system requires the
highest possible signal fidelity and stability for
clinical applications. Quadrature analog receivers have
problems with channel matching, dc offset and
analog-to-digital linearity. Fixed-point \ldots{}",
}
@InProceedings{Honda:2002:DFT,
author = "M. Honda and H. Harada and M. Fujise",
booktitle = "{VTC} Spring 2002, {IEEE 55th} Vehicular Technology
Conference, 6--9 May 2002",
title = "Design of fault-tolerant digital filters based on
redundant residue number arithmetic for over-the-air
reconfiguration in software radio communication
systems",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "280--284",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1109/VTC.2002.1002710",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Over-the-air reconfiguration is a key characteristic
of software defined radio communication systems. It
offers great advantages in terms of cost-effective
software deployment to a large number of user
terminals. It also enables manufacturers and \ldots{}",
}
@Article{Hug:2002:DBP,
author = "Hubert Hug and Rainer Schuler",
title = "{DNA}-based Parallel Computation of Simple
Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2340",
pages = "321--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:41 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2340.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2340/23400321.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2340/23400321.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Misc{Ide:2002:GTE,
author = "Nobuhiro Ide and Atsushi Kunimatsu and Maki Ueno",
title = "Graphic translate engine, floating point arithmetic
unit and floating point multiply-add calculation unit",
howpublished = "US Patent 6,388,672",
day = "14",
month = may,
year = "2002",
bibdate = "Thu Oct 17 11:19:42 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US6388672B1",
abstract = "An internal memory section is divided into plural
memory blocks. During a period of time, a relevant
memory block of the internal memory section is
connected to an external memory unit, while another
memory block thereof is connected to a data holding
section. During a succeeding period of time, the
relevant memory block is connected to the data holding
section, while the other memory block is connected to
the external memory unit. Data exchange between the
data holding section and the external memory unit via
the internal memory section is performed while the
alternative connection is repeated.",
acknowledgement = ack-nhfb,
remark = "Patent filed 31 January 1997, granted to Toshiba
Corporation on 14 May 2002, possibly expired on 31
January 2019.",
}
@InProceedings{Iso:2002:NCI,
author = "Yuusuke Iso and Hiroshi Fujiwara",
title = "Numerical Computations for Ill-conditioned Problems by
Multiple-Precision Systems",
crossref = "Babuska:2002:MMN",
volume = "19",
pages = "185--194",
year = "2002",
DOI = "https://doi.org/10.1007/978-3-642-56288-4_13",
bibdate = "Sat Dec 22 08:36:17 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncse.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-56288-4_13",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-56288-4",
book-URL = "http://www.springerlink.com/content/978-3-642-56288-4",
}
@PhdThesis{Jacobi:2002:FVF,
author = "Christian Jacobi",
title = "Formal verification of a fully {IEEE} compliant
floating point unit",
type = "{Ph.D.} thesis",
school = "Universit{\"a}t Saarbr{\"u}cken Fakult{\"a}t 6 ---
Naturwissenschaftlich-Technische Fakult{\"a}t I.
Fachrichtung 6.2 --- Informatik",
address = "Saarbr{\"u}cken, Germany",
year = "2002",
bibdate = "Tue May 07 16:38:40 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this thesis we describe the formal verification of
a fully IEEE compliant floating point unit (FPU). The
hardware is verified on the gate-level against a
formalization of the IEEE standard. The verification is
performed using the theorem proving system PVS. The FPU
supports both single and double precision floating
point numbers, normal and denormal numbers, all four
IEEE rounding modes, and exceptions as required by the
standard. Beside the verification of the combinatorial
correctness of the FPUs we pipeline the FPUs to allow
the integration into an out-of-order processor. We
formally define the correctness criterion the pipelines
must obey in order to work properly within the
processor. We then describe a new methodology based on
combining model checking and theorem proving for the
verification of the pipelines",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:2002:FPC,
author = "W. Kahan",
title = "{Fclass}: a Proposed Classification of Standard
Floating-Point Operands",
howpublished = "World-Wide Web document",
pages = "6",
day = "23",
month = mar,
year = "2002",
bibdate = "Mon Apr 25 17:53:00 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/ieee754status/Fclass.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kim:2002:BSA,
author = "Hyun-Sung Kim and Kee-Young Yoo",
title = "Bit-Serial {AOP} Arithmetic Architectures over {GF$
(2^m) $}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2437",
pages = "303--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Nov 30 20:57:24 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2437.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.de/link/service/series/0558/bibs/2437/24370303.htm;
http://link.springer.de/link/service/series/0558/papers/2437/24370303.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Kim:2002:IDS,
author = "Nam-Yeun Kim and Dae-Ghon Kho and Kee-Young Yoo",
title = "Inversion\slash Division Systolic Architecture for
Public-Key Cryptosystems in {GF($ 2^m $) }",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2433",
pages = "289--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Thu Sep 12 08:41:42 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2433.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2433/24330289.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2433/24330289.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Book{Koren:2002:CAA,
author = "Israel Koren",
title = "Computer Arithmetic Algorithms",
publisher = pub-A-K-PETERS,
address = pub-A-K-PETERS:adr,
edition = "Second",
pages = "xv + 281",
year = "2002",
ISBN = "1-56881-160-8 (hardcover), 1-4398-6371-7 (e-book)",
ISBN-13 = "978-1-56881-160-4 (hardcover), 978-1-4398-6371-8
(e-book)",
LCCN = "QA76.9.C62 K67",
bibdate = "Sat May 04 10:29:22 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
abstract = "Concentrating on the underlying principles, this book
explains the algorithms used in arithmetic operations
on digital computers. It identifies the similarities
between the different algorithms and provides guidance
for selecting the appropriate algorithms for a given
technology. Chapters cover conventional number systems,
unconventional fixed-radix number systems, sequential
algorithms for multiplication and division, binary
floating-point numbers, fast addition, high-speed
multiplication, fast division, division through
multiplication, the evaluations of elementary
functions, logarithmic number systems, and the residue
number system.",
acknowledgement = ack-nhfb,
tableofcontents = "1: Conventional Number Systems \\
2: Unconventional Fixed-Radix Number Systems \\
3: Sequential Algorithms for Multiplication and
Division \\
4: Binary Floating-Point Numbers \\
5: Fast Addition \\
6: High-Speed Multiplication \\
7: Fast Division \\
8: Division Through Multiplication \\
9: Evaluation of Elementary Functions \\
10: Logarithmic Number Systems \\
11: The Residue Number System",
}
@Article{Kornerup:2002:PRN,
author = "Peter Kornerup and Jean-Claude Bajard and Christiane
Frougny and Jean-Michel Muller",
title = "Preface: Real Numbers and Computers",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "133--134",
month = nov,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:15:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Koutroumpezis:2002:ADR,
author = "G. Koutroumpezis and K. Tatas and D. Soudris and S.
Blionas and K. Masselos and A. Thanailakis",
title = "Architecture Design of a Reconfigurable Multiplier for
Flexible Coarse-Grain Implementations",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2438",
pages = "1027--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24381027.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2438/24381027.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Misc{Krygowski:2002:FPM,
author = "C. A. Krygowski and E. M. Schwarz",
title = "Floating-point multiplier for de-normalized inputs",
day = "5",
month = sep,
year = "2002",
bibdate = "Fri Nov 28 15:26:12 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "U.S. Patent Application No. 2002/0124037 A1.",
acknowledgement = ack-nhfb,
}
@Article{Ku:2002:NPA,
author = "Kyo-Min Ku and Kyeoung-Ju Ha and Hyun-Sung Kim and
Kee-Young Yoo",
title = "New Parallel Architecture for Modular Multiplication
and Squaring Based on Cellular Automata",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2367",
pages = "359--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:54 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2367.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2367/23670359.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2367/23670359.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Book{Kulisch:2002:AAD,
author = "U. Kulisch",
title = "Advanced Arithmetic for the Digital Computer: Design
of Arithmetic Units",
publisher = pub-SPRINGER-WIEN,
address = pub-SPRINGER-WIEN:adr,
pages = "xii + 141",
year = "2002",
ISBN = "3-211-83870-8",
ISBN-13 = "978-3-211-83870-9",
LCCN = "QA76.9.C62 K85 2002",
bibdate = "Mon Feb 03 07:48:36 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "EUR 25.00",
URL = "http://www.springer.at/main/book.jsp?bookID=3-211-83870-8&categoryID=10",
acknowledgement = ack-nhfb,
keywords = "accuracy; computer algebra; floating-point arithmetic;
interval arithmetic; scalar product; speed of
computation; vector operations",
}
@InProceedings{Kulisch:2002:RNZ,
author = "Ulrich Kulisch",
editor = "Peter Kornerup and Jean-Claude Bajard and Christiane
Frougny and Jean-Michel Muller",
booktitle = "4th Real Numbers and Computers Conference, Dagstuhl,
Germany, 2000",
title = "Rounding near zero",
volume = "291(2)",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "23--29",
day = "5",
month = jan,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 24 09:14:41 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = j-THEOR-COMP-SCI,
acknowledgement = ack-nhfb,
remark = "This reference is incorrect: there is no paper by
Kulisch in this journal issue. Where was it
published??",
}
@Article{Kwon:2002:EBS,
author = "Soonhak Kwon and Heuisu Ryu",
title = "Efficient Bit Serial Multiplication Using Optimal
Normal Bases of Type {II} in {{\em GF\/}}$ (2^m) $",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2433",
pages = "300--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Thu Sep 12 08:47:11 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2433.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2433/24330300.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2433/24330300.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Lang:2002:FPF,
author = "T. Lang and J. Bruguera",
title = "Floating-point fused multiply-add with reduced
latency",
crossref = "IEEE:2002:IIC",
pages = "145--150",
year = "2002",
DOI = "https://doi.org/10.1109/ICCD.2002.1106762",
bibdate = "Fri Jun 24 14:33:25 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/dl/proceedings/iccd/2002/1700/00/17000145.pdf",
abstract = "We propose an architecture for the computation of the
floating-point multiply-add-fused (MAF) operation $ A +
(B \times C) $. This architecture is based on the
combined addition and rounding (using a dual adder) and
on the anticipation of the normalization step before
the addition. Because the normalization is performed
before the addition, it is not possible to overlap the
leading-zero-anticipator with the adder. Consequently,
to avoid the increase in delay we modify the design of
the LZA so that the leading bits of its output are
produced first and can be used to begin the
normalization. Moreover, parts of the addition are also
anticipated. We have estimated the delay of the
resulting architecture for double-precision format,
considering the load introduced by long connections,
and estimate a reduction of about 15\% to 20\% with
respect to traditional implementations of the
floating-point MAF unit.",
acknowledgement = ack-nhfb,
}
@Article{Lee:2002:DSS,
author = "Keon-Jik Lee and Kee-Won Kim and Kee-Young Yoo",
title = "Digit-serial-in-serial-out systolic multiplier for
{Montgomery} algorithm",
journal = j-INFO-PROC-LETT,
volume = "82",
number = "2",
pages = "65--71",
day = "30",
month = apr,
year = "2002",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Mon Jan 26 06:35:43 MST 2004",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.com/gej-ng/10/23/20/86/33/27/abstract.html",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@InProceedings{Lee:2002:PFP,
author = "B. Lee and N. Burgess",
title = "Parameterisable floating-point operations on {FPGA}",
crossref = "Matthews:2002:PTS",
volume = "2",
pages = "1064--1068",
year = "2002",
DOI = "https://doi.org/10.1109/ACSSC.2002.1196947",
bibdate = "Sat Oct 9 12:47:53 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper presents a group of IEEE 754-style
floating-point units targeted at Xilinx VirtexII FPGA.
Special features of the technology are taken advantage
of to produce optimised components. Pipelined designs
are given that show the latency of 100 MHz
single-precision components. Non-pipelined reference
designs are included for future comparison purposes.",
acknowledgement = ack-nhfb,
}
@TechReport{Leeser:2002:LPH,
author = "Miriam Leeser",
title = "A Library of Parameterized Hardware Modules for
Floating Point Arithmetic and Its Use",
type = "Technical report",
institution = "Department of Electrical and Computer Engineering,
Northeastern University",
address = "Boston, MA, USA",
pages = "28",
year = "2002",
bibdate = "Mon May 22 11:20:03 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Presented at High Performance Embedded Computing
(HPEC) Workshop (6th) held in Lexington, MA on 24--26
September 2002.",
acknowledgement = ack-nhfb,
}
@Article{Leong:2002:IMM,
author = "P. C. Leong and E. C. Tan and P. C. Tan",
title = "An iterative modular multiplication algorithm",
journal = j-COMPUT-MATH-APPL,
volume = "44",
number = "1--2",
pages = "175--180",
month = jul,
year = "2002",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:23 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122102001384",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Lester:2002:CAF,
author = "David Lester and Scott Chambers and Heoi Lee Lu",
title = "A constructive algorithm for finding the exact roots
of polynomials with computable real coefficients",
journal = j-THEOR-COMP-SCI,
volume = "279",
number = "1-2",
pages = "51--64",
month = may,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:08:56 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Lester:2002:UPV,
author = "David Lester and Paul Gowland",
title = "Using {PVS} to validate the algorithms of an exact
arithmetic",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "203--218",
month = nov,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:15:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Li:2002:DIT,
author = "Xiaoye S. Li and James W. Demmel and David H. Bailey
and Greg Henry and Yozo Hida and Jimmy Iskandar and
William Kahan and Suh Y. Kang and Anil Kapur and
Michael C. Martin and Brandon J. Thompson and Teresa
Tung and Daniel J. Yoo",
title = "Design, implementation and testing of extended and
mixed precision {BLAS}",
journal = j-TOMS,
volume = "28",
number = "2",
pages = "152--205",
month = jun,
year = "2002",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/567806.567808",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Nov 9 11:16:50 MST 2002",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://crd.lbl.gov/~xiaoye/XBLAS/",
abstract = "This paper describes the design rationale, a C
implementation, and conformance testing of a subset of
the new Standard for the BLAS (Basic Linear Algebra
Subroutines): Extended and Mixed Precision BLAS.
Permitting higher internal precision and mixed
input\slash output types and precisions allows us to
implement some algorithms that are simpler, more
accurate, and sometimes faster than possible without
these features. The new BLAS are challenging to
implement and test because there are many more
subroutines than in the existing Standard, and because
we must be able to assess whether a higher precision is
used for internal computations than is used for either
input or output variables. We have therefore developed
an automated process of generating and systematically
testing these routines. Our methodology is applicable
to languages besides C. In particular, our algorithms
used in the testing code will be valuable to all other
BLAS implementors. Our extra precision routines achieve
excellent performance---close to half of the machine
peak Megaflop rate even for the Level 2 BLAS, when the
data access is stride one.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accurate floating-point summation",
}
@TechReport{Li:2002:LLF,
author = "Ren-Cang Li and Peter Markstein and Jon P. Okada and
James W. Thomas",
title = "The {\tt libm} library and floating-point arithmetic
for {HP-UX} on {Itanium-2}",
type = "Technical report",
institution = inst-HP,
address = inst-HP:adr,
pages = "??",
year = "2002",
bibdate = "Tue Nov 18 15:06:56 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "????",
acknowledgement = ack-nhfb,
}
@PhdThesis{Liddicoat:2002:HPA,
author = "Albert Austin Liddicoat",
title = "High-performance arithmetic for division and the
elementary functions",
type = "{Ph.D.} Thesis",
school = "Stanford University",
address = "Stanford, CA, USA",
pages = "141",
year = "2002",
ISBN = "0-493-53347-8",
ISBN-13 = "978-0-493-53347-6",
bibdate = "Fri Oct 25 17:06:55 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://wwwlib.umi.com/dissertations/fullcit/3040035;
http://wwwlib.umi.com/dissertations/preview/3040035",
acknowledgement = ack-nhfb,
}
@InProceedings{Lienhart:2002:UFP,
author = "G. Lienhart and A. Kugel and R. Manner",
title = "Using floating-point arithmetic on {FPGAs} to
accelerate scientific {$N$}-body simulations",
crossref = "Pocek:2002:FAI",
pages = "182--191",
year = "2002",
DOI = "https://doi.org/10.1109/FPGA.2002.1106673",
bibdate = "Sat Oct 9 12:49:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper investigates the usage of floating-point
arithmetic on FPGAs for N-Body simulation in natural
science. The common aspect of these applications is the
simple computing structure where forces between a
particle and its surrounding particles are summed up.
The role of reduced precision arithmetic is discussed,
and our implementation of a floating-point arithmetic
library with parameterized operators is presented. On
the base of this library, implementation strategies of
complex arithmetic units are discussed. Finally the
realization of a fully pipelined pressure force
calculation unit consisting of 60 floating-point
operators with a resulting performance of 3.9 Gflops on
an off the shelf FPGA is presented.",
acknowledgement = ack-nhfb,
}
@Article{Loh:2002:RER,
author = "Eugene Loh and G. William Walster",
title = "{Rump}'s Example Revisited",
journal = j-RELIABLE-COMPUTING,
volume = "8",
number = "3",
pages = "245--248",
month = jun,
year = "2002",
CODEN = "RCOMF8",
DOI = "https://doi.org/10.1023/A:1015569431383",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
bibdate = "Sat Jan 5 10:21:56 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=8&issue=3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
URL = "http://link.springer.com/article/10.1023/A%3A1015569431383/;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=3&spage=245;
http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=3&spage=245-248",
acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
}
@Article{Lutz:2002:BGB,
author = "Michael J. Lutz",
title = "Bookshelf: Getting the Bugs Out [{Debugging: The 9
Indispensable Rules for Finding Even the Most Elusive
Software and Hardware Problems}]; Saving Time With
Arithmetic and Logic [{Hacker's Delight}]; Probability
and Computing [{Probability and Statistics with
Reliability, Queuing and Computer Science Applications,
2nd edition}]; Graphics Toolbox [{Guide to Graphics
Software Tools}]",
journal = j-COMPUTER,
volume = "35",
number = "12",
pages = "117--117",
month = dec,
year = "2002",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Dec 12 19:53:37 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/dl/mags/co/2002/12/rz117.htm;
http://csdl.computer.org/dl/mags/co/2002/12/rz117.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Madhukumar:2002:RNS,
author = "A. S. Madhukumar and F. Chin",
title = "Residue number system-based multicarrier {CDMA} system
for high-speed broadband wireless access",
journal = j-IEEE-TRANS-BROADCAST,
volume = "48",
number = "1",
pages = "46--52",
month = mar,
year = "2002",
CODEN = "IETBAC",
DOI = "https://doi.org/10.1109/11.992855",
ISSN = "????",
ISSN-L = "0018-9316",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=21407",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Broadcasting",
keywords = "residue arithmetic; residue number system",
summary = "This correspondence is concerned with a new method to
enhance the bandwidth efficiency of a multicarrier CDMA
system by using a residue number based representation
for information symbols. The residues are mapped into a
set of orthogonal sequences \ldots{}",
}
@Article{Matousek:2002:LNS,
author = "Rudolf Matousek and Milan Tich{\'y} and Zdenek Pohl
and Jir{\'\i} Kadlec and Chris Softley and Nick
Coleman",
title = "Logarithmic Number System and Floating-Point
Arithmetics on {FPGA}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2438",
pages = "175--188",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380627.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2438/24380627.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
xxpages = "627--??",
}
@Article{Matula:2002:PTP,
author = "David W. Matula and Lee D. McFearin",
title = "A $ p \times p $ bit fraction model of binary floating
point division and extremal rounding cases",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "159--182",
month = nov,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:15:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{McCluskey:2002:MLF,
author = "Glen McCluskey",
title = "Math library functions in {C9X}",
journal = j-LOGIN,
volume = "27",
number = "2",
pages = "9--13",
month = apr,
year = "2002",
CODEN = "LOGNEM",
ISSN = "1044-6397 (print), 2169-9364 (electronic)",
bibdate = "Sat May 04 10:26:38 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = ";login: the USENIX Association newsletter",
}
@PhdThesis{McIlhenny:2002:CNL,
author = "Robert Dean McIlhenny",
title = "Complex Number On-line Arithmetic for Reconfigurable
Hardware: Algorithms, Implementations, and
Application",
type = "{Ph.D.} dissertation",
school = "Computer Science Department, University of California,
Los Angeles",
address = "Los Angeles, CA, USA",
pages = "xiv + 182",
year = "2002",
ISBN = "0-493-82665-3",
ISBN-13 = "978-0-493-82665-3",
bibdate = "Sat Dec 04 09:27:33 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Complex number arithmetic plays an important role in
various signal processing tasks, such as correlations,
convolutions, and digital filtering. There is a need in
such applications to exploit parallelism in
implementing sequences of arithmetic expressions, as
well as to reduce the bandwidth of the data path.
Reconfigurable architectures are emerging as a viable
technology for mapping numeric-intensive computations
onto hardware. In order to provide efficient
implementations that can accommodate changes with a
minimal amount of redesign, the methodology for
deriving algorithms and corresponding implementations
must be flexible toward change.\par
In this dissertation, we present an efficient
representation which treats the real and imaginary
components as a unified number. We propose algorithms
for various complex number on-line floating-point
arithmetic operations. The algorithms are translated
into actual implementations mapped onto reconfigurable
hardware. The implementations are applied toward
computing the complex singular value decomposition of a
matrix, with a significant reduction in cost compared
to networks of real number on-line and parallel
arithmetic approaches.",
acknowledgement = ack-nhfb,
advisor = "Milo{\v{s}} Ercegovac",
}
@Article{Messine:2002:EAA,
author = "F. Messine",
title = "Extentions [sic] of Affine Arithmetic: Application to
Unconstrained Global Optimization",
journal = j-J-UCS,
volume = "8",
number = "11",
pages = "992--??",
day = "28",
month = nov,
year = "2002",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Tue Dec 16 10:06:03 MST 2003",
bibsource = "http://www.jucs.org/jucs;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/jucs_8_11/extentions_of_affine_arithmetic",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
keywords = "interval arithmetic",
}
@InProceedings{Molina:2002:BLA,
author = "M. C. Molina and J. M. Mendias and R. Hermida",
booktitle = "Proceedings of the Euromicro Symposium on Digital
System Design",
title = "Bit-level allocation of multiple-precision
specifications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "385--392",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper proposes an allocation algorithm able to
perform the combined resource selection and operation
binding of multiple-precision specifications that
maximizes the bit-level reuse of hardware resources.
Additionally, it presents an analytic \ldots{}",
}
@InProceedings{Molina:2002:HLS,
author = "M. C. Molina and J. M. Mendias and R. Hermida",
booktitle = "Proceedings of the 39th Design Automation Conference,
10--14 June 2002",
title = "High-level synthesis of multiple-precision circuits
independent of data-objects length",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "612--615",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper presents an heuristic method to perform the
high-level synthesis of multiple-precision
specifications. The scheduling is based on the balance
of the number of bits calculated per cycle, and the
allocation on the bit-level reuse of the \ldots{}",
}
@InProceedings{Molina:2002:MPC,
author = "M. C. Molina and J. M. Mendias and R. Hermida",
booktitle = "Proceedings of the Design, Automation and Test in
Europe Conference and Exhibition, 4--8 March 2002",
title = "Multiple-precision circuits allocation independent of
data-objects length",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "909--913",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:53:44 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper presents an heuristic method to solve the
combined resource selection and binding problems for
the high-level synthesis of multiple-precision
specifications. Traditionally, the number of functional
(and storage) units in a datapath is \ldots{}",
}
@Article{Moller:2002:PEC,
author = "Bodo M{\"o}ller",
title = "Parallelizable Elliptic Curve Point Multiplication
Method with Resistance against Side-Channel Attacks",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2433",
pages = "402--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:26 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2433.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2433/24330402.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2433/24330402.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Motegi:2002:EGG,
author = "Makoto Motegi and Naofumi Homma and Takafumi Aoki and
Tatsuo Higuchi",
title = "Evolutionary Graph Generation System and Its
Application to Bit-Serial Arithmetic Circuit
Synthesis",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2439",
pages = "831--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Nov 30 20:57:24 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2439.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.de/link/service/series/0558/bibs/2439/24390831.htm;
http://link.springer.de/link/service/series/0558/papers/2439/24390831.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Okeya:2002:FSM,
author = "Katsuyuki Okeya and Kunihiko Miyazaki and Kouichi
Sakurai",
title = "A Fast Scalar Multiplication Method with Randomized
Projective Coordinates on a {Montgomery}-Form Elliptic
Curve Secure against Side Channel Attacks",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2288",
pages = "428--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:14 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2288.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2288/22880428.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2288/22880428.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Book{Overton:2002:CNC,
author = "Michael L. Overton",
title = "{C}{\'o}mputo num{\'e}rico con aritm{\'e}tica de punto
flotante {IEEE}",
volume = "19",
publisher = "Sociedad Matem{\'a}tica Mexicana",
address = "M{\'e}xico",
pages = "xii + 123",
year = "2002",
ISBN = "970-32-0086-9",
ISBN-13 = "978-970-32-0086-3",
MRclass = "65-02 (65Bxx 65G30)",
MRnumber = "MR1925397 (2003g:65003)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Con un teorema, una regla emp{\'\i}rica y ciento un
ejercicios. [Including one theorem, one rule of thumb
and one hundred and one exercises], Translated from the
2001 English original by Alejandro Casares Maldonado",
series = "Aportaciones Matem\'aticas: Textos [Mathematical
Contributions: Texts]",
acknowledgement = ack-nhfb,
}
@InProceedings{Paliouras:2002:LPC,
author = "V. Paliouras and A. Skavantzos and T. Stouraitis",
booktitle = "{ISCAS 2002}, {IEEE} International Symposium on
Circuits and Systems, 26--29 May 2002",
title = "Low power convolvers using the {Polynomial Residue
Number System}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-748--II-751",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2002.1011461",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A novel approach for the reduction of the power
dissipated in a signal processing application is
introduced in this paper. By exploiting the properties
of the Polynomial Residue Number System (PRNS) and of
the arithmetic modulo (2/sup n/+1), the \ldots{}",
}
@InProceedings{Paliouras:2002:OLO,
author = "V. Paliouras",
booktitle = "{IEEE} International Symposium on Circuits and
Systems: {ISCAS 2002}, 26--29 May 2002",
title = "Optimization of {LNS} operations for embedded signal
processing applications",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-744--II-747",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper introduces an optimization technique for
the design of logarithmic arithmetic-based embedded
signal processors. The fundamental concept of the
proposed technique is the determination of the optimal
values of the logarithmic base b, which \ldots{}",
}
@Article{Park:2002:SPM,
author = "Young-Ho Park and Sangtae Jeong and Jongin Lim",
title = "Speeding Up Point Multiplication on Hyperelliptic
Curves with Efficiently-Computable Endomorphisms",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2332",
pages = "197--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:37 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2332.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2332/23320197.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2332/23320197.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Paul:2002:BB,
author = "Wolfgang J. Paul and Peter-Michael Seidel",
title = "To {Booth} or not to {Booth}?",
journal = j-INTEGRATION-VLSI-J,
volume = "32",
number = "1--3",
pages = "5--40",
month = nov,
year = "2002",
CODEN = "IVJODL",
ISSN = "0167-9260 (print), 1872-7522 (electronic)",
ISSN-L = "0167-9260",
bibdate = "Mon Dec 24 10:05:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Booth Recoding is a commonly used technique to recode
one of the operands in binary multiplication. In this
way the implementation of a multipliers' adder tree can
be improved in both cost and delay. The improvement due
to Booth Recoding is said to be due to improvements in
the layout of the adder tree especially regarding the
lengths of wire connections and thus cannot be analyzed
with a simple gate model. Although conventional VLSI
models consider wires in layouts, they usually neglect
wires when modeling the delay. To make the layout
improvements due to Booth recoding tractable in a
technology-independent way, we introduce a VLSI model
that also considers wire delays and constant factors.
Based on this model we consider the layouts of binary
multipliers in a parametric analysis providing answers
to the question whether to use Booth Recoding or not.
We formalize and prove the folklore theorems that Booth
recoding improves the cost and cycle time of standard'
multipliers by certain constant factors. We also
analyze the number of full adders in certain 4/2
trees.",
acknowledgement = ack-nhfb,
fjournal = "Integration, the VLSI journal",
}
@InProceedings{Pillmeier:2002:DAB,
author = "M. R. Pillmeier and M. J. Schulte",
title = "Design Alternatives for Barrel Shifters and Rotators",
crossref = "Luk:2002:PSA",
pages = "436--447",
year = "2002",
bibdate = "Sun Mar 04 17:45:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2002-02.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Pineiro:2002:HRL,
author = "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera",
booktitle = "Application-Specific Systems, Architectures and
Processors, 2002. Proceedings. The {IEEE} International
Conference on. 17--19 July 2002",
title = "High-radix logarithm with selection by rounding",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "101--110",
year = "2002",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "A high-radix digit-recurrence algorithm or the
computation of the logarithm is presented in this
paper. Selection by rounding is used in iterations
j/spl ges/2, and selection by table in the first
iteration is combined with a restricted digit-set
\ldots{}",
}
@Article{Pineiro:2002:HSD,
author = "J. A. Pi{\~n}eiro and J. D. Bruguera",
title = "High-Speed Double Precision Computation of Reciprocal,
Division, Square Root, and Inverse Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "12",
pages = "1377--1388",
month = dec,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2002.1146704",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1146704",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "A new method for the high-speed computation of
double-precision floating-point reciprocal, division,
square root, and inverse square root operations is
presented in this paper. This method employs a
second-degree minimax polynomial approximation to
\ldots{}",
}
@Article{Puchta:2002:RNN,
author = "Jan-Christoph Puchta",
title = "Representation of Numbers with Negative Digits and
Multiplication of Small Integers",
journal = j-FIB-QUART,
volume = "40",
number = "1",
pages = "66--67",
month = feb,
year = "2002",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:03:31 MDT 2011",
bibsource = "http://www.fq.math.ca/40-1.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Scanned/40-1/puchta1.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly. Official Organ of the
Fibonacci Association",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Ramasubramanian:2002:ACL,
author = "Narasimhan Ramasubramanian and Ram Subramanian and
Santosh Pande",
title = "Automatic Compilation of Loops to Exploit Operator
Parallelism on Configurable Arithmetic Logic Units",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "13",
number = "1",
pages = "45--66",
month = jan,
year = "2002",
CODEN = "ITDSEO",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Sat Feb 23 09:26:04 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dlib.computer.org/td/books/td2002/pdf/l0045.pdf;
http://www.computer.org/tpds/td2001/l0045abs.htm",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
}
@Article{Ramirez:2002:FRF,
author = "J. Ram{\'\i}rez and A. Garc{\'\i}a and U. Meyer-Baese
and A. Lloris",
title = "Fast {RNS} {FPL}-based Communications Receiver Design
and Implementation",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2438",
pages = "472--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380472.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2438/24380472.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Reid-Green:2002:TEA,
author = "Keith S. Reid-Green",
title = "Three early algorithms: [{Bresenham}'s line-drawing
algorithm; a square-root algorithm; {Machin}'s
algorithm: computation of $ \pi $ ]",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "24",
number = "4",
pages = "10--13",
month = oct,
year = "2002",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/MAHC.2002.1114866",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Sat Nov 29 16:19:45 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
URL = "http://csdl.computer.org/dl/mags/an/2002/04/a4010.htm;
http://csdl.computer.org/dl/mags/an/2002/04/a4010.pdf;
http://csdl.computer.org/dl/mags/an/2002/04/a4010abs.htm",
acknowledgement = ack-nhfb,
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}
@TechReport{Revol:2002:MAPa,
author = "N. Revol and F. Rouillier",
title = "Motivations for an Arbitrary Precision Interval
Arithmetic and the {MPFI Library}",
type = "Report",
institution = "Laboratoire ANO, University of Lille and
CNRS/ENSL/INRIA Project Arenaire LIP, {\'E}cole Normale
Sup{\'e}rieure de Lyon, France, Project Spaces,
LORIA/INRIA/LIP 6, France",
pages = "6",
day = "17",
month = apr,
year = "2002",
bibdate = "Fri Mar 10 16:23:31 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://pauillac.inria.fr/cdrom/www/mpfi/ValidC02.pdf",
acknowledgement = ack-nhfb,
keywords = "interval arithmetic; multiple precision",
}
@InProceedings{Revol:2002:MAPb,
author = "Nathalie Revol and Fabrice Rouillier",
editor = "R. Baker Kearfott",
booktitle = "{SIAM} Workshop on Validated Computing 2002, Toronto,
Canada, May 23--25, 2002: extended abstracts",
title = "Motivations for an Arbitrary Precision Interval
Arithmetic and the {MPFI Library}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
bookpages = "187",
pages = "??--??",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "QA76.76.R44 W67 2002",
bibdate = "Fri Jan 28 15:34:54 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "MPFI is a library implementing interval arithmetic
with arbitrary accuracy. It can be freely downloaded
(including source code and documentation). It is
written in C and is based on the MPFR library for
arbitrary precision floating-point arithmetic, which is
in turn built upon the GMP library. MPFR has been
chosen because it provides outward rounding, even for
the elementary functions, which is mandatory to
implement interval arithmetic. An important issue in
interval computation is ``computing in the large'',
i.e., getting tight enclosures for the range of a
function over a large interval. However, this issue has
no well established answer, and one common way to
circumvent the problem consists in bisecting the input
interval again and again, until the evaluation of the
function upon each sub-part is tight enough. For some
problems, such as roots approximations or optimization
of a ``very flat'' function, splitting beyond the
limits of usual (single or double) floating-point
capacities reveals necessary in order to reach the
required accuracy on the function evaluation.",
acknowledgement = ack-nhfb,
}
@Article{Reyhani-Masoleh:2002:NCM,
author = "A. Reyhani-Masoleh and M. A. Hasan",
title = "A new construction of {Massey--Omura} parallel
multiplier over {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "5",
pages = "511--520",
month = may,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2002.1004590",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 09:41:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1004590",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Roesler:2002:NOH,
author = "Eric Roesler and Brent Nelson",
title = "Novel Optimizations for Hardware Floating-Point Units
in a Modern {FPGA} Architecture",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2438",
pages = "637--646",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:28 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380637.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2438/24380637.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Saed:2002:NSC,
author = "A. Saed and M. Ahmadi and G. A. Jullien",
title = "A number system with continuous valued digits and
modulo arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "11",
pages = "1294--1305",
month = nov,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2002.1047754",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 09:42:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1047754",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Sahin:2002:FFP,
author = "Ibrahim Sahin and Clay S. Gloster and Christopher
Doss",
title = "Feasibility of floating-point arithmetic in
reconfigurable computing systems",
crossref = "Vladimirova:2002:TMA",
pages = "??--??",
year = "2002",
bibdate = "Sat Oct 9 12:59:55 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://klabs.org/richcontent/MAPLDCon00/Abstracts/sahin_a.txt",
abstract = "Reconfigurable Computing (RC) has emerged as a viable
computing solution for computationally intensive
applications. Applications mapped to RC systems include
image processing algorithms, pattern recognition in
high energy physics and genetic optimization
algorithms. Due to the hardware complexity of the
floating point modules and limited resources available
in prior RC systems, applications that required
floating point operations were either, not mapped to RC
systems, or converted to fixed point before developing
the RC implementation. Recent advances in Field
Programmable Gate Array (FPGA) technology offer the
user more hardware resources on a single FPGA device
and thus the greater potential to develop complex RC
systems. In this paper, the feasibility of mapping
applications containing floating point operations to RC
systems is presented. Three floating point modules:
vector addition, subtraction, and multiplication were
modeled using VHDL and mapped to a Xilinx XC4044XL FPGA
device. These modules are highly pipelined and
optimized for both speed and area. Our results verify
that floating point applications are feasible and that
significant speedup can be obtained when mapping these
applications to RC systems.",
acknowledgement = ack-nhfb,
}
@Article{Sakai:2002:AES,
author = "Yasuyuki Sakai and Kouichi Sakurai",
title = "Algorithms for Efficient Simultaneous Elliptic Scalar
Multiplication with Reduced Joint {Hamming} Weight
Representation of Scalars",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2433",
pages = "484--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:26 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2433.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2433/24330484.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2433/24330484.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Sawada:2002:FVD,
author = "J. Sawada",
title = "Formal verification of divide and square root
algorithms using series calculation",
crossref = "Borrione:2002:TIW",
pages = "31--49",
year = "2002",
bibdate = "Fri Jun 24 15:14:00 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sawada:2002:MVS,
author = "Jun Sawada and Ruben Gamboa",
title = "Mechanical Verification of a Square Root Algorithm
Using {Taylor}'s Theorem",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2517",
pages = "274--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Nov 30 20:58:00 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm;
http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Schwarz:2002:MIE,
author = "E. M. Schwarz and M. A. Check and C.-L. K. Shum and T.
Koehler and S. B. Swaney and J. D. MacDougall and C. A.
Krygowski",
title = "The microarchitecture of the {IBM eServer z900}
processor",
journal = j-IBM-JRD,
volume = "46",
number = "4/5",
pages = "381--395",
month = "????",
year = "2002",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Fri Nov 22 17:58:43 MST 2002",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/464/schwarz.html;
http://www.research.ibm.com/journal/rd/464/schwarz.pdf",
abstract = "The recent IBM ESA/390 CMOS line of processors, from
1997 to 1999, consisted of the G4, G5, and G6
processors. The architecture they implemented lacked
64-bit addressability and had only a limited set of
64-bit arithmetic instructions. The processors also
lacked data and instruction bandwidth, since they
utilized a unified cache. The branch performance was
good, but there were delays due to conflicts in
searching and writing the branch target buffer. Also,
the hardware data compression and decimal arithmetic
performance, though good, was in demand by database and
COBOL programmers. Most of the performance concerns
regarding prior processors were due to area
constraints. Recent technology advances have increased
the circuit density by 50 percent over that of the G6
processor. This has allowed the design of several
performance-critical areas to be revisited. The end
result of these efforts is the IBM eServer z900
processor, which is the first high-end processor based
on the new 64-bit z/Architecture{\TM}.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "decimal floating-point arithmetic",
ordernumber = "G322-0232",
}
@Article{Serebrenik:2002:TLP,
author = "Alexander Serebrenik and Danny De Schreye",
title = "On Termination of Logic Programs with Floating Point
Computations",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2477",
pages = "151--164",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRnumber = "MR2049473",
bibdate = "Tue Sep 10 19:11:24 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2477.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2477/24770151.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2477/24770151.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@MastersThesis{Shi:2002:SMF,
author = "Changchun Shi",
title = "Statistical method for floating-point to fixed-point
conversion",
type = "{Master of Science, Plan II}",
school = "Department of Electrical Engineering and Computer
Sciences, University of California, Berkeley",
address = "Berkeley, CA, USA",
pages = "x + 131",
year = "2002",
LCCN = "T7.49.2002 S55",
bibdate = "Thu Oct 24 14:20:51 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Soudris:2002:FAB,
author = "D. Soudris and M. Dasygenis and K. Mitroglou and K.
Tatas and A. Thanailakis",
booktitle = "9th International Conference on Electronics, Circuits
and Systems, 2002",
title = "A full adder based methodology for scaling operation
in residue number system",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "891--894",
year = "2002",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICECS.2002.1046391",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "A systematic methodology for designing
full-adder-based architectures in residue number system
for scaling operation and its software tool
development, are introduced. Starting from the
mathematical description of scaling operation in RNS,
we end up \ldots{}",
}
@Article{Spiteri:2002:PPA,
author = "Pierre Spiteri and Jean-Claude Miellou and Didier El
Baz",
title = "Perturbation of parallel asynchronous linear
iterations by floating point errors",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "13",
pages = "38--55",
year = "2002",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
MRclass = "65F10 (65G50 65Y05)",
MRnumber = "MR1924261 (2003h:65042)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://etna.mcs.kent.edu/vol.13.2002/pp38-55.dir/pp38-55.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Stakhov:2002:BTP,
author = "Alexey Stakhov",
title = "{Brousentsov}'s Ternary Principle, {Bergman}'s Number
System and Ternary Mirror-symmetrical Arithmetic",
journal = j-COMP-J,
volume = "45",
number = "2",
pages = "221--236",
month = "????",
year = "2002",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Apr 4 07:33:05 MST 2002",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_45/Issue_02/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_45/Issue_02/450221.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_45/Issue_02/pdf/450221.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Misc{Steele:2002:SMF,
author = "Guy L. {Steele Jr.}",
title = "System and method for floating-point computation",
howpublished = "US Patent 6356927",
day = "12",
month = mar,
year = "2002",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/6356927/fulltext.html",
abstract = "A system is disclosed for performing floating point
computation in connection with numbers in a base
floating point representation (such as the
representation defined in IEEE Std. 754) that defines a
plurality of formats, including a normalized format and
a de-normalized format, using a common floating point
representation that defines a unitary normalized
format. The system includes a base to common
representation converter, a processor and a common to
base representation converter. The base to common
representation converter converts numbers from the base
floating point representation to the common floating
point representation, so that all numbers involved in a
computation will be expressed in the unitary normalized
format. The processor is configured to perform a
mathematical operation of at least one predetermined
type in connection with the converted numbers generated
by the base to common representation converter to
generate a floating point result in the common
representation. The common to base representation
converter converts numbers from the common floating
point representation selectively to either the
normalized or de-normalized format of the base
representation.",
acknowledgement = ack-nhfb,
}
@TechReport{Stehle:2002:WCL,
author = "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
Zimmermann",
title = "Worst Cases and Lattice Reduction",
type = "Research Report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "10",
day = "15",
month = oct,
year = "2002",
bibdate = "Sun Sep 10 08:24:59 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/wclr.ps.gz",
abstract = "We propose a new algorithm to find worst cases for
correct rounding of an analytic function. We first
reduce this problem to the {\em real small value
problem} --- i.e., for polynomials with real
coefficients. Then we show that this second problem can
be solved efficiently, by extending Coppersmith's work
on the {\em integer small value problem} --- for
polynomials with integer coefficients --- using lattice
reduction [4, 5, 6].\par
For floating-point numbers with a mantissa less than
$N$, and a polynomial approximation of degree $d$, our
algorithm finds all worst cases at distance $ < N^{-d^2
/ (2d + 1)} $ from a machine number in time $ O(N^{(d +
1) / (2d + 1) + \epsilon }) $. For $ d = 2 $, this
improves on the $ O(N^{2 / 3 + \epsilon }) $ complexity
from Lef{\`e}vre's algorithm [12, 13] to $ O(N^{3 / 5 +
\epsilon }) $. We exhibit some new worst cases found
using our algorithm, for double-extended and quadruple
precision. For larger $d$, our algorithm can be used to
check that there exist no worst cases at distance $ <
N^{-k} $ in time $ O(N^{1 / 2 + O(1 / k)}) $.",
acknowledgement = ack-nhfb,
keywords = "Coppersmith's theorem; correct rounding; Exact
rounding; floating-point arithmetic; IEEE-754; lattice
reduction; table maker's dilemma; worst case",
}
@Article{Stoianov:2002:AAB,
author = "Ivilin Stoianov and Marco Zorzi and Suzanna Becker and
Carlo Umilta",
title = "Associative Arithmetic with {Boltzmann} Machines: The
Role of Number Representations",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2415",
pages = "277--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:10:20 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2415.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2415/24150277.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2415/24150277.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Manual{Sun:2002:BJP,
author = "{Sun Microsystems}",
title = "{BigDecimal (Java 2 Platform SE v1.4.0)}",
organization = "Sun Microsystems",
address = "Mountain View, CA, USA",
pages = "17",
year = "2002",
bibdate = "Fri Nov 28 11:16:16 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://java.sun/com/products",
abstract = "Immutable, arbitrary-precision signed decimal numbers.
A BigDecimal consists of an arbitrary precision integer
unscaled value and a non-negative 32-bit integer scale,
which represents the number of digits to the right of
the decimal point. The number represented by the
BigDecimal is $ (\mbox {unscaledValue} / 10^{\mbox
{scale}}) $. BigDecimal provides operations for basic
arithmetic, scale manipulation, comparison, hashing,
and format conversion.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Manual{TI:2002:TFL,
title = "{TMS320C67x FastRTS} Library Programmer's Reference
({SPRU100A})",
organization = "Texas Instruments",
address = "Dallas, TX, USA",
month = oct,
year = "2002",
bibdate = "Sat Jan 15 06:11:57 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The FastRTS library is a collection of 26 optimized
floating-point math functions for the TMS320C67x
device. This source code library includes C-callable
(ANSI-C-language compatible) optimized versions of the
floating-point math functions included in previous
run-time-support libraries.",
URL = "http://focus.ti.com/lit/ug/spru100a/spru100a.pdf",
acknowledgement = ack-nhfb,
}
@Article{Tornaria:2002:SRM,
author = "Gonzalo Tornar{\'\i}a",
title = "Square Roots Modulo $p$",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2286",
pages = "430--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:12 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Turner:2002:RPS,
author = "Peter R. Turner",
title = "Residue polynomial systems",
journal = j-THEOR-COMP-SCI,
volume = "279",
number = "1-2",
pages = "29--49",
month = may,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:08:56 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{vanEmden:2002:NDI,
author = "M. H. van Emden",
title = "New Developments in Interval Arithmetic and Their
Implications for Floating-Point Standardization",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--12",
day = "16",
month = oct,
year = "2002",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/cs/0210015",
abstract = "We consider the prospect of a processor that can
perform interval arithmetic at the same speed as
conventional floating-point arithmetic. This makes it
possible for all arithmetic to be performed with the
superior security of interval methods without any
penalty in speed. In such a situation the IEEE
floating-point standard needs to be compared with a
version of floating-point arithmetic that is ideal for
the purpose of interval arithmetic. Such a comparison
requires a succinct and complete exposition of interval
arithmetic according to its recent developments. We
present such an exposition in this paper. We conclude
that the directed roundings toward the infinities and
the definition of division by the signed zeros are
valuable features of the standard. Because the
operations of interval arithmetic are always defined,
exceptions do not arise. As a result neither Nans nor
exceptions are needed. Of the status flags, only the
inexact flag may be useful. Denormalized numbers seem
to have no use for interval arithmetic; in the use of
interval constraints, they are a handicap.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA)",
}
@InProceedings{Walters:2002:DTU,
author = "E. G. Walters and M. J. Schulte",
title = "Design Tradeoffs Using Truncated Multipliers in {FIR}
Filter Implementations",
crossref = "Luk:2002:PSA",
pages = "357--368",
year = "2002",
bibdate = "Sun Mar 04 17:47:29 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2002-03.pdf",
acknowledgement = ack-nhfb,
}
@Article{Winkler:2002:SVU,
author = "J{\"u}rgen F. H. Winkler",
title = "A safe variant of the unsafe integer arithmetic of
{Java$^{TM}$}",
journal = j-SPE,
volume = "32",
number = "7",
pages = "669--701",
month = jun,
year = "2002",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.454",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Wed Oct 16 18:25:58 MDT 2002",
bibsource = "http://www.interscience.wiley.com/jpages/0038-0644;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract/94515736/START;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=94515736&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "arithmetics in programming languages; divide-by-zero;
floating-point arithmetic; IEEE 754; Java; overflow;
program structure; range limitation; rounding; safe
arithmetic operations; underflow; zero-divide",
}
@Article{Wu:2002:BPF,
author = "Huapeng Wu",
title = "Bit-parallel finite field multiplier and squarer using
polynomial basis",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "7",
pages = "750--758",
month = jul,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2002.1017695",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 09:41:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1017695",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wu:2002:FFM,
author = "Huapeng Wu and M. A. Hasan and I. F. Blake and Shuhong
Gao",
title = "Finite field multiplier using redundant
representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "11",
pages = "1306--1316",
month = nov,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2002.1047755",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 09:42:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1047755",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wu:2002:MMS,
author = "Huapeng Wu",
title = "{Montgomery} multiplier and squarer for a class of
finite fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "51",
number = "5",
pages = "521--529",
month = may,
year = "2002",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2002.1004591",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 09:41:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1004591",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Yang:2002:RNSa,
author = "Lie-Liang Yang and L. Hanzo",
title = "A residue number system based parallel communication
scheme using orthogonal signaling. {II}. {Multipath}
fading channels",
journal = j-IEEE-TRANS-VEH-TECHNOL,
volume = "51",
number = "6",
pages = "1547--1559",
month = nov,
year = "2002",
CODEN = "ITUTAB",
DOI = "https://doi.org/10.1109/TVT.2002.804849",
ISSN = "0018-9545 (print), 1939-9359 (electronic)",
ISSN-L = "0018-9545",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26382",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Vehicular Technology",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
keywords = "residue arithmetic; residue number system",
summary = "For pt.I see ibid., vol.51, no.6, p.1534-46 (2002). A
novel signaling scheme is presented, where a set of
orthogonal signals is transmitted in parallel. The
signals are selected according to the so-called residue
number system (RNS). Hence the \ldots{}",
}
@Article{Yang:2002:RNSb,
author = "Lie-Liang Yang and L. Hanzo",
title = "A residue number system based parallel communication
scheme using orthogonal signaling. {I}. {System}
outline",
journal = j-IEEE-TRANS-VEH-TECHNOL,
volume = "51",
number = "6",
pages = "1534--1546",
month = nov,
year = "2002",
CODEN = "ITUTAB",
DOI = "https://doi.org/10.1109/TVT.2002.804850",
ISSN = "0018-9545 (print), 1939-9359 (electronic)",
ISSN-L = "0018-9545",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26382",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Vehicular Technology",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
keywords = "residue arithmetic; residue number system",
summary = "A novel signaling scheme is presented, where a set of
orthogonal signals is transmitted in parallel. The
signals are selected according to the so-called residue
number system (RNS). Hence the system is essentially a
multiple code parallel \ldots{}",
}
@Article{Yang:2002:RNSc,
author = "Lie-Liang Yang and L. Hanzo",
title = "Residue number system assisted fast frequency-hopped
synchronous ultra-wideband spread-spectrum
multiple-access: a design alternative to impulse
radio",
journal = j-IEEE-J-SEL-AREAS-COMMUN,
volume = "20",
number = "9",
pages = "1652--1663",
month = dec,
year = "2002",
CODEN = "ISACEM",
DOI = "https://doi.org/10.1109/JSAC.2002.805059",
ISSN = "0733-8716 (print), 1558-0008 (electronic)",
ISSN-L = "0733-8716",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24076",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal on Selected Areas in Communications",
keywords = "residue arithmetic; residue number system",
summary = "Ultra-wideband (UWB) systems having a bandwidth on the
order of gigahertz have received wide attention both in
the US and in Europe. The family of UWB systems may
communicate either, by generating ultra-wideband
signals or with the aid of \ldots{}",
}
@Article{Yen:2002:RSR,
author = "Sung-Ming Yen and Seungjoo Kim and Seongan Lim and
Sangjae Moon",
title = "{RSA} Speedup with Residue Number System Immune
against Hardware Fault Cryptanalysis",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2288",
pages = "397--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:14 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2288.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2288/22880397.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2288/22880397.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Ziv:2002:SGM,
author = "Abraham Ziv and Laurent Fournier",
title = "Solving the generalized mask constraint for test
generation of binary floating point add operation",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "183--201",
month = nov,
year = "2002",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Nov 20 18:15:29 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "floating-point testing",
}
@Article{Abed:2003:VIL,
author = "K. H. Abed and R. E. Siferd",
title = "{VLSI} implementation of a low-power antilogarithmic
converter",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "9",
pages = "1221--1228",
month = sep,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1228517",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1228517",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Agou:2003:SPR,
author = "Simon Joseph Agou and Marc Del{\'e}glise and
Jean-Louis Nicolas",
title = "Short Polynomial Representations for Square Roots
Modulo $p$",
journal = j-DESIGNS-CODES-CRYPTOGR,
volume = "28",
number = "1",
pages = "33--44",
month = jan,
year = "2003",
CODEN = "DCCREC",
ISSN = "0925-1022 (print), 1573-7586 (electronic)",
ISSN-L = "0925-1022",
bibdate = "Thu Dec 11 06:27:20 MST 2003",
bibsource = "http://www.wkap.nl/jrnltoc.htm/0925-1022;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Designs, codes, and cryptography",
journal-URL = "http://link.springer.com/journal/10623",
}
@InProceedings{Aharoni:2003:FTG,
author = "Merav Aharoni and Sigal Asaf and Laurent Fournier and
Anatoly Koifman and Raviv Nagel",
booktitle = "{Proceedings of the Eighth IEEE International
High-Level Design Validation and Test Workshop, 12--14
November, 2003 (HLDVT03)}",
title = "{FPgen} --- a Test Generation Framework for Datapath
Floating-Point Verification",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "viii + 178",
pages = "17--22",
month = nov,
year = "2003",
DOI = "https://doi.org/10.1109/HLDVT.2003.1252469",
ISBN = "0-7803-8236-6",
ISBN-13 = "978-0-7803-8236-7",
LCCN = "QA76.76.V47 I35 2003; TK7895.M5 I34 2003",
bibdate = "Tue Jun 22 06:49:59 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8873;
http://www.haifa.ibm.com/projects/verification/fpgen;
https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1252469;
https://www.research.ibm.com/haifa/projects/verification/fpgen/ieeets.html",
abstract = "FPgen is a new test generation framework targeted
toward the verification of the floating point (FP)
datapath, through the generation of test cases. This
framework provides the capacity to define virtually any
architectural FP coverage model, consisting of
verification tasks. The tool supplies strong constraint
solving capabilities, allowing the generation of random
tests that target these tasks. We present an overview
of FPgen's functionality, describe the results of its
use for the verification of several FP units, and
compare its efficiency with existing test generators.",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@InProceedings{Akkas:2003:QPD,
author = "A. Akkas and M. J. Schulte",
booktitle = "Proceedings of the 2003 Euromicro Symposium on Digital
System Design, Antalya, Turkey, September 2003",
title = "A Quadruple Precision and Dual Double Precision
Floating-Point Multiplier",
publisher = "????",
address = "????",
pages = "76--81",
year = "2003",
bibdate = "Fri Jun 11 05:37:57 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://home.ku.edu.tr/~ahakkas/publications/quadruple_multiplier.pdf;
http://mesa.ece.wisc.edu/publications/cp_2003-07.pdf",
acknowledgement = ack-nhfb,
}
@Article{Al-Radadi:2003:RSD,
author = "E. Al-Radadi and P. Siy",
title = "{RNS}: sign detector based on {Chinese Remainder
Theorem II} {(CRT II)}",
journal = j-COMPUT-MATH-APPL,
volume = "46",
number = "10--11",
pages = "1559--1570",
month = nov # "\slash " # dec,
year = "2003",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:30 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S089812210390191X",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Altman:2003:RAN,
author = "Micah Altman and Michael P. McDonald",
title = "Replication with Attention to Numerical Accuracy",
journal = j-POLIT-ANAL,
volume = "11",
number = "3",
pages = "302--307",
month = "Summer",
year = "2003",
DOI = "https://doi.org/10.1093/pan/mpg016",
ISSN = "1047-1987 (print), 1476-4989 (electronic)",
ISSN-L = "1047-1987",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Political Analysis",
journal-URL = "https://www.cambridge.org/core/journals/political-analysis/all-issues",
remark = "The authors attempt to replicate numerically two
papers in the \booktitle{American Journal of Political
Science}, and find that the results in those papers are
dependent on the statistical package used. Their
abstract concludes: ``In the course of our
replications, we uncover other pitfalls that may
prevent accurate replication, and make recommendations
to ensure the ability for future researchers to
replicate results.''",
}
@InProceedings{Ammar:2003:NDH,
author = "A. Ammar and A. S. S. El-Kabbany and M. I. Youssef and
A. Emam",
booktitle = "{NRSC 2003}, Proceedings of the Twentieth National
Radio Science Conference, 18--20 March 2003",
title = "A novel data hiding technique using residue number
system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "C15--1--12",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1109/NRSC.2003.1217348",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Data hiding technique is a very attractive field. The
field of data hiding in imagery is relatively very
young and is growing at an exponential rate. This field
is highly multidisciplinary field that combines image
and signal processing with \ldots{}",
}
@InProceedings{Anonymous:2003:AI,
author = "Anonymous",
title = "Author index",
crossref = "Bajard:2003:ISC",
pages = "281--281",
year = "2003",
bibdate = "Fri Nov 28 11:06:15 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@TechReport{Anonymous:2003:FFP,
author = "Anonymous",
title = "Fast Floating-Point Arithmetic Emulation on the
{Blackfin} Processor Platform",
type = "Engineer To Engineer Note",
number = "EE-185",
institution = "Analog Devices",
address = "????",
day = "26",
month = may,
year = "2003",
bibdate = "Fri May 20 12:26:05 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.analog.com/UploadedFiles/Application_Notes/47485184002118EE185.pdf",
acknowledgement = ack-nhfb,
remark = "Describes a software implementation of IEEE 754 32-bit
and 64-bit arithmetic for the Blackfin fixed-point
embedded processor.",
}
@Misc{Anonymous:2003:RHP,
author = "Anonymous",
title = "Recently heard {Pentium} jokes",
howpublished = "World Wide Web document",
day = "20",
month = oct,
year = "2003",
bibdate = "Fri Jul 29 16:01:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://web.archive.org/web/20031020012234/http://www-pcd.stanford.edu/cousins/pentium.html;
http://www-pcd.stanford.edu/cousins/pentium.html",
acknowledgement = ack-nhfb,
keywords = "Intel Pentium divide flaw; Thomas R. Nicely",
}
@Article{Arciniega:2003:REN,
author = "Armando Arciniega and Edward Allen",
title = "Rounding Error in Numerical Solution of Stochastic
Differential Equations",
journal = j-STOCH-ANAL-APPL,
volume = "21",
number = "2",
pages = "281--300",
month = jan,
year = "2003",
CODEN = "SAAPDA",
DOI = "https://doi.org/10.1081/sap-120019286",
ISSN = "0736-2994 (print), 1532-9356 (electronic)",
ISSN-L = "0736-2994",
bibdate = "Fri Apr 11 08:23:41 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.researchgate.net/publication/266011553_Rounding_Error_in_Numerical_Solution_of_Stochastic_Differential_Equations",
abstract = "The present investigation is concerned with estimating
the rounding error in numerical solution of stochastic
differential equations. A statistical rounding error
analysis of Euler's method for stochastic differential
equations is performed. In particular, numerical
evaluation of the quantities $ E|X(t_n) - Y^n|^2 $ and
$ E[F(Y^n) - F(X(t_n))] $ is investigated, where $
X(t_n) $ is the exact solution at the $n$ th time step
and $ Y^n$ is the approximate solution that includes
computer rounding error. It is shown that rounding
error is inversely proportional to the square root of
the step size. An extrapolation technique provides
second-order accuracy, and is one way to increase
accuracy while avoiding rounding error. Several
computational results are given.",
acknowledgement = ack-nhfb,
fjournal = "Stochastic Analysis and Applications",
}
@Article{Arnold:2003:FFT,
author = "M. Arnold and T. Bailey and J. Cowles and C. Walter",
title = "{Fast Fourier Transforms} Using the Complex
Logarithmic Number System",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "33",
number = "3",
pages = "325--335",
month = mar,
year = "2003",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1022236132192",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sat Aug 22 09:28:10 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The complex-logarithmic number system (CLNS), which
represents each complex point in log/polar coordinates,
may be practical to implement the Fast Fourier
Transform (FFT). The roots of unity needed by the FFT
have exact representations in CLNS and do not require a
ROM.\par
We present an error analysis and simulation results for
a radix-two FFT that compares a rectangular fixed-point
representation of complex numbers to CLNS. We observe
that CLNS saves 9--12 bits in word-size for 256--1024
point FFTs compared to the fixed-point number system
while producing comparable accuracy.\par
The consequence of the word-size advantage is that the
number of full adders required for CLNS is
significantly smaller than for an equivalent
fixed-point implementation. The major cost of CLNS is
the memory, which unlike conventional LNS, is addressed
by both real and imaginary parts. Table-reduction
techniques can mitigate this. The simplicity of the
CLNS approach requires significantly fewer full adders,
which pays for some or all of the extra memory. In
applications needing the magnitude of the complex
parts, such as a power spectrum, the CLNS approach can
actually require less memory than the conventional
approach.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Arnold:2003:ILN,
author = "Mark G. Arnold and Jesus Garcia and Michael J.
Schulte",
title = "The interval logarithmic number system",
crossref = "Bajard:2003:ISC",
pages = "253--261",
year = "2003",
bibdate = "Wed Nov 26 12:04:40 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2003-01.pdf;
http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Arnold.pdf",
abstract = "This paper introduces the Interval Logarithmic Number
System (ILNS), in which the Logarithmic Number System
(LNS) is used as the underlying number system for
interval arithmetic. The basic operations in ILNS are
introduced and an efficient method for performing ILNS
addition and subtraction is presented. The paper
compares ILNS to Interval Floating Point (IFP) for a
few sample applications. For applications like the
N-body problem, which have a large percentage of
multiplies, divides and square roots, ILNS provides
much narrower intervals than IFP. In other
applications, like the Fast Fourier Transform, where
addition and subtraction dominate, ILNS and IFP produce
intervals having similar widths. Based on our analysis,
ILNS is an attractive alternative to IFP for
application that can tolerate low to moderate
precisions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Bajard:2003:EMG,
author = "J.-C. Bajard and L. Imbert and C. N{\`e}gre and T.
Plantard",
title = "Efficient multiplication in {$ \mathrm {GF}(p_k) $}
for Elliptic Curve Cryptography",
crossref = "Bajard:2003:ISC",
pages = "181--187",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Bajard.pdf",
abstract = "We present a new multiplication algorithm for the
implementation of elliptic curve cryptography (ECC)
over the finite extension fields $ \mathrm {GF}(p_k) $
where $p$ is a prime number greater than $ 2 k $. In
the context of ECC we can assume that $p$ is a 7-to-10
bit number, and easily find values for $k$ which
satisfy: $ p > 2 k $, and for security reasons $ l o
g_2 (p) \times k \approx 160 $. All the computations
are performed within an alternate polynomial
representation of the field elements which is directly
obtained from the inputs. No conversion step is needed.
We describe our algorithm in terms of matrix operations
and point out some properties of the matrices that can
be used to improve the design. The proposed algorithm
is highly parallelizable and seems well adapted to
hardware implementation of elliptic curve
cryptosystems.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Bajard:2003:FII,
author = "Jean-Claude Bajard and Michael Schulte",
title = "Foreword: {16th IEEE International Symposium on
Computer Arithmetic}",
crossref = "Bajard:2003:ISC",
pages = "viii--viii",
year = "2003",
bibdate = "Sat Nov 17 21:53:37 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_contents.pdf;
http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_foreword.pdf;
http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_preface.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Article{Barrio:2003:NEL,
author = "Roberto Barrio and B. Melendo and S. Serrano",
title = "On the numerical evaluation of linear recurrences",
journal = j-J-COMPUT-APPL-MATH,
volume = "150",
number = "1",
pages = "71--86",
day = "1",
month = jan,
year = "2003",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:52:32 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042702005654",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Barrio:2003:URE,
author = "Roberto Barrio",
title = "A unified rounding error bound for polynomial
evaluation",
journal = j-ADV-COMPUT-MATH,
volume = "19",
number = "4",
pages = "385--399",
month = nov,
year = "2003",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1023/A:1024203520270",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
MRclass = "65G50",
MRnumber = "1989623",
bibdate = "Sat Feb 3 18:22:17 MST 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/article/10.1023/A:1024203520270",
acknowledgement = ack-nhfb,
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
keywords = "Bernstein polynomial; Clenshaw--Forsythe algorithm;
de-Casteljau algorithm; Horner's algorithm; polynomial
evaluation; recurrence relations; rounding errors;
Szeg{\H{o}} polynomial",
}
@Article{Bertoni:2003:EAA,
author = "Guido Bertoni and Jorge Guajardo and Sandeep Kumar and
Gerardo Orlando and Christof Paar and Thomas
Wollinger",
title = "Efficient $ {GF}(p^m) $ Arithmetic Architectures for
Cryptographic Applications",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2612",
pages = "158--175",
year = "2003",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 4 18:46:22 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "cryptology; Topics in Cryptology CT-RSA 2003",
}
@InProceedings{Boldo:2003:FPC,
author = "Sylvie Boldo and Marc Daumas and Laurent Th{\'e}ry",
editor = "Th{\'e}r{\`e}se Hardin and Renaud Rioboo",
booktitle = "{CALCULEMUS-2003: 11th} Symposium on the Integration
of Symbolic Computation and Mechanized Reasoning:
September 10--12, 2003, Roma, Italy",
title = "Formal proofs and computations in finite precision
arithmetic",
publisher = "????",
address = "????",
bookpages = "vii + 141",
pages = "101--111",
year = "2003",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Nov 23 10:09:27 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ftp.lip6.fr/lip6/reports/2003/lip6.2003.010.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Boldo:2003:RCT,
author = "Sylvie Boldo and Marc Daumas",
title = "Representable correcting terms for possibly
underflowing floating point operations",
crossref = "Bajard:2003:ISC",
pages = "79--86",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/proceedings/arith/2003/1894/00/1894toc.htm;
http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Boldo.pdf;
http://www.dec.usc.es/arith16/papers/paper-156.pdf",
abstract = "Studying floating point arithmetic, authors have shown
that the implemented operations (addition, subtraction,
multiplication, division and square root) can compute a
result and an exact correcting term using the same
format as the inputs. Following a path initiated in
1965, many authors supposed that neither underflow nor
overflow occurred in the process. Overflow is not
critical as this kind of exception creates persisting
nonnumeric quantities. Underflow may be fatal to the
process as it returns wrong numeric values with little
warning. Our new conditions guarantee that the
correcting term is exact when the result is a number.
We have validated our proofs against Coq automatic
proof checker. Our development has raised many
questions, some of them were expected while other ones
were surprising.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; ARITH-16",
}
@TechReport{Boldo:2003:STQ,
author = "Sylvie Boldo and Marc Daumas",
title = "A simple test qualifying the accuracy of {Horner}'s
rule for polynomials",
type = "Research Report",
number = "2003-01",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "41",
month = jan,
year = "2003",
bibdate = "Tue Nov 23 10:54:34 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2003/RR2003-01.ps.gz;
ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4707.pdf",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@InProceedings{Boullis:2003:SOH,
author = "Nicolas Boullis and Arnaud Tisserand",
title = "Some optimizations of hardware multiplication by
constant matrices",
crossref = "Bajard:2003:ISC",
pages = "20--27",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Boullis.pdf",
abstract = "This paper presents some improvements on the
optimization of hardware multiplication by constant
matrices. We focus on the automatic generation of
circuits that involve constant matrix multiplication
(CMM), i.e. multiplication of a vector by a constant
matrix. The proposed method, based on number recoding
and dedicated common sub-expression factorization
algorithms was implemented in a VHDL generator. The
obtained results on several applications have been
implemented on FPGAs and compared to previous
solutions. Up to 40\% area and speed savings are
achieved.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@TechReport{Brisebarre:2003:FTP,
author = "Nicolas Brisebarre and Jean-Michel Muller",
title = "Finding the ``truncated'' polynomial that is closest
to a function",
type = "Research Report",
number = "4787",
institution = "INRIA Rhone-Alpes",
address = "ZIRST, 655 Avenue de l'Europe, Montbonnot, 38334 Saint
Ismier cedex, France",
year = "2003",
bibdate = "Fri Jun 24 14:41:03 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4787.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4787.ps.gz;
http://arxiv.org/pdf/cs.MS/0307009;
http://www.inria.fr/rrrt/rr-4787.html",
abstract = "When implementing regular enough functions (e.g.,
elementary or special functions) on a computing system,
we frequently use polynomial approximations. In most
cases, the polynomial that best approximates (for a
given distance and in a given interval) a function has
coefficients that are not exactly representable with a
finite number of bits. And yet, the polynomial
approximations that are actually implemented do have
coefficients that are represented with a finite - and
sometimes small - number of bits: this is due to the
finiteness of the floating-point representations (for
software implementations), and to the need to have
small, hence fast and/or inexpensive, multipliers (for
hardware implementations). We then have to consider
polynomial approximations for which the degree-$i$
coefficient has at most $ m_i $ fractional bits (in
other words, it is a rational number with denominator $
2^{m_i} $). We provide a general method for finding the
best polynomial approximation under this constraint.
Then, we suggest refinements than can be used to
accelerate our method.",
acknowledgement = ack-nhfb,
}
@Misc{Brown:2003:DPA,
author = "Walter E. Brown",
title = "A [{DRAFT}] Proposal to Add Mathematical Special
Functions to the {C++ Standard Library}",
howpublished = "World-Wide Web document",
day = "3",
month = jan,
year = "2003",
bibdate = "Wed Jan 29 17:15:07 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://home.fnal.gov/~wb/N0000.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Burgess:2003:SRN,
author = "Neil Burgess",
title = "Scaling an {RNS} number using the core function",
crossref = "Bajard:2003:ISC",
pages = "262--269",
year = "2003",
bibdate = "Wed Nov 26 12:04:40 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Burgess.pdf",
abstract = "This paper introduces a method for extracting the core
of a Residue Number System (RNS) number within the RNS,
this affording a new method for scaling RNS numbers.
Suppose an RNS comprises a set of co-prime moduli, $
m_i $, with $ \prod m_i = M $. This paper describes a
method for approximately scaling such an RNS number by
a subset of the moduli, $ \prod m_j = M_J = \sqrt {M}
$, with the characteristic that all computations are
performed using the original moduli and one other
non-maintained short wordlength modulus.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Cao:2003:DHS,
author = "Bin Cao and T. Srikanthan and Chip-Hong Chang",
booktitle = "{ISCAS '03}, Proceedings of the 2003 International
Symposium on Circuits and Systems, 25--28 May 2003",
title = "Design of a high speed reverse converter for a new
$4$-moduli set residue number system",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "IV-520--IV-523",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2003.1205951",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents an elegant residue-to-binary
algorithm for a new 4-moduli set (2/sup n/ - 1, 2/sup
n/, 2/sup n/ + 1, 2/sup 2n/ + 1) Residue Number System.
Our reverse conversion algorithm takes advantage of the
special number properties of the \ldots{}",
}
@Article{Chaudhuri:2003:DAO,
author = "Ranjan Chaudhuri",
title = "Do the arithmetic operations really execute in
constant time?",
journal = j-SIGCSE,
volume = "35",
number = "2",
pages = "43--44",
month = jun,
year = "2003",
CODEN = "SIGSD3",
DOI = "https://doi.org/10.1145/782941.782977",
ISSN = "0097-8418 (print), 2331-3927 (electronic)",
ISSN-L = "0097-8418",
bibdate = "Sat Nov 17 16:57:02 MST 2012",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/sigcse/sigcse35.html#Chaudhuri03;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigcse2000.bib",
URL = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/DBLP/2003.bib",
abstract = "The paper emphasizes the need for exposing the
undergraduate computer science students to the
bit-level analysis of the run-times of certain computer
algorithms. These are algorithms where the input(s)
consist of one or more integers and only a bit-level
analysis yields a more realistic estimate of the
run-time behaviors of such algorithms.",
acknowledgement = ack-nhfb,
fjournal = "SIGCSE Bulletin (ACM Special Interest Group on
Computer Science Education)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J688",
}
@InProceedings{Chaves:2003:RRD,
author = "R. Chaves and L. Sousa",
booktitle = "Proceedings. Euromicro Symposium on Digital System
Design, 2003",
title = "{RDSP}: a {RISC} {DSP} based on residue number
system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "128--135",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1109/DSD.2003.1231911",
ISBN = "0-7695-2003-0",
ISBN-13 = "978-0-7695-2003-2",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper is focused on low power programmable fast
digital signal processors (DSP) design based on a
configurable 5-stage RISC core architecture and on
residue number systems (RNS). Several innovative
aspects are introduced at the control and \ldots{}",
}
@InProceedings{Chen:2003:PIC,
author = "Chichyang Chen and Rui-Lin Chen",
booktitle = "Proceedings of the {IEEE} International Conference on
Application-Specific Systems, Architectures, and
Processors, 24--26 June 2003",
title = "Performance-improved computation of very large
word-length {LNS} addition\slash subtraction using
signed-digit arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "337--347",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Pipelined computation of very large word-length LNS
addition/subtraction requires a significant amount of
hardware and long pipeline latency. We propose a base-e
exponential algorithm to simplify the exponential
computation and to replace half of \ldots{}",
}
@Article{Chevallier-Mames:2003:FDS,
author = "Beno{\^\i}t Chevallier-Mames and Marc Joye and Pascal
Paillierinst",
title = "Faster Double-Size Modular Multiplication from
{Euclidean} Multipliers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2779",
pages = "214--227",
year = "2003",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 4 18:12:50 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "CHES 2003; cryptography",
}
@InProceedings{Ciet:2003:PFI,
author = "M. Ciet and M. Neve and E. Peeters and J.-J.
Quisquater",
booktitle = "{MWSCAS '03}. Proceedings of the 46th {IEEE}
International Midwest Symposium on Circuits and
Systems",
title = "Parallel {FPGA} implementation of {RSA} with residue
number systems --- can side-channel threats be
avoided?",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "806--810",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1109/MWSCAS.2003.1562409",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper, the authors presented a new parallel
architecture to avoid side-channel analysis such as:
timing attack, simple/differential power analysis,
fault induction attack and simple/differential
electromagnetic analysis. Montgomery \ldots{}",
}
@Article{Constantinides:2003:BRB,
author = "George A. Constantinides",
title = "Book Review: {{\booktitle{Computer Arithmetic
Algorithms}}, by Israel Koren. A.K. Peters}",
journal = j-SIGACT,
volume = "34",
number = "3",
pages = "13--15",
month = sep,
year = "2003",
CODEN = "SIGNDM",
DOI = "https://doi.org/10.1145/945526.945532",
ISSN = "0163-5700 (print), 1943-5827 (electronic)",
ISSN-L = "0163-5700",
bibdate = "Wed Mar 21 18:30:26 MDT 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigact.bib",
note = "See \cite{Koren:1993:CAA,Koren:2002:CAA}.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGACT News",
journal-URL = "http://dl.acm.org/citation.cfm?id=J697",
}
@Article{Constantinides:2003:SSA,
author = "G. A. Constantinides and P. Y. K. Cheung and W. Luk",
title = "Synthesis of saturation arithmetic architectures",
journal = j-TODAES,
volume = "8",
number = "3",
pages = "334--354",
month = jul,
year = "2003",
CODEN = "ATASFO",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Thu Aug 7 11:12:06 MDT 2003",
bibsource = "http://www.acm.org/pubs/contents/journals/todaes/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Design Automation of Electronic
Systems (TODAES)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J776",
}
@Article{Conway:2003:NCB,
author = "R. Conway and J. Nelson",
title = "New {CRT}-based {RNS} converter using restricted
moduli set",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "5",
pages = "572--578",
month = may,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1197124",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:48 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1197124",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Cornea:2003:DSR,
author = "M. Cornea and J. Harrison and C. Iordache and B. Norin
and S. Story",
title = "Division, Square Root and Remainder Algorithms for the
{Intel Itanium} Architecture",
type = "Report",
institution = pub-INTEL,
address = pub-INTEL:adr,
month = nov,
year = "2003",
bibdate = "Fri Jun 24 12:05:58 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cotofana:2003:CAR,
author = "Sorin Cotofana and Casper Lageweg and Stamatis
Vassiliadis",
title = "On computing addition related arithmetic operations
via controlled transport of charge",
crossref = "Bajard:2003:ISC",
pages = "245--252",
year = "2003",
bibdate = "Wed Nov 26 12:04:40 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Cotofana.pdf",
abstract = "In this paper we investigate the implementation of
basic arithmetic functions, such as addition and
multiplication, in Single Electron Tunneling (SET)
technology. First, we describe the SET equivalents of
Boolean CMOS gates and Threshold logic gates. Second,
we propose a set of building blocks, which can be
utilized for a novel design style, namely arithmetic
operations performed by direct manipulation of the
location of individual electrons within the system.
Using this new set of building blocks, we propose
several novel approaches for computing addition related
arithmetic operations via the controlled transport of
charge (individual electrons). In particular, we prove
the following: $n$-bit addition can be implemented with
a depth-$2$ network built with $ O(n) $ circuit
elements; $n$-input parity can be computed with a
depth-$2$ network constructed with $ O(n) $ circuit
elements and the same applies for $ n | \log n $
counters; multiple operand addition of $ m | n $-bit
operands can be implemented with a depth-$2$ network
using $ O(m n) $ circuit elements; and finally $n$-bit
multiplication can be implemented with a depth-$3$
network built with $ O(n) $ circuit elements.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@TechReport{Cowlishaw:2003:DAE,
author = "Mike Cowlishaw",
title = "Decimal Arithmetic Encoding Strawman 4d",
type = "Report",
number = "Version 0.96",
institution = "IBM UK Laboratories",
address = "Hursley, UK",
day = "21",
month = feb,
year = "2003",
bibdate = "Fri Mar 03 07:15:51 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www2.hursley.ibm.com/decimal/decbits.pdf",
abstract = "This document describes proposed encodings suitable
for supporting the general purpose floating-point
decimal arithmetic defined in the Decimal Arithmetic
Specification, which allows fixed-point and integer
decimal arithmetic as subsets.
Three formats of decimal numbers are described: (1) a
decimal32 number, which is encoded in four consecutive
bytes (32 bits); (2) a decimal64 number, which is
encoded in eight consecutive bytes (64 bits); (3) a
decimal128 number, which is encoded in 16 consecutive
bytes (128 bits). The encodings provide ranges of
positive normal numbers of approximately $ [1.0 e - 95,
1.0 e + 97) $, $ [1.0 e - 383, 1.0 e + 385) $, and $
[1.0 e - 6143, 1.0 e6145) $, with precisions of 7, 16,
and 34 decimal digits respectively. Subnormals extended
the range down to 1.0e-390, 1.0e-398, and 1.0e-6176,
respectively.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Cowlishaw:2003:DFP,
author = "Michael F. Cowlishaw",
title = "Decimal floating-point: algorism for computers",
crossref = "Bajard:2003:ISC",
pages = "104--111",
year = "2003",
DOI = "https://doi.org/10.1109/ARITH.2003.1207666",
bibdate = "Fri Nov 28 11:02:29 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Cowlishaw.pdf;
http://www.dec.usc.es/arith16/papers/paper-107.pdf;
http://www2.hursley.ibm.com/decimal/IEEE-cowlishaw-arith16.pdf",
abstract = "Decimal arithmetic is the norm in human calculations,
and human-centric applications must use a decimal
floating-point arithmetic to achieve the same
results.\par
Initial benchmarks indicate that some applications
spend 50\% to 90\% of their time in decimal processing,
because software decimal arithmetic suffers a $ 100
\times $ to $ 1000 \times $ performance penalty over
hardware. The need for decimal floating-point in
hardware is urgent.\par
Existing designs, however, either fail to conform to
modern standards or are incompatible with the
established rules of decimal arithmetic. This paper
introduces a new approach to decimal floating-point
which not only provides the strict results which are
necessary for commercial applications but also meets
the constraints and requirements of the IEEE 854
standard.\par
A hardware implementation of this arithmetic is in
development, and it is expected that this will
significantly accelerate a wide variety of
applications.",
acknowledgement = ack-nhfb,
keywords = "algorism (the decimal system of numeration); ARITH-16;
decimal floating-point arithmetic",
}
@InProceedings{Daneshbeh:2003:UBS,
author = "Amir.K. Daneshbeh and M. A. Hasan",
title = "A unidirectional bit serial systolic architecture for
double-basis division over {$ \mathrm {GF}(2^m) $}",
crossref = "Bajard:2003:ISC",
pages = "174--180",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Daneshbeh.pdf",
abstract = "A unidirectional bit serial systolic architecture for
division over Galois field $ \mathrm {GF}(2^m) $ is
presented which uses both triangular and polynomial
basis representations. It is suitable for hardware
implementations where the dimension of the field is
large and may vary. This is the typical case for
cryptographic applications. This architecture is
simulated in Verilog-HDL and synthesized for a clock
period of $ 1.4 $ ns using Synopsys. The time and area
complexities are truly linear, since no carry
propagation structures are present, and the complexity
measures are equivalent or excel the best designs
proposed so far.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Article{Daumas:2003:FRR,
author = "Marc Daumas and David W. Matula",
title = "Further Reducing the Redundancy of a Notation Over a
Minimally Redundant Digit Set",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "33",
number = "1--2",
pages = "7--18",
month = jan,
year = "2003",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1021133616373",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Tue Nov 27 14:14:52 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Redundant notations are used implicitly or explicitly
in many digital designs. They have been studied in
details and a general framework is known to reduce the
redundancy of a notation down to the minimally
redundant digit set. We present here an operator to
further reduce the redundancy of such a representation.
It does not reduce the number of allowed digits since
removing one digit to a minimally redundant digit set
is a conversion to a non redundant digit set and this
is an expensive operation. Our operator introduces some
correlation between the digits to reduce the number of
possible redundant notations for any represented
number. This reduction is visible in small useful
operators like the elimination of leading zeros. We
also present a key application with a CMOS Booth
recoded multiplier. Our multiplier is able to accept
both a redundant or a non redundant input with very
little modifications and almost no penalty in time or
space compared to state-of-the-art non redundant
multipliers.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@PhdThesis{Defour:2003:FEA,
author = "David Defour",
title = "Fonctions {{\'E}}l{\'e}mentaires: Algorithmes et
Impl{\'e}mentations Efficaces pour {l'Arrondi} Correct
en Double Pr{\'e}cision. ({French}) [{Elementary}
Functions: Efficient Algorithms and Implementations for
Correct Rounding in Double Precision]",
school = "L'{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "Lyon, France",
pages = "viii + 133",
day = "9",
month = sep,
year = "2003",
bibdate = "Tue Dec 02 11:25:16 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://gala.univ-perp.fr/ddefour/research/thesis_dd.pdf;
http://www.ens-lyon.fr/LIP/Pub/Rapports/PhD/PhD2003/PhD2003-01.ps.gz;
https://theses.hal.science/tel-00006022v1",
abstract = "The representation formats and behaviors of floating
point arithmetics available in computers are defined by
the IEEE-754 standard. This standard imposes the system
to return as a result of one of the four basic
operations (+, *, /, sqrt), the rounding of the exact
result. This property is called <>,this warranties the
quality of the result. It enables construction of proof
that this particular algorithms can be manipulated
independently of the machine. However, due to the <>,
elementary functions (sine, cosine, exponential...) are
absent in the IEEE-754 standard. Contrary to basic
operations, it is difficult to discover the necessary
accuracy required to guarantee correct rounding for
elementary functions. However if the representation
format is set, it is possible that an exhaustive search
will help determine this bound: it was Lef{\`e}vre's
work for the double precision.\par
The objectives of this thesis is to exploit these
bounds for each functions and rounding modes, to
certify correct rounding in double precision. Thanks to
this bound we have defined an evaluation within 2
steps: a quick phase which is based on the property of
the IEEE standard that often proves satisfactory and an
accurate step based on multiprecision operations which
is precise all the time. For the second step we have
designed a multiprecision library which was optimized
in order to acquire precision corresponding to the
bound, and the characteristics of processors in 2003.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; floating-point arithmetic",
language = "French",
}
@Article{Demmel:2003:AEF,
author = "James Demmel and Yozo Hida",
title = "Accurate and Efficient Floating Point Summation",
journal = j-SIAM-J-SCI-COMP,
volume = "25",
number = "4",
pages = "1214--1248",
day = "5",
month = dec,
year = "2003",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G50 (65B10)",
MRnumber = "MR2045054 (2005b:65055)",
bibdate = "Mon Jan 12 19:00:46 MST 2004",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/25/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/40762",
abstract = "We present and analyze several simple algorithms for
accurately computing the sum of $n$ floating point
numbers using a wider accumulator. Let $f$ and $F$ be
the number of significant bits in the summands and the
accumulator, respectively. Then assuming gradual
underflow, no overflow, and round-to-nearest
arithmetic, up to approximately $ 2^{F - f} $ numbers
can be added accurately by simply summing the terms in
decreasing order of exponents, yielding a sum correct
to within about $ 1.5 $ units in the last place (ulps).
We apply this result to the floating point formats in
the IEEE floating point standard. For example, a dot
product of single precision vectors of length at most
33 computed using double precision and sorting is
guaranteed correct to nearly 1.5 ulps. If
double-extended precision is used, the vector length
can be as large as 65,537. We also investigate how the
cost of sorting can be reduced or eliminated while
retaining accuracy.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation",
}
@Article{Demmel:2003:CAF,
author = "James Demmel",
title = "The complexity of accurate floating point
computation",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "1",
month = may,
year = "2003",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
MRclass = "65F, 65G50, 65Y20, 68Q25",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in Proceedings of the ICM, Beijing 2002,
vol. 3, 697--706.",
URL = "http://arxiv.org/abs/math/0305004",
abstract = "Our goal is to find accurate and efficient algorithms,
when they exist, for evaluating rational expressions
containing floating point numbers, and for computing
matrix factorizations (like LU and the SVD) of matrices
with rational expressions as entries. More precisely,
{\em accuracy} means the relative error in the output
must be less than one (no matter how tiny the output
is), and {\em efficiency} means that the algorithm runs
in polynomial time. Our goal is challenging because our
accuracy demand is much stricter than usual.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (math.NA)",
}
@TechReport{Deshmukh:2003:HPS,
author = "R. G. Deshmukh and Hatim Ghazi Zaini",
title = "High performance signal processing through
computational enhancement and hardware integration",
institution = "Florida Institute of Technology",
address = "Melbourne, FL, USA",
pages = "320",
year = "2003",
bibdate = "Thu Aug 07 18:49:39 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Order Number AAI3099386.",
abstract = "Mathematical operations on complex numbers are
commonly required in numerous computer applications.
The use of complex number computations in the design
algorithms for various digital signal processing (DSP)
has received considerable attention in recent years.
Algorithms in complex orthogonal transformations,
correlations, and filtrations are a part of arithmetic
computations such as geometric analysis in graphics or
signal processing. The digital signal processing
algorithms and modern digital communication systems
such as equalization, modulation and demodulation are
all deal with data streams represented by complex
numbers. These applications require efficient
representation and manipulation, in addition to
treatment of complex numbers. These algorithms usually
include arithmetic operations. The digital signal
processing demands always increase and higher
performance in the implementation of algorithms are
investigated. Therefore, the implementations of the
arithmetic operations of the complex numbers for
high-performance especially for complex number
multiplier are of significant interest.\par
A novel method for complex numbers representation and
the arithmetic operations on them was introduced for
computer vision which is a relatively new area. The
proposed Redundant Complex Binary Number System (RCBNS)
was developed by combining a Redundant Binary Number
and a complex number in the base $ ( - 1 + j) $.\par
A Redundant Complex Binary Number System consists of
both the real and the imaginary parts presented by a
radix number system that forms a single redundant
integer digit set. This system is formed by using
complex radix of $ ( - 1 + j) $ and a digit set of $
\alpha = 3 $, where $ \alpha $ assumes a value of $ -
3, - 2, - 1, 0, 1, 2, 3 $. The arithmetic operations on
these complex numbers treat the real and the imaginary
parts as one unit. Carry-free addition is the advantage
in the arithmetic operations that uses operands in the
Redundant Complex Binary Number System.\par
Conversion of decimal complex numbers in the standard
binary form to the RCBNS form is accomplished by
converting the decimal complex number to the complex
binary form and then the real part and the imaginary
part to be treated in one unit. Two methods for the
conversion to the RCBNS form are presented. These
complex numbers in the RCBNS form are used to perform
arithmetic operations, addition, subtraction,
multiplication and division. The results of arithmetic
operations on complex number are available in the RCBNS
form. These results in the RCBNS form should be
converted back to the Standard Binary Number form. Two
methods are presented for the reconversion. Both
methods are based on separating the real part and the
imaginary part of each row of four digit positions of
the RCBNS number and forward them to two dedicated
registers. The comparisons of the proposed multiplier
with other existing multipliers were done. Finally,
methodology and processes of the proposed work were
modeled (functional and behavioral) using a hardware
description language, VHDL. In this research, the RCBNS
form for complex number reduces the number of steps
required to perform complex number arithmetic
operations, thus enhancing the speed.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@InProceedings{Detrey:2003:VLL,
author = "J{\'e}r{\'e}mie Detrey and Florent de Dinechim",
title = "A {VHDL} Library of {LNS} Operators",
crossref = "Matthews:2003:PTS",
pages = "2227--2231",
year = "2003",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://perso.ens-lyon.fr/jeremie.detrey/FPLibrary/;
http://perso.ens-lyon.fr/jeremie.detrey/publications/DetDin2003:asilomar.pdf",
acknowledgement = ack-nhfb,
keywords = "logarithmic number system (LNS)",
summary = "Not \ldots{}",
}
@Misc{DiBrino:2003:FPP,
author = "M. DiBrino and F. Karim",
title = "Floating-point pipeline with leading zeros anticipator
circuit",
howpublished = "US Patent 6542915",
month = apr,
year = "2003",
bibdate = "Fri Jun 24 10:46:57 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ercegovac:2003:CDP,
author = "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
title = "Complex Division with Prescaling of Operands",
crossref = "Deprettere:2003:IIC",
pages = "304--314",
year = "2003",
DOI = "https://doi.org/10.1109/ASAP.2003.1212854",
bibdate = "Sat Dec 04 09:09:15 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We adapt the radix-r digit-recurrence division
algorithm to complex division. By prescaling the
operands, we make the selection of quotient digits
simple. This leads to a simple hardware implementation,
and allows correct rounding of complex quotient. To
reduce large prescaling tables required for radices
greater than 4, we adapt the bipartite-table method to
multiple-operand functions.",
acknowledgement = ack-nhfb,
keywords = "bipartite-table method; complex division; correct
rounding; digital arithmetic; floating-point
arithmetic; multiple-operand function; number theory;
prescaling table; quotient digit selection; radix-r
digit-recurrence division algorithm; table lookup",
}
@InProceedings{Ercegovac:2003:DRA,
author = "M. D. Ercegovac and Jean-Michel Muller",
booktitle = "Conference Record of the Thirty-Seventh Asilomar
Conference on Signals, Systems and Computers, 2003",
title = "Digit-recurrence algorithms for division and square
root with limited precision primitives",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1440--1444",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We propose a digit-recurrence algorithm for square
root using limited-precision multipliers, adders, and
table-lookups. The algorithm, except in the
initialization, uses the digit-recurrence algorithm for
division with limited-precision primitives \ldots{}",
}
@InProceedings{Erdem:2003:LRV,
author = "Serdar S. Erdem and {\c{C}}etin K. Ko{\c{c}}",
title = "A less recursive variant of {Karatsuba--Ofman}
algorithm for multiplying operands of size a power of
two",
crossref = "Bajard:2003:ISC",
pages = "28--35",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Erdem.pdf",
abstract = "We propose a new algorithm for fast multiplication of
large integers having a precision of $ 2^k $ computer
words, where $k$ is an integer. The algorithm is
derived from the Karatsuba--Ofman Algorithm and has the
same asymptotic complexity. However, the running time
of the new algorithm is slightly better, and it makes
one third as many recursive calls.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Erle:2003:DMC,
author = "M. A. Erle and M. J. Schulte",
title = "Decimal multiplication via carry-save addition",
crossref = "Deprettere:2003:IIC",
pages = "348--358",
year = "2003",
bibdate = "Fri Mar 25 05:52:41 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2003-03.pdf",
abstract = "Decimal multiplication is important in many commercial
applications including financial analysis, banking, tax
calculation, currency conversion, insurance, and
accounting. This paper presents two novel designs for
fixed-point decimal multiplication that utilize decimal
carry-save addition to reduce the critical path delay.
First, a multiplier that stores a reduced number of
multiplicand multiples and uses decimal carry-save
addition in the iterative portion of the design is
presented. Then, a second multiplier design is proposed
with several notable improvements including fast
generation of multiplicand multiples that do not need
to be stored, the use of decimal (4:2) compressors, and
a simplified decimal carry-propagate addition to
produce the final product. When multiplying two
$n$-digit operands to produce a $ 2 n $-digit product,
the improved multiplier design has a worst-case latency
of $ n + 4 $ cycles and an initiation interval of $ n +
1 $ cycles. Three data-dependent optimizations, which
help reduce the multipliers' average latency, are also
described. The multipliers presented can be extended to
support decimal floating-point multiplication.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Even:2003:PEA,
author = "Guy Even and Peter-Michael Seidel and Warren E.
Ferguson",
title = "A parametric error analysis of {Goldschmidt}'s
division algorithm",
crossref = "Bajard:2003:ISC",
pages = "165--171",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Even.pdf",
abstract = "Back in the 60's Goldschmidt presented a variation of
Newton--Raphson iterations for division that is well
suited for pipelining. The problem in using
Goldschmidt's division algorithm is to present an error
analysis that enables one to save hardware by using
just the right amount of precision for intermediate
calculations while still providing correct rounding.
Previous implementations relied on combining formal
proof methods (that span thousands of lines) with
millions of test vectors. These techniques yield
correct designs but the analysis is hard to follow and
is not quite tight.\par
We present a simple parametric error analysis of
Goldschmidt's division algorithm. This analysis sheds
more light on the effect of the different parameters on
the error. In addition, we derive closed error formulae
that allow to determine optimal parameter choices in
four practical settings.\par
We apply our analysis to show that a few bits of
precision can be saved in the floating-point division
(FP-DIV) microarchitecture of the AMD-K7TM
microprocessor. These reductions in precision apply to
the initial approximation and to the lengths of the
multiplicands in the multiplier. When translated to
cost, the reductions reflect a savings of $ 10.6 \% $
in the overall cost of the FP-DIV micro-architecture.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16; correct rounding; floating-point
arithmetic",
}
@InProceedings{Even:2003:PMD,
author = "G. Even and P.-M. Seidel",
booktitle = "Proceedings of the 21st International Conference on
Computer Design",
title = "Pipelined multiplicative division with {IEEE}
rounding",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "240--245",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICCD.2003.1240901",
ISBN = "0-7695-2025-1",
ISBN-13 = "978-0-7695-2025-4",
ISSN = "1063-6404",
ISSN-L = "1063-6404",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We propose optimized pipelined implementations for
Goldschmidt's division algorithm with IEEE rounding
based on Booth radix-8 multiplication. Compared to
other FP-division algorithms, our implementations
require fewer clock cycles and admit shorter periods.
The considered optimizations for the quotient
approximation are based on a careful general analysis
of tight error bounds for the implementation and are
accompanied by the utilization of redundant
representations, partial compressions, injection-based
rounding, and rectangular multipliers for the internal
computations. To efficiently achieve IEEE compliant
rounding, we introduce the concept of dew-point
rounding that allows efficient implementation and
reduced requirements for the quotient approximation. On
this basis, we propose the implementation of different
versions of Goldschmidt's division algorithm with
different pipeline depths. None of these
implementations requires a full-sized multiplier at any
stage of the computations. In this way we reduce
latency, cost, and enable increased throughput at a
reasonable cost. We suggest a full range of pipelining
depths: On one extreme is a 3-stage pipeline with a
restart time that simply equals the latency minus the
number of pipeline stages. On the other extreme is a
fully pipelined design.",
}
@InProceedings{Fahmy:2003:CRF,
author = "Hossam A. H. Fahmy and Michael J. Flynn",
title = "The case for a redundant format in floating point
arithmetic",
crossref = "Bajard:2003:ISC",
pages = "95--102",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Fahmy.pdf",
abstract = "This work uses a partially redundant number system as
an internal format for floating point arithmetic
operations. The redundant number system enables carry
free arithmetic operations to improve performance.
Conversion from the proposed internal format back to
the standard IEEE format is done only when an operand
is written to memory. A detailed discussion of an adder
using the proposed format is presented and the specific
challenges of the design are explained. A brief
description of a multiplier and divider using the
proposed format is also presented. The proposed
internal format and arithmetic units comply with all
the rounding modes of the IEEE 754 floating point
standard. Transistor simulation of the adder and
multiplier confirm the performance advantage predicted
by the analytical model.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@PhdThesis{Fahmy:2003:RDF,
author = "Hossam A. H. Fahmy",
title = "A redundant digit floating point system",
type = "{Ph.D.} dissertation",
school = "Department of Computer Science, Stanford University",
address = "Stanford, CA, USA",
pages = "146",
month = nov,
year = "2003",
bibdate = "Wed Nov 15 07:59:18 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://wwwlib.umi.com/dissertations/fullcit/3090583",
abstract = "Arithmetic operations are among the most basic
instructions in microprocessors, digital signal
processors and graphics accelerators. Addition is the
most frequent arithmetic operation in numerically
intensive applications. Multiplication follows closely
and then division and other elementary functions. The
speed of those arithmetic operations is also often
directly linked to the overall performance of the
computers. The work presented in this thesis proposes
several techniques to improve the effectiveness of
floating point arithmetic units. A partially redundant
number system is used as an internal format for
floating point arithmetic operations. The redundant
number system is based on signed digits and enables
carry free arithmetic operations to improve the
performance. Conversion from the proposed internal
format back to the standard IEEE format is done only
when an operand is written to memory. A detailed
discussion of an adder and a multiplier using the
proposed format is presented and the specific
challenges of the designs are explained. Beside the
redundancy, the proposed units include further
enhancements that increase the floating point
performance such as a hexadecimal based number format
and a postponed rounding technique. A time delay model
is developed and applied to analytically predict the
performance of the floating point units. The predicted
delays are then compared to state-of-the-art designs.
The comparison is done over a range of operand widths,
fan-in and radices to show the merits of each
implementation. The proposed system achieves better
performance for double precision and larger operand
width. Transistor simulation of the complete adder and
multiplier confirm the performance advantage predicted
by the analytical model. A brief description of a
divider using; the proposed format is also presented.
The proposed internal format and arithmetic units
comply with all the rounding modes of the IEEE 754
floating point standard.",
acknowledgement = ack-nhfb,
}
@InProceedings{Fang:2003:FPE,
author = "Claire Fang Fang and Tsuhan Chen and Rob A. Rutenbar",
title = "Floating-point error analysis based on affine
arithmetic",
crossref = "IEEE:2003:IICa",
pages = "561--564",
year = "2003",
DOI = "https://doi.org/10.1109/ICASSP.2003.1202428",
bibdate = "Thu Mar 24 20:40:52 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://amp.ece.cmu.edu/Publication/Fang/icassp2003_fang.pdf",
acknowledgement = ack-nhfb,
}
@Article{Fernandez:2003:FPA,
author = "Jos{\'e}-Jes{\'u}s Fern{\'a}ndez and Inmaculada
Garc{\'\i}a and Ester M. Garz{\'o}n",
title = "Floating point arithmetic teaching for computational
science",
journal = j-FUT-GEN-COMP-SYS,
volume = "19",
number = "8",
pages = "1321--1334",
month = nov,
year = "2003",
CODEN = "FGSEVI",
ISSN = "0167-739X (print), 1872-7115 (electronic)",
ISSN-L = "0167-739X",
bibdate = "Sat Jan 10 10:03:38 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Computational science is based upon numerical
computing and, consequently, requires excellent
knowledge of floating point computer arithmetic. In
general, the average computational science student has
a relatively limited understanding of the implications
of floating point computation. This paper presents an
initiative to teach floating point number
representation and arithmetic in undergraduate courses
in computational science. The approach is based on
carefully designed practical exercises which highlight
the main properties and computational issues of finite
length number representation and arithmetic. In
conjunction to the exercises, an auxiliary educational
tool constitutes a valuable support for students to
learn and understand the concepts involved. Simpler
formats are used as an introduction to the IEEE 754
standard, with the aim of presenting the fundamentals
of the floating point computation and emphasizing its
limitations. This approach could be included in courses
related to computer organization, programming, discrete
mathematics, numerical methods or scientific computing
in computational science curricula.",
acknowledgement = ack-nhfb,
fjournal = "Future Generation Computer Systems",
journal-URL = "http://www.sciencedirect.com/science/journal/0167739X",
keywords = "Computational science education; Computer arithmetic;
Floating point computation",
remark = "Selected papers from the Workshop on Education in
Computational Sciences held at the International
Conference on Computational Science.",
}
@InProceedings{Fousse:2003:AST,
author = "L. Fousse and P. Zimmermann",
title = "Accurate Summation: Towards a Simpler and Formal
Proof",
crossref = "Anonymous:2003:CRN",
pages = "97--108",
year = "2003",
bibdate = "Sat Jun 25 14:56:11 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@InProceedings{Frougny:2003:LMR,
author = "Christiane Frougny and Athasit Surarerks",
title = "On-line multiplication in real and complex base",
crossref = "Bajard:2003:ISC",
pages = "212--219",
year = "2003",
bibdate = "Fri Nov 28 11:03:48 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Frougny.pdf",
abstract = "Multiplication of two numbers represented in base $
\beta $ is shown to be computable by an on-line
algorithm when $ \beta $ is a negative integer, a
positive non-integer real number, or a complex number
of the form $ i \sqrt {r} $, where $r$ is a positive
integer.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Book{Gansner:2003:SMB,
author = "Emden R. Gansner and John H. Reppy",
title = "The {Standard ML} Basis Manual",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "????",
year = "2003",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Jan 29 16:31:52 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "From \cite{Steele:2004:RHP}: ``toDecimal should
produce only as many digits as are necessary for
fromDecimal to convert back to the same number, i.e.,
for any Normal or SubNormal real value r, we have:
fromDecimal (toDecimal r) = r \ldots{} Algorithms for
accurately and efficiently converting between binary
and decimal real representations are readily available,
e.g., see the technical report \cite{Gay:1990:CRB}.''",
}
@InCollection{Gavrilova:2003:ESC,
author = "M. L. Gavrilova",
booktitle = "Computational science and its {applications---ICCSA
2003}. Part {III}",
title = "An explicit solution for computing the {Euclidean}
{$d$}-dimensional {Voronoi} diagram of spheres in a
floating-point arithmetic",
volume = "2669",
publisher = pub-SV,
address = pub-SV:adr,
pages = "827--835",
year = "2003",
MRclass = "68U05 (52B55)",
MRnumber = "MR2118360",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
}
@InProceedings{Geddes:2003:EFH,
author = "Keith O. Geddes and Wei Wei Zheng",
title = "Exploiting fast hardware floating point in high
precision computation",
crossref = "Senda:2003:IPI",
pages = "111--118",
year = "2003",
DOI = "https://doi.org/10.1145/860854.860886",
MRclass = "65G99",
MRnumber = "MR2035201 (2005d:65074)",
bibdate = "Sat Dec 13 18:17:28 MST 2003",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We apply an iterative refinement method based on a
linear Newton iteration to solve a particular group of
high precision computation problems. The method
generates an initial solution at hardware floating
point precision using a traditional method and then
repeatedly refines this solution to higher precision,
exploiting hardware floating point computation in each
iteration. This is in contrast to direct solution of
the high precision problem completely in software
floating point. Theoretical cost analysis, as well as
experimental evidence, shows a significant reduction in
computational cost is achieved by the iterative
refinement method on this group of problems.",
acknowledgement = ack-nhfb,
}
@Article{Geiselmann:2003:RRD,
author = "W. Geiselmann and R. Steinwandt",
title = "A redundant representation of {$ \mathrm {GF}(q^n) $}
for designing arithmetic circuits",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "7",
pages = "848--853",
month = jul,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1214334",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1214334",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Gerwig:2003:HPF,
author = "Guenter Gerwig and Holger Wetter and Eric M. Schwarz
and Juergen Haess",
title = "High performance floating-point unit with 116 bit wide
divider",
crossref = "Bajard:2003:ISC",
pages = "87--94",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Gerwig.pdf",
abstract = "The next generation zSeries floating-point unit is
unveiled which is the first IBM mainframe with a fused
multiply-add dataflow. It supports both S/390
hexadecimal floating-point architecture and the IEEE
754 binary floating-point architecture which was first
implemented in S/390 on the 1998 S/390 G5
floating-point unit. The new floating-point unit
supports a total of 6 formats including single, double,
and quadword formats implemented in hardware. The
floating-point pipeline is 5 cycles with a throughput
of 1 multiply-add per cycle. Both hexadecimal and
binary floating-point instructions are capable of this
performance due to a novel way of handling both
formats. Other key developments include new methods for
handling denormalized numbers and quad precision divide
engine dataflow. This divider uses a radix-4 SRT
algorithm and is able to handle quad precision divides
in multiple floating-point and fixed-point formats. The
number of iterations for fixed-point divisions depend
on the effective number of quotient bits. It uses a
reduced carry-save form for the partial remainder, with
only 1 carry bit for every 4 sum bits, to save area and
power.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Misc{Goldberg:2003:WEC,
author = "David Goldberg",
title = "What Every Computer Scientist Should Know About
Floating-Point Arithmetic",
howpublished = "Oracle Web site.",
year = "2003",
bibdate = "Wed Jun 19 07:57:39 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This is a reprint of \cite{Goldberg:1991:WEC} with a
new section, \booktitle{Differences Among IEEE 754
Implementations}, by Doug Priest.",
URL = "https://docs.oracle.com/cd/E19060-01/stud8.compiler/817-0932/ncg_goldberg.html",
acknowledgement = ack-nhfb,
}
@Book{Grabmeier:2003:CAH,
editor = "Johannes Grabmeier and Erich Kaltofen and Volker
Weispfenning",
title = "Computer algebra handbook: foundations, applications,
systems",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xx + 637",
year = "2003",
ISBN = "3-540-65466-6",
ISBN-13 = "978-3-540-65466-7",
LCCN = "QA155.7.E4 C64954 2003",
MRclass = "68W30, 00B15, 68-06",
bibdate = "Tue Nov 22 06:00:25 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Includes CD-ROM.",
URL = "http://www.springer.com/sgw/cda/frontpage/0,11855,1-102-22-1477871-0,00.html",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Aldor; AXIOM;
Derive; exact arithmetic; Macsyma; Magma; Maple
Mathematica; MuPAD; REDUCE; TI-92",
subject = "Algebra; Data processing",
}
@Article{Grossschadl:2003:ASL,
author = "Johann Gro{\ss}sch{\"a}dl",
title = "Architectural Support for Long Integer Modulo
Arithmetic on {RISC}-Based {Smart Cards}",
journal = j-IJHPCA,
volume = "17",
number = "2",
pages = "135--146",
month = "Summer",
year = "2003",
CODEN = "IHPCFL",
ISSN = "1094-3420 (print), 1741-2846 (electronic)",
ISSN-L = "1094-3420",
bibdate = "Fri Nov 28 06:52:13 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://hpc.sagepub.com/content/by/year",
keywords = "application-specific instruct set processor (ASIP);
coarsely-integrated operand scanning (CIOS);
Diffie--Hellman; inner-loop operation; Montgomery
multiplication; processor specialization; public-key
cryptography; Rivest-Shamir-Adelman",
}
@Article{Hanrot:2003:DRF,
author = "G. Hanrot and J. Rivat and G. Tenenbaum and P.
Zimmermann",
title = "Density results on floating-point invertible numbers",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "135--141",
year = "2003",
CODEN = "TCSDIQ",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
MRclass = "68M07 (65G30)",
MRnumber = "MR1957436 (2005b:68028)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Real numbers and computers (Schloss Dagstuhl, 2000)",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{Harrison:2003:FVS,
author = "John Harrison",
title = "Formal verification of square root algorithms",
journal = j-FORM-METHODS-SYST-DES,
volume = "22",
number = "2",
pages = "143--153",
month = mar,
year = "2003",
CODEN = "FMSDE6",
DOI = "https://doi.org/10.1023/A:1022973506233",
ISSN = "0925-9856 (print), 1572-8102 (electronic)",
ISSN-L = "0925-9856",
bibdate = "Sat Feb 08 08:47:21 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib",
URL = "https://dl.acm.org/doi/abs/10.1023/A:1022973506233",
abstract = "We discuss the formal verification of some low-level
mathematical software for the Intel Itanium
architecture. A number of important algorithms have
been proven correct using the HOL Light theorem prover.
After briefly surveying some of our formal verification
work, we discuss in more detail the verification of a
square root algorithm, which helps to illustrate why
some features of HOL Light, in particular
programmability, make it especially suitable for these
applications.",
acknowledgement = ack-nhfb,
fjournal = "Formal Methods in System Design",
journal-URL = "https://dl.acm.org/loi/fmsd",
}
@InProceedings{Harrison:2003:ICC,
author = "John Harrison",
title = "Isolating critical cases for reciprocals using integer
factorization",
crossref = "Bajard:2003:ISC",
pages = "148--157",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Harrison.pdf",
abstract = "One approach to testing and\slash or proving
correctness of a floating-point algorithm computing a
function $f$ is based on finding input floating-point
numbers $ \alpha $ such that the exact result $
f(\alpha) $ is very close to a ``rounding boundary'',
i.e. a floating-point number or a midpoint between
them. In the present paper we show how to do this for
the reciprocal function by utilizing prime
factorizations. We present the method and show
examples, as well as making a fairly detailed study of
its expected and worst-case behavior. We point out how
this analysis of reciprocals can be useful in analyzing
certain reciprocal algorithms, and also show how the
approach can be trivially adapted to the reciprocal
square root function.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16; correct rounding; floating-point
arithmetic",
}
@Article{Holmes:2003:PTC,
author = "Neville Holmes",
title = "The Profession: Truth and Clarity in Arithmetic",
journal = j-COMPUTER,
volume = "36",
number = "2",
pages = "108, 106--107",
month = feb,
year = "2003",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Dec 12 19:53:54 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/dl/mags/co/2003/02/r2108.htm;
http://csdl.computer.org/dl/mags/co/2003/02/r2108.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Huang:2003:HPL,
author = "Zhijun Huang and Milo{\v{s}} D. Ercegovac",
title = "High-performance left-to-right array multiplier
design",
crossref = "Bajard:2003:ISC",
pages = "4--11",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Huang.pdf",
abstract = "We propose a split array multiplier organized in a
left-to-right leapfrog (LRLF) structure with reduced
delay compared to conventional array multipliers.
Moreover, the proposed design shows equivalent
performance as tree multipliers for $ n \leq 32 $. An
efficient radix-4 recoding logic generates the partial
products in a left-to-right order. The partial products
are split into upper and lower groups. Each group is
reduced using [3:2] adders with optimized signal flows
and the carry-save results from two groups are combined
using a [4:2] adder. The final product is obtained with
a prefix adder optimized to match the non-uniform
arrival profile of the inputs. Layout experiments
indicate that upper\slash lower split multipliers have
slightly less area and power than optimized tree
multipliers while keeping the same delay for $ n \leq
32 $.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Misc{Intel:2003:DSR,
author = "{Intel}",
title = "Divide, Square Root, and Remainder Algorithms for the
{Itanium} Architecture",
howpublished = "Intel Software Development Products",
day = "18",
month = dec,
year = "2003",
bibdate = "Tue Nov 18 16:23:36 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm",
acknowledgement = ack-nhfb,
}
@Misc{Intel:2003:NID,
author = "{Intel}",
title = "Non-{IEEE} Division, Square Root, Reciprocal, and
Reciprocal Square Root Algorithms for the {Intel
Itanium} Architecture",
howpublished = "Intel Software Development Products",
day = "18",
month = dec,
year = "2003",
bibdate = "Tue Nov 18 16:23:36 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm",
acknowledgement = ack-nhfb,
}
@InProceedings{Iordache:2003:OFP,
author = "Cristina Iordache and Ping Tak Peter Tang",
title = "An overview of floating-point support and math library
on the {Intel XScale} architecture",
crossref = "Bajard:2003:ISC",
pages = "122--128",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Iordache.pdf",
abstract = "New microprocessor architectures often require
software support for basic arithmetic operations such
as divide, or square root. The Intel\reg{} XScale\TM{}
processor, designed for low power mobile devices,
provides no hardware support for floating-point. We
show that an efficient software implementation of the
basic operations and math library routines can achieve
competitive performance, and effectively hide the lack
of hardware floating-point for most applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Kaihara:2003:VAM,
author = "Marcelo E. Kaihara and Naofumi Takagi",
title = "A {VLSI} algorithm for modular multiplication\slash
division",
crossref = "Bajard:2003:ISC",
pages = "220--227",
year = "2003",
bibdate = "Wed Nov 26 12:04:40 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Kaihara.pdf",
abstract = "We propose an algorithm for modular
multiplication\slash division suitable for VLSI
implementation. The algorithm is based on Montgomery's
method for modular multiplication and on the extended
Binary GCD algorithm for modular division. It can
perform either of these operations with a reduced
amount of hardware. Both calculations are carried out
through iterations of simple operations such as shifts
and additions\slash subtractions. The radix-2
signed-digit representation is employed so that all
additions and subtractions are performed without carry
propagation. A modular multiplier\slash divider based
on this algorithm has a linear array structure with a
bit-slice feature and carries out an n-bit modular
multiplication in at most $ \floor {2(n + 2) / 3} + 3 $
clock cycles and an $n$-bit modular division in at most
$ 2 n + 5 $ clock cycles, where the length of the clock
cycle is constant and independent of $n$.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Article{Kaivola:2003:PEL,
author = "Roope Kaivola and Katherine Kohatsu",
title = "Proof engineering in the large: formal verification of
{Pentium\reg{}4} floating-point divider",
journal = j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
volume = "4",
number = "3",
pages = "323--334",
month = may,
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10009-002-0081-6",
ISSN = "1433-2779 (print), 1433-2787 (electronic)",
ISSN-L = "1433-2779",
bibdate = "Tue Nov 23 15:01:41 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal on Software Tools for Technology
Transfer: STTT",
journal-URL = "http://link.springer.com/journal/10009",
}
@Article{Katti:2003:LCM,
author = "R. Katti and J. Brennan",
title = "Low complexity multiplication in a finite field using
ring representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "4",
pages = "418--427",
month = apr,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1190583",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1190583",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Koren:2003:SCA,
author = "Israel Koren and Yaron Koren and Bejoy G. Oomman",
title = "Saturating counters: application and design
alternatives",
crossref = "Bajard:2003:ISC",
pages = "228--235",
year = "2003",
bibdate = "Wed Nov 26 12:04:40 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Koren.pdf",
abstract = "We define a new class of parallel counters, Saturating
Counters, which provide the exact count of the inputs
that are 1 only if this count is below a given
threshold. Such counters are useful in, for example, a
self-test and repair unit for embedded memories in a
system-on-a-chip. We describe this application and
present several alternatives for the design of the
saturating counter. We then compare the delay and area
of the proposed design alternatives.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Kornerup:2003:RSQ,
author = "Peter Kornerup",
title = "Revisiting {SRT} quotient digit selection",
crossref = "Bajard:2003:ISC",
pages = "38--45",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Kornerup.pdf",
abstract = "The quotient digit selection in the SRT division
algorithm is based on a few most significant bits of
the remainder and divisor, where the remainder is
usually represented in a redundant representation. The
number of leading bits needed depends on the quotient
radix and digit set, and is usually found by an
extensive search, to assure that the next quotient
digit can be chosen as valid for all points (remainder,
divisor) in a set defined by the truncated remainder
and divisor, i.e., an ``uncertainty
rectangle''.\par
This paper presents expressions for the number of bits
needed for the truncated remainder and divisor, thus
eliminating the need for a search through the
truncation parameter space for validation. It also
presents simple algorithms to properly map truncated
negative divisors and remainders into non-negative
values, allowing the quotient selection function only
to be defined on the smaller domain of non-negative
values.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Krithivasan:2003:MAM,
author = "S. Krithivasan and M. J. Schulte",
title = "Multiplier Architectures for Media Processing",
crossref = "Matthews:2003:PTS",
pages = "2193--2197",
year = "2003",
bibdate = "Sun Mar 04 17:52:49 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2003-08.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Kwon:2003:LCL,
author = "Soonhak Kwon",
title = "A low complexity and a low latency bit parallel
systolic multiplier over {$ \mathrm {GF}(2^m) $} using
an optimal normal basis of type {II}",
crossref = "Bajard:2003:ISC",
pages = "196--202",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Kwon.pdf",
abstract = "Using the self duality of an optimal normal basis
(ONB) of type II, we present a bit parallel systolic
multiplier over $ \mathrm {GF}(2^m) $ which has a low
hardware complexity and a low latency. We show that our
multiplier has a latency $ m + 1 $ and the basic cell
of our circuit design needs 5 latches (flip-flops). On
the other hand, most of other multipliers of the same
type have latency $ 3 m $ and the basic cell of each
multiplier needs 7 latches. Comparing the gates areas
in each basic cell, we find that the hardware
complexity of our multiplier is 25 percent reduced from
the multipliers with 7 latches.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Article{Lang:2003:RRS,
author = "Tom{\'a}s Lang and Elisardo Antelo",
title = "Radix-$4$ Reciprocal Square-root and Its Combination
with Division and Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "9",
pages = "1100--1114",
month = sep,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1228508",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1228508",
abstract = "In this work, we present a reciprocal square root
algorithm by digit recurrence and selection by a
staircase function and the radix-$4$ implementation. As
in similar algorithms for division and square root, the
results are obtained correctly rounded in a
straightforward manner (in contrast to existing methods
to compute the reciprocal square root). Although,
apparently, a single selection function can only be
used for $ j \geq 2 $ (the selection constants are
different for $ j = 0 $, $ j = 1 $, and $ j \geq 2 $) ,
we show that it is possible to use a single selection
function for all iterations. We perform a rough
comparison with existing methods and we conclude that
our implementation is a low hardware complexity
solution with moderate latency, especially for exactly
rounded results. We also extend the unit to support
division and square root with the same selection
function and with slight modifications in the
initialization of the reciprocal square root unit.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lee:2003:DPL,
author = "B. Lee and N. Burgess",
title = "A Dual-Path Logarithmic Number System Addition\slash
Subtraction Scheme for {FPGA}",
crossref = "Cheung:2003:FPL",
pages = "808--817",
year = "2003",
bibdate = "Fri Jun 24 18:24:42 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Lefevre:2003:FRR,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller",
title = "On-the-fly Range Reduction",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "33",
number = "1--2",
pages = "31--35",
month = jan,
year = "2003",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1021137717282",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Sat Jun 25 08:56:19 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In several cases, the input argument of an elementary
function evaluation is given bit-serially, most
significant bit first. We suggest a solution for
performing the first step of the evaluation (namely,
the range reduction) on the fly: the computation is
overlapped with the reception of the input bits. This
algorithm can be used for the trigonometric functions
sin, cos, tan as well as for the exponential
function.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
keywords = "range reduction",
}
@Misc{Lefevre:2003:TMD,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller",
title = "The {Table Maker's Dilemma}: our search for worst
cases",
howpublished = "World-Wide Web software project archive.",
day = "28",
month = oct,
year = "2003",
bibdate = "Fri Jun 24 20:08:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://perso.ens-lyon.fr/jean-michel.muller/Intro-to-TMD.htm",
abstract = "The Table Maker's Dilemma consists in finding, for a
given function and a given domain, the smallest value
of $m$ [the relative error is $ 2^{-m} $ ] such that
rounding this approximate value $ y* $ always gives the
same result as rounding the exact value $y$. This is
done by looking for ``worst cases'', that is, in the
considered domain, the values $x$ such that $ f(x) $ is
closest to an exactly representable number or the
mid-point of two exactly representable numbers.",
acknowledgement = ack-nhfb,
}
@TechReport{Lefevre:2003:WCC,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller",
title = "Worst Cases for Correct Rounding for the Elementary
Functions in Double Precision",
type = "Technical report",
institution = "INRIA, Projet Spaces, LORIA, Campus Scientifique",
address = "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
France",
day = "14",
month = aug,
year = "2003",
bibdate = "Thu Jul 08 08:27:53 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf",
abstract = "We give the results of our search for the worst cases
for correct rounding of the major elementary functions
in double precision floating-point arithmetic. These
results allow the design of reasonably fast routines
that will compute these functions with correct
rounding, at least in some interval, for any of the
four rounding modes specified by the IEEE-754 standard.
They will also allow one to easily test libraries that
are claimed to provide correctly rounded functions.",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic; correct rounding; elementary
functions; floating-point arithmetic; Table Maker's
Dilemma",
}
@InProceedings{Li:2003:TEA,
author = "Ren-Cang Li and Sylvie Boldo and Marc Daumas",
title = "Theorems on efficient argument reductions",
crossref = "Bajard:2003:ISC",
pages = "129--136",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/proceedings/arith/2003/1894/00/1894toc.htm;
http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Li.pdf",
abstract = "A commonly used argument reduction technique in
elementary function computations begins with two
positive floating point numbers $ \alpha $ and $ \gamma
$ that approximate (usually irrational but not
necessarily) numbers $ 1 / C $ and $C$, e.g., $ C = 2
\pi $ for trigonometric functions and $ \ln 2 $ for $
e^x $. Given an argument to the function of interest it
extracts $z$ as defined by $ x \alpha = z + \zeta $
with $ z = k2^{-N} $ and $ | \zeta | \leq 2^{N - 1} $
where $k$, $N$ are integers and $ N \geq 0 $ is
preselected, and then computes $ u = x - z \gamma $.
Usually $ z \gamma $ takes more bits than the working
precision provides for storing its significand, and
thus exact $ x - z \gamma $ may not be represented
exactly by a floating point number of the same
precision. This will cause a performance penalty when
the working precision is the highest available on the
underlying hardware and thus considerable extra work is
needed to get all the bits of $ x - z \gamma $ right.
This paper presents theorems that show under mild
conditions that can be easily met on today's computer
hardware and still allow $ \alpha \approx 1 / C $ and $
\gamma \approx C $ to almost the full working
precision, $ x - z \gamma $ is a floating point number
of the same precision. An algorithmic procedure based
on the theorems is obtained. The results will enhance
performance, in particular on machines that has
hardware support for fused multiply-add (fma)
instruction(s).",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Mamidi:2003:AGC,
author = "S. Mamidi and M. Senthilvelan and M. J. Schulte and S.
Krithivasan",
title = "Automated Generation of Configurable Media
Processors",
crossref = "Matthews:2003:PTS",
pages = "339--343",
year = "2003",
bibdate = "Sun Mar 04 17:51:05 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2003-09.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Markstein:2003:ASC,
author = "Peter Markstein",
title = "Accelerating sine and cosine evaluation with compiler
assistance",
crossref = "Bajard:2003:ISC",
pages = "137--140",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Markstein.pdf",
abstract = "Some software libraries add special entry points to
enable both the sine and cosine to be evaluated with
one call for performance reasons. This paper proposes
another methods which does not involve new function
names. By having the compiler front end recognize
trigonometric function invocations, and replace them
with a call to a common function followed by a short
routine to produce the desired computation, it is
possible to computer both the sine and the cosine when
needed in about the same time as to compute only one of
them.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Markstein:2003:FQP,
author = "Peter Markstein",
title = "A fast quad precision elementary function library for
{Itanium}",
crossref = "Anonymous:2003:CRN",
pages = "5--12",
year = "2003",
bibdate = "Fri Jun 24 20:14:39 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This talk will describe Itanium's floating point
architecture and how it has been used to produce a high
performance, highly accurate quad precision elementary
function library.\par
Itanium's floating-point features will first be
described, from the point of view of a computer
architect. Many conflicting requirements vie for
consideration during the design of a new computer
architecture. These include instruction word size,
number of registers, the set of operations, arithmetic
precisions supported, and memory access. Some of the
trade-offs during the design phase will be
discussed.\par
One of the objectives of the original Itanium design
was to accelerate quad precision arithmetic. The talk
will describe how the Itanium elementary function
library was constructed, with attention to performance
and accuracy. Because a pair of double-extended
floating point words are used for internal operations
involving quad precision numbers, intermediate results,
holding 128 bits, provide 15 guard bits during
intermediate calculations, resulting in a very low
percentage of misrounded results.",
acknowledgement = ack-nhfb,
}
@Article{Matula:2003:BFM,
author = "David W. Matula and Lee D. McFearin",
title = "A $ p \times p $ bit fraction model of binary floating
point division and extremal rounding cases",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "159--182",
year = "2003",
CODEN = "TCSDIQ",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
MRclass = "68M07 (65G30)",
MRnumber = "MR1957438 (2004e:68004)",
MRreviewer = "Jean-Marie Chesneaux",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Real numbers and computers (Schloss Dagstuhl, 2000)",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "rounding errors",
}
@InProceedings{Matula:2003:CAA,
author = "David W. Matula",
title = "Computer Arithmetic --- An Algorithm Engineer's
Perspective",
crossref = "Bajard:2003:ISC",
pages = "2--2",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Matula_keynote.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Matula:2003:PID,
author = "David W. Matula and Alex Fit-Florea",
title = "Prescaled integer division",
crossref = "Bajard:2003:ISC",
pages = "63--68",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Matula.pdf",
abstract = "We describe a high radix integer division algorithm
where the divisor is prescaled and the quotient is
post-scaled without modifying the dividend to obtain an
identity $ N = Q* \times D + R* $ with the quotient $
Q* $ differing from the desired integer quotient $Q$
only in its lowest order high radix digit. Here the
``oversized'' partial remainder $ R* $ is bounded by
the scaled divisor with at most one additional high
radix digit selection needed to reduce the partial
remainder and augment the quotient to obtain the
desired integer division result $ N = Q \times D + R $
with $ 0 \leq R \leq D - 1 $.\par
We present a high radix multiplicative version of this
algorithm where a $ k \times p $ digit base $ \beta $
rectangular aspect ratio multiplier allows quotient
digit selection in radix $ \beta^{k - 1} $ with a cost
of only one $ k \times p $ digit multiply per high
radix digit, plus the fixed pre- and post-scaling
operation costs. We also present a Booth radix $4$
additive version of this algorithm where appropriately
compressed representation of the partial remainder with
Booth digits $ \{ - 2, - 1, 0, 1, 2 \} $ allows
successive quotient digit selection from the leading
partial remainder digit without the iterative table
lookups required in SRT division.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{McCann:2003:SDA,
author = "Mark McCann and Nicholas Pippenger",
title = "{SRT} division algorithms as dynamical systems",
crossref = "Bajard:2003:ISC",
pages = "46--53",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_McCann.pdf",
abstract = "SRT division, as it was discovered in the late 1950s
represented an important improvement in the speed of
division algorithms for computers at the time. A
variant of SRT division is still commonly implemented
in computers today. Although some bounds on the
performance of the original SRT division method were
obtained, a great many questions remained unanswered.
In this paper, the original version of SRT division is
described as a dynamical system. This enables us to
bring modern dynamical systems theory, a relatively new
development in mathematics, to bear on an older
problem. In doing so, we are able to show that SRT
division is ergodic, and is even Bernoulli, for all
real divisors and dividends. With the Bernoulli
property, we are able to use entropy to prove that the
natural extensions of SRT division are isomorphic by
way of the Kolmogorov-Ornstein Theorem. We demonstrate
how our methods and results can be applied to a much
larger class of division algorithms.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Article{Montgomery:2003:FEC,
author = "Peter L. Montgomery {Kirsten Eisentr{\"a}ger, Kristin
Lauter}",
title = "Fast Elliptic Curve Arithmetic and Improved {Weil}
Pairing Evaluation",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2612",
pages = "343--354",
year = "2003",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 4 18:46:22 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "cryptology; Topics in Cryptology CT-RSA 2003",
}
@InProceedings{Muller:2003:SRS,
author = "Jean-Michel Muller",
title = "{``Partially} rounded'' small-order approximations for
accurate, hardware-oriented, table-based methods",
crossref = "Bajard:2003:ISC",
pages = "114--121",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Muller.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
summary = "We aim at evaluating elementary and special functions
using small tables and small, rectangular, multipliers.
To do that, we show how accurate polynomial
approximations whose order-1 coefficients are small in
size (a few bits only) can be computed. We compare the
obtained results with similar work in the recent
literature",
}
@InProceedings{Nannarelli:2003:PDT,
author = "A. Nannarelli and G. C. Cardarilli and M. Re",
booktitle = "{ISCAS '03}, Proceedings of the 2003 International
Symposium on Circuits and Systems, 25--28 May 2003",
title = "Power-delay tradeoffs in residue number system",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "V-413--V-416",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2003.1206300",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper we present some tradeoffs between delay
and power consumption in the design of digital
processors based on the Residue Number System (RNS). We
focus on reducing the switching capacitance, and
therefore the power, in modular adders and \ldots{}",
}
@Article{Nievergelt:2003:SFM,
author = "Yves Nievergelt",
title = "Scalar fused multiply-add instructions produce
floating-point matrix arithmetic provably accurate to
the penultimate digit",
journal = j-TOMS,
volume = "29",
number = "1",
pages = "27--48",
month = mar,
year = "2003",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/641876.641878",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "68W99 (65Y99 68M99)",
MRnumber = "MR2001452",
bibdate = "Fri Mar 28 08:17:55 MST 2003",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Combined with doubly compensated summation, scalar
fused multiply-add instructions redefine the concept of
floating-point arithmetic, because they allow for the
computation of sums of real or complex matrix products
accurate to the penultimate digit. Particular cases
include complex arithmetic, dot products, cross
products, residuals of linear systems, determinants of
small matrices, discriminants of quadratic, cubic, or
quartic equations, and polynomials.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accurate floating-point summation; algorithms; design;
doubly compensated summation; floating-point
arithmetic; fused multiply-add instruction; languages;
matrix arithmetic; provable accuracy; rounding error;
standardization; theory",
subject = "Primary Classification: B. Hardware, B.2 ARITHMETIC
AND LOGIC STRUCTURES, B.2.0 General;
Additional Classification: B. Hardware, B.7 INTEGRATED
CIRCUITS B.7.1 Types and Design Styles Subjects:
Algorithms implemented in hardware B.8 Performance and
Reliability B.8.2 Performance Analysis and Design
Aids
C. Computer Systems Organization C.0 GENERAL Subjects:
Instruction set design (e.g., RISC, CISC, VLIW)
F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND
PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and
Problems Subjects: Computations on matrices
G. Mathematics of Computing G.1 NUMERICAL ANALYSIS
G.1.0 General Subjects: Computer arithmetic; Multiple
precision arithmetic; Numerical algorithms; Error
analysis G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm
design and analysis; Certification and testing;
Reliability and robustness",
}
@Article{Okeya:2003:WNM,
author = "Katsuyuki Okeya and Tsuyoshi Takagi",
title = "The Width-$w$ {NAF} Method Provides Small Memory and
Fast Elliptic Scalar Multiplications Secure against
Side Channel Attacks",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2612",
pages = "328--342",
year = "2003",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 4 18:46:22 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "cryptology; Topics in Cryptology CT-RSA 2003",
}
@InProceedings{Oklobdzija:2003:EDE,
author = "Vojin G. Oklobdzija and Bart R. Zeydel and Hoang Dao
and Sanu Mathew and Ram Krishnamurthy",
title = "Energy-delay estimation technique for high-performance
microprocessor {VLSI} adders",
crossref = "Bajard:2003:ISC",
pages = "272--279",
year = "2003",
bibdate = "Wed Nov 26 12:04:40 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Oklobdzija.pdf",
abstract = "In this paper, we motivate the concept of comparing
VLSI adders based on their energy-delay trade-offs and
present a technique for estimating the energy-delay
space of various high-performance VLSI adder
topologies. Further, we show that our estimates
accurately represent tradeoffs in the energy-delay
space for high-performance 32-bit and 64-bit processor
adders in 0.13mm and 0.10mm CMOS technologies, with an
accuracy of 8\% in delay estimates and 20\% in energy
estimates, compared with simulated data.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Oklobdzija:2003:TDP,
author = "V. G. Oklobdzija and R. Krishnamurthy",
title = "Tutorial: Design of power efficient {VLSI} arithmetic:
speed and power trade-offs",
crossref = "Bajard:2003:ISC",
pages = "280--280",
year = "2003",
bibdate = "Wed Nov 26 12:04:40 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Article{ORourke:2003:ANM,
author = "C. O'Rourke and B. Sunar",
title = "Achieving {NTRU} with {Montgomery} multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "4",
pages = "440--448",
month = apr,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1190585",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1190585",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Parhami:2003:TUB,
author = "B. Parhami",
title = "Tight upper bounds on the minimum precision required
of the divisor and the partial remainder in high-radix
division",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "11",
pages = "1509--1514",
month = nov,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1244949",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1244949",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Paschalakis:2003:DPF,
author = "S. Paschalakis and P. Lee",
title = "Double precision floating-point arithmetic on
{FPGAs}",
crossref = "IEEE:2003:IICb",
pages = "352--358",
year = "2003",
DOI = "https://doi.org/10.1109/FPT.2003.1275775",
bibdate = "Sat Oct 9 12:57:30 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present low cost FPGA floating-point arithmetic
circuits for all the common operations, i.e.
addition/subtraction, multiplication, division and
square root. Such circuits can be extremely useful in
the FPGA implementation of complex systems that benefit
from the reprogrammability and parallelism of the FPGA
device but also require a general purpose arithmetic
unit. While previous work has considered circuits for
low precision floating-point formats, we consider the
implementation of 64-bit double precision circuits that
also provide rounding and exception handling.",
acknowledgement = ack-nhfb,
}
@Article{Percival:2003:RMM,
author = "Colin Percival",
title = "Rapid multiplication modulo the sum and difference of
highly composite numbers",
journal = j-MATH-COMPUT,
volume = "72",
number = "241",
pages = "387--395",
month = jan,
year = "2003",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri Nov 22 10:22:27 MST 2002",
bibsource = "http://www.ams.org/mcom/2003-72-241;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-02-01419-9;
http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/S0025-5718-02-01419-9.dvi;
http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/S0025-5718-02-01419-9.pdf;
http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/S0025-5718-02-01419-9.ps;
http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/S0025-5718-02-01419-9.tex",
abstract = "We extend the work of Richard Crandall et al. to
demonstrate how the Discrete Weighted Transform (DWT)
can be applied to speed up multiplication modulo any
number of the form $ a \pm b $ where $ \prod_{p \vert
ab}{p} $ is small. In particular this allows rapid
computation modulo numbers of the form $ k \cdot 2^n
\pm 1 $.\par
In addition, we prove tight bounds on the rounding
errors which naturally occur in floating-point
implementations of FFT and DWT multiplications. This
makes it possible for FFT multiplications to be used in
situations where correctness is essential, for example
in computer algebra packages.",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Phillips:2003:SRR,
author = "B. Phillips",
booktitle = "Conference Record of the Thirty-Seventh Asilomar
Conference on Signals, Systems and Computers, 2003",
title = "Scaling and reduction in the residue number system
with pairs of conjugate moduli",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2247--2251",
year = "2003",
CODEN = "????",
DOI = "https://doi.org/10.1109/ACSSC.2003.1292380",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The residue number system (RNS) with pairs of
conjugate moduli uses a modulus set containing pairs of
moduli of the form {2/sup k/-1, 2/sup k/+1}. This RNS
provides a good trade-off between large dynamic range
and channel width. It also supports \ldots{}",
}
@InProceedings{Pineiro:2003:HRI,
author = "J.-A. Pi{\~n}eiro and M. D. Ercegovac and J. D.
Bruguera",
title = "High-radix iterative algorithm for powering
computation",
crossref = "Bajard:2003:ISC",
pages = "204--211",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Pineiro.pdf",
abstract = "A high-radix composite algorithm for the computation
of the powering function ($ X^Y $) is presented in this
paper. The algorithm consists of a sequence of
overlapped operations: (i) digit-recurrence logarithm,
(ii) left-to-right carry-free (LRCF) multiplications,
and (iii) on-line exponential. A redundant number
system is used, and the selection in (i) and (iii) is
done by rounding except from the first iteration, when
selection by table look-up is necessary to guarantee
the convergence of the recurrences. A sequential
implementation of the algorithm is proposed, and the
execution times and hardware requirements are estimated
for single and double-precision floating-point
computations, for radix $ r = 128 $ showing that
powering can be computed with similar performance as
high-radix CORDIC algorithms.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Pineiro:2003:LHR,
author = "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac",
booktitle = "2003. {ISCAS '03}. Proceedings of the 2003
International Symposium on Circuits and Systems. 25--28
May 2003",
title = "On-line high-radix exponential with selection by
rounding",
volume = "4",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "IV-121--IV-124",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "An on-line high-radix algorithm for computing the
exponential function ($e^x$) with arbitrary precision
$n$ is presented. Selection by rounding and a redundant
digit-set for the digits $e_j$ are used, with selection
by table in the first \ldots{}",
}
@Article{Reyhani-Masoleh:2003:EMB,
author = "A. Reyhani-Masoleh and M. A. Hasan",
title = "Efficient multiplication beyond optimal normal bases",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "4",
pages = "428--439",
month = apr,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1190584",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1190584",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Reyhani-Masoleh:2003:FNB,
author = "A. Reyhani-Masoleh and M. A. Hasan",
title = "Fast normal basis multiplication using general purpose
processors",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "11",
pages = "1379--1390",
month = nov,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1244936",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1244936",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Reyhani-Masoleh:2003:LCB,
author = "Arash Reyhani-Masoleh and M. Anwar Hasan",
title = "On Low Complexity Bit Parallel Polynomial Basis
Multipliers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2779",
pages = "189--202",
year = "2003",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 4 18:12:50 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "CHES 2003; cryptography",
}
@InProceedings{Reyhani-Masoleh:2003:LCS,
author = "Arash Reyhani-Masoleh and M. Anwar Hasan",
title = "Low complexity sequential normal basis multipliers
over {$ \mathrm {GF}(2^m) $}",
crossref = "Bajard:2003:ISC",
pages = "188--195",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Reyhani-Masoleh.pdf",
abstract = "For efficient hardware implementation of finite field
arithmetic units, the use of a normal basis is
advantageous. In this article, two architectures for
multipliers over the finite field $ \mathrm {GF}(2^m) $
are proposed. Both of these multipliers are of
sequential type --- after receiving the coordinates of
the two input field elements, they go through $m$
iterations (or clock cycles) to finally yield all the
coordinates of the product in parallel. These
multipliers are highly area efficient and require fewer
number of logic gates even when compared with the most
area efficient multiplier available in the open
literature. This makes the proposed multipliers
suitable for applications where the value of is large
but space is of concern, e.g., resource constrained
cryptographic systems. Additionally, the AND gate count
for one of the multipliers is $ \floor {m / 2} + 1 $
only. This implies that if the multiplication over $
\mathrm {GF}(2^m) $ is performed using a suitable
subfield $ \mathrm {GF}(2^n) $ where $ n > 1 $ and $ n
| m $, then the corresponding multiplier architecture
will yield a highly efficient digit or word serial
multiplier.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Rice:2003:NIS,
author = "Eric Rice and Richard Hughey",
title = "A new iterative structure for hardware division: the
parallel paths algorithm",
crossref = "Bajard:2003:ISC",
pages = "54--62",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Rice.pdf",
abstract = "This paper presents a new approach to hardware
division --- the parallel paths algorithm. In this
approach, prescaling allows the division recurrence to
be implemented by three processes which can be
calculated in parallel during iterations. While two of
the processes must complete in a single iteration, the
third --- which includes the most expensive division
operations --- can be calculated over multiple
iterations. Iteration latency is determined by the
slowest of the three paths, and in many cases can be
limited to that of carry-save addition and latching. A
radix-4 implementation of the algorithm is shown to
achieve better performance than other commonly used
methods while requiring a modest increase in area.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Article{Rodriguez-Henriquez:2003:PMB,
author = "F. Rodriguez-Henriquez and {\c{C}}. K. Ko{\c{c}}",
title = "Parallel multipliers based on special irreducible
pentanomials",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "12",
pages = "1535--1542",
month = dec,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1252850",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:59 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1252850",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Schonfelder:2003:VPA,
author = "J. L. Schonfelder",
title = "Variable precision arithmetic: a {Fortran 95} module",
journal = j-SCI-PROG,
volume = "11",
number = "1",
pages = "67--76",
year = "2003",
CODEN = "SCIPEV",
ISSN = "1058-9244 (print), 1875-919X (electronic)",
ISSN-L = "1058-9244",
bibdate = "Mon Jan 12 06:28:15 MST 2004",
bibsource = "http://www.iospress.nl/site/html/10589244.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Scientific Programming",
journal-URL = "http://iospress.metapress.com/content/1058-9244",
}
@InProceedings{Schulte:2003:CMS,
author = "M. J. Schulte and L. P. Marquette and S. Krithivasan
and E. G. Walters and J. Glossner",
title = "Combined Multiplication and Sum of Squares Units",
crossref = "Deprettere:2003:IIC",
pages = "204--214",
year = "2003",
bibdate = "Sun Mar 04 20:46:13 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2003-02.pdf",
acknowledgement = ack-nhfb,
remark = "One of three finalists for the best paper award.",
}
@InProceedings{Schwarz:2003:HID,
author = "Eric M. Schwarz and Martin Schmookler and Son Dao
Trong",
title = "Hardware implementations of denormalized numbers",
crossref = "Bajard:2003:ISC",
pages = "70--78",
year = "2003",
DOI = "https://doi.org/10.1109/ARITH.2003.1207662",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Schwarz.pdf",
abstract = "Denormalized numbers are the most difficult type of
numbers to implement in floating-point units. They are
so complex that some designs have elected to handle
them in software rather than in hardware. This has
results in execution times in the tens of thousands of
cycle, which as made denormalized numbers useless to
programmers. This does not have to happen. With a small
amount of additional hardware, denormalized numbers and
underflows can be handled close to the speed of
normalized numbers. Most of the techniques discussed
here have only been discussed in filed or pending
patent applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Schwarz:2003:PRI,
author = "E. Schwarz",
title = "Panel: Revisions to the {IEEE 754} standard for
floating-point arithmetic",
crossref = "Bajard:2003:ISC",
pages = "112--112",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Seidel:2003:MPI,
author = "P.-M. Seidel",
booktitle = "{2003 IEEE International Symposium on
Micro-NanoMechatronics and Human Science}",
title = "Multiple Path {IEEE} Floating-Point Fused
Multiply-Add",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1359--1362",
year = "2003",
DOI = "https://doi.org/10.1109/MWSCAS.2003.1562547",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Jun 24 12:02:41 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We propose optimizations for the IEEE floating-point
fused multiply-add operation by considering multiple
exclusive parallel computation paths in the
implementation. For the proposed design we can show a
significant performance improvement over conventional
implementations. Considering a variable latency
implementation allows for further reduction of the
average latency.",
acknowledgement = ack-nhfb,
xxbooktitle = "Proc. 46th Int. IEEE MidWest Symposium on Circuits and
Systems (MWSCAS)",
}
@InProceedings{Senthilvelan:2003:FAL,
author = "M. Senthilvelan and M. J. Schulte",
title = "A Flexible Arithmetic and Logic Unit for Multimedia
Processing",
crossref = "Luk:2003:PSA",
pages = "520--528",
year = "2003",
bibdate = "Sun Mar 04 20:44:10 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2003-05.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Sheldon:2003:SRI,
author = "Jeffrey Sheldon and Walter Lee and Ben Greenwald and
Saman Amarasinghe",
title = "Strength Reduction of Integer Division and Modulo
Operations",
crossref = "Dietz:2003:LCP",
pages = "254--273",
year = "2003",
DOI = "https://doi.org/10.1007/3-540-35767-X_17",
bibdate = "Fri Jun 24 12:09:31 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/link.asp?id=3hfwyuyjxkf23nd2;
http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=2624&spage=254",
abstract = "Integer division, modulo, and remainder operations are
expressive and useful operations. They are logical
candidates to express complex data accesses such as the
wrap-around behavior in queues using ring buffers. In
addition, they appear frequently in address
computations as a result of compiler optimizations that
improve data locality, perform data distribution, or
enable parallelization. Experienced application
programmers, however, avoid them because they are slow.
Furthermore, while advances in both hardware and
software have improved the performance of many parts of
a program, few are applicable to division and modulo
operations. This trend makes these operations
increasingly detrimental to program performance. This
paper describes a suite of optimizations for
eliminating division, modulo, and remainder operations
from programs. These techniques are analogous to
strength reduction techniques used for multiplications.
In addition to some algebraic simplifications, we
present a set of optimization techniques that
eliminates division and modulo operations that are
functions of loop induction variables and loop
constants. The optimizations rely on algebra, integer
programming, and loop transformations.",
acknowledgement = ack-nhfb,
}
@Article{Singer:2003:REP,
author = "Sanja Singer and Sa{\v{s}}a Singer",
title = "Rounding error and perturbation bounds for the
symplectic {QR} factorization",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "358",
number = "1--3",
pages = "255--279",
day = "1",
month = jan,
year = "2003",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Apr 28 07:27:21 MDT 2003",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/207/25/39/abstract.html;
http://www.sciencedirect.com/science?_ob=GatewayURL&_origin=SOCJLA&_urlversion=4&_method=citationSearch&_version=1&_piikey=S002437950200263X&_volkey=00243795%23358%23255&_refkey=Singer%232003%23255%23279&md5=d630d009cc24a902e31bc6f9537af08c",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Smith:2003:UMP,
author = "David M. Smith",
title = "Using Multiple-Precision Arithmetic",
journal = j-COMPUT-SCI-ENG,
volume = "5",
number = "4",
pages = "88--93",
month = jul # "\slash " # aug,
year = "2003",
CODEN = "CSENFA",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Sat Jan 3 18:25:08 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/dl/mags/cs/2003/04/c4088.htm;
http://csdl.computer.org/dl/mags/cs/2003/04/c4088.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
summary = "High-precision arithmetic is useful in many different
computational problems. The most common is a
numerically unstable algorithm, for which, say, 53-bit
(ANSI/IEEE 754-1985 Standard) double precision would
not yield a sufficiently accurate result. \ldots{}",
}
@Article{Sofroniou:2003:IFR,
author = "Mark Sofroniou and Giulia Spaletta",
title = "Increment formulations for rounding error reduction in
the numerical solution of structured differential
systems",
journal = j-FUT-GEN-COMP-SYS,
volume = "19",
number = "3",
pages = "375--383",
month = apr,
year = "2003",
CODEN = "FGSEVI",
ISSN = "0167-739X (print), 1872-7115 (electronic)",
ISSN-L = "0167-739X",
bibdate = "Sat Jan 10 10:03:32 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Future Generation Computer Systems",
journal-URL = "http://www.sciencedirect.com/science/journal/0167739X",
}
@InProceedings{Stehle:2003:WCL,
author = "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
Zimmermann",
title = "Worst cases and lattice reduction",
crossref = "Bajard:2003:ISC",
pages = "142--147",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Stehle.pdf",
abstract = "We propose a new algorithm to find worst cases for
correct rounding of an analytic function. We first
reduce this problem to the real small value problem ---
i.e. for polynomials with real coefficients. Then we
show that this second problem can be solved
efficiently, by extending Coppersmith's work on the
integer small value problem --- for polynomials with
integer coefficients --- using lattice reduction [4, 5,
6].\par
For floating-point numbers with a mantissa less than
$N$, and a polynomial approximation of degree $d$, our
algorithm finds all worst cases at distance $ < N^{-d^2
/ (2d + 1)} $ from a machine number in time $ O(N^{(d +
1) / (2d + 1) + \epsilon }) $. For $ d = 2 $, this
improves on the $ O(N^{2 / 3} + \epsilon) $ complexity
from Lef{\'e}vre's algorithm [15, 16] to $ O(N^{3 / 5}
+ \epsilon) $. We exhibit some new worst cases found
using our algorithm, for double-extended and quadruple
precision. For larger $d$, our algorithm can be used to
check that there exist no worst cases at distance $ <
N^{-k} $ in time $ O(N^{1 / 2 + O(1 / k)}) $.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16; correct rounding; floating-point
arithmetic",
}
@InProceedings{Sun:2003:NAF,
author = "Haiping Sun and Minglun Gao",
title = "A novel architecture for floating-point
multiply-add-fused operation",
crossref = "IEEE:2004:PJC",
volume = "3",
pages = "1675--1679",
year = "2003",
DOI = "https://doi.org/10.1109/ICICS.2003.1292753",
bibdate = "Sun Feb 20 10:50:21 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Suvakovic:2003:EEA,
author = "Dusan Suvakovic and C. Andr{\'e} T. Salama",
title = "Energy Efficient Adiabatic Multiplier-Accumulator
Design",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "33",
number = "1",
pages = "83--103",
month = jan,
year = "2003",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/A:1021145919099",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Fri Jun 24 16:00:03 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a strategy for minimizing
non-adiabatic dissipation in adiabatic arithmetic
units. The non-adiabatic dissipation is minimized by
architectural design involving a small number of
complex logic gates. Circuit design of complex
adiabatic gates, based on ordered binary decision
diagrams (OBDD), is introduced. An optimized
architecture for adiabatic parallel multipliers is
proposed and savings in energy dissipation over
competing architectures are estimated. Experimental
results obtained from implementation of an adiabatic
multiply-accumulate (MAC) unit suggest that the
proposed strategy provides substantial improvement in
energy efficiency over equivalent non-adiabatic and
alternative adiabatic implementations, while achieving
a competitive operating speed.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@Article{Swider:2003:EEF,
author = "Zbigniew {\'S}wider",
title = "Errors of elementary floating-point operations in
control algorithms",
journal = "Arch. Control Sci.",
volume = "13(49)",
number = "4",
pages = "505--526",
year = "2003",
ISSN = "0004-072X",
MRclass = "65G50 (62J10)",
MRnumber = "MR2175804 (2006g:65076)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Archives of Control Sciences. Polish Academy of
Sciences. Committee of Automatic Control and Robotics",
keywords = "rounding errors",
}
@InProceedings{Tan:2003:MPF,
author = "Dimitri Tan and Albert Danysh and Michael Liebelt",
title = "Multiple-precision fixed-point vector
multiply-accumulator using shared segmentation",
crossref = "Bajard:2003:ISC",
pages = "12--19",
year = "2003",
bibdate = "Wed Nov 26 11:59:51 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Tan.pdf",
abstract = "We present a 64-bit fixed-point vector
multiply-accumulator (MAC) architecture capable of
supporting multiple precisions. The vector MAC can
perform one 64$ \times $64, two 32$ \times $32, four
16$ \times $16 or eight 8$ \times $8 bit signed\slash
unsigned multiply-accumulates using essentially the
same hardware as a scalar 64-bit MAC and with only a
small increase in delay. The scalar MAC architecture is
vectorized by inserting mode-dependent multiplexing
into the partial product generation and by inserting
mode-dependent kills in the carry chain of the
reduction tree and the final carry-propagate adder.
This is an example of ``shared segmentation'' in which
the existing scalar structure is segmented and then
shared between vector modes. The vector MAC is area
efficient and can be fully pipelined which makes it
suitable for high-performance processors and possibly
dynamically reconfigurable processors.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Article{Tenca:2003:SAM,
author = "A. F. Tenca and C. K. Koc",
title = "A scalable architecture for modular multiplication
based on {Montgomery}'s algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "9",
pages = "1215--1221",
month = sep,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1228516",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1228516",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Thomas:2003:IMF,
author = "James W. Thomas",
title = "Inlining of mathematical functions in {HP-UX} for
{Itanium 2}",
crossref = "IEEE:2003:PCI",
pages = "135--144",
year = "2003",
DOI = "https://doi.org/10.1109/CGO.2003.1191540",
bibdate = "Thu Jun 09 18:37:10 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "HP-UX compilers inline mathematical functions for
Itanium Processor Family (IPF) systems to improve
throughput 4X--8X versus external library calls,
achieving speeds comparable to highly tuned vector
functions, without requiring the user to code for a
vector interface and without sacrificing accuracy or
edge-case behaviors. This paper highlights IPF
architectural features that support implementation of
high-performance, high-quality math functions for
inlining. It discusses strategies for utilizing the
features and developing inlineable sequences on a large
scale, and it presents requisite compiler features and
language extensions. Also, this paper describes
compiler mechanisms that produce inlineable code and
inline it.",
acknowledgement = ack-nhfb,
keywords = "EPIC; Intel IA-64; Itanium",
}
@Article{Vergos:2003:DRA,
author = "H. T. Vergos and D. Nikolos and M. Bellos and C.
Efstathiou",
title = "Deterministic {BIST} for {RNS} adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "7",
pages = "896--906",
month = jul,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1214338",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1214338",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wahid:2003:EFA,
author = "K. A. Wahid and V. S. Dimitrov and G. A. Jullien",
title = "Error-free arithmetic for discrete wavelet transforms
using algebraic integers",
crossref = "Bajard:2003:ISC",
pages = "238--244",
year = "2003",
bibdate = "Wed Nov 26 12:04:40 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Jullien.pdf",
abstract = "In this paper a novel encoding scheme is introduced
with applications to error-free computation of Discrete
Wavelet Transforms (DWT) based on Daubechies wavelets.
The encoding scheme is based on an algebraic integer
decomposition of the wavelet coefficients. This work is
a continuation of our research into error-free
computation of DCTs and IDCTs, and this extension is
timely since the DWT is part of the new standard for
JPEG2000. This encoding technique eliminates the
requirements to approximate the transformation matrix
elements by obtaining their exact representations. As a
result, we achieve error-free calculations up to the
final reconstruction step where we are free to choose
an approximate substitution precision based on a
hardware\slash accuracy trade-off.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@InProceedings{Walters:2003:UTM,
author = "E. {Walters III} and M. G. Arnold and M. J. Schulte",
title = "Using Truncated Multipliers in {DCT} and {IDCT}
Hardware Accelerators",
crossref = "Luk:2003:PSA",
pages = "573--584",
year = "2003",
bibdate = "Sun Mar 04 17:56:12 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2003-06.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Wang:2003:TDF,
author = "Xiaojun Wang and B. E. Nelson",
booktitle = "{FCCM 2003}: 11th Annual {IEEE} Symposium on
Field-Programmable Custom Computing Machines, 9--11
April 2003",
title = "Tradeoffs of designing floating-point division and
square root on {Virtex FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "195--203",
year = "2003",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "Low latency, high throughput and small area are three
major design considerations of an FPGA (field
programmable gate array) design. In this paper, we
present a high radix SRT division algorithm and a
binary restoring square root algorithm. We \ldots{}",
}
@InCollection{Warren:2003:DLD,
author = "Henry S. Warren",
title = "The distribution of leading digits",
crossref = "Warren:2003:HD",
chapter = "15.3",
pages = "264--267",
year = "2003",
bibdate = "Fri Mar 16 08:02:56 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Wei:2003:REE,
author = "Musheng Wei and Qiaohua Liu",
title = "Roundoff error estimates of the modified
{Gram--Schmidt} algorithm with column pivoting",
journal = j-BIT-NUM-MATH,
volume = "43",
number = "3",
pages = "627--645",
month = sep,
year = "2003",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/B:BITN.0000007051.49808.04",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F20 (65G50)",
MRnumber = "MR2026721 (2004k:65070)",
bibdate = "Wed Jan 4 15:06:06 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=43&issue=3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=43&issue=3&spage=627",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Yan:2003:NSA,
author = "Z. Yan and D. V. Sarwate",
title = "New systolic architectures for inversion and division
in {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "52",
number = "11",
pages = "1514--1519",
month = nov,
year = "2003",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2003.1244950",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:52:58 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1244950",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Zhang:2003:DRV,
author = "Chang N. Zhang and Hua Li",
title = "Design of Reconfigurable {VLSI} Architecture for
Hybrid Arithmetic in {$ G F(2^m) $}",
journal = j-COMP-J,
volume = "46",
number = "4",
pages = "449--460",
month = jul,
year = "2003",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Sun Jun 29 07:07:13 MDT 2003",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_46/Issue_04/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_46/Issue_04/460449.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_46/Issue_04/pdf/460449.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Zielke:2003:GLL,
author = "Gerhard Zielke and Volker Drygalla",
title = "{Genaue L{\"o}sung linearer Gleichungssysteme}.
({German}) [{Exact} solution of linear systems of
equations]",
journal = j-GAMM-MIT,
volume = "26",
number = "??",
pages = "7--107",
month = "????",
year = "2003",
ISSN = "0936-7195",
MRclass = "65F99 (01A60 65-03 65G50 68-03)",
MRnumber = "MR2056620 (2005d:65069)",
bibdate = "Fri Jan 06 08:03:49 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "http://www.wiley-vch.de/publish/en/journals/alphabeticIndex/2250/",
acknowledgement = ack-nhfb,
ajournal = "GAMM Mitt., Ges. Angew. Math. Mech.",
fjournal = "Mitteilungen der Gesellschaft f{\"u}r Angewandte
Mathematik und Mechanik",
keywords = "accurate floating-point summation",
language = "German",
remark = "Contains MATLAB code for error-free accumulation of
floating-point sums and scalar products.",
xxnote = "No electronic copies available yet at publisher site,
and cannot find online copy in Web searches.",
}
@Article{Ziv:2003:SGM,
author = "Abraham Ziv and Laurent Fournier",
title = "Solving the generalized mask constraint for test
generation of binary floating point add operation",
journal = j-THEOR-COMP-SCI,
volume = "291",
number = "2",
pages = "183--201",
day = "27",
month = jan,
year = "2003",
CODEN = "TCSDIQ",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
MRclass = "68M07 (65G30)",
MRnumber = "MR1957439 (2004d:68005)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Real numbers and computers (Schloss Dagstuhl, 2000)",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "floating-point testing",
}
@InProceedings{Ziv:2003:SRC,
author = "Abraham Ziv and Merav Aharoni and Sigal Asaf",
title = "Solving range constraints for binary floating-point
instructions",
crossref = "Bajard:2003:ISC",
pages = "158--164",
year = "2003",
bibdate = "Wed Nov 26 12:04:35 MST 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present algorithms that solve the following
problem: given three ranges of floating-point numbers $
R_x $, $ R_y $, $ R_z $, a floating-point operation
(op), and a rounding-mode (round), generate three
floating-point numbers $ \bar {x} $, $ \bar {y} $, $
\bar {z} $ such that $ \bar {x} \in R_x $, $ \bar {y}
\in R_y $, $ \bar {z} \in R_z $ and $ \bar {z} =
\mathfun {round}(\bar {x} \mathop {op} \bar {y}) $.
This problem, although quite simple when dealing with
intervals of real numbers, is much more complex when
considering ranges of machine numbers. We provide full
solutions for add and subtract, and partial solutions
for multiply and divide. We use range constraints on
the input operands and on the result operand of
floating-point instructions to target corner cases when
generating test cases for use in verification of
floating-point hardware. The algorithms have been
implemented in a floating-point test-generator and are
currently being used to verify floating-point units of
several processors.",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
remark = "No PDF file at the ARITH-16 Web site, and no DOI for
the IEEE Xplore Web site.",
}
@Article{Abbasbandy:2004:USA,
author = "S. Abbasbandy and M. A. Fariborzi Araghi",
title = "The use of the stochastic arithmetic to estimate the
value of interpolation polynomial with optimal degree",
journal = j-APPL-NUM-MATH,
volume = "50",
number = "3--4",
pages = "279--290",
month = sep,
year = "2004",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2004.01.003",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Sat May 14 10:50:47 MDT 2005",
bibsource = "http://www.sciencedirect.com/science/journal/01689274;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0168927404000066",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@TechReport{Akutin:2004:HOM,
author = "Yuri Akutin and Cristina Anderson and Marius Cornea
and Alexey Ershov and Eugeny Gladkov and Evgeny Gvozdev
and Bob Hanek and John Harrison and Alexander Isaev and
Andrey Kolesov and Alexey Kovalev and Elena Luneva and
Sergey Maidanov and Andrey Naraikin and Bob Norin and
Pavel Shelepugin and Vladimir Sorokin and Shane Story
and Ping Tak Peter Tang",
title = "Highly Optimized Mathematical Functions for the
{IA-64} Architecture",
type = "Application note",
number = "245410-011",
institution = inst-INTEL,
address = inst-INTEL:adr,
pages = "14",
day = "16",
month = dec,
year = "2004",
bibdate = "Tue Nov 18 15:45:26 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://download.intel.com/software/opensource/numerics/libm.pdf;
http://www.intel.com/cd/software/products/asmo-na/eng/219868.htm;
http://www.intel.com/cd/software/products/asmo-na/eng/219871.htm?prn=y",
abstract = "Highly Optimized Mathematical Functions for the Intel
Itanium Architecture Intel Corporation is providing
Intel Itanium assembler source code to evaluate certain
core mathematical support functions for the C and
FORTRAN programming languages. The intent is that these
should replace less optimized implementations that
would normally be provided by the compiler or OS
vendor. The functions work well on the Itanium 2
processor as well as the original Itanium
processor.\par
The present document explains the rationale behind this
decision and summarizes important information on
performance and accuracy of the Intel-provided
functions.",
acknowledgement = ack-nhfb,
}
@Book{Altman:2004:NIS,
author = "Micah Altman and Jeff Gill and Michael McDonald",
title = "Numerical Issues in Statistical Computing for the
Social Scientist",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 323",
year = "2004",
DOI = "https://doi.org/10.1002/0471475769",
ISBN = "0-471-23633-0, 0-471-47574-2 (e-book), 0-471-47576-9
(e-book)",
ISBN-13 = "978-0-471-23633-7, 978-0-471-47574-3 (e-book),
978-0-471-47576-7 (e-book)",
LCCN = "QA276.4 .A398 2004",
bibdate = "Thu Oct 17 17:33:39 MDT 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyage",
abstract = "At last --- a social scientist's guide through the
pitfalls of modern statistical computing. Addressing
the current deficiency in the literature on statistical
methods as they apply to the social and behavioral
sciences, \booktitle{Numerical Issues in Statistical
Computing for the Social Scientist} seeks to provide
readers with a unique practical guidebook to the
numerical methods underlying computerized statistical
calculations specific to these fields. The authors
demonstrate that knowledge of these numerical methods
and how they are used in statistical packages is
essential for making accurate inferences.",
acknowledgement = ack-nhfb,
subject = "Estad{\'i}stica; Inform{\`a}tica; Ci{\`e}ncies
socials; M{\`e}todes estad{\'i}stics",
tableofcontents = "1: Introduction: Consequences of Numerical
Inaccuracy / 1 \\
1.1: Importance of Understanding Computational
Statistics / 1 \\
1.2: Brief History: Duhem to the Twenty-First Century /
3 \\
1.3: Motivating Example: Rare Events Counts Models / 6
\\
2: Sources of Inaccuracy in Statistical Computation /
12 \\
2.1.1: Revealing Example: Computing the Coefficient
Standard Deviation / 12 \\
2.1.2: Some Preliminary Conclusions / 13 \\
2.2: Fundamental Theoretical Concepts / 15 \\
2.2.1: Accuracy and Precision / 15 \\
2.2.2: Problems, Algorithms, and Implementations / 15
\\
2.3: Accuracy and Correct Inference / 18 \\
2.3.1: Brief Digression: Why Statistical Inference Is
Harder in Practice Than It Appears / 20 \\
2.4: Sources of Implementation Errors / 21 \\
2.4.1: Bugs, Errors, and Annoyances / 22 \\
2.4.2: Computer Arithmetic / 23 \\
2.5: Algorithmic Limitations / 29 \\
2.5.1: Randomized Algorithms / 30 \\
2.5.2: Approximation Algorithms for Statistical
Functions / 31 \\
2.5.3: Heuristic Algorithms for Random Number
Generation / 32 \\
2.5.4: Local Search Algorithms / 39 \\
3: Evaluating Statistical Software / 44 \\
3.1.1: Strategies for Evaluating Accuracy / 44 \\
3.1.2: Conditioning / 47 \\
3.2: Benchmarks for Statistical Packages / 48 \\
3.2.1: NIST Statistical Reference Datasets / 49 \\
3.2.2: Benchmarking Nonlinear Problems with StRD / 51
\\
3.2.3: Analyzing StRD Test Results / 53 \\
3.2.4: Empirical Tests of Pseudo-Random Number
Generation / 54 \\
3.2.5: Tests of Distribution Functions / 58 \\
3.2.6: Testing the Accuracy of Data Input and Output /
60 \\
3.3: General Features Supporting Accurate and
Reproducible Results / 63 \\
3.4: Comparison of Some Popular Statistical Packages /
64 \\
3.5: Reproduction of Research / 65 \\
3.6: Choosing a Statistical Package / 69 \\
4: Robust Inference / 71 \\
4.3: Sensitivity Tests / 73 \\
4.3.1: Sensitivity to Alternative Implementations and
Algorithms / 73 \\
4.3.2: Perturbation Tests / 75 \\
4.3.3: Tests of Global Optimality / 84 \\
4.4: Obtaining More Accurate Results / 91 \\
4.4.1: High-Precision Mathematical Libraries / 92 \\
4.4.2: Increasing the Precision of Intermediate
Calculations / 93 \\
4.4.3: Selecting Optimization Methods / 95 \\
4.5: Inference for Computationally Difficult Problems /
103 \\
4.5.1: Obtaining Confidence Intervals with Ill-Behaved
Functions / 104 \\
4.5.2: Interpreting Results in the Presence of Multiple
Modes / 106 \\
4.5.3: Inference in the Presence of Instability / 114
\\
5: Numerical Issues in Markov Chain Monte Carlo
Estimation / 118 \\
5.2: Background and History / 119 \\
5.3: Essential Markov Chain Theory / 120 \\
5.3.1: Measure and Probability Preliminaries / 120 \\
5.3.2: Markov Chain Properties / 121 \\
5.3.3: The Final Word (Sort of) / 125 \\
5.4: Mechanics of Common MCMC Algorithms / 126 \\
5.4.1: Metropolis--Hastings Algorithm / 126 \\
5.4.2: Hit-and-Run Algorithm / 127 \\
5.4.3: Gibbs Sampler / 128 \\
5.5: Role of Random Number Generation / 129 \\
5.5.1: Periodicity of Generators and MCMC Effects / 130
\\
5.5.2: Periodicity and Convergence / 132 \\
5.5.3: Example: The Slice Sampler / 135 \\
5.5.4: Evaluating WinBUGS / 137 \\
5.6: Absorbing State Problem / 139 \\
5.7: Regular Monte Carlo Simulation / 140 \\
5.8: So What Can Be Done? / 141 \\
6: Numerical Issues Involved in Inverting Hessian
Matrices / Jeff Gill, Gary King / 143 \\
6.2: Means versus Modes / 145 \\
6.3: Developing a Solution Using Bayesian Simulation
Tools / 147 \\
6.4: What Is It That Bayesians Do? / 148 \\
6.5: Problem in Detail: Noninvertible Hessians / 149
\\
6.6: Generalized Inverse/Generalized Cholesky Solution
/ 151 \\
6.7: Generalized Inverse / 151 \\
6.7.1: Numerical Examples of the Generalized Inverse /
154 \\
6.8: Generalized Cholesky Decomposition / 155 \\
6.8.1: Standard Algorithm / 156 \\
6.8.2: Gill--Murray Cholesky Factorization / 156 \\
6.8.3: Schnabel--Eskow Cholesky Factorization / 158 \\
6.8.4: Numerical Examples of the Generalized Cholesky
Decomposition / 158 \\
6.9: Importance Sampling and Sampling Importance
Resampling / 160 \\
6.9.1: Algorithm Details / 160 \\
6.9.2: SIR Output / 162 \\
6.9.3: Relevance to the Generalized Process / 163 \\
6.10: Public Policy Analysis Example / 163 \\
6.10.1: Texas / 164 \\
6.10.2: Florida / 168 \\
6.11: Alternative Methods / 171 \\
6.11.1: Drawing from the Singular Normal / 171 \\
6.11.2: Aliasing / 173 \\
6.11.3: Ridge Regression / 173 \\
6.11.4: Derivative Approach / 174 \\
6.11.5: Bootstrapping / 174 \\
6.11.6: Respecification (Redux) / 175 \\
7: Numerical Behavior of King's EI Method / 177 \\
7.2: Ecological Inference Problem and Proposed
Solutions / 179 \\
7.3: Numeric Accuracy in Ecological Inference / 180 \\
7.3.1: Case Study 1: Examples from King (1997) / 182
\\
7.3.2: Nonlinear Optimization / 186 \\
7.3.3: Pseudo-Random Number Generation / 187 \\
7.3.4: Platform and Version Sensitivity / 188 \\
7.4: Case Study 2: Burden and Kimball (1998) / 189 \\
7.4.1: Data Perturbation / 191 \\
7.4.2: Option Dependence / 194 \\
7.4.3: Platform Dependence / 195 \\
7.4.4: Discussion: Summarizing Uncertainty / 196 \\
8: Some Details of Nonlinear Estimation / B.D.
McCullough / 199 \\
8.2: Overview of Algorithms / 200 \\
8.3: Some Numerical Details / 204 \\
8.4: What Can Go Wrong? / 206 \\
8.5: Four Steps / 210 \\
8.5.1 Step 1: Examine the Gradient / 211 \\
8.5.2 Step 2: Inspect the Trace / 211 \\
8.5.3 Step 3: Analyze the Hessian / 212 \\
8.5.4 Step 4: Profile the Objective Function / 212 \\
8.6: Wald versus Likelihood Inference / 215 \\
9: Spatial Regression Models / James P. LeSage / 219
\\
9.2: Sample Data Associated with Map Locations / 219
\\
9.2.1: Spatial Dependence / 219 \\
9.2.2: Specifying Dependence Using Weight Matrices /
220 \\
9.2.3: Estimation Consequences of Spatial Dependence /
222 \\
9.3: Maximum Likelihood Estimation of Spatial Models /
223 \\
9.3.1: Sparse Matrix Algorithms / 224 \\
9.3.2: Vectorization of the Optimization Problem / 225
\\
9.3.3: Trade-offs between Speed and Numerical Accuracy
/ 226 \\
9.3.4: Applied Illustrations / 228 \\
9.4: Bayesian Spatial Regression Models / 229 \\
9.4.1: Bayesian Heteroscedastic Spatial Models / 230
\\
9.4.2: Estimation of Bayesian Spatial Models / 231 \\
9.4.3: Conditional Distributions for the SAR Model /
232 \\
9.4.4: MCMC Sampler / 234 \\
9.4.5: Illustration of the Bayesian Model / 234 \\
10: Convergence Problems in Logistic Regression / Paul
Allison / 238 \\
10.2: Overview of Logistic Maximum Likelihood
Estimation / 238 \\
10.3: What Can Go Wrong? / 240 \\
10.4: Behavior of the Newton--Raphson Algorithm under
Separation / 243 \\
10.4.1: Specific Implementations / 244 \\
10.4.2: Warning Messages / 244 \\
10.4.3: False Convergence / 246 \\
10.4.4: Reporting of Parameter Estimates and Standard
Errors / 247 \\
10.4.5: Likelihood Ratio Statistics / 247 \\
10.5: Diagnosis of Separation Problems / 247 \\
10.6: Solutions for Quasi-Complete Separation / 248 \\
10.6.1: Deletion of Problem Variables / 248 \\
10.6.2: Combining Categories / 248 \\
10.6.3: Do Nothing and Report Likelihood Ratio
Chi-Squares / 249 \\
10.6.4: Exact Inference / 249 \\
10.6.5: Bayesian Estimation / 250 \\
10.6.6: Penalized Maximum Likelihood Estimation / 250
\\
10.7: Solutions for Complete Separation / 251 \\
10.8: Extensions / 252 \\
11: Recommendations for Replication and Accurate
Analysis / 253 \\
11.1: General Recommendations for Replication / 253 \\
11.1.1: Reproduction, Replication, and Verification /
254 \\
11.1.2: Recreating Data / 255 \\
11.1.3: Inputting Data / 256 \\
11.1.4: Analyzing Data / 257 \\
11.2: Recommendations for Producing Verifiable Results
/ 259 \\
11.3: General Recommendations for Improving the Numeric
Accuracy of Analysis / 260 \\
11.4: Recommendations for Particular Statistical Models
/ 261 \\
11.4.1: Nonlinear Least Squares and Maximum Likelihood
/ 261 \\
11.4.2: Robust Hessian Inversion / 262 \\
11.4.3: MCMC Estimation / 263 \\
11.4.4: Logistic Regression / 265 \\
11.4.5: Spatial Regression / 266 \\
Where Do We Go from Here? / 266 \\
Bibliography / 267 \\
Author Index / 303 \\
Subject Index / 315",
}
@Article{Assimakopoulos:2004:IRM,
author = "C. Assimakopoulos and F.-N. Pavlidou",
title = "Integrated rounding method for real number bit
distribution over {DMT} systems",
journal = j-ELECT-LETTERS,
volume = "40",
number = "19",
pages = "1235--1236",
day = "16",
month = sep,
year = "2004",
CODEN = "ELLEAK",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
summary = "Most bit loading algorithms proposed in the literature
originally distribute a non-integer number of bits to
the subcarriers of a discrete multitone (DMT) system
and then, employing an iterative algorithm they round
these assigned numbers to \ldots{}",
}
@Article{Astola:2004:FAE,
author = "J. T. Astola and K. Egiazarian and M. Stankovi{\'c}
and R. S. Stankovi{\'c}",
title = "{Fibonacci} Arithmetic Expressions",
journal = j-AUTOMATION-REMOTE-CTL,
volume = "65",
number = "6",
pages = "842--856",
month = jun,
year = "2004",
CODEN = "AURCAT",
ISSN = "0005-1179 (print), 1608-3032 (electronic)",
ISSN-L = "0005-1179",
bibdate = "Thu Aug 07 19:27:43 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, we extend the arithmetic (AR)
expressions for functions on finite dyadic groups to
functions used in Fibonacci interconnection topologies.
We have introduced the Fibonacci-Arithmetic (FibAR)
expressions for representation of these functions. We
discussed the optimization of FibARs with respect to
the number of non-zero coefficients through the
Fixed-Polarity FibARs defined by using different
polarities for the Fibonacci variables. In this way, we
provide a base to extend the application of ARs and
related powerful CAD design tools for switching
functions to functions in Fibonacci interconnection
topologies.",
acknowledgement = ack-nhfb,
fjournal = "Automation and Remote Control",
}
@Article{Avot-Chotin:2004:HID,
author = "Roselyne Avot-Chotin and Habib Mehrez",
title = "Hardware Implementation of Discrete Stochastic
Arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "21--33",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 07:00:28 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/3/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "Special Issue: SCAN'2002 International Conference
(Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}
@InProceedings{Bachega:2004:HPS,
author = "L. Bachega and Siddhartha Chatterjee and K. A. Dockser
and J. A. Gunnels and Manish Gupta and F. G. Gustavson
and C. A. Lapkowski and G. K. Liu and M. P. Mendell and
C. D. Wait and T. J. C. Ward",
booktitle = "{PACT 2004}. Proceedings. 13th International
Conference on Parallel Architecture and Compilation
Techniques, 29 Sept.--3 Oct. 2004",
title = "A high-performance {SIMD} floating point unit for
{BlueGene/L}: architecture, compilation, and algorithm
design",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "85--96",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We describe the design, implementation, and evaluation
of a dual-issue SIMD-like extension of the PowerPC 440
floating-point unit (FPU) core. This extended FPU is
targeted at both IBM's massively parallel BlueGene/L
machine as well as more pervasive embedded platforms.",
acknowledgement = ack-nhfb,
}
@Article{Bajard:2004:FRI,
author = "J.-C. Bajard and L. Imbert",
title = "A full {RNS} implementation of {RSA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "6",
pages = "769--774",
month = jun,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.2",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1288551",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Bernstein:2004:FPA,
author = "Daniel J. Bernstein",
title = "Floating-Point Arithmetic and Message Authentication",
pages = "21",
day = "18",
month = sep,
year = "2004",
bibdate = "Mon May 13 10:25:28 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hash.bib",
note = "To be incorporated into the author's
\booktitle{High-Speed Cryptography} book. [As of 13 May
2024, this book seems not to have been published.]",
URL = "https://cr.yp.to/antiforgery/hash127-20040918.pdf",
abstract = "There is a well-known class of message authentication
systems guaranteeing that attackers will have a
negligible chance of successfully forging a message.
This paper shows how one of these systems can hash
messages at extremely high speed --- much more quickly
than previous systems at the same security level ---
using IEEE floating-point arithmetic. This paper also
presents a survey of the literature in a unified
mathematical framework.",
acknowledgement = ack-nhfb,
remark = "From the first page: ``What distinguishes $ h_r $ is
its speed: it is the first high-security system that
offers better speed than the MD5-based systems in
common use today.'' The section on Priority dates on
the second page notes earlier work back to April
1999.",
}
@TechReport{Bernstein:2004:RRH,
author = "Daniel J. Bernstein",
title = "Removing Redundancy in High-Precision {Newton}
Iteration",
type = "Technical Report",
institution = "Department of Mathematics, Statistics, and Computer
Science (M/C 249), The University of Illinois at
Chicago",
address = "Chicago, IL 60607-7045",
pages = "2",
day = "9",
month = mar,
year = "2004",
bibdate = "Sun Sep 10 07:51:20 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Hanrot:2004:NIR}.",
URL = "http://cr.yp.to/fastnewton.html;
http://cr.yp.to/fastnewton/fastnewton-20040309.pdf",
abstract = "This paper presents new algorithms for several
high-precision operations in the power series ring $
C[[x]] $. Compared to computing $n$ coefficients of a
product in $ C[[x]] $, computing $n$ coefficients of a
reciprocal in $ C[[x]] $ takes $ 1.5 + o(1) $ times
longer; a quotient or logarithm, $ 2.16666 \cdots {} +
o(1) $ times longer; a square root, $ 1.83333 \cdots {}
+ o(1) $ times longer; an exponential, $ 2.83333 \cdots
{} + o(1) $ times longer. Previous algorithms had worse
constants. The same ideas apply to high-precision
computations in $R$, $ Q_p $, etc.",
acknowledgement = ack-nhfb,
}
@TechReport{Bernstein:2004:SRT,
author = "Daniel J. Bernstein",
title = "Scaled Remainder Trees",
type = "Report",
institution = "University of Sydney",
address = "Sydney, NSW, Australia",
day = "20",
month = apr,
year = "2004",
bibdate = "Tue Oct 15 07:27:53 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Draft for \booktitle{Mathematics of Computation}, but
never published in that journal.",
URL = "http://cr.yp.to/arith/scaledmod-20040820.pdf",
abstract = "It is well known that one can compute $ U \bmod p_1 $,
$ U \bmod p_2 $, \ldots{} in time $ n(\lg n)^{2 + o(1)}
$ where $n$ is the number of bits in $U$, $ p_1$, $
p_2$, \ldots{}. Here $U$, $ p_1$, $ p_2$, \ldots{} can
be integers or polynomials over a fixed finite field.
Bostan, Lecerf, and Schost recently introduced an
algorithm for the polynomial case that takes time $
n(\lg n)^{2 + o(1)}$ with a smaller $ o(1)$. They did
not claim any similar speedup for integers; their
algorithm uses polynomial reversal and
coefficient-matrix transposition, neither of which
applies to integers. This paper presents a simpler
algorithm that achieves the same speedup and that works
for both polynomials and integers. This paper then
points out several redundancies that can be eliminated
from the algorithm, saving even more time.",
acknowledgement = ack-nhfb,
remark = "Paul Zimmermann reported on the gmp-devel mailing list
on Tue, 15 Oct 2019 10:40:48 +0200 that the remainder
algorithm in this report is rediscovered in
\cite{Lemire:2019:FRD}.",
}
@TechReport{Bertin:2004:FPL,
author = "C. Bertin and Nicolas Brisebarre and B. Dupont de
Dinechin and C.-P. Jeannerod and C. Monat and
Jean-Michel Muller and S. Raina and A. Tisserand",
title = "A floating-point library for integer processors",
type = "Research Report",
number = "RR2004-37",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 11",
month = jul,
year = "2004",
bibdate = "Mon Dec 06 11:02:55 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-37.ps.gz",
abstract = "This paper presents a C library for the software
support of single precision floating-point (FP)
arithmetic on processors without FP hardware units such
as VLIW or DSP processor cores for embedded
applications. This library provides several levels of
compliance to the IEEE 754 FP standard. The complete
specifications of the standard can be used or just some
relaxed characteristics such as restricted rounding
modes or computations without denormal numbers. This
library is evaluated on the ST200 VLIW processors from
STMicroelectronics.",
acknowledgement = ack-nhfb,
keywords = "addition; Computer arithmetic; division; DSP;
floating-point arithmetic; integer processor;
multiplication; square-root; VLIW",
remark = "Published in ``Advanced Signal Processing Algorithms,
Architectures, and Implementations XIV, Spie 2004.''",
}
@TechReport{Beuchat:2004:FMM,
author = "Jean-Luc Beuchat",
title = "A Family of Modulo $ (2^n + 1) $ Multipliers",
type = "Research Report",
number = "RR2004-39",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 13",
year = "2004",
bibdate = "Mon Dec 06 11:05:32 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-39.ps.gz",
abstract = "In this paper, we first describe a novel modulo $ (2^n
+ 1) $ addition algorithm suited to FPGA and ASIC
implementations, and discuss several architectures of
multioperand modulo $ (2^n + 1) $ adders. Then, we
propose three implementations of a modulo $ (2^n + 1) $
multiplication algorithm based on a paper by A.
Wrzyszcz and D. Milford. The first operator is based on
an $ n \times n $ multiplication and a subsequent
modulo $ (2^n + 1) $ correction, and takes advantage of
the arithmetic logic embedded in Spartan or Virtex
FPGAs. The second operator computes a sum of
modulo-reduced partial products by means of a
multioperand modulo $ (2^n + 1) $ adder. Then,
radix-$4$ modified Booth recoding reduces the number of
partial products, while making their generation more
complex. Finally, we provide a comparison of this
family of algorithms with existing solutions.",
acknowledgement = ack-nhfb,
keywords = "FPGA Implementation; Modular Arithmetic; Modulo
$(2^n+1)$ Addition; Modulo $(2^n+1)$ Multiplication",
}
@Article{Boggs:2004:MIP,
author = "Darrell Boggs and Aravindh Baktha and Jason Hawkins
and Deborah T. Marr and J. Alan Miller and Patrice
Roussel and Ronak Singhal and Bret Toll and K. S.
Venkatraman",
title = "The Microarchitecture of the {Intel{\reg}
Pentium{\reg} 4} Processor on 90nm Technology",
journal = j-INTEL-TECH-J,
volume = "8",
number = "1",
pages = "1--17",
month = feb,
year = "2004",
bibdate = "Mon Jul 11 08:46:53 2005",
bibsource = "http://developer.intel.com/technology/itj/archive/2004.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://developer.intel.com/technology/itj/2004/volume08issue01/foreword.htm",
acknowledgement = ack-nhfb,
keywords = "complex arithmetic; floating-point arithmetic;
Hyper-Threading Technology; microarchitecture;
Pentium{\reg} 4 processor",
remark = "From pp. 10--11: ``Five instructions have been added
to significantly accelerate complex arithmetic. Two
instructions (addsubps and addsubpd) perform a mix of
floating-point addition and subtraction, hence removing
the need for changing the sign of some operands. Three
others (movsldup, movshdup, movddup), in their memory
version, combine loads with some level of duplication,
hence saving the need for a shuffle instruction on the
loaded data.''",
}
@InProceedings{Boldo:2004:BGB,
author = "Sylvie Boldo",
title = "Bridging the gap between formal specification and
bit-level floating-point arithmetic",
crossref = "Frougny:2004:RCR",
pages = "22--36",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_04_boldo.pdf",
abstract = "Floating-point arithmetic is defined by the IEEE-754
standard and has often been formalized. We propose a
new Coq formalization based on the bit-level
representation of the standard and we prove strong
links between this new formalization and a previous
high-level one. In this process, we have defined
functions for any rounding mode described by the
standard. Our library can now be applied to certify
both software and hardware. Developing results in those
two dramatically different directions, like no other
formal development so far, guarantees that nothing was
forgotten or poorly specified in our formalization. It
also lets us compare our work with the existing
bit-level formalizations developed with other proof
assistants.",
acknowledgement = ack-nhfb,
keywords = "Coq; floating-point; formal proof checking; IEEE-754",
}
@PhdThesis{Boldo:2004:PFA,
author = "Sylvie Boldo",
title = "Preuves formelles en arithm{\'e}tiques {\`a} virgule
flottante. ({French}) [Formal proofs in floating-point
arithmetic]",
type = "{Ph.D.} thesis",
school = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "????",
month = nov,
year = "2004",
bibdate = "Tue Nov 23 09:53:06 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "French",
}
@Article{Boldo:2004:PTC,
author = "Sylvie Boldo and Marc Daumas",
title = "Properties of two's complement floating point
notations",
journal = j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
volume = "5",
number = "2--3",
pages = "237--246",
month = mar,
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10009-003-0120-y",
ISSN = "1433-2779 (print), 1433-2787 (electronic)",
ISSN-L = "1433-2779",
bibdate = "Tue Nov 23 09:56:44 2004",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1433-2779;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://perso.ens-lyon.fr/marc.daumas/SoftArith/BolDau04a.pdf",
abstract = "Few designs, mostly those of Texas Instruments,
continue to use two's complement floating point units.
Such units are simpler to build and to validate, but
they do not comply to the dominant IEEE standard for
floating point arithmetic. We compare some properties
of the two systems in this text. Some features are
lost, but others remain unchanged. One strong example
is the case of Sterbenz' theorem and our recent
extension. We show in the paper that the theorem and
its extension hold for the two's complement
architecture. Still, users should ensure that results
are large enough on circuits that do not implement
gradual underflow. Theorems have been proven and
validated using the Coq automatic proof checker.",
acknowledgement = ack-nhfb,
fjournal = "International Journal on Software Tools for Technology
Transfer: STTT",
journal-URL = "http://link.springer.com/journal/10009",
}
@Article{Boldo:2004:STQ,
author = "Sylvie Boldo and Marc Daumas",
title = "A Simple Test Qualifying the Accuracy of {Horner}'s
Rule for Polynomials",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "45--60",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 06:44:22 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
Ingenta database",
note = "SCAN2002 International Conference (Guest Editors: Rene
Alt and Jean-Luc Lamotte).",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "floating-point testing",
pagecount = "16",
}
@TechReport{Boldo:2004:WDR,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "When double rounding is odd",
type = "Research Report",
number = "RR2004-48",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 7",
month = nov,
year = "2004",
bibdate = "Mon Dec 06 11:18:07 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-48.pdf;
https://inria.hal.science/inria-00070603v2/file/BolMel.pdf",
abstract = "Double rounding consists in a first rounding in an
intermediate extended precision and then a second
rounding in the working precision. The natural question
is then of the precision and correctness of the final
result. Unfortunately, the used double rounding
algorithms do not obtain a correct rounding of the
initial value. We prove an efficient algorithm for the
double rounding to give the correct rounding to the
nearest value assuming the first rounding is to odd. As
this rounding is unusual and this property is
surprising, we formally proved this property using the
Coq automatic proof checker.",
acknowledgement = ack-nhfb,
keywords = "Coq; correct rounding; double rounding;
Floating-point; floating-point arithmetic; formal
proof; round-to-odd (RO(x))",
}
@Article{Brisebarre:2004:ACR,
author = "Nicolas Brisebarre and Jean-Michel Muller and Saurabh
Kumar Raina",
title = "Accelerating correctly rounded floating-point division
when the divisor is known in advance",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "8",
pages = "1069--1072",
month = aug,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.37",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1306999",
abstract = "We present techniques for accelerating the
floating-point computation of $ x / y $ when $y$ is
known before $x$. The proposed algorithms are oriented
toward architectures with available fused-mac
operations. The goal is to get exactly the same result
as with \ldots{}",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "We present techniques for accelerating the
floating-point computation of x/y when y is known
before x. The proposed algorithms are oriented toward
architectures with available fused-mac operations. The
goal is to get exactly the same result as with
\ldots{}",
}
@TechReport{Brisebarre:2004:CRM,
author = "Nicolas Brisebarre and Jean-Michel Muller",
title = "Correctly rounded multiplication by arbitrary
precision constants",
type = "Research Report",
number = "RR2004-44",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 14",
month = oct,
year = "2004",
bibdate = "Mon Dec 06 11:11:37 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-44.pdf",
abstract = "We introduce an algorithm for multiplying a
floating-point number $x$ by a constant $C$ that is not
exactly representable in floating-point arithmetic. Our
algorithm uses a multiplication and a fused multiply
accumulate instruction. We give methods for checking
whether, for a given value of $C$ and a given
floating-point format, our algorithm returns a
correctly rounded result for any $x$. When it does not,
our methods give the values $x$ for which the
multiplication is not correctly rounded.",
acknowledgement = ack-nhfb,
keywords = "Computer Arithmetic; Correct rounding; Floating-point
Arithmetic; Fused-mac; Multiplication by a constant",
}
@TechReport{Bruguera:2004:DDF,
author = "Javier D. Bruguera and Tom{\'a}s Lang",
title = "Double-Datapath Floating-point multiply-add fused:
latency reduction for floating-point addition",
type = "Report",
institution = "Grupo de Arquitectura de Computadores, Universidad de
Santiago de Compostela",
address = "Edificio Monte de la Condesa, Campus Sur, 15782
Santiago de Compostela, Spain",
pages = "24",
year = "2004",
bibdate = "Fri Jun 24 10:10:03 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www-gpaa.dec.usc.es/arquivos/articulos/2004/gac2004-i03.ps;
http://www.ac.usc.es/arquivos/articulos/2004/gac2004-i03.ps",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic; floating-point functional units;
multiply-add fused (MAF) operation; VLSI design",
}
@InProceedings{Busaba:2004:DFP,
author = "Fadi Busaba and Timothy Slegel and Steven Carlough and
Christopher Krygowski and John G. Rell",
title = "The design of the fixed point unit for the z990
microprocessor",
crossref = "ACM:2004:GVN",
pages = "364--367",
year = "2004",
bibdate = "Thu Aug 07 18:08:54 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper presents the design of the Fixed Point Unit
(FXU) for the IBM eServer z990 microprocessor
(announced in 2Q '03) that runs at 1.2 GHz [2]. The FXU
is capable of executing two Register-Memory
instructions including arithmetic instructions and a
branch instruction in a single cycle. The FXU executes
a total of 369 instructions that operate on variable
size operands (1 to 256 bytes). The instruction set
include decimal arithmetic with multiplies and divides,
binary arithmetic, shifts and rotates, loads/stores,
branches, long moves, logical operations, convert
instructions, and other special instructions. The FXU
consists of 64-bit dataflow stack that is custom
designed and a control stack that is synthesized. The
current FXU is the first superscalar design for the
CMOS z-series machines, has a new improved decimal
unit, and has for the first time a $ 16 \times 64 $ bit
binary multiplier.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic; microprocessor; superscalar FXU",
}
@InProceedings{Cagnard:2004:ABF,
author = "B. Cagnard and P. Simonnet",
title = "Automata, {Borel} functions and real numbers in
{Pisot} base",
crossref = "Frougny:2004:RCR",
pages = "37--54",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_05_cagnard.pdf",
abstract = "This note is about functions $ f : A^\omega \to
B^\omega $ whose graph is recognized by a B{\"u}chi
finite automaton on the product alphabet $ A \times B
$. These functions are Baire class 2 in the Baire
hierarchy of Borel functions and it is decidable
whether such functions are continuous or not. In 1920
W. Sierpinski showed that a function $ f : \mathbb {R}
\to \mathbb {R} $ is Baire class 1 if and only if both
the overgraph and the undergraph of $f$ are $ F_\sigma
$. We show that such characterization is also true for
functions on infinite words if we replace the real
ordering by the lexicographical ordering on $ B^\omega
$. From this we deduce that it is decidable whether
such functions are of Baire class 1 or not. We extend
this result to reals functions definable by automata in
Pisot base.",
acknowledgement = ack-nhfb,
keywords = "automata; Borel function; Borel set; sequential
machine",
}
@InProceedings{Cao:2004:DRB,
author = "B. Cao and T. Srikanthan and Chip-Hong Chang",
booktitle = "{ISCAS '04}, Proceedings of the 2004 International
Symposium on Circuits and Systems, 23--26 May 2004",
title = "Design of residue-to-binary converter for a new
$5$-moduli superset residue number system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-841--4",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1109/IECON.2004.1432111",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents an efficient residue-to-binary
(R/B) conversion algorithm for a new 5-moduli superset
{2/sup n/-1, 2/sup n/, 2/sup n/+1, 2/sup n+1/-1, 2/sup
n-1/-1} residue number system (RNS) when n is even. The
new moduli set is provided for \ldots{}",
}
@InProceedings{Cardarilli:2004:LPI,
author = "G. C. Cardarilli and A. Del Re and A. Nannarelli and
M. Re",
booktitle = "{ISCAS '04}, Proceedings of the 2004 International
Symposium on Circuits and Systems, 23--26 May 2004",
title = "Low-power implementation of polyphase filters in
{Quadratic Residue Number} system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-725--8",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1109/TWC.2004.833509",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The aim of this work is the reduction of the power
dissipated in digital filters, while maintaining the
timing unchanged. A polyphase filter bank in the
Quadratic Residue Number System (QRNS) has been
implemented and then compared, in terms of \ldots{}",
}
@InProceedings{Chakraborty:2004:GAL,
author = "M. Chakraborty and A. Mitra",
booktitle = "Proceedings. {(ICASSP '04)}. {IEEE} International
Conference on Acoustics, Speech, and Signal Processing,
17--21 May 2004",
title = "The gradient adaptive lattice algorithm in block
floating point format",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-849--II-852",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chirca:2004:SLP,
author = "K. Chirca and M. Schulte and J. Glossner and S. Mamidi
and S. Vassiliadis",
title = "A Static Low-Power, High-Performance 32-bit Carry Skip
Adder",
crossref = "Selvaraj:2004:PES",
pages = "615--619",
year = "2004",
bibdate = "Sun Mar 04 20:52:48 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-12.pdf",
acknowledgement = ack-nhfb,
}
@Article{Clinger:2004:HRF,
author = "William D. Clinger",
title = "How to read floating point numbers accurately",
journal = j-SIGPLAN,
volume = "39",
number = "4",
pages = "360--371",
month = apr,
year = "2004",
CODEN = "SINODQ",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Apr 12 09:38:13 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Clinger:2004:RHR,
author = "William D. Clinger",
title = "Retrospective: How to read floating point numbers
accurately",
journal = j-SIGPLAN,
volume = "39",
number = "4",
pages = "360--371",
month = apr,
year = "2004",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/989393.989430",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Wed May 26 06:21:19 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Best of PLDI 1979--1999. Reprint of, and retrospective
on, \cite{Clinger:1990:HRF}.",
abstract = "Converting decimal scientific notation into binary
floating point is nontrivial, but this conversion can
be performed with the best possible accuracy without
sacrificing efficiency. Consider the problem of
converting decimal scientific notation for a number
into the best binary floating point approximation to
that number, for some fixed precision. This problem
cannot be solved using arithmetic of any fixed
precision. Hence the IEEE Standard for Binary
Floating-Point Arithmetic does not require the result
of such a conversion to be the best approximation. This
paper presents an efficient algorithm that always finds
the best approximation. The algorithm uses a few extra
bits of precision to compute an IEEE-conforming
approximation while testing an intermediate result to
determine whether the approximation could be other than
the best. If the approximation might not be the best,
then the best approximation is determined by a few
simple operations on multiple-precision integers, where
the precision is determined by the input. When using 64
bits of precision to compute IEEE double precision
results, the algorithm avoids higher-precision
arithmetic over 99\% of the time. The input problem
considered by this paper is the inverse of an output
problem considered by Steele and White: Given a binary
floating point number, print a correctly rounded
decimal representation of it using the smallest number
of digits that will allow the number to be read without
loss of accuracy. The Steele and White algorithm
assumes that the input problem is solved; an imperfect
solution to the input problem, as allowed by the IEEE
standard and ubiquitous in current practice, defeats
the purpose of their algorithm.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Cowlishaw:2004:FFE,
author = "Mike Cowlishaw and Joshua Bloch and Joseph D. Darcy",
title = "Fixed, Floating, and Exact Computation in {Java}'s
{{\em BigDecimal\/}}: Calculations just got easier",
journal = j-DDJ,
volume = "29",
number = "7",
pages = "22, 24, 26--27",
month = jul,
year = "2004",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Thu Jun 03 07:31:12 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "decimal floating-point arithmetic",
}
@Article{Croot:2004:ACC,
author = "Ernie Croot and Ren-Cang Li and H. J. Hui June Zhu",
title = "The {\em abc\/} conjecture and correctly rounded
reciprocal square roots",
journal = j-THEOR-COMP-SCI,
volume = "315",
number = "2--3",
pages = "405--417",
day = "6",
month = may,
year = "2004",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Thu Nov 4 10:19:15 MST 2004",
bibsource = "http://www.sciencedirect.com/science/journal/03043975;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The reciprocal square root calculation $ \alpha = 1 /
\sqrt {x} $ is very common in scientific computations.
Having a correctly rounded implementation of it is of
great importance in producing numerically predictable
code among today's heterogeneous computing environment.
Existing results suggest that to get the correctly
rounded $ \alpha $ in a floating point number system
with $p$ significant bits, we may have to compute up to
$ 3 p + 1 $ leading bits of $ \alpha $. However,
numerical evidence indicates the actual number may be
as small as $ 2 p $ plus a few more bits. This paper
attempts to bridge the gap by showing that this is
indeed true, assuming the {\em abc\/} conjecture which
is widely purported to hold. (But our results do not
tell exactly how many more bits beyond the $ 2 p $
bits, due to the fact that the constants involved in
the conjecture are ineffective.) Along the way, rough
bounds which are comparable to the existing ones are
also proven. The technique used here is a combination
of the classical Liouville's estimation and
contemporary number theory.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@TechReport{Daumas:2004:GFCa,
author = "Marc Daumas and Guillaume Melquiond",
title = "Generating formally certified bounds on values and
round-off errors",
type = "Research Report",
number = "RR2004-36",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 24",
month = jul,
year = "2004",
bibdate = "Mon Dec 06 10:59:57 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-36.ps.gz",
abstract = "We present a new tool that generates bounds on the
values and the round-off errors of programs using
floating point operations. The tool is based on forward
error analysis and interval arithmetic. The novelty of
our tool is that it produces a formal proof of the
bounds that can be checked independently using an
automatic proof checker such as Coq and a complete
model of floating point arithmetic. For the first time
ever, we can easily certify that simple numerical
programs such as the ones usually found in real time
applications do not overflow and that round-off errors
are below acceptable thresholds. Such level of quality
should be compulsory on safety critical applications.
As our tool is easy to handle, it could also be used
for many pieces of software.",
acknowledgement = ack-nhfb,
keywords = "Certification; Formal proof; Overflow; Round-off
error; Safety critical",
}
@InProceedings{Daumas:2004:GFCb,
author = "Marc Daumas and Guillaume Melquiond",
title = "Generating formally certified bounds on values and
round-off errors",
crossref = "Frougny:2004:RCR",
pages = "55--70",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_06_daumas.pdf",
abstract = "We present a new tool that generates bounds on the
values and the round-off errors of programs using
floating point operations. The tool is based on forward
error analysis and interval arithmetic. The novelty of
our tool is that it produces a formal proof of the
bounds that can be checked independently using an
automatic proof checker such as Coq and a complete
model of floating point arithmetic. For the first time
ever, we can easily certify that simple numerical
programs such as the ones usually found in real time
applications do not overflow and that round-off errors
are contained. Such level of quality should be
compulsory on safety critical applications. As our tool
is easy to handle, it could be used for many pieces of
software.",
acknowledgement = ack-nhfb,
keywords = "Certification; Formal proof; Overflow; Round-off
error; Safety critical",
}
@Misc{deDinechin:2004:C,
author = "Florent de Dinechin",
title = "crlibm",
howpublished = "World-Wide Web software project archive.",
day = "16",
month = apr,
year = "2004",
bibdate = "Fri Jun 24 14:38:41 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://lipforge.ens-lyon.fr/projects/crlibm/",
abstract = "The purpose of this project is to offer a mathematical
library (libm) with proven, IEEE-754 compliant, correct
rounding in the four rounding modes, and performances
comparable to standard libms.",
acknowledgement = ack-nhfb,
}
@TechReport{deDinechin:2004:FCR,
author = "Florent de Dinechin and David Defour and Christoph
Lauter",
title = "Fast correct rounding of elementary functions in
double precision using double-extended arithmetic",
type = "Research Report",
number = "RR2004-10",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 12",
month = mar,
year = "2004",
bibdate = "Mon Dec 06 10:49:12 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-10.pdf",
abstract = "This article shows that IEEE-754 double-precision
correct rounding of the most common elementary
functions (exp/log, trigonometric and hyperbolic) is
achievable on current processors using only
double-double-extended arithmetic. This allows to
improve by several orders of magnitude the worst case
performance of a correctly-rounded mathematical
library, compared to the current state of the art. This
article builds up on previous work by Lef{\`e}vre and
Muller, who have shown that an intermediate accuracy of
up to 158 bits is required for the evaluation of some
functions. We show that the practical accuracy required
can always be reduced to less than 119 bits, which is
easy to obtain using well-known and well-proven
techniques of double-double-extended arithmetic. As an
example, a prototype implementation of the exponential
function on the Itanium has a worst-case time about
twice that of the standard, highly optimized libm by
Intel, which doesn't offer correct rounding. Such a
small performance penalty should allow correct rounding
of elementary functions to become the standard.",
acknowledgement = ack-nhfb,
keywords = "Correct Rounding; Double-extended Precision;
Elementary Functions; floating-point arithmetic;
IEEE-754",
}
@InProceedings{deDinechin:2004:PCR,
author = "Florent de Dinechin and Catherine Loirat and
Jean-Michel Muller",
title = "A proven correctly rounded logarithm in
double-precision",
crossref = "Frougny:2004:RCR",
pages = "71--85",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_07_dinechin.pdf",
abstract = "This article is a case study in the implementation of
a proven, portable, and efficient correctly rounded
elementary function in double-precision. We describe
the methodology used in the implementation of the
natural logarithm in the crlibm library. The discipline
required to prove a tight bound on the overall
evaluation error allows to design a very efficient
implementation with moderate effort.",
acknowledgement = ack-nhfb,
keywords = "arithmetic; correct rounding; elementary functions;
floating-point; libm; logarithm",
}
@TechReport{deDinechin:2004:TPU,
author = "Florent de Dinechin and Nicolas Gast",
title = "Towards the post-ultimate {\tt libm}",
type = "Research Report",
number = "RR2004-47",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
month = nov,
year = "2004",
bibdate = "Mon Dec 06 11:15:40 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-47.pdf",
abstract = "This article presents advances in the subject of
double-precision correctly rounded elementary functions
since the publication of the libultim mathematical
library developed by Ziv at IBM. This library
demonstrated that the performance overhead of correct
rounding could be made negligible in average. However,
the worst case execution time was up to 1000 times the
average time, and memory consumption was also a
problem. To address these questions, a range of new
techniques, from the more portable to the more
efficient, are presented, and demonstrated on two
typical functions, exponential and arctangent. The main
result of this paper is to show that the worst-case
execution time can be bounded within a factor of 2 to
10 of the average time, with memory consumption
comparable to current libms. This has in turn
implications on the techniques and tradeoffs for
correctly rounded functions. This article also shows
that these techniques make it much easier to prove the
correct rounding property. Thus, this article lifts the
last technical obstacles to a widespread use of (at
least some) correctly rounded double precision
elementary functions.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; Elementary Functions; floating-point
arithmetic; IEEE-754",
}
@Article{deFigueiredo:2004:AAC,
author = "Luiz Henrique de Figueiredo and Jorge Stolfi",
title = "Affine Arithmetic: Concepts and Applications",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "147--158",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 07:00:28 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/10/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "Special Issue: SCAN'2002 International Conference
(Guest Editors: Ren{\'e} Alt and Jean-Luc Lamotte)",
}
@Article{Defour:2004:PSM,
author = "David Defour and Guillaume Hanrot and Vincent
Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol
and Paul Zimmermann",
title = "Proposal for a Standardization of Mathematical
Function Implementation in Floating-Point Arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "367--375",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65D20 (65G50)",
MRnumber = "MR2109920",
bibdate = "Mon Dec 6 07:00:28 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm;
http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf;
http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "Special Issue: SCAN'2002 International Conference
(Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}
@InProceedings{DelRe:2004:TAG,
author = "A. {Del Re} and A. Nannaelli and M. Re",
booktitle = "Proc. Design Auto. Test Europe {(DATE)}, Vol. 1, Feb.
2004",
title = "A Tool for Automatic Generation of {RTL}-level {VHDL}
Description of {RNS FIR} Filters",
publisher = "????",
address = "????",
pages = "??--??",
year = "2004",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Jun 24 18:18:50 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Residue Number System (RNS)",
}
@InCollection{Demmel:2004:AEA,
author = "James Demmel and Plamen Koev",
title = "Accurate and efficient algorithms for floating point
computation",
crossref = "Hilledt:2004:AME",
pages = "73--88",
year = "2004",
MRclass = "65Gxx (65Fxx)",
MRnumber = "MR2296263",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Demmel:2004:FAF,
author = "James Demmel and Yozo Hida",
title = "Fast and Accurate Floating Point Summation with
Application to Computational Geometry",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "101--112",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65B10 (65D18)",
MRnumber = "MR2109897",
bibdate = "Mon Dec 6 07:00:28 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/6/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "accurate floating-point summation",
remark = "Special Issue: SCAN'2002 International Conference
(Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}
@TechReport{Detrey:2004:SOF,
author = "J{\'e}r{\'e}mie Detrey and Florent de Dinechin",
title = "Second Order Function Approximation with a Single
Small Multiplication",
type = "Research Report",
number = "RR2004-13",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 8",
month = mar,
year = "2004",
bibdate = "Mon Dec 06 10:51:35 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-13.ps.gz",
abstract = "This paper presents a new scheme for the hardware
evaluation of elementary functions, based on a
piecewise second order minimax approximation. The
novelty is that this evaluation requires only one small
rectangular multiplication. Therefore the resulting
architecture combines a small table size, thanks to
second-order evaluation, with a short critical path:
Consisting of one table lookup, the rectangular
multiplication, and one addition, the critical path is
shorter than that of a plain first-order evaluation.
Synthesis results for several functions show that this
method outperforms all the previously published methods
in both area and speed for precisions ranging from 12
to 24 bits.",
acknowledgement = ack-nhfb,
keywords = "Computer Arithmetic; Hardware Elementary Functions
Evaluation.",
}
@TechReport{Detrey:2004:TBP,
author = "J{\'e}r{\'e}mie Detrey and Florent de Dinechin",
title = "Table-based polynomials for fast hardware function
evaluation",
type = "Research Report",
number = "November 2004",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 11",
year = "2004",
bibdate = "Mon Dec 06 11:19:55 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-52.ps.gz",
abstract = "Many general table-based methods for the evaluation in
hardware of elementary functions have been published.
The bipartite and multipartite methods implement a
first-order approximation of the function using only
table lookups and additions. Recently, a
single-multiplier second-order method of similar
inspiration has also been published. This paper
presents a general framework extending such methods to
approximations of arbitrary order, using adders, small
multipliers, and very small ad-hoc powering units. We
obtain implementations that are both smaller and faster
than all previously published approaches. This paper
also deals with the FPGA implementation of such
methods. Previous work have consistently shown that the
more complex methods were also faster: The reduction of
the table size meant a reduction of its lookup time,
which compensated for the addition and multiplication
time. A second contribution is therefore to finally
create a tradeoff between space and time among
table-based methods.",
acknowledgement = ack-nhfb,
keywords = "FPGA; Function evaluation; hardware operators;
polynomial approximation; table-based method",
}
@TechReport{Detrey:2004:TUC,
author = "J{\'e}r{\'e}mie Detrey and Florent de Dinechin",
title = "A tool for unbiased comparison between logarithmic and
floating-point arithmetic",
type = "Research Report",
number = "RR2004-31",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 16",
month = jun,
year = "2004",
bibdate = "Mon Dec 06 10:56:33 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-31.ps.gz",
abstract = "This paper describes two concurrent libraries of
parameterized arithmetic operators for manipulating
high-dynamic numbers on FPGAs. One of them uses a
floating-point representation, the other one uses a
logarithmic representation. Along with their direct
interest, those two libraries allow
application-specific comparisons of those two number
representation systems. They are unbiased in the sense
that they tend to reflect the state-of-the-art for both
number arithmetic systems, and are freely available at
\path=http://www.ens-lyon.fr/LIP/Arenaire/=.",
acknowledgement = ack-nhfb,
keywords = "Arithmetic; Floating-Point; FPGA; Hardware Operators;
LNS; Logarithmic Number system; VHDL",
}
@InProceedings{Doss:2004:FBI,
author = "C. C. Doss and R. L. {Riley, Jr.}",
booktitle = "{FCCM 2004}. 12th Annual {IEEE} Symposium on
Field-Programmable Custom Computing Machines, 20--23
April 2004",
title = "{FPGA}-based implementation of a robust {IEEE-754}
exponential unit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "229--238",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 17:14:11 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This work explores the feasibility of implementing a
floating-point exponentiation unit on reconfigurable
computing systems. A table-driven exponentiation unit
was implemented using synthesizable VHDL. The project
included creating pipelined \ldots{}",
}
@Article{Efstathiou:2004:MBM,
author = "C. Efstathiou and H. T. Vergos and D. Nikolos",
title = "Modified {Booth} modulo $ 2^n - 1 $ multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "3",
pages = "370--374",
month = mar,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.1261842",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1261842",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Egner:2004:CTN,
author = "Sebastian Egner and Richard A. Kelsey and Michael
Sperber",
editor = "????",
booktitle = "Fifth Workshop on Scheme and Functional Programming.
{September 22, 2004, Snowbird, Utah, USA}",
title = "Cleaning up the Tower: Numbers in {Scheme}",
publisher = "????",
address = "????",
pages = "13",
day = "22",
month = sep,
year = "2004",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Mon Apr 25 06:55:59 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www-pu.informatik.uni-tuebingen.de/users/sperber/papers/numerical-tower.pdf",
acknowledgement = ack-nhfb,
}
@Article{ElHajji:2004:SIL,
author = "Said {El Hajji} and Nathalie Revol and Paul {Van
Dooren}",
title = "Special Issue on {Linear Algebra and Arithmetic,
Proceedings of the ALA'01 Conference held in Rabat,
Morocco on May 28--31, 2001}",
journal = j-J-COMPUT-APPL-MATH,
volume = "162",
number = "1",
pages = "ix--x",
day = "1",
month = jan,
year = "2004",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:59:56 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042703007428",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@TechReport{Ercegovac:2004:CSRa,
author = "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
title = "Complex Square Root with Operand Prescaling",
type = "Research Report",
number = "RR2004-42",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 12",
month = sep,
year = "2004",
bibdate = "Mon Dec 06 11:07:40 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-42.pdf",
abstract = "We propose a radix-$r$ digit-recurrence algorithm for
complex square-root. The operand is prescaled to allow
the selection of square-root digits by rounding of the
residual. This leads to a simple hardware
implementation. Moreover, the use of digit recurrence
approach allows correct rounding of the result. The
algorithm, compatible with the complex division, and
its design are described at a high-level. We also give
rough comparisons of its latency and cost with respect
to implementation based on standard floating-point
instructions as used in software routines for complex
square root.",
acknowledgement = ack-nhfb,
keywords = "complex square-root; Computer arithmetic; correct
rounding; digit-recurrence algorithm; floating-point
arithmetic; operand prescaling.",
}
@InProceedings{Ercegovac:2004:CSRb,
author = "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
booktitle = "{Proceedings of the 15th IEEE International Conference
on Application-Specific Systems, Architectures and
Processors, 2004}",
title = "Complex square root with operand prescaling",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "52--62",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1109/ASAP.2004.1342458",
ISBN = "0-7695-2226-2",
ISBN-13 = "978-0-7695-2226-5",
ISSN = "1063-6862",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "We propose a radix-r digit-recurrence algorithm for
complex square-root. The operand is prescaled to allow
the selection of square-root digits by rounding of the
residual. This leads to a simple hardware
implementation. Moreover, the use of digit \ldots{}",
}
@Book{Ercegovac:2004:DA,
author = "Milo{\v{s}} Dragutin Ercegovac and Tom{\'a}s Lang",
title = "Digital Arithmetic",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xxv + 709",
year = "2004",
ISBN = "1-55860-798-6",
ISBN-13 = "978-1-55860-798-9",
LCCN = "QA76.9.C62 E72 2004",
bibdate = "Thu Jun 20 10:19:42 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$89.95, UK\pounds 59.95",
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/;
http://www.loc.gov/catdir/description/els031/2002114337.html;
http://www.loc.gov/catdir/toc/els031/2002114337.html",
acknowledgement = ack-nhfb,
subject = "Computer arithmetic",
tableofcontents = "Counter Preface \\
1. Review of Basic Number Representations and
Arithmetic Algorithms \\
2. Two-Operand Addition \\
3. Multi-Operand Addition \\
4. Multiplication \\
5. Division by Digit Recurrence \\
6. Square Root by Digit Recurrence \\
7. Reciprocal, Division, Reciprocal Square Root and
Square Root by Iterative Approximation \\
8. Floating-Point Representation, Algorithms, and
Implementations \\
9. Digit-Serial Arithmetic \\
10. Function Evaluation \\
11. CORDIC Algorithm and Implementations",
}
@InProceedings{Ercegovac:2004:DCD,
author = "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
title = "Design of a complex divider",
crossref = "Luk:2004:ASP",
pages = "51--59",
year = "2004",
bibdate = "Sat Dec 04 10:02:00 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Fousse:2004:AST,
author = "Laurent Fousse and Paul Zimmermann",
title = "Accurate Summation: Towards a Simpler and Formal
Proof",
type = "Technical Report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "11",
day = "6",
month = sep,
year = "2004",
bibdate = "Sun Sep 10 08:08:04 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/rnc5.pdf",
abstract = "This paper provides a simpler proof of the accurate
summation algorithm proposed by Demmel and Hida in [1].
It also gives improved bounds in some cases, and
examples showing that those new bounds are optimal.
This simpler proof will be used to obtain a
computer-generated proof of Demmel--Hida's algorithm,
using a proof assistant like HOL, PVS or Coq.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; floating-point
arithmetic",
}
@InProceedings{Fousse:2004:CPE,
author = "L. Fousse and S. Schmitt",
title = "A comparison of polynomial evaluation schemes",
crossref = "Frougny:2004:RCR",
pages = "86--102",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_08_fousse.pdf",
abstract = "The goal of this paper is to analyze two polynomial
evaluation schemes for multiple precision floating
point arithmetic. Polynomials are used extensively in
numerical computations (Taylor series for mathematical
functions, root finding) but a rigorous bound of the
error on the final result is seldom provided. We
provide such an estimate for the two schemes and find
how to reduce the number of operations required at
run-time by a dynamic error analysis. This work is
useful for floating point polynomial arithmetic.",
acknowledgement = ack-nhfb,
keywords = "bounded error; correct rounding; floating-point
arithmetic; polynomial evaluation",
}
@TechReport{Fousse:2004:FPD,
author = "Laurent Fousse and Paul Zimmermann",
title = "A Formal Proof of {Demmel} and {Hida}'s Accurate
Summation Algorithm",
type = "Technical Report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "12",
month = jan,
year = "2004",
bibdate = "Sun Sep 10 07:58:09 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/tcs.ps.gz",
abstract = "A new proof of the ``accurate summation'' algorithm
proposed by Demmel and Hida is presented. The main part
of that proof has been written in the Coq language and
verified by the Coq proof assistant.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; bounded error;
floating-point arithmetic; formal proof",
}
@InProceedings{Frougny:2004:ICR,
author = "Christiane Frougny",
title = "Introduction: [6th conference on Real Numbers and
Computers]",
crossref = "Frougny:2004:RCR",
pages = "1--4",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_00_intro.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Fuchssteiner:2004:ILN,
author = "Benno Fuchssteiner",
title = "Invited Lecture: New ideas and results for solving
Differential equations symbolically [abstract only]",
crossref = "Frougny:2004:RCR",
pages = "5--5",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_01_fuchssteiner.pdf",
abstract = "The lecture is a report on current research activities
of the MuPAD group in the area of symbolic and numeric
solutions of ODE (ordinary differential
equations).\par
Based on a unification of Lie-point-symmetries and
Lie--B{\"a}cklund-symmetries the results of classical
Lie-symmetry approaches (for example Liouville--Arnold)
to ODE are generalized thus opening new avenues for
using integrability (around initial values) for wider
classes of differential equations.\par
Applications and numerical consequences of these
results will be discussed and plans how to extend
current solution methods, numerical as well as
symbolical, to wider classes of transcendents (i.e.
Painlev{\'e} transcendents) will be presented",
acknowledgement = ack-nhfb,
}
@InProceedings{Gaffar:2004:UBW,
author = "A. A. Gaffar and O. Mencer and W. Luk",
booktitle = "{FCCM 2004}. 12th Annual {IEEE} Symposium on
Field-Programmable Custom Computing Machines, 20--23
April 2004",
title = "Unifying bit-width optimisation for fixed-point and
floating-point designs",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "79--88",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a method that offers a uniform
treatment for bit-width optimisation of both
fixed-point and floating-point designs. Our work
utilises automatic differentiation to compute the
sensitivities of outputs to the bit-width of the
various operands in the design. \ldots{}",
acknowledgement = ack-nhfb,
}
@InProceedings{Gebali:2004:EAF,
author = "Fayez Gebali and Mohamed Watheq El-Kharashi",
title = "{ERL}: an algorithm for fast evaluation of
exponential, reciprocal, and logarithmic functions",
crossref = "Wahdan:2004:IHE",
pages = "269--272",
year = "2004",
bibdate = "Sat Jul 16 18:04:58 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A fast algorithm (ERL) is proposed for evaluating
Exponential, Reciprocal, and Logarithmic functions. The
algorithm requires two to three iterations to complete
using simple operations such as multiply, accumulate,
and table lookup. The algorithm is independent of the
number format used by the machine. Thus it can be
implemented using the IEEE 754 floating-point standard
or any other special format used by special-purpose
processors. The dynamic range of the algorithm is
limited only by the dynamic range of the machine on
which it is implemented Numerical simulations are
performed which verifies the speed and accuracy of the
algorithm.",
acknowledgement = ack-nhfb,
}
@Article{Gemignani:2004:REA,
author = "Luca Gemignani and Grazia Lotti",
title = "Rounding Error Analysis in Solving {$M$}-Matrix Linear
Systems of Block {Hessenberg} Form",
journal = j-NUMER-ALGORITHMS,
volume = "36",
number = "2",
pages = "157--168",
month = jun,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 07:00:32 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/54/A/4/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Gerwig:2004:IEZ,
author = "G. Gerwig and H. Wetter and E. M. Schwarz and J. Haess
and C. A. Krygowski and B. M. Fleischer and M.
Kroener",
title = "The {IBM eServer z990} floating-point unit",
journal = j-IBM-JRD,
volume = "48",
number = "3/4",
pages = "311--322",
month = "????",
year = "2004",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.483.0311",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Tue Sep 28 06:50:40 MDT 2004",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/483/gerwig.html;
http://www.research.ibm.com/journal/rd/483/gerwig.pdf",
abstract = "The floating-point unit (FPU) of the IBM z990 eServer
is the first one in an IBM mainframe with a fused
multiply-add dataflow. It also represents the first
time that an SRT divide algorithm (named after Sweeney,
Robertson, and Tocher, who independently proposed the
algorithm) was used in an IBM mainframe. The FPU
supports dual architectures: the zSeries hexadecimal
floating-point architecture and the IEEE 754 binary
floating-point architecture. Six floating-point formats
including short, long, and extended operands are
supported in hardware. The throughput of this FPU is
one multiply-add operation per cycle. The instructions
are executed in five pipeline steps, and there are
multiple provisions to avoid stalls in case of data
dependencies. It is able to handle denormalized input
operands and denormalized results without a stall
(except for architectural program exceptions). It has a
new extended-precision divide and square-root dataflow.
This dataflow uses a radix-4 SRT algorithm (radix-2 for
square root) and is able to handle divides and
square-root operations in multiple floating-point and
fixed-point formats. For fixed-point divisions, a new
mechanism improves the performance by using an
algorithm with which the number of divide iterations
depends on the effective number of quotient bits.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "decimal floating-point arithmetic",
ordernumber = "G322-0240",
}
@Article{Geyer:2004:DFD,
author = "Christina Lynn Geyer and Patricia Pepple Williamson",
title = "Detecting fraud in data sets using {Benford's Law}",
journal = j-COMMUN-STAT-SIMUL-COMPUT,
volume = "B33",
number = "1",
pages = "229--246",
month = "????",
year = "2004",
CODEN = "CSSCDB",
DOI = "https://doi.org/10.1081/SAC-120028442",
ISSN = "0361-0918",
ISSN-L = "0361-0918",
MRclass = "62-07",
MRnumber = "2044866",
bibdate = "Sat Nov 12 09:13:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Comm. Statist. Simulation Comput.",
fjournal = "Communications in Statistics: Simulation and
Computation",
journal-URL = "http://www.tandfonline.com/loi/lssp20",
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@InProceedings{Gok:2004:DSP,
author = "M. Gok and M. J. Schulte and S. Krithivasan",
editor = "????",
booktitle = "Proceedings of the Workshop on Application Specific
Processors, Stockholm, Sweden, August, 2004",
title = "Designs for Subword-Parallel Multiplications and Dot
Product Operations",
publisher = "????",
address = "????",
pages = "27--31",
year = "2004",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 04 20:51:24 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Govindu:2004:AHP,
author = "Gokul Govindu and L. Zhuo and S. Choi and V.
Prasanna",
booktitle = "Proceedings. 18th International Parallel and
Distributed Processing Symposium, 26--30 April 2004",
title = "Analysis of high-performance floating-point arithmetic
on {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "149--149",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Govindu:2004:HPE,
author = "G. Govindu and S. Choi and V. Prasanna and V. Daga and
S. Gangadharpalli and V. Sridhar",
booktitle = "Proceedings. 18th International Parallel and
Distributed Processing Symposium, 26--30 April 2004",
title = "A high-performance and energy-efficient architecture
for floating-point based {LU} decomposition on
{FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "149--149",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Graillat:2004:CRC,
author = "Stef Graillat and Philippe Langlois",
title = "A comparison of real and complex pseudozero sets for
polynomials with real coefficients",
crossref = "Frougny:2004:RCR",
pages = "103--112",
year = "2004",
MRclass = "65F35 68W30",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_09_graillat.pdf",
abstract = "Pseudozeros are useful to describe how perturbations
of polynomial coefficients affect its zeros. We compare
two types of pseudozero sets: the complex and the real
pseudozero sets. These sets differ with respect to the
type of perturbations. The first set --- complex
perturbations of a complex polynomial --- has been
intensively studied while the second one --- real
perturbations of a real polynomial --- seems to have
received no attention. We present a computable formula
for the real pseudozero set and a comparison between
these two pseudozero sets. We conclude that the complex
pseudozero sets have to be preferred except when the
perturbed real polynomials admit non-real zeros.",
acknowledgement = ack-nhfb,
keywords = "perturbation; polynomial root; pseudozero set;
uncertainty",
}
@Manual{Granlund:2004:GMG,
author = "Torbj{\"o}rn Granlund and Gunnar Sj{\"o}din and Hans
Riesel and Richard Stallman and Brian Beuning and Doug
Lea and John Amanatides and Paul Zimmermann and Ken
Weber and Per Bothner and Joachim Hollman and Bennet
Yee and Andreas Schwab and Robert Harley and David Seal
and Robert Harley and Torsten Ekedahl and Paul
Zimmermann and Linus Nordberg and Kent Boortz and Kevin
Ryde and Steve Root and Gerardo Ballabio and Hans
Thorsen",
title = "{GNU MP}: The {GNU} Multiple Precision Arithmetic
Library",
organization = pub-FSF,
address = pub-FSF:adr,
edition = "Version 4.1.4",
pages = "iv + 127",
day = "21",
month = sep,
year = "2004",
bibdate = "Wed Nov 24 08:41:48 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "GNUP MP development began in 1991. Earler versions are
1.0 (8-Aug-1991), 2.0 (24-Apr-1996), 3.0 (17-Apr-2000),
and 4.0 (1-Dec-2001).",
URL = "ftp://ftp.gnu.org/gnu/gmp/gmp-4.1.4.tar.gz;
http://www.swox.se/gmp/",
acknowledgement = ack-nhfb,
}
@InProceedings{Groza:2004:DIS,
author = "V. Groza and M. Debski and D. Ionescu",
booktitle = "{IMTC 04}. Proceedings of the 21st {IEEE}
Instrumentation and Measurement Technology Conference,
18--20 May 2004",
title = "Design and implementation of a self-calibrating
floating-point analog-to-digital converter",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "707--710",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point analog-to-digital converters (FP-ADC)
are characterized by a high relative precision, but, in
some applications, their absolute precision had to be
traded off for speed. This paper presents the
architecture, design and implementation of a
self-calibrating differential predictive floating point
analog-to-digital converter which is characterized by
high conversion rates while its precision is kept at
high values by additional hardware that periodically
performs calibration cycles.\ldots{}",
acknowledgement = ack-nhfb,
}
@InProceedings{Hack:2004:IPR,
author = "Michel Hack",
title = "On Intermediate Precision Required for
Correctly-Rounding Decimal-to-Binary Floating-Point
Conversion",
crossref = "Frougny:2004:RCR",
pages = "113--134",
year = "2004",
bibdate = "Thu Apr 28 05:55:01 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_10_hack.pdf",
abstract = "The algorithms developed ten years ago in preparation
for IBM's support of IEEE Floating-Point on its
mainframe S/390 processors use an overly conservative
intermediate precision to guarantee correctly-rounded
results across the entire exponent range. Here we study
the minimal requirement for both bounded and unbounded
precision on the decimal side (converting to machine
precision on the binary side). An interesting new
theorem on Continued Fraction expansions is offered, as
well as an open problem on the growth of partial
quotients for ratios of powers of two and five.",
acknowledgement = ack-nhfb,
keywords = "base conversion; Continued Fractions; correct
rounding; decimal floating-point arithmetic;
Floating-Point conversion",
remark = "Improvement on \cite{Abbott:1999:ASS}.",
}
@Article{Hanrot:2004:MPA,
author = "Guillaume Hanrot and Michel Quercia and Paul
Zimmermann",
title = "The Middle Product Algorithm {I}. Speeding up the
division and square root of power series",
journal = j-APPL-ALGEBRA-ENG-COMMUN-COMPUT,
volume = "14",
number = "6",
pages = "415--438",
month = mar,
year = "2004",
CODEN = "AAECEW",
DOI = "https://doi.org/10.1007/s00200-003-0144-2",
ISSN = "0938-1279 (print), 1432-0622 (electronic)",
ISSN-L = "0938-1279",
bibdate = "Sun Sep 10 08:12:01 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://springerlink.metapress.com/content/57p2fta5k71085wm/fulltext.pdf",
abstract = "We present new algorithms for the inverse, division,
and square root of power series. The key trick is a new
algorithm --- MiddleProduct or, for short, MP ---
computing the $n$ middle coefficients of a $ (2 n - 1)
\times n $ full product in the same number of
multiplications as a full $ n \times n $ product. This
improves previous work of Brent, Mulders, Karp and
Markstein, Burnikel and Ziegler. These results apply
both to series and polynomials.",
acknowledgement = ack-nhfb,
fjournal = "Applicable algebra in engineering, communication and
computing",
}
@TechReport{Hanrot:2004:NIR,
author = "Guillaume Hanrot and Paul Zimmermann",
title = "{Newton} Iteration Revisited",
type = "Technical Report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "2",
month = mar,
year = "2004",
bibdate = "Sun Sep 10 07:46:53 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Bernstein:2004:RRH}.",
URL = "http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz",
abstract = "On March 10, 2004, Dan Bernstein announced a revised
draft of his paper {\em Removing redundancy in
high-precision Newton iteration}
(\path=http://cr.yp.to/fastnewton.html=) with
algorithms that compute a reciprocal of order $n$ over
$ C[[x]] 1.5 + o(1) $ times longer than a product; a
quotient or logarithm $ 2.16666 \ldots {} + o(1) $
times longer; a square root $ 1.83333 \ldots {} + o(1)
$ times longer; an exponential $ 2.83333 \ldots {} +
o(1) $ times longer. We give better algorithms.",
acknowledgement = ack-nhfb,
remark = "Note added on March 24, 2004: the $ 1.5 + o(1) $
reciprocal algorithm was already published by
Sch{\"o}nhage ({\tm Information Processing Letters} 74,
2000, pp. 41--46).",
}
@Article{Herbst:2004:RWS,
author = "Klaus-Dieter Herbst",
title = "{Rezension: \booktitle{Wilhelm Schickard ---
Briefwechsel} von Friedrich Seck}",
journal = j-BER-WISSENSCHAFTGESCH,
volume = "27",
number = "4",
pages = "315--317",
month = dec,
year = "2004",
CODEN = "BEWID8",
DOI = "https://doi.org/10.1002/bewi.200490037",
ISSN = "0170-6233 (print), 1522-2365 (electronic)",
ISSN-L = "0170-6233",
bibdate = "Sun Aug 4 10:12:45 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/berwissenschaftgesch.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "{Ber. Wissenschaftgesch.}",
fjournal = "{Berichte zur Wissenschaftsgeschichte}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2365/",
language = "German",
onlinedate = "3 Jan 2005",
}
@Article{Hiasat:2004:SFR,
author = "Ahmad A. Hiasat",
title = "A Suggestion for a Fast Residue Multiplier for a
Family of Moduli of the Form $ (2 n - (2 p \pm 1)) $",
journal = j-COMP-J,
volume = "47",
number = "1",
pages = "93--??",
month = jan,
year = "2004",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Feb 26 06:22:27 2004",
bibsource = "http://www3.oup.co.uk/computer_journal/hdb/Volume_47/Issue_01/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_47/Issue_01/470093.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_47/Issue_01/pdf/470093.pdf",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Hormigo:2004:CPV,
author = "Javier Hormigo and Julio Villalba and Emilio L.
Zapata",
title = "{CORDIC} Processor for Variable-Precision Interval
Arithmetic",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "37",
number = "1",
pages = "21--39",
month = may,
year = "2004",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1023/B:VLSI.0000017001.88149.f4",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Thu Aug 07 19:16:20 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we present a specific CORDIC processor
for variable-precision coordinates. This system allows
us to specify the precision to perform the CORDIC
operation, and control the accuracy of the result, in
such a way that re-computation of inaccurate results
can be carried out with higher precision. It permits a
reliable and accurate evaluation of a wide range of
elementary functions. The specific architecture
designed greatly improves the computational time of
previous solutions based on classic polynomial
approximation. For controlling error in numerical
computation (where intervals are normally narrow) the
proposed design performs an interval operation in a
time close to that of a point operation.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@Manual{IBM:2004:ZAP,
author = "{IBM}",
title = "{z/Architecture} Principles of Operation",
organization = "IBM Corporation",
address = "Department 55JA Mail Station P384, 2455 South Road
Poughkeepsie, NY, 12601-5400, USA",
edition = "Fourth",
pages = "xxvi + 1124",
month = may,
year = "2004",
bibdate = "Sat Mar 11 17:19:27 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IBM order number SA22-7832-03.",
URL = "http://publibz.boulder.ibm.com/cgi-bin/bookmgr_OS390/download/DZ9ZR003.pdf",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "This manual continues a tradition of that began with
the publication in 1964 of the IBM System/360
Principles of Operation, long considered a classic and
a landmark description of the oldest computer
architecture in continuous use. Chapter 9 provides an
overview of the floating-point support, Chapter 18
describes the hexadecimal floating-point instructions,
and Chapter 19 the binary (IEEE 754) floating-point
instructions. Both hexadecimal and binary sets support
32-bit, 64-bit, and 128-bit formats, all in hardware on
the IBM G5 processors. However, the
recently-implemented decimal floating-point arithmetic
is not described in this edition.",
}
@Article{Jeong:2004:CEP,
author = "Jong-Chul Jeong and Woo-Chan Park and Woong Jeong and
Tack-Don Han and Moon-Key Lee",
title = "A cost-effective pipelined divider with a small lookup
table",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "4",
pages = "489--495",
month = apr,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.1268407",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:35 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1268407",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Kahan:2004:CFP,
author = "W. Kahan",
title = "On the Cost of Floating-Point Computation Without
Extra-Precise Arithmetic",
howpublished = "World-Wide Web document",
pages = "21",
day = "20",
month = nov,
year = "2004",
bibdate = "Mon Apr 25 17:44:03 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boldo:2009:KAC} for a proof of this
algorithm for accurate computation of the discriminant
needed for the solution of quadratic equations.",
URL = "http://www.cs.berkeley.edu/~wkahan/Qdrtcs.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:2004:HFM,
author = "W. Kahan",
title = "How Futile are Mindless Assessments of Roundoff in
Floating-Point Computation?",
howpublished = "World-Wide Web document",
pages = "37",
day = "1",
month = nov,
year = "2004",
bibdate = "Mon Apr 25 17:41:28 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/Mind1ess.pdf;
http://www.cs.berkeley.edu/~wkahan/Mindless.pdf",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; rounding errors",
}
@Misc{Kahan:2004:SSR,
author = "W. Kahan",
title = "$ 128 $ Squares of $ 128 $ Square Roots",
howpublished = "World-Wide Web document",
pages = "3",
day = "29",
month = jan,
year = "2004",
bibdate = "Mon Apr 25 18:25:57 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Lecture notes for Math 128.",
URL = "http://www.cs.berkeley.edu/~wkahan/Math128/SqSqrts.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Kahn:2004:CEA,
author = "Ken Kahn",
title = "The child-engineering of arithmetic in {ToonTalk}",
crossref = "Druin:2004:IDC",
pages = "141--142",
year = "2004",
DOI = "https://doi.org/10.1145/1017833.1017860",
bibdate = "Fri Aug 08 09:04:34 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Providing a child-appropriate interface to an
arithmetic package with large numbers and exact
fractions is surprisingly challenging. We discuss
solutions to problems ranging from how to present
fractions such as 1/3 to how to deal with numbers with
tens of thousands of digits. As with other objects in
ToonTalk, we strive to make the enhanced numbers work
in a concrete and playful manner.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kenney:2004:HFD,
author = "R. D. Kenney and M. J. Schulte and M. A. Erle",
title = "A high-frequency decimal multiplier",
crossref = "IEEE:2004:IICa",
pages = "26--29",
year = "2004",
bibdate = "Fri Mar 25 05:54:22 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-05.pdf",
abstract = "Decimal arithmetic is regaining popularity in the
computing community due to the growing importance of
commercial, financial, and Internet-based applications,
which process decimal data. This paper presents an
iterative decimal multiplier, which is operates at high
clock frequencies and scales well to large operand
sizes. The multiplier uses a new decimal representation
for intermediate products, which allows for a very fast
two- stage iterative multiplier design. Decimal
multipliers, which are synthesized using a 0.11 micron
CMOS standard cell library, operate at clock
frequencies close to 2 GHz. The latency of the proposed
design to multiply two n-digit BCD operands is $ (n +
8) $ cycles with a new multiplication able to begin
every $ (n + 1) $ cycles.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Kenney:2004:MDA,
author = "Robert D. Kenney and Michael J. Schulte and Mark A.
Erle",
title = "Multioperand Decimal Addition",
crossref = "Smailagic:2004:ETV",
pages = "251--253",
year = "2004",
bibdate = "Wed May 04 07:51:51 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-07.pdf",
abstract = "This paper introduces and analyzes four techniques for
performing fast decimal addition on multiple binary
coded decimal (BCD) operands. Three of the techniques
speculate BCD correction values and use chaining to
correct intermediate results. The first speculates over
one addition. The second speculates over two additions.
The third employs multiple instances of the second
technique in parallel and then merges the results. The
fourth technique uses a binary carry-save adder tree
and produces a binary sum. Combinational logic is then
used to correct the sum and determine the carry into
the next digit. Multioperand adder designs are
constructed and synthesized for four to sixteen input
operands. Analyses are performed on the synthesis
results and the merits of each technique are discussed.
Finally, these techniques are compared to previous
attempts made at speeding up decimal addition.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
pagecount = "10",
}
@Article{Kim:2004:AAA,
author = "Hyun-Sung Kim and Kee-Young Yoo",
title = "{AOP} arithmetic architectures over {$ \mathrm
{GF}(2^m) $}",
journal = j-APPL-MATH-COMP,
volume = "158",
number = "1",
pages = "7--18",
day = "25",
month = oct,
year = "2004",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Jul 4 09:15:36 MDT 2005",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Ko:2004:CCF,
author = "Sangho Ko and Robert R. Bitmead",
title = "Covariance calculation for floating-point state-space
realizations",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "52",
number = "12",
pages = "3370--3377",
month = dec,
year = "2004",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
MRclass = "93B15 (94A12)",
MRnumber = "MR2107918 (2005h:93033)",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper provides a new method for analyzing
floating-point roundoff error for digital filters by
using ``finite signal-to-noise'' models whose noise
sources have variances proportional to the variance or
power of the corrupted signals.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
summary = "This paper provides a new method for analyzing
floating-point roundoff error for digital filters by
using ``finite signal-to-noise'' models whose noise
sources have variances proportional to the variance or
power of the corrupted signals. With this model
\ldots{}",
}
@InProceedings{Kobayashi:2004:SHC,
author = "S. Kobayashi and I. Kozuka and W. H. Tang and D.
Landmann",
title = "A software\slash hardware codesigned hands free system
on a ``resizable'' block-floating-point {DSP}",
crossref = "IEEE:2004:IICc",
volume = "5",
pages = "V-149--V-152",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Kornerup:2004:RCN,
author = "Peter Kornerup and Jean-Michel Muller",
title = "{RN}-coding of numbers: definition and some
properties",
type = "Research Report",
number = "RR2004-43",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 9",
month = sep,
year = "2004",
bibdate = "Mon Dec 06 11:09:46 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-43.pdf",
abstract = "We define RN-codings as radix-$ \beta $ signed
representations of numbers for which rounding to the
nearest is always identical to truncation. After giving
characterizations of such representations, we
investigate some of their properties, and we suggest
algorithms for conversion to and from these codings.",
acknowledgement = ack-nhfb,
keywords = "Computer arithmetic; number systems",
}
@InProceedings{Krithivasan:2004:SPM,
author = "S. Krithivasan and M. J. Schulte and J. Glossner",
title = "A Subword-Parallel Multiplication and Sum-of-Squares
Unit",
crossref = "Smailagic:2004:ETV",
pages = "273--274",
year = "2004",
bibdate = "Sun Mar 04 20:59:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-03.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Krueger:2004:DLI,
author = "S. D. Krueger and P.-M. Seidel",
booktitle = "{FCCM 2004}. 12th Annual {IEEE} Symposium on
Field-Programmable Custom Computing Machines, 20--23
April 2004",
title = "Design of an on-line {IEEE} floating-point addition
unit for {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "239--246",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present the design of an on-line IEEE
floating-point (FP) adder. In on-line arithmetic a
result is computed as a digit serial output stream from
digit serial input streams. The result digits begin to
be produced a short delay after the first input arrive
and before all the input digits have been received.
\ldots{}",
acknowledgement = ack-nhfb,
}
@InProceedings{Kucukkabak:2004:DIR,
author = "U. Kucukkabak and A. Akkas",
editor = "Henry Selvaraj",
booktitle = "{DSD 2004: Euromicro Symposium on Digital System
Design: Architectures, Methods and Tools. Rennes,
France, August 31--September 2, 2004}",
title = "Design and implementation of reciprocal unit using
table look-up and {Newton--Raphson} iteration",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xiii + 631",
pages = "249--253",
year = "2004",
DOI = "https://doi.org/10.1109/dsd.2004.1333284",
ISBN = "0-7695-2203-3",
ISBN-13 = "978-0-7695-2203-6",
LCCN = "QA76.9.S88 E97 2004; TK7868.D5 E93 2004",
bibdate = "Thu Apr 10 14:57:55 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kwon:2004:SMI,
author = "Taek-Jun Kwon and Joong-Seok Moon and J. Sondeen and
J. Draper",
booktitle = "{ISCAS '04}. Proceedings of the 2004 International
Symposium on Circuits and Systems, 23--26 May 2004",
title = "A 0.18 /spl $ \mu $ /m implementation of a
floating-point unit for a processing-in-memory system",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-453--II-456",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Lang:2004:FPM,
author = "T. Lang and J. D. Bruguera",
title = "Floating-point multiply-add-fused with reduced
latency",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "8",
pages = "988--1003",
month = aug,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.44",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1306992;
http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j06.ps",
abstract = "We propose architecture for the computation of the
double-precision floating-point multiply-add-fused
(MAP) operation $ A + (B \times C) $. This architecture
is based on the combined addition and rounding (using a
dual adder) and in the anticipation of the
normalization step before the addition. Because the
normalization is performed before the addition, it is
not possible to overlap the leading-zero-anticipator
with the adder. Consequently, to avoid the increase in
delay, we modify the design of the LZA so that the
leading bits of its output are produced first and can
be used to begin the normalization. Moreover, parts of
the addition are also anticipated. We have estimated
the delay of the resulting architecture considering the
load introduced by long connections, and we estimate a
delay reduction of between 15 percent and 20 percent,
with respect to previous implementations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "We propose architecture for the computation of the
double-precision floating-point multiply-add-fused
(MAP) operation A + (B $\times$ C). This architecture
is based on the combined addition and rounding (using a
dual adder) and in the anticipation \ldots{}",
}
@TechReport{Lefevre:2004:AFF,
author = "Vincent Lef{\`e}vre and Paul Zimmermann",
title = "Arithm{\'e}tique flottante. ({French})
[{Floating-point} arithmetic]",
type = "Technical Report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "60",
month = feb,
year = "2004",
bibdate = "Sun Sep 10 08:03:11 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5105.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-5105.ps.gz",
abstract = "This document releases lecture notes given during 2003
at University Henri Poincar{\'e} (Nancy, France). These
notes are mainly based on the book {\em Elementary
Functions. Algorithms and Implementation\/} by
Jean-Michel Muller.",
acknowledgement = ack-nhfb,
keywords = "arbitrary precision; correct rounding; fixed
precision; floating-point number; IEEE 754 standard",
language = "French",
}
@InProceedings{Lefevre:2004:GMP,
author = "Vincent Lef{\`e}vre",
title = "The Generic Multiple-Precision Floating-Point Addition
With Exact Rounding (as in the {MPFR} Library)",
crossref = "Frougny:2004:RCR",
pages = "135--145",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_11_lefevre.pdf",
abstract = "We study the multiple-precision addition of two
positive floating-point numbers in base 2, with exact
rounding, as specified in the MPFR library, i.e. where
each number has its own precision. We show how the best
possible complexity (up to a constant factor that
depends on the implementation) can be obtain.",
acknowledgement = ack-nhfb,
keywords = "addition; exact rounding; floating point; multiple
precision",
}
@InProceedings{Leyva:2004:GHS,
author = "G. Leyva and G. Caffarena and C. Carreras and O.
Nieto-Taladriz",
booktitle = "{FCCM 2004}. 12th Annual {IEEE} Symposium on
Field-Programmable Custom Computing Machines, 20--23
April 2004",
title = "A generator of high-speed floating-point modules",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "306--307",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Hardware implementation of arithmetic modules is a
time-consuming task. Consequently, there is a demand
for CAD tools that help the designer in reducing design
times. This paper presents a floating-point module
generator that allows user specification of the
mantissa, exponent bit-width and clock period.
\ldots{}",
acknowledgement = ack-nhfb,
}
@InProceedings{Lin:2004:SFP,
author = "Hung-Yueh Lin and Tay-Jyi Lin and Chie-Min Chao and
Yen-Chin Liao and Chih-Wei Liu and Chein-Wei Jen",
booktitle = "{ISCAS '04}. Proceedings of the 2004 International
Symposium on Circuits and Systems, 23--26 May 2004",
title = "Static floating-point unit with implicit exponent
tracking for embedded {DSP}",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-821--II-824",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Lu:2004:ALC,
author = "Mi Lu",
title = "Arithmetic and logic in computer systems",
volume = "169",
publisher = pub-WILEY-INTERSCIENCE,
address = pub-WILEY-INTERSCIENCE:adr,
pages = "xxi + 246",
year = "2004",
ISBN = "0-471-46945-9 (cloth)",
ISBN-13 = "978-0-471-46945-2 (cloth)",
LCCN = "QA76.9.C62 L8 2004",
bibdate = "Thu Nov 18 08:57:10 MST 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "iley Series in Microwave and Optical Engineering",
URL = "http://www.loc.gov/catdir/bios/wiley046/2003062036.html;
http://www.loc.gov/catdir/description/wiley041/2003062036.html;
http://www.loc.gov/catdir/toc/wiley041/2003062036.html",
acknowledgement = ack-nhfb,
subject = "Computer arithmetic; Logic programming",
tableofcontents = "Addition and Subtraction 29 \\
High-Speed Adder 53 \\
Sequential Multiplication 77 \\
Parallel Multiplication 103 \\
Sequential Division 135 \\
Fast Array Dividers 167 \\
Floating Point Operations 183 \\
Residue Number Operations 199 \\
Operations through Logarithms 221 \\
Signed-Digit Number Operations 235 \\
Index 245",
}
@InProceedings{Lutz:2004:NFP,
author = "D. R. Lutz and C. N. Hinds",
booktitle = "Conference Record of the Thirty-Eighth Asilomar
Conference on Signals, Systems and Computers, Nov.
7--10, 2004",
title = "A new floating-point architecture for wireless {$3$D}
graphics",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1879--1883",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Madhukumar:2004:EAR,
author = "A. S. Madhukumar and F. Chin",
title = "Enhanced architecture for residue number system-based
{CDMA} for high-rate data transmission",
journal = j-IEEE-TRANS-WIREL-COMMUN,
volume = "3",
number = "5",
pages = "1363--1368",
month = sep,
year = "2004",
CODEN = "ITWCAX",
DOI = "https://doi.org/10.1109/TWC.2004.833509",
ISSN = "1536-1276 (print), 1558-2248 (electronic)",
ISSN-L = "1536-1276",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=29589",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Wirel. Commun.",
fjournal = "IEEE Transactions on Wireless Communications",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693",
keywords = "residue arithmetic; residue number system",
summary = "This paper presents an advanced architecture for
residue number system (RNS)-based code-division
multiple-access (CDMA) system for high-rate data
transmission by combining RNS representation, phase
shift keying/quadrature amplitude modulation (PSK/
\ldots{})",
}
@InProceedings{Marcus:2004:FSS,
author = "G. Marcus and P. Hinojosa and A. Avila and J.
Nolazco-Flores",
booktitle = "Proceedings of the Fifth {IEEE} International Caracas
Conference on Devices, Circuits and Systems, November
3--5, 2004",
title = "A fully synthesizable single-precision, floating-point
adder\slash subtractor and multiplier in {VHDL} for
general and educational use",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "319--323",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Markov:2004:SAA,
author = "Svetoslav Markov and Rene Alt",
title = "Stochastic arithmetic: Addition and multiplication by
scalars",
journal = j-APPL-NUM-MATH,
volume = "50",
number = "3--4",
pages = "475--488",
month = sep,
year = "2004",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Sat May 14 10:50:47 MDT 2005",
bibsource = "http://www.sciencedirect.com/science/journal/01689274;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Markov:2004:SAS,
author = "Svetoslav Markov and Rene Alt and Jean-Luc Lamotte",
title = "Stochastic Arithmetic: $s$-spaces and Some
Applications",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "275--284",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 07:00:28 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/22/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "Special Issue: SCAN'2002 International Conference
(Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}
@InProceedings{Markstein:2004:SDS,
author = "Peter Markstein",
title = "Software Division and Square Root Using
{Goldschmidt}'s Algorithms",
crossref = "Frougny:2004:RCR",
pages = "146--157",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_12_markstein.pdf",
abstract = "Goldschmidt's Algorithms for division and square root
are often characterized as being useful for hardware
implementation, and lacking self-correction. A
reexamination of these algorithms show that there are
good software counterparts that retain the speed
advantage of Goldschmidt's Algorithm over the
Newton--Raphson iteration. A final step is needed,
however, to get the last bit rounded correctly.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; division; floating-point arithmetic;
Goldschmidt; square root",
}
@Article{McIvor:2004:IMM,
author = "C. McIvor and M. McLoone and J. V. McCanny",
title = "Improved {Montgomery} modular inverse algorithm",
journal = j-ELECT-LETTERS,
volume = "40",
number = "18",
pages = "1110--1112",
day = "2",
month = sep,
year = "2004",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:20045610",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Wed Dec 28 18:13:01 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1335002",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@Article{McKenzie:2004:ACP,
author = "Pierre McKenzie and Heribert Vollmer and Klaus W.
Wagner",
title = "Arithmetic Circuits and Polynomial Replacement
Systems",
journal = j-SIAM-J-COMPUT,
volume = "33",
number = "6",
pages = "1513--1531",
month = dec,
year = "2004",
CODEN = "SMJCAT",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Sat Apr 16 10:19:28 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/33/6;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/39207",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{McLaughlin:2004:NFM,
author = "Philip B. {McLaughlin, Jr.}",
title = "New frameworks for {Montgomery}'s modular
multiplication method",
journal = j-MATH-COMPUT,
volume = "73",
number = "246",
pages = "899--906",
month = apr,
year = "2004",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Aug 11 08:23:05 MDT 2004",
bibsource = "http://www.ams.org/mcom/2004-73-246;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/home.html;
http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/S0025-5718-03-01543-6.dvi;
http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/S0025-5718-03-01543-6.pdf;
http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/S0025-5718-03-01543-6.ps;
http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/S0025-5718-03-01543-6.tex",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Mitra:2004:NAB,
author = "A. Mitra and M. Chakraborty",
title = "The {NLMS} algorithm in block floating-point format",
journal = j-IEEE-SIGNAL-PROCESS-LETT,
volume = "11",
number = "3",
pages = "301--304",
month = mar,
year = "2004",
CODEN = "ISPLEM",
ISSN = "1070-9908 (print), 1558-2361 (electronic)",
ISSN-L = "1070-9908",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a novel scheme to implement the normalized
least mean square algorithm in block floating-point
(BFP) format, which permits processing of data over a
wide dynamic range, at a cost significantly less than
that of a floating-point processor.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Signal Processing Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
summary = "We present a novel scheme to implement the normalized
least mean square algorithm in block floating-point
(BFP) format, which permits processing of data over a
wide dynamic range, at a cost significantly less than
that of a floating-point processor. \ldots{}",
}
@Manual{MPFRTeam:2004:MMP,
author = "{The MPFR Team}",
title = "{MPFR}: {The} {Multiple Precision Floating-Point
Reliable Library}: Edition 2.1.0: {November 2004}",
pages = "ii + 35",
year = "2004",
bibdate = "Thu Dec 15 18:49:26 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.mpfr.org/mpfr-current/mpfr.pdf",
acknowledgement = ack-nhfb,
}
@Article{Muller:2004:CSR,
author = "Siguna M{\"u}ller",
title = "On the Computation of Square Roots in Finite Fields",
journal = j-DESIGNS-CODES-CRYPTOGR,
volume = "31",
number = "3",
pages = "301--312",
month = mar,
year = "2004",
CODEN = "DCCREC",
ISSN = "0925-1022 (print), 1573-7586 (electronic)",
ISSN-L = "0925-1022",
bibdate = "Tue Aug 3 16:38:18 MDT 2004",
bibsource = "http://www.wkap.nl/jrnltoc.htm/0925-1022;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp008.kluweronline.com/IPS/content/ext/x/J/4630/I/61/A/8/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Designs, codes, and cryptography",
journal-URL = "http://link.springer.com/journal/10623",
}
@TechReport{Muller:2004:DCS,
author = "Jean-Michel Muller and A. Tisserand and B. Dupont de
Dinechin and C. Monat",
title = "Division by Constant for the {ST100} {DSP}
Microprocessor",
type = "Research Report",
number = "RR2004-45",
institution = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "69364 Lyon Cedex 07, France",
pages = "2 + 10",
month = oct,
year = "2004",
bibdate = "Mon Dec 06 11:14:04 2004",
bibsource = "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-45.ps.gz",
abstract = "Algorithms for Euclidean (i.e., integer) division by a
constant operation are presented. They allow fast
computation for some values of the divisor (known at
compile time) or also when both quotient and modulus
are required. These algorithms are based on the
multiply-accumulate instruction and the 40-bit
arithmetic available in many DSPs. The results are
demonstrated on the ST100 DSP from STMicroelectronics
in the case of standard speech coding applications.",
acknowledgement = ack-nhfb,
keywords = "Compiler; Computer Arithmetic; Division by Constant;
DSP; Euclidean Division; Software Division",
}
@Article{Nguyen:2004:LDL,
author = "P. Nguyen and D. Stehle",
title = "Low-dimensional lattice basis reduction revisited
(extended abstract)",
journal = j-LECT-NOTES-COMP-SCI,
volume = "3076",
pages = "338--357",
year = "2004",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/b98210",
ISBN = "3-540-22156-5",
ISBN-13 = "978-3-540-22156-2",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Jun 24 14:49:07 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Nievergelt:2004:AAP,
author = "Yves Nievergelt",
title = "Analysis and applications of {Priest}'s distillation",
journal = j-TOMS,
volume = "30",
number = "4",
pages = "402--433",
month = dec,
year = "2004",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1039813.1039815",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Apr 12 06:34:31 MDT 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Correcting an infinite loop in Douglas M. Priest's
renormalization algorithm, the theory proved here
supports streamlined algorithms to resolve the
tablemaker's dilemma for the floating-point computation
of real and complex sums and dot-products, properly
rounded to the ultimate digit. Applications include
computations of areas, volumes, and intersections.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accurate floating-point summation; correct rounding;
floating-point arithmetic",
}
@Article{Ogasawara:2004:OPO,
author = "Takeshi Ogasawara and Hideaki Komatsu and Toshio
Nakatani",
title = "Optimizing precision overhead for x86 processors",
journal = j-SPE,
volume = "34",
number = "9",
pages = "875--893",
day = "25",
month = jul,
year = "2004",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.596",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat Apr 16 07:26:31 MDT 2005",
bibsource = "http://www.interscience.wiley.com/jpages/0038-0644;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "It is a major challenge for a Java JIT compiler to
perform single-precision floating-point operations
efficiently for the x86 processors. In previous
research, the double-precision mode is set as the
default precision mode when methods are invoked.
Sophisticated approaches then use heuristic approaches
to optimization by considering the trade-offs between
roundings and mode switches. However, this convention
introduces redundant mode switches across method
boundaries. Furthermore, methods that include both
single- and double-precision operations cannot switch
the mode, even if single-precision operations are
dominant. We propose a new approach to these problems.
We eliminate redundant mode switches by ignoring the
default precision mode and calling a method in the same
precision mode as the caller. For methods that include
both single- and double-precision methods, we reduce
the overhead of rounding by isolating code segments of
a given method that should be executed in the
single-precision mode. We implemented our approach in
IBM's Just-in-Time compiler, and obtained experimental
results demonstrating that, in SPECjvm98, it
consistently shows the best performance in any
configuration of benchmark programs, inline policies,
and processor architectures compared with previous
research approaches.",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "floating-point operations; Java; precision control;
x86 processors",
onlinedate = "27 Apr 2004",
}
@TechReport{Ogita:2004:ASDa,
author = "Takeshi Ogita and Siegfried M. Rump and Shin'ichi
Oishi",
title = "Accurate Sum and Dot Product",
type = "Technical Report",
number = "04.1",
institution = "Forschungsschwerpunkt Informations- und
Kommunikationstechnik, Technical University
Hamburg-Harburg",
address = "Hamburg, Germany",
pages = "4",
year = "2004",
bibdate = "Fri Nov 26 15:58:09 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; distillation",
}
@InProceedings{Ogita:2004:ASDb,
author = "Takeshi Ogita and Siegfried M. Rump and Shin'ichi
Oishi",
title = "Accurate Sum and Dot Product with Applications",
crossref = "IEEE:2004:IIS",
pages = "152--155",
year = "2004",
bibdate = "Fri Nov 26 15:55:22 2004",
bibsource = "http://www.oishi.info.waseda.ac.jp/~ogita/index.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://citeseer.ist.psu.edu/cache/papers/cs2/255/http:zSzzSzwww.oishi.info.waseda.ac.jpzSz~ogitazSzdoczSzsum040921.pdf/accurate-sum-and-dot.pdf;
http://www.ti3.tu-harburg.de/paper/rump/OgRuOi04a.pdf",
abstract = "In a recent paper the authors presented a new and very
fast algorithm for accurate computation and inclusion
of the sum and dot product of floating point numbers.
In this paper we show that the algorithms can be used
to compute a very accurate inclusion of the solution of
systems of linear equations. As a basic building block,
accurate solution of linear equations has applications
in very many areas.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@InProceedings{Olausson:2004:RFP,
author = "M. Olausson and A. Ehliar and J. Eilert and D. Liu",
booktitle = "{ISCAS '04}. Proceedings of the 2004 International
Symposium on Circuits and Systems, 23--26 May 2004",
title = "Reduced floating point for {MPEG1/2} layer {III}
decoding",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "V-209--V-212",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A new approach to decode MPEG 1/2-layer III, mp3, is
presented. Instead of converting the algorithm to fixed
point, we propose a 16-bit floating point
implementation. These 16 bits include 1 sign bit and 15
bits of both mantissa and exponent. \ldots{}",
acknowledgement = ack-nhfb,
}
@InProceedings{Ortiz:2004:SPI,
author = "I. Ortiz and M. Jimenez",
booktitle = "{MWSCAS '04}. The 2004 47th Midwest Symposium on
Circuits and Systems. 25--28 July 2004",
title = "Scalable pipeline insertion in floating-point division
and square root units",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-225--II-228",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 15:28:14 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Division and square root are important operations in a
number of data processing algorithms. They are
inherently time consuming operations and can require a
significant amount of resources when implemented in
hardware. This work reports the development of
scalable, floating-point (FP) division and square root
operators with adjustable precision, range, and
pipeline granularity. An algorithm for pipeline
insertion was used for both operators, enabling speeds
up to 204MFLOPS when implemented on a Xilinx Virtex II
FPGA.",
acknowledgement = ack-nhfb,
summary = "Division and square root are important operations in a
number of data processing algorithms. They are
inherently time consuming operations and can require a
significant amount of resources when implemented in
hardware. This work reports the \ldots{}",
}
@Article{Pace:2004:ERL,
author = "L. Pace and A. Salvan and L. Ventura",
title = "The Effects of Rounding on Likelihood Procedures",
journal = j-J-APPL-STAT,
volume = "31",
number = "1",
pages = "29--48",
month = jan,
year = "2004",
CODEN = "????",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Sat Dec 4 12:10:37 MST 2004",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
}
@Article{Page:2004:PCA,
author = "D. Page and N. P. Smart",
title = "Parallel cryptographic arithmetic using a redundant
{Montgomery} representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "11",
pages = "1474--1482",
month = nov,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.100",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1336767",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Paul:2004:SMR,
author = "L. J. Paul and P. H. Bauer and C. Lorand and K.
Premaratne",
booktitle = "{MWSCAS '04}. The 2004 47th Midwest Symposium on
Circuits and Systems, 25--28 July 2004",
title = "Stabilizing mantissa rates in feedback systems with
floating-point quantization",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-501--II-504",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Petkovic:2004:GCS,
author = "M. S. Petkovi{\'c} and L. Ranci{\'c}",
title = "On the guaranteed convergence of the square-root
iteration method",
journal = j-J-COMPUT-APPL-MATH,
volume = "170",
number = "1",
pages = "169--179",
day = "1",
month = sep,
year = "2004",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:00:00 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042704000184",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Pineiro:2004:AAL,
author = "J. A. Pi{\~n}eiro and M. D. Ercegovac and J. D.
Bruguera",
title = "Algorithm and Architecture for Logarithm, Exponential
and Powering Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "9",
pages = "1085--1096",
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.53",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 10:05:48 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j05.ps",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Plouffe:2004:ILS,
author = "Simon Plouffe",
title = "Invited Lecture: A survey of Integer Relations
algorithms and rational numbers [abstract only]",
crossref = "Frougny:2004:RCR",
pages = "",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_02_plouffe.pdf",
abstract = "It is widely believed that Integer Relations
algorithms such as LLL, Lattice reduction or PSLQ which
are implemented in most computer algebra systems are
generalizations of the Euclidian algorithm or the
continued fraction algorithm.\par
We give simple examples of cases where the programs
fails to find a solution and in general examples of
problem that could hardly be solved using such
tools.\par
Most of the examples are either large rational numbers
or near rational numbers, the difference being so small
that even very high precision do not guarantee to have
results",
acknowledgement = ack-nhfb,
keywords = "Algebraic numbers; Coordination sequences; Golden
ratio; Integer Relations; Lattice Reduction; LLL; Pisot
sequences; PSLQ; Zeolites",
}
@Article{Priest:2004:ESC,
author = "Douglas M. Priest",
title = "Efficient scaling for complex division",
journal = j-TOMS,
volume = "30",
number = "4",
pages = "389--401",
month = dec,
year = "2004",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1039813.1039814",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Apr 12 06:34:31 MDT 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We develop a simple method for scaling to avoid
overflow and harmful underflow in complex division. The
method guarantees that no overflow will occur unless at
least one component of the quotient must overflow,
otherwise the normwise error in the computed result is
at most a few units in the last place. Moreover, the
scaling requires only four floating point
multiplications and a small amount of integer
arithmetic to compute the scale factor. Thus, on many
modern CPUs, our method is both safer and faster than
Smith's widely used algorithm.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "complex division",
}
@Article{Putot:2004:SAB,
author = "Sylvie Putot and Eric Goubault and Matthieu Martel",
title = "Static Analysis-Based Validation of Floating-Point
Computations",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2991",
pages = "306--313",
year = "2004",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Mar 10 06:51:00 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springeronline.com/3-540-21260-4",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Quach:2004:SIR,
author = "N. T. Quach and N. Takagi and M. J. Flynn",
title = "Systematic {IEEE} rounding method for high-speed
floating-point multipliers",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "12",
number = "5",
pages = "511--521",
month = may,
year = "2004",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2004.825860",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Sat Jul 16 11:25:05 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "For performance reasons, many high-speed
floating-point multipliers today precompute multiple
significand values (SVs) in advance. The final
normalization and rounding steps are then performed by
selecting the appropriate SV. While having speed
advantages, this integrated rounding method complicates
the development of the rounding logic significantly,
hence, requiring a systematic rounding method.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
summary = "For performance reasons, many high-speed
floating-point multipliers today precompute multiple
significand values (SVs) in advance. The final
normalization and rounding steps are then performed by
selecting the appropriate SV. While having speed
advantages \ldots{}",
}
@Article{Radecka:2004:DVT,
author = "K. Radecka and Z. Zilic",
title = "Design verification by test vectors and arithmetic
transform universal test set",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "5",
pages = "628--640",
month = may,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.1275301",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:36 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1275301",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Rettinger:2004:FAJ,
author = "R. Rettinger",
title = "A Fast Algorithm for {Julia} Sets of Hyperbolic
Rational Functions",
crossref = "Frougny:2004:RCR",
pages = "158--171",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_13_rettinger.pdf",
abstract = "Although numerous computer programs have been written
to compute sets of points which claim to approximate
Julia sets, no reliable high precision pictures of
nontrivial Julia sets are currently known. Usually, no
error estimates are added and even those algorithms
which work reliable in theory, become unreliable in
practice due to rounding errors and the use of fixed
length floating point numbers.\par
In this paper we prove the existence of polynomial time
algorithms to approximate the Julia sets of given
hyperbolic rational functions. We will give a strict
computable error estimation w.r.t. the Hausdorff metric
on the complex sphere. This extends a result on
polynomials $ z \to z^2 + c $, where $ |c| < 1 / 4 $,
in [RW03] and an earlier result in [Zho98] on the
recursiveness of the Julia sets of hyperbolic
polynomials.\par
The algorithm given in this paper computes Julia sets
locally in time $ O(k \cdot M(k)) $ (where $ M(k) $
denotes the time needed to multiply two $k$-bit
numbers). Roughly speaking, the local time complexity
is the number of Turing machine steps to decide a set
of disks of spherical diameter $ 2^{-k}$ so that the
union of these disks has Hausdorff distance at most $
2^{-k + 2}$. This allows to give reliable pictures of
Julia sets to arbitrary precision.",
acknowledgement = ack-nhfb,
keywords = "Computational Complexity; Julia Sets",
}
@Article{Reyhani-Masoleh:2004:EDS,
author = "Arash Reyhani-Masoleh and M. Anwar Hasan",
title = "Efficient digit-serial normal basis multipliers over
binary extension fields",
journal = j-TECS,
volume = "3",
number = "3",
pages = "575--592",
month = aug,
year = "2004",
CODEN = "????",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Fri Oct 29 06:35:47 MDT 2004",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}
@Article{Reyhani-Masoleh:2004:LCB,
author = "A. Reyhani-Masoleh and M. A. Hasan",
title = "Low complexity bit parallel architectures for
polynomial basis multiplication over {$ {\rm GF}(2^m)
$}",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "8",
pages = "945--959",
month = aug,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.47",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1306989",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Riley:2004:HAE,
author = "Joseph Riley and Michael J. Schulte",
title = "A Hardware Accelerator for Elliptic Curve Cryptography
over {$ \mathrm {GF}(2^m) $}",
journal = j-INT-J-COMP-RESEARCH,
volume = "??",
number = "??",
pages = "??--??",
year = "2004",
ISSN = "1535-6698",
bibdate = "Sun Mar 04 20:54:26 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Special Issue on Cryptographic Hardware and Embedded
Systems",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-10.pdf",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Computer Research",
}
@InProceedings{Roy:2004:ACF,
author = "S. Roy and P. Banerjee",
booktitle = "Proceedings. 41st Design Automation Conference, June
7--11, 2004",
title = "An algorithm for converting floating-point
computations to fixed-point in {MATLAB} based {FPGA}
design",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "484--487",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sadaghdar:2004:BFP,
author = "M. Sadaghdar and K. Iniewski and M. Syrzycki",
booktitle = "Canadian Conference on Electrical and Computer
Engineering, 2--5 May 2004",
title = "11-bit floating-point pipelined analog to digital
converter in 0.18$ \mu $ m {CMOS}",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1503--1506",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Schimmler:2004:BSF,
author = "Manfred Schimmler and Bertil Schmidt and Hans-Werner
Lang",
title = "A bit-serial floating-point unit for a massively
parallel system on a chip",
journal = j-PARALLEL-ALGORITHMS-APPL,
volume = "19",
number = "2-3",
pages = "79--95",
year = "2004",
CODEN = "PAAPEC",
ISSN = "1063-7192",
ISSN-L = "1026-7689",
MRclass = "Database Expansion Item",
MRnumber = "MR2113359",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Parallel Algorithms and Applications",
journal-URL = "http://www.tandfonline.com/loi/gpaa20",
}
@InProceedings{Schirra:2004:ILR,
author = "Stefan Schirra",
title = "Invited Lecture: Real Numbers and Robustness in
Computational Geometry",
crossref = "Frougny:2004:RCR",
pages = "7--21",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_03_schirra.pdf",
abstract = "Robustness issues due to imprecise arithmetic used in
place of exact real number computation are a notorious
problem in the implementation of geometric algorithms.
We briefly address some robustness issues and discuss
approaches to resolve them.",
acknowledgement = ack-nhfb,
keywords = "computational geometry; exact geometric computation;
robustness",
}
@TechReport{Schulte:2004:DED,
author = "Michael J. Schulte and Eric Schwarz",
title = "Design Exploration for Decimal Floating-Point
Arithmetic {IBM} University Partnership Program
Proposal",
type = "Technical report",
institution = "University of Wisconsin-Madison and IBM Systems and
Technology Group",
address = "Madison, WI, USA",
pages = "4",
day = "11",
month = mar,
year = "2004",
bibdate = "Sat Mar 03 19:24:05 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://domino.research.ibm.com/acas/w3www_acas.nsf/images/proposals_04.05/%24FILE/schulte.pdf",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Schulte:2004:LPC,
author = "M. J. Schulte and K. Chirca and J. Glossner and H.
Wang and S. Mamidi and P. I. Balzola and S.
Vassiliadis",
title = "A Low-Power Carry Skip Adder with Fast Saturation",
crossref = "IEEE:2004:IICb",
pages = "269--279",
year = "2004",
bibdate = "Sun Mar 04 20:56:38 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-11.pdf",
acknowledgement = ack-nhfb,
}
@Article{Seidel:2004:DOI,
author = "P.-M. Seidel and G. Even",
title = "Delay-optimized implementation of {IEEE}
floating-point addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "2",
pages = "97--113",
month = feb,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.1261822",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1261822",
abstract = "We present an IEEE floating-point adder (FP-adder)
design. The adder accepts normalized numbers, supports
all four IEEE rounding modes, and outputs the correctly
normalized rounded sum\slash difference in the format
required by the IEEE Standard.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "We present an IEEE floating-point adder (FP-adder)
design. The adder accepts normalized numbers, supports
all four IEEE rounding modes, and outputs the correctly
normalized rounded sum/difference in the format
required by the IEEE Standard. The FP-adder \ldots{}",
}
@InProceedings{Seidel:2004:LIF,
author = "P.-M. Seidel",
booktitle = "Conference Record of the Thirty-Eighth Asilomar
Conference on Signals, Systems and Computers, Nov.
7--10, 2004",
title = "On-line {IEEE} floating-point multiplication and
division for reduced power dissipation",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "498--502",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Shi:2004:FPF,
author = "Changchun Shi and R. W. Brodersen",
title = "Floating-point to fixed-point conversion with decision
errors due to quantization",
crossref = "IEEE:2004:IICc",
volume = "5",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "V-41--V-44",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Steele:2004:RHP,
author = "Guy L. {Steele Jr.} and Jon L. White",
title = "Retrospective: How to Print Floating-Point Numbers
Accurately",
journal = j-SIGPLAN,
volume = "39",
number = "4",
pages = "372--389",
month = apr,
year = "2004",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/989393.989431",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Jun 15 10:00:43 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Best of PLDI 1979--1999. Reprint of, and retrospective
on, \cite{Steele:1990:HPF}.",
abstract = "We present algorithms for accurately converting
floating-point numbers to decimal representation. The
key idea is to carry along with the computation an
explicit representation of the required rounding
accuracy. We begin with the simpler problem of
converting fixed-point fractions. A modification of the
well-known algorithm for radix-conversion of
fixed-point fractions by multiplication explicitly
determines when to terminate the conversion process; a
variable number of digits are produced. The algorithm
has these properties: (*) No information is lost; the
original fraction can be recovered from the output by
rounding. (*) No ``garbage digits'' are produced. (*)
The output is correctly rounded. (*) It is never
necessary to propagate carries on rounding. We then
derive two algorithms for free-format out-put of
floating-point numbers. The first simply scales the
given floating-point number to an appropriate
fractional range and then applies the algorithm for
fractions. This is quite fast and simple to code but
has inaccuracies stemming from round-off errors and
oversimplification. The second algorithm guarantees
mathematical accuracy by using multiple-precision
integer arithmetic and handling special cases. Both
algorithms produce no more digits than necessary
(intuitively, the ``1.3 prints as 1.2999999'' problem
does not occur). Finally, we modify the free-format
conversion algorithm for use in fixed-format
applications. Information may be lost if the fixed
format provides too few digit positions, but the output
is always correctly rounded. On the other hand, no
``garbage digits'' are ever produced, even if the fixed
format specifies too many digit positions (intuitively,
the ``4/3 prints as 1.333333328366279602'' problem does
not occur).",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Misc{Stehle:2004:GAT,
author = "D. Stehl{\'e} and P. Zimmermann",
title = "{Gal}'s Accurate Tables Method Revisited",
howpublished = "World-Wide Web document",
year = "2004",
bibdate = "Fri Jun 24 14:56:03 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~stehle/downloads/2x-double.txt;
http://www.loria.fr/~stehle/downloads/sincos-double.txt;
http://www.loria.fr/~stehle/IMPROVEDGAL.html",
abstract = "Gal's accurate tables algorithm aims at providing an
efficient implementation of elementary functions with
correct rounding as often as possible. This method
requires an expensive pre-computation of a table made
of the values taken by the function --- or by several
related functions --- at some distinguished points. Our
improvements of Gal's method are two-fold: on the one
hand we describe what is the arguably best set of
distinguished values and how it improves the efficiency
and correctness of the implementation of the function,
and on the other hand we give an algorithm which
drastically decreases the cost of the pre-computation.
These improvements are related to the worst cases for
the correct rounding of mathematical functions and to
the algorithms for finding them. We show that the whole
method can be turned into practice by giving complete
tables for $ 2^x $ and $ \sin x $ for $x$ in $ [1 / 2,
1) $, in double precision.\par
Here are the two tables mentioned in the article: the $
\sin x $ table and the $ 2^x $ table.\par
Erratum in the final version of the paper: in Section
4, the simultaneous worst case for sin and cos is t0 =
1f09c0c6cde5e3 and not t0 = 31a93fddd45e3.",
acknowledgement = ack-nhfb,
}
@Book{Stine:2004:DCA,
author = "James E. Stine",
title = "Digital computer arithmetic datapath design using
{Verilog HDL}",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xi + 180",
year = "2004",
ISBN = "1-4020-7710-6",
ISBN-13 = "978-1-4020-7710-4",
LCCN = "TK7868.D5 S75 2004",
bibdate = "Thu Nov 18 09:03:42 MST 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0820/2003064036-d.html;
http://www.loc.gov/catdir/enhancements/fy0820/2003064036-t.html",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic; computers / cad-cam; computers /
hardware / personal computers / general; computers /
logic design; computers / programming languages /
general; computers / systems architecture / general;
digital electronics; mathematics / discrete
mathematics; technology \& engineering / electrical;
technology \& engineering / electronics / circuits /
general; technology \& engineering / electronics /
digital; Verilog (computer hardware description
language)",
subject = "Digital electronics; Verilog (Computer hardware
description language); Computer arithmetic",
}
@Misc{Sun:2004:LBR,
author = "{Sun Microsystems, Inc.}",
title = "Libmcr 0.9 beta: a reference correctly-rounded library
of basic double-precision transcendental elementary
functions",
howpublished = "World-Wide Web software project archive",
year = "2004",
bibdate = "Fri Jun 24 14:59:44 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sun.com/download/products.xml?id=41797765",
acknowledgement = ack-nhfb,
}
@Article{Sunar:2004:GMC,
author = "B. Sunar",
title = "A generalized method for constructing subquadratic
complexity {$ \mathrm {GF}(2^k) $} multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "9",
pages = "1097--1105",
month = sep,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.52",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 24 21:17:30 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Sypniewski:2004:IAU,
author = "M. Sypniewski and W. K. Gwarek",
booktitle = "2004 {IEEE} {MTT-S} International Microwave Symposium
Digest. 6--11 June 2004",
title = "On the influence of arithmetic underflow rounding
standard on the speed of {FDTD} modeling",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1795--1798",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 11:25:06 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper presents the influence of arithmetic
underflow rounding operations on the speed of FDTD
analysis. It is shown that the underflow treatment
according to the IEEE standard 754 (commonly accepted
and implemented in modern arithmetic \ldots{}).",
}
@InProceedings{Tadaki:2004:ECH,
author = "Kohtaro Tadaki",
title = "An extension of Chaitin's halting probability {$
\Omega $} to measurement operator in infinite
dimensional quantum system",
crossref = "Frougny:2004:RCR",
pages = "172--191",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_14_tadaki.pdf",
abstract = "This paper proposes an extension of Chaitin's halting
probability $ \Omega $ to measurement operator in
infinite dimensional quantum system. Chaitin's $ \Omega
$ is defined as the probability that the universal
self-delimiting Turing machine $U$ halts, and plays a
central role in the development of algorithmic
information theory. In the theory, there are two
equivalent ways to define the program-size complexity $
H(s)$ of a given finite binary string s. In the
standard way, $ H(s)$ is defined as the length of the
shortest input string for U to output s. In the other
way, the so-called universal probability $m$ is
introduced first, and then $ H(s)$ is defined as $ -
\log_2 m(s)$ without reference to the concept of
program-size.\par
Mathematically, the statistics of outcomes in a quantum
measurement are described by a positive operator-valued
measure (POVM) in the most general setting. Based on
the theory of computability structures on a Banach
space developed by Pour-El and Richards, we extend the
universal probability to an analogue of POVM in
infinite dimensional quantum system, called universal
semi-POVM. We also give another characterization of
Chaitin's $ \Omega $ numbers by universal
probabilities. Then, based on this characterization, we
propose to define an extension of $ \Omega $ as a sum
of the POVM elements of a universal semi-POVM. The
validity of this definition is discussed.\par
In what follows, we introduce an operator version $
\hat {H}(s)$ of $ H(s) $ in a Hilbert space of infinite
dimension using universal semi-POVM, and study the
properties of $ \hat {H}(s)$.",
acknowledgement = ack-nhfb,
keywords = "algorithmic information theory; Chaitin's $\Omega$;
computability in analysis; POVM; quantum measurement;
universal probability",
}
@TechReport{Thomas:2004:LLF,
author = "James W. Thomas and Jon P. Okada and Peter Markstein
and Ren-Cang Li",
title = "The {{\tt Libm}} Library and Floating-Point Arithmetic
in {HP-UX} for {Itanium}-Based Systems: Updated for
{HP-UX 11i v2}",
type = "Technical report",
institution = "Hewlett--Packard Company",
address = "Palo Alto, CA, USA",
pages = "26",
day = "3",
month = dec,
year = "2004",
bibdate = "Fri Jun 24 20:12:09 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf",
abstract = "The HP-UX libm library provides mathematical functions
for C, C++, and Fortran 90. The HP-UX libm library and
compilers for Itanium-based systems provide a leading
combination of functionality, quality, and
performance.With inlining and software pipelining,
commonly used math functions can achieve throughput
comparable to hand-tuned vector routines without
requiring user code to be written for a vector
interface, and with no loss of accuracy or edge-case
behavior: For example, the single precision exponential
can exceed 400 million evaluations per second on a 1.5
GHz Itanium 2 system. The math API encompasses C99,
X/Open, and other popular functionality and offers four
fully supported IEEE floating types. The libm library
and compilers provide features that facilitate
programming techniques that have not been practical
heretofore. The libm implementation for Itanium-based
systems, introduced in 2001 in HP-UX B.11.20 (11i
v1.5), has been upgraded in B.11.22 (11i v1.6), B.11.23
(11i v2), and most recently in B.11.23 AR1204 and the
associated Math Library Cumulative Patch PHSS_31853
with improved performance and overall quality and with
a few new functions. The AR1204 compilers are available
as patches for B.11.22; the associated Math patch for
B.11.22 is PHSS_32066. This paper (1) describes the
latest libm library (including sequences the compilers
inline) in terms of functionality, speed, accuracy,
standards, and special-case behavior; (2) discusses
programming techniques that exploit the floating-point
capabilities of HP-UX on Itanium- based systems; and
(3) describes motivations, goals, and development
strategies for the libm library and the compiler
floating-point facilities.",
acknowledgement = ack-nhfb,
}
@InProceedings{Thompson:2004:BDF,
author = "J. Thompson and N. Karra and M. J. Schulte",
booktitle = "Proceedings. {IEEE Computer Society Annual Symposium
on VLSI, 19--20 February 2004}",
title = "A 64-bit decimal floating-point adder",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "297--298",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-08.pdf",
abstract = "Due to rapid growth in financial, commercial, and
Internet-based applications, there is an increasing
desire to allow computers to operate on both binary and
decimal floating-point numbers. Consequently,
specifications for decimal floating-point support are
being added to the IEEE-754 Standard for Floating-Point
Arithmetic. In this paper, we present the design and
implementation of a decimal floating-point adder that
is compliant with the current draft revision of this
standard. The adder supports operations on 64-bit
(16-digit) decimal floating-point operands. We provide
synthesis results indicating the estimated area and
delay for our design when it is pipelined to various
depths.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Manual{TI:2004:TUG,
title = "{TMS320C3x} User's Guide",
organization = "Texas Instruments",
address = "Post Office box 655303, Dallas, TX 75265, USA",
pages = "770",
year = "2004",
bibdate = "Wed Nov 24 09:20:17 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Literature Number: SPRU031F 2558539-9761 revision L
March 2004",
URL = "http://www-s.ti.com/sc/psheets/spru031f/spru031f.pdf",
acknowledgement = ack-nhfb,
keywords = "digital signal processor (DSP)",
}
@InProceedings{Tsoi:2004:ALA,
author = "K. H. Tsoi and C. H. Ho and H. C. Yeung and P. H. W.
Leong",
title = "An Arithmetic Library and its Application to the
{$N$}-body Problem",
crossref = "Arnold:2004:PAI",
pages = "68--78",
year = "2004",
DOI = "https://doi.org/10.1109/FCCM.2004.14",
bibdate = "Sat Jun 25 12:45:15 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cse.cuhk.edu.hk/~phwl/mt/public/archives/papers/cast_fccm04.pdf",
abstract = "Computer arithmetic is a specialist field of study,
and it is very difficult for designers to choose the
most efficient method for implementing a given
algorithm due to the large number of design choices
available. In this paper, an object oriented arithmetic
library is presented which can be used to simulate and
generate designs which use fixed, floating, logarithmic
and hybrid number representations. The advantages of
this approach are that a user can explore tradeoffs
concerning precision, accuracy and speed from single
high level description. Furthermore, users need not be
intimately familiar with the implementation details of
the underlying libraries, thus allowing users to
develop systems employing advanced computer arithmetic
without detailed knowledge of its implementation. The
application of this library to a coprocessor which
implements the force pipeline for an N-body solver is
described.",
acknowledgement = ack-nhfb,
}
@InProceedings{Underwood:2004:CGC,
author = "K. D. Underwood and K. S. Hemmert",
booktitle = "{FCCM 2004}. 12th Annual {IEEE} Symposium on
Field-Programmable Custom Computing Machines, 20--23
April 2004",
title = "Closing the gap: {CPU} and {FPGA} trends in
sustainable floating-point {BLAS} performance",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "219--228",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Field programmable gate arrays (FPGAs) have long been
an attractive alternative to microprocessors for
computing tasks--as long as floating-point arithmetic
is not required. Fueled by the advance of Moore's law,
FPGAs are rapidly reaching sufficient densities to
enhance peak floating-point performance as well. The
question, however, is how much of this peak performance
can be sustained. This paper examines three of the
basic linear algebra subroutine (BLAS) functions:
vector dot product, matrix-vector multiply, and matrix
multiply. A comparison of microprocessors, FPGAs, and
reconfigurable computing platforms is performed for
each operation. The analysis highlights the amount of
memory bandwidth and internal storage needed to sustain
peak performance with FPGAs. This analysis considers
the historical context of the last six years and is
extrapolated for the next six years.",
acknowledgement = ack-nhfb,
}
@InProceedings{Underwood:2004:FVC,
author = "Keith D. Underwood",
title = "{FPGAs} vs. {CPUs}: Trends in peak floating-point
performance",
crossref = "ACM:2004:FAS",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "171--180",
year = "2004",
DOI = "https://doi.org/10.1145/968280.968305",
bibdate = "Sat Oct 9 13:06:11 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Moore's Law states that the number of transistors on a
device doubles every two years; however, it is often
(mis)quoted based on its impact on CPU performance.
This important corollary of Moore's Law states that
improved clock frequency plus improved architecture
yields a doubling of CPU performance every 18 months.
This paper examines the impact of Moore's Law on the
peak floating-point performance of FPGAs. Performance
trends for individual operations are analyzed as well
as the performance trend of a common instruction mix
(multiply accumulate). The important result is that
peak FPGA floating-point performance is growing
significantly faster than peak floating-point
performance for a CPU.",
acknowledgement = ack-nhfb,
}
@Article{Vignes:2004:DSA,
author = "Jean Vignes",
title = "Discrete Stochastic Arithmetic for Validating Results
of Numerical Software",
journal = j-NUMER-ALGORITHMS,
volume = "37",
number = "1--4",
pages = "377--390",
month = dec,
year = "2004",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Dec 6 07:00:28 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/31/abstract.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "Special Issue: SCAN'2002 International Conference
(Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte).",
}
@Article{vonzurGathen:2004:FAG,
author = "J. Joachim von zur Gathen and Michael N{\"o}cker",
title = "Fast arithmetic with general {Gau{\ss}} periods",
journal = j-THEOR-COMP-SCI,
volume = "315",
number = "2--3",
pages = "419--452",
day = "6",
month = may,
year = "2004",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Thu Nov 4 10:19:15 MST 2004",
bibsource = "http://www.sciencedirect.com/science/journal/03043975;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We show how to apply fast arithmetic in conjunction
with general Gau{\ss} periods in finite fields. This is
an essential ingredient for some efficient
exponentiation algorithms.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
keywords = "Efficient arithmetic; Exponentiation; Finite fields;
Gau{\ss} period; Normal basis",
}
@InProceedings{Voronenko:2004:AGI,
author = "Y. Voronenko and M. Puschel",
title = "Automatic generation of implementations for {DSP}
transforms on fused multiply-add architectures",
crossref = "IEEE:2004:IICc",
volume = "5",
pages = "V-101--V-104",
year = "2004",
DOI = "https://doi.org/10.1109/ICASSP.2004.1327057",
bibdate = "Sun Feb 20 10:05:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Many modern computer architectures feature fused
multiply-add (FMA) instructions, which offer
potentially faster performance for numerical
applications. For DSP transforms, compilers can only
generate FMA code to a very limited extent because
optimal use of FMAs requires modifying the chosen
algorithm. In this paper, we present a framework for
automatically generating FMA code for every linear DSP
transform, which we implemented as an extension to the
SPIRAL code generation system. We show that for many
transforms and transform sizes, our generated FMA code
matches the best-known hand-derived FMA algorithms in
terms of arithmetic cost. Further, we present actual
runtime results that show the speed-up obtained by
using FMA instructions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Walters:2004:TSC,
author = "E. G. Walters and M. J. Schulte and M. G. Arnold",
title = "Truncated Squarers with Constant and Variable
Correction",
crossref = "Luk:2004:ASP",
year = "2004",
bibdate = "Sun Mar 04 20:49:55 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-14.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Wang:2004:DFP,
author = "Liang-Kai Wang and M. J. Schulte",
booktitle = "Proceedings. 15th {IEEE} International Conference on
Application-Specific Systems, Architectures and
Processors, 27--29 Sept. 2004",
title = "Decimal floating-point division using
{Newton--Raphson} iteration",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "84--95",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-06.pdf",
abstract = "Decreasing feature sizes allow additional
functionality to be added to future microprocessors to
improve the performance of important application
domains. As a result of rapid growth in financial,
commercial, and Internet-based applications, hardware
support for decimal floating-point arithmetic is now
being considered by various computer manufacturers and
specifications for decimal floating-point arithmetic
have been added to the draft revision of the IEEE-754
Standard for Floating-Point Arithmetic (IEEE-754R).
This work presents an efficient arithmetic algorithm
and hardware design for decimal floating-point
division. \ldots{}",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Weaver:2004:MFD,
author = "B. J. Weaver and Y. V. Zakharov and T. C. Tozer",
title = "Multiplication-free division of complex numbers",
crossref = "Anonymous:2004:ICM",
pages = "211--214",
year = "2004",
bibdate = "Sat Dec 04 09:59:02 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Wu:2004:HSL,
author = "Chien-Hsing Wu and Chien-Ming Wu and Ming-Der Shieh
and Yin-Tsung Hwang",
title = "High-speed, low-complexity systolic designs of novel
iterative division algorithms in {$ \mathrm {GF}(2^m)
$}",
journal = j-IEEE-TRANS-COMPUT,
volume = "53",
number = "3",
pages = "375--380",
month = mar,
year = "2004",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2004.1261843",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jul 5 08:12:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1261843",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wu:2004:ORF,
author = "Jun Wu and Sheng Chen and James F. Whidborne and Jian
Chu",
title = "Optimal realizations of floating-point implemented
digital controllers with finite word length
considerations",
journal = j-INT-J-CONTROL,
volume = "77",
number = "5",
pages = "427--440",
year = "2004",
CODEN = "IJCOAZ",
ISSN = "0020-7179 (print), 1366-5820 (electronic)",
ISSN-L = "0020-7179",
MRclass = "93B15 (93C57)",
MRnumber = "MR2052876",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Control",
journal-URL = "http://www.tandfonline.com/loi/tcon20",
}
@InProceedings{Yang:2004:EEP,
author = "Xiao Yang and S. K. Valia and M. J. Schulte and R. B.
Lee",
booktitle = "Conference Record of the Thirty-Eighth Asilomar
Conference on Signals, Systems and Computers, Nov.
7--10, 2004",
title = "Exploration and evaluation of {PLX} floating-point
instructions and implementations for {$3$D} graphics",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1873--1878",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2004-18.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Yang:2004:PFE,
author = "Xiao Yang and R. B. Lee",
booktitle = "{ICME '04}. 2004 {IEEE} International Conference on
Multimedia and Expo, 27--30 June 2004",
title = "{PLX FP}: an efficient floating-point instruction set
for {$3$D} graphics",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "137--140",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "3D graphics is an important component in the workload
of today's computing platforms. Many ISA extensions for
3D graphics have been proposed and implemented. We
describe PLX FP, a new floating-point extension to the
PLX architecture, designed to support very efficiently
the essential operations needed for the 3D graphics
pipeline. Very high performance floating-point 3D
graphics processing is achieved, using a low-cost PLX
processor.",
acknowledgement = ack-nhfb,
}
@InProceedings{Yoon:2004:IPT,
author = "Han-Ul Yoon and Kyoung-Taik Park and Kwee-Bo Sim",
booktitle = "{IECON 2004}, 30th Annual Conference of {IEEE}
Industrial Electronics Society",
title = "Improvement of processing time using residue number
system and sorting network in controller design",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2046--2051",
year = "2004",
CODEN = "????",
DOI = "https://doi.org/10.1109/IECON.2004.1432111",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents and proposes two approaches to
speed up for the controller unit. One is a residue
number system (RNS), the other is a sorting network.
Using an RNS reduces the total bit size of adder and
carry-propagation delays. Also, using \ldots{}",
}
@InProceedings{Zhang:2004:PBL,
author = "W. Zhang and G. A. Jullien and V. S. Dimitrov",
booktitle = "Proceedings of the 2004 International Symposium on
Circuits and Systems: {ISCAS '04}, 23--26 May 2004",
title = "A programmable base {$2$D}-{LNS} {MAC} with
self-generated look-up tables",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-789--92",
year = "2004",
CODEN = "????",
ISSN = "????",
bibdate = "Sat Jul 16 16:14:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
summary = "This paper presents a new architecture for a
programmable second base 2-dimensional logarithmic
number system (2D LNS) Multiply Accumulator Cell (MAC)
using DRAMs to store the conversion look-up tables
(LUTs). It uses a direct mapping from non- \ldots{}",
}
@InProceedings{Zheng:2004:HRN,
author = "Xizhong Zheng",
title = "On the Hierarchy of {$ \Delta_2^0 $}-Real Numbers",
crossref = "Frougny:2004:RCR",
pages = "192--215",
year = "2004",
bibdate = "Fri Nov 17 07:00:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_15_zheng.pdf",
abstract = "A real number x is called $ \Delta_2^0 $ if its binary
expansion corresponds to a $ \Delta_2^0 $-set of
natural numbers. Such reals are just the limits of
computable sequences of rational numbers and hence also
called computably approximable. Depending on how fast
the sequences converge, $ \Delta_2^0 $-reals have
different levels of effectiveness. This leads to
various hierarchies of $ \Delta_2^0 $ reals. In this
paper we summarize several recent developments related
to such kind of hierarchies",
acknowledgement = ack-nhfb,
keywords = "$ \Delta_2^0 $-reals; Computably approximable reals;
hierarchy",
}
@Article{Zhu:2004:ISR,
author = "Hufei Zhu and Zhongding Lei and F. P. S. Chin",
title = "An improved square-root algorithm for {BLAST}",
journal = j-IEEE-SIGNAL-PROCESS-LETT,
volume = "11",
number = "9",
pages = "772--775",
month = sep,
year = "2004",
CODEN = "ISPLEM",
ISSN = "1070-9908 (print), 1558-2361 (electronic)",
ISSN-L = "1070-9908",
bibdate = "Sat Jul 16 15:28:13 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Signal Processing Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
summary = "In this letter, an improved square-root algorithm for
Bell Labs Layered Space-Time (BLAST) system is
proposed. It speeds up the original square-root
algorithm by 36\% in terms of the number of
multiplications and additions. Compared with the
\ldots{}",
}
@InProceedings{Zhuo:2004:SMA,
author = "L. Zhuo and V. K. Prasanna",
booktitle = "Proceedings. 18th International Parallel and
Distributed Processing Symposium, 26--30 April 2004",
title = "Scalable and modular algorithms for floating-point
matrix multiplication on {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "92--92",
year = "2004",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Zimmerman:2004:DCI,
author = "T. Zimmerman and J. R. Hoff",
title = "The design of a charge-integrating modified
floating-point {ADC} chip",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "39",
number = "6",
pages = "895--905",
month = jun,
year = "2004",
CODEN = "IJSCBC",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
summary = "One of the challenges posed by calorimeters in
high-energy physics experiments is digitizing wide
dynamic range charge signals at high rate to a
specified precision. One response to this challenge is
the development of the QIE (charge integrator and
\ldots{}).",
}
@Article{Abdallah:2005:MRN,
author = "M. Abdallah and A. Skavantzos",
title = "On {MultiModuli} residue number systems with moduli of
forms $ r^a $, $ r^b - 1 $, $ r^c + 1 $",
journal = j-IEEE-TRANS-CIRCUITS-SYST-1,
volume = "52",
number = "7",
pages = "1253--1266",
month = jul,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1109/TCSI.2005.851388",
ISSN = "????",
ISSN-L = "1549-8328",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=32002",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I: Regular
Papers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
keywords = "residue arithmetic; residue number system",
summary = "The residue number system (RNS) is an integer system
appropriate for implementing fast digital signal
processors since it can support parallel, carry-free,
high-speed arithmetic. One of the most important
considerations when designing RNS systems is \ldots{}",
}
@Article{Abtahi:2005:CFR,
author = "M. Abtahi and P. Siy",
title = "Core function of an {RNS} number with no ambiguity",
journal = j-COMPUT-MATH-APPL,
volume = "50",
number = "3--4",
pages = "459--470",
month = aug,
year = "2005",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:46 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122105002890",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Adharapurapu:2005:LSO,
author = "Pavan Adharapurapu and Milo{\v{s}} Ercegovac",
title = "A Linear-System Operator based Scheme for Evaluation
of Multinomials",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-178.pdf",
abstract = "We present a radix-2 online computational scheme for
evaluating multinomials in a fixed-point number
representation system. Its main advantage is that it
can adapt to any evaluation graph representing the
multinomial. Evaluation graphs are efficient
representations of multinomials in a factored form. The
proposed scheme maps subgraphs of the evaluation graph
using linear-system operators. These operators
transform the expressions represented by the subgraphs
into systems of linear equations. The linear equations
are then solved in an online,
most-significant-digit-first fashion. The scheme
produces, after an initial delay, one output digit per
iteration for inputs within range. The iteration time
is equal to the sum of the delays of a redundant adder,
multiplexer, register and a selection unit and is
independent of the size of the multinomial and the
precision of the inputs/outputs. The initial delay is
proportional to the diameter of the evaluation graph
and the maximum number of children of any addition node
in the graph. The proposed method lends itself to
implementation using simple, highly regular hardware
with serial interconnections between modules.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@InProceedings{Aharoni:2005:SCI,
author = "Merav Aharoni and Sigal Asaf and Ron Maharik and Ilan
Nehama and Ilya Nikulshin and Abraham Ziv",
title = "Solving Constraints on the Invisible Bits of the
Intermediate Result for Floating-Point Verification",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-136.pdf",
abstract = "Test generation for datapath floating-point
verification involves targeting intricate corner cases,
which can often be solved only through complex
constraint solving.\par
In the process of calculating the result, we use an
intermediate result whose significand comprises a
finite number of bits and a sticky bit that is 0 if and
only if the intermediate result is exact. We refer to
all the bits beyond those represented in the final
result as the invisible bits. We deal with corner cases
that can only be defined via constraints on the
intermediate result.\par
Our work investigates the following problem: Given a
floating-point operation, and constraints on the
invisible bits and the sticky bit, find two inputs for
the operation that yield an intermediate result
compatible with the constraints.\par
The paper supplies a deterministic solution for
addition and subtraction, and probabilistic solutions
for multiplication and division. It also discusses the
application of these algorithms to the verification of
floating-point implementations.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Article{Alvarez:2005:FMF,
author = "C. Alvarez and J. Corbal and M. Valero",
title = "Fuzzy Memoization for Floating-Point Multimedia
Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "7",
pages = "922--927",
month = jul,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.119",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1432675",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
summary = "Instruction memoization is a promising technique to
reduce the power consumption and increase the
performance of future low-end/mobile multimedia
systems. Power and performance efficiency can be
improved by reusing instances of an already executed
\ldots{}",
}
@Misc{Anonymous:2005:HAP,
author = "Anonymous",
title = "How to Avoid Performance Penalties for
Gradual-Underflow Behavior",
howpublished = "World-Wide Web document",
year = "2005",
bibdate = "Fri Oct 14 17:01:56 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/cd/ids/developer/asmo-na/eng/dc/pentium4/knowledgebase/90575.htm",
abstract = "The Pentium 4 processor supports calculation involving
sub-normals with special code stored in 'Read Only
Memory', which is not pipelined as are calculations in
the normalized range. In order to avoid the performance
penalty, such processors often support an
abrupt-underflow mode, where sub-normals are
``flushed'' immediately to zero. Where an Intel
processor supports FTZ, it is possible to set the mode
at run-time and to change it to suit the requirements
of a program that may require full protection of
accuracy in certain code sequences and fast execution
in others.",
acknowledgement = ack-nhfb,
remark = "Discusses mechanisms for selecting flush-to-zero
behavior on Pentium 4 processors in Microsoft Windows
and GNU/Linux.",
}
@Misc{Anonymous:2005:TMF,
author = "Anonymous",
title = "Test of Mathematical Functions of the {Standard C
Library}",
howpublished = "World-Wide Web software project archive",
month = jun,
year = "2005",
bibdate = "Fri Jun 24 19:55:16 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.vinc17.org/research/testlibm/",
abstract = "Some of the mathematical functions of the standard C
library have been tested on worst cases for the exact
rounding in double precision. The following table gives
the ratio or the number of incorrect roundings for
various machines, in the rounding to nearest mode.",
acknowledgement = ack-nhfb,
xxnote = "LOOK AT THIS MORE!!!",
}
@Article{Antelo:2005:DRD,
author = "E. Antelo and T. Lang and P. Montuschi and A.
Nannarelli",
title = "Digit-recurrence dividers with reduced logical depth",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "7",
pages = "837--851",
month = jul,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.115",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1432667",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Antelo:2005:LLD,
author = "Elisardo Antelo and Tom{\'a}s Lang and Paolo Montuschi
and Alberto Nannarelli",
title = "Low Latency Digit-Recurrence Reciprocal and
Square-Root Reciprocal Algorithm and Architecture",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-116.pdf",
abstract = "The reciprocal and square-root reciprocal operations
are important in several applications. For the
operations, we present algorithms that combine a
digit-by-digit module and one iteration of a
quadratic-convergence approximation. The latter is
implemented by a digit-recurrence, which uses the
digits produced by the digit-by-digit part. In this
way, both parts execute in an overlapped manner, so
that the total number of cycles is about half the
number that would be required by the digit-by-digit
part alone. Because of the approximation, correct
rounding of the result cannot be obtained directly in
all cases; we propose a variable-time implementation
that produces the correctly rounded result with a small
average overhead. Radix-4 implementations are described
and have been synthesized. They achieve the same cycle
time as the standard digit-by-digit implementation,
resulting in a speed-up of about 2 and, because of the
approximation part, the area factor is also about 2. We
also show a combined implementation for both operations
that has essentially the same complexity as that for
square-root reciprocal alone.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; correct rounding; floating-point
arithmetic",
pagecount = "8",
}
@InProceedings{Antelo:2005:LLP,
author = "Elisardo Antelo and Julio Villalba",
title = "Low Latency Pipelined Circular {CORDIC}",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-132.pdf",
abstract = "The pipelined CORDIC with linear approximation to
rotation has been proposed to achieve reductions in
delay, power and area; however, the schemes for
rotation (multiplication) and vectoring (division)
complicate implementation in a single unit. In this
work, we improve the linear approximation scheme,
leading to a unified implementation for rotation and
vectoring where fully parallel tree multipliers are
used instead of the second half of CORDIC iterations.
We also combine the linear approximation to rotation
with the scale factor compensation so that the
compensation is performed concurrently with the
rotation process. Comparison with other designs is also
provided.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@InProceedings{Arnold:2005:BIR,
author = "M. G. Arnold and J. Ruan",
title = "Bipartite Implementation of the Residue Logarithmic
Number System",
crossref = "Luk:2005:ASP",
pages = "??--??",
year = "2005",
bibdate = "Fri Jun 24 18:11:43 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Accepted for publication.",
acknowledgement = ack-nhfb,
}
@InProceedings{Arnold:2005:RLN,
author = "Mark Arnold",
title = "The Residue Logarithmic Number System: Theory and
Implementation",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-163.pdf;
http://www.cse.lehigh.edu/~caar/rlns.pdf",
abstract = "The Residue Logarithmic Number System (RLNS)
represents real values as quantized logarithms which,
in turn, are represented using the Residue Number
System (RNS). Compared to the conventional Logarithmic
Number System (LNS) in which quantized logarithms are
represented as binary integers, RLNS offers faster
multiplication and division times. RLNS and LNS use a
table lookup involving all bits for addition. The
width, dynamic range, precision and na{\"\i}ve table
size of RLNS (with careful moduli selection) is as good
as those for conventional LNS.\par
Conventional LNS can be more efficient than na{\"\i}ve
addition lookup. First, commutativity allows
interchanging arguments. Second, the addition function
is often essentially zero, and does not have to be
tabulated. In binary, comparisons are easy. In residue,
comparisons are slow. Although RLNS inherently demands
comparison, this paper shows a novel way comparisons
can be performed in parallel to the lookup from a small
table. This paper also describes a novel tool that
generates synthesizable Verilog, making RLNS viable in
practical applications that can benefit from shorter
multiply and divide times.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; Logarithmic Number System; Residue Number
System",
pagecount = "10",
}
@Misc{Bailey:2005:DFDa,
author = "David H. Bailey",
title = "{DDFUN90}: {Fortran-90} double-double package",
howpublished = "World-Wide Web site with software archives.",
day = "11",
month = mar,
year = "2005",
bibdate = "Tue Nov 22 05:48:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://crd.lbl.gov/~dhbailey/mpdist/;
http://crd.lbl.gov/~dhbailey/mpdist/ddfun90.tar.gz",
abstract = "This package contains software for performing
double-double arithmetic (approximately 32 decimal
digits). It is similar to the qd package above in
functionality, and in fact, an application program
written for one should be compatible with the other.
However this is entirely written in Fortran-90.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Misc{Bailey:2005:DFDb,
author = "David H. Bailey",
title = "{DSFUN90}: {Fortran-90} double-single package",
howpublished = "World-Wide Web site with software archives.",
day = "11",
month = mar,
year = "2005",
bibdate = "Tue Nov 22 05:48:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://crd.lbl.gov/~dhbailey/mpdist/;
http://crd.lbl.gov/~dhbailey/mpdist/dsfun90.tar.gz",
abstract = "This package contains software for performing
double-single arithmetic (approximately 15 decimal
digits). It is entirely written in Fortran-90. It is
targeted to systems, such as game systems, that do not
support IEEE 64-bit floating-point arithmetic.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Bailey:2005:HPF,
author = "David H. Bailey",
title = "High-Precision Floating-Point Arithmetic in Scientific
Computation",
journal = j-COMPUT-SCI-ENG,
volume = "7",
number = "3",
pages = "54--61",
month = may # "\slash " # jun,
year = "2005",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCSE.2005.52",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/mags/cs/2005/03/c3054abs.htm;
http://csdl.computer.org/dl/mags/cs/2005/03/c3054.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
summary = "IEEE 64-bit floating-point arithmetic is sufficient
for most scientific applications, but a rapidly growing
body of scientific computing applications requires a
higher level of numeric precision. Software packages
have yielded interesting scientific \ldots{}",
}
@Misc{Bailey:2005:QDD,
author = "David H. Bailey",
title = "{QD}: double-double and quad double package",
howpublished = "World-Wide Web site with software archives.",
day = "24",
month = aug,
year = "2005",
bibdate = "Tue Nov 22 05:48:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://crd.lbl.gov/~dhbailey/mpdist/;
http://crd.lbl.gov/~dhbailey/mpdist/qd.tar.gz",
abstract = "This package supports both a double-double datatype
(approx. 32 decimal digits) and a quad-double datatype
(approx. 64 decimal digits). The computational library
is written in C++. Both C++ and Fortran-90 high-level
language interfaces are provided to permit one to use
convert an existing C++ or Fortran-90 program to use
the library with only minor changes to the source code.
In most cases only a few type statements and (for
Fortran-90 programs) read\slash write statements need
to be changed. PSLQ and numerical quadrature programs
are included.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bajard:2005:AOP,
author = "Jean-Claude Bajard and Laurent Imbert and Thomas
Plantard",
title = "Arithmetic Operations in the Polynomial Modular Number
System",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-168.pdf",
abstract = "We propose a new number representation and arithmetic
for the elements of the ring of integers modulo p. The
so-called Polynomial Modular Number System (PMNS)
allows for fast polynomial arithmetic and easy
parallelization. The most important contribution of
this paper is the fundamental theorem of a Modular
Number System, which provides a bound for the
coefficients of the polynomials used to represent the
set $ \mathbb {Z}_p $. However, we also propose a
complete set of algorithms to perform the arithmetic
operations over a PMNS, which make this system of
practical interest for people concerned about efficient
implementation of modular arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; Lattice theory; Modular arithmetic; Number
system; Table-based methods",
pagecount = "8",
}
@InProceedings{Bajard:2005:PMM,
author = "Jean-Claude Bajard and Laurent Imbert and Graham
Jullien",
title = "Parallel {Montgomery} Multiplication in {$ \mathrm
{GF}(2^k) $} using Trinomial Residue Arithmetic",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-169.pdf",
abstract = "We propose the first general multiplication algorithm
in $ \mathrm {GF}(2^k) $ with a subquadratic area
complexity of $ \mathcal {O}(k^{8 / 5}) = \mathcal
{O}(k^{1.6}) $. Using the Chinese Remainder Theorem, we
represent the elements of $ \mathrm {GF}(2^k) $; i.e.,
the polynomials in $ \mathrm {GF}(2)[X] $ of degree at
most $ k - 1 $, by the remainder modulo a set of $n$
pairwise prime trinomials, $ T_1, \ldots {}, T_n $, of
degree $d$ and such that $ n d \geq k $. Our algorithm
is based on Montgomery's multiplication applied to the
ring formed by the direct product of the trinomials.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Misc{Beebe:2005:MPA,
author = "Nelson H. F. Beebe",
title = "Multiple-precision arithmetic {FAQ}",
howpublished = "World-Wide Web frequently-asked question document.",
month = sep,
year = "2005",
bibdate = "Wed Aug 30 17:46:43 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This report is updated frequently.",
URL = "https://www.math.utah.edu/faq/mp/",
acknowledgement = ack-nhfb,
}
@InProceedings{Beuchat:2005:MAR,
author = "Jean-Luc Beuchat and Jean-Michel Muller",
editor = "Stamatis Vassiliadis and Nikitas J. Dimopoulos and
Sanjay Vishnu Rajopadhye",
booktitle = "{Proceedings of the 16th IEEE International Conference
on Application-Specific Systems, Architectures, and
Processors (ASAP 2005), 23--25 July 2005, Samos,
Greece}",
title = "Multiplication algorithms for Radix-2 {RN}-codings and
two's complement numbers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xiii + 419",
pages = "303--308",
year = "2005",
DOI = "https://doi.org/10.1109/ASAP.2005.45",
ISBN = "0-7695-2407-9",
ISBN-13 = "978-0-7695-2407-8",
ISSN = "1063-6862",
LCCN = "",
bibdate = "Sun Jun 19 14:52:45 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=10334",
acknowledgement = ack-nhfb,
}
@Article{Blanck:2005:EEC,
author = "J. Blanck",
title = "Efficient exact computation of iterated maps",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "41--59",
month = jul,
year = "2005",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.004",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
bibdate = "Thu Oct 17 10:09:18 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
remark = "Special issue on Practical development of exact real
number computation.",
}
@Article{Boehm:2005:CRJ,
author = "Hans-J. Boehm",
title = "The constructive reals as a {Java Library}",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "3--11",
month = jul,
year = "2005",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.002",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
bibdate = "Wed Oct 16 18:43:22 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/java2000.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S1567832604000736",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
remark = "Special issue on Practical development of exact real
number computation.",
}
@InProceedings{Boldo:2005:SFC,
author = "Sylvie Boldo and Jean-Michel Muller",
title = "Some Functions Computable with a Fused-mac",
crossref = "Montuschi:2005:PIS",
pages = "52--58",
year = "2005",
DOI = "https://doi.org/10.1109/ARITH.2005.39",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-106.pdf",
abstract = "The fused multiply accumulate instruction (fused-mac)
that is available on some current processors such as
the Power PC or the Itanium eases some calculations. We
give examples of some floating-point functions (such as
ulp(x) or Nextafter(x, y)), or some useful tests, that
are easily computable using a fused-mac. Then, we show
that, with rounding to the nearest, the error of a
fused-mac instruction is exactly representable as the
sum of two floating-point numbers. We give an algorithm
that computes that error.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "7",
}
@Article{Bowman:2005:AVS,
author = "K. O. Bowman and L. R. Shenton",
title = "The asymptotic variance and skewness of maximum
likelihood estimators using {Maple}",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "75",
number = "12",
pages = "975--986",
year = "2005",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949650412331321142",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:12:30 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@InProceedings{Brisebarre:2005:CRM,
author = "Nicolas Brisebarre and Jean-Michel Muller",
title = "Correctly Rounded Multiplication by Arbitrary
Precision Constants",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-122.pdf",
abstract = "We introduce an algorithm for multiplying a
floating-point number $x$ by a constant $C$ that is not
exactly representable in floating-point arithmetic. Our
algorithm uses a multiplication and a fused multiply
and add instruction. We give methods for checking
whether, for a given value of $C$ and a given
floating-point format, our algorithm returns a
correctly rounded result for any $x$. When it does not,
our methods give the values $x$ for which it does
not.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; correct rounding; floating-point
arithmetic",
pagecount = "8",
}
@Article{Brisebarre:2005:NRR,
author = "Nicolas Brisebarre and David Defour and Peter Kornerup
and Jean-Michel Muller and Nathalie Revol",
title = "A New Range-Reduction Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "331--339",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.36",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0331abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0331.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0331.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388197",
abstract = "Range-reduction is a key point for getting accurate
elementary function routines. We introduce a new
algorithm that is fast for input arguments belonging to
the most common domains, yet accurate over the full
double-precision range.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16; range reduction",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@InProceedings{Bruguera:2005:FPF,
author = "Javier Bruguera and Tom{\'a}s Lang",
title = "Floating-point Fused Multiply-Add: Reduced Latency for
Floating-Point Addition",
crossref = "Montuschi:2005:PIS",
pages = "42--51",
year = "2005",
DOI = "https://doi.org/10.1109/ARITH.2005.22",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-102.pdf",
abstract = "In this paper we propose an architecture for the
computation of the double precision floating point
multiply add fused (MAF) operation $ A + (B \times C) $
that permits to compute the floating point addition
with lower latency than floating point multiplication
and MAF. While previous MAF architectures compute the
three operations with the same latency, the proposed
architecture permits to skip the first pipeline stages,
those related with the multiplication $ B \times C $,
in case of an addition. For instance, for a MAF unit
pipelined into three or five stages, the latency of the
floating point addition is reduced to two or three
cycles, respectively. To achieve the latency reduction
for floating-point addition, the alignment shifter,
which in previous organizations is in parallel with the
multiplication, is moved so that the multiplication can
be bypassed. To avoid that this modification increases
the critical path, a double-datapath organization is
used, in which the alignment and normalization are in
separate paths. Moreover, we use the techniques
developed previously of combining the addition and the
rounding and of performing the normalization before the
addition.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "10",
}
@Article{Burgess:2005:PRI,
author = "N. Burgess",
title = "Prenormalization rounding in {IEEE} floating-point
operations using a flagged prefix adder",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "13",
number = "2",
pages = "266--277",
month = feb,
year = "2005",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2004.840764",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper demonstrates how IEEE 754 floating-point
standard compliant rounding can be merged with
carry-propagate addition in floating-point unit (FPU)
designs by using a novel adaptation of the prefix
adder. The paper considers add/subtract, multiply,
\ldots{}",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
summary = "This paper demonstrates how IEEE 754 floating-point
standard compliant rounding can be merged with
carry-propagate addition in floating-point unit (FPU)
designs by using a novel adaptation of the prefix
adder. The paper considers add/subtract, multiply
\ldots{}",
}
@Article{Chakraborty:2005:BFP,
author = "M. Chakraborty and A. Mitra",
title = "A block floating-point realization of the gradient
adaptive lattice filter",
journal = j-IEEE-SIGNAL-PROCESS-LETT,
volume = "12",
number = "4",
pages = "265--268",
month = apr,
year = "2005",
CODEN = "ISPLEM",
ISSN = "1070-9908 (print), 1558-2361 (electronic)",
ISSN-L = "1070-9908",
bibdate = "Sat Jul 16 08:40:52 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Signal Processing Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
summary = "We present a novel scheme to implement the gradient
adaptive lattice (GAL) algorithm using block floating
point (BFP) arithmetic that permits processing of data
over a wide dynamic range at a cost significantly less
than that of a floating point (FP) \ldots{}",
}
@Article{Chang:2005:LCB,
author = "Ku-Young Chang and Dowon Hong and Hyun-Sook Cho",
title = "Low complexity bit-parallel multiplier for {$ {\rm
GF}(2^m) $} defined by all-one polynomials using
redundant representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "12",
pages = "1628--1630",
month = dec,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.199",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1524942",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Chaniotakis:2005:LNB,
author = "Eleftherios Chaniotakis and Paraskevas Kalivas and
Kiamal Pekmestzi",
title = "Long Number Bit-Serial Squarers",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-162.pdf",
abstract = "New bit serial squarers for long numbers in LSB first
form, are presented in this paper. The first presented
scheme is a 50\% operational efficient squarer than has
the half number of cells compared to the traditional
squarers. The second scheme is a 100\% operational
efficient squarer. In this scheme, the number of the
cells remain unchanged compared to other proposed
schemes but the number of the required registers is
reduced significantly. Both schemes are presented in
non-systolic and systolic form and are compared against
other squarers presented in the bibliography from the
aspect of hardware complexity.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Article{Chatterjee:2005:DEH,
author = "S. Chatterjee and L. R. Bachega and P. Bergner and K.
A. Dockser and J. A. Gunnels and M. Gupta and F. G.
Gustavson and C. A. Lapkowski and G. K. Liu and M.
Mendell and R. Nair and C. D. Wait and T. J. C. Ward
and P. Wu",
title = "Design and exploitation of a high-performance {SIMD}
floating-point unit for {Blue Gene/L}",
journal = j-IBM-JRD,
volume = "49",
number = "2/3",
pages = "377--391",
month = "????",
year = "2005",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Wed Jun 1 08:14:41 MDT 2005",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/492/chatterjee.pdf",
abstract = "We describe the design of a dual-issue
single-instruction, multiple-data-like (SIMD-like)
extension of the IBM PowerPC 440 floating-point unit
(FPU) core and the compiler and algorithmic techniques
to exploit it. This extended FPU is targeted at both
the IBM massively parallel Blue Gene/L machine and the
more pervasive embedded platforms. We discuss the
hardware and software codesign that was essential in
order to fully realize the performance benefits of the
FPU when constrained by the memory bandwidth
limitations and high penalties for misaligned data
access imposed by the memory hierarchy on a Blue Gene/L
node. Using both hand-optimized and compiled code for
key linear algebraic kernels, we validate the
architectural design choices, evaluate the success of
the compiler, and quantify the effectiveness of the
novel algorithm design techniques. Our measurements
show that the combination of algorithm, compiler, and
hardware delivers a significant fraction of peak
floating-point performance for compute-bound-kernels,
such as matrix multiplication, and delivers a
significant fraction of peak memory bandwidth for
memory-bound kernels, such as DAXPY, while remaining
largely insensitive to data alignment.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
ordernumber = "G322-0240",
}
@InProceedings{Choi:2005:PPA,
author = "Youngmoon Choi and Earl Swartzlander",
title = "Parallel Prefix Adder Design with Matrix
Representation",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-107.pdf",
abstract = "This paper presents a one-shot batch process that
generates a wide range of designs for a group of
parallel prefix adders. The prefix adders are
represented by two two-dimensional matrixes and two
vectors. This matrix representation makes it possible
to compose two functions for gate sizing which
calculate the delay and the total transistor width of
the carry propagation graph of adders. After gate
sizing, the critical path net-lists of the carry
propagation graph are generated from the matrix
representation for spice delay calculation. The process
is illustrated by generating sets of delay and total
transistor width pairs for 32-bit and 64-bit cases.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "9",
}
@Article{Cotofana:2005:ARA,
author = "Sorin Cotofana and Casper Lageweg and Stamatis
Vassiliadis",
title = "Addition Related Arithmetic Operations via Controlled
Transport of Charge",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "243--256",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.40",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0243abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0243.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0243.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388190.pdf?isnumber=30205&prod=JNL&arnumber=1388190&arSt=+243&ared=+256&arAuthor=Cotofana%2C+S.%3B+Lageweg%2C+C.%3B+Vassiliadis%2C+S.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388190&count=13&index=1;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388190",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@TechReport{Cowlishaw:2005:GDA,
author = "Mike Cowlishaw",
title = "General Decimal Arithmetic Specification",
type = "Report",
number = "Version 1.50",
institution = "IBM UK Laboratories",
address = "Hursley, UK",
pages = "iii + 63",
day = "9",
month = dec,
year = "2005",
bibdate = "Thu Mar 02 10:58:02 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www2.hursley.ibm.com/decimal/decarith.pdf;
http://www2.hursley.ibm.com/decimal/decarith.ps",
abstract = "This document defines a general purpose decimal
arithmetic. A correct implementation of this
specification is a decimal arithmetic which conforms to
the requirements of the IEEE standard 854-1987, while
supporting integer and unrounded floating-point
arithmetic as subsets.
Appendix A describes a simplified subset of the full
arithmetic which implements the decimal floating-point
arithmetic defined in ANSI Standard X3.274-1996 (the
REXX programming language) (this provides the model for
the unrounded floating-point rules). Appendix B
summarizes the design concepts behind the decimal
arithmetic. Appendix C lists the changes to this
specification.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; decimal floating-point arithmetic",
}
@Article{Daneshbeh:2005:CUB,
author = "Amir K. Daneshbeh and M. Anwar Hasan",
title = "A Class of Unidirectional Bit Serial Systolic
Architectures for Multiplicative Inversion and Division
over {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "370--380",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.35",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0370abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0370.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0370.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388201.pdf?isnumber=30205&prod=JNL&arnumber=1388201&arSt=+370&ared=+380&arAuthor=Daneshbeh%2C+A.K.%3B+Hasan%2C+M.A.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388201&count=13&index=12;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388201",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@Article{Danysh:2005:AIV,
author = "Albert Danysh and Dimitri Tan",
title = "Architecture and Implementation of a Vector\slash
{SIMD} Multiply-Accumulate Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "284--293",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.41",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0284abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0284.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0284.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388193.pdf?isnumber=30205&prod=JNL&arnumber=1388193&arSt=+284&ared=+293&arAuthor=Danysh%2C+A.%3B+Tan%2C+D.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388193&count=13&index=4;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388193",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@Manual{Daramy-Loirat:2005:CLL,
author = "Catherine Daramy-Loirat and David Defour and Florent
de Dinechin and Matthieu Gallet and Nicolas Gast and
Jean-Michel Muller",
title = "{CR-LIBM}: a library of correctly rounded elementary
functions in double-precision",
organization = "Laboratoire de l'Informatique du Parall{\'e}lisme",
address = "Lyon, France",
pages = "138",
day = "16",
month = sep,
year = "2005",
bibdate = "Thu Dec 15 16:27:30 2005",
bibsource = "http://lipforge.ens-lyon.fr/projects/crlibm/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://lipforge.ens-lyon.fr/frs/download.php/11/crlibm.pdf",
abstract = "The crlibm project aims at developing a portable,
proven, correctly rounded, and efficient mathematical
library ({\tt libm}) for double precision. Current libm
implementations do not always return the floating-point
number that is closest to the exact mathematical
result. As a consequence, different libm
implementations will return different results for the
same input, which prevents full portability of
floating-point applications. In addition, few libraries
support but the round-to-nearest mode of the
IEEE754/IEC 60559 standard for floating-point
arithmetic (hereafter usually referred to as the
IEEE-754 standard). crlibm provides the four rounding
modes: To nearest, to $ + \infty $ , to $ - \infty $
and to zero.",
acknowledgement = ack-nhfb,
}
@InProceedings{Daumas:2005:GPU,
author = "Marc Daumas and Guillaume Melquiond and C{\'e}sar
Mu{\~n}oz",
title = "Guaranteed Proofs Using Interval Arithmetic",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-155.pdf",
abstract = "This paper presents a set of tools for mechanical
reasoning of numerical bounds using interval
arithmetic. The tools implement two techniques for
reducing decorrelation: interval splitting and Taylor's
series expansions. Although the tools are designed for
the proof assistant system PVS, expertise on PVS is not
required. The ultimate goal of the tools is to provide
guaranteed proofs of numerical properties with a
minimal human-theorem prover interaction.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Article{deDinechin:2005:MTM,
author = "Florent de Dinechin and Arnaud Tisserand",
title = "Multipartite Table Methods",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "319--330",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.54",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0319abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0319.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0319.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388196.pdf?isnumber=30205&prod=JNL&arnumber=1388196&arSt=+319&ared=+330&arAuthor=de+Dinechin%2C+F.%3B+Tisserand%2C+A.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388196&count=13&index=7;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388196",
abstract = "A unified view of most previous
table-lookup-and-addition methods (bipartite tables,
SBTM, STAM, and multipartite methods) is presented.
This unified view allows a more accurate computation of
the error entailed by these methods, which enables a
wider design space exploration, leading to tables
smaller than the best previously published ones by up
to 50 percent. The synthesis of these multipartite
architectures on Virtex FPGAs is also discussed.
Compared to other methods involving multipliers, the
multipartite approach offers the best speed/area
tradeoff for precisions up to 16 bits. A reference
implementation is available at
http://www.ens-lyon.fr/LIP/Arenaire/.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@InProceedings{deDinechin:2005:TPU,
author = "Florent de Dinechin and Alexey Ershov and Nicolas
Gast",
title = "Towards the Post-ultimate {\tt libm}",
crossref = "Montuschi:2005:PIS",
pages = "288--295",
year = "2005",
DOI = "https://doi.org/10.1109/ARITH.2005.46",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-165.pdf",
abstract = "This article presents advances on the subject of
correctly rounded elementary functions since the
publication of the {\tt libultim} mathematical library
developed by Ziv at IBM. This library showed that the
average performance and memory overhead of correct
rounding could be made negligible. However, the
worst-case overhead was still a factor 1000 or more. It
is shown here that, with current processor technology,
this worst-case overhead can be kept within a factor of
2 to 10 of current best libms. This low overhead has
very positive consequences on the techniques for
implementing and proving correctly rounded functions,
which are also studied. These results lift the last
technical obstacles to a generalisation of (at least
some) correctly rounded double precision elementary
functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; correct rounding; floating-point
arithmetic",
pagecount = "8",
}
@InProceedings{Dou:2005:BFP,
author = "Y. Dou and S. Vassiliadis and G. K. Kuzmanov and G. N.
Gaydadjiev",
title = "64-bit floating-point {FPGA} matrix multiplication",
crossref = "ACM:2005:FAS",
pages = "86--95",
year = "2005",
DOI = "https://doi.org/10.1145/1046192.1046204",
bibdate = "Sat Oct 9 12:38:44 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We introduce a 64-bit ANSI/IEEE Std 754-1985 floating
point design of a hardware matrix multiplier optimized
for FPGA implementations. A general block matrix
multiplication algorithm, applicable for an arbitrary
matrix size is proposed. The algorithm potentially
enables optimum performance by exploiting the data
locality and reusability incurred by the general matrix
multiplication scheme and considering the limitations
of the I/O bandwidth and the local storage volume. We
implement a scalable linear array of processing
elements (PE) supporting the proposed algorithm in the
Xilinx Virtex II Pro technology. Synthesis results
confirm a superior performance-area ratio compared to
related recent works. Assuming the same FPGA chip, the
same amount of local memory, and the same I/O
bandwidth, our design outperforms related proposals by
at least 1.7X and up to 18X consuming the least
reconfigurable resources. A total of 39 PEs can be
integrated into the xc2vp125-7 FPGA, reaching
performance of, e.g., 15.6 GFLOPS with 1600 KB local
memory and 400 MB/s external memory bandwidth.",
acknowledgement = ack-nhfb,
}
@Article{Efstathiou:2005:EDM,
author = "C. Efstathiou and H. T. Vergos and G. Dimitrakopoulos
and D. Nikolos",
title = "Efficient diminished-$1$ modulo $ 2^n + 1 $
multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "4",
pages = "491--496",
month = apr,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.63",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1401868",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Eggert:2005:PEN,
author = "P. R. Eggert and D. S. Parker",
title = "Perturbing and evaluating numerical programs without
recompilation --- the wonglediff way",
journal = j-SPE,
volume = "35",
number = "4",
pages = "313--322",
day = "10",
month = apr,
year = "2005",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.637",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat Apr 16 07:26:37 MDT 2005",
bibsource = "http://www.interscience.wiley.com/jpages/0038-0644;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "wonglediff is a program that tests the sensitivity of
arbitrary program executables or processes to changes
that are introduced by a process that runs in parallel.
On Unix and Linux kernels, wonglediff creates a
supervisor process that runs applications and, on the
fly, introduces desired changes to their process state.
When execution terminates, it then summarizes the
resulting changes in the output files. The technique
employed has a variety of uses. This paper describes an
implementation of wonglediff that checks the
sensitivity of programs to random changes in the
floating-point rounding modes. It runs a program
several times, wongling it each time: randomly toggling
the IEEE-754 rounding mode of the program as it
executes. By comparing the resulting output, one gets a
poor man's numerical stability analysis for the
program. Although the analysis does not give any kind
of guarantee about a program's stability, it can reveal
genuine instability, and it does serve as a
particularly useful and revealing idiot light. In our
implementation, differences among the output files from
the program's multiple runs are summarized in a report.
This report is in fact an HTML version of the output
file, with inline mark-up summarizing individual
differences among the multiple instances. When viewed
with a browser, the differences can be highlighted or
rendered in many different ways.",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "diff; IEEE-754 floating point arithmetic; numerical
instability checking; random rounding; rounding modes;
sensitivity analysis",
onlinedate = "21 Dec 2004",
}
@Article{Eleftheriou:2005:SFF,
author = "M. Eleftheriou and B. G. Fitch and A. Rayshubskiy and
T. J. C. Ward and R. S. Germain",
title = "Scalable framework for {$3$D} {FFTs} on the {Blue
Gene/L} supercomputer: Implementation and early
performance measurements",
journal = j-IBM-JRD,
volume = "49",
number = "2/3",
pages = "457--464",
month = "????",
year = "2005",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Wed Jun 1 08:14:41 MDT 2005",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/492/eleftheriou.pdf",
abstract = "This paper presents results on a
communications-intensive kernel, the three-dimensional
fast Fourier transform (3D FFT), running on the
2,048-node Blue Gene/L (BG/L) prototype. Two
implementations of the volumetric FFT algorithm were
characterized, one built on the Message Passing
Interface library and another built on an active packet
Application Program Interface supported by the hardware
bring-up environment, the BG/L advanced diagnostics
environment. Preliminary performance experiments on the
BG/L prototype indicate that both of our
implementations scale well up to 1,024 nodes for $3$D
FFTs of size $ 128 \time 128 \times 128 $. The
performance of the volumetric FFT is also compared with
that of the Fastest Fourier Transform in the West
(FFTW) library. In general, the volumetric FFT
outperforms a port of the FFTW Version 2.1.5 library on
large-node-count partitions.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
ordernumber = "G322-0240",
}
@Article{Enenkel:2005:CMF,
author = "R. F. Enenkel and B. G. Fitch and R. S. Germain and F.
G. Gustavson and A. Martin and M. Mendell and J. W.
Pitera and M. C. Pitman and A. Rayshubskiy and F. Suits
and W. C. Swope and T. J. C. Ward",
title = "Custom math functions for molecular dynamics",
journal = j-IBM-JRD,
volume = "49",
number = "2/3",
pages = "465--474",
month = "????",
year = "2005",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Wed Jun 1 08:14:41 MDT 2005",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/492/enenkel.pdf",
abstract = "While developing the protein folding application for
the IBM Blue Gene/L supercomputer, some frequently
executed computational kernels were encountered. These
were significantly more complex than the linear algebra
kernels that are normally provided as tuned libraries
with modern machines. Using regular library functions
for these would have resulted in an application that
exploited only 5--10\% of the potential floating-point
throughput of the machine. This paper is a tour of the
functions encountered; they have been expressed in C++
(and could be expressed in other languages such as
Fortran or C). With the help of a good optimizing
compiler, floating-point efficiency is much closer to
100\%. The protein folding application was initially
run by the life science researchers on IBM POWER3e
machines while the computer science researchers were
designing and bringing up the Blue Gene/L hardware.
Some of the work discussed resulted in enhanced
compiler optimizations, which now improve the
performance of floating-point-intensive applications
compiled by the IBM VisualAgent series of compilers for
POWER3, POWER4e, POWER4+, and POWER5. The
implementations are offered in the hope that they may
help in other implementations of molecular dynamics or
in other fields of endeavor, and in the hope that
others may adapt the ideas presented here to deliver
additional mathematical functions at high throughput.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
ordernumber = "G322-0240",
}
@InProceedings{Erle:2005:DME,
author = "Mark Erle and Eric Schwarz and Michael Schulte",
title = "Decimal Multiplication With Efficient Partial Product
Generation",
crossref = "Montuschi:2005:PIS",
pages = "21--28",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-183.pdf;
http://mesa.ece.wisc.edu/publications/cp_2005-07.pdf",
abstract = "Decimal multiplication is important in many commercial
applications including financial analysis, banking, tax
calculation, currency conversion, insurance, and
accounting. This paper presents a novel design for
fixed-point decimal multiplication that utilizes a
simple recoding scheme to produce signed-magnitude
representations of the operands thereby greatly
simplifying the process of generating partial products
for each multiplier digit. The partial products are
generated using a digit-by-digit multiplier on a
word-by-digit basis, first in a signed-digit form with
two digits per position, and then combined via a
combinational circuit. As the signed-digit partial
products are developed one at a time while traversing
the recoded multiplier operand from the least
significant digit to the most significant digit, each
partial product is added along with the accumulated sum
of previous partial products via a signed-digit adder.
This work is significantly different from other work
employing digit-by-digit multipliers due to the
efficiency gained by restricting the range of digits
throughout the multiplication process.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; decimal floating-point arithmetic",
pagecount = "8",
}
@InProceedings{Etiemble:2005:CBF,
author = "D. Etiemble and S. Bouaziz and L. Lacassagne",
title = "Customizing 16-bit floating point instructions on a
{NIOS II} processor for {FPGA} image and media
processing",
crossref = "IEEE:2005:PWE",
pages = "61--66",
year = "2005",
DOI = "https://doi.org/10.1109/ESTMED.2005.1518073",
bibdate = "Sat Oct 9 12:40:19 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We have implemented customized SIMD 16-bit floating
point instructions on a NIOS II processor. On several
image processing and media benchmarks for which the
accuracy and dynamic range of this format is
sufficient, a speed-up ranging from 1.5 to more than 2
is obtained versus the integer implementation. The
hardware overhead remains limited and is compatible
with the capacities of today's FPGAs.",
acknowledgement = ack-nhfb,
}
@Article{Even:2005:PEA,
author = "Guy Even and Peter-M. Seidel and Warren E. Ferguson",
title = "A parametric error analysis of {Goldschmidt}'s
division algorithm",
journal = j-J-COMP-SYS-SCI,
volume = "70",
number = "1",
pages = "118--139",
month = feb,
year = "2005",
CODEN = "JCSSBM",
DOI = "https://doi.org/10.1016/j.jcss.2004.08.004",
ISSN = "0022-0000 (print), 1090-2724 (electronic)",
ISSN-L = "0022-0000",
bibdate = "Tue Jan 29 15:26:56 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcompsyssci.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0022000004000960",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computer and System Sciences",
journal-URL = "http://www.sciencedirect.com/science/journal/00220000",
}
@Article{Fan:2005:FBP,
author = "Haining Fan and Yiqi Dai",
title = "Fast bit-parallel {$ \mathrm {GF}(2^n) $} multiplier
for all trinomials",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "4",
pages = "485--490",
month = apr,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.64",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1401867",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fit-Florea:2005:ABE,
author = "A. Fit-Florea and D. W. Matula and M. A. Thornton",
title = "Addition-based exponentiation modulo $ 2^k $",
journal = j-ELECT-LETTERS,
volume = "41",
number = "2",
pages = "56--57",
day = "20",
month = jan,
year = "2005",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:20057538",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Jun 24 15:17:52 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/iel5/2220/30332/01393468.pdf",
abstract = "A novel method for performing exponentiation modulo $
2^k $ is described. The algorithm has a critical path
consisting of $k$ dependent shift-and-add modulo $ 2^k
$ operations. Although $3$ is the preferred exponent
base, the algorithm can be extended easily in order to
perform the general binary powering operation.",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}
@TechReport{Fousse:2005:MMP,
author = "Laurent Fousse and Guillaume Hanrot and Vincent
Lef{\`e}vre and Patrick P{\'e}lissier and Paul
Zimmermann",
title = "{MPFR}: a Multiple-Precision Binary Floating-Point
Library With Correct Rounding",
type = "Technical Report",
number = "RR-5753",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "15",
month = nov,
year = "2005",
bibdate = "Sun Sep 10 07:26:55 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5753.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-5753.ps.gz;
http://www.inria.fr/rrrt/rr-5753.html",
abstract = "This paper presents a multiple-precision binary
floating-point library, written in the ISO C language,
and based on the GNU MP library. Its particularity is
to extend ideas from the IEEE-754 standard to arbitrary
precision, by providing correct rounding",
acknowledgement = ack-nhfb,
}
@Article{Fraysse:2005:ASG,
author = "Val{\'r}ie Frayss{\'e} and Luc Giraud and Serge
Gratton and Julien Langou",
title = "{Algorithm 842}: a set of {GMRES} routines for real
and complex arithmetics on high performance computers",
journal = j-TOMS,
volume = "31",
number = "2",
pages = "228--238",
month = jun,
year = "2005",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1067967.1067970",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jun 21 16:55:57 MDT 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this article we describe our implementations of the
GMRES algorithm for both real and complex, single and
double precision arithmetics suitable for serial,
shared memory and distributed memory computers. For the
sake of portability, simplicity, flexibility and
efficiency the GMRES solvers have been implemented in
Fortran 77 using the reverse communication mechanism
for the matrix-vector product, the preconditioning and
the dot product computations. For distributed memory
computation, several orthogonalization procedures have
been implemented to reduce the cost of the dot product
calculation, which is a well-known bottleneck of
efficiency for the Krylov methods. Either implicit or
explicit calculation of the residual at restart are
possible depending on the actual cost of the
matrix-vector product. Finally the implemented stopping
criterion is based on a normwise backward error.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@TechReport{Giles:2005:BLN,
author = "David E. Giles",
title = "{Benford's Law} and Naturally Occurring Prices in
Certain {ebaY} Auctions",
type = "Econometrics Working Paper",
number = "EWP0505",
institution = "Department of Economics, University of Victoria",
address = "Victoria, BC, Canada",
month = may,
year = "2005",
ISSN = "1485-6441",
bibdate = "Thu Feb 15 16:24:39 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://web.uvic.ca/econ/ewp0505.pdf",
abstract = "We show that certain the winning bids for certain ebaY
auctions obey Benford's Law. One implication of this is
that it is unlikely that these bids are subject to
collusion among bidders, or ``shilling'' on the part of
sellers. Parenthetically, we also show that numbers
from the naturally occurring Fibonacci and Lucas
sequences also obey Benford's Law.",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}
@Article{Giraud:2005:REA,
author = "Luc Giraud and Julien Langou and Miroslav
Rozlozn{\'\i}k and Jasper van den Eshof",
title = "Rounding error analysis of the classical
{Gram--Schmidt} orthogonalization process",
journal = j-NUM-MATH,
volume = "101",
number = "1",
pages = "87--100",
month = jul,
year = "2005",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-005-0615-4",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F25, 65G50, 15A23",
bibdate = "Tue Oct 11 18:59:06 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=101&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=101&issue=1&spage=87",
abstract = "This paper provides two results on the numerical
behavior of the classical Gram--Schmidt algorithm. The
first result states that, provided the normal equations
associated with the initial vectors are numerically
nonsingular, the loss of orthogonality of the vectors
computed by the classical Gram--Schmidt algorithm
depends quadratically on the condition number of the
initial vectors. The second result states that,
provided the initial set of vectors has numerical full
rank, two iterations of the classical Gram--Schmidt
algorithm are enough for ensuring the orthogonality of
the computed vectors to be close to the unit roundoff
level.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Glusker:2005:TCM,
author = "Mark Glusker and David M. Hogan and Pamela Vass",
title = "The Ternary Calculating Machine of {Thomas Fowler}",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "27",
number = "3",
pages = "4--22",
month = jul # "\slash " # sep,
year = "2005",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/MAHC.2005.49",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Mon Nov 7 18:51:49 MST 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In 1840, Thomas Fowler, a self-taught English
mathematician and inventor, created a unique ternary
calculating machine. Until recently, all detail of this
machine was lost. A research project begun in 1997
uncovered sufficient information to enable the
recreation of a physical concept model of Fowler's
machine. The next step is to create a historically
accurate replica.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
keywords = "19th century; Augustus De Morgan; balanced ternary;
base-3; calculating machine; historical reconstruction;
signed ternary; ternary; Thomas Fowler",
}
@TechReport{Graillat:2005:CHS,
author = "S. Graillat and P. Langlois and N. Louvet",
title = "Compensated {Horner} Scheme",
type = "Research Report",
number = "RR2005-04",
institution = "{\'E}quipe de Recherche DALI, Laboratoire LP2A,
Universit{\'e} de Perpignan, Via Domitia",
address = "Perpignan, France",
pages = "ii + 25",
day = "24",
month = jul,
year = "2005",
bibdate = "Fri Jan 06 07:45:03 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://gala.univ-perp.fr/~graillat/papers/rr2005-04.pdf",
abstract = "We present a compensated Horner scheme, that is an
accurate and fast algorithm to evaluate univariate
polynomials in floating point arithmetic. The accuracy
of the computed result is similar to the one given by
the Horner scheme computed in twice the working
precision. This compensated Horner scheme runs at least
as fast as existing implementations producing the same
output accuracy. We also propose to compute in pure
floating point arithmetic a valid error estimate that
bound the actual accuracy of the compensated
evaluation. Numerical experiments involving
ill-conditioned polynomials illustrate these results.
All algorithms are performed at a given working
precision and are portable assuming the floating point
arithmetic satisfies the IEEE-754 standard.",
acknowledgement = ack-nhfb,
amsclass = "65G, 65Y99",
keywords = "compensated Horner scheme; error-free transformations;
extended precision; IEEE-754 floating point arithmetic;
polynomial evaluation; running error bound",
}
@TechReport{Graillat:2005:ICH,
author = "S. Graillat and P. Langlois and N. Louvet",
title = "Improving the compensated {Horner} scheme with a fused
multiply and add",
type = "Research Report",
number = "RR2005-05",
institution = "{\'E}quipe de Recherche DALI, Laboratoire LP2A,
Universit{\'e} de Perpignan, Via Domitia",
address = "Perpignan, France",
month = nov,
year = "2005",
bibdate = "Sat Feb 26 18:45:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Guizzo:2005:IRS,
author = "E. Guizzo",
title = "{IBM} reclaims supercomputer lead",
journal = j-IEEE-SPECTRUM,
volume = "42",
number = "2",
pages = "15--16",
month = feb,
year = "2005",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2005.1389501",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Sep 01 16:25:09 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "70 Tflops; floating-point arithmetic; IBM Glue
Gene/L",
}
@InProceedings{Haijun:2005:ROT,
author = "Sun Haijun and Shao Zhibiao and Zom Gang and Zhao
Ning",
booktitle = "Proceedings of {2005 IEEE International Workshop on
VLSI Design and Video Technology, 28--30 May 2005}",
title = "The research on optimization techniques of 32-bit
floating-point {RISC} microprocessor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "63--66",
year = "2005",
DOI = "https://doi.org/10.1109/iwvdvt.2005.1504465",
bibdate = "Wed Dec 13 09:49:47 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "XJ-1 processor",
}
@Book{Hally:2005:EBS,
author = "Mike Hally",
title = "Electronic Brains: Stories from the Dawn of the
Computer Age",
publisher = pub-JOSEPH-HENRY,
address = pub-JOSEPH-HENRY:adr,
pages = "xxiii + 275",
year = "2005",
ISBN = "0-309-09630-8 (hardcover)",
ISBN-13 = "978-0-309-09630-0 (hardcover)",
LCCN = "QA76.17 .H35 2005",
bibdate = "Wed Aug 9 07:02:58 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://catdir.loc.gov/catdir/toc/ecip0514/2005016583.html;
http://library.ccsu.edu/help/spcoll/oconnell/index.htm",
abstract = "By the 1960s, IBM, once a manufacturer of mechanical
tabulators, had beaten all rivals and dominated the
world computer market. But IBM came late to the race.
From the 1930s to the 1950s, small independent teams on
four continents worked on the development of the very
first modern computers --- practical, electronic,
multipurpose, digital machines with memory for data and
programs. From interviews with surviving members of
those original pioneering teams, the author builds up a
picture of the eccentric, obsessive and fiercely loyal
men and women who laid the foundations for the
computerized world we now live in, and re-creates the
atmosphere of those early days.",
acknowledgement = ack-nhfb,
subject = "Computers; History; Ordinateurs; Histoire; Computers.;
Computers.",
tableofcontents = "From ABC to ENIAC \\
UNIVAC \\
Saviour of the Census \\
Saluting the Moose \\
When Britain Led the Computing World \\
LEO the Lyons Computer \\
So Then We Took the Roof Off \\
Wizards of Oz \\
Water on the Brain \\
It's Not About Being First: the Rise and Rise of IBM
\\
Arithmetic \\
Technical bits",
}
@Book{Hanss:2005:AFA,
author = "Michael Hanss",
title = "Applied fuzzy arithmetic: an introduction with
engineering applications",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 256",
year = "2005",
ISBN = "3-540-24201-5",
ISBN-13 = "978-3-540-24201-7",
LCCN = "QA248.5 .H36 2005",
bibdate = "Mon Oct 29 18:21:47 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0662/2004117177-d.html",
acknowledgement = ack-nhfb,
subject = "Fuzzy arithmetic; Fuzzy logic",
}
@InProceedings{Hariri:2005:SMS,
author = "A. Hariri and K. Navi and R. Rastegar",
booktitle = "{EUROCON 2005, The International Conference on
``Computer as a Tool'': proceedings: Belgrade, Serbia
and Montenegro: November 21--24, 2005}",
title = "A Simplified Modulo $ (2^n - 1) $ Squaring Scheme for
Residue Number System",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "615--618",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1109/EURCON.2005.1630004",
ISBN = "1-4244-0049-X",
ISBN-13 = "978-1-4244-0049-2",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue Number System (RNS) is a valuable tool for
fast and parallel arithmetic and has a variety of
applications in digital signal processing, fault
tolerant systems, etc. One of the most fundamental
moduli in Residue Number System is modulo (2
\ldots{})",
}
@InProceedings{Harris:2005:IUS,
author = "David Harris and Ram Krishnamurthy and Mark Anders and
Sanu Mathew and Steven Hsu",
title = "An Improved Unified Scalable Radix-$2$ {Montgomery}
Multiplier",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-109.pdf",
abstract = "This paper describes an improved version of the
Tenca-Ko{\c{c}} unified scalable radix-2 Montgomery
multiplier with half the latency for small and moderate
precision operands and half the queue memory
requirement. Like the Tenca-Ko{\c{c}} multiplier, this
design is reconfigurable to accept any input precision
in either $ \mathrm {GF}(p) $ or $ \mathrm {GF}(2 n) $
up to the size of the on-chip memory. An FPGA
implementation can perform 1024-bit modular
exponentiation in 16 ms using 5598 4-input lookup
tables, making it the fastest unified scalable design
yet reported.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "7",
}
@InProceedings{He:2005:MAF,
author = "Hu He and Zheng Li and Yihe Sun",
title = "Multiply-add fused float point unit with on-fly
denormalized number processing",
crossref = "IEEE:2005:MSC",
pages = "1466--1468",
year = "2005",
DOI = "https://doi.org/10.1109/MWSCAS.2005.1594389",
bibdate = "Sun Feb 20 10:45:46 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Denormalized numbers are the most difficult type of
numbers to implement in float-point units. They are so
complex that many designs avoid handling them in
hardware. The denormalized number processing cost two
much extra clock cycle in software implementation. In
this paper, an on-fly floating point denormalized
number processing implemented in a multiply-add-fused
(MAF) with little extra latency is presented. The
denormalized number processing is embedded in a popular
MAF data path and fused with the MAF smoothly by
representing the denormalized number. The extra latency
introduced by the denormalized number processing is
cost by the denormalized number detection.",
acknowledgement = ack-nhfb,
}
@Article{Hernandez:2005:ACN,
author = "M. A. Hern{\'a}ndez and N. Romero",
title = "Accelerated convergence in {Newton}'s method for
approximating square roots",
journal = j-J-COMPUT-APPL-MATH,
volume = "177",
number = "1",
pages = "225--229",
day = "1",
month = may,
year = "2005",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:00:04 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042704004315",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InCollection{Huang:2005:EMP,
author = "Liusheng Huang and Hong Zhong and Hong Shen and
Yonglong Luo",
editor = "Hong Shen and Koji Nakano",
booktitle = "{Sixth International Conference on Parallel and
Distributed Computing, Applications and Technologies,
2005. PDCAT 2005: 5--8 December 2005, Dalian, China}",
title = "An Efficient Multiple-Precision Division Algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xxvi + 1091",
pages = "971--974",
year = "2005",
DOI = "https://doi.org/10.1109/PDCAT.2005.79",
ISBN = "0-7695-2405-2",
ISBN-13 = "978-0-7695-2405-4",
LCCN = "QA76.58 .I5752 2005",
bibdate = "Mon Dec 09 14:30:16 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc2010.bib",
note = "The authors present an integer-division algorithm that
runs three to five times faster than Knuth's 1981
original. However, there is an error in the
renormalization algorithm that is corrected in
\cite{Mukhopadhyay:2014:EMP}, while retaining the
speedup.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=10544",
}
@Article{Huang:2005:HPL,
author = "Zhijun Huang and Milo{\v{s}} D. Ercegovac",
title = "High-Performance Low-Power Left-to-Right Array
Multiplier Design",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "272--283",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.51",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0272abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0272.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0272.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388192.pdf?isnumber=30205&prod=JNL&arnumber=1388192&arSt=+272&ared=+283&arAuthor=Zhijun+Huang%3B+Ercegovac%2C+M.D.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388192&count=13&index=3;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388192",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@InProceedings{Jacobi:2005:AFV,
author = "C. Jacobi and K. Weber and V. Paruthi and J.
Baumgartner",
title = "Automatic formal verification of fused-multiply-add
{FPUs}",
crossref = "IEEE:2005:DAT",
volume = "2",
pages = "1298--1303",
year = "2005",
DOI = "https://doi.org/10.1109/DATE.2005.75",
bibdate = "Sun Feb 20 09:57:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we describe a fully-automated
methodology for formal verification of
fused-multiply-add floating point units (FPU). Our
methodology verifies an implementation FPU against a
simple reference model derived from the processor's
architectural specification, which may include all
aspects of the IEEE specification including denormal
operands and exceptions. Our strategy uses a
combination of BDD- and SAT-based symbolic simulation.
To make this verification task tractable, we use a
combination of case-splitting, multiplier isolation,
and automatic model reduction techniques. The
case-splitting is defined only in terms of the
reference model, which makes this approach easily
portable to new designs. The methodology is directly
applicable to multi-GHz industrial implementation
models (e.g., HDL or gate-level circuit
representations) that contain all details of the
high-performance transistor-level model, such as
aggressive pipelining, clocking, etc. Experimental
results are provided to demonstrate the computational
efficiency of this approach.",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:2005:BTG,
author = "William Kahan",
title = "A Brief Tutorial on Gradual Underflow",
howpublished = "World-Wide Web lecture notes.",
pages = "15",
day = "8",
month = jul,
year = "2005",
bibdate = "Fri Jul 15 11:38:13 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Prepared for ARITH 17, Tues. 28 June 2005, and
subsequently augmented.",
URL = "http://www.cs.berkeley.edu/~wkahan/ARITH_17U.pdf",
acknowledgement = ack-nhfb,
}
@Manual{Kahan:2005:DP,
author = "William Kahan",
title = "A Demonstration of Presubstitution for $ \infty /
\infty $",
pages = "10",
day = "5",
month = jul,
year = "2005",
bibdate = "Fri Jul 15 11:47:46 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.berkeley.edu/~wkahan/Grail.pdf",
acknowledgement = ack-nhfb,
}
@Misc{Kahan:2005:FPA,
author = "William Kahan",
title = "Floating-Point Arithmetic Besieged by {``Business}
Decisions''",
howpublished = "World-Wide Web lecture notes.",
pages = "28",
day = "5",
month = jul,
year = "2005",
bibdate = "Fri Jul 15 12:07:31 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "A Keynote Address, prepared for the IEEE-Sponsored
ARITH 17 Symposium on Computer Arithmetic, delivered on
Mon. 27 June 2005 in Hyannis, Massachusetts.",
URL = "http://www.cs.berkeley.edu/~wkahan/ARITH_17.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kahan:2005:OQD,
author = "William Kahan and Dan Zuras",
title = "An Open Question to Developers of Numerical Software",
journal = j-COMPUTER,
volume = "38",
number = "5",
pages = "91--94",
month = may,
year = "2005",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Wed May 04 15:33:06 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/mags/co/2005/05/r5091abs.htm;
http://csdl.computer.org/comp/mags/co/2005/05/r5toc.htm;
http://csdl.computer.org/dl/mags/co/2005/05/r5091.pdf",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
subject = "Are signaling NaNs needed?",
}
@Article{Kaihara:2005:HAM,
author = "M. E. Kaihara and N. Takagi",
title = "A hardware algorithm for modular multiplication\slash
division",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "1",
pages = "12--21 54",
month = jan,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.1(410)",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:14 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1362636",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Karlsson:2005:IIL,
author = "Kent Karlsson",
title = "{ISO\slash IEC 10967, Language Independent Arithmetic
(LIA)}",
howpublished = "Wikipedia article",
day = "31",
month = oct,
year = "2005",
bibdate = "Sat Dec 17 10:42:52 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://en.wikipedia.org/wiki/ISO/IEC_10967;
http://www.open-std.org/JTC1/SC22/WG11/docs/n364.pdf;
http://www.open-std.org/JTC1/SC22/WG11/docs/n462.pdf;
http://www.open-std.org/jtc1/sc22/wg11/docs/n490.pdf",
abstract = "ISO/IEC 10967, Language independent arithmetic (LIA),
is a series of standards on computer arithmetic. It is
compatible with IEC 60559 (more known as IEEE 754 or
IEC 559), and indeed much of the specifications in
parts 2 and 3 are for IEEE 754 special values (though
such values are not required).\par
LIA currently consists of three parts:\par
\begin{itemize}
\item[Part 1] Integer and floating point arithmetic,
first edition published 1994.
\item[Part 2] Elementary numerical functions, first
edition published 2001.
\item[Part 3] Complex integer and floating point
arithmetic and complex elementary numerical functions,
first edition is now (2005) in FDIS
stage.
\end{itemize}",
acknowledgement = ack-nhfb,
}
@Article{Kenney:2005:HSM,
author = "R. D. Kenney and M. J. Schulte",
title = "High-Speed Multioperand Decimal Adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "8",
pages = "953--963",
month = aug,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.129",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1453497;
http://mesa.ece.wisc.edu/publications/cp_2005-04.pdf",
abstract = "There is increasing interest in hardware support for
decimal arithmetic as a result of recent growth in
commercial, financial, and Internet-based applications.
Consequently, new specifications for decimal
floating-point arithmetic have been added to the draft
revision of the IEEE-754 Standard for Floating-Point
Arithmetic. This paper introduces and analyzes three
techniques for performing fast decimal addition on
multiple binary coded decimal (BCD) operands. Two of
the techniques speculate BCD correction values and
correct intermediate results while adding the input
operands. The first speculates over one addition. The
second speculates over two additions. The third
technique uses a binary carry-save adder tree and
produces a binary sum. Combinational logic is then used
to correct the sum and determine the carry into the
next more significant digit. Multioperand adder designs
are constructed and synthesized for four to 16 input
operands. Analyses are performed on the synthesis
results and the merits of each technique are discussed.
Finally, these techniques are compared to several
previous techniques for high-speed decimal addition.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "computer arithmetic; decimal arithmetic; decimal
floating-point arithmetic; hardware designs;
multioperand adders",
}
@Article{Khabbazian:2005:NMA,
author = "M. Khabbazian and T. A. Gulliver and V. K. Bhargava",
title = "A new minimal average weight representation for
left-to-right point multiplication methods",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "11",
pages = "1454--1459",
month = nov,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.173",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1514423",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Klarer:2005:DTC,
author = "Robert Klarer",
title = "Decimal Types for {C++}: Second Draft",
type = "Report",
number = "C22/WG21/N1839 J16/05-0099",
institution = "IBM Canada, Ltd.",
address = "Toronto, ON, Canada",
day = "24",
month = jun,
year = "2005",
bibdate = "Thu Mar 02 10:47:15 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1839.html",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Kornerup:2005:DSS,
author = "Peter Kornerup",
title = "Digit Selection for {SRT} Division and Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "294--303",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.47",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0294abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0294.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0294.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388194.pdf?isnumber=30205&prod=JNL&arnumber=1388194&arSt=+294&ared=+303&arAuthor=Kornerup%2C+P.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388194&count=13&index=5;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388194",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
summary = "The quotient digit selection in the SRT division
algorithm is based on a few most significant bits of
the remainder and divisor, where the remainder is
usually represented in a redundant representation. The
number of leading bits needed depends on \ldots{}",
}
@InProceedings{Kornerup:2005:LGD,
author = "Peter Kornerup and Jean-Michel Muller",
title = "Leading Guard Digits in Finite Precision Redundant
Representations",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Fri Jun 24 20:32:32 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.imada.sdu.dk/~kornerup/papers/red-add.pdf",
abstract = "Redundant number representations are generally used to
allow constant time additions, based on the fact that
only bounded carry-ripples take place. But carries may
ripple out into positions which may not be needed to
represent the final value of the result, and thus a
certain amount of leading guard digits are needed to
correctly determine the result. Also when cancellation
during subtractions occur, there may be nonzero digits
in positions not needed to represent the result of the
calculation. It is shown here that for normal redundant
digit sets with radix greater than two, a single guard
digit is sufficient to determine the value of such an
arbitrary length prefix of leading non-zero digits.
This is also the case for the unsigned carry-save
representation, whereas two guard digits are necessary
and sufficient for additions in the binary signed-digit
and 2's complement carry-save representations.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; Leading guard digits; Multi-operand
additions; Redundant representations",
pagecount = "6",
}
@InProceedings{Kornerup:2005:RCN,
author = "Peter Kornerup and Jean-Michel Muller",
booktitle = "Proceedings of the International Meeting on Automated
Compliance Systems {(IMACS'05)}, July 2005",
title = "{RN}-coding of numbers: Definition and some
properties",
publisher = "????",
address = "????",
pages = "??--??",
year = "2005",
bibdate = "Sun Jun 19 14:24:12 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.researchgate.net/publication/243786550_RN-coding_of_numbers_definition_and_some_properties",
acknowledgement = ack-nhfb,
}
@InProceedings{Kornerup:2005:SPR,
author = "Peter Kornerup and David Matula",
title = "Single Precision Reciprocals by Multipartite Table
Lookup",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-177.pdf",
abstract = "We develop the foundations for confirming monotonicity
of a multi-term reciprocal function approximation. We
introduce the concept of operand recoding to improve
the accuracy of multipartite approximation. The results
are applied to provide a proposed four-partite
reciprocal implementation with total table size $
\approx 27 $ Kbytes, that yields an IEEE standard,
single precision sized format (24 bit) reciprocal
instruction, that is a one-ulp monotonic reciprocal.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "9",
}
@Article{Kulikova:2005:CAS,
author = "A. A. Kulikova and Yu. V. Prokhorov",
title = "Completely Asymmetric Stable Laws and {Benford's
Law}",
journal = j-THEORY-PROBAB-APPL,
volume = "49",
number = "1",
pages = "163--169",
month = mar,
year = "2005",
CODEN = "TPRBAU",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Thu Jul 7 19:15:48 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/98094",
acknowledgement = ack-nhfb,
fjournal = "Theory of Probability and its Applications",
journal-URL = "http://epubs.siam.org/tvp",
keywords = "Benford's Law; Zipf's Law",
}
@Article{Lang:2005:HTC,
author = "Tom{\'a}s Lang and Elisardo Antelo",
title = "High-Throughput {CORDIC}-Based Geometry Operations for
{$3$D} Computer Graphics",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "347--361",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.53",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0347abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0347.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0347.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388199.pdf?isnumber=30205&prod=JNL&arnumber=1388199&arSt=+347&ared=+361&arAuthor=Lang%2C+T.%3B+Antelo%2C+E.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388199&count=13&index=10;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388199",
abstract = "Graphics processors require strong arithmetic support
to perform computational kernels over data streams.
Because of the current implementation using the basic
arithmetic operations, the algorithms are given in
algebraic terms. However, since the operations are
really of a geometric nature, it seems to us that more
flexibility in the implementation is obtained if the
description is given in a high-level geometrical form.
As a consequence of this line of thought, this paper is
an attempt to reconsider some kernels in a graphics
processor to obtain implementations that are
potentially more scalable than just replicating the
modules used in conventional implementations. We
present the formulation of representative 3D computer
graphics operations in terms of CORDIC-type primitives.
Then, we briefly outline a stream processor based on
CORDIC-type modules to efficiently implement these
graphic operations. We perform a rough comparison with
current implementations and conclude that the
CORDIC-based alternative might be attractive.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@TechReport{Langlois:2005:STS,
author = "P. Langlois and N. Louvet",
title = "Solving Triangular Systems More Accurately and
Efficiently",
type = "Research Report",
number = "RR2005-02",
institution = "{\'E}quipe de Recherche DALI, Laboratoire LP2A,
Universit{\'e} de Perpignan, Via Domitia",
address = "Perpignan, France",
pages = "15",
day = "9",
month = may,
year = "2005",
bibdate = "Fri Jan 06 07:54:13 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://webdali.univ-perp.fr/RR/rr2005-02.pdf",
abstract = "We present a new algorithm that solves linear
triangular systems accurately and efficiently. By
accurately, we mean that this algorithm should yield a
solution as accurate as the one computed in twice the
working precision. By efficiently, we mean that its
implementation should run faster than the corresponding
XBLAS routine with the same output accuracy.",
acknowledgement = ack-nhfb,
keywords = "error-free transformations; extended precision;
IEEE-754 floating point arithmetic; substitution
algorithm; triangular linear system; XBLAS",
}
@TechReport{Lauter:2005:BBB,
author = "Christoph Quirin Lauter",
title = "Basic building blocks for a triple-double intermediate
format",
type = "Technical Report",
number = "RR-5702",
institution = "Inria",
address = "????",
pages = "iii + 67 + i",
year = "2005",
bibdate = "Sat Apr 01 08:05:25 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hal.inria.fr/inria-00070314;
https://hal.inria.fr/inria-00070314/document",
abstract = "The implementation of correctly rounded elementary
functions needs high intermediate accuracy before final
rounding. This accuracy can be provided by (pseudo-)
expansions of size three, i.e. a triple-double format.
The report presents all basic operators for such a
format. Triple-double numbers can be redundant. A
renormalization procedure is presented and proven.
Elementary functions' implementations need addition and
multiplication sequences. These operators must take
operands in double, double-double and triple-double
format. The results must be accordingly in one of the
formats. Several procedures are presented. Proofs are
given for their accuracy bounds. Intermediate
triple-double results must finally be correctly rounded
to double precision. Two effective rounding sequences
are presented, one for round-to-nearest mode, one for
the directed rounding modes. Their complete proofs
constitute half of the report.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; floating-point arithmetic",
}
@Misc{Lawlor:2005:PDP,
author = "Orion Lawlor and Hari Govind and Isaac Dooley and
Michael Breitenfeld and Laxmikant Kale",
title = "Performance Degradation in the Presence of Subnormal
Floating-Point Values",
howpublished = "World-Wide Web slides from the Workshop on Operating
System Interfaces in High Performance Applications
2005",
year = "2005",
bibdate = "Sat Mar 04 17:10:07 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://charm.cs.uiuc.edu/presentations/OSIHPA/html/",
acknowledgement = ack-nhfb,
}
@Article{Lee:2005:LCB,
author = "Chiou-Yng Lee and Jenn-Shyong Horng and I-Chang Jou
and Erl-Huei Lu",
title = "Low-complexity bit-parallel systolic {Montgomery}
multipliers for special classes of {$ \mathrm {GF}(2^m)
$}",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "9",
pages = "1061--1070",
month = sep,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.147",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:18 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1471668",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lee:2005:OHF,
author = "D.-U. Lee and A. A. Gaffar and O. Mencer and W. Luk",
title = "Optimizing hardware function evaluation",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "12",
pages = "1520--1531",
month = dec,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.201",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:04:26 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a methodology and an automated system for
function evaluation unit generation. Our system selects
the best function evaluation hardware for a given
function, accuracy requirements, technology mapping,
and optimization metrics, such as area, throughput, and
latency. Function evaluation $ f(x) $ typically
consists of range reduction and the actual evaluation
on a small convenient interval such as $ [0, \pi / 2) $
for $ \sin (x) $. We investigate the impact of hardware
function evaluation with range reduction for a given
range and precision of $x$ and $ f(x) $ on area and
speed. An automated bit-width optimization technique
for minimizing the sizes of the operators in the data
paths is also proposed. We explore a vast design space
for fixed-point $ \sin (x) $, $ \log (x) $, and $ \sqrt
{x} $ accurate to one unit in the last place using
MATLAB and ASC, a stream compiler for
field-programmable gate arrays (FPGAs). In this study,
we implement over 2,000 placed-and-routed FPGA designs,
resulting in over 100 million application-specific
integrated circuit (ASIC) equivalent gates. We provide
optimal function evaluation results for range and
precision combinations between 8 and 48 bits.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "application specific integrated circuits;
application-specific integrated circuit equivalent
gates; ASC; ASIC; automated bit-width optimization
technique; circuit optimisation; computer arithmetic;
elementary function approximation; field programmable
gate arrays; field-programmable gate arrays; fixed
point arithmetic; fixed-point arithmetic; FPGA;
hardware function evaluation optimisation; logic
design; MATLAB; minimax approximation; range reduction;
stream compiler",
}
@Article{Lefevre:2005:GMP,
author = "Vincent Lef{\`e}vre",
title = "The Generic Multiple-Precision Floating-Point Addition
With Exact Rounding (as in the {MPFR} Library)",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "11",
month = may,
year = "2005",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/cs/0505027",
abstract = "We study the multiple-precision addition of two
positive floating-point numbers in base 2, with exact
rounding, as specified in the MPFR library, i.e. where
each number has its own precision. We show how the best
possible complexity (up to a constant factor that
depends on the implementation) can be obtain.",
acknowledgement = ack-nhfb,
subject = "Data Structures and Algorithms (cs.DS)",
}
@InProceedings{Lefevre:2005:NRD,
author = "Vincent Lef{\`e}vre",
title = "New Results on the Distance Between a Segment and {$
\mathbb {Z}^2 $}. Application to the Exact Rounding",
crossref = "Montuschi:2005:PIS",
pages = "68--75",
year = "2005",
DOI = "https://doi.org/10.1109/ARITH.2005.32",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-147.pdf",
abstract = "This paper presents extensions to Lef{\'e}vre's
algorithm that computes a lower bound on the distance
between a segment and a regular grid $ Z^2 $. This
algorithm and, in particular, the extensions are useful
in the search for worst cases for the exact rounding of
unary elementary functions or base-conversion
functions. The proof that is presented here is simpler
and less technical than the original proof. This paper
also gives benchmark results with various optimization
parameters, explanations of these results, and an
application to base conversion.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@InProceedings{Li:2005:HIA,
author = "L. Li and A. Fit-Florea and M. A. Thornton and D. W.
Matula",
title = "Hardware Implementation of an Additive Bit-Serial
Algorithm for the Discrete Logarithm Modulo-$ 2^k $",
crossref = "IEEE:2005:ICS",
pages = "??--??",
year = "2005",
bibdate = "Fri Jun 24 15:56:30 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2005:NBI,
author = "L. Li and A. Fit-Florea and M. A. Thornton and D. W.
Matula",
title = "A New Binary Integer Number System with Simplified
Hardware Support",
crossref = "IEEE:2005:PII",
pages = "??--??",
year = "2005",
bibdate = "Fri Jun 24 15:58:49 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Submitted.",
acknowledgement = ack-nhfb,
}
@Article{Li:2005:RPE,
author = "C. Li and S. Pion and C. K. Yap",
title = "Recent progress in exact geometric computation",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "85--111",
month = jul,
year = "2005",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.006",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
bibdate = "Thu Oct 17 10:09:18 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
remark = "Special issue on Practical development of exact real
number computation.",
}
@Article{Lorencz:2005:SFA,
author = "R{\'o}bert L{\'o}rencz and Josef Hlav{\'a}{\v{c}}",
title = "Subtraction-free {Almost Montgomery Inverse}
algorithm",
journal = j-INFO-PROC-LETT,
volume = "94",
number = "1",
pages = "11--14",
day = "15",
month = apr,
year = "2005",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Thu Mar 31 18:41:00 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Lorenz:2005:VTB,
author = "J. Lorenz and S. Kral and F. Franchetti and C. W.
Ueberhuber",
title = "Vectorization techniques for the {Blue Gene/L} double
{FPU}",
journal = j-IBM-JRD,
volume = "49",
number = "2/3",
pages = "437--446",
month = "????",
year = "2005",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Wed Jun 1 08:14:41 MDT 2005",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/492/lorenz.pdf",
abstract = "This paper presents vectorization techniques tailored
to meet the specifics of the two-way single-instruction
multiple-data (SIMD) double-precision floating-point
unit (FPU), which is a core element of the node
application-specific integrated circuit (ASIC) chips of
the IBM 360-teraflops Blue Gene/L supercomputer. This
paper focuses on the general-purpose basic-block
vectorization and optimization methods as they are
incorporated in the Vienna MAP vectorizer and
optimizer. The innovative technologies presented here,
which have consistently delivered superior performance
and portability across a wide range of platforms, were
carried over to prototypes of Blue Gene/L and joined
with the automatic performance-tuning system known as
Fastest Fourier Transform in the West (FFTW). FFTW
performance-optimization facilities working with the
compiler technologies presented in this paper are able
to produce vectorized fast Fourier transform (FFT)
codes that are tuned automatically to single Blue
Gene/L processors and are up to 80\% faster than the
best-performing scalar FFT codes generated by FFTW.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
ordernumber = "G322-0240",
}
@InProceedings{Macchetti:2005:QPH,
author = "Marco Macchetti and Luigi Dadda",
title = "Quasi-Pipelined Hash Circuits",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-149.pdf",
abstract = "Hash functions are an important cryptographic
primitive. They are used to obtain a fixed-size
fingerprint, or hash value, of an arbitrary long
message. We focus particularly on the class of
dedicated hash functions, whose general construction is
presented; the peculiar arrangement of sequential and
combinational units makes the application of pipelining
techniques to these constructions not trivial. We
formalize here an optimization technique called
quasipipelining, whose goal is to optimize the critical
path and thus to increase the clock frequency in
dedicated hardware implementations. The SHA-2 algorithm
has been previously examined by Dadda et al., with
specific versions of quasipipelining; here, a full
generalization of the technique is presented, along
with application to the SHA-1 algorithm.
Quasi-pipelining could be as well applied to future
hashing algorithms, provided they are designed along
the same lines as those of the SHA family.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@InProceedings{Markstein:2005:FSM,
author = "Peter Markstein",
title = "A Fast-Start Method for Computing the Inverse
Tangent",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-112.pdf",
abstract = "In a search for an algorithm to compute $ \atan (x) $
which has both low latency and few floating point
instructions, an interesting variant of familiar
trigonometry formulas was discovered that allow the
start of argument reduction to commence before any
references to tables stored in memory are needed. Low
latency makes the method suitable for a closed
subroutine, and few floating point operations make the
method advantageous for a software-pipelined
implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; IA-64; Itanium-2",
pagecount = "6",
}
@TechReport{Marques:2005:BIF,
author = "Osni A. Marques and E. Jason Riedy and Christof
V{\"o}mel",
title = "Benefits of {IEEE-754} Features in Modern Symmetric
Tridiagonal Eigensolvers",
type = "LAPACK Working Note",
number = "172",
institution = "Computer Science Division, University of California,
Berkeley",
address = "Berkeley, CA, USA",
pages = "22",
day = "30",
month = sep,
year = "2005",
MRclass = "15A18, 15A23.",
bibdate = "Mon Mar 20 12:18:56 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also issued as Technical Report UCB//CSD-05-1414.",
URL = "http://www.netlib.org/lapack/lawnspdf/lawn172.pdf",
abstract = "Bisection is one of the most common methods used to
compute the eigenvalues of symmetric tridiagonal
matrices. Bisection relies on the Sturm count: for a
given shift $ \sigma $, the number of negative pivots
in the factorization $ T \sigma I = L D L^T $ equals
the number of eigenvalues of $T$ that are smaller than
$ \sigma $. In IEEE-754 arithmetic, the value $ \infty
$ permits the computation to continue past a zero
pivot, producing a correct Sturm count when $T$ is
unreduced. Demmel and Li showed in the 90s that using $
\infty $ rather than testing for zero pivots within the
loop could improve performance significantly on certain
architectures.
When eigenvalues are to be computed to high relative
accuracy, it is often preferable to work with $ L D L^T
$ factorizations instead of the original tridiagonal
$T$, see for example the MRRR algorithm. In these
cases, the Sturm count has to be computed from $ L D
L^T $. The differential stationary and progressive qds
algorithms are the methods of choice.
While it seems trivial to replace $T$ by $ L D L^T $,
in reality these algorithms are more complicated: in
IEEE-754 arithmetic, a zero pivot produces an overflow,
followed by an invalid exception (NaN), that renders
the Sturm count incorrect.
We present alternative, safe formulations that are
guaranteed to produce the correct result.
Benchmarking these algorithms on a variety of platforms
shows that the original formulation without tests is
always faster provided no exception occurs. The
transforms see speed-ups of up to $ 2.6 \times $ over
the careful formulations.
Tests on industrial matrices show that encountering
exceptions in practice is rare. This leads to the
following design: First, compute the Sturm count by the
fast but unsafe algorithm. Then, if an exception
occurred, recompute the count by a safe, slower
alternative. The new Sturm count algorithms improve the
speed of bisection by up to $ 2 \times $ on our test
matrices. Furthermore, unlike the traditional
tiny-pivot substitution, proper use of IEEE-754
features provides a careful formulation that imposes no
input range restrictions.",
acknowledgement = ack-nhfb,
keywords = "differential qds algorithms; IEEE-754 arithmetic;
IEEE-754 performance; LAPACK; MRRR algorithm; NaN
arithmetic",
}
@InProceedings{Matula:2005:TLS,
author = "David Matula and Alex Fit-Florea and Mitchell
Thornton",
title = "Table Lookup Structures for Multiplicative Inverses
Modulo $ 2^k $",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-160.pdf",
abstract = "We introduce an inheritance property and related table
lookup structures applicable to simplified evaluation
of the modular operations ``multiplicative inverse'',
``discrete log'', and ``exponential residue'' in the
particular modulus $ 2^k $. Regarding applications, we
describe an integer representation system of Benschop
for transforming integer multiplications into additions
which benefits from our table lookup function
evaluation procedures.\par We focus herein on the
multiplicative inverse modulo $ 2^k $ to exhibit
simplifications in hardware implementations realized
from the inheritance property. A table lookup structure
given by a bit string that can be interpreted with
reference to a binary tree is described and analyzed.
Using observed symmetries, the lookup structure size is
reduced allowing a novel direct lookup process for
multiplicative inverses for all 16-bit odd integers to
be obtained from a table of size less than two KBytes.
The 16-bit multiplicative inverse operation is also
applicable for providing a seed inverse for obtaining
32/64-bit multiplicative inverses by one/two iterations
of a known quadratic refinement algorithm.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Article{McCann:2005:SDA,
author = "Mark McCann and Nicholas Pippenger",
title = "{SRT} Division Algorithms as Dynamical Systems",
journal = j-SIAM-J-COMPUT,
volume = "34",
number = "6",
pages = "1279--1301",
month = dec,
year = "2005",
CODEN = "SMJCAT",
DOI = "https://doi.org/10.1137/S009753970444106X",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
MRclass = "68W40, 37E05",
bibdate = "Fri Dec 30 06:20:35 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/34/6;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/44106",
abstract = "Sweeney--Robertson--Tocher (SRT) division, as it was
discovered in the late 1950s, represented an important
improvement in the speed of division algorithms for
computers at the time. A variant of SRT division is
still commonly implemented in computers today. Although
some bounds on the performance of the original SRT
division method were obtained, a great many questions
remained unanswered. In this paper, the original
version of SRT division is described as a dynamical
system. This enables us to bring modern dynamical
systems theory, a relatively new development in
mathematics, to bear on an older problem. In doing so,
we are able to show that SRT division is ergodic, and
is even Bernoulli, for all real divisors and dividends.
With the Bernoulli property, we are able to use entropy
to prove that the natural extensions of SRT division
are isomorphic by way of the Kolmogorov--Ornstein
theorem. We demonstrate how our methods and results can
be applied to a much larger class of division
algorithms.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
keywords = "SRT division, ergodic, Bernoulli, dynamical systems,
entropy",
}
@InProceedings{Mei:2005:LZA,
author = "Xiao-Lu Mei",
title = "Leading zero anticipation for latency improvement in
floating-point fused multiply-add units",
crossref = "Tang:2005:AIC",
pages = "53--56",
year = "2005",
DOI = "https://doi.org/10.1109/ICASIC.2005.1611267",
bibdate = "Sun Feb 20 09:52:59 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The leading zero anticipation (LZA) is vital in the
floating-point fused multiply-add (FMA) units. The
general LZA algorithms can only deal with 2 operands.
It increases the critical path delay of high
performance floating-point FMA units. The paper
presents a novel LZA algorithm to deal with 3 operands
directly and implemented the 106-bit leading zero
anticipator in the high performance floating-point FMA
with the general LZA algorithm and the proposed LZA
algorithm respectively. Compared with the general
leading zero anticipator, the proposed leading zero
anticipator can reduce the delay of the critical path
by 16.67\% and reduce the area by 19.63\%
approximately.",
acknowledgement = ack-nhfb,
}
@Article{Menissier-Morain:2005:APR,
author = "Val{\'e}rie M{\'e}nissier-Morain",
title = "Arbitrary precision real arithmetic: design and
algorithms",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "13--39",
month = jul,
year = "2005",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.003",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
bibdate = "Thu Oct 17 10:09:18 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
remark = "Special issue on Practical development of exact real
number computation.",
}
@Article{Mitra:2005:BFP,
author = "Abhijit Mitra and Mrityunjoy Chakraborty and Hideaki
Sakai",
title = "A block floating-point treatment to the {LMS}
algorithm: efficient realization and a roundoff error
analysis",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "53",
number = "12",
pages = "4536--4544",
year = "2005",
CODEN = "ITPRED",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
MRclass = "Database Expansion Item",
MRnumber = "MR2246666",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}
@Book{Mitzenmacher:2005:PCI,
author = "Michael Mitzenmacher and Eli Upfal",
title = "Probability and Computing: an Introduction to
Randomized Algorithms and Probabilistic Analysis",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvi + 352",
year = "2005",
DOI = "https://doi.org/10.1017/cbo9780511813603",
ISBN = "0-521-83540-2 (print), 0-511-81360-0 (e-book)",
ISBN-13 = "978-0-521-83540-4 (print), 978-0-511-81360-3
(e-book)",
LCCN = "QA274 .M574 2005",
bibdate = "Fri Sep 22 17:57:47 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "Algorithms; Probabilities; Stochastic analysis;
Algorithmes; Probabilit{\'e}s; Analyse stochastique",
tableofcontents = "Events and probability \\
Discrete random variables and expectation \\
Moments and deviations \\
Chernoff bounds \\
Balls, bins and random graphs \\
The probabilistic method \\
Markov chains and random walks \\
Continuous distributions and the Poisson process \\
Entropy, randomness, and information \\
The Monte Carlo method \\
Coupling of Markov chains \\
Martingales \\
Pairwise independence and universal hash functions \\
Balanced allocations",
}
@Article{Montgomery:2005:FSS,
author = "Peter L. Montgomery",
title = "Five, Six, and Seven-Term {Karatsuba}-Like Formulae",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "362--369",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.49",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0362abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0362.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0362.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388200.pdf?isnumber=30205&prod=JNL&arnumber=1388200&arSt=+362&ared=+369&arAuthor=Montgomery%2C+P.L.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388200&count=13&index=11;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388200",
abstract = "The Karatsuba--Ofman algorithm starts with a way to
multiply two 2-term (i.e., linear) polynomials using
three scalar multiplications. There is also a way to
multiply two 3-term (i.e., quadratic) polynomials using
six scalar multiplications. These are used within
recursive constructions to multiply two higher-degree
polynomials in subquadratic time. We present
division-free formulae, which multiply two 5-term
polynomials with 13 scalar multiplications, two 6-term
polynomials with 17 scalar multiplications, and two
7-term polynomials with 22 scalar multiplications.
These formulae may be mixed with the 2-term and 3-term
formulae within recursive constructions, leading to
improved bounds for many other degrees. Using only the
6-term formula leads to better asymptotic performance
than standard Karatsuba. The new formulae work in any
characteristic, but simplify in characteristic 2. We
describe their application to elliptic curve arithmetic
over binary fields. We include some timing data.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@InProceedings{Morris:2005:FBF,
author = "G. Morris and V. Prasanna",
title = "An {FPGA}-based floating-point {Jacobi} iterative
solver",
crossref = "Bein:2005:PIS",
pages = "420--427",
year = "2005",
DOI = "https://doi.org/10.1109/ISPAN.2005.18",
bibdate = "Sat Oct 9 12:54:52 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Within the parallel computing domain, field
programmable gate arrays (FPGA) are no longer
restricted to their traditional role as substitutes for
application-specific integrated circuits --- as
hardware `hidden' from the end user. Several high
performance computing vendors offer parallel
reconfigurable computers employing user-programmable
FPGAs. These exciting new architectures allow end-users
to, in effect, create reconfigurable coprocessors
targeting the computationally intensive parts of each
problem. The increased capability of contemporary FPGAs
coupled with the embarrassingly parallel nature of the
Jacobi iterative method make the Jacobi method an ideal
candidate for hardware acceleration. This paper
introduces a parameterized design for a deeply
pipelined, highly parallelized IEEE 64-bit
floating-point version of the Jacobi method. A Jacobi
circuit is implemented using a Xilinx Virtex-II Pro as
the target FPGA device. Implementation statistics and
performance estimates are presented.",
acknowledgement = ack-nhfb,
}
@InProceedings{Mueller:2005:VFP,
author = "Silvia M. Mueller and Christian Jacobi and Hwa-Joon Oh
and Kevin D. Tran and Cottier Scott and Brad W. Michael
and Hiroo Nishikawa and Yonetaro Totsuka and Tatsuya
Namatame and Naoka Yano and Takashi Machida and Sang H.
Dhong",
title = "The Vector Floating-Point Unit in a Synergistic
Processor Element of a {CELL} Processor",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-151.pdf",
abstract = "The floating-point unit in the Synergistic Processor
Element of the 1st generation multi-core CELL Processor
is described. The FPU supports 4-way SIMD single
precision and integer operations and 2-way SIMD double
precision operations. The design required a
high-frequency, low latency, power and area efficiency
with primary application to the multimedia streaming
workloads, such as 3D graphics. The FPU has 3 different
latencies, optimizing the performance critical single
precision FMA operations, which are executed with a
6-cycle latency at an 11FO4 cycle time. The latency
includes the global forwarding of the result. These
challenging performance, power, and area goals were
achieved through the co-design of architecture and
implementation with optimizations at all levels of the
design. This paper focuses on the logical and
algorithmic aspects of the FPU we developed, to achieve
these goals.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "9",
}
@TechReport{Muller:2005:D,
author = "Jean-Michel Muller",
title = "On the Definition of {\tt ulp(x)}",
type = "Rapport de recherche",
number = "LIP RR2005-09, INRIA RR-5504",
institution = "Laboratoire de l'Informatique du Parall{\'e}lisme",
address = "Lyon, France",
pages = "19",
month = feb,
year = "2005",
ISSN = "0249-6399",
bibdate = "Wed Jun 24 22:44:21 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5504.pdf",
abstract = "Function ulp (acronym for \emph{unit in the last
place}) is frequently used for expressing errors in
floating-point computations. We present several
previously suggested definitions of that function, and
analyse some of their properties.",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic; floating-point arithmetic; ULP;
unit in the last place",
}
@InProceedings{Muller:2005:DCS,
author = "Jean-Michel Muller and Arnaud Tisserand and Benoit de
Dinechin and Christophe Monat",
title = "Division by Constant for the {ST100 DSP}
Microprocessor",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-133.pdf",
abstract = "Algorithms for Euclidean (i.e., integer) division by a
constant operation are presented. They allow fast
computation for some values of the divisor (known at
compile time) or also when both quotient and modulus
are required. These algorithms are based on the
multiply-accumulate instruction and the 40-bit
arithmetic available in DSPs such as the ST100 DSP from
STMicroelectronics. The results are demonstrated in the
case of standard speech coding applications.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "7",
}
@Article{Muller:2005:GEI,
author = "Norbert M{\"u}ller and Martin Escardo and Paul
Zimmermann",
title = "Guest editors' introduction: Special issue on
practical development of exact real number
computation",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "1--2",
month = jul,
year = "2005",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.001",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
bibdate = "Thu Oct 17 10:09:18 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
remark = "Special issue on Practical development of exact real
number computation.",
}
@Article{Muscedere:2005:ETB,
author = "Roberto Muscedere and Vassil Dimitrov and Graham A.
Jullien and William C. Miller",
title = "Efficient Techniques for Binary-to-Multidigit
Multidimensional Logarithmic Number System Conversion
Using Range-Addressable Look-Up Tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "257--271",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.48",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0257abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0257.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0257.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388191.pdf?isnumber=30205&prod=JNL&arnumber=1388191&arSt=+257&ared=+271&arAuthor=Muscedere%2C+R.%3B+Dimitrov%2C+V.%3B+Jullien%2C+G.A.%3B+Miller%2C+W.C.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388191&count=13&index=2;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388191",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@Article{Muscedere:2005:LPT,
author = "Roberto Muscedere and Vassil Dimitrov and Graham
Jullien and William Miller",
title = "A low-power two-digit multi-dimensional logarithmic
number system filterbank architecture for a digital
hearing aid",
journal = j-EURASIP-J-ADV-SIGNAL-PROCESS,
volume = "1",
pages = "3015--3025",
year = "2005",
DOI = "https://doi.org/10.1155/ASP.2005.3015",
ISSN = "1110-8657 (print), 1687-0433 (electronic)",
ISSN-L = "1110-8657",
bibdate = "Fri Aug 8 08:37:33 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper addresses the implementation of a
filterbank for digital hearing aids using a
multi-dimensional logarithmic number system (MDLNS).
The MDLNS, which has similar properties to the
classical logarithmic number system (LNS), provides
more degrees of freedom than the LNS by virtue of
having two, or more, orthogonal bases and the ability
to use multiple MDLNS components or digits. The
logarithmic properties of the MDLNS also allow for
reduced complexity multiplication and large dynamic
range, and a multiple-digit MDLNS provides a
considerable reduction in hardware complexity compared
to a conventional LNS approach. We discuss an improved
design for a two-digit 2D MDLNS filterbank
implementation which reduces power and area by over two
times compared to the original design.",
acknowledgement = ack-nhfb,
ajournal = "EURASIP J. Appl. Signal Process.",
articleno = "326504",
fjournal = "EURASIP Journal on Advances in Signal Processing",
journal-URL = "https://asp-eurasipjournals.springeropen.com/",
}
@Article{Newman:2005:PLP,
author = "M. E. J. Newman",
title = "Power laws, {Pareto} distributions and {Zipf}'s law",
journal = j-CONTEMP-PHYS,
volume = "46",
number = "5",
pages = "323--351",
month = sep,
year = "2005",
CODEN = "CTPHAF",
DOI = "https://doi.org/10.1080/00107510500052444",
ISSN = "0010-7514 (print), 1366-5812 (electronic)",
ISSN-L = "0010-7514",
bibdate = "Thu Feb 18 20:07:22 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/contempphys.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When the probability of measuring a particular value
of some quantity varies inversely as a power of that
value, the quantity is said to follow a power law, also
known variously as Zipf's law or the Pareto
distribution. Power laws appear widely in physics,
biology, earth and planetary sciences, economics and
finance, computer science, demography and the social
sciences. For instance, the distributions of the sizes
of cities, earthquakes, forest fires, solar flares,
moon craters and people's personal fortunes all appear
to follow power laws. The origin of power-law behaviour
has been a topic of debate in the scientific community
for more than a century. Here we review some of the
empirical evidence for the existence of power-law forms
and the theories proposed to explain them.",
acknowledgement = ack-nhfb,
fjournal = "Contemporary Physics",
journal-URL = "http://www.tandfonline.com/loi/tcph20",
keywords = "Benford's Law; critical phenomena; Legendre beta
function; Pareto distribution; percolation; phase
transitions; power-law distributions; random walks;
Riemann zeta function; scale-free distributions; Yule
process; Zipf's Law",
remark = "This article is an excellent survey of continuous and
discrete distributions that follow a power law, and
some that do not. It is well worth reading.",
subject = "astrophysics; atomic and nuclear physics; chemical
physics; computational physics; condensed matter
physics; environmental physics; experimental physics;
general physics; particle and high energy physics;
plasma physics; space science; theoretical physics",
}
@Article{Nguyen:2005:FPL,
author = "P. Nguyen and D. Stehle",
title = "Floating-Point {LLL} Revisited",
journal = j-LECT-NOTES-COMP-SCI,
volume = "3494",
pages = "215--233",
year = "2005",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/11426639_13",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Jun 24 14:51:11 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Lenstra-Lenstra-Lov{\'a}sz lattice basis reduction
algorithm (LLL or $ L^3 $) is a very popular tool in
public-key cryptanalysis and in many other fields.
Given an integer $d$-dimensional lattice basis with
vectors of norm less than $B$ in an $n$-dimensional
space, $ L^3 $ outputs a so-called $ L^3 $-reduced
basis in polynomial time $ O(d^5 n \log^3 B) $, using
arithmetic operations on integers of bit-length $ O(d l
o g B) $. This worst-case complexity is problematic for
lattices arising in cryptanalysis where $d$ or/and $
\log B $ are often large. As a result, the original $
L^3 $ is almost never used in practice. Instead, one
applies floating-point variants of $ L^3 $, where the
long-integer arithmetic required by Gram--Schmidt
orthogonalisation (central in $ L^3 $) is replaced by
floating-point arithmetic. Unfortunately, this is known
to be unstable in the worst-case: the usual
floating-point $ L^3 $ is not even guaranteed to
terminate, and the output basis may not be $ L^3
$-reduced at all. In this article, we introduce the $
L^2 $ algorithm, a new and natural floating-point
variant of $ L^3 $ which provably outputs $ L^3
$-reduced bases in polynomial time $ O(d^4 n (d + \log
B) \log B) $. This is the first $ L^3 $ algorithm whose
running time (without fast integer arithmetic) provably
grows only quadratically with respect to $ \log B $,
like the well-known Euclidean and Gaussian algorithms,
which it generalizes.",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "$L^3$; Lattice Reduction; LLL; Public-Key
Cryptanalysis",
}
@InProceedings{Oberman:2005:HPA,
author = "Stuart Oberman and Michael Siu",
title = "A High-Performance Area-Efficient Multifunction
Interpolator",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-164.pdf",
abstract = "This paper presents the algorithms and implementation
of a high-performance functional unit used for multiple
interpolation applications. Graphics processing units
(GPUs) frequently perform two classes of floating point
interpolation within programmable shaders: per-pixel
attribute interpolation and transcendental function
approximation. We present a design that efficiently
performs both classes of interpolation on a shared
functional unit. Enhanced minimax approximations with
quadratic interpolation minimize lookup-table sizes and
datapath widths for fully-pipelined function
approximation. Rectangular multipliers support both
sign-magnitude and two's complement inputs of variable
widths. Superpipelining is used throughout the design
to increase operating frequency and interpolation
throughput while maximizing area efficiency.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Article{Ogita:2005:ASD,
author = "Takeshi Ogita and Siegfried M. Rump and Shin'ichi
Oishi",
title = "Accurate Sum and Dot Product",
journal = j-SIAM-J-SCI-COMP,
volume = "26",
number = "6",
pages = "1955--1988",
month = nov,
year = "2005",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/030601818",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "5-04, 65G99, 65-04",
bibdate = "Mon Nov 21 14:52:48 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/26/6;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/60181",
abstract = "Algorithms for summation and dot product of
floating-point numbers are presented which are fast in
terms of measured computing time. We show that the
computed results are as accurate as if computed in
twice or K-fold working precision, $ K \ge 3 $. For
twice the working precision our algorithms for
summation and dot product are some 40\% faster than the
corresponding XBLAS routines while sharing similar
error estimates. Our algorithms are widely applicable
because they require only addition, subtraction, and
multiplication of floating-point numbers in the same
working precision as the given data. Higher precision
is unnecessary, algorithms are straight loops without
branch, and no access to mantissa or exponent is
necessary.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate dot product; accurate floating-point
summation; fast algorithms; high precision; verified
error bounds",
}
@InProceedings{Oh:2005:FPS,
author = "H.-J. Oh and S. M. Mueller and C. Jacobi and K. D.
Tran and S. R. Cottier and B. W. Michael and H.
Nishikawa and Y. Totsuka and T. Namatame and N. Yano
and T. Machida and S. H. Dhong",
booktitle = "{2005 Symposium on VLSI Circuits, June 16--18th, 2005,
Rhiga Royal Hotel Kyoto, Kyoto, Japan}",
title = "A Fully-Pipelined Single-Precision Floating Point Unit
in the Synergistic Processor Element of a {CELL}
Processor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "??--??",
year = "2005",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Jun 24 14:35:04 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Paper 2.4",
URL = "http://www.vlsisymposium.org/circuits/technical.html",
abstract = "The floating point unit in the synergistic processor
element of a CELL processor is a fully-pipelined 4-way
SIMD unit designed to accelerate media and data
streaming. It supports 32-bit single-precision floating
point and 16-bit integer operands with two different
latencies, optimizing the performance of critical
single-precision multiply-add operations. It employs
fine-grained clock gating for power saving.
Architecture, logic, circuits and integration are
co-designed to meet the performance, power, and area
goals.",
acknowledgement = ack-nhfb,
}
@InProceedings{Pareto:2005:GAL,
author = "Lena Pareto",
title = "Graphical arithmetic for learners with dyscalculia",
crossref = "ACM:2005:ASI",
pages = "214--215",
year = "2005",
DOI = "https://doi.org/10.1145/1090785.1090836",
bibdate = "Thu Aug 07 18:43:59 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We propose a model for arithmetic, based on graphical
representations, to complement the symbolic language of
mathematics. The focus is conceptual understanding of
arithmetic. We argue that the graphical model supports
understanding concepts known to be difficult for
learners with dyscalculia, such as number-sense and
decimal system. The proposed graphical representation
share properties of the decimal system, but is closer
to the semantic representation of numbers vital to the
number-sense. The model is evaluated with
school-children, but needs to be further tested by
learners with dyscalculia.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic",
}
@InProceedings{Phatak:2005:FMR,
author = "Dhananjay Phatak and Tom Goff",
title = "Fast Modular Reduction for Large Wordlengths via One
Linear and One Cyclic Convolution",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-156.pdf",
abstract = "Modular reduction is a fundamental operation in
cryptographic systems. Most well known modular
reduction methods including Barrett's and Montgomery's
algorithms leverage some-pre computations to avoid
divisions so that the main complexity of these methods
lies in a sequence of two long multiplications. For
large wordlengths a multiplication which is tantamount
to a linear convolution is performed via the Fast
Fourier Transform (FFT) or other transform-based
techniques as in the Schonhage-Strassen multiplication
algorithm.\par
We show a fundamental property (the separation
principle): in a modular reduction based on long
multiplications, the linear convolution required by one
of the two long multiplications can be replaced by a
cyclic convolution, and the halves can be separated
using other information available due to the intrinsic
redundancy of the operations. This reduces the number
of operations by about 25\%. We demonstrate that both
Barrett's and Montgomery's methods can be sped up by
using the aforementioned fundamental principle. It is
shown that a direct application of this algorithm to
modular exponentiation (either using Barrett's or
Montgomery's methods) can be expected to yield about
17\% speedup.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; cryptography; cyclic convolution;
elliptic-curve; fast modular reduction; FFT multiply;
large wordlength; linear convolution; number theoretic
transforms; principle of separation",
pagecount = "8",
}
@Article{Pineiro:2005:HSF,
author = "Jose-Alejandro Pi{\~n}eiro and Stuart F. Oberman and
Jean-Michel Muller and Javier D. Bruguera",
title = "High-Speed Function Approximation Using a Minimax
Quadratic Interpolator",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "304--318",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.52",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0304abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0304.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0304.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388195.pdf?isnumber=30205&prod=JNL&arnumber=1388195&arSt=+304&ared=+318&arAuthor=Pineiro%2C+J.-A.%3B+Oberman%2C+S.F.%3B+Muller%2C+J.-M.%3B+Bruguera%2C+J.D.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388195&count=13&index=6;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388195",
abstract = "A table-based method for high-speed function
approximation in single-precision floating-point format
is presented in this paper. Our focus is the
approximation of reciprocal, square root, square root
reciprocal, exponentials, logarithms, trigonometric
functions, powering (with a fixed exponent $p$) , or
special functions. The algorithm presented here
combines table look-up, an enhanced minimax quadratic
approximation, and an efficient evaluation of the
second-degree polynomial (using a specialized squaring
unit, redundant arithmetic, and multioperand addition).
The execution times and area costs of an architecture
implementing our method are estimated, showing the
achievement of the fast execution times of linear
approximation methods and the reduced area requirements
of other second-degree interpolation algorithms.
Moreover, the use of an enhanced minimax approximation
which, through an iterative process, takes into account
the effect of rounding the polynomial coefficients to a
finite size allows for a further reduction in the size
of the look-up tables to be used, making our method
very suitable for the implementation of an elementary
function generator in state-of-the-art DSPs or graphics
processing units (GPUs).",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@Article{Revol:2005:TMF,
author = "N. Revol and K. Makino and M. Berz",
title = "{Taylor} models and floating-point arithmetic: proof
that arithmetic operations are validated in {COSY}",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "135--154",
month = jul,
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.008",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
MRclass = "65G20",
MRnumber = "MR2137738 (2006a:65071)",
bibdate = "Thu Oct 17 10:09:18 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bt.pa.msu.edu/pub/papers/TMJLAP03/TMJLAP03.pdf",
abstract = "The goal of this paper is to prove that the
implementation of Taylor models in COSY, based on
floating-point arithmetic, computes results satisfying
the ``containment property'', i.e., guaranteed
results.\par
First, Taylor models are defined and their
implementation in the COSY software by Makino and Berz
is detailed. Afterwards IEEE-754 floating-point
arithmetic is introduced. Then the core of this paper
is given: the algorithms implemented in COSY for
multiplying a Taylor model by a scalar, for adding or
multiplying two Taylor models are given and are proven
to return Taylor models satisfying the containment
property.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
keywords = "Containment property; COSY software; Floating-point
operation; Rounding error; Taylor model; Validated
result",
remark = "Special issue on Practical development of exact real
number computation.",
}
@Article{Reyhani-Masoleh:2005:LCW,
author = "A. Reyhani-Masoleh and M. A. Hasan",
title = "Low complexity word-level sequential normal basis
multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "2",
pages = "98--110",
month = feb,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.29",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1377149",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Robison:2005:BUD,
author = "Arch Robison",
title = "{$N$}-Bit Unsigned Division Via {$N$}-Bit
Multiply-Add",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-104.pdf",
abstract = "Integer division on modern processors is expensive
compared to multiplication. Previous algorithms for
performing unsigned division by an invariant divisor,
via reciprocal approximation, suffer in the worst case
from a common requirement for $ n + 1 $ bit
multiplication, which typically must be synthesized
from $n$-bit multiplication and extra arithmetic
operations. This paper presents, and proves, a hybrid
of previous algorithms that replaces $ n + 1 $ bit
multiplication with a single fused multiply-add
operation on $n$-bit operands, thus reducing any
$n$-bit unsigned division to the upper $n$ bits of a
multiply-add, followed by a single right shift. An
additional benefit is that the prerequisite
calculations are simple and fast. On the Itanium 2
processor, the technique is advantageous for as few as
two quotients that share a common run-time divisor.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "9",
}
@TechReport{Rump:2005:AFP,
author = "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
Oishi",
title = "Accurate Floating-Point Summation",
type = "Technical Report",
number = "05.12",
institution = "Faculty for Information- and Communication Sciences,
Hamburg University of Technology",
address = "Hamburg, Germany",
day = "13",
month = nov,
year = "2005",
bibdate = "Wed Jan 04 12:31:28 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ti3.tu-harburg.de/paper/rump/Ru05d.pdf",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; distillation",
}
@Article{Savas:2005:CFA,
author = "E. Savas",
title = "A carry-free architecture for {Montgomery} inversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "12",
pages = "1508--1519",
month = dec,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.188",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:19 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1524933",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Sax:2005:FPN,
author = "Jeffrey Sax",
title = "Floating Point in {.NET} part 1: {Concepts} and
Formats",
howpublished = "World-Wide Web document",
day = "18",
month = apr,
year = "2005",
bibdate = "Wed Mar 15 06:07:27 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.codeproject.com/dotnet/ExtremeFloatingPoint1.asp;
http://www.codeproject.com/dotnet/ExtremeFloatingPoint1/ExtremeFloatingPoint1.zip",
acknowledgement = ack-nhfb,
remark = "Introductory tutorial on floating-point formats.
Cannot find parts 2 and 3.",
}
@Article{Schulte:2005:GEI,
author = "Michael J. Schulte and Jean-Claude Bajard",
title = "{Guest Editors}' Introduction: Special Issue on
Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "241--242",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.50",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Apr 27 18:04:38 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0241.pdf;
http://csdl.computer.org/dl/trans/tc/2005/03/t0241.htm",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "From the article: ``This special issue presents recent
high-quality research in computer arithmetic. The 12
papers included in this special issue were selected
from 36 papers submitted in response to an open call
for papers. This call for papers followed the 16th IEEE
International Symposium on Computer Arithmetic, which
took place in Santiago de Compostella in June 2003.
Each paper received at least three reviews and the top
papers were selected for inclusion in this special
issue. Six papers are expanded versions of the papers
presented at the 16th IEEE Symposium on Computer
Arithmetic, three are expanded versions of papers
presented at other conferences, and three are original
contributions.''",
}
@InProceedings{Schulte:2005:PED,
author = "M. J. Schulte and N. Lindberg and A. Laxminarain",
booktitle = "Proceedings of the 6th {IBM} Austin Center for
Advanced Studies Conference, Austin, {TX}, February,
2005",
title = "Performance Evaluation of Decimal Floating-Point
Arithmetic",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "??--??",
year = "2005",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 04 10:14:56 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://domino.watson.ibm.com/acas/w3www_acas.nsf/images/conf05/%24FILE/schulte.pdf;
http://mesa.ece.wisc.edu/publications/cp_2005-14.pdf",
abstract = "The prominence of decimal data in commercial and
financial applications has led researchers to pursue
efficient techniques for performing decimal
floating-point arithmetic. While several software
implementations of decimal floating-point arithmetic
have been implemented, there is a growing need to
provide hardware support for decimal floating-point
arithmetic to keep up with the processing demands of
emerging commercial and financial applications. This
paper evaluates and compares the performance of decimal
floating-point arithmetic operations when implemented
on superscalar processors using either software
libraries or specialized hardware designs. Our
comparisons show that hardware implementations of
decimal floating-point arithmetic operations are one to
two orders of magnitude faster than software
implementations.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Seidel:2005:HRI,
author = "Peter-Michael Seidel",
title = "High-Radix Implementation of {IEEE} Floating-Point
Addition",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-192.pdf",
abstract = "We are proposing a micro-architecture for
high-performance IEEE floating-point addition that is
based on a (non-redundant) high-radix representation of
the floating-point operands. The main improvement of
the proposed IEEE FP addition implementation is
achieved by avoiding the computation of full alignment
and normalization shifts which impose major delays in
conventional implementations of IEEE FP addition. This
reduction is achieved at the cost of wider operand
interfaces and an increased complexity for IEEE
compliant rounding. We present a detailed discussion of
an IEEE FP adder implementation using the proposed
high-radix format and explain the specific benefits and
challenges of the design.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Article{Seidel:2005:SRR,
author = "P.-M. Seidel and L. D. McFearin and D. W. Matula",
title = "Secondary radix recodings for higher radix
multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "2",
pages = "111--123",
month = feb,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.32",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 16:17:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1377150",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Serebrenik:2005:TFP,
author = "Alexander Serebrenik and Danny {De Schreye}",
title = "Termination of Floating-Point Computations",
journal = j-J-AUTOM-REASON,
volume = "34",
number = "2",
pages = "141--177",
month = dec,
year = "2005",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-005-6546-z",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
MRclass = "68N17 (65G99 68Q60)",
MRnumber = "MR2213571 (2007d:68022)",
MRreviewer = "Andrzej Kozlowski",
bibdate = "Sat Apr 2 10:50:29 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "http://link.springer.com/article/10.1007/s10817-005-6546-z",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
}
@InProceedings{Setiaarif:2005:NMS,
author = "E. Setiaarif and P. Siy",
booktitle = "{NAFIPS 2005}, Annual Meeting of the North American
Fuzzy Information Processing Society, 26--28 June
2005",
title = "A new moduli set selection technique to improve sign
detection and number comparison in residue number
system ({RNS})",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "766--768",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1109/NAFIPS.2005.1548635",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "Residue number system (RNS) offers a promising future
because its carry-free operations in addition,
subtraction and multiplication. This inherent property
of RNS can be used to reduce the complexity of
calculation in many applications, such as \ldots{}",
}
@InProceedings{Soderstrand:2005:RNS,
author = "M. A. Soderstrand and G. Y. Cho and L. G. Johnson",
booktitle = "{ISCAS 2005}, {IEEE} International Symposium on
Circuits and Systems, 23--26 May 2005",
title = "Residue number system implementations of complex
heterodyne tunable filters",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "548--551",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2005.1464646",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "The heterodyne signals for a complex heterodyne filter
based upon M/2 equally-spaced heterodyne frequencies
between DC and the Nyquist frequency can be generated
from taking integer powers of the M/sup th/ root of
one. In residue number systems (RNS) \ldots{}",
}
@Article{Sofroniou:2005:PNC,
author = "Mark Sofroniou and Giulia Spaletta",
title = "Precise numerical computation",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "113--134",
month = jul,
year = "2005",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.007",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
bibdate = "Thu Oct 17 10:09:18 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1567832604000785",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
keywords = "accuracy and precision; computer algebra systems;
computer aspects of numerical algorithms; condition
number; error analysis; floating-point arithmetic;
interval arithmetic; Mathematica; significance
arithmetic; symbolic algebra",
remark = "Special issue on Practical development of exact real
number computation. Paper dedicated to Jerry B. Keiper
(1953--1995) and Nicholas C. Metropolis (1915--1999).
It is primarily about describing Mathematica's
significance arithmetic.",
}
@Article{Sofronioua:2005:PNC,
author = "Mark Sofronioua and Giulia Spalettab",
title = "Precise numerical computation",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "113--134",
month = jul,
year = "2005",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.007",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
bibdate = "Fri Apr 04 08:12:14 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S1567832604000785",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
keywords = "accuracy and precision; computer algebra systems;
computer aspects of numerical algorithms; condition
number; error analysis; floating-point arithmetic;
interval arithmetic; Mathematica; significance
arithmetic; symbolic algebra",
}
@Misc{Steele:2005:SME,
author = "Guy L. {Steele Jr.}",
title = "System and method for extracting the high part of a
floating point operand",
howpublished = "US Patent 6976050",
day = "13",
month = dec,
year = "2005",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/6976050/fulltext.html",
abstract = "A method and system determine a high part of a
floating point operand. Exponent field bits and
fraction field bits of a result are set to a zero if
the determined format is an infinity format or an
overflow format. The exponent field bits and the
fraction field bits of the result are set to
corresponding exponent field bits and corresponding
fraction field bits of the floating point operand if
the determined format is a not-a-number (NaN) format.
At least one of the fraction field bits of the result
is adaptively cleared if the determined format is a
denormalized format or a delimited format.",
acknowledgement = ack-nhfb,
patentdate = "12/13/2005",
}
@Misc{Steele:2005:SMF,
author = "Guy L. {Steele Jr.}",
title = "System and method for forcing floating point status
information to selected values",
howpublished = "US Patent 6970898",
day = "29",
month = nov,
year = "2005",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/6970898/fulltext.html",
abstract = "A floating point flag forcing circuit comprising an
circuit and a result assembler. The circuit receives a
plurality of floating point operands, analyzes the
floating point operand, receives one or more control
input signals, determines one or more predetermined
formats in which the plurality of operands are
represented, and generates one or more control signals.
The result assembler receives the control signals from
the circuit, along with one or more inputs, and
assembles a result.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2005:SMG,
author = "Guy L. {Steele Jr.}",
title = "System and method for generating an integer part of a
logarithm of a floating point operand",
howpublished = "US Patent 6961744",
day = "01",
month = nov,
year = "2005",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/6961744/fulltext.html",
abstract = "A logarithm unit computes an integer part of a
logarithm of a floating point operand according to an
embodiment of the present invention. The logarithm unit
analyzes a format of the floating point operand and
generates at least one signal representative of the
format. The logarithm unit determines a magnitude of an
unbiased exponent of the floating point operand as an
intermediate result based on the at least one signal,
wherein the unbiased exponent is represented by
unbiased exponent bits. Still further, the logarithm
unit determines an exponent field and a fraction field
high part of the intermediate result. A result is
assembled equaling the integer part of the logarithm of
the floating point operand based on the at least one
signal wherein, if the floating point operand is in at
least one of a denormalized format, a normalized
non-zero format, and a delimited format, an exponent
field of the result equals the exponent field of the
intermediate result and a fraction field high part of
the result equals the fraction field high part of the
intermediate result.",
acknowledgement = ack-nhfb,
}
@PhdThesis{Stehle:2004:ARR,
author = "Damien Stehl{\'e}",
title = "Algorithmique de la r{\'e}duction de r{\'e}seaux et
application {\`a} la recherche de pires cas pour
l'arrondi de fonctions math{\'e}matiques. ({French})
[{Algorithmics} of network reduction and application to
the search for worst cases for rounding of mathematical
functions]",
type = "Doctorat de {l'Universit{\'e} Henri Poincar{\'e} ---
Nancy 1 (sp{\'e}cialit{\'e} informatique)}",
school = "Universit{\'e} Henri Poincar{\'e} --- Nancy",
address = "Nancy, France",
pages = "xvi + 252",
year = "2004",
bibdate = "Fri Dec 08 09:38:41 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://theses.hal.science/tel-01748080/",
abstract = "Euclidean lattices are a powerful tool for several
algorithmic topics, among which are cryptography and
algorithmic number theory. The contributions of this
thesis are twofold: we improve lattice basis reduction
algorithms, and we introduce a new application of
lattice reduction, in computer arithmetic. Concerning
lattices, we consider both small dimensions and
arbitrary dimensions, for which we improve the
classical LLL algorithm. Concerning the application, we
make use of Coppersmith's method for computing the
small roots of multivariate modular polynomials, in
order to find the worst cases for the rounding of
mathematical functions, when the function, the rounding
mode and the precision are fixed. We also generalise
our technique to find input numbers that are
simultaneously bad for two functions. These two methods
are expensive pre-computations, but once performed,
they help speeding up the implementations of elementary
mathematical functions in fixed precision.",
acknowledgement = ack-nhfb,
}
@InProceedings{Stehle:2005:GAT,
author = "Damien Stehl{\'e} and Paul Zimmermann",
title = "{Gal}'s Accurate Tables Method Revisited",
crossref = "Montuschi:2005:PIS",
pages = "275--264",
year = "2005",
DOI = "https://doi.org/10.1109/ARITH.2005.24",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-152.pdf",
abstract = "Gal's accurate tables algorithm aims at providing an
efficient implementation of mathematical functions with
correct rounding as often as possible. This method
requires an expensive pre-computation of the values
taken by the function or by several related functions
at some distinguished points. Our improvements of Gal's
method are two-fold: on the one hand we describe what
is the arguably best set of distinguished values and
how it improves the efficiency and accuracy of the
function implementation, and on the other hand we give
an algorithm which drastically decreases the cost of
the pre-computation. These improvements are related to
the worst cases for the correct rounding of
mathematical functions and to the algorithms for
finding them. We demonstrate how the whole method can
be turned into practice for $ 2^x $ and $ \sin x $ for
$ x \in [1 / 2, 1) $, in double precision.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; correct rounding; floating-point
arithmetic",
pagecount = "8",
}
@Article{Stehle:2005:SWC,
author = "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
Zimmermann",
title = "Searching Worst Cases of a One-Variable Function Using
Lattice Reduction",
journal = j-IEEE-TRANS-COMPUT,
volume = "54",
number = "3",
pages = "340--346",
month = mar,
year = "2005",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2005.55",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 30 12:14:00 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/comp/trans/tc/2005/03/t0340abs.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0340.htm;
http://csdl.computer.org/dl/trans/tc/2005/03/t0340.pdf;
http://ieeexplore.ieee.org/iel5/12/30205/01388198.pdf?isnumber=30205&prod=JNL&arnumber=1388198&arSt=+340&ared=+346&arAuthor=Stehle%2C+D.%3B+Lefevre%2C+V.%3B+Zimmermann%2C+P.;
http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388198&count=13&index=9;
http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388198",
abstract = "We propose a new algorithm to find worst cases for the
correct rounding of a mathematical function of one
variable. We first reduce this problem to the real
small value problem---i.e., for polynomials with real
coefficients. Then, we show that this second problem
can be solved efficiently by extending Coppersmith's
work on the integer small value problem---for
polynomials with integer coefficients---using lattice
reduction. For floating-point numbers with a mantissa
less than $N$ and a polynomial approximation of degree
$d$, our algorithm finds all worst cases at distance
less than $ N^{\frac {-d^2}{2d + 1}} $ from a machine
number in time $ O(N^{{\frac {d + 12d + 1}} +
\varepsilon }) $. For $ d = 2 $, a detailed study
improves on the $ O(N^{2 / 3 + \varepsilon }) $
complexity from Lef{\`e}vre's algorithm to $ O(N^{4 / 7
+ \varepsilon }) $. For larger $d$, our algorithm can
be used to check that there exist no worst cases at
distance less than $ N^{-k} $ in time $ O(N^{1 / 2 +
\varepsilon }) $.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "ARITH-16; Computer arithmetic; correct rounding;
multiple precision arithmetic; special function
approximations",
remark = "Special issue on computer arithmetic: selected papers
from ARITH-16.",
}
@InProceedings{Stine:2005:CTC,
author = "J. E. Stine and M. J. Schulte",
title = "A Combined Two's Complement and Floating-Point
Comparator",
crossref = "IEEE:2005:IIS",
pages = "89--92",
year = "2005",
bibdate = "Sun Mar 04 21:02:35 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2005-09.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Takagi:2005:HAI,
author = "Naofumi Takagi and Shunsuke Kadowaki and Kazuyoshi
Takagi",
title = "A Hardware Algorithm for Integer Division",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-113.pdf",
abstract = "A hardware algorithm for integer division is proposed.
It is based on the digit-recurrence, non-restoring
division algorithm. Fast computation is achieved by the
use of the radix-2 signed-digit representation. The
algorithm does not require normalization of the
divisor, and hence, does not require area-consuming
leading one (or zero) detection nor shifts of
variable-amount. Combinational (unfolded)
implementation of the algorithm yields a regularly
structured array divider, where pipelining is possible
for increasing the throughput. Sequential
implementation yields a compact divider.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "7",
}
@Article{Takahashi:2005:AMP,
author = "Daisuke Takahashi",
title = "An algorithm for multiple-precision floating-point
multiplication",
journal = j-APPL-MATH-COMP,
volume = "166",
number = "2",
pages = "291--298",
day = "15",
month = jul,
year = "2005",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "65G99",
MRnumber = "MR2143788 (2006a:65075)",
bibdate = "Mon Jul 4 09:15:46 MDT 2005",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present an algorithm for multiple-precision
floating-point multiplication. The conventional
algorithms based on the fast Fourier transform (FFT)
multiply two $n$-bit numbers to obtain a $ 2 n $-bit
result. In multiple-precision floating-point
multiplication, we need only the returned result whose
precision is equal to the multiple-precision
floating-point number. We show that the overall
arithmetic operations for FFT-based multiple-precision
floating-point multiplication are reduced by
decomposition of the full-length multiplication into
shorter-length multiplication.",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "Fast Fourier transform; Multiple-precision arithmetic;
Multiplication; Program derivation",
}
@TechReport{Tang:2005:BBI,
author = "Ping Tak Peter Tang",
title = "{BID} --- Binary-Integer Decimal Encoding for Decimal
Floating Point: a Format Friendly to Software Emulation
and Compiler Native Support",
type = "Technical report",
institution = "Intel Corporation",
address = "San Jose, CA, USA",
day = "17",
month = jun,
year = "2005",
bibdate = "Thu Oct 14 14:50:39 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "BID (Binary-Integer Decimal) Encoding; decimal
floating point arithmetic",
remark = "Last Updated: July 12, 2005. Minor Modifications:
January 3, 2006",
}
@TechReport{Tang:2005:GBE,
author = "Ping Tak Peter Tang",
title = "On Generalized {BCD} Encodings for Decimal Floating
Point",
type = "Technical comment",
institution = "Software and Solutions Group, Intel Corporation",
address = "San Jose, CA, USA",
day = "7",
month = mar,
year = "2005",
bibdate = "Sat Nov 05 21:19:43 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Tsuiki:2005:RNC,
author = "Hideki Tsuiki",
title = "Real number computation with committed choice logic
programming languages",
journal = j-J-LOGIC-ALG-PROG,
volume = "64",
number = "1",
pages = "61--84",
month = jul,
year = "2005",
DOI = "https://doi.org/10.1016/j.jlap.2004.07.005",
ISSN = "1567-8326 (print), 1873-5940 (electronic)",
ISSN-L = "1567-8326",
bibdate = "Thu Oct 17 10:09:18 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Logic and Algebraic Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/15678326",
remark = "Special issue on Practical development of exact real
number computation.",
}
@InCollection{Turing:2005:PEC,
author = "Alan M. Turing",
title = "Proposed Electronic Calculator (1945)",
crossref = "Copeland:2005:ATA",
pages = "??--??",
year = "2005",
DOI = "https://doi.org/10.1093/acprof:oso/9780198565932.003.0021",
bibdate = "Mon Nov 01 18:47:26 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This chapter presents Alan M. Turing's report,
`Proposed Electronic Calculator'. The report was
submitted to the Executive Committee of the National
Physical Laboratory in February 1946, under the
description `Report by Dr. A. M. Turing on Proposals
for the Development of an Automatic Computing Engine
(ACE)'. The design set out in `Proposed Electronic
Calculator' was the basis for all the ACE computers.",
acknowledgement = ack-nhfb,
author-dates = "Alan Mathison Turing (23 June 1912--7 June 1954)",
}
@InProceedings{Usevitch:2005:JCL,
author = "B. Usevitch",
booktitle = "Proceedings. {DCC 2005} Data Compression Conference,
29--31 March 2005",
title = "{JPEG2000} Compliant Lossless Coding of Floating Point
Data",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "484--484",
year = "2005",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Verdonk:2005:BSI,
author = "B. Verdonk and J. Vervloet and A. Cuyt",
title = "Blending Set and Interval Arithmetic for Maximal
Reliability",
journal = j-COMPUTING,
volume = "74",
number = "1",
pages = "41--65",
month = feb,
year = "2005",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-004-0090-2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Jul 5 09:25:15 MDT 2005",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=74&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=74&issue=1&spage=41",
abstract = "In both [3] and [8], the authors review the
implementation of the basic operations in interval
arithmetic, and in particular discuss the different
approaches given in the literature for interval
division when the divisor interval contains zero. In
these papers, and in the references therein, the basic
operations are defined for real or extended real
interval operands.\par
Division by an interval containing zero is a special
case of an interval function for which the input
arguments contain points outside the domain of the
underlying point function. A number of approaches exist
in the literature, [7], [12], to remove restrictions on
the domain of interval functions and hence obtain a
closed, exception-free interval system.\par
In this paper, we present an alternative approach to
remove restrictions on the domain of interval functions
and to guarantee the inclusion property in all
situations, even when some input intervals contain
points that lie outside the domain of the underlying
point function. To achieve this, we allow for the
(efficient) set-based representation of non-real
results. The computed intervals are sharp, yet contain
more information and the resulting interval system is
closed and exception-free. We also show how the
presented ideas can be implemented in an interval
arithmetic library. The performance overhead is
negligible compared to the fact that the implementation
using the new approach offers 100\% reliability in
return.\par
The structure of the paper is as follows. We set off
with a motivating example in Sect. 1. In Sect. 2, we
review various approaches to interval division and then
introduce vset-division of real intervals, based on the
newly introduced concept of value set or vset. In Sect.
3, we give a formal definition of real vset-intervals
and arithmetic on these intervals. We prove a number of
essential properties and point out the likenesses and
differences with other approaches. Finally, in Sect. 4,
we discuss the implementation of vset-interval
arithmetic in a floating-point context.",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "inclusion property; Interval arithmetic",
}
@InProceedings{Wahid:2005:EFC,
author = "Khan Wahid and Vassil Dimitrov and Graham Jullien",
title = "Error-Free Computation of $ 8 \times 8 $ {$2$-D} {DCT}
and {IDCT} using Two-Dimensional Algebraic Integer
Quantization",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-138.pdf",
abstract = "This paper presents a novel error-free
(infinite-precision) architecture for the fast
implementation of both $ 8 \times 8 $ $2$-D Discrete
Cosine Transform and Inverse DCT. The architecture uses
a new algebraic integer quantization of a $1$-D radix-8
DCT that allows the separable computation of a $2$-D $
8 \times 8 $ DCT without any intermediate number
representation conversions. This is a considerable
improvement on previously introduced algebraic integer
encoding techniques to compute both DCT and IDCT which
eliminates the requirements to approximate the
transformation matrix elements by obtaining their exact
representations and hence mapping the transcendental
functions without any errors. Using this encoding
scheme, an entire $ 8 \times 8 $ $1$-D DCT-SQ (scalar
quantization) algorithm can be implemented with only 24
adders. Apart from the multiplication-free nature, this
new mapping scheme fits to this algorithm, eliminating
any computational or quantization errors and resulting
short-word-length and high-speed-design.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Article{Wait:2005:IPF,
author = "C. D. Wait",
title = "{IBM PowerPC 440 FPU} with complex-arithmetic
extensions",
journal = j-IBM-JRD,
volume = "49",
number = "2/3",
pages = "249--254",
month = "????",
year = "2005",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Wed Jun 1 08:14:41 MDT 2005",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/492/wait.pdf",
abstract = "The PowerPC 440 floating-point unit (FPU) with
complex-arithmetic extensions is an embedded
application-specific integrated circuit (ASIC) core
designed to be used with the IBM PowerPC 440 processor
core on the Blue Gene/L compute chip. The FPU core
implements the floating-point instruction set from the
PowerPC Architecture and the floating-point instruction
extensions created to aid in matrix and
complex-arithmetic operations. The FPU instruction
extensions de ne double-precision operations that are
primarily single-instruction multiple-data (SIMD) and
require two (primary and secondary) arithmetic
pipelines and floating-point register files. However,
to aid complex-arithmetic routines, some FPU extensions
actually perform different (yet closely related)
operations while executing in the arithmetic pipelines.
The FPU core implements an operand crossbar between the
primary and secondary arithmetic datapaths to enable
each pipeline operand access from the primary or
secondary register file. The PowerPC 440 processor core
provides 128-bit storage buses and simultaneous issue
of an arithmetic instruction with a storage
instruction, allowing the FPU core to fully utilize the
parallel arithmetic pipes.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
ordernumber = "G322-0240",
}
@InProceedings{Walter:2005:DDP,
author = "Colin Walter and David Samyde",
title = "Data Dependent Power Use in Multipliers",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-126.pdf",
abstract = "Recent research has demonstrated the vulnerability of
certain smart card architectures to power and
electromagnetic analysis when multiplier operations are
insufficiently shielded from external monitoring. Here
several standard multipliers are investigated in more
detail in order to provide the foundation for
understanding potential weaknesses and enabling the
subsequent successful repair of those systems. A model
is built which accurately predicts power use as a
function of the Hamming weights of inputs without the
combinatorial explosion of exhaustive simulation. This
confirms that power use is indeed data dependent at
least for those multipliers. Laboratory experiments
confirm that EMR also corresponds closely to these
power predictions over a wide range of frequencies.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17; Differential power analysis; DPA; EMA;
multiplication; multiplier; RSA cryptosystem.; smart
card",
pagecount = "9",
}
@InProceedings{Walters:2005:EFA,
author = "George Walters and Michael Schulte",
title = "Efficient Function Approximation Using Truncated
Multipliers and Squarers",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-190.pdf",
abstract = "This paper presents a technique for designing linear
and quadratic interpolators for function approximation
using truncated multipliers and squarers. Initial
coefficient values are found using a Chebyshev series
approximation, and then adjusted through exhaustive
simulation to minimize the maximum absolute error of
the interpolator output. This technique is suitable for
any function and any precision up to 24-bits (IEEE
single precision). Designs for linear and quadratic
interpolators that implement the reciprocal function, $
f(x) = 1 / x, $ are presented and analyzed as an
example. We show that a 24-bit truncated reciprocal
quadratic interpolator with a design specification of $
\pm 1 $ ulp error requires 24.1\% fewer partial
products to implement than a comparable standard
interpolator with the same error specification.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@InProceedings{Wang:2005:DFPa,
author = "L.-K. Wang and M. J. Schulte",
title = "Decimal Floating-Point Square Root Using
{Newton--Raphson} Iteration",
crossref = "Vassiliadis:2005:IIC",
pages = "309--315",
year = "2005",
bibdate = "Sun Mar 04 10:19:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mesa.ece.wisc.edu/publications/cp_2005-05.pdf",
abstract = "With continued reductions in feature size, additional
functionality may be added to future microprocessors to
boost the performance of important application domains.
Due to growth in commercial, financial, and
Internet-based applications, decimal floating point
arithmetic is now attracting more attention and
hardware support for decimal operations is being
considered by various computer manufacturers. In order
to standardize decimal number formats and operations,
specifications for decimal floating-point arithmetic
have been added to the draft revision of the IEEE-754
Standard for Floating-Point Arithmetic (IEEE-754R).
This paper presents an efficient arithmetic algorithm
and hardware design for decimal floating-point square
root. This design uses an optimized piecewise linear
approximation, a modified Newton--Raphson iteration, a
specialized rounding technique, and a modified decimal
multiplier. Synthesis results show that a 64-bit
(16-digit) implementation of decimal square root, which
is compliant with IEEE-754R, has an estimated critical
path delay of 0.95 ns and a maximum latency of 210
clock cycles when implemented using a sequential
multiplier and LSI Logic's 0.11 micron Gflx-P standard
cell library.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Whidborne:2005:OCF,
author = "James F. Whidborne and Da-Wei Gu and Jun Wu and Sheng
Chen",
title = "Optimal controller and filter realizations using
finite-precision, floating-point arithmetic",
journal = j-INT-J-SYST-SCI,
volume = "36",
number = "7",
pages = "405--413",
year = "2005",
CODEN = "IJSYA9",
ISSN = "0020-7721 (print), 1464-5319 (electronic)",
ISSN-L = "0020-7721",
MRclass = "93B50 (93B40 93E11)",
MRnumber = "MR2152458",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Systems Science. Principles
and Applications of Systems and Integration",
journal-URL = "http://www.tandfonline.com/loi/tsys20",
}
@InCollection{Wilkinson:2005:PAN,
author = "James H. Wilkinson",
title = "The {Pilot ACE} at the {National Physical
Laboratory}",
crossref = "Copeland:2005:ATA",
pages = "93--105",
year = "2005",
DOI = "https://doi.org/10.1093/acprof:oso/9780198565932.003.0005",
bibdate = "Mon Nov 01 18:18:06 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ingentaconnect.com/content/oso/2353639/2005/00000001/00000001/art00006",
abstract = "This chapter discusses the pilot Automatic Computing
Engine (ACE) project at the National Physical
Laboratory. The Pilot ACE had been designed purely as
an experimental machine to demonstrate the competence
of the team as computer engineers. It was originally
intended that when it was successfully completed a
full-scale computer would be built. However, when it
was successful, it was the only electronic computer in
a government department and the engineers came under
very heavy pressure to use the Pilot ACE for serious
computing. They implemented a small set of
modifications which included the addition of an
automatic multiplier and improvements to the control
unit which made programming a little less arduous. The
computer was then put into general use and did yeoman
service for a number of years.",
acknowledgement = ack-nhfb,
remark = "Reprint of article in {\em The Radio and Electronic
Engineer, Vol. 45, No. 7, pp. 336--340, July 1975}.
From the article:\par
``A great deal of quite detailed coding was done by the
ACE team in the period from 1946--1948. It included
basic subroutines for such things as multi-length
arithmetic (including multiplication, division and
square roots), floating-point arithmetic (both
single-precision and double-precision) and interval
arithmetic. The subroutines for floating-point
arithmetic were particularly detailed; they were coded
by G. G. Alway and myself in 1947 and were for both
Version V and Version VII. They were almost certainly
the earliest floating-point subroutines and it is
interesting that those for the Version V were
essentially the same as the subroutines which were
subsequently used on the Pilot ACE itself. At a time
when the arithmetic provided on modern computers is
often so disappointing it is interesting to recall that
the subroutines included provision for accumulating
inner-products in double-precision floating-point
arithmetic and all rounding was
immaculate.''\par
``Even double precision and triple precision
floating-point routines were reasonably fast and we
gained extensive experience with such computation long
before it was much used elsewhere. I think it is not
unreasonable to claim that the development of
floating-point error analysis at NPL, which was well in
advance of that elsewhere, was an indirect consequence
of our use of optimum coding.''",
}
@InProceedings{Wo:2005:SSC,
author = "Zhaojun Wo and Israel Koren",
title = "Synthesis of Saturating Counters Using Traditional and
Non-traditional Basic Counters",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-191.pdf",
abstract = "Saturating counters are a newly defined class of
generalized parallel counters that provide the exact
number of inputs which are equal to 1 only if this
number is below a given threshold. Such counters are
useful in, for example, self-test and repair units for
embedded memories. This paper defines saturating
counters for arbitrary threshold values and presents
several alternatives for their implementation. The
delay and area of the proposed design alternatives are
then estimated using a 0.25$ \mu $ m cell library.
Finally, we study the behavior of saturating counters
when the threshold approaches the number of input bits,
i.e., the special case of non-saturating parallel
counters.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "8",
}
@Article{Yang:2005:IMM,
author = "Jen-Ho Yang and Chin-Chen Chang and Chih-Hung Wang",
title = "An iterative modular multiplication algorithm in
{RNS}",
journal = j-APPL-MATH-COMP,
volume = "171",
number = "1",
pages = "637--645",
day = "1",
month = dec,
year = "2005",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:02:51 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@InProceedings{Yatskiv:2005:MAB,
author = "V. Yatskiv and N. Yatskiv",
booktitle = "Proceedings of The Third Workshop 2005 {IEEE}
Intelligent Data Acquisition and Advanced Computing
Systems: Technology and Applications",
title = "Multiple Access on the Basis of Residue Number System
Transformation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "527--530",
year = "2005",
CODEN = "????",
DOI = "https://doi.org/10.1109/IDAACS.2005.283039",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper research of efficiency channelizing
methods on the basis of residue number of classes of
transformation is conducted. Research is conducted on
the basis of calculation of delay mean time before
transmission. The results of \ldots{}",
}
@InProceedings{Zeydel:2005:EMA,
author = "Bart Zeydel and Theo Kluter and Vojin Oklobdzija",
title = "Efficient Mapping of Addition Recurrence Algorithms in
{CMOS}",
crossref = "Montuschi:2005:PIS",
pages = "??--??",
year = "2005",
bibdate = "Wed Jun 22 07:02:55 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arith17.polito.it/final/paper-181.pdf",
abstract = "Efficient adder design requires proper selection of a
recurrence algorithm and its realization. Each of the
algorithms: Weinberger's, Ling's and Doran's were
analyzed for its flexibility in representation and
suitability for realization in CMOS. We describe
general techniques for developing efficient
realizations based on CMOS technology constraints when
using Ling's algorithm. From these techniques we
propose two high-performance realizations that achieve
1 FO4 delay improvement at the same energy and 50\%
energy reduction at the same delay than existing Ling
and Weinberger designs.",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
pagecount = "7",
}
@Article{Zhu:2005:NDA,
author = "Yong-Kang Zhu and Jun-Hai Yong and Guo-Qin Zheng",
title = "A New Distillation Algorithm for Floating-Point
Summation",
journal = j-SIAM-J-SCI-COMP,
volume = "26",
number = "6",
pages = "2066--2078",
month = nov,
year = "2005",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/030602009",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65G05, 65B10",
MRnumber = "MR2196589 (2006i:65078)",
bibdate = "Mon Nov 21 14:52:48 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/26/6;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/60200",
abstract = "The summation of $n$ floating-point numbers is
ubiquitous in numerical computations. We present a new
distillation algorithm for floating-point summation
which is stable, efficient, and accurate. The algorithm
iteratively ``distills'' the summands without
discarding any significant digit until the partial sums
cannot change the whole sum. It uses standard
floating-point arithmetic and does not rely on the
choice of radix or any other specific assumption.
Furthermore, the error bound of our algorithm is
independent of $n$ and less than 1 ulp.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; distillation;
rounding error",
}
@InProceedings{Zhuo:2005:DSF,
author = "Ling Zhuo and G. R. Morris and V. K. Prasanna",
booktitle = "Proceedings. 19th {IEEE} International Parallel and
Distributed Processing Symposium, 04--08 April 2005",
title = "Designing Scalable {FPGA}-Based Reduction Circuits
Using Pipelined Floating-Point Cores",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "147a-147a",
year = "2005",
bibdate = "Wed Apr 27 18:18:12 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The use of pipelined floating-point arithmetic cores
to create high-performance FPGA-based computational
kernels has introduced a new class of problems that do
not exist when using single-cycle arithmetic cores.
\ldots{}",
acknowledgement = ack-nhfb,
}
@Misc{Zimmermann:2005:EBC,
author = "Paul Zimmermann and Richard Brent and Colin Percival",
title = "Error bounds on complex floating-point
multiplication",
howpublished = "World-Wide Web slides",
day = "14",
month = dec,
year = "2005",
bibdate = "Wed Dec 14 09:56:25 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/talks/cm.pdf",
abstract = "Providing that no overflow or underflow occur, no
denormal values are produced, arithmetic results are
correctly rounded to a nearest representable value, $
z_0 z_1 \neq 0 $, and $ \epsilon \leq 2^{-5} $, the
relative error $ |z_2 (z_0 z_1)^{-1} - 1 | $ is less
than $ \epsilon \sqrt {5} = (1 / 2) \beta^{1 - t} \sqrt
{5} $.",
acknowledgement = ack-nhfb,
keywords = "complex floating-point arithmetic; correct rounding;
floating-point arithmetic",
remark = "Article submitted to Mathematics of Computation
(2005), 12 pages.",
}
@Misc{Zimmermann:2005:MPT,
author = "Paul Zimmermann and Nathalie Revol and Patrick
P{\'e}lissier",
title = "{{\tt mpcheck}}: a program to test the accuracy of
elementary functions",
howpublished = "World-Wide Web software archive",
year = "2005",
bibdate = "Sat Nov 05 21:16:00 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/free/mpcheck-1.1.0.tar.gz;
http://www.loria.fr/~zimmerma/mpcheck/",
acknowledgement = ack-nhfb,
}
@TechReport{Zimmermann:2005:MVC,
author = "Paul Zimmermann",
title = "{MPFR}: vers un calcul flottant correct ? ({French})
[{MPFR}: Towards correct floating-point arithmetic?]",
type = "Online interactive report.",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
year = "2005",
bibdate = "Sun Sep 10 07:38:21 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://interstices.info/display.jsp?id=c_9345",
abstract = "Obtenir un seul r{\'e}sultat pour un calcul donn{\'e}:
{\`a} premi{\`e}re vue, cela semble une {\'e}vidence;
c'est en fait un vaste sujet de recherche auquel les
chercheurs apportent petit {\`a} petit leurs
contributions. Une nouvelle {\'e}tape est franchie
aujourd'hui gr{\^a}ce {\`a} MPFR, une biblioth{\`e}que
de calcul multi-pr{\'e}cision sur les nombres
flottants. ({French}) [Getting a single result for a
given calculation seems obvious at first sight. In
fact, it is a vast area of research to which
researchers are adding their contributions little by
little. A new level is reached today thanks to MPFR, a
multiple-precision library for floating-point
arithmetic.]",
acknowledgement = ack-nhfb,
language = "French",
}
@Misc{Zimmermann:2005:WTA,
author = "Paul Zimmermann",
title = "Why transcendentals and arbitrary precision?",
howpublished = "World-Wide Web slides",
day = "15",
month = dec,
year = "2005",
bibdate = "Thu Dec 15 15:03:09 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/talks/why.pdf",
acknowledgement = ack-nhfb,
summary = "This talk surveys the state of the computation of
transcendental functions on current hardware platforms,
and discusses the cost of implementing
correctly-rounded results.",
}
@TechReport{Zimmermann:2005:XXX,
author = "Paul Zimmermann",
title = "5,341,321",
type = "Technical report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "2",
day = "8",
month = jun,
year = "2005",
bibdate = "Sun Sep 10 07:32:04 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/5341321.ps.gz",
abstract = "This short note shows the nasty effects of patents for
the development of free software, even for patents that
were not written with software applications in mind.",
acknowledgement = ack-nhfb,
keywords = "floating-point division; Karp--Markstein patent on
modified Newton--Raphson iteration",
remark = "The title is the number of the U.S. Patent on the
algorithm described in the article, which is a
completely trivial modification of Newton--Raphson
iteration, published in \cite{Karp:1997:HPD}. The
patent itself is \cite{Karp:1994:FPA}, and it expired
on 5 May 2013.",
}
@InProceedings{Anderson:2006:AMF,
author = "Cristina S. Anderson and Shane Story and Nikita
Astafiev",
title = "Accurate Math Functions on the {Intel IA-32}
Architecture: a Performance-Driven Design",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Misc{Anonymous:2006:IFPa,
author = "Anonymous",
title = "{Intel} and Floating Point: Updating One of the
Industry's Most Successful Standards",
howpublished = "World-Wide Web document",
day = "20",
month = jul,
year = "2006",
bibdate = "Wed Nov 22 21:51:25 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/standards/floatingpoint.pdf",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Misc{Anonymous:2006:IFPb,
author = "Anonymous",
title = "{IBM}'s forthcoming {Power6} processor can count to
10",
howpublished = "World-Wide Web document",
month = oct,
year = "2006",
bibdate = "Wed Oct 11 07:44:23 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://news.zdnet.com/2100-9584_22-6124451.html",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
remark = "Reports that the 5GHz Power6 is due in mid-2007, and
adds hardware support for decimal floating-point
arithmetic.",
}
@Misc{Anonymous:2006:RSI,
author = "Anonymous",
title = "Reference Software Implementation of the {IEEE 754R}
Decimal Floating-Point Arithmetic",
howpublished = "World-Wide Web document",
year = "2006",
bibdate = "Wed Nov 22 21:40:41 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://cache-www.intel.com/cd/00/00/29/43/294339_294339.pdf",
acknowledgement = ack-nhfb,
keywords = "BID encoding; decimal floating-point arithmetic",
remark = "Describes new rounding algorithms that eliminate the
need to convert a binary integer decimal representation
to decimal, round, and convert back. The article claims
median speedups of 6 to 60 over the IBM densely packed
format used in the decNumber package. However, no
information is given about the availability of this
reference implementation. See also
\cite{Cornea:2006:SII}.",
}
@Article{Avanzi:2006:SMK,
author = "Roberto M. Avanzi and Clemens Heuberger and Helmut
Prodinger",
title = "Scalar Multiplication on {Koblitz} Curves Using the
{Frobenius} Endomorphism and Its Combination with Point
Halving: Extensions and Mathematical Analysis",
journal = j-ALGORITHMICA,
volume = "46",
number = "3--4",
pages = "249--270",
month = nov,
year = "2006",
CODEN = "ALGOEJ",
DOI = "https://doi.org/10.1007/s00453-006-0105-9",
ISSN = "0178-4617 (print), 1432-0541 (electronic)",
ISSN-L = "0178-4617",
bibdate = "Wed Jul 9 22:25:03 MDT 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0178-4617&volume=46&issue=3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0178-4617&volume=46&issue=3&spage=249",
acknowledgement = ack-nhfb,
fjournal = "Algorithmica",
journal-URL = "http://link.springer.com/journal/453",
}
@Article{Bajard:2006:AOF,
author = "J.-C. Bajard and L. Imbert and C. Negre",
title = "Arithmetic Operations in Finite Fields of Medium Prime
Characteristic Using the {Lagrange} Representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "9",
pages = "1167--1177",
month = sep,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.136",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1668044",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bartzis:2006:EBB,
author = "Constantinos Bartzis and Tevfik Bultan",
title = "Efficient {BDDs} for bounded arithmetic constraints",
journal = j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
volume = "8",
number = "1",
pages = "26--36",
month = feb,
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10009-004-0171-8",
ISSN = "1433-2779 (print), 1433-2787 (electronic)",
ISSN-L = "1433-2779",
bibdate = "Wed Jul 9 18:12:21 MDT 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1433-2779&volume=8&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1433-2779&volume=8&issue=1&spage=26",
acknowledgement = ack-nhfb,
fjournal = "International Journal on Software Tools for Technology
Transfer: STTT",
journal-URL = "http://link.springer.com/journal/10009",
keywords = "BDD; Integer arithmetic; Model checking; SMV",
}
@Article{Bernal:2006:IRD,
author = "Javier Bernal and Christoph J. Witzgall",
title = "Integer Representation of Decimal Numbers for Exact
Computations",
journal = j-J-RES-NATL-BUR-STAND,
volume = "111",
number = "2",
pages = "79--88",
month = mar # "\slash " # apr,
year = "2006",
DOI = "https://doi.org/10.6028/jres.111.006",
bibdate = "Tue Nov 05 15:32:18 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/jres/111/2/V111.N02.A02.pdf",
abstract = "A scheme is presented and software is documented for
representing as integers input decimal numbers that
have been stored in a computer as double precision
floating point numbers and for carrying out
multiplications, additions and subtractions based on
these numbers in an exact manner. The input decimal
numbers must not have more than nine digits to the left
of the decimal point. The decimal fractions of their
floating point representations are all first rounded
off at a prespecified location, a location no more than
nine digits away from the decimal point. The number of
digits to the left of the decimal point for each input
number besides not being allowed to exceed nine must
then be such that the total number of digits from the
leftmost digit of the number to the location where
round-off is to occur does not exceed fourteen.",
acknowledgement = ack-nhfb,
keywords = "computational geometry; Delaunay triangulation; exact
integer arithmetic; power diagram; regular
triangulation; robustness; Voronoi diagram",
}
@TechReport{Bertot:2006:PGS,
author = "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
title = "A proof of {GMP} square root using the {Coq}
assistant",
type = "Research Report",
number = "RR-4475",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "28",
year = "2006",
bibdate = "Sun Sep 10 08:34:35 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4475.pdf;
ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4475.ps.gz;
http://www.inria.fr/rrrt/rr-4475.html",
abstract = "We present a formal proof (at the implementation
level) of an efficient algorithm proposed in to compute
square roots of arbitrarily large integers. This
program, which is part of the GNU Multiple Precision
Arithmetic Library (GMP), is completely proven within
the system. Proofs are developed using the Correctness
tool to deal with imperative features of the program.
The formalization is rather large (more than 13000
lines) and requires some advanced techniques for proof
management and reuse.",
acknowledgement = ack-nhfb,
}
@Article{Bik:2006:MVF,
author = "Aart J. C. Bik and Xinmin Tian and Milind B. Girkar",
title = "Multimedia vectorization of floating-point {MIN\slash
MAX} reductions",
journal = j-CCPE,
volume = "18",
number = "9",
pages = "997--1007",
day = "10",
month = aug,
year = "2006",
CODEN = "CCPEBO",
DOI = "https://doi.org/10.1002/cpe.1009",
ISSN = "1532-0626 (print), 1532-0634 (electronic)",
ISSN-L = "1532-0626",
bibdate = "Mon Dec 5 10:08:04 MST 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1532-0626;
https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Concurrency and Computation: Prac\-tice and
Experience",
journal-URL = "http://www.interscience.wiley.com/jpages/1532-0626",
onlinedate = "12 Jan 2006",
}
@Article{Boldo:2006:PFF,
author = "S. Boldo",
title = "Pitfalls of a full floating-point proof: example on
the formal proof of the {Veltkamp\slash Dekker}
algorithms",
journal = j-LECT-NOTES-COMP-SCI,
volume = "4130",
pages = "52--66",
year = "2006",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/11814771_6",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRnumber = "MR2354672",
bibdate = "Sun Feb 19 07:32:26 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Misc{Bonten:2006:ACF,
author = "J. H. M. Bonten",
title = "Arithmetic Computer Formats",
howpublished = "Web document",
day = "5",
month = oct,
year = "2006",
bibdate = "Tue Oct 30 11:08:12 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://home.hetnet.nl/mr_1/81/jhm.bonten/computers/bitsandbytes/wordsizes/",
abstract = "This map contains a set of descriptions of the
memory-word formats for the floating point numbers used
in some extinct, old and modern species of the
computer-fauna. Also it contains some theory about the
storage of these numbers. And it gives some proposals
to improve the use of decimal numbers, both in Cobol
and in Fortran/C/C++.",
acknowledgement = ack-nhfb,
keywords = "Burroughs 6700; Burroughs 7700; Burroughs 7900; Cray
1; DEC Alpha; DEC PDP-10; DEC PDP-11; DEC VAX; IBM
7094; IEEE-754; Unisys-A; Univac 1100; Univac 418",
}
@Article{Briggs:2006:IER,
author = "Keith Briggs",
title = "Implementing exact real arithmetic in {\tt python},
{C++} and {C}",
journal = j-THEOR-COMP-SCI,
volume = "351",
number = "1",
pages = "74--81",
day = "14",
month = feb,
year = "2006",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Tue Mar 29 06:48:55 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/03043975;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "I discuss the design and performance issues arising in
the efficient implementation of the scaled-integer
exact real arithmetic model introduced by Boehm and
others. This system represents a real number with a
automatically controlled level of precision by a
rational with implicit denominator. I describe three
practical codes, in python, C++ and C. These allow the
convenient use of this computational paradigm in
commonly used imperative languages.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@InProceedings{Castellanos:2006:BDF,
author = "I. D. Castellanos and J. E. Stine",
title = "A 64-bit Decimal Floating-Point Comparator",
crossref = "Dimopoulos:2006:IIC",
pages = "138--144",
year = "2006",
DOI = "https://doi.org/10.1109/ASAP.2006.2",
bibdate = "Mon Mar 19 10:17:28 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal arithmetic is growing in importance as
scientific studies reveal that current financial and
commercial applications spend a high percentage
overhead in this type of calculations. Typically,
software is utilized to emulate decimal floating point
arithmetic in these applications. On the other hand,
functional units that employ decimal floating point
hardware can improve performance by two or three orders
of magnitude. This paper presents the design and
implementation of a novel decimal floating-point
comparator compliant with the current draft revision of
the IEEE-754 Standard for floating-point arithmetic. It
utilizes a novel BCD magnitude comparator with
logarithmic delay and it supports 64-bit decimal
floating-point numbers. Area and delay results are
examined for an implementation in TSMC SCN6M SCMOS
technology.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Chang:2006:DAR,
author = "Chin-Chen Chang and Yeu-Pong Lai",
title = "A division algorithm for residue numbers",
journal = j-APPL-MATH-COMP,
volume = "172",
number = "1",
pages = "368--378",
day = "1",
month = jan,
year = "2006",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2005.02.008",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:02:52 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the residue number system, modular multiplication,
modular addition, and modular subtraction are closure
operations. However, modular division is also important
for applying the residue number system. Inspired by
Gamberger's work, we create a division operation to be
used in residue number system. In Gamberger's scheme,
the transformation from residues to a binary integer is
required for keeping the remainder. To eliminate the
overhead in transformation, our scheme uses only the
residues so that the computing efficiency can be
improved. Besides, we also provide an efficient way to
find a multiplicative inverse.",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@InProceedings{Choi:2006:DCB,
author = "Sung Woo Choi and Sung-il Pae and Hyungju Park and
Chee Yap",
title = "Decidability of Collision between a Helical Motion and
an Algebraic Motion",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Cornea:2006:SII,
author = "Marius Cornea and Cristina Anderson",
title = "Software Implementation of the {IEEE 754R} Decimal
Floating-Point Architecture",
howpublished = "World-Wide Web slides",
day = "10--12",
month = jul,
year = "2006",
bibdate = "Wed Nov 22 21:47:16 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also \cite{Anonymous:2006:RSI}.",
URL = "http://rnc7.loria.fr/cornea_poster.pdf",
acknowledgement = ack-nhfb,
keywords = "BID encoding; decimal floating-point arithmetic",
}
@Manual{Cowlishaw:2006:DCL,
author = "Mike Cowlishaw",
title = "The {decNumber C} library",
organization = pub-IBM,
address = pub-IBM:adr,
day = "22",
month = nov,
year = "2006",
bibdate = "Fri Apr 20 08:02:33 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Version 3.37",
URL = "http://download.icu-project.org/ex/files/decNumber/decNumber-icu-337.zip",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; DPD encoding",
}
@Article{Dahab:2006:SMU,
author = "R. Dahab and D. Hankerson and F. Hu and M. Long and J.
Lopez and A. Menezes",
title = "Software multiplication using {Gaussian} normal
bases",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "8",
pages = "974--984",
month = aug,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.132",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1650195",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{deDinechin:2006:STP,
author = "Florent de Dinechin and Sergey Maidanov",
title = "Software techniques for perfect elementary functions
in floating-point interval arithmetic",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions",
}
@Article{Demmel:2006:EBE,
author = "James Demmel and Yozo Hida and William Kahan and
Xiaoye S. Li and Sonil Mukherjee and E. Jason Riedy",
title = "Error bounds from extra-precise iterative refinement",
journal = j-TOMS,
volume = "32",
number = "2",
pages = "325--351",
month = jun,
year = "2006",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1141885.1141894",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Aug 23 10:29:48 MDT 2006",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We present the design and testing of an algorithm for
iterative refinement of the solution of linear
equations where the residual is computed with extra
precision. This algorithm was originally proposed in
1948 and analyzed in the 1960s as a means to compute
very accurate solutions to all but the most
ill-conditioned linear systems. However, two obstacles
have until now prevented its adoption in standard
subroutine libraries like LAPACK: (1) There was no
standard way to access the higher precision arithmetic
needed to compute residuals, and (2) it was unclear how
to compute a reliable error bound for the computed
solution. The completion of the new BLAS Technical
Forum Standard has essentially removed the first
obstacle. To overcome the second obstacle, we show how
the application of iterative refinement can be used to
compute an error bound in any norm at small cost and
use this to compute both an error bound in the usual
infinity norm, and a componentwise relative error
bound. We report extensive test results on over $ 6.2 $
million matrices of dimensions $5$, $ 10$, $ 100$, and
$ 1000$. As long as a normwise (componentwise)
condition number computed by the algorithm is less than
$ 1 / m a x \{ 10, \sqrt {n} \} \varepsilon_w$, the
computed normwise (componentwise) error bound is at
most $ 2 m a x \{ 10, \sqrt {n} \} \cdot
\varepsilon_w$, and indeed bounds the true error. Here,
$n$ is the matrix dimension and $ \varepsilon_w =
2^{-24}$ is the working precision. Residuals were
computed in double precision (53 bits of precision). In
other words, the algorithm always computed a tiny error
at negligible extra cost for most linear systems. For
worse conditioned problems (which we can detect using
condition estimation), we obtained small correct error
bounds in over 90\% of cases.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Deng:2006:IMM,
author = "Rui Deng and Yujie Zhou",
title = "Improvement to {Montgomery} Modular Inverse
Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "9",
pages = "1207--1210",
month = sep,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.150",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1668048",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Deschamps:2006:SAC,
author = "Jean-Pierre Deschamps and G{\'e}ry Jean Antoine Bioul
and Gustavo D. Sutter",
title = "Synthesis of arithmetic circuits: {FPGA}, {ASIC}, and
embedded systems",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xix + 556",
year = "2006",
ISBN = "0-471-68783-9 (hardcover)",
ISBN-13 = "978-0-471-68783-2 (hardcover)",
LCCN = "TK7895.A65 D47 2006",
bibdate = "Wed Oct 1 10:16:56 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0621/2005003237-b.html;
http://www.loc.gov/catdir/enhancements/fy0621/2005003237-d.html;
http://www.loc.gov/catdir/toc/ecip057/2005003237.html",
acknowledgement = ack-nhfb,
author-dates = "1945--",
subject = "Computer arithmetic and logic units; Digital
electronics; Embedded computer systems",
tableofcontents = "Mathematical background \\
Number representation \\
Arithmetic operations: addition and subtraction \\
Arithmetic operations: multiplication \\
Arithmetic operations: division \\
Other arithmetic operations \\
Finite field operations \\
Hardware platforms \\
Circuit synthesis: general principles \\
Adders and subtractors \\
Multipliers \\
Dividers \\
Other arithmetic operators \\
Circuits for finite field operations \\
Floating-point unit",
}
@Misc{Detrey:2006:FVL,
author = "J{\'e}r{\'e}mie Detrey and Florent de Dinechin",
title = "{FPLibrary}. {A} {VHDL} library of parametrisable
floating-point and {LNS} operators for {FPGA}",
howpublished = "Web site and source code.",
year = "2006",
bibdate = "Sat Oct 9 12:42:00 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The FPLibrary has been superceded by the FloPoCo
project \cite{deDinechin:2010:FGA}.",
URL = "http://www.ens-lyon.fr/LIP/Arenaire/Ware/FPLibrary/",
acknowledgement = ack-nhfb,
}
@Article{Dietz:2006:FPC,
author = "Hank Dietz and Bill Dieter and Randy Fisher and
Kungyen Chang",
title = "Floating-Point Computation with Just Enough Accuracy",
journal = j-LECT-NOTES-COMP-SCI,
volume = "3991",
pages = "226--233",
year = "2006",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Jan 06 09:42:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ICCS 2006, Part I, conference proceedings.",
URL = "http://aggregate.org/NPAR/iccs2006.pdf",
abstract = "Most mathematical formulae are defined in terms of
operations on real numbers, but computers can only
operate on numeric values with finite precision and
range. Using floating-point values as real numbers does
not clearly identify the precision with which each
value must be represented. Too little precision yields
inaccurate results; too much wastes computational
resources.\par
The popularity of multimedia applications has made fast
hardware support for low-precision floating-point
arithmetic common in Digital Signal Processors (DSPs),
SIMD Within A Register (SWAR) instruction set
extensions for general purpose processors, and in
Graphics Processing Units (GPUs). In this paper, we
describe a simple approach by which the speed of these
low-precision operations can be speculatively employed
to meet user-specified accuracy constraints. Where the
native precision(s) yield insufficient accuracy, a
simple technique is used to efficiently synthesize
enhanced precision using pairs of native values.",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "Digital Signal Processors (DSPs); double-double
arithmetic; native pair; pair-precision arithmetic;
SIMD Within A Register (SWAR)",
}
@InProceedings{Diniz:2006:DFP,
author = "P. C. Diniz and G. Govindu",
title = "Design of field-programmable dual-precision
floating-point arithmetic units",
crossref = "Bertels:2006:FPI",
pages = "1--4",
year = "2006",
DOI = "https://doi.org/10.1109/FPL.2006.311302",
bibdate = "Sat Oct 9 12:37:10 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The growth in FPGA capacity and the inclusion of
embedded arithmetic cores has enabled the use of these
devices for general purpose floating-point computing.
Despite their clock rate handicap with respect to
contemporary general-purpose processors, these devices
can be field-programmable to meet the precision
requirements and operator-level parallelism of a
specific computation. In this paper we describe and
evaluate the performance of dual-precision, pipelined,
floating-point arithmetic cores for addition,
multiplication and division. Each of these arithmetic
cores can be switched at run-time to perform either one
double-precision operation, or with the same hardware
resources, perform two single-precision operations. We
also implemented quad-precision cores which can be
switched to perform either one quad-precision operation
or two double-precision operations. As an application
of these cores, we describe and evaluate the
performance potential of a custom, but flexible, vector
processing units as part of a system-level architecture
targeting a Xilinx Virtex-II Prom 100 FPGA device
connected to multiple SRAM banks.",
acknowledgement = ack-nhfb,
xxpages = "733--736",
}
@Article{Enge:2006:CCP,
author = "Andreas Enge",
title = "The complexity of class polynomial computation via
floating point approximations",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "24",
month = jan,
year = "2006",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in Mathematics of Computation 78, {\bf 266}
(2009) 1089--1107.",
URL = "http://arxiv.org/abs/cs/0601104",
abstract = "We analyse the complexity of computing class
polynomials, that are an important ingredient for CM
constructions of elliptic curves, via complex floating
point approximations of their roots. The heart of the
algorithm is the evaluation of modular functions in
several arguments. The fastest one of the presented
approaches uses a technique devised by Dupont to
evaluate modular functions by Newton iterations on an
expression involving the arithmetic-geometric mean. It
runs in time $ O (|D| \log^5 |D| \log \log |D|) = O
(|D|^{1 + \epsilon }) = O (h^{2 + \epsilon }) $ for any
$ \epsilon > 0 $, where $D$ is the CM discriminant and
$h$ is the degree of the class polynomial. Another fast
algorithm uses multipoint evaluation techniques known
from symbolic computation; its asymptotic complexity is
worse by a factor of $ \log |D|$. Up to logarithmic
factors, this running time matches the size of the
constructed polynomials. The estimate also relies on a
new result concerning the complexity of enumerating the
class group of an imaginary-quadratic order and on a
rigorously proven upper bound for the height of class
polynomials.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA); Symbolic Computation
(cs.SC); Number Theory (math.NT)",
}
@Article{Fan:2006:RBM,
author = "H. Fan and M. A. Hasan",
title = "Relationship between {$ \mathrm {GF}(2^m) $}
{Montgomery} and Shifted Polynomial Basis
Multiplication Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "9",
pages = "1202--1206",
month = sep,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.152",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1668047",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Feldstein:2006:GTO,
author = "Alan Feldstein and Peter R. Turner",
title = "Gradual and tapered overflow and underflow: a
functional differential equation and its
approximation",
journal = j-APPL-NUM-MATH,
volume = "56",
number = "3--4",
pages = "517--532",
month = mar # "\slash " # apr,
year = "2006",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Tue Aug 24 11:17:20 MDT 2010",
bibsource = "http://www.sciencedirect.com/science/journal/01689274;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Gandhi:2006:DRA,
author = "Rajiv Gandhi and Samir Khuller and Srinivasan
Parthasarathy and Aravind Srinivasan",
title = "Dependent rounding and its applications to
approximation algorithms",
journal = j-J-ACM,
volume = "53",
number = "3",
pages = "324--360",
month = may,
year = "2006",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/1147954.1147956",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Aug 23 06:38:20 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Gochman:2006:IIC,
author = "Simcha Gochman and Avi Mendelson and Alon Naveh and
Efraim Rotem",
title = "Introduction to {Intel Core Duo} Processor
Architecture",
journal = j-INTEL-TECH-J,
volume = "10",
number = "2",
pages = "89--97",
day = "15",
month = may,
year = "2006",
DOI = "https://doi.org/10.1535/itj.1002",
ISSN = "1535-766X",
bibdate = "Tue Jun 20 07:47:25 2006",
bibsource = "ftp://download.intel.com/technology/itj/2006/volume10issue02/vol10_iss02.pdf;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://developer.intel.com/technology/itj/2006/volume10issue02/art01_Intro_to_Core_Duo/p01_abstract.htm",
acknowledgement = ack-nhfb,
remark = "From p. 91: ``Another bottleneck that was discovered
was the handling of the floating point (FP) Control
Word (CW). The FP CW is part of the x87 state and was
usually viewed as `constant'; namely it is loaded once
at the beginning and stays constant throughout the
program. This is indeed the way the FP CW is used by
most of the programs. However there are some FP
applications that manipulate the `rounding control'
which is located in this register: the default rounding
mode is `rounding to nearest even' but before
converting results to fixed point, some applications
change the round control to `chop' (this is the rule
with C programs for example). Such behavior was treated
rather inefficiently by the Pentium M core: each
manipulation of the FP CW was effectively stalling the
pipeline until its completion. The Intel Core Duo core
introduced a new renaming mechanism for the FP CW so
that four different versions of this register can
coexist on the fly without stalling the machine.''",
}
@Article{Gok:2006:IMO,
author = "M. Gok and M. J. Schulte and M. G. Arnold",
title = "Integer multipliers with overflow detection",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "8",
pages = "1062--1066",
month = aug,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.126",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1650203",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Goubault:2006:SAN,
author = "Eric Goubault and Sylvie Putot",
title = "Static analysis of numerical algorithms",
crossref = "Yi:2006:SAI",
pages = "18--34",
year = "2006",
DOI = "https://doi.org/10.1007/11823230_3",
bibdate = "Sat Apr 01 08:03:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/chapter/10.1007/11823230_3",
acknowledgement = ack-nhfb,
}
@InProceedings{Graa:2006:IFF,
author = "Guillaume Da Gra{\c{c}}a and David Defour",
title = "Implementation of float-float operators on graphics
hardware",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Graca:2006:ODE,
author = "Daniel S. Gra{\c{c}}a and Ning Zhong and Jorge
Buescu",
title = "The ordinary differential equation defined by a
computable function whose maximal interval of existence
is non-computable",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Graillat:2006:ICH,
author = "Stef Graillat and Philippe Langlois and Nicolas
Louvet",
title = "Improving the Compensated {Horner} Scheme with a Fused
Multiply and Add",
crossref = "Haddad:2006:ACP",
pages = "1323--1327",
year = "2006",
DOI = "https://doi.org/10.1145/1141277.1141585",
bibdate = "Sat Feb 26 18:19:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Several different techniques and softwares intend to
improve the accuracy of results computed in a fixed
finite precision. Here we focus on a method to improve
the accuracy of the polynomial evaluation. It is well
known that the use of the Fused Multiply and Add
operation available on some microprocessors like Intel
Itanium improves slightly the accuracy of the Horner
scheme. In this paper, we propose an accurate
compensated Horner scheme specially designed to take
advantage of the Fused Multiply and Add. We prove that
the computed result is as accurate as if computed in
twice the working precision. The algorithm we present
is fast since it only requires well optimizable
floating point operations, performed in the same
working precision as the given data.",
acknowledgement = ack-nhfb,
}
@InProceedings{Harrison:2006:FPV,
author = "John Harrison",
title = "Floating-point verification using theorem proving",
crossref = "Cimatti:2006:FMH",
pages = "211--242",
year = "2006",
DOI = "https://doi.org/10.1007/11757283_8",
bibdate = "Wed Nov 26 22:40:10 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hars:2006:MIA,
author = "Laszlo Hars",
title = "Modular Inverse Algorithms Without Multiplications for
Cryptographic Applications",
journal = j-EURASIP-J-EMBED-SYS,
volume = "2006",
pages = "1--13",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1155/ES/2006/32192",
ISSN = "1687-3955 (print), 1687-3963 (electronic)",
ISSN-L = "1687-3955",
bibdate = "Wed Dec 28 09:54:06 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Article ID 32192.",
URL = "http://downloads.hindawi.com/journals/es/2006/032192.pdf",
abstract = "Hardware and algorithmic optimization techniques are
presented to the left-shift, right-shift, and the
traditional Euclidean-modular inverse algorithms.
Theoretical arguments and extensive simulations
determined the resulting expected running time. On many
computational platforms these turn out to be the
fastest known algorithms for moderate operand lengths.
They are based on variants of Euclidean-type extended
GCD algorithms. On the considered computational
platforms for operand lengths used in cryptography, the
fastest presented modular inverse algorithms need about
twice the time of modular multiplications, or even
less. Consequently, in elliptic curve cryptography
delaying modular divisions is slower (affine
coordinates are the best) and the RSA and ElGamal
cryptosystems can be accelerated.",
acknowledgement = ack-nhfb,
fjournal = "EURASIP Journal on Embedded Systems",
}
@Article{Hill:2006:QUB,
author = "M. Hill and I. Robinson",
title = "Quadrature using 64-bit {IEEE} arithmetic for
integrands over $ [0, 1] $ with a singularity at $1$",
journal = j-THEOR-COMP-SCI,
volume = "351",
number = "1",
pages = "82--100",
day = "14",
month = feb,
year = "2006",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Tue Mar 29 06:48:55 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/03043975;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a detailed study of some problems
encountered when quadrature over $ [0, 1] $ is
attempted with integrands that have a singularity at
$1$. Methods designed to increase the accuracy of such
quadratures, for example, the application of
periodising transformations, are examined in the
context of the representational limitations of 64-bit
IEEE arithmetic near $1$ in $ [0, 1] $. A heuristic is
proposed for the forecasting of a lower bound on the
irremovable error due to these limitations. We conclude
by affirming the commonly accepted procedure that where
possible, integrals should be symbolically transformed
so that any remaining singularity occurs at $0$.",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{How:2006:RRN,
author = "H. T. How and T. H. Liew and Ee-Lin Kuan and Lie-Liang
Yang and L. Hanzo",
title = "A redundant residue number system coded burst-by-burst
adaptive joint-detection based {CDMA} speech
transceiver",
journal = j-IEEE-TRANS-VEH-TECHNOL,
volume = "55",
number = "1",
pages = "387--396",
month = jan,
year = "2006",
CODEN = "ITUTAB",
DOI = "https://doi.org/10.1109/TVT.2005.861175",
ISSN = "0018-9545 (print), 1939-9359 (electronic)",
ISSN-L = "0018-9545",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=33430",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Vehicular Technology",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
keywords = "residue arithmetic; residue number system",
summary = "A burst-by-burst (BbB) adaptive speech transceiver is
proposed, which can drop its source coding rate and
speech quality under transceiver control in order to
invoke a more error resilient modem mode among less
favorable channel conditions. The \ldots{}",
}
@TechReport{Hurlimann:2006:BLB,
author = "Werner H{\"u}rlimann",
title = "{Benford's Law} from 1881 to 2006: a bibliography",
type = "Report",
address = "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland",
pages = "15",
day = "5",
month = jul,
year = "2006",
bibdate = "Fri Mar 30 11:32:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/pdf/math.ST/0607168",
acknowledgement = ack-nhfb,
keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
remark = "This bibliography lists 325 references on the title
subject, with these (years) and counts: (1881) 1,
(1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1,
(1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1,
(1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2,
(1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1,
(1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2,
(1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3,
(1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4,
(1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1,
(1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6,
(1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4,
(1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12,
(2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29,
(2005) 34, (2006) 18.",
}
@Manual{IBM:2006:PDF,
author = "{IBM Corporation}",
title = "Preliminary Decimal-Floating-Point Architecture",
publisher = pub-IBM,
address = pub-IBM:adr,
pages = "viii + 52",
month = nov,
year = "2006",
bibdate = "Sat Apr 07 12:13:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Form number SA23-2232-00.",
URL = "http://publibz.boulder.ibm.com/epubs/pdf/a2322320.pdf;
http://www-03.ibm.com/servers/eserver/zseries/zos/bkserv/r3pdf/zarchpops.html",
abstract = "This is a preliminary description of the
decimal-floating-point (DFP) facility and the
floating-point support-enhancement facility. It will be
superseded by the next published version of the {\em
IBM z/Architecture Principles of Operation\/}
(SA22-7832).",
acknowledgement = ack-nhfb,
}
@Article{Imana:2006:BPF,
author = "J. L. Imana and J. M. Sanchez and F. Tirado",
title = "Bit-parallel finite field multipliers for irreducible
trinomials",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "5",
pages = "520--533",
month = may,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.69",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:54 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1613833",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Intel:2006:IFP,
author = "{Intel}",
title = "{Intel} and Floating Point: Updating One of the
Industry's Most Successful Standards",
type = "{Web} report",
institution = "Intel Corporation",
address = "San Jose, CA, USA",
pages = "11",
day = "17",
month = jul,
year = "2006",
bibdate = "Thu Oct 14 14:43:38 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.intel.com/standards/floatingpoint.pdf",
acknowledgement = ack-nhfb,
remark = "Includes mention of some major historical systems
failures due to faulty handling of floating-point
arithmetic, and discusses future directions for decimal
arithmetic.",
}
@Book{ISO:2006:IIIa,
author = "{ISO}",
title = "{ISO\slash IEC 10967-3}: {Information} technology ---
{Language} independent arithmetic --- {Part} 3:
{Complex} integer and floating point arithmetic and
complex elementary numerical functions",
publisher = pub-ISO,
address = pub-ISO:adr,
pages = "viii + 149",
day = "15",
month = aug,
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sun Mar 15 11:09:44 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://standards.iso.org/ittf/PubliclyAvailableStandards/c037994_ISO_IEC_10967-3_2006(E).zip;
http://www.iso.ch/cate/d24427.html",
acknowledgement = ack-nhfb,
}
@Misc{ISO:2006:IIJa,
author = "{ISO}",
title = "{ISO\slash IEC JTC1 SC22 WG14 N1154}: Extension for
the programming language {C} to support decimal
floating-point arithmetic",
howpublished = "World-Wide Web document",
day = "27",
month = feb,
year = "2006",
bibdate = "Tue Mar 07 18:23:45 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1154.pdf",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Misc{ISO:2006:IIJb,
author = "{ISO}",
title = "{ISO\slash IEC JTC1 SC22 WG14 N1161}: Rationale for
{TR 24732}: Extension to the programming language {C}:
Decimal Floating-Point Arithmetic",
howpublished = "World-Wide Web document",
day = "27",
month = feb,
year = "2006",
bibdate = "Tue Mar 07 18:23:45 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1161.pdf",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Misc{ISO:2006:IIJc,
author = "{ISO}",
title = "{ISO\slash IEC JTC1 SC22 WG14 N1176}: Extension for
the programming language {C} to support decimal
floating-point arithmetic",
howpublished = "World-Wide Web document",
pages = "iii + 33",
day = "24",
month = may,
year = "2006",
bibdate = "Sat Feb 24 20:00:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://open-std.org/jtc1/sc22/wg14/www/docs/n1176.pdf",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Misc{Kahan:2006:AIR,
author = "William Kahan",
title = "Applications of {IEEE 754r}'s Rounding Modes",
howpublished = "World-Wide Web document.",
day = "16",
month = feb,
year = "2006",
bibdate = "Fri Feb 17 17:54:50 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://nonabelian.com/754/RNDGMODE.TXT",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaivani:2006:RID,
author = "A. Kaivani and A. Zaker Alhosseini and S. Gorgin and
M. Fazlali",
title = "Reversible Implementation of Densely-Packed-Decimal
Converter to and from Binary-Coded-Decimal Format Using
in {IEEE-754R}",
crossref = "Mohanty:2006:IIC",
pages = "273--276",
year = "2006",
bibdate = "Thu Aug 07 18:12:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Binary Coded Decimal (BCD) encoding has always
dominated the decimal arithmetic algorithms and their
hardware implementation. Due to importance of decimal
arithmetic, the decimal format defined in lEEE 754
floating point standard has been revisited. It uses
Densely Packed Decimal (DPD) encoding to store
significand part of a decimal floating point number.
Furthermore in recent years reversible logic has
attracted the attention of engineers for designing low
power CMOS circuits, as it is not possible to realize
quantum computing without reversible logic
implementation. This paper derives the reversible
implementation of DPD converter to and from
conventional BCD format using in IEEE 754R.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Kang:2006:SHS,
author = "J.-Y. Kang and J.-L. Gaudiot",
title = "A Simple High-Speed Multiplier Design",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "10",
pages = "1253--1258",
month = oct,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.156",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1683756",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kettani:2006:CBN,
author = "Houssain Kettani",
title = "On the Conversion Between Number Systems",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "53",
number = "11",
pages = "1255--1258",
month = nov,
year = "2006",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/TCSII.2006.882856",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Mon Mar 19 10:05:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This brief revisits the problem of conversion between
number systems and asks the following question: given a
nonnegative decimal number, what is the value of the
digit at position in the corresponding base number?
Thus, we do not require the knowledge of other digits
except the one we are interested in. Accordingly, we
present a conversion function that relates each digit
in a base system to the decimal value that is equal to
the base number in question. We also show some
applications of this new algorithm in the areas of
parallel computing and cryptography.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems. 2, Analog
and Digital Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "Algorithm's efficiency; base numbers; conversion",
}
@Article{Kong:2006:IGA,
author = "Fanyu Kong and Zhun Cai and Jia Yu and Daxing Li",
title = "Improved generalized {Atkin} algorithm for computing
square roots in finite fields",
journal = j-INFO-PROC-LETT,
volume = "98",
number = "1",
pages = "1--5",
day = "15",
month = apr,
year = "2006",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Thu Mar 31 18:41:08 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Kornerup:2006:CSV,
author = "Peter Kornerup and Jean-Michel Muller",
title = "Choosing starting values for certain {Newton--Raphson}
iterations",
journal = j-THEOR-COMP-SCI,
volume = "351",
number = "1",
pages = "101--110",
day = "14",
month = feb,
year = "2006",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Tue Mar 29 06:48:55 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tcs2005.bib",
abstract = "We aim at finding the best possible seed values when
computing $ a^{1 / p} $ using the Newton--Raphson
iteration in a given interval. A natural choice of the
seed value would be the one that best approximates the
expected result. It turns out that in most cases, the
best seed value can be quite far from this natural
choice. When we evaluate a monotone function $ f(a) $
in the interval $ [a_\mathrm {min}, a_\mathrm {max}] $,
by building the sequence $ x_n $ defined by the
Newton--Raphson iteration, the natural choice consists
in choosing $ x_0 $ equal to the arithmetic mean of the
endpoint values. This minimizes the maximum possible
distance between $ x_0 $ and $ f(a) $. And yet, if we
perform $n$ iterations, what matters is to minimize the
maximum possible distance between $ x_n $ and $ f(a) $.
In several examples, the value of the best starting
point varies rather significantly with the number of
iterations.",
acknowledgement = ack-nhfb,
ajournal = "Theor. Comput. Sci.",
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975/",
}
@InProceedings{Kornerup:2006:RCN,
author = "Peter Kornerup and Jean-Michel Muller",
title = "{RN}-Codings: New Insights and Some Applications",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Kulikova:2006:HFD,
author = "A. A. Kulikova and Yu. V. Prokhorov and V. I.
Khokhlov",
title = "{H.F.D.} ({$H$}-function Distribution) and {Benford's
Law}. {I}",
journal = j-THEORY-PROBAB-APPL,
volume = "50",
number = "2",
pages = "311--315",
month = jan,
year = "2006",
CODEN = "TPRBAU",
DOI = "https://doi.org/10.1137/S0040585X97981706",
ISSN = "0040-585X (print), 1095-7219 (electronic)",
ISSN-L = "0040-585X",
bibdate = "Wed May 19 18:14:51 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theory of Probability and its Applications",
journal-URL = "http://epubs.siam.org/tvp",
}
@Article{Kumar:2006:ODS,
author = "Sandeep Kumar and T. Wollinger and C. Paar",
title = "Optimum Digit Serial {$ \mathrm {GF}(2^m) $}
Multipliers for Curve-Based Cryptography",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "10",
pages = "1306--1311",
month = oct,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.165",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1683761",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kushner:2006:I,
author = "David Kushner",
title = "The Insomniacs",
journal = j-IEEE-SPECTRUM,
volume = "43",
number = "12",
pages = "24--29",
month = dec,
year = "2006",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2006.253405",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Sep 01 16:23:03 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "floating-point arithmetic; IBM Cell processor; Sony
Playstation 3",
}
@InProceedings{Lang:2006:SRI,
author = "Tomas Lang and Javier D. Bruguera",
title = "The sunity representation to improve the accuracy of
some computations",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Langou:2006:EPBa,
author = "Julie Langou and Julien Langou and Piotr Luszczek and
Jakub Kurzak and Alfredo Buttari and Jack Dongarra",
title = "Exploiting the Performance of 32 bit Floating Point
Arithmetic in Obtaining 64 bit Accuracy (Revisiting
Iterative Refinement for Linear Systems)",
type = "LAPACK Working Note",
number = "175",
institution = inst-UT-CS,
address = inst-UT-CS:adr,
pages = "17",
month = jun,
year = "2006",
bibdate = "Mon Oct 09 12:05:43 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.netlib.org/lapack/lawnspdf/lawn175.pdf;
http://www.netlib.org/lapack/lawnspdf/lawn175.ps",
abstract = "Recent versions of microprocessors exhibit performance
characteristics for 32 bit floating point arithmetic
(single precision) that is substantially higher than 64
bit floating point arithmetic (double precision).
Examples include the Intel's Pentium IV and M
processors, AMD's Opteron architectures and the IBM's
Cell Broad Engine processor. When working in single
precision, floating point operations can be performed
up to two times faster on the Pentium and up to ten
times faster on the Cell over double precision. The
performance enhancements in these architectures are
derived by accessing extensions to the basic
architecture, such as SSE2 in the case of the Pentium
and the vector functions on the IBM Cell. The
motivation for this paper is to exploit single
precision operations whenever possible and resort to
double precision at critical stages while attempting to
provide the full double precision results. The results
described here are fairly general and can be applied to
various problems in linear algebra such as solving
large sparse systems, using direct or iterative methods
and some eigenvalue problems. There are limitations to
the success of this process, such as when the
conditioning of the problem exceeds the reciprocal of
the accuracy of the single precision computations. In
that case the double precision algorithm should be
used.",
acknowledgement = ack-nhfb,
}
@InProceedings{Langou:2006:EPBb,
author = "Julie Langou and Julien Langou and Piotr Luszczek and
Jakub Kurzak and Alfredo Buttari and Jack Dongarra",
title = "Exploiting the performance of 32 bit floating point
arithmetic in obtaining 64 bit accuracy (revisiting
iterative refinement for linear systems)",
crossref = "ACM:2006:SCH",
pages = "??--??",
year = "2006",
DOI = "https://doi.org/10.1145/1188455.1188573",
bibdate = "Thu Nov 08 20:00:17 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recent versions of microprocessors exhibit performance
characteristics for 32 bit floating point arithmetic
(single precision) that is substantially higher than 64
bit floating point arithmetic (double precision).
Examples include the Intel's Pentium IV and M
processors, AMD's Opteron architectures and the IBM's
Cell Broad Engine processor. When working in single
precision, floating point operations can be performed
up to two times faster on the Pentium and up to ten
times faster on the Cell over double precision. The
performance enhancements in these architectures are
derived by accessing extensions to the basic
architecture, such as SSE2 in the case of the Pentium
and the vector functions on the IBM Cell. The
motivation for this paper is to exploit single
precision operations whenever possible and resort to
double precision at critical stages while attempting to
provide the full double precision results. The results
described here are fairly general and can be applied to
various problems in linear algebra such as solving
large sparse systems, using direct or iterative methods
and some eigenvalue problems. There are limitations to
the success of this process, such as when the
conditioning of the problem exceeds the reciprocal of
the accuracy of the single precision computations. In
that case the double precision algorithm should be
used.",
acknowledgement = ack-nhfb,
articleno = "113",
}
@TechReport{Lefevre:2006:WCE,
author = "Vincent Lef{\`e}vre and Damien Stehl{\'e} and Paul
Zimmermann",
title = "Worst Cases for the Exponential Function in the {IEEE
754r} {{\tt decimal64}} Format",
type = "Technical report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "14",
month = sep,
year = "2006",
bibdate = "Wed Sep 06 07:31:38 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "To appear in a special LNCS issue following the
Dagstuhl seminar 06021: Reliable Implementation of Real
Number Algorithms: Theory and Practice.",
URL = "http://www.loria.fr/~zimmerma/papers/decimalexp-lncs-final.pdf;
http://www.loria.fr/~zimmerma/wc/decimal32.html;
http://www.loria.fr/~zimmerma/wc/decimal64.html",
abstract = "We searched for the worst cases for correct rounding
of the exponential function in the IEEE 754r decimal64
format, and computed all the bad cases whose distance
from a breakpoint (for all rounding modes) is less than
$ 10^{-15} $ ulp, and we give the worst ones. In
particular, the worst case for $ |x| \geq 3 \times
10^{-11} $ is $ \exp (9.407822313572878 \times 10^{-2})
= 1.098645682066338 \, 50000000000000000 \, 278 \ldots
{} $. This work can be extended to other elementary
functions in the decimal64 format and allows the design
of reasonably fast routines that will evaluate these
functions with correct rounding, at least in some
domains.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; decimal floating-point arithmetic",
}
@Article{Liew:2006:SRR,
author = "T. H. Liew and Lie-Liang Yang and L. Hanzo",
title = "Systematic redundant residue number system codes:
analytical upper bound and iterative decoding
performance over {AWGN} and {Rayleigh} channels",
journal = j-IEEE-TRANS-COMM,
volume = "54",
number = "6",
pages = "1006--1016",
month = jun,
year = "2006",
CODEN = "IECMBT",
DOI = "https://doi.org/10.1109/TCOMM.2006.876843",
ISSN = "0090-6778 (print), 1558-0857 (electronic)",
ISSN-L = "0090-6778",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=34443",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Communications",
keywords = "residue arithmetic; residue number system",
summary = "The novel family of redundant residue number system
(RRNS) codes is studied. RRNS codes constitute
maximum-minimum distance block codes, exhibiting
identical distance properties to Reed--Solomon codes.
Binary to RRNS symbol-mapping methods are \ldots{}",
}
@Article{Lindstrom:2006:FEC,
author = "Peter Lindstrom and Martin Isenburg",
title = "Fast and Efficient Compression of Floating-Point
Data",
journal = j-IEEE-TRANS-VIS-COMPUT-GRAPH,
volume = "12",
number = "5",
pages = "1245--1250",
month = sep # "\slash " # oct,
year = "2006",
CODEN = "ITVGEA",
DOI = "https://doi.org/10.1109/TVCG.2006.143",
ISSN = "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
ISSN-L = "1077-2626",
bibdate = "Thu Jul 3 15:20:21 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Visualization and Computer
Graphics",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945",
}
@Article{Mahalingam:2006:IAM,
author = "Venkatraman Mahalingam and Nagarajan Ranganathan",
title = "Improving Accuracy in {Mitchell}'s Logarithmic
Multiplication Using Operand Decomposition",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "12",
pages = "1523--1535",
month = dec,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.198",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1717385",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "See \cite{Mitchell:1962:CMD}.",
}
@Article{Marques:2006:BIF,
author = "Osni A. Marques and E. Jason Riedy and Christof
V{\"o}mel",
title = "Benefits of {IEEE-754} Features in Modern Symmetric
Tridiagonal Eigensolvers",
journal = j-SIAM-J-SCI-COMP,
volume = "28",
number = "5",
pages = "1613--1633",
month = jan,
year = "2006",
CODEN = "SJOCE3",
DOI = "",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:43:43 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/28/5;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{Maslennikowa:2006:DFB,
author = "N. Maslennikowa and O. Maslennikow and R. Berezowski
and J.-P. Lienou",
booktitle = "{MIXDES 2006}, Proceedings of the International
Conference Mixed Design of Integrated Circuits and
System, 22--24 June 2006",
title = "Design of {FPGA}-based Multi-operand Modular Adders
for Residue Number System Converters",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "264--268",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2006.1693181",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
}
@PhdThesis{Melquiond:2006:AIC,
author = "Guillaume Melquiond",
title = "De l'arithm{\'e}tique d'intervalles {\`a} la
certification de programmes. ({French}) [{From}
interval arithmetic to program certification]",
type = "Ph.D. dissertation",
school = "{\'E}cole normale sup{\'e}rieure de Lyon",
address = "Lyon, France",
pages = "vi + 126",
day = "21",
month = nov,
year = "2006",
bibdate = "Fri Sep 22 16:41:05 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://theses.hal.science/tel-01094485/file/06-these.pdf",
abstract = "Computer numbers are usually limited, both in range
and in precision. As a consequence, a careful
certification has to be performed for applications that
compute with these sets of numbers. Unfortunately,
performing such a certification by hand is error-prone.
Formal methods can ensure that the certification is
correct, but making use of them is usually long and
tedious, even for experts. This thesis aims at
improving the availability of these methods to
developers by automatizing their implementation. The
key concepts are the use of interval arithmetic, a
database of theorems on computer arithmetics, and a
system for rewriting expressions in order to compute
tight bounds on rounding errors.\par
This approach has led to the development of the Gappa
tool. It is designed to verify the numeric properties
of programs relying on floating-point or fixed-point
arithmetic. When verifying these properties, the tool
also generates formal proofs of their correctness.
These proofs can later be mechanically checked by the
Coq proof assistant. Gappa has been successfully used
for certifying some functions of the CRlibm, CGAL, and
FLIP libraries, among others",
acknowledgement = ack-nhfb,
keywords = "Coq proof assistant; correct rounding; fixed-point
arithmetic; floating-point arithmetic; formal methods;
interval arithmetic; program certification",
}
@Article{Meurant:2006:LCG,
author = "G{\'e}rard Meurant and Zden{\v{e}}k Strako{\v{s}}",
title = "The {Lanczos} and conjugate gradient algorithms in
finite precision arithmetic",
journal = j-ACTA-NUMERICA,
volume = "15",
pages = "471--542",
year = "2006",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S096249290626001X",
ISBN = "0-521-86815-7",
ISBN-13 = "978-0-521-86815-0",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "65F15 (65F10 65G50)",
MRnumber = "2269746 (2007m:65031)",
MRreviewer = "A. Bultheel",
bibdate = "Sat Sep 24 10:35:17 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Lanczos and conjugate gradient algorithms were
introduced more than five decades ago as tools for
numerical computation of dominant eigenvalues of
symmetric matrices and for solving linear algebraic
systems with symmetric positive definite matrices,
respectively. Because of their fundamental relationship
with the theory of orthogonal polynomials and Gauss
quadrature of the Riemann--Stieltjes integral, the
Lanczos and conjugate gradient algorithms represent
very interesting general mathematical objects, with
highly nonlinear properties which can be conveniently
translated from algebraic language into the language of
mathematical analysis, and vice versa. The algorithms
are also very interesting numerically, since their
numerical behaviour can be explained by an elegant
mathematical theory, and the interplay between analysis
and algebra is useful there too.\par
Motivated by this view, the present contribution wishes
to pay a tribute to those who have made an
understanding of the Lanczos and conjugate gradient
algorithms possible through their pioneering work, and
to review recent solutions of several open problems
that have also contributed to knowledge of the
subject.",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "16 May 2006",
}
@Misc{Muller:2006:CLA,
author = "Jean-Michel Muller",
title = "{CR-LIBM}, and {Arenaire}'s results on function
implementation",
howpublished = "World-Wide Web slides.",
pages = "92",
month = nov,
year = "2006",
bibdate = "Wed Nov 15 07:54:31 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://grouper.ieee.org/groups/754/email/pdfNTnWzhjsBA.pdf",
acknowledgement = ack-nhfb,
}
@Book{Muller:2006:EFA,
author = "Jean-Michel Muller",
title = "Elementary functions: algorithms and implementation",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
edition = "Second",
pages = "xxii + 266",
year = "2006",
ISBN = "0-8176-4372-9",
ISBN-13 = "978-0-8176-4372-0",
LCCN = "QA331 .M866 2006",
bibdate = "Fri Jul 25 12:00:55 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$59.95",
URL = "http://perso.ens-lyon.fr/jean-michel.muller/SecondEdition.html;
http://www.springer.com/sgw/cda/frontpage/0,,4-40109-22-72377986-0,00.html",
acknowledgement = ack-nhfb,
subject = "Functions; Data processing; Algorithms",
tableofcontents = "Preface to the second edition \\
Preface to the first edition \\
Introduction \\
Some basic things about computer arithmetic \\
Part I. Algorithms based on polynomial approximation
and/or table lookup, multiple-precision evaluation of
functions \\
Polynomial or rational approximations \\
Table-based methods \\
Multiple-precision evaluation of functions \\
Part II. Shift-and-add algorithms \\
Introduction to shift-and-add algorithms \\
The CORDIC algorithm \\
Some other shift-and-add algorithms \\
Part III. Range reduction, final rounding and
exceptions \\
Range reduction \\
Final rounding \\
Miscellaneous \\
Examples of implementation \\
Bibliography \\
Index",
}
@Article{Nievergelt:2006:EPD,
author = "Yves Nievergelt",
title = "Extensions of {Priest}'s Double-Precision Summation",
journal = j-SIAM-J-SCI-COMP,
volume = "28",
number = "5",
pages = "1837--1850",
month = jan,
year = "2006",
CODEN = "SJOCE3",
DOI = "",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:43:43 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/28/5;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation",
}
@Article{Nikmehr:2006:FDF,
author = "H. Nikmehr and B. Phillips and C.-C. Lim",
title = "Fast Decimal Floating-Point Division",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "14",
number = "9",
pages = "951--961",
month = sep,
year = "2006",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2006.884047",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Mon Mar 19 10:15:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A new implementation for decimal floating-point (DFP)
division is introduced. The algorithm is based on
high-radix SRT division The SRT division algorithm is
named after D. Sweeney, J. E. Robertson, and T. D.
Tocher. with the recurrence in a new decimal
signed-digit format. Quotient digits are selected using
comparison multiples, where the magnitude of the
quotient digit is calculated by comparing the truncated
partial remainder with limited precision multiples of
the divisor. The sign is determined concurrently by
investigating the polarity of the truncated partial
remainder. A timing evaluation using a logic synthesis
shows a significant decrease in the division execution
time in contrast with one of the fastest DFP dividers
reported in the open literature",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
keywords = "decimal floating-point arithmetic",
}
@Article{OLeary:2006:CMA,
author = "Dianne P. O'Leary",
title = "Computer Memory and Arithmetic: a Look under the
Hood",
journal = j-COMPUT-SCI-ENG,
volume = "8",
number = "3",
pages = "54--59",
month = may # "\slash " # jun,
year = "2006",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCSE.2006.39",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Thu Jul 3 11:16:38 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Computers have a hierarchy of storage units. Memory
management systems try to store information that you
will soon need in a unit that gives fast access. This
means that large vectors and arrays are broken up and
moved piece by piece as needed. You can write a correct
computer program without ever knowing about memory
management, but attention to memory management allows
you to consistently write programs that don't have
excessive memory delays. In this paper, we consider a
model of computer memory organization. We hide some
detail but give enough information to let us make
decisions about how to organize our computations for
efficiency. We use mathematical modeling to estimate a
typical computer's memory parameters, and then we see
how important these parameters are relative to the
speed of floating-point arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}
@Article{Ou:2006:DSE,
author = "Jingzhao Ou and Viktor K. Prasanna",
title = "Design space exploration using arithmetic-level
hardware--software cosimulation for configurable
multiprocessor platforms",
journal = j-TECS,
volume = "5",
number = "2",
pages = "355--382",
month = may,
year = "2006",
CODEN = "????",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Wed Aug 23 05:26:43 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}
@Article{Ozban:2006:NMA,
author = "Ahmet Ya{\c{s}}ar {\"O}zban",
title = "New methods for approximating square roots",
journal = j-APPL-MATH-COMP,
volume = "175",
number = "1",
pages = "532--540",
day = "1",
month = apr,
year = "2006",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:02:54 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Park:2006:EBP,
author = "Sun-Mi Park and Ku-Young Chang and Dowon Hong",
title = "Efficient Bit-Parallel Multiplier for Irreducible
Pentanomials Using a Shifted Polynomial Basis",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "9",
pages = "1211--1215",
month = sep,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.146",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1668049",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Parks:2006:UTS,
author = "Michael Parks",
title = "Unifying Tests for Square Root",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "elementary functions; floating-point testing",
}
@Article{Perry:2006:BSF,
author = "Tekla S. Perry",
title = "Building a supercomputer in a flash",
journal = j-IEEE-SPECTRUM,
volume = "41",
number = "6",
pages = "24--25",
month = jun,
year = "2006",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2004.1303368",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Thu Sep 01 16:21:26 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "floating-point arithmetic",
remark = "Flash mob linked 669 PCs at UCSF in six hours to
produce a LINPACK speed of 180 Gflops (below the 500
Gflops goal).",
}
@InProceedings{Persson:2006:RCA,
author = "A. Persson and L. Bengtsson",
booktitle = "{ISCAS 2006}, Proceedings, 2006 {IEEE} International
Symposium on Circuits and Systems, 21--24 May 2006",
title = "Reverse conversion architectures for signed-digit
residue number systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "4",
year = "2006",
CODEN = "????",
DOI = "https://doi.org/10.1109/ISCAS.2006.1693181",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "This paper presents circuits for conversion from
radix-2 signed-digit residue numbers to binary form.
Four reverse converters for combined RNS/SD number
systems based on different moduli sets are presented.
Implementations are compared with respect \ldots{}",
}
@InProceedings{Piso:2006:OMD,
author = "D. Piso and J. D. Bruguera",
editor = "????",
booktitle = "Proceedings of the {XXI} Conference on Design of
Circuits and Integrated Systems ({DSIS2006, Barcelona,
2006})",
title = "Optimizing the Multiplier Design for {Goldschmidt}'s
Division and Reciprocal Units",
publisher = "????",
address = "????",
pages = "1C.3--??",
year = "2006",
bibdate = "Sun Dec 10 14:00:32 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "TO DO: [11-Dec-2023] I cannot yet locate this
article.",
}
@Article{Pryce:2006:IAC,
author = "J. D. Pryce and G. F. Corliss",
title = "Interval Arithmetic with Containment Sets",
journal = j-COMPUTING,
volume = "78",
number = "3",
pages = "251--276",
month = nov,
year = "2006",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-006-0180-4",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "54D35; 65-02; 65G30; 65G40",
bibdate = "Tue Jul 8 22:32:47 MDT 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=78&issue=3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=78&issue=3&spage=251",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "containment set; cset; division by zero; infinity;
interval arithmetic; validated computation",
}
@Article{Qian:2006:HMP,
author = "Jianbo Qian and Cao An Wang",
title = "How much precision is needed to compare two sums of
square roots of integers?",
journal = j-INFO-PROC-LETT,
volume = "100",
number = "5",
pages = "194--198",
day = "16",
month = dec,
year = "2006",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Thu Mar 31 15:52:31 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Rajagopal:2006:TOA,
author = "S. Rajagopal and J. R. Cavallaro",
title = "Truncated Online Arithmetic with Applications to
Communication Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "10",
pages = "1240--1252",
month = oct,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.168",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:56 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1683755",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Shen:2006:TAS,
author = "Xunyang Shen and Peter R. Turner",
title = "{Taylor} approximation for symmetric level-index
arithmetic processing",
journal = j-IMA-J-NUMER-ANAL,
volume = "26",
number = "3",
pages = "584--603",
month = jul,
year = "2006",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drl004",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Tue Jun 24 12:23:09 MDT 2008",
bibsource = "http://imanum.oxfordjournals.org/content/vol26/issue3/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/cgi/content/abstract/26/3/584;
http://comjnl.oxfordjournals.org/cgi/reprint/26/3/584",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Shou:2006:MAA,
author = "Huahao Shou and Hongwei Lin and Ralph R. Martin and
Guojin Wang",
title = "Modified affine arithmetic in tensor form for
trivariate polynomial evaluation and algebraic surface
plotting",
journal = j-J-COMPUT-APPL-MATH,
volume = "195",
number = "1--2",
pages = "155--171",
day = "15",
month = oct,
year = "2006",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:12:01 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042705004814",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Singh:2006:IEE,
author = "S. B. Singh and H. S. Kasana",
title = "Improved estimates for error in floating point
representation analysis",
journal = j-BULL-CALCUTTA-MATH-SOC,
volume = "98",
number = "2",
pages = "117--124",
year = "2006",
CODEN = "BCMSA5",
ISSN = "0008-0659",
MRclass = "65G50",
MRnumber = "MR2217971 (2006k:65128)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Calcutta Mathematical Society",
journal-URL = "http://bulletin.calmathsoc.org/database.php",
keywords = "rounding errors",
}
@Article{Solymosi:2006:APS,
author = "J{\'o}zsef Solymosi",
title = "Arithmetic Progressions in Sets with Small Sumsets",
journal = j-COMBIN-PROBAB-COMPUT,
volume = "15",
number = "4",
pages = "597--603",
month = jul,
year = "2006",
CODEN = "CPCOFG",
DOI = "https://doi.org/10.1017/S0963548306007516",
ISSN = "0963-5483 (print), 1469-2163 (electronic)",
ISSN-L = "0963-5483",
bibdate = "Mon Jul 7 15:38:18 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://journals.cambridge.org/action/displayIssue?jid=CPC&volumeId=15&issueId=04",
acknowledgement = ack-nhfb,
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=CPC",
}
@Book{StDenis:2006:BMH,
author = "Tom {St Denis} and Greg Rose",
title = "{BigNum} Math: Implementing Cryptographic Multiple
Precision Arithmetic",
publisher = pub-SYNGRESS,
address = pub-SYNGRESS:adr,
pages = "xviii + 296",
year = "2006",
ISBN = "1-59749-112-8",
ISBN-13 = "978-1-59749-112-9",
LCCN = "QA402.5 2006",
bibdate = "Fri Jun 12 07:26:51 MDT 2009",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.bibsys.no:2100/BIBSYS",
URL = "http://www.oreilly.com/catalog/1597491128/index.html",
acknowledgement = ack-nhfb,
keywords = "Karatsuba multiplication; modular exponentiation;
Montgomery reduction",
tableofcontents = "Introduction \\
Multiple Precision Arithmetic \\
Exercises \\
Portability and Stability \\
Getting Started \\
Maintenance Algorithms \\
Basic Operations \\
Sign Manipulation \\
Basic Arithmetic \\
Multiplication and Squaring \\
The Multipliers \\
Multiplication \\
Modular Reduction \\
Basics of Modular Reduction \\
Exponentiation \\
Exponentiation Basics \\
Higher Level Algorithms \\
Number Theoretic Algorithms",
}
@Book{StDenis:2006:BMI,
author = "Tom {St. Denis}",
title = "{BigNum} Math: Implementing Cryptographic Multiple
Precision Arithmetic",
publisher = pub-SYNGRESS,
address = pub-SYNGRESS:adr,
pages = "xviii + 296",
year = "2006",
ISBN = "1-59749-112-8",
ISBN-13 = "978-1-59749-112-9",
LCCN = "QA402.5 .S73 2006",
bibdate = "Thu Oct 19 19:07:57 2006",
bibsource = "clas.caltech.edu:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$49.95",
URL = "http://www.oreilly.com/catalog/1597491128/index.html",
acknowledgement = ack-nhfb,
keywords = "Karatsuba multiplication; modular exponentiation;
Montgomery reduction",
}
@Misc{Steele:2006:FPM,
author = "Guy L. {Steele Jr.}",
title = "Floating point multiplier for delimited operands",
howpublished = "US Patent 7003540",
day = "21",
month = feb,
year = "2006",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7003540/fulltext.html",
abstract = "A method for providing a floating point product
consistent with the present invention includes
multiplying a subprecise operand and a non-subprecise
operand using a plurality of intermediate stages. The
method further includes correcting an error introduced
by the subprecise operand by performing an operation in
conjunction with a one of the plurality of intermediate
stages utilizing a compensating summand.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2006:FPSa,
author = "Guy L. {Steele Jr.}",
title = "Floating point system with improved support of
interval arithmetic",
howpublished = "US Patent 7069288",
day = "27",
month = jun,
year = "2006",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7069288/fulltext.html",
abstract = "Embodiments consistent with the principles of the
present invention provide improved results, compared to
IEEE Std. 754, for floating point operations used in
interval arithmetic calculations. One embodiment
consistent with the principles of the present invention
provides a method of enhancing support of an interval
computation when performing a floating point arithmetic
operation, comprising the steps, performed by a
processor, of receiving a first floating point operand,
receiving a second floating point operand, executing
the floating point arithmetic operation on the first
floating point operand and the second floating point
operand, determining whether a NaN substitution is
necessary, producing a floating point result if the NaN
substitution is determined to be unnecessary, and
substituting an alternative value as the floating point
result if the NaN substitution is determined to be
necessary.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2006:FPSb,
author = "Guy L. {Steele Jr.}",
title = "Floating point status information testing circuit",
howpublished = "US Patent 7016928",
day = "21",
month = mar,
year = "2006",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7016928/fulltext.html",
abstract = "A floating point operand testing circuit includes an
analysis circuit and a result generator circuit coupled
to the analysis circuit. The analysis circuit
determines the status of a floating point operand based
upon data within the operand. An operand buffer may
supply the operand to the analysis circuit. The result
generator circuit is responsive to at least one control
signal and asserts a result signal if the floating
point analysis circuit matches the floating point
status to a predetermined format specified by the
control signal. The result signal can condition the
outcome of a floating point instruction. The result
generator may also respond to multiple control signals
asserted when testing a single operand for different
formats, such as not-a-number (NaN), infinity,
normalized, denormalized, invalid operation, overflow,
underflow, division by zero, exact, and inexact.",
acknowledgement = ack-nhfb,
keywords = "floating-point testing",
}
@Misc{Steele:2006:FPU,
author = "Guy L. {Steele Jr.}",
title = "Floating point unit for detecting and representing
inexact computations without flags or traps",
howpublished = "US Patent 7069289",
day = "27",
month = jun,
year = "2006",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7069289/fulltext.html",
abstract = "A method and system perform a rounding step of a
floating point computation on at least one floating
point operand to preserve an inexact status. Inexact
status information generated from the rounding step may
be encoded within the result, instead of requiring a
separate floating point status register for the inexact
status information. In one embodiment, inexact status
information is preserved by determining whether the at
least one operand is inexact. Further, an intermediate
result of the floating point computation is analyzed to
determine whether it is inexact. Finally, the
intermediate result is rounded based on whether the at
least one operand is inexact and whether the
intermediate result is inexact to preserve an inexact
status of the at least one operand and the intermediate
result.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2006:SMP,
author = "Guy L. {Steele Jr.}",
title = "System and method for performing floating point
operations involving extended exponents",
howpublished = "US Patent 6993549",
day = "31",
month = jan,
year = "2006",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/6993549/fulltext.html",
abstract = "An extended exponent floating point unit performs an
extended exponent floating point operation on a
plurality of operands to produce a product of the
plurality of operands. The extended exponent floating
point unit groups the plurality of operands into at
least one group, determines a plurality of scale
factors for the plurality of operands, respectively,
and provides a running sum of the plurality of scale
factors. The extended exponent floating point unit
further scales the plurality of operands to obtain a
plurality of scaled operands, multiplies the plurality
of scaled operands to obtain a group product, and
scales the group product to obtain a scaled group
product. The scaled group product is adjusted based on
the running sum. The plurality of operands are grouped
such that when all the plurality of scaled operands in
the at least one group are multiplied an overflow or
underflow will not occur.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2006:TOC,
author = "Guy L. {Steele Jr.}",
title = "Total order comparator unit for comparing values of
two floating point operands",
howpublished = "US Patent 7133890",
day = "07",
month = nov,
year = "2006",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7133890/fulltext.html",
abstract = "A floating point total order comparator circuit for
comparing a first floating point operand and a second
floating point operand includes a first analysis
circuit for determining a format of the first floating
point operand based upon floating point status
information encoded within the first floating point
operand, a second analysis circuit for determining a
format of the second floating point operand based upon
floating point status information encoded within the
second floating point operand, and a result generator
circuit coupled to the analysis circuits for producing
a result indicating a total order comparative
relationship between the first floating point operand
and the second floating point operand based on the
format of the first floating point operand and the
format of the second floating point operand. The result
can condition the outcome of a floating point
instruction. The floating point total order comparator
circuit may recognize several predetermined operand
formats, such as not-a-number (NaN), infinity,
normalized, denormalized, invalid operation, overflow,
underflow, division by zero, positive zero, negative
zero, exact, and inexact.",
acknowledgement = ack-nhfb,
}
@Article{Strzebonski:2006:CAD,
author = "Adam W. Strzebo{\'n}ski",
title = "{Cylindrical Algebraic Decomposition} using validated
numerics",
journal = j-J-SYMBOLIC-COMP,
volume = "41",
number = "9",
pages = "1021--1038",
month = sep,
year = "2006",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Wed Aug 25 20:13:18 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171/",
}
@InProceedings{Strzodka:2006:PMP,
author = "R. Strzodka and D. Goddeke",
title = "Pipelined mixed precision algorithms on {FPGAs} for
fast and accurate {PDE} solvers from low precision
components",
crossref = "Pocek:2006:FAI",
pages = "259--270",
year = "2006",
bibdate = "Sat Oct 9 13:03:16 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Taylor:2006:IAI,
author = "Paul Taylor",
title = "Interval Analysis Without Intervals",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Thakkar:2006:PDP,
author = "Anuja J. Thakkar and Abdel Ejnioui",
title = "Pipelining of double precision floating point division
and square root operations",
crossref = "Menezes:2006:PAS",
pages = "488--493",
year = "2006",
DOI = "https://doi.org/10.1145/1185448.1185555",
bibdate = "Sat Oct 9 13:04:49 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Space applications rely increasingly on high data rate
DSP algorithms. These algorithms use double precision
floating point arithmetic operations. While most DSP
applications can be compiled on DSP processors, high
data rate DSP computations require novel implementation
technologies to support their high throughputs. Only
recently, gate densities in FPGAs have reached a level
which makes them attractive platforms to implement
compute-intensive DSP applications. In this context,
this paper presents the sequential and pipelined
designs of a double precision floating point divider
and square root unit on FPGAs. Contrary to pipelined
parallel implementations, the pipelining of these units
is based on unrolling the iterations in low-radix digit
recurrence algorithms. These units are mapped on
generic FPGA reconfigurable fabric without taking
advantage of any advanced architectural components
available in high capacity FPGAs. The implementations
of these designs show that their performances are
comparable to, and sometimes higher than, the
performances of non-iterative designs based of high
radix numbers. The iterative divider and square root
unit occupy less than 1\% of an XC2V6000 FPGA chip
while their pipelined counterparts can produce
throughputs that reach the 100 MFLOPS mark by consuming
a modest 8\% of the chip area.",
acknowledgement = ack-nhfb,
}
@Article{Thapliyal:2006:CIF,
author = "Himanshu Thapliyal and Hamid R. Arabnia and A. P.
Vinod",
title = "Combined Integer and Floating Point Multiplication
Architecture ({CIFM}) for {FPGAs} and Its Reversible
Logic Implementation",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "14",
month = oct,
year = "2006",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/cs/0610090",
abstract = "In this paper, the authors propose the idea of a
combined integer and floating point multiplier(CIFM)
for FPGAs. The authors propose the replacement of
existing 18x18 dedicated multipliers in FPGAs with
dedicated 24x24 multipliers designed with small 4x4 bit
multipliers. It is also proposed that for every
dedicated 24x24 bit multiplier block designed with 4x4
bit multipliers, four redundant 4x4 multiplier should
be provided to enforce the feature of self
repairability (to recover from the faults). In the
proposed CIFM reconfigurability at run time is also
provided resulting in low power. The major source of
motivation for providing the dedicated 24x24 bit
multiplier stems from the fact that single precision
floating point multiplier requires 24x24 bit integer
multiplier for mantissa multiplication. A
reconfigurable, self-repairable 24x24 bit multiplier
(implemented with 4x4 bit multiply modules) will
ideally suit this purpose, making FPGAs more suitable
for integer as well floating point operations. A
dedicated 4x4 bit multiplier is also proposed in this
paper. Moreover, in the recent years, reversible logic
has emerged as a promising technology having its
applications in low power CMOS, quantum computing,
nanotechnology, and optical computing. It is not
possible to realize quantum computing without
reversible logic. Thus, this paper also paper provides
the reversible logic implementation of the proposed
CIFM. The reversible CIFM designed and proposed here
will form the basis of the completely reversible
FPGAs.",
acknowledgement = ack-nhfb,
subject = "Hardware Architecture (cs.AR)",
}
@InProceedings{Thapliyal:2006:DNR,
author = "Himanshu Thapliyal and Sumedha K. Gupta",
title = "Design of Novel Reversible Carry Look-Ahead {BCD}
Subtractor",
crossref = "Mohanty:2006:IIC",
pages = "253--258",
year = "2006",
DOI = "https://doi.org/10.1109/ICIT.2006.44",
bibdate = "Thu Aug 07 19:09:50 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "IEEE 754r is the ongoing revision to the IEEE 754
floating point standard. A major enhancement to the
standard is the addition of decimal format, thus the
design of BCD arithmetic units is likely to get
significant attention. Firstly, this paper introduces a
novel carry look-ahead BCD adder and then builds a
novel carry look-ahead BCD subtractor based on it.
Secondly, it introduces the reversible logic
implementation of the proposed carry look-ahead BCD
subtractor. We have tried to design the reversible
logic implementation of the BCD Subtractor optimal in
terms of number of reversible gates used and garbage
outputs produced. Thus, the proposed work will be of
significant value as the technologies mature.",
acknowledgement = ack-nhfb,
}
@InProceedings{Thapliyal:2006:NBA,
author = "H. Thapliyal and S. Kotiyal and M. B. Srinivas",
title = "Novel {BCD} adders and their reversible logic
implementation for {IEEE 754R} format",
crossref = "IEEE:2006:ICV",
year = "2006",
DOI = "https://doi.org/10.1109/VLSID.2006.122",
bibdate = "Mon Mar 19 10:19:57 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "IEEE 754r is the ongoing revision to the IEEE 754
floating point standard and a major enhancement to the
standard is the addition of decimal format. This paper
proposes two novel BCD adders called carry skip and
carry look-ahead BCD adders respectively. Furthermore,
in the recent years, reversible logic has emerged as a
promising technology having its applications in low
power CMOS, quantum computing, nanotechnology, and
optical computing. It is not possible to realize
quantum computing without reversible logic. Thus, this
paper also paper provides the reversible logic
implementation of the conventional BCD adder as the
well as the proposed carry skip BCD adder using a
recently proposed TSG gate. Furthermore, a new
reversible gate called TS-3 is also being proposed and
it has been shown that the proposed reversible logic
implementation of the BCD adders is much better
compared to recently proposed one, in terms of number
of reversible gates used and garbage outputs produced.
The reversible BCD circuits designed and proposed here
form the basis of the decimal ALU of a primitive
quantum CPU.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Toivonen:2006:VFF,
author = "T. Toivonen and J. Heikkila",
title = "Video filtering with {Fermat} number theoretic
transforms using residue number system",
journal = j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH,
volume = "16",
number = "1",
pages = "92--101",
month = jan,
year = "2006",
CODEN = "ITCTEM",
DOI = "https://doi.org/10.1109/TCSVT.2005.858612",
ISSN = "1051-8215 (print), 1558-2205 (electronic)",
ISSN-L = "1051-8215",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=33196",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems for Video
Technology",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=76",
keywords = "residue arithmetic; residue number system",
summary = "We investigate image and video convolutions based on
Fermat number transform (FNT) modulo q=2/sup M/+1 where
M is an integer power of two. These transforms are
found to be ideal for image convolutions, except that
the choices for the word length, \ldots{}",
}
@Book{Trott:2006:MGN,
author = "Michael Trott",
title = "The {Mathematica} guidebook for numerics",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxvi + 1208",
year = "2006",
ISBN = "0-387-95011-7",
ISBN-13 = "978-0-387-95011-2",
LCCN = "QA76.95 .T773 2006",
MRclass = "65-00",
MRnumber = "MR2174594 (2006m:65001)",
bibdate = "Thu Nov 8 19:02:51 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With 1 DVD (Windows, Macintosh, Mac, UNIX)",
acknowledgement = ack-nhfb,
}
@Article{VanMeter:2006:DAQ,
author = "Rodney {Van Meter} and Kae Nemoto and W. J. Munro and
Kohei M. Itoh",
title = "Distributed Arithmetic on a Quantum Multicomputer",
journal = j-COMP-ARCH-NEWS,
volume = "34",
number = "2",
pages = "354--365",
year = "2006",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Mon Aug 21 15:00:05 MDT 2006",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@InProceedings{Vazquez:2006:CSD,
author = "Alvaro Vazquez and Elisardo Antelo",
title = "Conditional Speculative Decimal Addition",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Villalba:2006:DRM,
author = "J. Villalba and T. Lang and M. A. Gonzalez",
title = "Double-residue modular range reduction for
floating-point hardware implementations",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "3",
pages = "254--267",
month = mar,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.38",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:53 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1583556",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wang:2006:ACV,
author = "X. Wang and S. Braganza and M. Leeser",
title = "Advanced components in the variable precision
floating-point library",
crossref = "Pocek:2006:FAI",
pages = "249--258",
year = "2006",
DOI = "https://doi.org/10.1109/FCCM.2006.21",
bibdate = "Sat Oct 9 13:07:28 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Optimal reconfigurable hardware implementations may
require the use of arbitrary floating-point formats
that do not necessarily conform to IEEE specified
sizes. The authors have previously presented a variable
precision floating-point library for use with
reconfigurable hardware. The authors recently added
three advanced components: floating-point division,
floating-point square root and floating-point
accumulation to our library. These advanced components
use algorithms that are well suited to FPGA
implementations and exhibit a good tradeoff between
area, latency and throughput. The floating-point format
of our library is both general and flexible. All IEEE
formats, including 64-bit double-precision format, are
a subset of our format. All previously published
floating-point formats for reconfigurable hardware are
a subset of our format as well. The generic
floating-point format supported by all of our library
components makes it easy and convenient to create a
pipelined, custom data path with optimal bitwidth for
each operation. Our library can be used to achieve more
parallelism and less power dissipation than adhering to
a standard format. To further increase parallelism and
reduce power dissipation, our library also supports
hybrid fixed and floating point operations in the same
design. The division and square root designs are based
on table lookup and Taylor series expansion, and make
use of memories and multipliers embedded on the FPGA
chip. The iterative accumulator utilizes the library
addition module as well as buffering and control logic
to achieve performance similar to that of the addition
by itself. They are all fully pipelined designs with
clock speed comparable to that of other library
components to aid the designer in implementing fast,
complex, pipelined designs.",
acknowledgement = ack-nhfb,
}
@Article{Wang:2006:PAN,
author = "Chengpu Wang",
title = "Precision Arithmetic: A New Floating-Point
Arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "25",
month = jun,
year = "2006",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
MRclass = "65Y04, 65T50",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/cs/0606103",
abstract = "A new deterministic floating-point arithmetic called
precision arithmetic is developed to track precision
for arithmetic calculations. It uses a novel rounding
scheme to avoid excessive rounding error propagation of
conventional floating-point arithmetic. Unlike interval
arithmetic, its uncertainty tracking is based on
statistics and the central limit theorem, with a much
tighter bounding range. Its stable rounding error
distribution is approximated by a truncated normal
distribution. Generic standards and systematic methods
for validating uncertainty-bearing arithmetics are
discussed. The precision arithmetic is found to be
better than interval arithmetic in both
uncertainty-tracking and uncertainty-bounding for
normal usages. The precision arithmetic is available
publicly at
\url{http://precisionarithm.sourceforge.net/}",
acknowledgement = ack-nhfb,
remark = "This document has been updated 21 times from 25 Jun
2006 to 3 Apr 2014.",
subject = "Discrete Mathematics (cs.DM); Data Structures and
Algorithms (cs.DS); Numerical Analysis (cs.NA)",
}
@Article{Wires:2006:RRS,
author = "Kent E. Wires and Michael J. Schulte",
title = "Reciprocal and Reciprocal Square Root Units with
Operand Modification and Multiplication",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "42",
number = "3",
pages = "257--272",
month = mar,
year = "2006",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/s11265-006-4186-0",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Mar 05 08:26:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://springerlink.metapress.com/content/t6027p6713727606/fulltext.pdf",
abstract = "Reciprocals and reciprocal square roots are used in
several digital signal processing, multimedia, and
scientific computing applications. This paper presents
high-speed methods for computing reciprocals and
reciprocal square roots. These methods use a table
lookup, operand modification, and multiplication to
obtain an initial approximation. This is followed by a
modified Newton--Raphson iteration, which improves the
accuracy of the initial approximation. The initial
approximation and Newton--Raphson iteration employ
specialized hardware to reduce the delay, area, and
power dissipation. The application of these methods is
illustrated through the design of reciprocal and
reciprocal square root units for operands in the IEEE
single precision format. These designs are pipelined to
produce a new result every clock cycle.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
keywords = "computer arithmetic; function approximation;
Newton--Raphson iteration; reciprocal; reciprocal
square root; table lookup",
}
@Article{Wong:2006:FES,
author = "K. W. Wong and Edward C. W. Lee and L. M. Cheng and
Xiaofeng Liao",
title = "Fast elliptic scalar multiplication using new
double-base chain and point halving",
journal = j-APPL-MATH-COMP,
volume = "183",
number = "2",
pages = "1000--1007",
day = "15",
month = dec,
year = "2006",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:00 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Xenoulis:2006:TAS,
author = "G. Xenoulis and M. Psarakis and D. Gizopoulos and A.
Paschalis",
title = "Testability Analysis and Scalable Test Generation for
High-Speed Floating-Point Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "55",
number = "11",
pages = "1449--1457",
month = nov,
year = "2006",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2006.187",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:35:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1705453",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Xia:2006:RSI,
author = "Bican Xia and Ting Zhang",
title = "Real solution isolation using interval arithmetic",
journal = j-COMPUT-MATH-APPL,
volume = "52",
number = "6--7",
pages = "853--860",
month = sep # "\slash " # oct,
year = "2006",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:55 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122106002896",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Manual{XILINX:2006:XLF,
author = "{XILINX}",
title = "{XILINX LogiCORE} floating-point operator v3.0 product
specification",
organization = "Xilinx, Inc.",
day = "28",
month = sep,
year = "2006",
bibdate = "Sat Oct 9 13:09:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.xilinx.com/bvdocs/ipcenter/data_sheet/floating_point_ds335.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{You:2006:DDA,
author = "Younggap You and Yong Dae Kim and Jong Hwa Choi",
title = "Dynamic Decimal Adder Circuit Design by using the
Carry Lookahead",
crossref = "IEEE:2006:PIW",
pages = "242--244",
year = "2006",
bibdate = "Mon Mar 19 11:11:29 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/iel5/10974/34591/01649627.pdf",
abstract = "This paper presents a carry lookahead (CLA) circuitry
design based on dynamic circuit aiming at delay
reduction in addition of BCD coded decimal numbers. The
performance of the proposed dynamic decimal adder is
analyzed demonstrating its speed improvement. Timing
simulation on the proposed decimal addition circuit
employing 0.25 $ \mu $ m CMOS technology yields the
worst case delay of 622ns.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Zhu:2006:FGA,
author = "Yong-Kang Zhu and Wayne Hayes",
title = "Fast, guaranteed-accurate sums of many floating-point
numbers",
crossref = "Anonymous:2006:PCR",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 27 10:28:05 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@TechReport{Zimmermann:2006:AFD,
author = "Paul Zimmermann",
title = "Asymptotically Fast Division for {GMP}",
type = "Technical report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
day = "31",
month = aug,
year = "2006",
bibdate = "Sun Sep 10 07:18:34 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/invert.pdf",
abstract = "Until version 4.2.1, GNU MP (GMP for short) division
has complexity O(M(n) log n), which is not
asymptotically optimal. We propose here some division
algorithms that achieve O(M(n)) with small constants.",
acknowledgement = ack-nhfb,
}
@TechReport{Zimmermann:2006:EBC,
author = "Paul Zimmermann and Richard Brent and Colin Percival",
title = "Errors Bounds on Complex Floating-Point
Multiplication",
type = "Technical report",
institution = inst-LORIA-INRIA-LORRAINE,
address = inst-LORIA-INRIA-LORRAINE:adr,
pages = "????",
year = "2006",
bibdate = "Sun Sep 10 07:21:42 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/papers/index.html",
abstract = "Given floating-point arithmetic with $t$-digit base-$
\beta $ significands in which all arithmetic operations
are performed as if calculated to infinite precision
and rounded to a nearest representable value, we prove
that the product of complex values $ z_0 $ and $ z_1 $
can be computed with maximum absolute error $ |z_0 |
|z_1 | (1 / 2) \beta^{1 - t} \sqrt {5} $. In
particular, this provides relative error bounds of $ {2
- 24} \sqrt {5} $ and $ {2 - 53} \sqrt {5} $ for IEEE
754 single and double precision arithmetic
respectively, provided that overflow, underflow, and
denormals do not occur. We also provide the numerical
worst cases for IEEE 754 single and double precision
arithmetic.",
acknowledgement = ack-nhfb,
xxnote = "Check author order?? Paper not yet online.",
}
@Misc{Zimmermann:2006:WC,
author = "Paul Zimmermann",
title = "Worst Cases for $ \sin (\hbox {BIG}) $",
howpublished = "World-Wide Web slides.",
day = "2",
month = nov,
year = "2006",
bibdate = "Wed Nov 15 07:56:07 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.loria.fr/~zimmerma/talks/sinbig.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Zimmermann:2006:YE,
author = "Paul Zimmermann and Bruce Dodson",
title = "20 Years of {ECM}",
crossref = "Hess:2006:ANT",
pages = "525--541",
year = "2006",
DOI = "https://doi.org/10.1007/11792086_37",
bibdate = "Mon May 31 12:31:07 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://members.loria.fr/PZimmermann/papers/40760525.pdf",
abstract = "The Elliptic Curve Method for integer factorization
(ECM) was invented by H. W. Lenstra, Jr., in 1985 [14].
In the past 20 years, many improvements of ECM were
proposed on the mathematical, algorithmic, and
implementation sides. This paper summarizes the current
state-of-the-art, as implemented in the GMP-ECM
software.",
acknowledgement = ack-nhfb,
keywords = "assembly code; elliptic curve; Fermat number; modular
multiplication; quadratic domain",
}
@Article{Abtahi:2007:FSD,
author = "M. Abtahi and P. Siy",
title = "The Factor-2 Sign Detection Algorithm using a core
function for {RNS} numbers",
journal = j-COMPUT-MATH-APPL,
volume = "53",
number = "9",
pages = "1455--1463",
month = may,
year = "2007",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:01 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122107001150",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Aharoni:2007:SCI,
author = "Merav Aharoni and Ron Maharik and Abraham Ziv",
title = "Solving Constraints on the Intermediate Result of
Decimal Floating-Point Operations",
crossref = "Kornerup:2007:PIS",
pages = "38--45",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.33",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.lirmm.fr/arith18/papers/aharoni-DecimalConstraints.pdf",
abstract = "The draft revision of the IEEE Standard for Floating-
Point Arithmetic (IEEE P754) includes a definition for
decimal floating-point (FP) in addition to the widely
used binary FP specification. The decimal standard
raises new concerns with regard to the verification of
hardware- and software-based designs. The verification
process normally emphasizes intricate corner cases and
uncommon events. The decimal format introduces several
new classes of such events in addition to those
characteristic of binary FP. Our work addresses the
following problem: Given a decimal floating-point
operation, a constraint on the intermediate result, and
a constraint on the representation selected for the
result, find random inputs for the operation that yield
an intermediate result compatible with these
specifications. The paper supplies efficient analytic
solutions for addition and for some cases of
multiplication and division. We provide probabilistic
algorithms for the remaining cases. These algorithms
prove to be efficient in the actual implementation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Anonymous:2007:AI,
author = "Anonymous",
title = "Author Index",
crossref = "Kornerup:2007:PIS",
pages = "269--269",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.12",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Anonymous:2007:CPSa,
author = "Anonymous",
title = "Call for Papers for Special Issue on Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "1",
pages = "144--144",
month = jan,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.250631",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Anonymous:2007:CPSb,
author = "Anonymous",
title = "Call for Papers for Special Section on Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "2",
pages = "287--287",
month = feb,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.22",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Balasubramaniam:2007:ECS,
author = "P. Balasubramaniam and E. Karthikeyan",
title = "Elliptic curve scalar multiplication algorithm using
complementary recoding",
journal = j-APPL-MATH-COMP,
volume = "190",
number = "1",
pages = "51--56",
day = "1",
month = jul,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:06 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Balasubramaniam:2007:FSS,
author = "P. Balasubramaniam and E. Karthikeyan",
title = "Fast simultaneous scalar multiplication",
journal = j-APPL-MATH-COMP,
volume = "192",
number = "2",
pages = "399--404",
day = "15",
month = sep,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:08 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Beebe:2007:ETM,
author = "Nelson H. F. Beebe",
title = "Extending {\TeX} and {\MF} with floating-point
arithmetic",
journal = j-TUGboat,
volume = "28",
number = "3",
pages = "319--328",
year = "2007",
ISSN = "0896-3207",
ISSN-L = "0896-3207",
bibdate = "Tue Oct 23 19:13:23 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/index-table-t.html#tugboat;
https://www.math.utah.edu/pub/tex/bib/tugboat.bib;
https://www.tug.org/tug2007/",
URL = "https://tug.org/TUGboat/tb28-3/tb90beebe.pdf",
abstract = "The article surveys the state of arithmetic in \TeX{}
and \MF{}, suggests that they could usefully be
extended to support floating-point arithmetic, and
shows how this could be done with a relatively small
effort, \emph{without} loss of the important feature of
platform-independent results from those programs, and
\emph{without} invalidating any existing documents, or
software written for those programs, including output
drivers.",
acknowledgement = ack-bnb # " and " # ack-nhfb,
confnote = "TUG 2007 Proceedings (San Diego, CA, USA).",
errata = "P. 502, column 1, bottom of page: ``use a'' -> ``use
as a''; \\
p. 504, column 1, middle of page: ``beeen'' ->
``been''; \\
p. 505, column 1, top of page: ``power of base'' ->
``power of the base''",
fjournal = "TUGboat",
issue = "90",
journal-URL = "https://tug.org/TUGboat/",
ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
remark = "Advanced{\Dash}floating-point history, problems, and
futures.",
}
@InProceedings{Beebe:2007:NDF,
author = "Nelson H. F. Beebe",
title = "New directions in floating-point arithmetic",
crossref = "Simos:2007:CMS",
volume = "2A",
publisher = pub-AIP,
address = pub-AIP:adr,
pages = "155--158",
year = "2007",
bibdate = "Thu Feb 21 14:34:40 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Beuchat:2007:ANP,
author = "Jean-Luc Beuchat and Masaaki Shirase and Tsuyoshi
Takagi and Eiji Okamoto",
title = "An Algorithm for the {$ \eta T $} Pairing Calculation
in Characteristic Three and its Hardware
Implementation",
crossref = "Kornerup:2007:PIS",
pages = "97--104",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.10",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, we propose a modified $ \eta T $
pairing algorithm in characteristic three which does
not need any cube root extraction. We also discuss its
implementation on a low cost platform which hosts an
Altera Cyclone II FPGA device. Our pairing accelerator
is ten times faster than previous known FPGA
implementations in characteristic three",
acknowledgement = ack-nhfb,
keywords = "ARITH-18; characteristic three; elliptic curve; eta T
pairing; FPGA; hardware accelerator; Tate pairing",
}
@InProceedings{Bodrato:2007:IPM,
author = "Marco Bodrato and Alberto Zanoni",
title = "Integer and polynomial multiplication: towards optimal
{Toom--Cook} matrices",
crossref = "Brown:2007:PIS",
pages = "17--24",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277552",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Karatsuba and Toom--Cook are well-known methods used
to multiply efficiently long integers. There have been
different proposal about the interpolating values used
to determine the matrix to be inverted and the sequence
of operations to invert it. A definitive word about
which is the optimal matrix (values) and the (number
of) basic operations to invert it seems still not to
have been said. In this paper we present some
particular examples of useful matrices and a method to
generate automatically, by means of optimised
exhaustive searches on a graph, the best sequence of
basic operations to invert them.",
acknowledgement = ack-nhfb,
keywords = "integer and polynomial multiplication; interpolation;
Karatsuba; matrix inversion; squaring; Toom--Cook",
}
@Article{Boldo:2007:FPD,
author = "Sylvie Boldo and Marc Daumas and Pascal Giorgi",
title = "Formal proof for delayed finite field arithmetic using
floating point operators",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "6",
month = mar,
year = "2007",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/cs/0703026",
abstract = "Formal proof checkers such as Coq are capable of
validating proofs of correction of algorithms for
finite field arithmetics but they require extensive
training from potential users. The delayed solution of
a triangular system over a finite field mixes
operations on integers and operations on floating point
numbers. We focus in this report on verifying proof
obligations that state that no round off error occurred
on any of the floating point operations. We use a tool
named Gappa that can be learned in a matter of minutes
to generate proofs related to floating point arithmetic
and hide technicalities of formal proof checkers. We
found that three facilities are missing from existing
tools. The first one is the ability to use in Gappa new
lemmas that cannot be easily expressed as rewriting
rules. We coined the second one ``variable
interchange'' as it would be required to validate loop
interchanges. The third facility handles massive loop
unrolling and argument instantiation by generating
traces of execution for a large number of cases. We
hope that these facilities may sometime in the future
be integrated into mainstream code validation.",
acknowledgement = ack-nhfb,
subject = "Symbolic Computation (cs.SC)",
}
@InProceedings{Boldo:2007:FVF,
author = "Sylvie Boldo and Jean-Christophe Filliatre",
title = "Formal Verification of Floating-Point Programs",
crossref = "Kornerup:2007:PIS",
pages = "187--194",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.20",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.lri.fr/~filliatr/ftp/publis/caduceus-floats.pdf",
abstract = "This paper introduces a methodology to perform formal
verification of floating-point C programs. It extends
an existing tool for the verification of C programs,
Caduceus, with new annotations specific to
floating-point arithmetic. The Caduceus first-order
logic model for C programs is extended accordingly.
Then verification conditions expressing the correctness
of the programs are obtained in the usual way and can
be discharged interactively with the Coq proof
assistant, using an existing Coq formalization of
floating-point arithmetic. This methodology is already
implemented and has been successfully applied to
several short floating-point programs, which are
presented in this paper.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Boldo:2007:PCA,
author = "Sylvie Boldo and Marc Daumas and William Kahan and
Guillaume Melquiond",
title = "Proof and certification of an accurate discriminant",
crossref = "Luther:2007:GII",
pages = "??--??",
year = "2007",
bibdate = "Wed Jun 24 22:27:02 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Brent:2007:EBC,
author = "Richard Brent and Colin Percival and Paul Zimmermann",
title = "Error bounds on complex floating-point
multiplication",
journal = j-MATH-COMPUT,
volume = "76",
number = "259",
pages = "1469--1481",
year = "2007",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-07-01931-X",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65G50",
MRnumber = "MR2299783 (2008b:65062)",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Given floating-point arithmetic with $t$-digit base-$
\beta $ significands in which all arithmetic operations
are performed as if calculated to infinite precision
and rounded to a nearest representable value, we prove
that the product of complex values $ z_0 $ and $ z_1 $
can be computed with maximum absolute error $ \vert z_0
\Vert z_1 \vert \frac {1}{2} \beta^{1 - t} \sqrt {5} $.
In particular, this provides relative error bounds of $
2^{-24} \sqrt {5} $ and $ 2^{-53} \sqrt {5} $ for IEEE
754 single and double precision arithmetic
respectively, provided that overflow, underflow, and
denormals do not occur. We also provide the numerical
worst cases for IEEE 754 single and double precision
arithmetic.",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "rounding errors",
}
@Article{Brisebarre:2007:CRA,
author = "Nicolas Brisebarre and Jean-Michel Muller",
title = "Correct rounding of algebraic functions",
journal = j-INFORM-THEOR-APPL,
volume = "41",
number = "1",
pages = "71--83",
month = jan,
year = "2007",
CODEN = "RSITD7, RITAE4",
DOI = "https://doi.org/10.1051/ita:2007002",
ISSN = "0988-3754 (print), 1290-385X (electronic)",
ISSN-L = "0988-3754",
bibdate = "Fri Dec 8 09:49:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "RAIRO. Informatique th{\'e}orique et applications :=
Theoretical informatics and applications",
}
@InProceedings{Brisebarre:2007:EPA,
author = "Nicolas Brisebarre and Sylvain Chevillard",
title = "Efficient polynomial {$ L^\infty $}-approximations",
crossref = "Kornerup:2007:PIS",
pages = "169--176",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.17",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We address the problem of computing a good
floating-point-coefficient polynomial approximation to
a function, with respect to the supremum norm. This is
a key step in most processes of evaluation of a
function. We present a fast and efficient method, based
on lattice basis reduction, that often gives the best
polynomial possible and most of the time returns a very
good approximation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Brisebarre:2007:FPA,
author = "Nicolas Brisebarre and Guillaume Hanrot",
title = "Floating-point {$ L^2 $}-approximations to functions",
crossref = "Kornerup:2007:PIS",
pages = "177--186",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.38",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the present paper, we investigate the approximation
of a function by a polynomial with floating-point
coefficients; we are looking for the best approximation
in the $ L^2 $ sense. Finding a best polynomial $ L^2
$-approximation with real coefficients is an easy
exercise about orthogonal projections. However,
truncating the coefficients to floating-point numbers,
which is needed for further computations, makes the
approximation way worse. Hence, we study the problem of
computing best approximations under the constraint that
coefficients are floating-point numbers. We show that
the corresponding problem is NP-hard, by reduction to
the CVP problem. We investigate the practical behaviour
of exact and approximate algorithms for this problem.
The conclusion is that it is possible in a short amount
of time to obtain a relative or absolute best $ L^2
$-approximation. The main applications are for large
dimension, as a preliminary step of finding
$L$-approximations and for functions with large
variations, for which relative best approximation is by
far more interesting than absolute.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Burgess:2007:DAV,
author = "Neil Burgess and Chris N. Hinds",
title = "Design of the {ARM VFP11} Divide and Square Root
Synthesisable Macrocell",
crossref = "Kornerup:2007:PIS",
pages = "87--96",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.15",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents the detailed design of the ARM
VFP11 Divide and Square Root synthesisable macrocell.
The macrocell was designed using the minimum-redundancy
radix-4 SRT digit recurrence algorithm, and this paper
describes a novel acceleration technique employed to
achieve the required processor clock frequency of up to
750MHz in 90nm CMOS. Logical Effort theory is used to
provide a delay analysis of the unit, which
demonstrates the balanced nature of the two critical
paths therein.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Ceberio:2007:ITA,
author = "Martine Ceberio and Vladik Kreinovich and Sanjeev
Chopra and Luc Longpr{\'e} and Hung T. Nguyen and
Bertram Lud{\"a}scher and Chitta Baral",
title = "Interval-type and affine arithmetic-type techniques
for handling uncertainty in expert systems",
journal = j-J-COMPUT-APPL-MATH,
volume = "199",
number = "2",
pages = "403--410",
day = "15",
month = feb,
year = "2007",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:12:04 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270500779X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Chaves:2007:IRN,
author = "R. Chaves and L. Sousa",
title = "Improving residue number system multiplication with
more balanced moduli sets and enhanced modular
arithmetic structures",
journal = "IET Computers \& Digital Techniques",
volume = "1",
number = "5",
pages = "472--480",
month = sep,
year = "2007",
CODEN = "ICDTEA, ICDTEX",
DOI = "https://doi.org/10.1049/iet-cdt:20060059",
ISSN = "1751-8601 (print), 1751-861X (electronic)",
ISSN-L = "1751-8601",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4117424;
http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4312767",
acknowledgement = ack-nhfb,
ajournal = "IEE Proc.-Comput. Digit. Tech",
journal-URL = "https://digital-library.theiet.org/content/journals/iet-cdt;jsessionid=1s2tx6k4du6p5.x-iet-live-01",
keywords = "residue arithmetic; residue number system",
}
@Article{Chen:2007:NSA,
author = "Gang Chen and Guoqiang Bai and Hongyi Chen",
title = "A New Systolic Architecture for Modular Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "2",
pages = "282--286",
month = feb,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.20",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4042687",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cho:2007:BBL,
author = "Wendy K. Tam Cho and Brian J. Gaines",
title = "Breaking the {(Benford) Law}",
journal = j-AMER-STAT,
volume = "61",
number = "3",
pages = "218--223",
month = aug,
year = "2007",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/000313007X223496",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Thu Aug 26 21:48:27 MDT 2010",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@InProceedings{Cho:2007:SPM,
author = "Heumpil Cho and Earl E. {Swartzlander, Jr.}",
title = "Serial Parallel Multiplier Design in Quantum-dot
Cellular Automata",
crossref = "Kornerup:2007:PIS",
pages = "7--15",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.32",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An emerging nanotechnology, quantum-dot cellular
automata (QCA), has the potential for attractive
features such as faster speed, smaller size, and lower
power consumption than transistor based technology.
Quantum-dot cellular automata has a simple cell as the
basic element. The cell is used as a building block to
construct gates, wires, and memories. Several adder
designs have been proposed, but multiplier design in
QCA is a rather unexplored research area. This paper
utilizes the QCA characteristics to design serial
parallel multipliers. Two types of serial parallel
multipliers are designed and simulated with several
different operand sizes. Those designs are compared in
terms of complexity, area, and latency. The serial
parallel multipliers have simple and regular
structures.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Chung:2007:ASF,
author = "Jaewook Chung and M. Anwar Hasan",
title = "Asymmetric Squaring Formulae",
crossref = "Kornerup:2007:PIS",
pages = "113--122",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.11",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present efficient squaring formulae based on the
Toom--Cook multiplication algorithm. The latter always
requires at least one non-trivial constant division in
the interpolation step. We show such non-trivial
divisions are not needed in the case two operands are
equal for three, four and five-way squarings. Our
analysis shows that our 3-way squaring algorithms have
much less overhead than the best known 3-way Toom--Cook
algorithm. Our experimental results show that one of
our new 3-way squaring methods performs faster than
mpz\_mul() in GNU multiple precision library (GMP) for
squaring integers of approximately 2400-6700 bits on
Pentium IV Prescott 3.2GHz. For squaring in $ Z[x] $,
our 3-way squaring algorithms are much superior to
other known squaring algorithms for small input size.
In addition, we present 4-way and 5-way squaring
formulae which do not require any constant divisions by
integers other than a power of 2. Under some reasonable
assumptions, our 5-way squaring formula is faster than
the recently proposed Montgomery's 5-way Karatsuba-like
formulae.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18; Cook multiplication algorithm; Karatsuba
algorithm; Karatsuba-like formulae; Montgomery's
Squaring; Toom-multiple-precision arithmetic",
}
@Article{Chung:2007:LWP,
author = "Jaewook Chung and M. Anwar Hasan",
title = "Low-Weight Polynomial Form Integers for Efficient
Modular Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "1",
pages = "44--57",
month = jan,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.250622",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:36 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4016496",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Chung:2007:MRA,
author = "Jaewook Chung and M. Anwar Hasan",
title = "{Montgomery} Reduction Algorithm for Modular
Multiplication Using Low-Weight Polynomial Form
Integers",
crossref = "Kornerup:2007:PIS",
pages = "230--239",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.23",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, we extend a recent piece of work on
low-weight polynomial form integers (LWPFIs). We
present a new coefficient reduction algorithm based on
the Montgomery reduction algorithm and provide its
detailed analysis results. We give a condition for
eliminating the final subtractions at the end of our
Montgomery reduction algorithm adapted to perform the
coefficient reduction. Our experimental results show
that a new coefficient reduction algorithm is indeed
more efficient than the one presented in [1].",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Cornea:2007:SII,
author = "Marius Cornea and Cristina Anderson and John Harrison
and Ping Tak Peter Tang and Eric Schneider and Charles
Tsen",
title = "A Software Implementation of the {IEEE 754R} Decimal
Floating-Point Arithmetic Using the Binary Encoding
Format",
crossref = "Kornerup:2007:PIS",
pages = "29--37",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.7",
bibdate = "Tue Oct 09 12:00:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.lirmm.fr/arith18/papers/CorneaM_Decimal_ARITH18.pdf",
abstract = "The IEEE Standard 754-1985 for Binary Floating-Point
Arithmetic [1] was revised [2], and an important
addition is the definition of decimal floating-point
arithmetic. This is intended mainly to provide a
robust, reliable framework for financial applications
that are often subject to legal requirements concerning
rounding and precision of the results, because the
binary floating-point arithmetic may introduce small
but unacceptable errors. Using binary floating-point
calculations to emulate decimal calculations in order
to correct this issue has led to the existence of
numerous proprietary software packages, each with its
own characteristics and capabilities. IEEE 754R decimal
arithmetic should unify the ways decimal floating-point
calculations are carried out on various platforms. New
algorithms and properties are presented in this paper
which are used in a software implementation of the IEEE
754R decimal floating-point arithmetic, with emphasis
on using binary operations efficiently. The focus is on
rounding techniques for decimal values stored in binary
format, but algorithms for the more important or
interesting operations of addition, multiplication,
division, and conversions between binary and decimal
floating-point formats are also outlined. Performance
results are included for a wider range of operations,
showing promise that our approach is viable for
applications that require decimal floating-point
calculations",
acknowledgement = ack-nhfb,
keywords = "ARITH-18; BID rounding; correct rounding;
floating-point arithmetic",
}
@Manual{Cowlishaw:2007:DCL,
author = "Mike Cowlishaw",
title = "The {decNumber C} library",
organization = pub-IBM,
address = pub-IBM:adr,
day = "18",
month = apr,
year = "2007",
bibdate = "Fri Apr 20 08:02:33 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Version 3.40",
URL = "http://download.icu-project.org/ex/files/decNumber/decNumber-icu-340.zip",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; DPD encoding",
}
@Article{Dadda:2007:MPD,
author = "Luigi Dadda",
title = "Multioperand Parallel Decimal Adder: a Mixed Binary
and {BCD} Approach",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "10",
pages = "1320--1328",
month = oct,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.1067",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 07 17:48:41 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal arithmetic has been in recent years revived
due to the large amount of data in commercial
applications. We consider the problem of Multi Operand
Parallel Decimal Addition with an approach that uses
binary arithmetic, suggested by the adoption of BCD
numbers. This involves corrections in order to obtain
the BCD result, or a binary to decimal conversion. We
adopt the latter approach, particularly efficient for a
large number of addends. Conversion requires a
relatively small area and can afford fast operation.
The BD conversion, moreover, allows an easy alignment
of the sums of adjacent columns. We treat the design of
BCD digit adders using fast carry free adders and the
conversion problem through a known parallel scheme
using elementary conversion cells. Spreadsheets have
been developed for adding several BCD digits and for
simulating the binary to decimal conversion as design
tool.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
author-dates = "29 April 1923--26 October 2012",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "decimal floating-point arithmetic",
}
@Article{David:2007:HCM,
author = "J. P. David and K. Kalach and N. Tittley",
title = "Hardware Complexity of Modular Multiplication and
Exponentiation",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "10",
pages = "1308--1319",
month = oct,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.1084",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4302704",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{deDinechin:2007:FCR,
author = "Florent de Dinechin and Christoph Lauter and
Jean-Michel Muller",
title = "Fast and correctly rounded logarithms in
double-precision",
journal = j-INFORM-THEOR-APPL,
volume = "41",
number = "1",
pages = "85--102",
month = jan,
year = "2007",
CODEN = "RSITD7, RITAE4",
DOI = "https://doi.org/10.1051/ita:2007003",
ISSN = "0988-3754 (print), 1290-385X (electronic)",
ISSN-L = "0988-3754",
bibdate = "Fri Dec 8 09:46:23 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "RAIRO. Informatique th{\'e}orique et applications :=
Theoretical informatics and applications",
}
@InProceedings{Detrey:2007:RHF,
author = "Jeremie Detrey and Florent de Dinechin and Xavier
Pujol",
title = "Return of the hardware floating-point elementary
function",
crossref = "Kornerup:2007:PIS",
pages = "161--168",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.29",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The study of specific hardware circuits for the
evaluation of floating-point elementary functions was
once an active research area, until it was realized
that these functions were not frequent enough to
justify dedicating silicon to them. Research then
turned to software functions. This situation may be
about to change again with the advent of reconfigurable
co-processors based on field-programmable gate arrays.
Such co-processors now have a capacity that allows them
to accommodate double-precision floating-point
computing. Hardware operators for elementary functions
targeted to such platforms have the potential to vastly
outperform software functions, and will not permanently
waste silicon resources. This article studies the
optimization, for this target technology, of operators
for the exponential and logarithm functions up to
double-precision. These operators are freely available
from http://www.ens-lyon.fr/LIP/Arenaire/.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Detrey:2007:TUC,
author = "J{\'e}r{\'e}mie Detrey and Florent Dinechin",
title = "A Tool for Unbiased Comparison between Logarithmic and
Floating-point Arithmetic",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "49",
number = "1",
pages = "161--175",
month = oct,
year = "2007",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/s11265-007-0048-7",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Nov 05 19:20:45 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "For applications requiring a large dynamic, real
numbers may be represented either in floating-point, or
in the logarithm number system (LNS). Which system is
best for a given application is difficult to know in
advance, because the cost and performance of LNS
operators depend on the target accuracy in a highly non
linear way. Therefore, a comparison of the pros and
cons of both number systems in terms of cost,
performance and overall accuracy is only relevant on a
per-application basis. To make such a comparison
possible, two concurrent libraries of parameterized
arithmetic operators, targeting recent
field-programmable gate arrays, are presented. They are
unbiased in the sense that they strive to reflect the
state-of-the-art for both number systems. These
libraries are freely available at
http://www.ens-lyon.fr/LIP/Arenaire/.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@Article{Diekmann:2007:FDU,
author = "Andreas Diekmann",
title = "Not the First Digit! Using {Benford's Law} to Detect
Fraudulent Scientific Data",
journal = j-J-APPL-STAT,
volume = "34",
number = "3",
pages = "321--329",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1080/02664760601004940",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Wed Aug 25 11:41:54 MDT 2010",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Digits in statistical data produced by natural or
social processes are often distributed in a manner
described by 'Benford's law'. Recently, a test against
this distribution was used to identify fraudulent
accounting data. This test is based on the supposition
that first, second, third, and other digits in real
data follow the Benford distribution while the digits
in fabricated data do not. Is it possible to apply
Benford tests to detect fabricated or falsified
scientific data as well as fraudulent financial data?
We approached this question in two ways. First, we
examined the use of the Benford distribution as a
standard by checking the frequencies of the nine
possible first and ten possible second digits in
published statistical estimates. Second, we conducted
experiments in which subjects were asked to fabricate
statistical estimates (regression coefficients). The
digits in these experimental data were scrutinized for
possible deviations from the Benford distribution.
There were two main findings. First, both digits of the
published regression coefficients were approximately
Benford distributed or at least followed a pattern of
monotonic decline. Second, the experimental results
yielded new insights into the strengths and weaknesses
of Benford tests. Surprisingly, first digits of faked
data also exhibited a pattern of monotonic decline,
while second, third, and fourth digits were distributed
less in accordance with Benford's law. At least in the
case of regression coefficients, there were indications
that checks for digit-preference anomalies should focus
less on the first (i.e. leftmost) and more on later
digits.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
keywords = "Benford's Law; data fabrication; digital analysis;
distribution of digits from regression coefficients;
first digit law; Zipf's Law",
}
@Article{Dieter:2007:LCM,
author = "W. R. Dieter and A. Kaveti and H. G. Dietz",
title = "Low-Cost Microarchitectural Support for Improved
Floating-Point Accuracy",
journal = j-IEEE-COMPUT-ARCHIT-LETT,
volume = "6",
number = "1",
pages = "13--16",
month = jan,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1109/L-CA.2007.1",
ISSN = "1556-6056 (print), 1556-6064 (electronic)",
ISSN-L = "1556-6056",
bibdate = "Fri Jun 21 05:49:19 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib",
abstract = "Some processors designed for consumer applications,
such as graphics processing units (CPUs) and the CELL
processor, promise outstanding floating-point
performance for scientific applications at commodity
prices. However, IEEE single precision is the most
precise floating-point data type these processors
directly support in hardware. Pairs of native
floating-point numbers can be used to represent a base
result and a residual term to increase accuracy, but
the resulting order of magnitude slowdown dramatically
reduces the price/performance advantage of these
systems. By adding a few simple microarchitectural
features, acceptable accuracy can be obtained with
relatively little performance penalty. To reduce the
cost of native-pair arithmetic, a residual register is
used to hold information that would normally have been
discarded after each floating-point computation. The
residual register dramatically simplifies the code,
providing both lower latency and better
instruction-level parallelism.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Computer Architecture Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208",
keywords = "Application software; B Hardware; B.2 Arithmetic and
Logic Structures; B.2.4 High-Speed Arithmetic; B.2.4.b
Cost/performance; C Computer Systems Organization; C.0
General; C.0.b Hardware/software interfaces; C.1
Processor Architectures; C.1.5 Micro-architecture
implementation considerations; CELL processor; computer
architecture; Costs; floating point arithmetic;
floating-point accuracy; Floating-point arithmetic; G
Mathematics of Computing; G.1 Numerical Analysis; G.1.0
General; G.1.0.e Multiple precision arithmetic;
Graphics; graphics processing units; Hardware; I
Computing Methodologies; I.3 Computer Graphics; I.3.1
Hardware Architecture; I.3.1.a Graphics processors;
IEEE single precision; instruction-level parallelism;
microarchitectural support; Microarchitecture; parallel
processing; Pipelines; Registers; Software algorithms;
Software performance",
}
@InProceedings{Dimitrov:2007:MCS,
author = "Vassil Dimitrov and Laurent Imbert and Andrew
Zakaluzny",
title = "Multiplication by a Constant is Sublinear",
crossref = "Kornerup:2007:PIS",
pages = "261--268",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.24",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper explores the use of the double-base number
system (DBNS) for constant integer multiplication. The
DBNS recoding scheme represents integers --- in this
case constants --- in a multiple-radix way in the hope
of minimizing the number of additions to be performed
during constant multiplication. On the theoretical
side, we propose a formal proof which shows that our
recoding technique diminishes the number of additions
in a sublinear way. Therefore, we prove Lef{\`e}vre's
conjecture that the multiplication by an integer
constant is achievable in sublinear time. In a second
part, we investigate various strategies and we provide
numerical data showcasing the potential interest of our
approach.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18; Double-Based Number System (DBNS)",
}
@Article{Doornik:2007:CHP,
author = "Jurgen A. Doornik",
title = "Conversion of high-period random numbers to floating
point",
journal = j-TOMACS,
volume = "17",
number = "1",
pages = "??--??",
month = jan,
year = "2007",
CODEN = "ATMCEZ",
DOI = "https://doi.org/10.1145/1189756.1189759",
ISSN = "1049-3301 (print), 1558-1195 (electronic)",
ISSN-L = "1049-3301",
bibdate = "Sat Apr 14 09:34:46 MDT 2007",
bibsource = "http://www.acm.org/pubs/contents/journals/tomacs/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Modeling and Computer Simulation",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J781",
}
@Article{Duale:2007:DFP,
author = "A. Y. Duale and M. H. Decker and H.-G. Zipperer and M.
Aharoni and T. J. Bohizic",
title = "Decimal floating-point in {z9}: An implementation and
testing perspective",
journal = j-IBM-JRD,
volume = "51",
number = "1/2",
pages = "217--227",
month = jan # " \slash " # mar,
year = "2007",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/rd.511.0217",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Fri Feb 9 20:31:06 MST 2007",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/511/duale.html",
abstract = "Although decimal arithmetic is widely used in
commercial and financial applications, the related
computations are handled in software. As a result,
applications that use decimal data may experience
performance degradations. Use of the newly defined
decimal floating-point (DFP) format instead of binary
floating-point is expected to significantly improve the
performance of such applications. System z9 is the
first IBM machine to support the DFP instructions. We
present an overview of this implementation and provide
some measurement of the performance gained using
hardware assists. Various tools and techniques employed
for the DFP verification on unit, element, and system
levels are presented in detail. Several groups within
IBM collaborated on the verification of the new DFP
facility, using a common reference model to predict DFP
results.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "decimal floating-point arithmetic",
ordernumber = "????",
}
@Article{Eisen:2007:IPA,
author = "L. Eisen and J. W. {Ward III} and H.-W. Tast and N.
M{\"a}ding and J. Leenstra and S. M. Mueller and C.
Jacobi and J. Preiss and E. M. Schwarz and S. R.
Carlough",
title = "{IBM POWER6} accelerators: {VMX} and {DFU}",
journal = j-IBM-JRD,
volume = "51",
number = "6",
pages = "663--683",
month = nov,
year = "2007",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Mon Jul 7 21:49:07 MDT 2008",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/516/eisen.html",
abstract = "The IBM POWER6 microprocessor core includes two
accelerators for increasing performance of specific
workloads. The vector multimedia extension (VMX)
provides a vector acceleration of graphic and
scientific workloads. It provides single instructions
that work on multiple data elements. The instructions
separate a 128-bit vector into different components
that are operated on concurrently. The decimal
floating-point unit (DFU) provides acceleration of
commercial workloads, more specifically, financial
transactions. It provides a new number system that
performs implicit rounding to decimal radix points, a
feature essential to monetary transactions. The IBM
POWER processor instruction set is substantially
expanded with the addition of these two accelerators.
The VMX architecture contains 176 instructions, while
the DFU architecture adds 54 instructions to the base
architecture. The IEEE 754R Binary Floating-Point
Arithmetic Standard defines decimal floating-point
formats, and the POWER6 processor---on which a
substantial amount of area has been devoted to
increasing performance of both scientific and
commercial workloads---is the first commercial hardware
implementation of this format.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "decimal floating-point arithmetic",
}
@Article{Eisinberg:2007:AFP,
author = "A. Eisinberg and G. Fedele",
title = "Accurate floating-point summation: a new approach",
journal = j-APPL-MATH-COMP,
volume = "189",
number = "1",
pages = "410--424",
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "65B10",
MRnumber = "MR2330219",
bibdate = "Thu Nov 8 19:16:14 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The aim of this paper is to find an accurate and
efficient algorithm for evaluating the summation of
large sets of floating-point numbers. We present a new
representation of the floating-point number system in
which a number is represented as a linear combination
of integers and the coefficients are powers of the base
of the floating-point system. The approach allows to
build up an accurate floating-point summation algorithm
based on the fact that no rounding error occurs
whenever two integer numbers are summed or a
floating-point number is multiplied by powers of the
base of the floating-point system. The proposed
algorithm seems to be competitive in terms of
computational effort and, under some assumptions, the
computed sum is greatly accurate. With such
assumptions, less-conservative in the practical
applications, we prove that the relative error of the
computed sum is bounded by the unit roundoff.",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "accurate floating-point summation",
}
@Article{Ercegovac:2007:CSR,
author = "Milo{\v{s}} D. Ercegovac and Jean-Michel Muller",
title = "Complex Square Root with Operand Prescaling",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "49",
number = "1",
pages = "19--30",
month = oct,
year = "2007",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/s11265-006-0029-2",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Nov 05 19:24:36 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We propose a radix-$r$ digit-recurrence algorithm for
complex square-root. The operand is prescaled to allow
the selection of square-root digits by rounding of the
residual. This leads to a simple hardware
implementation of digit selection. Moreover, the use of
digit recurrence approach allows correct rounding of
the result if needed. The algorithm, compatible with
the complex division presented in Ercegovac and Muller
(``Complex Division with Prescaling of the Operands,''
in Proc. Application-Specific Systems, Architectures,
and Processors (ASAP'03), The Hague, The Netherlands,
June 24---26, 2003), and its design are described. We
also give rough estimates of its latency and cost with
respect to implementation based on standard
floating-point instructions as used in software
routines for complex square root.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Ercegovac:2007:HOM,
author = "Milo{\v{s}} D. Ercegovac and Jean-Michel Muller",
editor = "{IEEE}",
booktitle = "{2007 IEEE International Conference on
Application-specific Systems, Architectures and
Processors (ASAP), Montr{\'e}al, Canada, July 8--11,
2007}",
title = "A Hardware-Oriented Method for Evaluating Complex
Polynomials",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "122--127",
year = "2007",
DOI = "https://doi.org/10.1109/ASAP.2007.4429968",
ISBN = "1-4244-1027-4",
ISBN-13 = "978-1-4244-1027-9",
bibdate = "Fri Sep 29 10:42:47 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Erle:2007:DFP,
author = "Mark A. Erle and Michael J. Schulte and Brian J.
Hickmann",
title = "Decimal Floating-Point Multiplication Via Carry-Save
Addition",
crossref = "Kornerup:2007:PIS",
pages = "46--55",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.14",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.lirmm.fr/arith18/papers/erlem-DFPmultiplication-v2.pdf",
abstract = "Decimal multiplication is important in many commercial
applications including financial analysis, banking, tax
calculation, currency conversion, insurance, and
accounting. This paper presents the design of a decimal
floating-point multiplier that complies with
specifications for decimal multiplication given in the
draft revision of the IEEE 754 Standard for
Floating-point Arithmetic (IEEE 754R). This multiplier
extends a previously published decimal fixedpoint
multiplier design by adding several features including
exponent generation, sticky bit generation, shifting of
the intermediate product, rounding, and exception
detection and handling. The core of the decimal
multiplication algorithm is an iterative scheme of
partial product accumulation employing decimal
carry-save addition to reduce the critical path delay.
Novel features of the proposed multiplier include
support for decimal floating-point numbers, on-the-fly
generation of the sticky bit, early estimation of the
shift amount, and efficient decimal rounding. Area and
delay estimates are provided for a verified Verilog
register transfer level model of the multiplier.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Fan:2007:NAS,
author = "Haining Fan and M. Anwar Hasan",
title = "A New Approach to Subquadratic Space Complexity
Parallel Multipliers for Extended Binary Fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "2",
pages = "224--233",
month = feb,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.19",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4042682",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fan:2007:SCC,
author = "Haining Fan and M. Anwar Hasan",
title = "Subquadratic Computational Complexity Schemes for
Extended Binary Field Multiplication Using Optimal
Normal Bases",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "10",
pages = "1435--1437",
month = oct,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.1076",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4302715",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Fousse:2007:AMP,
author = "Laurent Fousse",
title = "Accurate Multiple-Precision {Gauss--Legendre}
Quadrature",
crossref = "Kornerup:2007:PIS",
pages = "150--160",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.8",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Numerical integration is an operation that is
frequently available in multiple precision numerical
software packages. The different quadrature schemes
used are considered well studied but the rounding
errors that result from the computation are often
neglected, and the actual accuracy of the results are
therefore seldom rigorously proven. We propose an
implementation of the Gauss--Legendre quadrature scheme
with bounded error: given a bound on the derivatives of
a function we are able to compute an interval
containing the true value of the integral, in arbitrary
precision. The error analysis is given as well as
experimental error measurements and timings, and a
complete quadrature example.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Fousse:2007:MMP,
author = "Laurent Fousse and Guillaume Hanrot and Vincent
Lef{\`e}vre and Patrick P{\'e}lissier and Paul
Zimmermann",
title = "{MPFR}: a multiple-precision binary floating-point
library with correct rounding",
journal = j-TOMS,
volume = "33",
number = "2",
pages = "1--15",
month = jun,
year = "2007",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1236463.1236468",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G99",
MRnumber = "MR2326955",
bibdate = "Thu Jul 26 17:36:59 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "This article presents a multiple-precision binary
floating-point library, written in the ISO C language,
and based on the GNU MP library. Its particularity is
to extend to arbitrary-precision, ideas from the IEEE
754 standard, by providing correct rounding and
exceptions. We demonstrate how these strong semantics
are achieved---with no significant slowdown with
respect to other arbitrary-precision tools---and
discuss a few applications where such a library can be
useful.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Fousse:2007:MPC,
author = "Laurent Fousse",
title = "Multiple-Precision Correctly rounded {Newton--Cotes}
quadrature",
journal = j-INFORM-THEOR-APPL,
volume = "41",
number = "1",
pages = "103--121",
month = jan,
year = "2007",
CODEN = "RSITD7, RITAE4",
DOI = "https://doi.org/10.1051/ita:2007004",
ISSN = "0988-3754 (print), 1290-385X (electronic)",
ISSN-L = "0988-3754",
bibdate = "Fri Dec 8 09:50:26 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "RAIRO. Informatique th{\'e}orique et applications :=
Theoretical informatics and applications",
}
@Article{Frommer:2007:PEZ,
author = "A. Frommer and F. Hoxha and B. Lang",
title = "Proving the existence of zeros using the topological
degree and interval arithmetic",
journal = j-J-COMPUT-APPL-MATH,
volume = "199",
number = "2",
pages = "397--402",
day = "15",
month = feb,
year = "2007",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:12:04 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042705007788",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Furer:2007:FIM,
author = "Martin F{\"u}rer",
title = "Faster integer multiplication",
crossref = "ACM:2007:SPA",
pages = "57--66",
year = "2007",
DOI = "https://doi.org/10.1145/1250790.1250800",
bibdate = "Fri Jun 20 18:28:53 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "For more than 35 years, the fastest known method for
integer multiplication has been the
Sch{\"o}nhage-Strassen algorithm running in time $ O(n
\log n \log \log n) $. Under certain restrictive
conditions there is a corresponding $ \Omega (n \log n)
$ lower bound. The prevailing conjecture has always
been that the complexity of an optimal algorithm is $
\Theta (n \log n) $. We present a major step towards
closing the gap from above by presenting an algorithm
running in time $ n \log n, 2^{O(\log * n)} $.\par
The main result is for Boolean circuits as well as for
multitape Turing machines, but it has consequences to
other models of computation as well.",
acknowledgement = ack-nhfb,
keywords = "complexity; computer arithmetic; discrete Fourier
transform; FFT; integer multiplication",
}
@InProceedings{Gaudry:2007:GBI,
author = "Pierrick Gaudry and Alexander Kruppa and Paul
Zimmermann",
title = "A {\tt gmp}-based implementation of
{Sch{\"o}nhage--Strassen}'s large integer
multiplication algorithm",
crossref = "Brown:2007:PIS",
pages = "167--174",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277572",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Sch{\"o}nhage--Strassen's algorithm is one of the best
known algorithms for multiplying large integers.
Implementing it efficiently is of utmost importance,
since many other algorithms rely on it as a subroutine.
We present here an improved implementation, based on
the one distributed within the GMP library. The
following ideas and techniques were used or tried:
faster arithmetic modulo $ 2^n + 1 $, improved cache
locality, Mersenne transforms, Chinese Remainder
Reconstruction, the $ \sqrt 2 $ trick, Harley's and
Granlund's tricks, improved tuning.",
acknowledgement = ack-nhfb,
keywords = "integer multiplication; multiprecision arithmetic",
}
@Article{Goel:2007:RMS,
author = "S. Goel and S. K. Dash",
title = "Response of model simulated weather parameters to
round-off-errors on different systems",
journal = "Environmental Modelling \& Software",
volume = "22",
number = "8",
pages = "1164--1174",
month = aug,
year = "2007",
CODEN = "EMSOFT",
DOI = "https://doi.org/10.1016/j.envsoft.2006.06.011",
ISSN = "1364-8152 (print), 1873-6726 (electronic)",
ISSN-L = "1364-8152",
bibdate = "Fri Aug 08 08:49:37 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this study, the weather forecasting model of the
National Centre for Medium Range Weather Forecasting
(NCMRWF) is used for examining the characteristics of
round-off-errors on three different computer
architectures --- PARAM 10K, SUNFIRE 6800 and Dec Alpha
for several meteorological parameters such as
precipitation, temperature at the surface and
mid-atmosphere, and upper and lower level winds. It is
well known that the implementation of floating point
arithmetic varies from one computing system to another.
As a result, meteorological parameters simulated by
numerical models on two different systems may deviate
from each other and the difference field becomes larger
as the model is integrated for longer time, for
example, in the scale of several months. This paper
focuses on the reduction of such round-off-errors by a
simple method of modifying the format representation of
the initial data supplied to the model. In all the
three systems, the model has been integrated for 4
months starting from 4th May, 1996. It is found that
after 5 days of model integration with the modified
data, the round-off-errors become insignificant. The
rate of reduction of round-off-errors is fast up to a
month of model integration and thereafter the rate
slows down and stabilises. It is further noticed that
at the end of four months of integration, the reduction
in round-off-errors over the tropical region and oceans
is much more than over the rest of the globe.",
acknowledgement = ack-nhfb,
ajournal = "Environ. Model. Softw.",
journal-URL = "https://www.sciencedirect.com/journal/environmental-modelling-and-software",
keywords = "round-off error; rounding error",
}
@InProceedings{Goldberg:2007:FIP,
author = "R. Goldberg and G. Even and P.-M. Seidel",
title = "An {FPGA} implementation of pipelined multiplicative
division with {IEEE} rounding",
crossref = "Pocek:2007:PAI",
pages = "185--196",
year = "2007",
DOI = "https://doi.org/10.1109/FCCM.2007.59",
bibdate = "Sat Oct 9 12:43:39 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We report the results of an FPGA implementation of
double precision floating-point division with IEEE
rounding. We achieve a total latency (i.e., cycles
times clock period) that is 2:6 times smaller than the
latency of the fastest previous implementation on
FPGAs. The amount of hardware, on the other hand, is
comparable to commercial cores. The division circuit is
based on Goldschmidt's algorithm. All IEEE rounding
modes are supported and are implemented using dewpoint
rounding. The precision of the initial approximation of
the reciprocal is 14 bits. To save hardware and reduce
the critical path, a half-sized 62x30 Booth radix-8
multiplier is used. This multiplier can receive both
the multiplicand and the multiplier in carry-save
representation. The division circuit is partitioned
into four pipeline stages, has a latency of 11 cycles,
and may restart a new double precision division
operation after 8 cycles. Synthesis results of an
implementation (not including the computation of the
initial approximation of the reciprocal and the
exponent path) guarantee a clock frequency of 131 MHz
on an Altera Stratix II using 3592 ALMs. The
implementation was successfully tested with over 10
million random vectors as well as over a million
hard-to-round vectors.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hanrot:2007:WCP,
author = "Guillaume Hanrot and Vincent Lef{\`e}vre and Damien
Stehle and Paul Zimmermann",
title = "Worst Cases of a Periodic Function for Large
Arguments",
crossref = "Kornerup:2007:PIS",
pages = "133--140",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.37",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One considers the problem of finding hard to round
cases of a periodic function for large floating-point
inputs, more precisely when the function cannot be
efficiently approximated by a polynomial. This is one
of the last few issues that prevents from guaranteeing
an efficient computation of correctly rounded
transcendentals for the whole IEEE-754 double precision
format. The first non-naive algorithm for that problem
is presented, with a heuristic complexity of O(20.676p)
for a precision of p bits. The efficiency of the
algorithm is shown on the largest IEEE-754 double
precision binade for the sine function, and some
corresponding bad cases are given. We can hope that all
the worst cases of the trigonometric functions in their
whole domain will be found within a few years, a task
that was considered out of reach until now.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18; correct rounding; floating-point
arithmetic",
}
@Article{Harrison:2007:FPV,
author = "J. Harrison",
title = "Floating-Point Verification",
journal = j-J-UCS,
volume = "13",
number = "5",
pages = "629--638",
month = "????",
year = "2007",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Thu Jul 10 06:41:41 MDT 2008",
bibsource = "http://www.jucs.org/jucs;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/jucs_13_5/floating_point_verification",
abstract = "This paper overviews the application of formal
verification techniques to hardware in general, and to
floating-point hardware in particular. A specific
challenge is to connect the usual mathematical view of
continuous arithmetic operations with the discrete
world, in a credible and verifiable way.",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@InProceedings{Hasenplaugh:2007:FMR,
author = "William Hasenplaugh and Gunnar Gaubatz and Vinodh
Gopal",
title = "Fast Modular Reduction",
crossref = "Kornerup:2007:PIS",
pages = "225--229",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.18",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "It is widely acknowledged that efficient modular
multiplication is a key to high-performance
implementation of public-key cryptography, be it
classical RSA, Diffie--Hellman, or (hyper-) elliptic
curve algorithms. In the recent decade, practitioners
have relied mainly on two popular methods: Montgomery
Multiplication and regular long-integer multiplication
in combination with Barrett's modular reduction
technique. In this paper, we propose a modification to
Barrett's algorithm that leads to a significant
reduction (25\% to 75\%) in multiplications and
additions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Hernandez:2007:MPO,
author = "M. A. Hern{\'a}ndez and N. Romero",
title = "Methods with prefixed order for approximating square
roots with global and general convergence",
journal = j-APPL-MATH-COMP,
volume = "194",
number = "2",
pages = "346--353",
day = "15",
month = dec,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:09 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@InProceedings{Hilewitz:2007:PAB,
author = "Yedidya Hilewitz and Ruby B. Lee",
title = "Performing Advanced Bit Manipulations Efficiently in
General-Purpose Processors",
crossref = "Kornerup:2007:PIS",
pages = "251--260",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.27",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes a new basis for the
implementation of a shifter functional unit. We present
a design based on the inverse butterfly and butterfly
datapath circuits that performs the standard shift and
rotate operations, as well as more advanced extract,
deposit and mix operations found in some processors.
Additionally, it also supports important new classes of
even more advanced bit manipulation instructions
recently proposed: these include arbitrary bit
permutations, bit scatter and bit gather instructions.
The new functional unit's datapath is comparable in
latency to that of the classic barrel shifter. It
replaces two existing functional units --- shifter and
mix --- with a much more powerful one.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Holmes:2007:BA,
author = "Neville Holmes",
title = "Binary Arithmetic",
journal = j-COMPUTER,
volume = "40",
number = "6",
pages = "90--93",
month = jun,
year = "2007",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/MC.2007.196",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Jun 29 14:19:11 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "complete arithmetic; interval arithmetic",
}
@Article{Homann:2007:IFPa,
author = "Holger Homann and J{\"u}rgen Dreher and Rainer
Grauer",
title = "Impact of the floating-point precision and
interpolation scheme on the results of {DNS} of
turbulence by pseudo-spectral codes",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "22",
month = may,
year = "2007",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in \cite{Homann:2007:IFPb}.",
URL = "http://arxiv.org/abs/0705.3144",
abstract = "In this paper we investigate the impact of the
floating-point precision and interpolation scheme on
the results of direct numerical simulations (DNS) of
turbulence by pseudo-spectral codes. Three different
types of floating-point precision configurations show
no differences in the statistical results. This implies
that single precision computations allow for increased
Reynolds numbers due to the reduced amount of memory
needed. The interpolation scheme for obtaining velocity
values at particle positions has a noticeable impact on
the Lagrangian acceleration statistics. A tri-cubic
scheme results in a slightly broader acceleration
probability density function than a tri-linear scheme.
Furthermore the scaling behavior obtained by the cubic
interpolation scheme exhibits a tendency towards a
slightly increased degree of intermittency compared to
the linear one.",
acknowledgement = ack-nhfb,
subject = "Computational Physics (physics.comp-ph); Fluid
Dynamics (physics.flu-dyn)",
}
@Article{Homann:2007:IFPb,
author = "Holger Homann and J{\"u}rgen Dreher and Rainer
Grauer",
title = "Impact of the floating-point precision and
interpolation scheme on the results of {DNS} of
turbulence by pseudo-spectral codes",
journal = j-COMP-PHYS-COMM,
volume = "177",
number = "7",
pages = "560--565",
day = "1",
month = oct,
year = "2007",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2007.05.019",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 23:42:25 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465507002998",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Hosangadi:2007:AMO,
author = "Anup Hosangadi and Farzan Fallah and Ryan Kastner",
title = "Algebraic Methods for Optimizing Constant
Multiplications in Linear Systems",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "49",
number = "1",
pages = "31--50",
month = oct,
year = "2007",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/s11265-007-0137-7",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Nov 05 19:29:43 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Constant multiplications can be efficiently
implemented in hardware by converting them into a
sequence of nested additions and shift operations. They
can be optimized further by finding common
subexpressions among these operations. In this work, we
present algebraic methods for eliminating common
subexpressions. Algebraic techniques are established in
multi-level logic synthesis for the minimization of the
number of literals and hence gates to implement Boolean
logic. In this work we use the concepts of two of these
methods, namely rectangle covering and fast extract
(FX) and adapt them to the problem of optimizing linear
arithmetic expressions. The main advantage of using
such methods is that we can optimize systems consisting
of multiple variables, which is not possible using the
conventional optimization techniques. Our optimizations
are aimed at reducing the area and power consumption of
the hardware, and experimental results show up to
30.3\% improvement in the number of operations over
conventional techniques. Synthesis and simulation
results show up to 30\% area reduction and up to 27\%
power reduction. We also modified our algorithm to
perform delay aware optimization, where we perform
common subexpression elimination such that the delay is
not exceeded beyond a particular value.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@InProceedings{Hosseinzadeh:2007:NMS,
author = "M. Hosseinzadeh and K. Navi and S. Gorgin",
booktitle = "{ICEE '07}, International Conference on Electrical
Engineering, 11--12 April 2007",
title = "A New Moduli Set for Residue Number System: $ \{ r^n -
2, r^n - 1, r^n \} $",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1109/ICEE.2007.4287306",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper a new moduli set is for Residue Number
System: introduced where $r = 2k + 1$ and $k = 1, 2, 3,
\ldots{}$. This moduli set includes pair wise
relatively prime moduli, so it offers the maximum
possible dynamic range. For this moduli set, the
related circuits are simply realizable in the Multiple
Valued Logic (MVL) and arithmetic in this moduli set
enjoys very high speed operations and simple
reverse\slash forward conversion (RNS to MVL\slash MVL
to RNS).\par
After introducing the new moduli set, we design its
related circuits and converters. Finally, we compare
the results of those of similar moduli sets and show
that our moduli set significantly improves the time
complexity while offering greater dynamic range.",
}
@InProceedings{Huang:2007:NAM,
author = "Libo Huang and Li Shen and Kui Dai and Zhiying Wang",
title = "A New Architecture for Multiple-Precision
Floating-Point Multiply-Add Fused Unit Design",
crossref = "Kornerup:2007:PIS",
pages = "69--76",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.5",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The floating-point multiply-add fused (MAF) unit sets
a new trend in the processor design to speed up
floating-point performance in scientific and multimedia
applications. This paper proposes a new architecture
for the MAF unit that supports multiple IEEE precisions
multiply-add operation (A*B+C) with Single Instruction
Multiple Data (SIMD) feature. The proposed MAF unit can
perform either one double-precision or two parallel
single-precision operations using about 18\% more
hardware than a conventional double-precision MAF unit
and with 9\% increase in delay. To accommodate the
simultaneous computation of two single-precision MAF
operations, several basic modules of double-precision
MAF unit are redesigned. They are either segmented by
precision mode dependent multiplexers or attached by
the duplicated hardware. The proposed MAF unit can be
fully pipelined and the experimental results show that
it is suitable for processors with floating-point unit
(FPU).",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Iguchi:2007:DRC,
author = "Yukihiro Iguchi and Tsutomu Sasao and Munehiro
Matsuura",
title = "On Designs of Radix Converters Using Arithmetic
Decompositions---Binary to Decimal Converters---",
crossref = "IEEE:2007:IPI",
pages = "32--32",
year = "2007",
DOI = "https://doi.org/10.1109/ISMVL.2007.39",
bibdate = "Thu Aug 07 17:34:11 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In digital signal processing, radixes other than two
are often used for high-speed computation. In the
computation for finance, decimal numbers are used
instead of binary numbers. In such cases, radix
converters are necessary. This paper considers design
methods for binary to $q$-nary converters. It
introduces a new design technique based on weighted-sum
(WS) functions. The method computes a WS function for
each digit by an LUT cascade and a binary adder, then
adds adjacent digits with $q$-nary adders. A 16-bit
binary to decimal converter is designed to show the
method.",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Ihsberner:2007:REA,
author = "Katja Ihsberner",
title = "Roundoff error analysis of fast {DCT} algorithms in
fixed point arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "46",
number = "1",
pages = "1--22",
month = sep,
year = "2007",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-007-9123-1",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "subject classification (2000); 65T50; 65G50",
bibdate = "Tue Jul 8 19:14:29 MDT 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=46&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=46&issue=1&spage=1",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Discrete cosine transform; Factorization of cosine
matrix; Fast cosine transform; Fixed point arithmetic;
Numerical stability; Roundoff error",
}
@InProceedings{James:2007:QAD,
author = "Rekha K. James and Shahana T. K. and K. Poulose Jacob
and Sreela Sasi",
title = "Quick Addition of Decimals Using Reversible
Conservative Logic",
crossref = "IEEE:2007:API",
pages = "191--195",
year = "2007",
DOI = "https://doi.org/10.1109/ADCOM.2007.108",
bibdate = "Thu Aug 07 18:33:41 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In recent years, reversible logic has emerged as one
of the most important approaches for power optimization
with its application in low power CMOS, nanotechnology
and quantum computing. This research proposes quick
addition of decimals (QAD) suitable for multi-digit BCD
addition, using reversible conservative logic. The
design makes use of reversible fault tolerant Fredkin
gates only. The implementation strategy is to reduce
the number of levels of delay there by increasing the
speed, which is the most important factor for high
speed circuits.",
acknowledgement = ack-nhfb,
keywords = "decimal arithmetic; delay reduction; fault detection;
reversible logic",
}
@InProceedings{Kapre:2007:OPF,
author = "Nachiket Kapre and Andre DeHon",
title = "Optimistic Parallelization of Floating-Point
Accumulation",
crossref = "Kornerup:2007:PIS",
pages = "205--216",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.25",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating-point arithmetic is notoriously
nonassociative due to the limited precision
representation which demands intermediate values be
rounded to fit in the available precision. The
resulting cyclic dependency in floating-point
accumulation inhibits parallelization of the
computation, including efficient use of pipelining. In
practice, however, we observe that floating-point
operations are ``mostly'' associative. This observation
can be exploited to parallelize floating-point
accumulation using a form of optimistic concurrency. In
this scheme, we first compute an optimistic associative
approximation to the sum and then relax the computation
by iteratively propagating errors until the correct sum
is obtained. We map this computation to a network of 16
statically-scheduled, pipelined, double-precision
floating-point adders on the Virtex-4 LX160 (-12)
device where each floating-point adder runs at 296MHz
and has a pipeline depth of 10. On this 16 PE design,
we demonstrate an average speedup of 6{\AA} -- with
randomly generated data and 3-7{\AA} --- with
summations extracted from Conjugate Gradient
benchmarks.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Kechagias:2007:CME,
author = "P. S. Kechagias and Basil K. Papadopoulos",
title = "Computational method to evaluate fuzzy arithmetic
operations",
journal = j-APPL-MATH-COMP,
volume = "185",
number = "1",
pages = "169--177",
day = "1",
month = feb,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:01 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Khabbazian:2007:DPC,
author = "M. Khabbazian and T. A. Gulliver and V. K. Bhargava",
title = "Double Point Compression with Applications to Speeding
Up Random Point Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "3",
pages = "305--313",
month = mar,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.47",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4079514",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Knowles:2007:RSE,
author = "Simon Knowles",
title = "The Return of Silicon Efficiency",
crossref = "Kornerup:2007:PIS",
pages = "3--3",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.36",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The economic and physical forces which have always
shaped the business of digital chip design are again
evolving to change the priorities of designers. Key
physical trends include the end of gate oxide thickness
scaling, and the effect of small dopant populations on
threshold voltage variance. Key economic trends include
the need to tolerate specification shift and design
error, and the need to amortise chip development cost
over multiple market sockets.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Kobayashi:2007:AIG,
author = "Katsuki Kobayashi and Naofumi Takagi and Kazuyoshi
Takagi",
title = "An Algorithm for Inversion in {$ \mathrm {GF}(2^m) $}
Suitable for Implementation Using a Polynomial Multiply
Instruction on {$ \mathrm {GF}(2) $}",
crossref = "Kornerup:2007:PIS",
pages = "105--112",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.9",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "An algorithm for inversion in $ \mathrm {GF}(2^m) $
suitable for implementation using a polynomial multiply
instruction on $ \mathrm {GF}(2) $ is proposed. It is
based on the extended Euclid's algorithm. In the
algorithm, operations corresponding to several
contiguous iterations of the VLSI algorithm proposed by
Brunner et al. is represented as a matrix. They are
calculated at once through the matrix efficiently by
means of a polynomial multiply instruction on $ \mathrm
{GF}(2) $. For example, in the case where the word size
of a processor and $m$ are $ 32 $ and $ 571 $,
respectively, the algorithm calculates inversion with
about the half number of instructions of the
conventional algorithm on the average.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Kornerup:2007:CIPa,
author = "Peter Kornerup and Vincent Lef{\`e}vre and Jean-Michel
Muller",
title = "Computing Integer Powers in Floating-Point
Arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "30",
month = may,
year = "2007",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in \cite{Kornerup:2007:CIPb}.",
URL = "http://arxiv.org/abs/0705.4369",
abstract = "We introduce two algorithms for accurately evaluating
powers to a positive integer in floating-point
arithmetic, assuming a fused multiply-add (fma)
instruction is available. We show that our log-time
algorithm always produce faithfully-rounded results,
discuss the possibility of getting correctly rounded
results, and show that results correctly rounded in
double precision can be obtained if extended-precision
is available with the possibility to round into double
precision (with a single rounding).",
acknowledgement = ack-nhfb,
keywords = "correct rounding; floating-point arithmetic",
subject = "Numerical Analysis (cs.NA); Mathematical Software
(cs.MS)",
}
@InProceedings{Kornerup:2007:CIPb,
author = "Peter Kornerup and Vincent Lefevre and Jean-Michel
Muller",
editor = "Michael B. Matthews",
booktitle = "{2007 Conference Record of the Forty-First Asilomar
Conference on Signals, Systems and Computers, November
4--7, 2007. Pacific Grove, California}",
title = "Computing Integer Powers in Floating-Point
Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "343--347",
year = "2007",
DOI = "https://doi.org/10.1109/ACSSC.2007.4487226",
ISBN = "1-4244-2110-1",
ISBN-13 = "978-1-4244-2110-7",
ISSN = "1058-6393",
ISSN-L = "1058-6393",
bibdate = "Fri Sep 29 10:55:50 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We introduce two algorithms for accurately evaluating
powers to a positive integer in floating-point
arithmetic, assuming a fused multiply-add (fma)
instruction is available. We show that our log-time
algorithm always produce faithfully-rounded results,
discuss the possibility of getting correctly rounded
results, and show that results correctly rounded in
double precision can be obtained if extended precision
is available with the possibility to round into double
precision (with a single rounding).",
acknowledgement = ack-nhfb,
}
@Article{Kuliamin:2007:STI,
author = "V. V. Kuliamin",
title = "Standardization and testing of implementations of
mathematical functions in floating point numbers",
journal = j-PROG-COMP-SOFT,
volume = "33",
number = "3",
pages = "154--173",
year = "2007",
CODEN = "PCSODA",
DOI = "https://doi.org/10.1134/S036176880703005X",
ISSN = "0361-7688 (print), 1608-3261 (electronic)",
ISSN-L = "0361-7688",
bibdate = "Fri Aug 08 09:01:30 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Requirements definition and test suites development
for implementations of mathematical functions in
floating point arithmetic in the framework of the IEEE
754 standard are considered. A method based on this
standard is proposed for defining requirements for such
functions. This method can be used for the
standardization of implementations of such functions;
this kind of standardization extends IEEE 754. A method
for designing test suites for the verification of those
requirements is presented. The proposed methods are
based on specific properties of the representation of
floating point numbers and on some features of the
functions under examination.",
acknowledgement = ack-nhfb,
fjournal = "Programming and Computer Software; translation of
Programmirovaniye (Moscow, USSR) Plenum",
journal-URL = "http://link.springer.com/journal/11086",
keywords = "floating-point function testing and verification",
}
@Article{Lambov:2007:REI,
author = "Branimir Lambov",
title = "{RealLib}: An efficient implementation of exact real
arithmetic",
journal = "Mathematical Structures in Computer Science",
volume = "17",
number = "1",
pages = "81--98",
month = feb,
year = "2007",
ISSN = "0960-1295",
bibdate = "Thu Aug 07 19:25:30 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.brics.dk/~barnie/RealPractical.pdf",
abstract = "This paper is an introduction to the RealLib package
for exact real number computations. The library
provides certified accuracy, but tries to achieve this
at performance close to the performance of hardware
floating point for problems that do not require higher
precision. The paper gives the motivation and features
of the design of the library and compares it with other
packages for exact real arithmetic.",
acknowledgement = ack-nhfb,
}
@Article{Lang:2007:RDR,
author = "Tomas Lang and Alberto Nannarelli",
title = "A Radix-10 Digit-Recurrence Division Unit: Algorithm
and Architecture",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "6",
pages = "727--739",
month = jun,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.1038",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4167785",
abstract = "In this work, we present a radix-10 division unit that
is based on the digit-recurrence algorithm. The
previous decimal division designs do not include recent
developments in the theory and practice of this type of
algorithm, which were developed for radix-$ 2^k $
dividers. In addition to the adaptation of these
features, the radix-10 quotient digit is decomposed
into a radix-2 digit and a radix-5 digit in such a way
that only five and two times the divisor are required
in the recurrence. Moreover, the most significant slice
of the recurrence, which includes the selection
function, is implemented in radix-2, avoiding the
additional delay introduced by the radix--10 carry-save
additions and allowing the balancing of the paths to
reduce the cycle delay. The results of the
implementation of the proposed radix-10 division unit
show that its latency is close to that of radix-16
division units (comparable dynamic range of
significands) and it has a shorter latency than a
radix-10 unit based on the Newton--Raphson
approximation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "algorithms and architectures for floating-point
arithmetic; decimal arithmetic; decimal division;
decimal floating-point arithmetic; digit-recurrence
division",
}
@InProceedings{Langlois:2007:HEF,
author = "Philippe Langlois and Nicolas Louvet",
title = "How to Ensure a Faithful Polynomial Evaluation with
the Compensated {Horner} Algorithm",
crossref = "Kornerup:2007:PIS",
pages = "141--149",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.21",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The compensated Horner algorithm improves the accuracy
of polynomial evaluation in IEEE-754 floating point
arithmetic: the computed result is as accurate as if it
was computed with the classic Horner algorithm in twice
the working precision. Since the condition number still
governs the accuracy of this computation, it may return
an arbitrary number of inexact digits. We address here
how to compute a faithfully rounded result, that is one
of the two floating point neighbors of the exact
evaluation. We propose an a priori sufficient condition
on the condition number to ensure that the compensated
evaluation is faithfully rounded. We also propose a
validated and dynamic method to test at the running
time if the compensated result is actually faithfully
rounded. Numerical experiments illustrate the behavior
of these two conditions and that the associated running
time over-cost is really interesting.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@TechReport{Langlois:2007:MIL,
author = "Philippe Langlois and Nicolas Louvet",
title = "More Instruction Level Parallelism Explains the Actual
Efficiency of Compensated Algorithms",
institution = "Laboratoire de Physique Appliqu{\'e}e et
d'Automatique",
address = "Perpignan, France",
pages = "11",
year = "2007",
bibdate = "Sat Apr 01 07:54:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hal.archives-ouvertes.fr/hal-00165020;
https://hal.archives-ouvertes.fr/hal-00165020/document",
abstract = "The compensated Horner algorithm and the Horner
algorithm with double-double arithmetic improve the
accuracy of polynomial evaluation in IEEE-754 floating
point arithmetic. Both yield a polynomial evaluation as
accurate as if it was computed with the classic Horner
algorithm in twice the working precision. Both
algorithms also share the same low-level computation of
the floating point rounding errors and cost a similar
number of floating point operations. We report
numerical experiments to exhibit that the compensated
algorithm runs at least twice as fast as the
double-double one on modern processors. We propose to
explain such efficiency by identifying more instruction
level parallelism in the compensated implementation.
Such property also applies to other compensated
algorithms for summation, dot product and triangular
linear system solving. More generally this paper
illustrates how this kind of performance analysis may
be useful to highlight the actual efficiency of
numerical algorithms.",
acknowledgement = ack-nhfb,
}
@Article{Laurie:2007:VPA,
author = "Dirk Laurie",
title = "Variable-precision arithmetic considered perilous ---
a detective story",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "28",
pages = "168--173",
year = "2007\slash 2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:30 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Special volume for Gene Golub.",
URL = "http://etna.mcs.kent.edu/vol.28.2007-2008/pp168-173.dir/pp168-173.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@TechReport{Lefevre:2007:SNP,
author = "Vincent Lef{\'e}vre and Jean-Michel Muller",
title = "Some notes on the possible under\slash overflow of the
most common elementary functions",
type = "Report",
institution = "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "Lyon, France",
pages = "7",
year = "2007",
bibdate = "Fri May 25 16:18:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://prunel.ccsd.cnrs.fr/ensl-00149414",
abstract = "The purpose of this short note is not to describe when
underflow or overflow must be signalled (it is quite
clear that the rules are the same as for the basic
arithmetic operations). We just want to show that for
some of the most common functions and floating-point
formats, in many cases, we can know in advance that the
results will always lie in the range of the numbers
that are representable by normal floating-point
numbers, so that in these cases there is no need to
worry about underflow or overflow. Note that when it is
not the case, an implementation is still possible using
a run-time test.",
acknowledgement = ack-nhfb,
keywords = "elementary functions; floating-point arithmetic;
overflow; underflow",
}
@InProceedings{Li:2007:DDP,
author = "Zhaolin Li and Gongqiong Li",
title = "Design of a Double-Precision Floating-Point
Multiply-Add-Fused Unit with Consideration of Data
Dependence",
crossref = "Becker:2007:EVT",
pages = "492--497",
year = "2007",
DOI = "https://doi.org/10.1109/ISVLSI.2007.37",
bibdate = "Sun Feb 20 10:48:57 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2007:DEF,
author = "Zhaolin Li and Gongqiong Li",
title = "Design of an Extended Floating-Point
Multiply-Add-Fused Unit for Exploiting
Instruction-Level Parallelism",
crossref = "IEEE:2007:ICI",
pages = "17--20",
year = "2007",
DOI = "https://doi.org/10.1109/ISICIR.2007.4441785",
bibdate = "Sun Feb 20 10:13:02 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents an extended single-precision
floating-point multiply-add-fused unit, called EMAF
unit, which is designed for exploiting
instruction-level parallelism. Concurrent addition and
multiplication instructions can be executed in parallel
besides traditional multiply-add-fused instructions.
Moreover, some other kinds of two consecutive but
dependent instructions can also be accelerated without
stalling anyone. At the same time the accuracy is also
increased over the traditional multiply-add-fused
units. The EMAF unit is implemented with three pipeline
stages. Experiment results show that compared with the
traditional multiply-add-fused unit up to 26\% cycle
reduction is gained at the cost of 0.1 ns time
penalty.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2007:DFP,
author = "Gongqiong Li and Zhaolin Li",
title = "Design of a Fully Pipelined Single-Precision
Multiply-Add-Fused Unit",
crossref = "IEEE:2007:ICV",
pages = "318--323",
year = "2007",
DOI = "https://doi.org/10.1109/VLSID.2007.64",
bibdate = "Sun Feb 20 10:15:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The floating point multiply-add operation A+BtimesC is
fundamental in many scientific and multimedia
applications. This paper presents a fully pipelined
single-precision multiply-add fused unit, which is
based on the combination of the final addition with
rounding. Normalization is performed before the final
addition to determine the rounding position. A
three-step normalization method is proposed for
attaining latency reduction. Moreover, this paper
presents a method to eliminate a one-bit error of the
multiply result for increasing the precision. Finally,
a new technique to deal with the number of 1, which is
added in the LSB of the operand to get 2's complement,
is proposed to reduce logic complexity and time delay.
The overall MAF unit has a latency of 5 cycles, a
throughput of 1 cycle, and a cycle time of 1.82 ns in
0.18 mum CMOS technology.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2007:FAT,
author = "Xin Li and Marc Moreno Maza and {\'E}ric Schost",
title = "Fast arithmetic for triangular sets: from theory to
practice",
crossref = "Brown:2007:PIS",
pages = "269--276",
year = "2007",
DOI = "https://doi.org/10.1145/1277548.1277585",
bibdate = "Fri Jun 20 08:46:50 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We study arithmetic operations for triangular families
of polynomials, concentrating on multiplication in
dimension zero. By a suitable extension of fast
univariate Euclidean division, we obtain theoretical
and practical improvements over a direct recursive
approach; for a family of special cases, we reach
quasi-linear complexity. The main outcome we have in
mind is the acceleration of higher-level algorithms, by
interfacing our low-level implementation with languages
such as AXIOM or Maple We show the potential for huge
speed-ups, by comparing two AXIOM implementations of
van Hoeij and Monagan's modular GCD algorithm.",
acknowledgement = ack-nhfb,
keywords = "high-performance; multiplication; triangular set",
}
@InProceedings{Lopez:2007:EIF,
author = "Guillermo A. Lopez and Michela Taufer and Patricia J.
Teller",
title = "Evaluation of {IEEE 754} floating-point arithmetic
compliance across a wide range of heterogeneous
computers",
crossref = "Morales:2007:TRT",
pages = "1--4",
year = "2007",
bibdate = "Fri Aug 08 08:39:30 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Scientific applications rely heavily on floating-point
arithmetic and, therefore, are affected by the
precision and implementation of floating-point
operations. Although the computers we use are IEEE
compliant, this only assures the same representation of
floating-point numbers; it does not guarantee that
floating-point operations will be performed in the same
way on all computers. As a result the same program run
on different computers may yield different results.
This paper is a first step in understanding the reason
for this, in particular, different results for the
execution of the application Charmm on different
computers. We report on our use of a well-known test
suite, IeeeCC754, to evaluate IEEE 754 compliance
across a wide range of heterogeneous computers with
different architectures, operating systems, precisions,
and compilers.",
acknowledgement = ack-nhfb,
}
@PhdThesis{Louvet:2007:ACA,
author = "Nicolas Louvet",
title = "Algorithmes compens{\'e}s en arithm{\'e}tique
flottante: pr{\'e}cision, validation, performances",
type = "{Docteur de l'universit{\'e} de Perpignan
sp{\'e}cialit{\'e}: Informatique}",
school = "Laboratoire ELIAUS: {\'E}lectronique, Informatique,
Automatique et Syst{\`e}mes, Universit{\'e} de
Perpignan Via Domitia",
address = "Perpignan, France",
pages = "vi + 188",
day = "27",
month = nov,
year = "2007",
bibdate = "Mon Mar 19 14:32:15 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://tel.archives-ouvertes.fr/tel-01315543/en",
abstract = "Rounding error may totally corrupt the result of a
floating point computation. How to improve and validate
the accuracy of a floating point computation, without
large computing time overheads ? We consider two case
studies: polynomial evaluation and linear triangular
system solving. In both cases we use compensation of
the rounding errors to improve the accuracy of the
computed result. The contributions of this work are
divided into three levels. (1) Improving the accuracy.
We propose a compensated Horner scheme that computes
polynomial evaluation with the same accuracy as the
classic Horner algorithm performed in twice the working
precision. Generalizing this algorithm, we present
another compensated version of the Horner scheme
simulating $K$ times the working precision ($ K > 1$).
We also show how to compensate the rounding errors
generated by the substitution algorithm for triangular
system solving. (2) Validating the computed result. We
show how to validate the quality of the compensated
polynomial evaluation. We propose a method to compute
an ``a posteriori'' error bound together with the
compensated result. This error bound is computed using
only basic floating point operations, which ensures
portability and efficiency of the method. (3)
Performances of compensated algorithms. Our computing
time measures show the interest of compensated
algorithms compared to other software solutions that
provide the same output accuracy. We also justify good
practical performances of compensated algorithms thanks
to a detailed study of the instruction-level
parallelism they contain.",
acknowledgement = ack-nhfb,
keywords = "compensated algorithms; Computer arithmetic; efficient
algorithms; IEEE-754 standard; numerical algorithms",
}
@Misc{Lundvall:2007:CDF,
author = "Shawn D. Lundvall and Eric M. Schwarz and Ronald M.
{Smith, Sr.} and Phil C. Yeh",
title = "Composition of decimal floating point data, and
methods therefor",
howpublished = "US Patent 8060545B2.",
day = "26",
month = apr,
year = "2007",
bibdate = "Thu Mar 15 09:28:54 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US8060545",
abstract = "A decimal floating point finite number in a decimal
floating point format is composed from the number in a
different format. A decimal floating point format
includes fields to hold information relating to the
sign, exponent and significand of the decimal floating
point finite number. Other decimal floating point data,
including infinities and NaNs (not a number), are also
composed. Decimal floating point data are also
decomposed from the decimal floating point format to a
different format.",
acknowledgement = ack-nhfb,
}
@Misc{Lundvall:2007:DDF,
author = "Shawn D. Lundvall and Eric M. Schwarz and Ronald M.
{Smith, Sr.} and Phil C. Yeh",
title = "Decomposition of decimal floating point data",
howpublished = "US Patent 9690580B2.",
day = "26",
month = apr,
year = "2007",
bibdate = "Thu Mar 15 09:31:05 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US9690580B2/en",
abstract = "A decimal floating point finite number in a decimal
floating point format is composed from the number in a
different format. A decimal floating point format
includes fields to hold information relating to the
sign, exponent and significand of the decimal floating
point finite number. Other decimal floating point data,
including infinities and NaNs (not a number), are also
composed. Decimal floating point data are also
decomposed from the decimal floating point format to a
different format.",
acknowledgement = ack-nhfb,
}
@InProceedings{Maslennikow:2007:DFB,
author = "Oleg Maslennikow and Natalia Maslennikowa and
Magdalena Rajewska and Dariusz Gretkowski and
Jean-Pierre Lienou",
booktitle = "{CADSM '07}. 9th International Conference --- The
Experience of Designing and Applications of {CAD}
Systems in Microelectronics",
title = "Design of {FPGA}-based Residue Number System
Converters for Digital Signal Processing Systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "194--201",
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1109/CADSM.2007.4297523",
ISSN = "????",
bibdate = "Fri Nov 9 11:38:59 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "residue arithmetic; residue number system",
summary = "In this paper, two new and simple structures of the
q-operands multi-operand modular adder have been
proposed, which are adapted to realization in the
Xilinx FPGA devices. The main purpose of new MOMA
designs has been the reduction of hardware \ldots{}",
}
@Article{Melquiond:2007:FCF,
author = "Guillaume Melquiond and Sylvain Pion",
title = "Formally certified floating-point filters for
homogeneous geometric predicates",
journal = j-INFORM-THEOR-APPL,
volume = "41",
number = "1",
pages = "57--69",
year = "2007",
CODEN = "RSITD7, RITAE4",
DOI = "https://doi.org/10.1051/ita:2007005",
ISSN = "0988-3754 (print), 1290-385X (electronic)",
ISSN-L = "0988-3754",
MRclass = "68U05 (65G50)",
MRnumber = "MR2330043",
bibdate = "Thu Nov 08 19:16:32 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Informatics and Applications. Informatique
Th\'eorique et Applications",
}
@Article{Mine:2007:RAD,
author = "Antoine Min{\'e}",
title = "Relational Abstract Domains for the Detection of
Floating-Point Run-Time Errors",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "15",
month = mar,
year = "2007",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in European Symposium on Programming (ESOP)
(03/2004) 3--17.",
URL = "http://arxiv.org/abs/cs/0703077",
abstract = "We present a new idea to adapt relational abstract
domains to the analysis of IEEE 754-compliant
floating-point numbers in order to statically detect,
through abstract Interpretation-based static analyses,
potential floating-point run-time exceptions such as
overflows or invalid operations. In order to take the
non-linearity of rounding into account, expressions are
modeled as linear forms with interval coefficients. We
show how to extend already existing numerical abstract
domains, such as the octagon abstract domain, to
efficiently abstract transfer functions based on
interval linear forms. We discuss specific fixpoint
stabilization techniques and give some experimental
results.",
acknowledgement = ack-nhfb,
subject = "Programming Languages (cs.PL)",
}
@TechReport{Mitchell:2007:MFP,
author = "D. Mitchell and S. Noble",
title = "Multiprecision floating-point arithmetic on {Apple}
systems",
type = "Report",
institution = "Advanced Computation Group, Apple Computer",
address = "Cupertino, CA, USA",
pages = "23",
day = "13",
month = mar,
year = "2007",
bibdate = "Tue Mar 19 10:22:50 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://images.apple.com/acg/pdf/MP_Floating_Point_20070313.pdf",
acknowledgement = ack-nhfb,
keywords = "ARPREC; GMP",
}
@Article{Miyajima:2007:ETS,
author = "Shinya Miyajima and Masahide Kashiwagi",
title = "Existence test for solution of nonlinear systems
applying affine arithmetic",
journal = j-J-COMPUT-APPL-MATH,
volume = "199",
number = "2",
pages = "304--309",
day = "15",
month = feb,
year = "2007",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:12:04 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270500765X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Monniaux:2007:AZT,
author = "David Monniaux",
title = "Applying the {$Z$}-transform for the static analysis
of floating-point numerical filters",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "2",
month = jun,
year = "2007",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/0706.0252",
abstract = "Digital linear filters are used in a variety of
applications (sound treatment, control/command, etc.),
implemented in software, in hardware, or a combination
thereof. For safety-critical applications, it is
necessary to bound all variables and outputs of all
filters. We give a compositional, effective abstraction
for digital linear filters expressed as block diagrams,
yielding sound, precise bounds for fixed-point or
floating-point implementations of the filters.",
acknowledgement = ack-nhfb,
subject = "Programming Languages (cs.PL); Numerical Analysis
(cs.NA)",
}
@TechReport{Monniaux:2007:PVFa,
author = "David Monniaux",
title = "The pitfalls of verifying floating-point
computations",
type = "Technical report",
number = "HAL-00128124",
institution = "CNRS\slash {\'E}cole Normale Sup{\'e}rieure",
address = "45, rue d'Ulm 75230 Paris cedex 5, France",
pages = "44",
day = "29",
month = jun,
year = "2007",
bibdate = "Fri Jul 06 18:10:00 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in \cite{Monniaux:2008:PVF}.",
URL = "http://hal.archives-ouvertes.fr/docs/00/15/88/63/PDF/floating-point.pdf",
abstract = "Current critical systems often use a lot of
floating-point computations, and thus the testing or
static analysis of programs containing floating-point
operators has become a priority. However, correctly
defining the semantics of common implementations of
floating-point is tricky, because semantics may change
according to many factors beyond source-code level,
such as choices made by compilers. We here give
concrete examples of problems that can appear and
solutions for implementing in analysis software",
acknowledgement = ack-nhfb,
}
@Article{Monniaux:2007:PVFb,
author = "David Monniaux",
title = "The pitfalls of verifying floating-point
computations",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "30",
month = jan,
year = "2007",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in \cite{Monniaux:2008:PVF}.",
URL = "http://arxiv.org/abs/cs/0701192",
abstract = "Current critical systems commonly use a lot of
floating-point computations, and thus the testing or
static analysis of programs containing floating-point
operators has become a priority. However, correctly
defining the semantics of common implementations of
floating-point is tricky, because semantics may change
with many factors beyond source-code level, such as
choices made by compilers. We here give concrete
examples of problems that can appear and solutions to
implement in analysis software.",
acknowledgement = ack-nhfb,
subject = "Programming Languages (cs.PL); Numerical Analysis
(cs.NA)",
}
@Article{Montuschi:2007:DDA,
author = "P. Montuschi and J. D. Bruguera and L. Ciminiera and
J.-A. Pieiro",
title = "A Digit-by-Digit Algorithm for $m$ th Root
Extraction",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "12",
pages = "1696--1706",
month = dec,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70764",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358221",
abstract = "A general digit-recurrence algorithm for the
computation of the $m$ th root (with an $m$ integer) is
presented in this paper. Based on the concept of
completing the mth root, a detailed analysis of the
convergence conditions is performed and iteration-
independent digit-selection rules are obtained for any
radix and redundant digit set. A radix-2 version for
mth rooting is also studied, together with closed
formulas for both the digit selection rules and the
number of bits required to perform correct
selections.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Muller-Olm:2007:AMA,
author = "Markus M{\"u}ller-Olm and Helmut Seidl",
title = "Analysis of modular arithmetic",
journal = j-TOPLAS,
volume = "29",
number = "5",
pages = "29:1--29:27",
month = aug,
year = "2007",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/1275497.1275504",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Wed Jun 11 19:22:40 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toplas/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We consider integer arithmetic modulo a power of 2 as
provided by mainstream programming languages like Java
or standard implementations of C. The difficulty here
is that, for $ w > 1 $, the ring $ Z_m $ of integers
modulo $ m = 2^w $ has zero divisors and thus cannot be
embedded into a field. Not withstanding that, we
present intra- and interprocedural algorithms for
inferring for every program point u affine relations
between program variables valid at $u$. If conditional
branching is replaced with nondeterministic branching,
our algorithms are not only sound but also complete in
that they detect all valid affine relations in a
natural class of programs. Moreover, they run in time
linear in the program size and polynomial in the number
of program variables and can be implemented by using
the same modular integer arithmetic as the target
language to be analyzed. We also indicate how our
analysis can be extended to deal with equality guards,
even in an interprocedural setting.",
acknowledgement = ack-nhfb,
articleno = "29",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
}
@Article{Nikmehr:2007:FRF,
author = "Hooman Nikmehr and Braden Phillips and Cheng-Chew
Lim",
title = "A Fast Radix-4 Floating-Point Divider with Quotient
Digit Selection by Comparison Multiples",
journal = j-COMP-J,
volume = "50",
number = "1",
pages = "81--92",
month = jan,
year = "2007",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxl048",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Apr 28 14:33:32 MDT 2010",
bibsource = "http://comjnl.oxfordjournals.org/content/vol50/issue1/index.dtl;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/cgi/content/abstract/50/1/81;
http://comjnl.oxfordjournals.org/cgi/content/full/50/1/81;
http://comjnl.oxfordjournals.org/cgi/reprint/50/1/81",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@InProceedings{Osborne:2007:AAG,
author = "W. Osborne and R. Cheung and J. Coutinho and W. Luk
and O. Mencer",
title = "Automatic accuracy-guaranteed bit-width optimization
for fixed and floating-point systems",
crossref = "Bertels:2007:PIC",
pages = "617--620",
year = "2007",
bibdate = "Thu Mar 24 20:53:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4380601",
acknowledgement = ack-nhfb,
}
@TechReport{Pan:2007:EFS,
author = "V. Y. Pan and B. Murphy and G. Qian and R. E.
Rosholt",
title = "Error-free summations via floating-point operations",
type = "Report",
number = "2007010 and 2007013",
institution = "CUNY Ph.D. Program in Computer Science, Graduate
Center, City University of New York",
address = "New York, NY, USA",
year = "2007",
bibdate = "Mon Mar 06 17:24:08 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Pan:2007:SAS,
author = "V. Y. Pan and B. Murphy and R. E. Rosholt and M.
Tabanjeh",
editor = "Jan Verschelde and Stephen M. Watt",
booktitle = "{SNC'07: proceedings of the 2007 International
Workshop on Symbolic--Numeric Computation, London
(Ontario, Canada), July 25--27, 2007}",
title = "The {Schur} aggregation for solving linear systems of
equations",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "viii + 299",
pages = "142--151",
year = "2007",
DOI = "https://doi.org/10.1145/1277500.1277522",
ISBN = "1-59593-744-7 (paperback)",
ISBN-13 = "978-1-59593-744-5 (paperback)",
LCCN = "QA9.59 .S53 2007",
bibdate = "Mon Mar 06 17:26:18 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
abstract = "According to our previous theoretical and experimental
study, additive preconditioners can be readily computed
for ill conditioned matrices, but application of such
preconditioners to facilitating matrix computations is
not straight-forward. In the present paper we develop
some nontrivial techniques for this task.They enabled
us to confine the original numerical problems to the
computation of the Schur aggregates of smaller sizes.
We overcome these problems by extending the Wilkinson's
iterative refinement and applying some advanced
semi-symbolic algorithms for multiplication and
summation.In particular with these techniques we
control precision throughout our computations.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; Additive
preconditioning; Determinants; Iterative refinement;
Linear systems of equations; Sherman Morrison Woodbury
formula",
subject = "Computable functions; Data processing; Congresses;
Numerical analysis; Logic, Symbolic and mathematical",
}
@Article{Patel:2007:FMA,
author = "R. A. Patel and M. Benaissa and S. Boussakta",
title = "Fast Modulo $ 2^n - (2^{n - 2} + 1) $ Addition: a New
Class of Adder for {RNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "4",
pages = "572--576",
month = apr,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.1001",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4118680",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "residue number system (RNS)",
}
@InProceedings{Patil:2007:REE,
author = "Dinesh Patil and Omid Azizi and Mark Horowitz and Ron
Ho and Rajesh Ananthraman",
title = "Robust Energy-Efficient Adder Topologies",
crossref = "Kornerup:2007:PIS",
pages = "16--28",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.31",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we explore the relationship between
adder topology and energy efficiency. We compare the
energy-delay tradeoff curves of selected 32-bit adder
topologies, to determine how architectural features and
design techniques affect energy efficiency. Optimizing
different adders for the supply and threshold voltages,
and transistor sizing, we show that topologies with the
least number of logic stages having an average fanin of
two per stage, and fewest wires are most energy
efficient. While a design with fully custom sizes can
be extremely tedious to layout, we show that custom
sizing can be used as a guide to group different gates
in the design, resulting in a manageable layout
overhead without significant loss of energy
efficiency.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Pearce:2007:MLH,
author = "Roman Pearce and Michael Monagan",
title = "A {Maple} library for high performance sparse
polynomial arithmetic",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "41",
number = "3",
pages = "110--111",
month = sep,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1145/1358190.1358203",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Wed Jun 18 09:23:01 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We have developed a library for sparse polynomial
arithmetic to supplement Maple's internal routines.
Along the way we identified three common sources of
inefficiency in existing implementations.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
issue = "161",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Rauh:2007:ROI,
author = "Andreas Rauh and Marco Kletting and Harald Aschemann
and Eberhard P. Hofer",
title = "Reduction of overestimation in interval arithmetic
simulation of biological wastewater treatment
processes",
journal = j-J-COMPUT-APPL-MATH,
volume = "199",
number = "2",
pages = "207--212",
day = "15",
month = feb,
year = "2007",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:12:04 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042705007521",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Saldamli:2007:SME,
author = "Gokay Saldamli and Cetin K. Koc",
title = "Spectral Modular Exponentiation",
crossref = "Kornerup:2007:PIS",
pages = "123--132",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.34",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We describe a new method to perform the modular
exponentiation operation, i.e., the computation of $ c
= m e \bmod n $, where $c$, $m$, $e$ and $n$ are large
integers. The new method uses the discrete Fourier
transform over a finite ring, and relies on new
techniques to perform multiplication and reduction
operations. The method yields efficient and highly
parallel architectures for hardware realizations of
public-key cryptosystems requiring the modular
exponentiation as the core computation, such as the RSA
and Diffie--Hellman algorithms.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Saqib:2007:CAI,
author = "Nazar Abbas Saqib",
title = "Complexity Analysis for 4-Input\slash 1-Output {FPGAs}
Applied to Multiplier Designs",
journal = j-SCPE,
volume = "8",
number = "4",
pages = "411--422",
month = dec,
year = "2007",
CODEN = "????",
ISSN = "1895-1767",
bibdate = "Thu Sep 2 11:55:11 MDT 2010",
bibsource = "http://www.scpe.org/content/8/4.toc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.scpe.org/vols/vol08/no4/SCPE_8_4_07.pdf;
http://www.scpe.org/vols/vol08/no4/SCPE_8_4_07.zip",
acknowledgement = ack-nhfb,
journal-URL = "http://www.scpe.org/",
}
@InProceedings{Schulte:2007:FPD,
author = "M. J. Schulte and D. Tan and C. E. Lemonds",
editor = "{IEEE}",
booktitle = "Proceedings of the 25th {IEEE} International
Conference on Computer Design: {7--10 October 2007}",
title = "Floating-Point Division Algorithms for an x86
Microprocessor with a Rectangular Multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "304--310",
year = "2007",
DOI = "https://doi.org/10.1109/ICCD.2007.4601917",
bibdate = "Sun Dec 10 14:03:42 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating-point division is an important operation in
scientific computing and multimedia applications. This
paper presents and compares two division algorithms for
an x86 microprocessor, which utilizes a rectangular
multiplier that is optimized for multimedia
applications. The proposed division algorithms are
based on Goldschmidt's division algorithm and provide
correctly rounded results for IEEE 754 single, double,
and extended precision floating-point numbers. Compared
to a previous Goldschmidt division algorithm, the
fastest proposed algorithm requires 25\% to 37\% fewer
cycles, while utilizing a multiplier that is roughly
2.5 times smaller.",
acknowledgement = ack-nhfb,
}
@Article{Scott:2007:NHC,
author = "N. S. Scott and F. J{\'e}z{\'e}quel and C. Denis and
J.-M. Chesneaux",
title = "Numerical `health check' for scientific codes: the
{CADNA} approach",
journal = j-COMP-PHYS-COMM,
volume = "176",
number = "8",
pages = "507--521",
day = "15",
month = apr,
year = "2007",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2007.01.005",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 23:42:15 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465507000331",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Shams:2007:EHA,
author = "R. Shams and R. Kennedy",
editor = "????",
booktitle = "{Proceedings of the International Conference on Signal
Processing and Communications Systems (ICSPCS), Gold
Coast, Australia, 2007}",
title = "Efficient histogram algorithms for {NVIDIA CUDA}
compatible devices",
publisher = "????",
address = "????",
pages = "418--422",
year = "2007",
bibdate = "Sat Oct 31 07:03:20 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Shpilka:2007:IDA,
author = "Amir Shpilka",
title = "Interpolation of depth-3 arithmetic circuits with two
multiplication gates",
crossref = "ACM:2007:SPA",
pages = "284--293",
year = "2007",
DOI = "https://doi.org/10.1145/1250790.1250833",
bibdate = "Fri Jun 20 18:28:53 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "arithmetic circuits; depth-3; exact learning;
interpolation",
}
@InProceedings{Sousa:2007:EMM,
author = "Leonel Sousa",
title = "Efficient Method for Magnitude Comparison in {RNS}
Based on Two Pairs of Conjugate Moduli",
crossref = "Kornerup:2007:PIS",
pages = "240--250",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.16",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The non-positional nature of Residue Number Systems
(RNS) is very useful to achieve carry free arithmetic.
However it makes the comparison of numbers more
difficult than in the traditional weighted number
systems: there is no any efficient general method for
magnitude comparison in RNS. Moreover, magnitude
comparison for RNS that rely on pairs of conjugate
moduli, which are not relatively prime moduli sets
recently proposed because of the large dynamic ranges
and the simplicity of the arithmetic units, is a new
unsolved problem. In this paper an efficient method and
a VLSI architecture is proposed for magnitude
comparison in RNS based on sets formed by two pairs of
conjugate moduli. This proposed method is much more
efficient than the other known ones and is the only one
valid for moduli sets not formed by relatively prime
integers. The method has been applied to design a very
fast Sum-of-Absolute Differences (SAD) unit for motion
estimation in video sequences that performs the
function entirely within the RNS channels. Experimental
results show that this new SAD unit, implemented in the
internal memory blocks of the xc2vp50-7 FPGA, is
capable of achieving the high throughput required to
perform real-time motion estimation in high resolution
images.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Misc{Steele:2007:CSP,
author = "Guy L. {Steele Jr.}",
title = "Circuit for selectively providing maximum or minimum
of a pair of floating point operands",
howpublished = "US Patent 7228324",
day = "05",
month = jun,
year = "2007",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7228324/fulltext.html",
abstract = "A floating point max/min circuit for determining the
maximum or minimum of two floating point operands
includes a first analysis circuit configured to
determine a format of a first floating point operand of
the two floating point operands based upon floating
point tatus information encoded within the first
floating point operand, a second analysis circuit
configured to determine a format of a second floating
point operand of the two floating point operands based
upon floating point status information encoded within
the second floating point operand, a decision circuit,
coupled to the first analysis circuit and to the second
analysis circuit and responding to a function control
signal that indicates the threshold condition is one of
a maximum of the two floating point operands and a
minimum of the two floating point operands, for
generating at least one assembly control signal based
on the format of a first floating point operand, the
format of a second floating point operand, and the
function control signal, and a result assembler
circuit, coupled to the decision circuit, for producing
a result indicating which of the first floating point
operand and the second floating point operand meet the
threshold condition, based on the at least one assembly
control signal. The format of the floating point
operands may be from a group comprising: not-a-number
(NaN), positive infinity, negative infinity,
normalized, denormalized, positive overflow, negative
overflow, positive underflow, negative underflow,
inexact, exact, division by zero, invalid operation,
positive zero, and negative zero. The result produced
may be a third floating point operand having encoded
floating point status information, and at least part of
the encoded floating point status information in the
result may come from either the first floating point
operand or the second floating point operand.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2007:CUC,
author = "Guy L. {Steele Jr.}",
title = "Comparator unit for comparing values of floating point
operands",
howpublished = "US Patent 7191202",
day = "13",
month = mar,
year = "2007",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7191202/fulltext.html",
abstract = "A floating point comparator circuit for comparing a
plurality of floating point operands includes a
plurality of analysis circuits, one for each of the
floating point operands, configured to determine a
format of each of the floating point operands based
upon floating point status information encoded within
each of the floating point operands, and a result
generator circuit coupled to the analysis circuits, the
result generator circuit configured to generate a
result signal based on the format determined by each
analysis circuit and based on a comparative
relationship among the floating point operands. The
format of each of the floating point operands may be
from a group including: not-a-number (NaN), infinity,
normalized, denormalized, zero, invalid operation,
overflow, underflow, division by zero, exact, and
inexact. The result generator circuit may ignore the
encoded floating point statuses of the plurality of
floating point operands when comparing just the
magnitudes of the plurality of floating point
operands.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2007:MSCa,
author = "Guy L. {Steele Jr.}",
title = "Methods and systems for computing the quotient of
floating-point intervals",
howpublished = "US Patent 7236999",
day = "26",
month = jun,
year = "2007",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7236999/fulltext.html",
abstract = "Computing an output interval includes producing a
first result from a conditional selection using a first
operand, a second operand, and a third operand, the
operands respectively including a second input interval
upper-point, a first input interval upper-point, and a
first input interval lower-point. Next, computing an
output interval includes producing a second result from
the conditional selection, the operands respectively
including a second input interval upper-point, the
first input interval upper-point, and the first input
interval lower-point. Furthermore, computing an output
interval includes producing a third result from a
conditional division using the first operand, the
second operand, and the third operand, the operands
respectively including the first result, the second
input interval upper-point, and the second input
interval lower-point. And finally, a fourth result is
produced from the conditional division, the operands
respectively including the second result, the second
input interval lower-point, and the second input
interval upper-point.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2007:MSCb,
author = "Guy L. {Steele Jr.}",
title = "Methods and systems for computing floating-point
intervals",
howpublished = "US Patent 7219117",
day = "15",
month = may,
year = "2007",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7219117/fulltext.html",
abstract = "Computing an output interval includes producing a
first product resulting from a conditional
multiplication using a first operand, a second operand,
and a third operand. Next a second product is produced
resulting from the conditional multiplication using the
first operand, the second operand, and the third
operand. Then a third product is produced resulting
from the conditional multiplication using the first
operand, the second operand, and the third operand.
Next a fourth product is produced resulting from the
conditional multiplication using the first operand, the
second operand, and the third operand. And finally, the
output interval is produced including an output
interval lower-point and an output interval
upper-point, the output interval lower-point being the
minimum of the first product and the third product, and
the output interval upper-point being the maximum of
the second product and the fourth product.",
acknowledgement = ack-nhfb,
}
@Article{Stern:2007:MLA,
author = "Richard Stern",
title = "Micro Law: Antitrust Division Gives {IEEE Standard}
Setters the Okay to Ask Patentees How {RAND} They Are",
journal = j-IEEE-MICRO,
volume = "27",
number = "3",
pages = "106--109",
month = may # "\slash " # jun,
year = "2007",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2007.47",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Wed Jul 2 21:58:03 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Stoutemyer:2007:UCN,
author = "David R. Stoutemyer",
title = "Useful Computations Need Useful Numbers",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "41",
number = "3",
pages = "75--99",
month = sep,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1145/1358190.1358192",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Wed Jun 18 09:23:01 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Most of us have taken the exact rational and
approximate numbers in our computer algebra systems for
granted for a long time, not thinking to ask if they
could be significantly better. With exact rational
arithmetic and adjustable-precision floating-point
arithmetic to precision limited only by the total
computer memory or our patience, what more could we
want for such numbers? It turns out that there is much
more that can be done that permits us to obtain exact
results more often, more intelligible results,
approximate results guaranteed to have requested error
bounds, and recovery of exact results from approximate
ones.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
issue = "161",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
keywords = "interval arithmetic",
}
@Article{Swartzlander:2007:NTC,
author = "Earl E. {Swartzlander, Jr.}",
title = "The Negative Two's Complement Number System",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "49",
number = "1",
pages = "177--183",
month = oct,
year = "2007",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/s11265-007-0052-y",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Nov 05 19:26:21 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The two's complement fractional fixed-point number
system is widely used to implement digital signal
processing on VLSI chips. It has a range of values from
$ - 1 $ to one least significant bit below +1. Either
the multiplication of $ - 1 $ - $ - 1 $ or taking the
absolute value of $ - 1 $ produces a result ($ + 1 $)
that cannot be represented. A new system, the negative
two's complement number system, is described here that
has a range of one least significant bit above $ - 1 $
to $ + 1 $ which eliminates the problem. This paper
presents the new number system and describes algorithms
for the basic arithmetic operations.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
xxnote = "Check math in abstract??",
}
@InProceedings{Tang:2007:MMU,
author = "Ping Tak Peter Tang",
title = "Modular Multiplication using Redundant Digit
Division",
crossref = "Kornerup:2007:PIS",
pages = "217--224",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.22",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Most implementations of the modular exponentiation, $
M E \bmod N $, computation in cryptographic algorithms
employ Montgomery multiplication, $ (A B R - 1) \bmod N
$, instead of modular multiplication, $ A B \bmod N $,
even the former requires some transformational
overheads. This is so because a state-of-the-art
Montgomery multiplication implementation has a
performance advantage over direct modular
multiplication based on the Barrett algorithm that more
than compensates for the overhead. In this paper, we
present a direct modular multiplication method that is
comparable in speed to Montgomery multiplication. One
consequence is that when the exponent in small, direct
computation (which does not incur the transformational
overhead) using the modular multiplication algorithm
presented here results in practical performance gain.
For the exponent 17, for instance, which requires five
modular multiplication, a saving of up to 40\% can be
achieved.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Thapliyal:2007:CIV,
author = "Himanshu Thapliyal and Hamid R. Arabnia and Rajnish
Bajpai and Kamal K. Sharma",
title = "Combined Integer and Variable Precision {(CIVP)}
Floating Point Multiplication Architecture for
{FPGAs}",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "16",
month = nov,
year = "2007",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/0711.2671",
abstract = "In this paper, we propose an architecture/methodology
for making FPGAs suitable for integer as well as
variable precision floating point multiplication. The
proposed work will of great importance in applications
which requires variable precision floating point
multiplication such as multi-media processing
applications. In the proposed architecture/methodology,
we propose the replacement of existing 18x18 bit and
25x18 bit dedicated multipliers in FPGAs with dedicated
24x24 bit and 24x9 bit multipliers, respectively. We
have proved that our approach of providing the
dedicated 24x24 bit and 24x9 bit multipliers in FPGAs
will make them efficient for performing integer as well
as single precision, double precision, and Quadruple
precision floating point multiplications.",
acknowledgement = ack-nhfb,
subject = "Hardware Architecture (cs.AR)",
}
@InProceedings{Trong:2007:PBF,
author = "Son Dao Trong and Martin Schmookler and Eric. M.
Schwarz and Michael Kroener",
title = "{P6} Binary Floating-Point Unit",
crossref = "Kornerup:2007:PIS",
pages = "77--86",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.26",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The floating point unit of the next generation PowerPC
is detailed. It has been tested at over 5 GHz. The
design supports an extremely aggressive cycle time of
13 FO4 using a technology independent measure. For most
dependent instructions, its fused multiply-add dataflow
has only 6 effective pipeline stages. This is nearly
equivalent to its predecessor, the Power 5, even though
its technology independent frequency has increased over
70\%. Overall the frequency has improved over 100\%. It
achieves this high performance through aggressive
feedback paths, circuit design and layout. The pipeline
has 7 stages but data may be fed back to dependent
operations prior to rounding and complete
normalization. Division and square root algorithms are
also described which take advantage of high-precision
linear approximation hardware for obtaining a
reciprocal or reciprocal square root approximation",
acknowledgement = ack-nhfb,
keywords = "aggressive data forwarding; ARITH-18; data processing
without stalls; denormal result handling;
floating-point unit; high-frequency design",
}
@InProceedings{Tsen:2007:HDBa,
author = "C. Tsen and S. Gonzalez-Navarro and M. Schulte",
title = "Hardware Design of a Binary Integer Decimal-based
Floating-point Adder",
crossref = "IEEE:2007:ICC",
pages = "288--295",
year = "2007",
DOI = "https://doi.org/10.1109/ICCD.2007.4601915",
bibdate = "Sat Dec 04 10:20:58 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Because of the growing importance of decimal
floating-point (DFP) arithmetic, specifications for it
are included in the IEEE Draft Standard for
Floating-point Arithmetic (IEEE P754). In this paper,
we present a novel algorithm and hardware design for a
DFP adder. The adder performs addition and subtraction
on 64-bit operands that use the IEEE P754 binary
encoding of DFP numbers, widely known as the binary
integer decimal (BID) encoding. The BID adder uses a
novel hardware component for decimal digit counting and
an enhanced version of a previously published BID
rounding unit. By adding more sophisticated control,
operations are performed with variable latency to
optimize for common cases. We show that a BID-based DFP
adder design can be achieved with a modest area
increase compared to a single 2-stage pipelined 64-bit
fixed-point multiplier. Over 70\% of the BID adder's
area is due to the 64-bit fixed-point multiplier, which
can be shared with a binary floating-point multiplier
and hardware for other DFP operations. To our
knowledge, this is the first hardware design for adding
and subtracting IEEE P754 BID-encoded DFP numbers",
acknowledgement = ack-nhfb,
}
@InProceedings{Tsen:2007:HDBb,
author = "Charles Tsen and Michael Schulte and Sonia
Gonzalez-Navarro",
title = "Hardware Design of a Binary Integer Decimal-based
{IEEE P754} Rounding Unit",
crossref = "IEEE:2007:ACP",
pages = "115--121",
year = "2007",
bibdate = "Sun Feb 20 17:42:56 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Because of the growing importance of decimal
floating-point (DFP) arithmetic, specifications for it
were recently added to the draft revision of the IEEE
754 Standard (IEEE P754). In this paper, we present a
hardware design for a rounding unit for 64-bit DFP
numbers (decimal 64) that use the IEEE P754 binary
encoding of DFP numbers, which is widely known as the
Binary Integer Decimal (BID) encoding. We summarize the
technique used for rounding, present the theory and
design of the BID rounding unit, and evaluate its
critical path delay, latency, and area for
combinational and pipelined designs. Over 86\% of the
rounding unit's area is due to a 55-bit by 54-bit
binary multiplier, which can be shared with a
double-precision binary floating-point multiplier. To
our knowledge, this is the first hardware design for
rounding IEEE P754 BID-encoded DFP numbers.",
acknowledgement = ack-nhfb,
keywords = "BID rounding; binary integer decimal encoding; decimal
floating-point arithmetic; double-precision binary
floating-point multiplier; hardware design; IEEE 754
standard; IEEE P754 binary encoding; IEEE P754 rounding
unit",
}
@Article{Vasudevan:2007:AVA,
author = "S. Vasudevan and V. Viswanath and R. W. Sumners and J.
A. Abraham",
title = "Automatic Verification of Arithmetic Circuits in {RTL}
Using Stepwise Refinement of Term Rewriting Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "56",
number = "10",
pages = "1401--1414",
month = oct,
year = "2007",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.1073",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 15:03:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4302711",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Vazquez:2007:NFH,
author = "Alvaro Vazquez and Elisardo Antelo and Paolo
Montuschi",
title = "A New Family of High-Performance Parallel Decimal
Multipliers",
crossref = "Kornerup:2007:PIS",
pages = "195--204",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.6",
bibdate = "Tue Oct 9 17:16:03 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.lirmm.fr/arith18/papers/vazquez-DecimalMultiplier.pdf",
abstract = "This paper introduces two novel architectures for
parallel decimal multipliers. Our multipliers are based
on a new algorithm for decimal carry-save multioperand
addition that uses a novel BCD-4221 recoding for
decimal digits. It significantly improves the area and
latency of the partial product reduction tree with
respect to previous proposals. We also present three
schemes for fast and efficient generation of partial
products in parallel. The recoding of the BCD-8421
multiplier operand into minimally redundant
signed-digit radix-10, radix-4 and radix-5
representations using new recoders reduces the
complexity of partial product generation. In addition,
SD radix-4 and radix-5 recodings allow the reuse of a
conventional parallel binary radix-4 multiplier to
perform combined binary/ decimal multiplications.
Evaluation results show that the proposed architectures
have interesting area-delay figures compared to
conventional Booth radix-4 and radix-8 parallel binary
multipliers and other representative alternatives for
decimal multiplication.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@InProceedings{Veeramachaneni:2007:NHS,
author = "Sreehari Veeramachaneni and M. Kirthi Krishna and
Lingamneni Avinash and Reddy P. Sreekanth and M. B.
Srinivas",
title = "Novel, High-Speed 16-Digit {BCD} Adders Conforming to
{IEEE 754r} Format",
crossref = "Becker:2007:EVT",
pages = "343--350",
year = "2007",
DOI = "https://doi.org/10.1109/ISVLSI.2007.71",
bibdate = "Thu Aug 07 18:55:05 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In view of increasing prominence of commercial,
financial and Internet-based applications that process
data in decimal format, there is a renewed interest in
providing hardware support to handle decimal data. In
this paper, a new architecture for efficient 1-digit
decimal addition of binary coded decimal (BCD)
operands, which is the core of high speed multi-operand
adders and floating decimal-point arithmetic, is
proposed. Based on this 1-digit BCD adder, novel
architectures for higher order (n-digit) BCD adders
such as ripple carry adder and carry look-ahead adder
are derived. The proposed circuits are compared (both
qualitatively as well as quantitatively) with the
existing circuits in literature and are shown to
perform better. Simulation results show that the
proposed 1-digit BCD adder achieves an improvement of
40\% in delay. The 16-digit BCD lookahead adder using
prefix logic is shown to perform at least 80\% faster
than the existing ripple carry one.",
acknowledgement = ack-nhfb,
}
@Article{Voronenko:2007:MMC,
author = "Yevgen Voronenko and Markus P{\"u}schel",
title = "Multiplierless multiple constant multiplication",
journal = j-TALG,
volume = "3",
number = "2",
pages = "11:1--11:??",
month = may,
year = "2007",
CODEN = "????",
DOI = "https://doi.org/10.1145/1240233.1240234",
ISSN = "1549-6325 (print), 1549-6333 (electronic)",
ISSN-L = "1549-6325",
bibdate = "Mon Jun 16 11:54:42 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A variable can be multiplied by a given set of
fixed-point constants using a multiplier block that
consists exclusively of additions, subtractions, and
shifts. The generation of a multiplier block from the
set of constants is known as the multiple constant
multiplication (MCM) problem. Finding the optimal
solution, namely, the one with the fewest number of
additions and subtractions, is known to be NP-complete.
We propose a new algorithm for the MCM problem, which
produces solutions that require up to 20\% less
additions and subtractions than the best previously
known algorithm. At the same time our algorithm, in
contrast to the closest competing algorithm, is not
limited by the constant bitwidths. We present our
algorithm using a unifying formal framework for the
best, graph-based MCM algorithms and provide a detailed
runtime analysis and experimental evaluation. We show
that our algorithm can handle problem sizes as large as
100 32-bit constants in a time acceptable for most
applications. The implementation of the new algorithm
is available at \url{www.spiral.net}.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Algorithms (TALG)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982",
keywords = "Addition chains; directed graph; FIR filter;
fixed-point arithmetic; strength reduction",
}
@InProceedings{Vouzis:2007:MCL,
author = "P. Vouzis and M. Arnold and S. Collange and M.
Kothare",
title = "{Monte Carlo} logarithmic number system for model
predictive control",
crossref = "Bertels:2007:PIC",
pages = "453--458",
year = "2007",
bibdate = "Thu Mar 24 20:58:01 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Wang:2007:DFPa,
author = "Liang-Kai Wang and Michael J. Schulte",
title = "Decimal Floating-Point Adder and Multifunction Unit
with Injection-Based Rounding",
crossref = "Kornerup:2007:PIS",
pages = "56--68",
year = "2007",
DOI = "https://doi.org/10.1109/ARITH.2007.13",
bibdate = "Tue Oct 9 16:32:41 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.lirmm.fr/arith18/papers/wang_schulte-multifunction_unit.pdf",
abstract = "Shrinking feature sizes gives more headroom for
designers to extend the functionality of
microprocessors. The IEEE 754R working group has
revised the IEEE 754-1985 Standard for Binary
Floating-Point Arithmetic to include specifications for
decimal floating-point arithmetic and IBM recently
announced incorporating a decimal floating-point unit
into their POWER6 processor. As processor support for
decimal floating-point arithmetic emerges, it is
important to investigate efficient algorithms and
hardware designs for common decimal floating-point
arithmetic algorithms. This paper presents novel
designs for a decimal floating-point adder and a
decimal floating-point multifunction unit. To reduce
their delay, both the adder and the multifunction unit
use decimal injection-based rounding, a new form of
decimal operand alignment, and a fast flag-based method
for rounding and overflow detection. Synthesis results
indicate that the proposed adder is roughly 21\% faster
and 1.6\% smaller than a previous decimal
floating-point adder design, when implemented in the
same technology. Compared to the decimal floating-point
adder, the decimal floating-point multifunction unit
provides six additional operations, yet only has
2.8\%more delay and 9.7\% more area.",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Article{Wang:2007:DFPb,
author = "Liang-Kai Wang and Michael J. Schulte",
title = "A Decimal Floating-Point Divider Using
{Newton--Raphson} Iteration",
journal = j-J-VLSI-SIGNAL-PROC,
volume = "49",
number = "1",
pages = "3--18",
month = oct,
year = "2007",
CODEN = "JVSPED",
DOI = "https://doi.org/10.1007/s11265-007-0058-5",
ISSN = "0922-5773 (print), 1573-109x (electronic)",
ISSN-L = "0922-5773",
bibdate = "Mon Nov 05 19:17:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Increasing chip densities and transistor counts
provide more room for designers to add functionality
for important application domains into future
microprocessors. As a result of rapid growth in
financial, commercial, and Internet-based applications,
hardware support for decimal floating-point arithmetic
is now being considered by various computer
manufacturers and specifications for decimal
floating-point arithmetic have been added to the draft
revision of the IEEE-754 Standard for Floating-Point
Arithmetic (IEEE P754). In this paper, we presents an
efficient arithmetic algorithm and hardware design for
decimal floating-point division. The design uses an
efficient piecewise linear approximation, a modified
Newton---Raphson iteration, a specialized rounding
technique, and a simplified decimal incrementer and
decrementer. Synthesis results show that a 64-bit
(16-digit) implementation of the decimal divider, which
is compliant with the current version of IEEE P754, has
an estimated critical path delay of 0.69 ns (around 13
FO4 inverter delays) when implemented using LSI Logic's
0.11 micron Gflx-P standard cell library.",
acknowledgement = ack-nhfb,
fjournal = "Journal of VLSI Signal Processing",
}
@PhdThesis{Wang:2007:PSD,
author = "Liang-Kai Wang",
title = "Processor support for decimal floating-point
arithmetic",
type = "{Ph.D.} thesis",
school = "The University of Wisconsin --- Madison",
address = "Madison, WI, USA",
pages = "157",
year = "2007",
ISBN = "0-549-19463-0",
ISBN-13 = "978-0-549-19463-7",
bibdate = "Thu Aug 07 16:22:03 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal data permeates society, as humans most
commonly use base-ten numbers. Although microprocessors
normally use base-two binary arithmetic to obtain
faster execution times and simpler circuitry, binary
numbers cannot represent decimal fractions exactly.
This leads to large errors being accumulated after
several decimal operations. Furthermore, binary
floating-point arithmetic operations perform binary
rounding instead of decimal rounding. Consequently,
applications, such as financial, commercial, tax, and
Internet-based applications, which are sensitive to
representation and rounding errors, often require
decimal arithmetic. Due to the increasing importance of
and demand for decimal arithmetic, its formats and
operations have been specified in the IEEE Draft
Standard for Floating-point Arithmetic (IEEE
P754).\par
Most decimal applications use software routines and
binary arithmetic to emulate decimal operations.
Although this approach eliminates errors due to
converting between binary and decimal numbers and
provides decimal rounding to mirror manual
calculations, it results in long latencies for
numerically intensive commercial applications. This is
because software emulation of decimal floating-point
(DFP) arithmetic has significant overhead due to
function calls, dealing with decimal formats, operand
alignment, decimal rounding, and special case and
exception handling.\par
This dissertation investigates processor support for
decimal floating-point arithmetic. It first reviews
recent progress in decimal arithmetic, including
decimal encodings, the IEEE P754 Draft Standard, and
software packages, hardware designs, and benchmark
suites for decimal arithmetic. Next, this dissertation
presents novel arithmetic algorithms and hardware
designs for basic DFP operations, including DFP
addition, subtraction, division, square root, and
others. Most of the hardware designs presented in this
dissertation are the first published designs compliant
with the IEEE P754 Draft Standard. Finally, to study
the performance impact of DFP instructions and
hardware, this dissertation presents the first publicly
available benchmark suite for DFP arithmetic. This
benchmark suite, along with instruction set extensions
and a decimal-enhanced processor simulator, are used to
demonstrate that providing fast hardware support for
DFP operations leads to significant performance
benefits to DFP-intensive applications.",
acknowledgement = ack-nhfb,
advisor = "Michael J. Schulte",
}
@Article{Wu:2007:FBM,
author = "Chia-Long Wu and Der-Chyuan Lou and Te-Jen Chang",
title = "Fast binary multiplication by performing dot counting
and complement recoding",
journal = j-APPL-MATH-COMP,
volume = "191",
number = "1",
pages = "132--139",
day = "1",
month = aug,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:07 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Wu:2007:FMM,
author = "Chia-Long Wu and Der-Chyuan Lou and Jui-Chang Lai and
Te-Jen Chang",
title = "Fast modular multi-exponentiation using modified
complex arithmetic",
journal = j-APPL-MATH-COMP,
volume = "186",
number = "2",
pages = "1065--1074",
day = "15",
month = mar,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:03 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Xu:2007:HWP,
author = "Fei Xu and Chip-Hong Chang and Ching-Chuen Jong",
title = "{Hamming} weight pyramid --- a new insight into
canonical signed digit representation and its
applications",
journal = j-COMPUT-ELECTR-ENG,
volume = "33",
number = "3",
pages = "195--207",
month = may,
year = "2007",
CODEN = "CPEEBQ",
DOI = "https://doi.org/10.1016/j.compeleceng.2006.09.001",
ISSN = "0045-7906 (print), 1879-0755 (electronic)",
ISSN-L = "0045-7906",
bibdate = "Thu Aug 07 19:18:35 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Signed-power-of-two terms are widely used in design
automation algorithms for digital filter synthesis and
optimization, linear transformation and other multiple
constant multiplication problems. In these
applications, the computation efficiency or solution
quality tends to degrade with the number of nonzero
digits in the signed digit representation of the a
priori fixed coefficients. This paper provides a new
perspective to interpret the hamming weights of
fixed-point coefficients represented in
signed-power-of-two terms with minimal number of
nonzero digits, called the minimal signed digit (MSD)
representation. A new hamming weight pyramid (HWP) is
proposed to succinctly compress the information about
the distribution of the hamming weights of canonical
signed digit (CSD) representation in a visually
appealing manner for analysis and synthesis. CSD is a
unique and popularly used subset of the general MSD
representation. Many interesting properties of CSD are
uncovered in this regularly structured HWP. These
properties are exploited to develop a novel and elegant
algorithm for the direct conversion of decimal number
to CSD representation. We also show that the HWP can
also be employed to overcome the limit imposed on the
word length of the coefficients for the reduced adder
graph (RAG) algorithm and filter coefficient
synthesis.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Electrical Engineering",
}
@Article{Yen:2007:ICM,
author = "Sung-Ming Yen and Wei-Chih Lien and SangJae Moon",
title = "Inefficiency of common-multiplicand multiplication and
exponentiation algorithms by performing binary
complements",
journal = j-APPL-MATH-COMP,
volume = "189",
number = "1",
pages = "285--290",
day = "1",
month = jun,
year = "2007",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:05 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@PhdThesis{Yu:2007:DPE,
author = "Xian-Yan Yu",
title = "Design of Power-Efficient Floating-Point Adder
Blocks",
type = "{Ph.D.} thesis",
school = "Advanced Computer Systems Engineering Laboratory,
University of California, Davis",
address = "Davis, CA, USA",
pages = "????",
month = may,
year = "2007",
bibdate = "Tue Oct 09 18:04:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "IBM Power6",
}
@Article{Zhuo:2007:SMA,
author = "Ling Zhuo and Viktor K. Prasanna",
title = "Scalable and Modular Algorithms for Floating-Point
Matrix Multiplication on Reconfigurable Computing
Systems",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "18",
number = "4",
pages = "433--448",
month = apr,
year = "2007",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/TPDS.2007.1001",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Thu Jul 3 14:26:52 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
}
@Article{Aamodt:2008:CTI,
author = "Tor M. Aamodt and Paul Chow",
title = "Compile-time and instruction-set methods for improving
floating- to fixed-point conversion accuracy",
journal = j-TECS,
volume = "7",
number = "3",
pages = "26:1--26:??",
month = apr,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1145/1347375.1347379",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Jun 12 15:22:21 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper proposes and evaluates compile time and
instruction-set techniques for improving the accuracy
of signal-processing algorithms run on fixed-point
embedded processors. These techniques are proposed in
the context of a profile guided floating- to
fixed-point compiler-based conversion process. A novel
fixed-point scaling algorithm (IRP) is introduced that
exploits correlations between values in a program by
applying fixed-point scaling, retaining as much
precision as possible without causing overflow. This
approach is extended into a more aggressive scaling
algorithm (IRP-SA) by leveraging the modulo nature of
2's complement addition and subtraction to discard most
significant bits that may not be redundant
sign-extension bits. A complementary scaling technique
(IDS) is then proposed that enables the fixed-point
scaling of a variable to be parameterized, depending
upon the context of its definitions and uses. Finally,
a novel instruction-set enhancement--- fractional
multiplication with internal left shift (FMLS)---is
proposed to further leverage interoperand correlations
uncovered by the IRP-SA scaling algorithm. FMLS
preserves a different subset of the full product's bits
than traditional fractional fixed-point or integer
multiplication. On average, FMLS combined with IRP-SA
improves accuracy on processors with uniform bitwidth
register architectures by the equivalent of 0.61 bits
of additional precision for a set of signal-processing
benchmarks (up to 2 bits). Even without employing FMLS,
the IRP-SA scaling algorithm achieves additional
accuracy over two previous fixed-point scaling
algorithms by averages of 1.71 and 0.49 bits.
Furthermore, as FMLS combines multiplication with a
scaling shift, it reduces execution time by an average
of 9.8\%. An implementation of IDS, specialized to
single-nested loops, is found to improve accuracy of a
lattice filter benchmark by the equivalent of more than
16-bits of precision.",
acknowledgement = ack-nhfb,
articleno = "26",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J840",
keywords = "compilation; digital signal processing; fixed-point;
fractional multiplication; scaling; signal-to-noise
ratio",
}
@Article{Ahmadi:2008:PFS,
author = "O. Ahmadi and D. Hankerson and F.
Rodr{\'\i}guez-Henr{\'\i}quez",
title = "Parallel Formulations of Scalar Multiplication on
{Koblitz} Curves",
journal = j-J-UCS,
volume = "14",
number = "3",
pages = "481--504",
month = "????",
year = "2008",
CODEN = "????",
ISSN = "0948-6968",
ISSN-L = "0948-6968",
bibdate = "Thu Jul 10 06:41:41 MDT 2008",
bibsource = "http://www.jucs.org/jucs;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jucs.org/jucs_14_3/parallel_formulations_of_scalar",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
keywords = "cryptography",
}
@Book{ASTM:2008:AES,
author = "{ASTM}",
title = "{ASTM E29-08}: Standard Practice for Using Significant
Digits in Test Data to Determine Conformance with
Specifications",
publisher = "ASTM International",
address = "West Conshohocken, PA, USA",
year = "2008",
DOI = "https://doi.org/10.1520/E0029",
bibdate = "Mon May 21 17:19:21 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.astm.org/Standards/E29.htm",
abstract = "This practice is intended to assist the various
technical committees in the use of uniform methods of
indicating the number of digits which are to be
considered significant in specification limits, for
example, specified maximum values and specified minimum
values. Its aim is to outline methods which should aid
in clarifying the intended meaning of specification
limits with which observed values or calculated test
results are compared in determining conformance with
specifications. Two commonly accepted methods of
rounding data, identified as the absolute method and
the rounding method are described. The guidelines for
retaining significant figures in calculation and
reporting of test results are presented in details.",
acknowledgement = ack-nhfb,
}
@Article{Bapst:2008:SIO,
author = "Frederic Bapst and Fran{\c{c}}ois Kilchoer",
title = "Signalling Integer Overflows in {Java}: a tool for
checking overflows in {Java} code",
journal = j-DDJ,
volume = "33",
number = "9",
pages = "54--58",
month = sep,
year = "2008",
CODEN = "DDJOEB",
ISSN = "1044-789X",
bibdate = "Tue Aug 12 18:02:50 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://home.hefr.ch/bapst/cojac",
acknowledgement = ack-nhfb,
fjournal = "Dr. Dobb's Journal of Software Tools",
keywords = "integer overflow detection; Java",
remark = "The COJAC (Checking Overflows in JAva Code) tool
instruments a compiled {\tt .class} file, replacing
integer instructions subject to overflow with calls to
routines that report any overflow.",
}
@Article{Beuchat:2008:AGM,
author = "Jean-Luc Beuchat and Jean-Michel Muller",
title = "Automatic Generation of Modular Multipliers for {FPGA}
Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "12",
pages = "1600--1613",
month = dec,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.102",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4564441",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Boldo:2008:EFC,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "Emulation of a {FMA} and Correctly Rounded Sums:
Proved Algorithms Using Rounding to Odd",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "4",
pages = "462--471",
month = apr,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70819",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358278;
https://ens-lyon.hal.science/inria-00080427/file/odd-rounding.pdf",
abstract = "Rounding to odd is a nonstandard rounding on
floating-point numbers. By using it for some
intermediate values instead of rounding to nearest,
correctly rounded results can be obtained at the end of
computations. We present an algorithm for emulating the
fused multiply-and-add operator. We also present an
iterative algorithm for computing the correctly rounded
sum of a set of floating-point numbers under mild
assumptions. A variation on both previous algorithms is
the correctly rounded sum of any three floating-point
numbers. This leads to efficient implementations, even
when this rounding is not available. In order to
guarantee the correctness of these properties and
algorithms, we formally proved them by using the Coq
proof checker.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keyword = "round-to-odd (RO(x))",
}
@Article{Brisebarre:2008:CRM,
author = "Nicolas Brisebarre and Jean-Michel Muller",
title = "Correctly Rounded Multiplication by Arbitrary
Precision Constants",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "2",
pages = "165--174",
month = feb,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70813",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358257",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Brisebarre:2008:EME,
author = "Nicolas Brisebarre and Sylvain Chevillard and
Milo{\v{s}} D. Ercegovac and Jean-Michel Muller and
Serge Torres",
title = "An Efficient Method for Evaluating Polynomial and
Rational Function Approximations",
crossref = "IEEE:2008:ICA",
pages = "233--238",
year = "2008",
DOI = "https://doi.org/10.1109/ASAP.2008.4580185",
bibdate = "Mon Feb 10 07:28:25 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brisebarre:2008:IFP,
author = "Nicolas Brisebarre and Florent de Dinechin and
Jean-Michel Muller",
title = "Integer and floating-point constant multipliers for
{FPGAs}",
crossref = "IEEE:2008:ICA",
pages = "239--244",
year = "2008",
DOI = "https://doi.org/10.1109/ASAP.2008.4580184",
bibdate = "Mon Feb 10 08:12:58 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Buttari:2008:UMP,
author = "Alfredo Buttari and Jack Dongarra and Jakub Kurzak and
Piotr Luszczek and Stanimir Tomov",
title = "Using Mixed Precision for Sparse Matrix Computations
to Enhance the Performance while Achieving 64-bit
Accuracy",
journal = j-TOMS,
volume = "34",
number = "4",
pages = "17:1--17:22",
month = jul,
year = "2008",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1377596.1377597",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Jul 16 11:30:01 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "By using a combination of 32-bit and 64-bit floating
point arithmetic, the performance of many sparse linear
algebra algorithms can be significantly enhanced while
maintaining the 64-bit accuracy of the resulting
solution. These ideas can be applied to sparse
multifrontal and supernodal direct techniques and
sparse iterative techniques such as Krylov subspace
methods. The approach presented here can apply not only
to conventional processors but also to exotic
technologies such as Field Programmable Gate Arrays
(FPGA), Graphical Processing Units (GPU), and the Cell
BE processor.",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "floating point; iterative refinement; linear systems;
precision",
}
@Article{Carnicer:2008:REP,
author = "J. M. Carnicer and T. N. T. Goodman and J. M.
Pe{\~n}a",
title = "Roundoff errors for polynomial evaluation by a family
of formulae",
journal = j-COMPUTING,
volume = "82",
number = "2--3",
pages = "199--215",
month = jul,
year = "2008",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Sun Oct 31 11:09:47 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=82&issue=2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=82&issue=2&spage=199",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Castaldo:2008:RFP,
author = "Anthony M. Castaldo and R. Clint Whaley and Anthony T.
Chronopoulos",
title = "Reducing Floating Point Error in Dot Product Using the
Superblock Family of Algorithms",
journal = j-SIAM-J-SCI-COMP,
volume = "31",
number = "2",
pages = "1156--1174",
month = "????",
year = "2008",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/070679946",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:44:14 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper discusses both the theoretical and
statistical errors obtained by various well-known dot
products, from the canonical to pairwise algorithms,
and introduces a new and more general framework that we
have named superblock which subsumes them and permits a
practitioner to make trade-offs between computational
performance, memory usage, and error behavior. We show
that algorithms with lower error bounds tend to behave
noticeably better in practice. Unlike many such
error-reducing algorithms, superblock requires no
additional floating point operations and should be
implementable with little to no performance loss,
making it suitable for use as a performance-critical
building block of a linear algebra kernel.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; floating-point dot
product",
}
@InProceedings{Castellanos:2008:CTD,
author = "Ivan D. Castellanos and James E. Stine",
title = "Compressor trees for decimal partial product
reduction",
crossref = "ACM:2008:GPA",
pages = "107--110",
year = "2008",
DOI = "https://doi.org/10.1145/1366110.1366137",
bibdate = "Thu Aug 07 17:39:02 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal multiplication has grown in interest due to
the recent announcement of new IEEE 754R standards and
the availability of high-speed decimal computation
hardware. Prior research enabled partial products to be
coded more efficiently for their use in radix 10
architectures. This paper clarifies previous techniques
for partial product reduction using carry-save adders
and presents a new 4:2 compressor structure. This new
structure improves performance at the expense of more
gates, however, regularity is introduced into the
circuit to promote implementations in Very Large Scale
Integration (VLSI) Designs. Results are presented and
compared for several designs using a TSMC SCN6M $ 0.18
\mu $ m feature size.",
acknowledgement = ack-nhfb,
}
@Article{Cavagnino:2008:EAI,
author = "D. Cavagnino and A. E. Werbrouck",
title = "Efficient Algorithms for Integer Division by Constants
Using Multiplication",
journal = j-COMP-J,
volume = "51",
number = "4",
pages = "470--480",
month = jul,
year = "2008",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxm082",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Apr 28 14:33:34 MDT 2010",
bibsource = "http://comjnl.oxfordjournals.org/content/vol51/issue4/index.dtl;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/cgi/content/abstract/51/4/470;
http://comjnl.oxfordjournals.org/cgi/content/full/51/4/470;
http://comjnl.oxfordjournals.org/cgi/reprint/51/4/470",
abstract = "We present a complete analysis of the integer division
of a single unsigned dividend word by a single unsigned
divisor word based on double-word multiplication of the
dividend by an inverse of the divisor. The well-known
advantage of this method yields run-time efficiency, if
the inverse of the divisor can be calculated at compile
time, since multiplication is much faster than division
in arithmetic units. Our analysis leads to the
discovery of a limit to the straightforward application
of this method in the form of a critical dividend,
which fortunately associates with a minority of the
possible divisors (20\%) and defines only a small upper
part of the available dividend space. We present two
algorithms for ascertaining whether a critical dividend
exists and, if so, its value along with a circumvention
of this limit. For completeness, we include an
algorithm for integer division of a unsigned
double-word dividend by an unsigned single-word divisor
in which the quotient is not limited to a single word
and the remainder is an intrinsic part of the result.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "division by multiplication; efficiency; integer
constants; integer division; multiplicative inverse",
remark = "See \cite{Cavagnino:2011:AAD}.",
}
@Article{Colon-Bonet:2008:MEF,
author = "Glenn Col{\'o}n-Bonet and Paul {Winterrowd, Jr.}",
title = "Multiplier Evolution: a Family of Multiplier {VLSI}
Implementations",
journal = j-COMP-J,
volume = "51",
number = "5",
pages = "585--594",
month = sep,
year = "2008",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxm123",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Apr 28 14:33:34 MDT 2010",
bibsource = "http://comjnl.oxfordjournals.org/content/vol51/issue5/index.dtl;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/cgi/content/abstract/51/5/585;
http://comjnl.oxfordjournals.org/cgi/content/full/51/5/585;
http://comjnl.oxfordjournals.org/cgi/reprint/51/5/585",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Cordeiro:2008:MSI,
author = "Gauss M. Cordeiro and Borko D. Stosi{\'c}",
title = "{Maple} script for improving test statistics",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "78",
number = "11",
pages = "1045--1053",
year = "2008",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949650701490969",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Apr 22 09:12:46 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
}
@InProceedings{De:2008:FIM,
author = "Anindya De and Piyush P. Kurur and Chandan Saha and
Ramprasad Saptharishi",
title = "Fast integer multiplication using modular arithmetic",
crossref = "ACM:2008:SPA",
pages = "499--506",
year = "2008",
DOI = "https://doi.org/10.1145/1374376.1374447",
bibdate = "Fri Jun 20 18:31:53 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We give an $ O(N \log N 2^{O(\log *N)}) $ algorithm
for multiplying two $N$-bit integers that improves the
$ O(N \log N \log \log N) $ algorithm by
Sch{\"o}nhage--Strassen. Both these algorithms use
modular arithmetic. Recently, F{\"u}rer gave an $ O(N
\log N 2^{O(\log *N)}) $ algorithm which however uses
arithmetic over complex numbers as opposed to modular
arithmetic. In this paper, we use multivariate
polynomial multiplication along with ideas from
F{\"u}rer's algorithm to achieve this improvement in
the modular setting. Our algorithm can also be viewed
as a $p$-adic version of F{\"u}rer's algorithm. Thus,
we show that the two seemingly different approaches to
integer multiplication, modular and complex arithmetic,
are similar.",
acknowledgement = ack-nhfb,
keywords = "computational algebra; integer multiplication; modular
arithmetic",
}
@Article{DeDinechin:2008:CFP,
author = "Florent {De Dinechin} and Christoph Quirin Lauter and
Guillaume Melquiond",
title = "Certifying floating-point implementations using
{Gappa}",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "3",
month = jan,
year = "2008",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/0801.0523",
abstract = "High confidence in floating-point programs requires
proving numerical properties of final and intermediate
values. One may need to guarantee that a value stays
within some range, or that the error relative to some
ideal value is well bounded. Such work may require
several lines of proof for each line of code, and will
usually be broken by the smallest change to the code
(e.g. for maintenance or optimization purpose).
Certifying these programs by hand is therefore very
tedious and error-prone. This article discusses the use
of the Gappa proof assistant in this context. Gappa has
two main advantages over previous approaches: Its input
format is very close to the actual C code to validate,
and it automates error evaluation and propagation using
interval arithmetic. Besides, it can be used to
incrementally prove complex mathematical properties
pertaining to the C code. Yet it does not require any
specific knowledge about automatic theorem proving, and
thus is accessible to a wide community. Moreover, Gappa
may generate a formal proof of the results that can be
checked independently by a lower-level proof assistant
like Coq, hence providing an even higher confidence in
the certification of the numerical code. The article
demonstrates the use of this tool on a real-size
example, an elementary function with correctly rounded
output.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA); Mathematical Software
(cs.MS)",
}
@Article{DeDinechin:2008:OPF,
author = "Florent {De Dinechin} and Christoph Quirin Lauter",
title = "Optimizing polynomials for floating-point
implementation",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--12",
day = "4",
month = mar,
year = "2008",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/0803.0439",
abstract = "The floating-point implementation of a function on an
interval often reduces to polynomial approximation, the
polynomial being typically provided by Remez algorithm.
However, the floating-point evaluation of a Remez
polynomial sometimes leads to catastrophic
cancellations. This happens when some of the polynomial
coefficients are very small in magnitude with respects
to others. In this case, it is better to force these
coefficients to zero, which also reduces the operation
count. This technique, classically used for odd or even
functions, may be generalized to a much larger class of
functions. An algorithm is presented that forces to
zero the smaller coefficients of the initial polynomial
thanks to a modified Remez algorithm targeting an
incomplete monomial basis. One advantage of this
technique is that it is purely numerical, the function
being used as a numerical black box. This algorithm is
implemented within a larger polynomial implementation
tool that is demonstrated on a range of examples,
resulting in polynomials with less coefficients than
those obtained the usual way.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA); Mathematical Software
(cs.MS)",
}
@Article{Dimitrov:2008:PSP,
author = "V. S. Dimitrov and K. U. Jarvinen and M. J. Jacobson
and W. Chan and Zhun Huang",
title = "Provably Sublinear Point Multiplication on {Koblitz}
Curves and Its Hardware Implementation",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "11",
pages = "1469--1481",
month = nov,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.65",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
note = "See comments \cite{Lee:2012:CPS}.",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4487060",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Dvir:2008:HRT,
author = "Zeev Dvir and Amir Shpilka and Amir Yehudayoff",
title = "Hardness-randomness tradeoffs for bounded depth
arithmetic circuits",
crossref = "ACM:2008:SPA",
pages = "741--748",
year = "2008",
DOI = "https://doi.org/10.1145/1374376.1374482",
bibdate = "Fri Jun 20 18:31:53 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we show that lower bounds for bounded
depth arithmetic circuits imply derandomization of
polynomial identity testing for bounded depth
arithmetic circuits. More formally, if there exists an
explicit polynomial $ f(x_1, \ldots {}, x_m) $ that
cannot be computed by a depth $d$ arithmetic circuit of
small size then there exists an efficient deterministic
algorithm to test whether a given depth $ d - 8 $
circuit is identically zero or not (assuming the
individual degrees of the tested circuit are not too
high). In particular, if we are guaranteed that the
circuit computes a multilinear polynomial then we can
perform the identity test efficiently. To the best of
our knowledge this is the first hardness-randomness
tradeoff for bounded depth arithmetic circuits. The
above results are obtained using the arithmetic
Nisan-Wigderson generator of Impagliazzo and Kabanets
together with a new theorem on bounded depth circuits,
which is the main technical contribution of our work.
This theorem deals with polynomial equations of the
form $ P(x_1, \ldots {}, x_n, y) \equiv 0 $ and shows
that if $P$ has a circuit of depth $d$ and size $s$ and
if the polynomial $ f(x_1, \ldots {}, x_n) $ satisfies
$ P(x_1, \ldots {}, x_n, f(x_1, \ldots {}, x_n)) \equiv
0 $ then $f$ has a circuit of depth $ d + 3 $ and size
$ O(s \times r + m^r) $, where $m$ is the degree of $f$
and $r$ is the highest degree of the variable $y$
appearing in $P$. In the other direction we observe
that the methods of Impagliazzo and Kabanets imply that
if we can derandomize polynomial identity testing for
bounded depth circuits then NEXP does not have bounded
depth arithmetic circuits. That is, either NEXP $ \not
\subset $ P/poly or the Permanent is not computable by
polynomial size bounded depth arithmetic circuits.",
acknowledgement = ack-nhfb,
keywords = "arithmetic circuits; bounded depth circuits;
hardness-randomness tradeoffs; identity testing; lower
bounds",
}
@Article{Edmonson:2008:ISS,
author = "W. W. Edmonson and M. H. van Emden",
title = "Interval Semantics for Standard Floating-Point
Arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--10",
day = "23",
month = oct,
year = "2008",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/0810.4196",
abstract = "If the non-zero finite floating-point numbers are
interpreted as point intervals, then the effect of
rounding can be interpreted as computing one of the
bounds of the result according to interval arithmetic.
We give an interval interpretation for the signed zeros
and infinities, so that the undefined operations 0*inf,
inf - inf, inf/inf, and 0/0 become defined. In this way
no operation remains that gives rise to an error
condition. Mathematically questionable features of the
floating-point standard become well-defined sets of
reals. Interval semantics provides a basis for the
verification of numerical algorithms. We derive the
results of the newly defined operations and consider
the implications for hardware implementation.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA); Hardware Architecture
(cs.AR)",
}
@PhdThesis{Erle:2008:AHD,
author = "Mark A. Erle",
title = "Algorithms and Hardware Designs for Decimal
Multiplication",
type = "{Ph.D.} Thesis",
school = "Department of Computer Engineering, Lehigh
University",
address = "Bethlehem, PA, USA",
pages = "xviii + 221",
day = "21",
month = nov,
year = "2008",
bibdate = "Tue Mar 01 19:53:02 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://speleotrove.com/decimal/erle2008-decimal-multipliers-dissertation-duplex.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Gonzalez-Navarro:2008:BID,
author = "S. Gonzalez-Navarro and C. Tsen and M. Schulte",
title = "Binary Integer Decimal-based Multiplier for Decimal
Floating-Point Arithmetic",
crossref = "Matthews:2008:CRF",
pages = "353--357",
year = "2008",
DOI = "https://doi.org/10.1109/ACSSC.2007.4487228",
bibdate = "Sat Dec 04 10:25:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Demand for decimal floating-point (DFP) arithmetic is
increasing because global business, e-commerce,
financial applications, and the standards and laws that
govern them require it. The IEEE P754 draft standard
for floating-point arithmetic specifies formats and
operations for DFP numbers. In this paper, we present
an IEEE P754-compliant multiplier that operates on
values that use the binary encoding of DFP numbers,
commonly referred to as the binary integer decimal
(BID) encoding. Our BID-based DFP multiplier uses
high-speed binary hardware, has variable latency, and
is optimized for the common case that the product does
not need to be rounded. Our multiplier also uses a
novel technique that estimates the number of product
digits that needed to be rounded in parallel with the
significant multiplication. In this design, a single
multiplier is used to multiply the significants and
round the product. We believe this the first hardware
design of a DFP multiplier for BID-encoded numbers.",
acknowledgement = ack-nhfb,
}
@Article{Graillat:2008:ASZ,
author = "Stef Graillat",
title = "Accurate simple zeros of polynomials in floating point
arithmetic",
journal = j-COMPUT-MATH-APPL,
volume = "56",
number = "4",
pages = "1114--1120",
month = aug,
year = "2008",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122108001120",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Book{Hardy:2008:ITN,
author = "G. H. (Godfrey Harold) Hardy and Edward Maitland
Wright and D. R. Heath-Brown and Joseph H. Silverman",
title = "An introduction to the theory of numbers",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
edition = "Sixth",
pages = "xxi + 621",
year = "2008",
ISBN = "0-19-921985-0 (hardcover), 0-19-921986-9 (paperback)",
ISBN-13 = "978-0-19-921985-8 (hardcover), 978-0-19-921986-5
(paperback)",
LCCN = "QA241 .H28 2008",
bibdate = "Thu Nov 18 09:18:59 MST 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Oxford mathematics",
acknowledgement = ack-nhfb,
author-dates = "G. H. Hardy (1877--1947)",
remark = "Previous (fifth) edition 1979.",
subject = "Number theory",
}
@Article{Homma:2008:SAD,
author = "N. Homma and T. Aoki and T. Higuchi",
title = "A Systematic Approach for Designing Redundant
Arithmetic Adders Based on Counter Tree Diagrams",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "12",
pages = "1633--1646",
month = dec,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.106",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4569835",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Jager:2008:DAD,
author = "Hendrik Jager and Pierre Liardet",
title = "Distributions arithm{\'e}tiques des d{\'e}nominateurs
de convergents de fractions continues. ({French})
[Arithmetic distributions of the denominators of
continued fractions]",
journal = "Proceedings of the Koninklijke Nederlandse Akademie
van Wetenschappen, Series A, Indagationes
mathematicae",
volume = "91",
number = "2",
pages = "181--197",
day = "20",
month = jun,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1016/S1385-7258(88)80026-X",
ISSN = "1385-7258 (print), 1878-5972 (electronic)",
bibdate = "Tue Nov 22 11:28:19 MST 2011",
bibsource = "http://www.sciencedirect.com/;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S138572588880026X",
acknowledgement = ack-nhfb,
fjournal = "Indagationes Mathematicae (Proceedings)",
keywords = "Benford's Law",
language = "French",
xxjournal = "Indagationes Mathematicae (Proceedings)",
}
@Article{Jezequel:2008:CLE,
author = "Fabienne J{\'e}z{\'e}quel and Jean-Marie Chesneaux",
title = "{CADNA}: a library for estimating round-off error
propagation",
journal = j-COMP-PHYS-COMM,
volume = "178",
number = "12",
pages = "933--955",
day = "15",
month = jun,
year = "2008",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2008.02.003",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 23:42:31 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465508000775",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Jimeno:2008:BBA,
author = "Antonio Jimeno and Higinio Mora and Jose L. Sanchez
and Francisco Pujol",
title = "A {BCD}-based architecture for fast coordinate
rotation",
journal = j-J-SYST-ARCH,
volume = "54",
number = "8",
pages = "829--840",
month = aug,
year = "2008",
CODEN = "JSARFB",
DOI = "https://doi.org/10.1016/j.sysarc.2008.02.001",
ISSN = "1383-7621 (print), 1873-6165 (electronic)",
ISSN-L = "1383-7621",
bibdate = "Thu Aug 07 18:04:43 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Although radix 10 based arithmetic has been gaining
renewed importance over the last few years, decimal
systems are not efficient enough and techniques are
still under development. In this paper, an improvement
of the CORDIC (coordinate rotation digital computer)
method for decimal representation is proposed and
applied to produce fast rotations. The algorithm uses
BCD operands as inputs, combining the advantages of
both decimal and binary systems. The result is a
reduction of 50\% in the number of iterations if
compared with the original Decimal CORDIC method.
Finally, we present a hardware architecture useful to
produce BCD coordinates rotations accurately and fast,
and different experiments demonstrating the advantages
of the new method are shown. A reduction of 75\% in a
single stage delay is obtained, whereas the circuit
area just increases in about 5\%.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Systems Architecture: the EUROMICRO
Journal",
keywords = "binary coded decimals; computer performance; CORDIC;
decimal arithmetic; digital arithmetic",
}
@Misc{Kahan:2008:BFU,
author = "William Kahan",
title = "Back to the Future of Undebuggable Floating-Point
Computation in Science and Engineering",
howpublished = "Web document",
day = "30",
month = mar,
year = "2008",
bibdate = "Mon Mar 31 16:50:19 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The Bay Area Scientific Computing Day, BASCD08,
honoring Profs. Kahan and Parlett, 29--30 March,
2008.",
URL = "http://math.berkeley.edu/bascd08;
http://www.eecs.berkeley.edu/~wkahan/BASCD08K.pdf",
abstract = "When I began to program an electronic computer in
1953, von Neumann was still disparaging floating-point
computation, which was generally deemed impervious to
error-analysis. Occasional anomalous results were
expected. Often they were attributed wrongly to
``Ill-Condition''. Putting one's data through several
numerical methods some of whose results might agree was
a prudent policy. Those days are back. Their challenges
will be illustrated by a program like some used by
structural engineers for forty years. To cope, we need
debugging aids like those in Section 14 of my web
page's {\tt Mindless.pdf}. Help can come only from the
designers of hardware, compilers and software
development systems after they are persuaded that the
demand for such aids is commercially significant.",
acknowledgement = ack-nhfb,
}
@Article{Kaihara:2008:BMM,
author = "M. E. Kaihara and N. Takagi",
title = "Bipartite Modular Multiplication Method",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "2",
pages = "157--164",
month = feb,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70793",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358245",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Khalid:2008:NRE,
author = "M. S. Khalid and M. R. Amin and M. M. Hossain and M.
Anwer",
editor = "{IEEE}",
booktitle = "{Proceedings of 10th International Conference on
Computer and Information Technology (ICCIT 2007),
27-29, December 2007, United International University,
Dhanmondi, Dhaka-1209, Bangladesh}",
title = "Numerical round-off error in cellular phone services
billing system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "534 + 7",
pages = "1--5",
year = "2008",
DOI = "https://doi.org/10.1109/ICCITECHN.2007.4579417",
ISBN = "1-4244-1550-0, 1-4244-1551-9",
ISBN-13 = "978-1-4244-1550-2, 978-1-4244-1551-9",
LCCN = "QA75.5 .I574 2007",
bibdate = "Wed Jul 06 19:14:16 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Cellular phone services billing for per minute tariff
plan and 1-second pulse involve floating point division
and multiplication operation to calculate per call
bill. Monthly customer billing involves addition
operations on per call bills, which are floating point
numbers. Round-off errors occur due to floating point
numberspsila computer representation limitations and
for storing limited significant figures during billing.
The study analyzed post-paid itemized bills of a
cellular phone service operator in Bangladesh and
identified that accumulated round-off error for active
post-paid subscribers is significantly high for
subscriber group of large number. The research
recommends a per second tariff plan to completely
eliminate round-off error which also reduces floating
point number operations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kong:2008:RMI,
author = "I. Kong and E. E. {Swartzlander, Jr.}",
editor = "Michael B. Matthews",
booktitle = "42nd Asilomar Conference on Signals, Systems and
Computers: {October 26--29, 2008, Pacific Grove,
California}",
title = "A Rounding Method with Improved Error Tolerance for
Division by Convergence",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1814--1818",
year = "2008",
DOI = "https://doi.org/10.1109/ACSSC.2008.5074740",
ISBN = "1-4244-2941-2",
ISBN-13 = "978-1-4244-2941-7",
ISSN = "1058-6393",
ISSN-L = "1058-6393",
LCCN = "TK7801 .A83 2008",
bibdate = "Sun Dec 10 14:05:54 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A new rounding method for division by convergence is
presented. It allows twice the error tolerance of
current methods, so it allows the multiplier of a
3-iteration Goldschmidt divider to be implemented using
only 3 extra bits. The new rounding method applies
special truncation methods at the final iteration step,
and it requires a minor modification in rounding
constants of the multiplier. It has been verified using
a SystemC model of the Goldschmidt divider supporting
variable precision. The verification consists of two
parts: the maximum error of approximate quotients and
the rounding result correctness. The maximum error of
approximate quotients is checked by analysis and via
simulation. The final rounding results are checked with
both random double precision floating-point
significands and exhaustive 17-bit precision test
vectors",
acknowledgement = ack-nhfb,
}
@Book{Kulisch:2008:CAV,
author = "Ulrich Kulisch",
title = "Computer Arithmetic and Validity --- Theory,
Implementation, and Applications",
publisher = pub-GRUYTER,
address = pub-GRUYTER:adr,
pages = "410 (est.)",
year = "2008",
ISBN = "3-11-020318-9 (hardcover)",
ISBN-13 = "978-3-11-020318-9 (hardcover)",
ISSN = "0179-0986",
LCCN = "????",
bibdate = "Wed Jun 11 14:53:52 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$108.00",
series = "De Gruyter Studies in Mathematics",
abstract = "A New Approach to Scientific Computation is a
collection of papers delivered at a symposium held at
the IBM Thomas J. Watson Research Center on August 3,
1982. The symposium provided a forum for reviewing
various aspects of an approach to scientific
computation based on a systematic theory of computer
arithmetic. Computer demonstration packages for
standard problems of numerical mathematics are
considered. Comprised of 12 chapters, this volume
begins by summarizing an extensive research activity in
scientific computation as well as the experience gained
through various implementations \ldots{}",
acknowledgement = ack-nhfb,
}
@PhdThesis{Lauter:2008:ACF,
author = "Christoph Quirin Lauter",
title = "Arrondi correct de fonctions math{\'e}matiques ---
Fonctions univari{\'e}es et bivari{\'e}es,
certification et automatisation. ({French}) [{Correct}
rounding of mathematical functions --- univariate and
bivariate functions, certification and automation]",
type = "{Ph.D.} dissertation",
school = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "Lyon, France",
pages = "xiii + 197 + 3",
month = oct,
year = "2008",
bibdate = "Fri Dec 08 10:03:47 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.christoph-lauter.org/these.pdf",
acknowledgement = ack-nhfb,
advisor = "Florent de Dinechin and Jean-Michel Muller",
}
@Article{Lefevre:2008:WCE,
author = "Vincent Lef{\`e}vre and Damien Stehl{\'e} and Paul
Zimmermann",
title = "Worst Cases for the Exponential Function in the {IEEE
754r decimal64} Format",
journal = j-LECT-NOTES-COMP-SCI,
volume = "5045",
pages = "114--126",
year = "2008",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-540-85521-7_7",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Thu Oct 1 11:29:36 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2008a.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-85521-7_7.pdf",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-540-85521-7",
book-URL = "http://www.springerlink.com/content/978-3-540-85521-7",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
remark = "From the abstract: ``the worst case for $ |x| \geq 3
\times 10^{-11} $ is exp(9.407822313572878e-2) =
1.09864568206633850000000000000000278.''",
}
@Article{Li:2008:MLB,
author = "Xin Li and Marc Moreno Maza and Raqeeb Rasheed and
{\'E}ric Schost",
title = "The {\tt modpn} library: bringing fast polynomial
arithmetic into {MAPLE}",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "42",
number = "3",
pages = "172--174",
month = sep,
year = "2008",
CODEN = "????",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Fri Feb 13 18:17:36 MST 2009",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Liu:2008:FIM,
author = "J. Liu and B. Weaver and Y. Zakharov",
title = "{FPGA} implementation of multiplication-free complex
division",
journal = j-ELECT-LETTERS,
volume = "44",
number = "2",
pages = "5--96",
day = "17",
month = jan,
year = "2008",
CODEN = "ELLEAK",
DOI = "https://doi.org/10.1049/el:20082567",
ISSN = "0013-5194 (print), 1350-911X (electronic)",
ISSN-L = "0013-5194",
bibdate = "Fri Dec 03 14:53:57 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The FPGA implementation of a new complex division
algorithm is described. It is based on the dichotomous
co-ordinate descent method and requires only bit-shift
and addition operations. Consequently, the footprint of
the new complex division core is remarkably small.",
acknowledgement = ack-nhfb,
fjournal = "Electronics Letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
keyword = "FPGA; bit-shift; dichotomous coordinate descent
method; multiplication-free complex division; field
programmable gate arrays; signal processing",
}
@Misc{Melquiond:2008:DRA,
author = "Guillaume Melquiond and Sylvain Pion",
title = "Directed Rounding Arithmetic Operations",
howpublished = "Web document",
day = "05",
month = dec,
year = "2008",
bibdate = "Mon Dec 08 14:57:52 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ISO WG21 Document N2811=08-0321, posted to the
stds-1788 mailing list on 8-Dec-2008.",
acknowledgement = ack-nhfb,
}
@Article{Monniaux:2008:PVF,
author = "David Monniaux",
title = "The pitfalls of verifying floating-point
computations",
journal = j-TOPLAS,
volume = "30",
number = "3",
pages = "12:1--12:41",
month = may,
year = "2008",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/1353445.1353446",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Wed Jun 11 19:14:53 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toplas/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Current critical systems often use a lot of
floating-point computations, and thus the testing or
static analysis of programs containing floating-point
operators has become a priority. However, correctly
defining the semantics of common implementations of
floating-point is tricky, because semantics may change
according to many factors beyond source-code level,
such as choices made by compilers. We here give
concrete examples of problems that can appear and
solutions for implementing in analysis software.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
}
@Article{Moore:2008:IMB,
author = "Samuel K. Moore",
title = "{Intel} Makes A Big Jump In Computer Math",
journal = j-IEEE-SPECTRUM,
volume = "45",
number = "2",
pages = "14--15",
month = feb,
year = "2008",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/SPEC.2008.4445770",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 12:29:46 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum2000.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "45-nanometer processors; Clocks; Computer
architecture; computer math; Convergence; Crops;
Digital arithmetic; financial computing; Frequency
conversion; Intel; Intel Pentium; Loans and mortgages;
microprocessor chips; Microprocessors; Penryn; Penryn
chip; Programming profession; scientific computing;
Scientific computing; size 45 nm; SRT Radix-4 (Sweeney,
Robertson, Tocher) division",
}
@Article{Morris:2008:PLC,
author = "Gerald R. Morris and Viktor K. Prasanna",
title = "A pipelined-loop-compatible architecture and algorithm
to reduce variable-length sets of floating-point data
on a reconfigurable computer",
journal = j-J-PAR-DIST-COMP,
volume = "68",
number = "7",
pages = "913--921",
month = jul,
year = "2008",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Fri Jul 11 20:32:36 MDT 2008",
bibsource = "http://www.sciencedirect.com/science/journal/07437315;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
}
@Article{Nakamori:2008:SRA,
author = "S. Nakamori",
title = "Square-root algorithms of {RLS Wiener} filter and
fixed-point smoother in linear discrete stochastic
systems",
journal = j-APPL-MATH-COMP,
volume = "203",
number = "1",
pages = "186--193",
day = "1",
month = sep,
year = "2008",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Sep 3 10:53:23 MDT 2010",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Namin:2008:NFF,
author = "A. H. Namin and Huapeng Wu and M. Ahmadi",
title = "A New Finite-Field Multiplier Using Redundant
Representation",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "5",
pages = "716--720",
month = may,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70834",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4378354",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{P754:2008:ISF,
author = "{IEEE Task P754}",
title = "{IEEE 754-2008, Standard for Floating-Point
Arithmetic}",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "58",
day = "29",
month = aug,
year = "2008",
DOI = "https://doi.org/10.1109/IEEESTD.2008.4610935",
ISBN = "0-7381-5753-8 (paper), 0-7381-5752-X (electronic)",
ISBN-13 = "978-0-7381-5753-5 (paper), 978-0-7381-5752-8
(electronic)",
LCCN = "????",
bibdate = "Thu Sep 25 09:50:30 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeestd.bib",
URL = "http://en.wikipedia.org/wiki/IEEE_754-2008;
http://ieeexplore.ieee.org/servlet/opac?punumber=4610933",
abstract = "This standard specifies interchange and arithmetic
formats and methods for binary and decimal
floating-point arithmetic in computer programming
environments. This standard specifies exception
conditions and their default handling. An
implementation of a floating-point system conforming to
this standard may be realized entirely in software,
entirely in hardware, or in any combination of software
and hardware. For operations specified in the normative
part of this standard, numerical results and exceptions
are uniquely determined by the values of the input
data, sequence of operations, and destination formats,
all under user control.",
acknowledgement = ack-nhfb,
}
@Article{Pan:2008:SAL,
author = "V. Y. Pan and D. Grady and B. Murphy and G. Qian and
R. E. Rosholt and A. D. Ruslanov",
title = "{Schur} aggregation for linear systems and
determinants",
journal = j-THEOR-COMP-SCI,
volume = "409",
number = "2",
pages = "255--268",
day = "17",
month = dec,
year = "2008",
CODEN = "TCSCDI",
DOI = "https://doi.org/10.1016/j.tcs.2008.09.005",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Mon Mar 28 21:21:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tcs2005.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975/",
keywords = "accurate floating-point summation; Additive
preconditioning; Determinants; Iterative refinement;
Linear systems of equations; Sherman Morrison Woodbury
formula",
}
@InCollection{Patterson:2008:AC,
author = "David A. Patterson and John L. Hennessy",
title = "Arithmetic for Computers",
crossref = "Patterson:2008:COD",
chapter = "3",
pages = "222--297",
year = "2008",
bibdate = "Thu Dec 04 18:36:00 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic",
}
@InCollection{Patterson:2008:GCG,
author = "David A. Patterson and John L. Hennessy",
title = "Graphics and Computing {GPUs}",
crossref = "Patterson:2008:COD",
chapter = "A",
pages = "A-1--A-77",
year = "2008",
bibdate = "Thu Dec 04 18:36:00 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; GPU",
}
@Article{Pineiro:2008:RDD,
author = "J.-A. Pineiro and J. D. Bruguera and F. Lamberti and
P. Montuschi",
title = "A Radix-2 Digit-by-Digit Architecture for Cube Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "4",
pages = "562--566",
month = apr,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70848",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4407683",
abstract = "A radix-2 digit-recurrence algorithm and architecture
for the computation of the cube root are presented in
this paper. The original recurrence based on the
concept of completing the cube is modified to allow an
efficient implementation of the algorithm and the cycle
time and area cost of the resulting architecture are
estimated as 7.5 times the delay of a full adder and
around 9,000 nand2 cells, respectively, for
double-precision computations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Piso:2008:FOS,
author = "D. Piso and J. D. Bruguera",
editor = "Michael B. Matthews",
booktitle = "42nd Asilomar Conference on Signals, Systems and
Computers: {October 26--29, 2008, Pacific Grove,
California}",
title = "Forcing {\em one-sided\/} results in {Goldschmidt}
algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1830--1833",
month = oct,
year = "2008",
DOI = "https://doi.org/10.1109/acssc.2008.5074743",
ISBN = "1-4244-2941-2",
ISBN-13 = "978-1-4244-2941-7",
ISSN = "1058-6393",
ISSN-L = "1058-6393",
LCCN = "TK7801 .A83 2008",
bibdate = "Mon Dec 11 08:10:00 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a method to obtain one-sided error
results from Goldschmidt (GLD) algorithm. In some
applications is useful to obtain a one-sided error
result. This is done introducing error bias in the
intermediate iterations. An error analysis permits to
obtain expressions to estimate the loss of precision
and to compensate it. In this way, the one-sided error
results are obtained without significant additional
hardware requirement.",
acknowledgement = ack-nhfb,
}
@InProceedings{Piso:2008:NRA,
author = "D. Piso and J. D. Bruguera",
editor = "Luca Fanucci",
booktitle = "Proceedings: {11th Euromicro Symposium on Digital
Systems Design: Architectures, Methods and Tools (DSD
2008), Parma, Italy, September 3--5, 2008}",
title = "A New Rounding Algorithm for Variable Latency Division
and Square Root Implementations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "760--767",
year = "2008",
DOI = "https://doi.org/10.1109/DSD.2008.28.",
ISBN = "0-7695-3277-2",
ISBN-13 = "978-0-7695-3277-6",
bibdate = "Sun Dec 10 13:55:38 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The aim of this work is to present a method for
rounding quadratically converging algorithms that
improves their performance. This method is able to
reduce significantly the number of cases where the
remainder calculation is necessary. It is based on
previous methods and incorporates additional bits of
the result approximation to be checked. This work
includes the result of exhaustive simulations that
permit us to measure exactly how many calculations are
avoided. Using these simulations, it is concluded that
the presented method is able to reduce by half the
number of remainder calculations. Using adequate result
approximations the remainder calculation is necessary
in only 5\% of the total cases",
acknowledgement = ack-nhfb,
}
@Article{Quinnell:2008:BFP,
author = "E. Quinnell and E. E. Swartzlander and C. Lemonds",
title = "Bridge Floating-Point Fused Multiply-Add Design",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "16",
number = "12",
pages = "1727--1731",
year = "2008",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2008.2001944",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Sat Feb 19 18:54:07 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@InProceedings{Quinnell:2008:FPF,
author = "E. Quinnell and E. E. Swartzlander and C. Lemonds",
title = "Floating-Point Fused Multiply-Add Architectures",
crossref = "Matthews:2008:CRF",
pages = "331--337",
year = "2008",
DOI = "https://doi.org/10.1109/ACSSC.2007.4487224",
bibdate = "Sat Feb 19 18:56:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Two new floating-point fused multiply-add
architectures for the single instruction execution of $
(A \times B) + C $ are presented. The three-path
architecture uses parallel hardware paths similar to
those in dual-path floating-point adders. The new
bridge architecture re-uses common floating-point
components to add a fused multiply-add instruction.
Each new architecture as well as a collection of
floating-point arithmetic units and a classic fused
multiplier-adder have been designed using the Advanced
Micro Devices 65 nanometer silicon on insulator CMOS
technology to fairly compare the new architectures.",
acknowledgement = ack-nhfb,
}
@Article{Rahaman:2008:CTB,
author = "H. Rahaman and J. Mathew and D. K. Pradhan and A. M.
Jabir",
title = "{C}-testable bit parallel multipliers over {$ {\rm
GF}(2^m) $}",
journal = j-TODAES,
volume = "13",
number = "1",
pages = "5:1--5:??",
month = jan,
year = "2008",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/1297666.1297671",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Thu Jun 12 18:10:00 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/todaes/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a C-testable design of polynomial basis
(PB) bit-parallel (BP) multipliers over GF(2 m) for
100\% coverage of stuck-at faults. Our design method
also includes the method for test vector generation,
which is simple and efficient. C-testability is
achieved with three control inputs and approximately
6\% additional hardware. Only 8 constant vectors are
required irrespective of the sizes of the fields and
primitive polynomial. We also present a Built-In
Self-Test (BIST) architecture for generating the test
vectors efficiently, which eliminates the need for the
extra control inputs. Since these circuits have
critical applications as parts of cryptography (e.g.,
Elliptic Curve Crypto (ECC) systems) hardware, the BIST
architecture may provide with added level of security,
as the tests would be done internally and without the
requirement of probing by external testing equipment.
Finally we present experimental results comprising the
area, delay and power of the testable multipliers of
various sizes with the help of the Synopsys{\reg} tools
using UMC 0. 18 micron CMOS technology library.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems (TODAES)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J776",
keywords = "built-in self-test; C-testable; cryptography; digital
signal processing; error control code; fault;
floating-point testing; Galois field; multiplier;
polynomials; stuck-at fault; testing; TPG; VLSI
design",
}
@Article{Rahaman:2008:DRT,
author = "H. Rahaman and J. Mathew and D. K. Pradhan and A. M.
Jabir",
title = "Derivation of Reduced Test Vectors for Bit-Parallel
Multipliers over {$ \mathrm {GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "9",
pages = "1289--1294",
month = sep,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.63",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4487058",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ravikumar:2008:BND,
author = "Bala Ravikumar",
title = "The {Benford--Newcomb} Distribution and Unambiguous
Context-Free Languages",
journal = j-INT-J-FOUND-COMP-SCI,
volume = "19",
number = "3",
pages = "717--727",
month = jun,
year = "2008",
CODEN = "IFCSEN",
DOI = "https://doi.org/10.1142/S0129054108005905",
ISSN = "0129-0541 (print), 1793-6373 (electronic)",
ISSN-L = "0129-0541",
bibdate = "Tue Aug 31 07:37:14 MDT 2010",
bibsource = "http://ejournals.wspc.com.sg/ijfcs/mkt/archive.shtml;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Foundations of Computer
Science (IJFCS)",
journal-URL = "http://www.worldscientific.com/loi/ijfcs",
}
@InProceedings{Raz:2008:EFL,
author = "Ran Raz",
title = "Elusive functions and lower bounds for arithmetic
circuits",
crossref = "ACM:2008:SPA",
pages = "711--720",
year = "2008",
DOI = "https://doi.org/10.1145/1374376.1374479",
bibdate = "Fri Jun 20 18:31:53 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A basic fact in linear algebra is that the image of
the curve $ f(x) = (x^1, x^2, x^3, \ldots {}, x^m) $,
say over $C$, is not contained in any $ m - 1 $
dimensional affine subspace of $ C^m $. In other words,
the image of $f$ is not contained in the image of any
polynomial-mapping $ \Gamma : C^{m - 1} \rightarrow C^m
$ of degree 1 (that is, an affine mapping). Can one
give an explicit example for a polynomial curve $ f : C
\rightarrow C^m $, such that, the image of $f$ is not
contained in the image of any polynomial-mapping $
\Gamma : C^{m - 1} \rightarrow C^m $ of degree 2? In
this paper, we show that problems of this type are
closely related to proving lower bounds for the size of
general arithmetic circuits. For example, any explicit
$f$ as above (with the right notion of explicitness)
implies super-polynomial lower bounds for computing the
permanent over $C$. More generally, we say that a
polynomial-mapping $ f : F^n \rightarrow F^m $ is $ (s,
r) $-elusive, if for every polynomial-mapping $ \Gamma
: F^s \rightarrow F^m $ of degree $r$, $ I m(f) \not
\subset I m(\Gamma) $. We show that for many settings
of the parameters $ n, m, s, r $, explicit
constructions of elusive polynomial-mappings imply
strong (up to exponential) lower bounds for general
arithmetic circuits. Finally, for every $r$, of degree
$ O(r) $, that is $ (s, r) $-elusive for $ s = n^{1 +
\Omega (1 / r)} $. We use this to construct for any
$r$, an explicit example for an $n$-variate polynomial
of total-degree $ O(r) $, with coefficients in $ \{ 0,
1, \} $ such that, any depth $r$ arithmetic circuit for
this polynomial (over any field) is of size $ \geq n^{1
+ \Omega (1 / r)} $. In particular, for any constant
$r$, this gives a constant degree polynomial, such
that, any depth $r$ arithmetic circuit for this
polynomial is of size $ \geq n^{1 + \Omega (1)} $.
Previously, only lower bounds of the type $ \Omega (n
\lambda_r (n)) $, where $ \lambda_r (n) $ are extremely
slowly growing functions (e.g., $ \lambda_5 (n) = \log
n $, and $ \lambda_7 (n) = \log * \log * n $) , were
known for constant-depth arithmetic circuits for
polynomials of constant degree.",
acknowledgement = ack-nhfb,
keywords = "arithmetic circuits; bounded depth circuits; circuit
complexity; lower bounds",
}
@Article{Raz:2008:LBS,
author = "Ran Raz and Amir Shpilka and Amir Yehudayoff",
title = "A Lower Bound for the Size of Syntactically
Multilinear Arithmetic Circuits",
journal = j-SIAM-J-COMPUT,
volume = "38",
number = "4",
pages = "1624--1647",
month = "????",
year = "2008",
CODEN = "SMJCAT",
DOI = "",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Tue May 18 08:22:01 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/38/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{Rodriguez-Henriquez:2008:LCB,
author = "F. Rodriguez-Henriquez and G. Morales-Luna and J.
Lopez",
title = "Low-Complexity Bit-Parallel Square Root Computation
over {$ \mathrm {GF}(2^m) $} for All Trinomials",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "4",
pages = "472--480",
month = apr,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2007.70822",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358282",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ruiz:2008:EIR,
author = "Gustavo A. Ruiz and Mercedes Granda",
title = "Efficient implementation of {3X} for radix-8
encoding",
journal = j-MICROELECT-J,
volume = "39",
number = "1",
pages = "152--159",
month = jan,
year = "2008",
CODEN = "MICEB9",
DOI = "https://doi.org/10.1016/j.mejo.2007.10.006",
ISSN = "0026-2692 (print), 1879-2391 (electronic)",
ISSN-L = "0026-2692",
bibdate = "Wed Dec 13 09:54:52 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Microelectronics Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/00262692",
keywords = "Booth-3 encoding; computation of $3 x$; Goldschmidt
division algorithm",
}
@Article{Rump:2008:AFPa,
author = "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
Oishi",
title = "Accurate Floating-Point Summation. {Part I}: Faithful
Rounding",
journal = j-SIAM-J-SCI-COMP,
volume = "31",
number = "1",
pages = "189--224",
month = "????",
year = "2008",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/050645671",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:44:12 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Given a vector of floating-point numbers with exact
sum $s$, we present an algorithm for calculating a
faithful rounding of $s$, i.e., the result is one of
the immediate floating-point neighbors of $s$. If the
sum $s$ is a floating-point number, we prove that this
is the result of our algorithm. The algorithm adapts to
the condition number of the sum, i.e., it is fast for
mildly conditioned sums with slowly increasing
computing time proportional to the logarithm of the
condition number. All statements are also true in the
presence of underflow. The algorithm does not depend on
the exponent range. Our algorithm is fast in terms of
measured computing time because it allows good
instruction-level parallelism, it neither requires
special operations such as access to mantissa or
exponent, it contains no branch in the inner loop, nor
does it require some extra precision: The only
operations used are standard floating-point addition,
subtraction, and multiplication in one working
precision, for example, double precision. Certain
constants used in the algorithm are proved to be
optimal.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; distillation",
}
@Article{Rump:2008:AFPb,
author = "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
Oishi",
title = "Accurate Floating-Point Summation. {Part II}: Sign,
{$K$}-Fold Faithful and Rounding to Nearest",
journal = j-SIAM-J-SCI-COMP,
volume = "31",
number = "2",
pages = "1269--1302",
month = "????",
year = "2008",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/07068816X",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:44:14 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In Part II of this paper we first refine the analysis
of error-free vector transformations presented in Part
I. Based on that we present an algorithm for
calculating the rounded-to-nearest result of $ s :=
\sum p_i $ for a given vector of floating-point numbers
$ p_i $, as well as algorithms for directed rounding. A
special algorithm for computing the sign of $s$ is
given, also working for huge dimensions. Assume a
floating-point working precision with relative rounding
error unit eps. We define and investigate a $K$-fold
faithful rounding of a real number $r$. Basically the
result is stored in a vector $ \mathtt {Res}_{\nu } $
of $K$ nonoverlapping floating-point numbers such that
$ \sum \mathtt {Res}_{\nu } $ approximates $r$ with
relative accuracy $ \mathtt {eps}^K $, and replacing $
\mathtt {Res}_K $ by its floating-point neighbors in $
\sum \mathtt {Res}_{\nu } $ forms a lower and upper
bound for $r$. For a given vector of floating-point
numbers with exact sum $s$, we present an algorithm for
calculating a $K$-fold faithful rounding of $s$ using
solely the working precision. Furthermore, an algorithm
for calculating a faithfully rounded result of the sum
of a vector of huge dimension is presented. Our
algorithms are fast in terms of measured computing time
because they allow good instruction-level parallelism,
they neither require special operations such as access
to mantissa or exponent, they contain no branch in the
inner loop, nor do they require some extra precision.
The only operations used are standard floating-point
addition, subtraction, and multiplication in one
working precision, for example, double precision.
Certain constants used in the algorithms are proved to
be optimal.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; distillation",
}
@TechReport{Rump:2008:UFA,
author = "Siegfried M. Rump",
title = "Ultimately Fast Accurate Summation",
type = "Technical Report",
institution = "Institute for Reliable Computing, Technische
Universit{\"a}t Hamburg",
address = "Hamburg, Germany",
pages = "28",
day = "19",
month = oct,
year = "2008",
MRclass = "15-04, 65G99, 65-04",
bibdate = "Sat Oct 25 15:15:14 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ti3.tu-harburg.de/paper/rump/Ru08b.pdf",
abstract = "We present two new algorithms FastAccSum and
FastPrecSum, one to compute a faithful rounding of the
sum of floating-point numbers, and the other for a
result ``as if'' computed in $K$-fold precision.
Faithful rounding means the result is one of the
immediate floating-point neighbors of the exact result,
or the exact sum if it is a floating-point number. The
algorithms are based on our previous algorithms AccSum
and PrecSum and improve them by up to 25\%. The first
algorithm adapts to the condition number of the sum,
i.e., the computing time is proportional to the
logarithm of the condition number. The second algorithm
does not need extra memory, and the computing time
depends only on the dimension and $K$. Both algorithms
are the fastest known in terms of flops. They allow
good instruction-level parallelism so that they are
also fast in terms of measured computing time. The
algorithms require only standard floating-point
addition, subtraction and multiplication in one working
precision, for example double precision.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; distillation; error
analysis; error-free transformation; faithful rounding;
high accuracy; K-fold precision; maximally accurate
summation; XBLAS",
remark = "Submitted for publication.",
}
@Article{Russell:2008:BOR,
author = "Craig Russell",
title = "Bridging the Object-Relational Divide",
journal = j-QUEUE,
volume = "6",
number = "3",
pages = "18--28",
month = may # "\slash " # jun,
year = "2008",
CODEN = "AQCUAE",
DOI = "https://doi.org/10.1145/1394127.1394139",
ISSN = "1542-7730 (print), 1542-7749 (electronic)",
ISSN-L = "1542-7730",
bibdate = "Tue Aug 5 19:04:31 MDT 2008",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "ORM technologies can simplify data access, but be
aware of the challenges that come with introducing this
new layer of abstraction.",
acknowledgement = ack-nhfb,
fjournal = "ACM Queue: Tomorrow's Computing Today",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J882",
}
@Article{Schreppers:2008:ACC,
author = "Walter Schreppers and Annie Cuyt",
title = "{Algorithm 871}: a {C\slash C++} precompiler for
autogeneration of multiprecision programs",
journal = j-TOMS,
volume = "34",
number = "1",
pages = "5:1--5:20",
month = jan,
year = "2008",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1322436.1322441",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Mar 12 17:39:58 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the past decade a number of libraries for
multiprecision floating-point arithmetic have been
developed. We describe an easy to use, generic C/C++
transcription program or precompiler for the conversion
of C or C++ source code into new code that uses a C++
multiprecision library of choice. The precompiler can
convert any type in the input source code to another
type in the output source code. The input source can be
either C or C++ , while the output code generated by
the precompiler and using the new types, is C++. The
type conversion is based on a simple XML configuration
file which is provided by either the developer of the
multiprecision library or by the user of the
precompiler. The precompiler can also convert to data
types with additional features, which are not supported
in the types of the source code. Applicability of the
precompiler is shown with the successful conversion of
large subsets of the GNU Scientific Library and
Numerical Recipes.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Misc{Steele:2008:FPA,
author = "Guy L. {Steele Jr.}",
title = "Floating point adder with embedded status
information",
howpublished = "US Patent 7366749",
day = "29",
month = apr,
year = "2008",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7366749/fulltext.html",
abstract = "A system for providing a floating point sum includes
an analyzer circuit configured to determine a first
status of a first floating point operand and a second
status of a second floating point operand based upon
data within the first floating point operand and data
with the second floating point operand respectively. In
addition, the system includes a results circuit coupled
to the analyzer circuit. The results circuit is
configured to assert a resulting floating point operand
containing the sum of the first floating point operand
and the second floating point operand and a resulting
status embedded within the resulting floating point
operand.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2008:FPD,
author = "Guy L. {Steele Jr.}",
title = "Floating point divider with embedded status
information",
howpublished = "US Patent 7363337",
day = "22",
month = apr,
year = "2008",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7363337/fulltext.html",
abstract = "A system for providing floating point division
includes an analyzer circuit configured to determine a
first status of a first floating point operand and a
second status of a second floating point operand based
upon data within the first floating point operand and
data within the second floating point operand
respectively. In addition, the system includes a
results circuit coupled to the analyzer circuit. The
results circuit is configured to assert a resulting
floating point operand containing the result of the
division of the first floating point operand by the
second floating point operand. Additionally, the
results circuit provides resulting status embedded
within the resulting floating point operand.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2008:FPSa,
author = "Guy L. {Steele Jr.}",
title = "Floating point status information accumulation
circuit",
howpublished = "US Patent 7444367",
day = "28",
month = oct,
year = "2008",
bibdate = "Tue Dec 23 15:05:52 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7444367/fulltext.html",
abstract = "A floating point flag combining or accumulating
circuit includes an analysis circuit that receives a
plurality of floating point operands, each having
encoded status flag information, and a result
assembler. The analysis circuit analyzes the plurality
of floating point operands and provides an indication
of one or more predetermined formats in which the
plurality of floating point operands are represented.
The result assembler receives the indication from the
analysis circuit and assembles an accumulated result
that represents a value and combines the encoded status
flag information from at least two of the plurality of
floating point operands.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2008:FPSb,
author = "Guy L. {Steele Jr.}",
title = "Floating point square root provider with embedded
status information",
howpublished = "US Patent 7430576",
day = "30",
month = sep,
year = "2008",
bibdate = "Tue Dec 23 15:06:43 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7430576/fulltext.html",
abstract = "A system for providing a floating point square root
comprises an analyzer circuit configured to determine a
first status of a first floating point operand based
upon data within the first floating point operand. In
addition, the system comprises a results circuit
coupled to the analyzer circuit. The results circuit is
configured to assert a resulting floating point operand
containing the square root of the first floating point
operand and a resulting status embedded within the
resulting floating point operand.",
acknowledgement = ack-nhfb,
}
@Misc{Steele:2008:FPSc,
author = "Guy L. {Steele Jr.}",
title = "Floating point system that represents status flag
information within a floating point operand",
howpublished = "US Patent 7395297",
day = "01",
month = jul,
year = "2008",
bibdate = "Tue Dec 23 15:06:47 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.patentstorm.us/patents/7395297/fulltext.html",
abstract = "A floating point unit generates results in which
status information generated for an operation is
encoded within the resulting operand, instead of
requiring a separate floating point status register for
the status information. In one embodiment, a floating
point operand data structure includes a first portion
having floating point operand data and a second portion
having embedded status information associated with at
least one status condition of the operand data. The
status condition may be determined from only the
embedded status information. The status condition may
also be associated with at least one floating point
operation that generated the operand data structure.
The outcome of a conditional floating point instruction
may be based on the embedded status information without
regard to contents of the floating point status
register. The second portion of the data structure may
also have at least one bit indicative of the status
condition, such as an invalid operation status, an
overflow status, an underflow status, a division by
zero status, an infinity status, and an inexact
status.",
acknowledgement = ack-nhfb,
}
@Article{Sun:2008:HPM,
author = "Junqing Sun and G. D. Peterson and O. O. Storaasli",
title = "High-Performance Mixed-Precision Linear Solver for
{FPGAs}",
journal = j-IEEE-TRANS-COMPUT,
volume = "57",
number = "12",
pages = "1614--1623",
month = dec,
year = "2008",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.89",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 12:17:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4531732",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Thill:2008:EMP,
author = "M. Thill",
title = "Erratum: a more precise rounding algorithm for
rational numbers",
journal = j-COMPUTING,
volume = "82",
number = "4",
pages = "261--262",
month = sep,
year = "2008",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-008-0013-8",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Sun Oct 31 11:09:49 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=82&issue=4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Thill:2008:MPR}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=82&issue=4&spage=261",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Thill:2008:MPR,
author = "M. Thill",
title = "A more precise rounding algorithm for rational
numbers",
journal = j-COMPUTING,
volume = "82",
number = "2--3",
pages = "189--198",
month = jul,
year = "2008",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-008-0006-7",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Sun Oct 31 11:09:47 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=82&issue=2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See erratum \cite{Thill:2008:EMP}.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=82&issue=2&spage=189",
abstract = "We adjoin a more precise companion to the classical
mediant rounding algorithm for rational numbers.",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Tsigaridas:2008:CRR,
author = "Elias P. Tsigaridas and Ioannis Z. Emiris",
title = "On the complexity of real root isolation using
continued fractions",
journal = j-THEOR-COMP-SCI,
volume = "392",
number = "1--3",
pages = "158--173",
day = "28",
month = feb,
year = "2008",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Mon Mar 28 21:49:12 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/03043975;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@Article{VanMeter:2008:ADM,
author = "Rodney {Van Meter} and W. J. Munro and Kae Nemoto and
Kohei M. Itoh",
title = "Arithmetic on a distributed-memory quantum
multicomputer",
journal = j-JETC,
volume = "3",
number = "4",
pages = "2:1--2:??",
month = jan,
year = "2008",
CODEN = "????",
DOI = "https://doi.org/10.1145/1324177.1324179",
ISSN = "1550-4832 (print), 1550-4840 (electronic)",
ISSN-L = "1550-4832",
bibdate = "Fri Jun 20 11:04:00 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/jetc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We evaluate the performance of quantum arithmetic
algorithms run on a distributed quantum computer (a
quantum multicomputer). We vary the node capacity and
I/O capabilities, and the network topology. The
tradeoff of choosing between gates executed remotely,
through ``teleported gates'' on entangled pairs of
qubits (telegate), versus exchanging the relevant
qubits via quantum teleportation, then executing the
algorithm using local gates (teledata), is examined. We
show that the teledata approach performs better, and
that carry-ripple adders perform well when the
teleportation block is decomposed so that the key
quantum operations can be parallelized. A node size of
only a few logical qubits performs adequately provided
that the nodes have two transceiver qubits. A linear
network topology performs acceptably for a broad range
of system sizes and performance parameters. We
therefore recommend pursuing small, high-I/O bandwidth
nodes and a simple network. Such a machine will run
Shor's algorithm for factoring large numbers
efficiently.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J967",
keywords = "quantum computer architecture; Quantum computing",
}
@Article{Webb:2008:IZN,
author = "Charles F. Webb",
title = "{IBM z10}: The Next-Generation Mainframe
Microprocessor",
journal = j-IEEE-MICRO,
volume = "28",
number = "2",
pages = "19--29",
month = mar # "\slash " # apr,
year = "2008",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2008.26",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Wed Jul 2 21:58:04 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IBM system z10 includes four microprocessor cores
--- each with a private 3-Mbyte cache --- and
integrated accelerators for decimal floating-point
computation, cryptography, and data compression. A
separate SMP hub chip provides a shared third-level
cache and interconnect fabric for multiprocessor
scaling. This article focuses on the high-frequency
design techniques used to achieve a 4.4-GHz system, and
on the pipeline design that optimizes z10's CPU
performance.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "decimal floating-point arithmetic",
}
@TechReport{Wirth:2008:ND,
author = "Niklaus Wirth",
title = "A Note on Division",
type = "Note",
institution = inst-ETH,
address = inst-ETH:adr,
pages = "4",
day = "20",
month = aug,
year = "2008",
bibdate = "Tue Jan 09 07:42:36 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wirth-niklaus.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://people.inf.ethz.ch/wirth/Miscellaneous/Division.pdf",
acknowledgement = ack-nhfb,
author-dates = "Niklaus Wirth (15 February 1934--1 January 2024)",
}
@Article{Yamanaka:2008:PAA,
author = "Naoya Yamanaka and Takeshi Ogita and Siegfried M. Rump
and Shin'ichi Oishi",
title = "A parallel algorithm for accurate dot product",
journal = j-PARALLEL-COMPUTING,
volume = "34",
number = "6--8",
pages = "392--410",
month = jul,
year = "2008",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/j.parco.2008.02.002",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Thu Sep 2 17:51:09 MDT 2010",
bibsource = "http://www.sciencedirect.com/science/journal/01678191;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Parallel algorithms for accurate summation and dot
product are proposed. They are parallelized versions of
fast and accurate algorithms of calculating sum and dot
product using error-free transformations which are
recently proposed by Ogita et al. [T. Ogita, S. M.
Rump, S. Oishi, Accurate sum and dot product, SIAM J.
Sci. Comput. 26(6) (2005) 1955--1988]. They have shown
their algorithms are fast in terms of measured
computing time. However, due to the strong data
dependence in the process of their algorithms, it is
difficult to parallelize them. Similarly to their
algorithms, the proposed parallel algorithms in this
paper are designed to achieve the results as if
computed in K-fold working precision with keeping the
fastness of their algorithms. Numerical results are
presented showing the performance of the proposed
parallel algorithm of calculating dot product.",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
keywords = "accurate dot product; accurate summation; DotK; higher
precision; parallel algorithm; PDotK; PSumK; SumK",
remark = "See \cite{Ogita:2005:ASD} for the cited paper.",
}
@InProceedings{Adikari:2009:HBT,
author = "Jithra Adikari and Vassil Dimitrov and Laurent
Imbert",
title = "Hybrid Binary-Ternary Joint Form and Its Application
in Elliptic Curve Cryptography",
crossref = "Bruguera:2009:PIS",
pages = "76--83",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Multi-exponentiation is a common and time consuming
operation in public-key cryptography. Its elliptic
curve counterpart, called multi-scalar multiplication
is extensively used for digital signature verification.
Several algorithms have been proposed to speed-up those
critical computations. They are based on simultaneously
recoding a set of integers in order to minimize the
number of general multiplications or point additions.
When signed-digit recoding techniques can be used, as
in the world of elliptic curves, Joint Sparse Form
(JSF) and interleaving w-NAF are the most efficient
algorithms. In this paper, a novel recoding algorithm
for a pair of integers is proposed, based on a
decomposition that mixes powers of 2 and powers of 3.
The so-called Hybrid Binary-Ternary Joint Form require
fewer digits and is sparser than the JSF and the
interleaving w-NAF. Its advantages are illustrated for
elliptic curve double-scalar multiplication; the
operation counts show a gain of up to 19\%.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@InProceedings{Amaricai:2009:DFP,
author = "A. Amaricai and M. Vladutiu and O. Boncalo",
title = "Design of floating point units for interval
arithmetic",
crossref = "IEEE:2009:PDR",
year = "2009",
DOI = "https://doi.org/10.1109/RME.2009.5201307",
bibdate = "Thu Mar 24 21:37:47 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, hardware units for interval addition,
multiplication and divide-add fused are presented.
Regarding interval addition, a new architecture of
double path adder, is presented. This architecture
exploits the parallel structure of double path adder.
Regarding multiplication, the proposed architecture is
based on a dual result multiplier (floating point
multiplication unit with two differently rounded
results for the same pair of operands) and two floating
point comparators. The goal of the divide-add fused
unit is to increase the performance of the interval
Newton's method. Algorithm and architecture for this
operation, inspired by the ones used for multiply-add
fused, are proposed.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anderson:2009:PAD,
author = "Michael J. Anderson and Charles Tsen and Liang-Kai
Wang and Katherine Compton and Michael J. Schulte",
title = "Performance analysis of decimal floating-point
libraries and its impact on decimal hardware and
software solutions",
crossref = "IEEE:2009:IICb",
pages = "465--471",
year = "2009",
DOI = "https://doi.org/10.1109/ICCD.2009.5413114",
bibdate = "Thu Feb 17 08:05:14 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IEEE Standards Committee recently approved the
IEEE 754-2008 Standard for Floating-point Arithmetic,
which includes specifications for decimal
floating-point (DFP) arithmetic. A growing number of
DFP solutions have emerged, and developers now have
many DFP design choices including arbitrary or fixed
precision, binary or decimal significand encodings,
64-bit or 128-bit DFP operands, and software or
hardware implementations.\par
There is a need for accurate analysis of these
solutions on representative DFP benchmarks. In this
paper, we expand previous DFP benchmark and performance
analysis research. We employ a DFP benchmark suite that
currently supports several DFP solutions and is easily
extendable. We also present performance analysis that
(1) provides execution profiles for various DFP
encodings and types, (2) gives the average number
cycles for common DFP operations and the total number
of each DFP operation in each benchmark, and (3)
highlights the tradeoffs between using 64-bit and
128-bit DFP operands for both binary and decimal
significand encodings. This analysis can help guide the
design of future DFP hardware and software solutions.",
acknowledgement = ack-nhfb,
keywords = "binary significand encodings; decimal floating-point
arithmetic; decimal floating-point libraries; decimal
significand encodings; DFP encodings; DFP hardware
solutions; DFP operands; DFP software solutions; IEEE
754-2008 standard; IEEE Standards Committee;
performance analysis",
}
@InProceedings{Anonymous:2009:AI,
author = "Anonymous",
title = "Author Index",
crossref = "Bruguera:2009:PIS",
pages = "235--235",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Anonymous:2009:CPC,
author = "Anonymous",
title = "Call-for-Papers on Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "5",
pages = "719--719",
month = may,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.47",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Arnold:2009:DPR,
author = "Mark G. Arnold and Sylvain Collange",
title = "A Dual-Purpose Real\slash Complex Logarithmic Number
System {ALU}",
crossref = "Bruguera:2009:PIS",
pages = "15--24",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The real Logarithmic Number System (LNS) allows fast
and inexpensive multiplication and division but more
expensive addition and subtraction as precision
increases. Recent advances in higher-order and
multipartite table methods, together with
cotransformation, allow real LNS ALUs to be implemented
effectively on FPGAs for a wide variety of
medium-precision special-purpose applications. The
Complex LNS (CLNS) is a generalization of LNS which
represents complex values in log-polar form. CLNS is a
more compact representation than traditional
rectangular methods, reducing the cost of busses and
memory in intensive complex-number applications like
the FFT; however, prior CLNS implementations were
either slow CORDIC-based or expensive 2D-table-based
approaches. This paper attempts to leverage the recent
advances made in real-valued LNS units for the more
specialized context of CLNS. This paper proposes a
novel approach to reduce the cost of CLNS addition by
re-using a conventional real-valued LNS ALU with
specialized CLNS hardware that is smaller than the
real-valued LNS ALU to which it is attached. The
resulting ALU is much less expensive than prior fast
CLNS units at the cost of some extra delay. The extra
hardware added to the ALU is for trigonometric-related
functions, and may be useful in LNS applications other
than CLNS. The novel algorithm proposed here is
implemented using the FloPoCo library (which
incorporates recent HOTBM advances in function-unit
generation), and FPGA synthesis results are reported.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; complex arithmetic; FPGA; hardware function
evaluation; logarithmic number system",
}
@Article{Baboulin:2009:ASC,
author = "Marc Baboulin and Alfredo Buttari and Jack Dongarra
and Jakub Kurzak and Julie Langou and Julien Langou and
Piotr Luszczek and Stanimire Tomov",
title = "Accelerating scientific computations with mixed
precision algorithms",
journal = j-COMP-PHYS-COMM,
volume = "180",
number = "12",
pages = "2526--2533",
month = dec,
year = "2009",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2008.11.005",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Mon Feb 13 23:42:47 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465508003846",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Bajard:2009:SRB,
author = "J. C. Bajard and M. Kaihara and T. Plantard",
title = "Selected {RNS} Bases for Modular Multiplication",
crossref = "Bruguera:2009:PIS",
pages = "25--31",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The selection of the elements of the bases in an RNS
modular multiplication method is crucial and has a
great impact in the overall performance. This work
proposes specific sets of optimal RNS moduli with
elements of Hamming weight three whose inverses used in
the MRS reconstruction have very small Hamming weight.
This property is exploited in RNS bases conversions, to
completely remove and replace the products by few
additions/subtractions and shifts, reducing the time
complexity of modular multiplication. These bases are
specially crafted to computation with operands of sizes
256 or more and are suitable for cryptographic
applications such as the ECC protocols.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Barsi:2009:ECP,
author = "Ferruccio Barsi and Maria Cristina Pinotti",
title = "Error control by product codes in arithmetic units",
journal = j-INT-J-PAR-EMER-DIST-SYS,
volume = "24",
number = "5",
pages = "407--419",
year = "2009",
CODEN = "????",
ISSN = "1744-5760 (print), 1744-5779 (electronic)",
ISSN-L = "1744-5760",
bibdate = "Thu Sep 2 08:12:37 MDT 2010",
bibsource = "http://www.informaworld.com/smpp/title~content=t713729127~link=cover;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://www.tandfonline.com/loi/gpaa20",
}
@Article{Bayat-Sarmadi:2009:CED,
author = "S. Bayat-Sarmadi and M. A. Hasan",
title = "Concurrent Error Detection in Finite-Field Arithmetic
Operations Using Pipelined and Systolic Architectures",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "11",
pages = "1553--1567",
month = nov,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.62",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4815219",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Beebe:2009:NML,
author = "Nelson H. F. Beebe",
title = "A new math library",
journal = j-IJQC,
volume = "109",
number = "13",
pages = "3008--3025",
day = "5",
month = nov,
year = "2009",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/qua.22266",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Tue Sep 08 18:56:33 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The design and development of a new mathematical
function library is described. The library extends
programming support to decimal, as well as binary,
arithmetic, and aims to influence the future evolution
of floating-point support in programming languages,
libraries, and hardware. It encourages and facilitates
research in new computer-arithmetic designs, and the
analysis and comparison of historical ones.",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
keywords = "binary arithmetic; computer arithmetic; decimal
arithmetic; elementary functions; floating-point
arithmetic; hexadecimal arithmetic; input/output
conversions; integer arithmetic; interpreted languages;
mathematical software library; number bases;
octuple-precision arithmetic; pair-precision
arithmetic; programming languages; scripting languages;
special functions; wobbling precision",
pagecount = "15",
remark = "Submitted 28 January 2009; accepted 17 March 2009.",
}
@Article{Blomquist:2009:MSC,
author = "Frithjof Blomquist and Werner Hofschuster and Walter
Kr{\"a}mer",
title = "A Modified Staggered Correction Arithmetic with
Enhanced Accuracy and Very Wide Exponent Range",
journal = j-LECT-NOTES-COMP-SCI,
volume = "5492",
pages = "41--67",
year = "2009",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-01591-5_4",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 10 08:32:19 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/content/k038294004403504/",
acknowledgement = ack-nhfb,
author-dates = "1952--2014 (WK)",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "C-XSC; complex interval functions; interval
computation; multiple precision; reliable numerical
computations; staggered correction; wide exponent
range",
remark = "Conference on Numerical Validation in Current Hardware
Architectures",
remark-2 = "Includes algorithms for division, $\exp(x)$, $(1 +
x)^n$, $\log(x)$, $\log(1 + x)$, and $\sqrt{x}$.
Staggered arithmetic represents numbers with tuples
$(e, x_1, x_2, \ldots{}, x_n)$ where $e$ is either
integer or a floating-point whole number, the $x_k$ are
floating-point, and a number has the value $2^e \sum_{k
= 1}^n x_k$. For interval arithmetic, the last element
is a pair of lower and upper bounds.",
}
@Article{Boldo:2009:CCG,
author = "Sylvie Boldo and Jean-Christophe Filli{\^a}tre and
Guillaume Melquiond",
title = "Combining {Coq} and {Gappa} for Certifying
Floating-Point Programs",
journal = j-LECT-NOTES-COMP-SCI,
pages = "59--74",
year = "2009",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-02614-0_10",
ISBN = "978-36420-2-6-1-4-0",
ISBN-13 = "978-3-642-02614-0",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Jun 8 08:31:22 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "Intelligent Computer Mathematics",
}
@Article{Boldo:2009:FRC,
author = "Sylvie Boldo",
title = "Floats and Ropes: a Case Study for Formal Numerical
Program Verification",
journal = j-LECT-NOTES-COMP-SCI,
volume = "5556",
pages = "91--102",
year = "2009",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-02930-1_8",
ISBN = "97-83642-029-3-0-1",
ISBN-13 = "978-3-642-02930-1",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Jun 8 08:25:53 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "Automata, Languages and Programming. ICALP 2009",
}
@Article{Boldo:2009:FVA,
author = "S. Boldo and M. Daumas and Ren-Cang Li",
title = "Formally Verified Argument Reduction with a Fused
Multiply-Add",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "8",
pages = "1139--1145",
month = aug,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.216",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4711042",
abstract = "The Cody and Waite argument reduction technique works
perfectly for reasonably large arguments, but as the
input grows, there are no bits left to approximate the
constant with enough accuracy. Under mild assumptions,
we show that the result computed with a fused
multiply-add provides a fully accurate result for many
possible values of the input with a constant almost
accurate to the full working precision. We also present
an algorithm for a fully accurate second reduction step
to reach full double accuracy (all the significand bits
of two numbers are accurate) even in the worst cases of
argument reduction. Our work recalls the common
algorithms and presents proofs of correctness. All the
proofs are formally verified using the Coq automatic
proof checker.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Boldo:2009:KAC,
author = "S. Boldo",
title = "{Kahan}'s Algorithm for a Correct Discriminant
Computation at Last Formally Proven",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "220--225",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.200",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 12 08:51:00 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Kahan:2004:CFP} for the original
algorithm.",
abstract = "This article tackles Kahan's algorithm to compute
accurately the discriminant. This is a known difficult
problem, and this algorithm leads to an error bounded
by 2 ulps of the floating-point result. The proofs
involved are long and tricky and even trickier than
expected as the test involved may give a result
different from the result of the same test without
rounding. We give here the total demonstration of the
validity of this algorithm, and we provide sufficient
conditions to guarantee that neither overflow nor
underflow will jeopardize the result. The IEEE-754
double-precision program is annotated using the Why
platform and the proof obligations are done using the
Coq automatic proof checker.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Coq; correct rounding; discriminant; floating point;
formal proof; Why platform",
remark = "Extended version of ARITH-18 article
\cite{Boldo:2007:FVF}.",
}
@Article{Bryant:2009:ABD,
author = "Randal E. Bryant and Daniel Kroening and Jo{\"e}l
Ouaknine and Sanjit A. Seshia and Ofer Strichman and
Bryan Brady",
title = "An abstraction-based decision procedure for bit-vector
arithmetic",
journal = j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
volume = "11",
number = "2",
pages = "95--104",
month = apr,
year = "2009",
CODEN = "????",
ISSN = "1433-2779 (print), 1433-2787 (electronic)",
ISSN-L = "1433-2779",
bibdate = "Sat Sep 11 07:13:37 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1433-2779&volume=11&issue=2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1433-2779&volume=11&issue=2&spage=95",
acknowledgement = ack-nhfb,
fjournal = "International Journal on Software Tools for Technology
Transfer: STTT",
journal-URL = "http://link.springer.com/journal/10009",
}
@Article{Bullynck:2009:MAB,
author = "Maarten Bullynck",
title = "Modular arithmetic before {C. F. Gauss}:
Systematizations and discussions on remainder problems
in {18th-Century Germany}",
journal = j-HIST-MATH,
volume = "36",
number = "1",
pages = "48--72",
month = feb,
year = "2009",
CODEN = "HIMADS",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Jun 26 06:21:00 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086008000670",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860/",
}
@Article{Burtscher:2009:FHS,
author = "M. Burtscher and P. Ratanaworabhan",
title = "{FPC}: a High-Speed Compressor for Double-Precision
Floating-Point Data",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "1",
pages = "18--31",
month = jan,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.131",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4589203",
abstract = "Many scientific programs exchange large quantities of
double-precision data between processing nodes and with
mass storage devices. Data compression can reduce the
number of bytes that need to be transferred and stored.
However, data compression is only likely to be employed
in high-end computing environments if it does not
impede the throughput. This paper describes and
evaluates FPC, a fast lossless compression algorithm
for linear streams of 64-bit floating-point data. FPC
works well on hard-to-compress scientific data sets and
meets the throughput demands of high-performance
systems. A comparison with five lossless compression
schemes, BZIP2, DFCM, FSD, GZIP, and PLMI, on 4
architectures and 13 data sets shows that FPC
compresses and decompresses one to two orders of
magnitude faster than the other algorithms at the same
geometric-mean compression ratio. Moreover, FPC
provides a guaranteed throughput as long as the
prediction tables fit into the L1 data cache. For
example, on a 1.6-GHz Itanium 2 server, the throughput
is 670 Mbytes/s regardless of what data are being
compressed.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "BZIP2; data compression; DFCM; double-precision
floating-point data; floating point compression; FSD;
geometric-mean compression ratio; GZIP; linear streams;
lossless compression algorithm; PLMI; scientific data
sets compression; scientific programs",
}
@InProceedings{Cenk:2009:PMF,
author = "Murat Cenk and {\c{C}}etin Kaya Ko{\c{c}} and Ferruh
{\"O}zbudak",
title = "Polynomial Multiplication over Finite Fields Using
Field Extensions and Interpolation",
crossref = "Bruguera:2009:PIS",
pages = "84--91",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A method for polynomial multiplication over finite
fields using field extensions and polynomial
interpolation is introduced. The proposed method uses
polynomial interpolation as Toom--Cook method together
with field extensions. Furthermore, the proposed method
can be used when Toom--Cook method cannot be applied
directly. Explicit formulae improving the previous
results in many cases are obtained.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; correct rounding; floating-point
arithmetic",
}
@Article{Chabert:2009:PEA,
author = "Gilles Chabert and Luc Jaulin",
title = "A Priori Error Analysis and Spring Arithmetic",
journal = j-SIAM-J-SCI-COMP,
volume = "31",
number = "3",
pages = "2214--2230",
month = "????",
year = "2009",
CODEN = "SJOCE3",
DOI = "",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:44:16 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{Chen:2009:BDF,
author = "Dongdong Chen and Yu Zhang and Younhee Choi and Moon
Ho Lee and Seok-Bum Ko",
title = "A 32-bit Decimal Floating-Point Logarithmic
Converter",
crossref = "Bruguera:2009:PIS",
pages = "195--203",
year = "2009",
DOI = "https://doi.org/10.1109/ARITH.2009.22",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a new design and implementation of
a 32-bit decimal floating-point (DFP) logarithmic
converter based on the digit-recurrence algorithm. The
converter can calculate accurate logarithms of 32-bit
DFP numbers which are defined in the IEEE 754-2008
standard. Redundant digit $ e_1 $ is obtained by
look-up table in the first iteration and the rest
redundant digits $ e_j $ are selected by rounding the
scaled remainder during the succeeding iterations. The
sequential architecture of the proposed 32-bit DFP
logarithmic converter is implemented on Xilinx
Virtex-II Pro P30 FPGA device and then synthesized with
TMSC 0.18-$ \mu $ m standard cell library. The
implementation results indicate that the maximum
frequency of the proposed architecture is 47.7 MHz in
FPGA and 107.9 MHz in TMSC 0.18-$ \mu $ m technology.
The faithful 32-bit DFP logarithm results can be
obtained in 18 cycles.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; decimal floating-point; decimal logarithmic
converter; digit-recurrence algorithm; selection by
rounding.",
}
@InProceedings{Chen:2009:NDA,
author = "Dongdong Chen and Yu Zhang and D. Teng and K. Wahid
and Moon Ho Lee and Seok-Bum Ko",
title = "A new decimal antilogarithmic converter",
crossref = "IEEE:2009:IIS",
pages = "445--448",
year = "2009",
DOI = "https://doi.org/10.1109/ISCAS.2009.5117781",
bibdate = "Thu Feb 17 08:34:31 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cheng:2009:DSE,
author = "Chung-Kuan Cheng",
title = "Design Space Exploration for Power-Efficient
Mixed-Radix {Ling} Adders",
crossref = "Bruguera:2009:PIS",
pages = "212--212",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present an integer linear programming (ILP) method
that optimizes generalized prefix Ling adders in terms
of area, delay, and power. The contribution is listed
in the following.\par
(1) We devise an ILP formulation based on logical
effort models so that we can use ILP solver, CPLEX, to
produce minimum power solutions with given structural,
area and timing constraints. The formulation allows the
adjustment of parameters and constraints, e.g. the
radix numbers and the ratio of static and dynamic
power. We implement the flow for the users to
automatically synthesize the adders.\par
(2) We engineer sets of integer decision variables and
linear constraints to depict the prefix topology,
signal delay, and power characterization. Since the
design space of prefix adders is large, optimal
solutions are usually hard to generate without good
formulations. We generate redundant constraints to
prune the search space. The approach significantly
reduces the execution time.\par
(3) We explore mixed radices for prefix topologies,
i.e. GP cells have radices 2, 3, or 4, and a prefix
network can contain cells of different radices. This
mixed-radix feature expands the design space for better
solutions. High-radix adders reduce logic levels and
thus can serve for high performance applications. On
the other hand, high-radix cells take more logical
effort, longer parasitic delay, and more power
consumption. These factors are all taken care of in the
devised ILP formulation.\par
(4) We adopt the structure of Ling adders to produce
faster sum and carry responses. The experiments show
that Ling adders achieve better results than normal
prefix adders.\par
(5) We apply hierarchical design methods to handle high
bit-width modules. One weakness of ILP solver is the
scaleability of computational time with the bit-width.
We use a divide-and-conquer strategy to synthesize
64-bit adders.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
remark = "Only abstract published.",
}
@InProceedings{Chevillard:2009:CFC,
author = "Sylvain Chevillard and Mioara Joldes and Christoph
Lauter",
title = "Certified and Fast Computation of Supremum Norms of
Approximation Errors",
crossref = "Bruguera:2009:PIS",
pages = "169--176",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In many numerical programs there is a need for a
high-quality floating-point approximation of useful
functions $f$, such as such as $ \exp $, $ \sin $, $
\erf $. In the actual implementation, the function is
replaced by a polynomial $p$, which leads to an
approximation error (absolute or relative) $ \epsilon =
p - f $ or $ \epsilon = p / f - 1 $. The tight yet
certain bounding of this error is an important step
towards safe implementations. The problem is difficult
mainly because that approximation error is very small
and the difference $ p - f $ is subject to high
cancellation. Previous approaches for computing the
supremum norm in this degenerate case, have proven to
be unsafe, not sufficiently tight or too tedious in
manual work. We present a safe and fast algorithm that
computes a tight lower and upper bound for the supremum
norms of approximation errors. The algorithm is based
on a combination of several techniques, including
enhanced interval arithmetic, automatic differentiation
and isolation of the roots of a polynomial. We have
implemented our algorithm and give timings on several
examples.",
acknowledgement = ack-nhfb,
keywords = "approximation error; ARITH-19; automatic/algorithmic
differentiation; certified computation; elementary
function; interval arithmetic; roots isolation
technique.; supremum/infinity norm",
}
@Article{Cho:2009:AMD,
author = "H. Cho and E. E. Swartzlander",
title = "Adder and Multiplier Design in Quantum-Dot Cellular
Automata",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "6",
pages = "721--727",
month = jun,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.21",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:41 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4760137",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Chouliaras:2009:CLF,
author = "V. A. Chouliaras and K. Manolopoulos and D. Reisis",
title = "A configurable length, Fused Multiply-Add floating
point unit for a {VLIW} processor",
crossref = "Sezer:2009:IIS",
pages = "93--96",
year = "2009",
DOI = "https://doi.org/10.1109/SOCCON.2009.5398088",
bibdate = "Sun Feb 20 10:03:30 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The efficiency of fused multiply add units plays a key
role in the processor's performance for a variety of
applications. A design keeping the advantages of the
FMA regarding the latency and the hardware utilization
and also improving the result's accuracy in both
normalized and denormalized numbers is the subject of
this work. The FMA unit has configurable latency and it
is integrated in a VLIW processor. The VLSI TSMC 0.13
implementation achieved an operating frequency of 232.6
MHz and a final post-routed area of 121900.478 $ \mu $
m$^2$.",
acknowledgement = ack-nhfb,
}
@Article{Cilardo:2009:EBP,
author = "A. Cilardo",
title = "Efficient Bit-Parallel {$ \mathrm {GF}(2^m) $}
Multiplier for a Large Class of Irreducible
Pentanomials",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "7",
pages = "1001--1008",
month = jul,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.16",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4752811",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Colberg:2009:HAS,
author = "Peter H. Colberg and Felix H{\"o}fling",
title = "Highly accelerated simulations of glassy dynamics
using {GPUs}: caveats on limited floating-point
precision",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--12",
day = "20",
month = dec,
year = "2009",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in Comp. Phys. Comm. {\bf 182}, 1120
(2011).",
URL = "http://arxiv.org/abs/0912.3824",
abstract = "Modern graphics processing units (GPUs) provide
impressive computing resources, which can be accessed
conveniently through the CUDA programming interface. We
describe how GPUs can be used to considerably speed up
molecular dynamics (MD) simulations for system sizes
ranging up to about 1 million particles. Particular
emphasis is put on the numerical long-time stability in
terms of energy and momentum conservation, and caveats
on limited floating-point precision are issued. Strict
energy conservation over $ 10^8 $ MD steps is obtained
by double-single emulation of the floating-point
arithmetic in accuracy-critical parts of the algorithm.
For the slow dynamics of a supercooled binary
Lennard-Jones mixture, we demonstrate that the use of
single-floating point precision may result in
quantitatively and even physically wrong results. For
simulations of a Lennard-Jones fluid, the described
implementation shows speedup factors of up to 80
compared to a serial implementation for the CPU, and a
single GPU was found to compare with a parallelised MD
simulation using 64 distributed cores.",
acknowledgement = ack-nhfb,
subject = "Computational Physics (physics.comp-ph); Soft
Condensed Matter (cond-mat.soft); Distributed,
Parallel, and Cluster Computing (cs.DC)",
}
@InProceedings{Cornea:2009:IDF,
author = "Marius Cornea",
title = "{IEEE 754-2008} Decimal Floating-Point for {Intel}
Architecture Processors",
crossref = "Bruguera:2009:PIS",
pages = "225--228",
year = "2009",
DOI = "https://doi.org/10.1109/ARITH.2009.35",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A brief description is provided of the decimal
floating-point support available for Intel Architecture
processors, compliant with the IEEE Standard 754-2008
for Floating-Point Arithmetic [1]. Some performance
results are included.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Cornea:2009:SII,
author = "M. Cornea and J. Harrison and C. Anderson and P. Tang
and E. Schneider and E. Gvozdev",
title = "A Software Implementation of the {IEEE 754R} Decimal
Floating-Point Arithmetic Using the Binary Encoding
Format",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "148--162",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.209",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4674342",
abstract = "The IEEE Standard 754-1985 for Binary Floating-Point
Arithmetic [19] was revised [20], and an important
addition is the definition of decimal floating-point
arithmetic [8], [24]. This is intended mainly to
provide a robust reliable framework for financial
applications that are often subject to legal
requirements concerning rounding and precision of the
results, because the binary floating-point arithmetic
may introduce small but unacceptable errors. Using
binary floating-point calculations to emulate decimal
calculations in order to correct this issue has led to
the existence of numerous proprietary software
packages, each with its own characteristics and
capabilities. The IEEE 754R decimal arithmetic should
unify the ways decimal floating-point calculations are
carried out on various platforms. New algorithms and
properties are presented in this paper, which are used
in a software implementation of the IEEE 754R decimal
floating-point arithmetic, with emphasis on using
binary operations efficiently. The focus is on rounding
techniques for decimal values stored in binary format,
but algorithms are outlined for the more important or
interesting operations of addition, multiplication, and
division, including the case of nonhomogeneous
operands, as well as conversions between binary and
decimal floating-point formats. Performance results are
included for a wider range of operations, showing
promise that our approach is viable for applications
that require decimal floating-point calculations. This
paper extends an earlier publication [6].",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "binary-decimal conversion.; computer arithmetic;
correct rounding; decimal floating-point;
floating-point arithmetic; multiple-precision
arithmetic",
remark = "Extended version of ARITH-18 article
\cite{Cornea:2007:SII}.",
}
@Article{Csuros:2009:ACF,
author = "Miklos Csuros",
title = "Approximate counting with a floating-point counter",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "20",
month = apr,
year = "2009",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/0904.3062",
abstract = "Memory becomes a limiting factor in contemporary
applications, such as analyses of the Webgraph and
molecular sequences, when many objects need to be
counted simultaneously. Robert Morris [Communications
of the ACM, 21:840--842, 1978] proposed a probabilistic
technique for approximate counting that is extremely
space-efficient. The basic idea is to increment a
counter containing the value $X$ with probability $
2^{-X}$. As a result, the counter contains an
approximation of $ \lg n$ after $n$ probabilistic
updates stored in $ \lg \lg n$ bits. Here we revisit
the original idea of Morris, and introduce a binary
floating-point counter that uses a $d$-bit significand
in conjunction with a binary exponent. The counter
yields a simple formula for an unbiased estimation of
$n$ with a standard deviation of about $ 0.6 \cdot
n2^{-d / 2}$, and uses $ d + \lg \lg n$ bits. We
analyze the floating-point counter's performance in a
general framework that applies to any probabilistic
counter, and derive practical formulas to assess its
accuracy.",
acknowledgement = ack-nhfb,
subject = "Data Structures and Algorithms (cs.DS)",
}
@Article{Daumas:2009:VRN,
author = "M. Daumas and D. Lester and C. Muoz",
title = "Verified Real Number Calculations: a Library for
Interval Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "226--237",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.213",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4685896",
abstract = "Real number calculations on elementary functions are
remarkably difficult to handle in mechanical proofs. In
this paper, we show how these calculations can be
performed within a theorem prover or proof assistant in
a convenient and highly automated as well as
interactive way. First, we formally establish upper and
lower bounds for elementary functions. Then, based on
these bounds, we develop a rational interval arithmetic
where real number calculations take place in an
algebraic setting. In order to reduce the dependency
effect of interval arithmetic, we integrate two
techniques: interval splitting and Taylor series
expansions. This pragmatic approach has been developed,
and formally verified, in a theorem prover. The formal
development also includes a set of customizable
strategies to automate proofs involving explicit
calculations over real numbers. Our ultimate goal is to
provide guaranteed proofs of numerical properties with
minimal human theorem-prover interaction.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "interval arithmetic; proof checking; real number
calculations; theorem proving",
remark = "Extended version of ARITH-18 article
\cite{Daumas:2009:VRN}.",
}
@Article{Davida:2009:FAU,
author = "George Davida and Bruce Litow and Guangwu Xu",
title = "Fast arithmetics using {Chinese} remaindering",
journal = j-INFO-PROC-LETT,
volume = "109",
number = "13",
pages = "660--662",
day = "15",
month = jun,
year = "2009",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Thu Mar 31 15:53:33 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Book{Deschamps:2009:HIF,
author = "Jean-Pierre Deschamps and Jos{\'e} Luis Ima{\~n}a and
Gustavo D. Sutter",
title = "Hardware implementation of finite-field arithmetic",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xiii + 347",
year = "2009",
ISBN = "0-07-154581-6 (hardcover)",
ISBN-13 = "978-0-07-154581-5 (hardcover)",
LCCN = "TK7895.E42 D466 2009",
bibdate = "Sat Sep 20 16:04:08 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Electronic engineering",
abstract = "Master cutting-edge electronic circuit synthesis and
design with help from this detailed guide. Hardware
Implementation of Finite-Field Arithmetic describes
algorithms and circuits for executing finite-field
operations, including addition, subtraction,
multiplication, squaring, exponentiation, and
division.\par
This comprehensive resource begins with an overview of
mathematics, covering algebra, number theory, finite
fields, and cryptography. The book then presents
algorithms which can be executed and verified with
actual input data. Logic schemes and VHDL models are
described in such a way that the corresponding circuits
can be easily simulated and synthesized. The book
concludes with a real-world example of a finite-field
application --- elliptic-curve cryptography. This is an
essential guide for hardware engineers involved in the
development of embedded systems.",
acknowledgement = ack-nhfb,
author-dates = "1945--",
subject = "Embedded computer systems; Design and construction;
Field programmable gate arrays; Application-specific
integrated circuits; Computer arithmetic",
tableofcontents = "1. Mathematical background / 1--24 \\
2. Mod $m$ reduction / 25--60 \\
3. Mod $m$ operations / 61--90 \\
4. Operations over ${\rm GF}(p)$ / 91--116 \\
5. Operations over $Z_p[x] / f(x)$ / 117--138 \\
6. Operations over ${\rm GF}(p^n)$ / 139--162 \\
7. Operations over ${\rm GF}(2^m)$ --- Polynomial bases
/ 163--234 \\
8. Operations over ${\rm GF}(2^m)$ --- Normal bases /
235--268 \\
9. Operations over ${\rm GF}(2^m)$ --- Other bases /
269--286 \\
10. An Example of Application --- Elliptic curve
cryptography / 287--312 \\
Appendix A. $p = 2^{192} - 2^{64} - 1$ / 313--318 \\
Appendix B. Optical Extension Fields / 319--330 \\
Appendix C. Binary Fields / 331--334 \\
Appendix D. Ada versus VHDL / 337--340 \\
Index / 341--347",
}
@InProceedings{Dormiani:2009:DIR,
author = "P. Dormiani and M. D. Ercegovac and Jean-Michel
Muller",
title = "Design and Implementation of a Radix-4 Complex
Division Unit with Prescaling",
crossref = "IEEE:2009:IICa",
pages = "83--90",
year = "2009",
DOI = "https://doi.org/10.1109/ASAP.2009.32",
bibdate = "Fri Dec 03 15:01:28 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a design and implementation of a radix-4
complex division unit with prescaling of the operands.
Specifically, we extend the treatment of the residual
bound and errors due to the use of truncated redundant
representation. The requirements for prescaling tables
are simplified and a detailed specification of the
table design is given. All principal components used in
the design are described and the proposed optimizations
are explained. The target platform for implementation
was an Altera Stratix II FPGA for which we report
timing and area requirements. For a precision of 36
bits, the implementation uses 1185 ALUTs, achieving a
latency of 157 ns. The maximum clock frequency is
173.49 MHz.",
acknowledgement = ack-nhfb,
keywords = "Altera Stratix II FPGA; digital arithmetic; field
programmable gate arrays; frequency 173.49 MHz;
integrated circuit design; logic design; operand
prescaling; prescalers; prescaling tables; radix-4
complex division unit; table design",
}
@InProceedings{Dormiani:2009:LPT,
author = "Pouya Dormiani and Milo D. Ercegovac and Jean-Michel
Muller",
editor = "Michael B. Matthews",
booktitle = "{2009 Conference Record of the Forty-Third Asilomar
Conference on Signals, Systems and Computers. November
1--4, 2009. Pacific Grove, California}",
title = "Low precision table based complex reciprocal
approximation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1803--1807",
year = "2009",
DOI = "https://doi.org/10.1109/ACSSC.2009.5470209",
ISBN = "1-4244-5827-7",
ISBN-13 = "978-1-4244-5827-1",
ISSN = "1058-6393",
ISSN-L = "1058-6393",
bibdate = "Fri Sep 29 10:50:54 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Duff:2009:GMA,
author = "Bob Duff",
title = "Gem \#26: the {\tt mod} attribute",
journal = j-SIGADA-LETTERS,
volume = "29",
number = "1",
pages = "33--34",
month = apr,
year = "2009",
CODEN = "AALEE5",
DOI = "https://doi.org/10.1145/1541788.1541795",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Mon Jun 21 14:03:13 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
abstract = "Ada Gem \#26 --- T'Mod can be used to convert signed
integers to modular integers using modular (wraparound)
arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
}
@InProceedings{Edmonson:2009:IIS,
author = "William Edmonson and Guillaume Melquiond",
title = "{IEEE Interval Standard Working Group --- P1788}:
Current Status",
crossref = "Bruguera:2009:PIS",
pages = "231--234",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Late 2008, at SCAN 2008 in El Paso, TX, an effort to
standardize interval computations was started by a
working group of the IEEE Microprocessor Standards
Committee, titled the Interval Arithmetic Working Group
of the IEEE P1788 Standard. This paper describes the
goals of this effort, the history of the working group,
and how it relates to the IEEE 754 Standard. It gives a
brief overview of the policies and procedures for
constructing the standard, and its expected structure.
It also presents some of the questions the group may
have to solve in the future.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Enge:2009:CCP,
author = "Andreas Enge",
title = "The complexity of class polynomial computation via
floating point approximations",
journal = j-MATH-COMPUT,
volume = "78",
number = "266",
pages = "1089--1107",
month = apr,
year = "2009",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri May 14 06:20:58 MDT 2010",
bibsource = "http://www.ams.org/mcom/2009-78-266;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ams.org/journals/mcom/2009-78-266/S0025-5718-08-02200-X/home.html;
http://www.ams.org/journals/mcom/2009-78-266/S0025-5718-08-02200-X/S0025-5718-08-02200-X.pdf",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "roots of elliptic curves",
}
@Manual{Enge:2009:MLM,
author = "Andreas Enge and Philippe Th{\'e}veny and Paul
Zimmermann",
title = "{\texttt{mpc}} --- a library for multiprecision
complex arithmetic with exact rounding",
organization = "INRIA",
address = "France",
edition = "0.8.1",
month = dec,
year = "2009",
bibdate = "Sun May 2 09:31:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://mpc.multiprecision.org/",
acknowledgement = ack-nhfb,
}
@Article{Erle:2009:DFP,
author = "Mark A. Erle and Brian J. Hickmann and Michael J.
Schulte",
title = "Decimal Floating-Point Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "7",
pages = "902--916",
month = jul,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.218",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4711044",
abstract = "Decimal multiplication is important in many commercial
applications including financial analysis, banking, tax
calculation, currency conversion, insurance, and
accounting. This paper presents the design of two
decimal floating-point multipliers: one whose partial
product accumulation strategy employs decimal
carry-save addition and one that employs binary
carry-save addition. The multiplier based on decimal
carry-save addition favors a nonpipelined iterative
implementation. The multiplier utilizing binary
carry-save addition allows for an efficient pipelined
implementation when latency and throughput are
considered more important than area. Both designs
comply with specifications for decimal multiplication
given in the IEEE 754 Standard for Floating-Point
Arithmetic (IEEE 754-2008). The multipliers extend
previously published decimal fixed-point multipliers by
adding several features, including exponent generation,
sticky bit generation, shifting of the intermediate
product, rounding, and exception detection and
handling. Novel features of the multipliers include
support for decimal floating-point numbers, on-the-fly
generation of the sticky bit in the iterative design,
early estimation of the shift amount, and efficient
decimal rounding. Iterative and parallel decimal
fixed-point and floating-point multipliers are compared
in terms of their area, delay, latency, and throughput
based on verified Verilog register-transfer-level
models.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "arithmetic and logic units; binary coded decimal;
computer arithmetic; decimal multiplication;
floating-point arithmetic; general high-speed
arithmetic; parallel multiplication; pipelined
multiplication; serial multiplication",
}
@InProceedings{Fahmy:2009:EDI,
author = "Hossam A. H. Fahmy and Ramy Raafat and Amira M.
Abdel-Majeed and Rodina Samy and Tarek ElDeeb and
Yasmin Farouk",
title = "Energy and Delay Improvement via Decimal Floating
Point Units",
crossref = "Bruguera:2009:PIS",
pages = "221--224",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Interest in decimal arithmetic increased considerably
in recent years. This paper presents new designs for
decimal floating point (DFP) addition, multiplication,
fused multiply-add, division, and square root. It
stresses the importance of energy savings achieved by
hardware implementations of the IEEE standard for
decimal floating point. To the best of the authors
knowledge, this is the first work to discuss energy
savings in DFP and the first to present a hardware
implementation of a fused multiply-add. Our
Newton--Raphson based divider is over three times
faster than the similar design previously reported.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Fewster:2009:SEB,
author = "R. M. Fewster",
title = "A Simple Explanation of {Benford's Law}",
journal = j-AMER-STAT,
volume = "63",
number = "1",
pages = "26--32",
month = feb,
year = "2009",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/tast.2009.0005",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Thu Aug 26 21:48:27 MDT 2010",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Fit-Florea:2009:DLN,
author = "A. Fit-Florea and L. Li and M. A. Thornton and D. W.
Matula",
title = "A Discrete Logarithm Number System for Integer
Arithmetic Modulo $ 2^k $: Algorithms and Lookup
Structures",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "163--174",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.204",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663061",
abstract = "We present a $k$-bit encoding of the $k$-bit binary
integers based on a discrete logarithm representation.
The representation supports a discrete logarithm number
system (DLS) that allows integer multiplication to be
reduced to addition and integer exponentiation to be
reduced to multiplication. We introduce right-to-left
bit serial conversion, deconversion, and unified
conversion/deconversion algorithms between binary and
DLS. The conversion algorithms utilize $ O(k) $
additions, do not require the use of a multiplier, and
are applicable at least up to 128-bit integers. We
illustrate the use of the representation in determining
a novel and efficient integer power modulo $ 2^k $
operation $ |x^y|_{2k} $ and compare hardware
performance with a current state-of-the-art method.
Furthermore, we describe properties of the conversion
mappings that allow compact table lookup structures to
be employed for direct conversion to and deconversion
from the DLS encoding. Our lookup architecture allows
16-bit conversion and deconversion mappings to be
realized with table sizes of order 2--8 Kbytes, which
is up to a $ 64 \times $ size reduction of the 128
Kbytes of an arbitrary 16-bits-in, 16-bits-out function
table. Performance and area results that demonstrate
the effectiveness of the table lookup architecture are
given. The lookup methodology extends to other 16-bit
integer functions such as multiplicative inverse and
squaring operations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "arithmetic and logic units; bit serial; computer
arithmetic; conversions; discrete logarithm; high-speed
arithmetic; integer power; number encodings; table
lookup",
}
@Article{Fraysse:2009:ASF,
author = "Val{\'e}rie Frayss{\'e} and Luc Giraud and Serge
Gratton",
title = "{Algorithm 881}: a Set of Flexible {GMRES} Routines
for Real and Complex Arithmetics on High-Performance
Computers",
journal = j-TOMS,
volume = "35",
number = "2",
pages = "13:1--13:12",
month = jul,
year = "2009",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1377612.1377617",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Aug 5 18:13:00 MDT 2008",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this article we describe our implementations of the
FGMRES algorithm for both real and complex, single and
double precision arithmetics suitable for serial,
shared-memory, and distributed-memory computers. For
the sake of portability, simplicity, flexibility, and
efficiency, the FGMRES solvers have been implemented in
Fortran 77 using the reverse communication mechanism
for the matrix-vector product, the preconditioning, and
the dot-product computations. For distributed-memory
computation, several orthogonalization procedures have
been implemented to reduce the cost of the dot-product
calculation, which is a well-known bottleneck of
efficiency for Krylov methods. Furthermore, either
implicit or explicit calculation of the residual at
restart is possible depending on the actual cost of the
matrix-vector product. Finally, the implemented
stopping criterion is based on a normwise backward
error.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "distributed memory; FGMRES; flexible Krylov methods;
high-performance computing; linear systems; reverse
communication",
}
@Article{Furer:2009:FIM,
author = "Martin F{\"u}rer",
title = "Faster Integer Multiplication",
journal = j-SIAM-J-COMPUT,
volume = "39",
number = "3",
pages = "979--1005",
month = "????",
year = "2009",
CODEN = "SMJCAT",
DOI = "",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Tue May 18 08:22:12 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/39/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{Gavrilova:2009:ESC,
author = "Marina L. Gavrilova",
title = "An Explicit Solution for Computing the Vertices of the
{Euclidean} $d$-Dimensional {Voronoi} Diagram of
Spheres in a Floating-Point Arithmetic",
journal = j-INT-J-COMPUT-GEOM-APPL,
volume = "19",
number = "5",
pages = "415--424",
month = oct,
year = "2009",
CODEN = "IJCAEV",
DOI = "https://doi.org/10.1142/S0218195909003040",
ISSN = "0218-1959",
bibdate = "Mon Aug 30 10:25:06 MDT 2010",
bibsource = "http://ejournals.wspc.com.sg/ijcga/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International journal of computational geometry and
applications",
journal-URL = "http://www.worldscientific.com/loi/ijcga",
}
@InCollection{Gentle:2009:CSA,
author = "James E. Gentle",
booktitle = "Computational Statistics",
title = "Computer Storage and Arithmetic",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xxi + 727",
pages = "85--105",
year = "2009",
DOI = "https://doi.org/10.1007/978-0-387-98144-4_2",
ISBN = "0-387-98143-8 (print), 0-387-98144-6 (electronic)",
ISBN-13 = "978-0-387-98143-7 (print), 978-0-387-98144-4
(electronic)",
LCCN = "QA276.4 .G46 2009",
bibdate = "Mon May 06 17:36:21 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Statistics and Computing",
URL = "http://link.springer.com/chapter/10.1007/978-0-387-98144-4_2",
acknowledgement = ack-nhfb,
tableofcontents = "Part I, Preliminaries. Mathematical and statistical
preliminaries \\
Part II, Statistical computing \\
Computer storage and arithmetic \\
algorithm and programming \\
Approximation of functions and numerical quadrature \\
Numerical linear algebra \\
Solution of nonlinear equations and optimization \\
Generation of random numbers \\
Part III, Methods of computational statistics \\
Graphical methods in computational statistics \\
Tools for identification of structure in data \\
Estimation of functions \\
Monte Carlo methods for statistical inference \\
Data randomization, partitioning, and augmentation \\
Bootstrap methods \\
Part IV, Exploring data density and relationships \\
Estimation of probability density functions using
parametric models \\
Nonparametric estimation of probability density
functions \\
Statistical learning and data mining \\
Statistical models of dependencies",
}
@InProceedings{Gonzalez-Navarro:2009:CDB,
author = "Sonia Gonzalez-Navarro and Alberto Nannarelli and
Michael J. Schulte and Charles Tsen",
title = "A combined decimal and binary floating-point divider",
crossref = "Matthews:2009:CRF",
pages = "930--934",
year = "2009",
DOI = "https://doi.org/10.1109/ACSSC.2009.5470014",
bibdate = "Thu Feb 17 08:16:50 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, we present the hardware design of a
combined decimal and binary floating-point divider,
based on specifications in the IEEE 754-2008 Standard
for Floating-point Arithmetic. In contrast to most
recent decimal divider designs, which are based on the
Binary Coded Decimal (BCD) encoding, our divider
operates on either 64-bit binary encoded decimal
floating-point (DFP) numbers or 64-bit binary
floating-point (BFP) numbers. The division approach
implemented in our design is based on a
digit-recurrence algorithm. We describe the hardware
resources shared between the two floating-point
datatypes and demonstrate that hardware sharing is
advantageous. Compared to a standalone DFP divider, the
combined divider has the same worst case delay and 17\%
more area.",
acknowledgement = ack-nhfb,
}
@InProceedings{Gorgin:2009:FRD,
author = "Saeid Gorgin and Ghassem Jaberipur",
title = "Fully Redundant Decimal Arithmetic",
crossref = "Bruguera:2009:PIS",
pages = "145--152",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Hardware implementation of all the basic radix-10
arithmetic operations is evolving as a new trend in the
design and implementation of general purpose digital
processors. Redundant representation of partial
products and remainders is common in the multiplication
and division hardware algorithms, respectively.
Carry-free implementation of the more frequent
add/subtract operations, with the byproduct of
enhancing the speed of multiplication and division, is
possible with redundant number representation. However,
conversion of redundant results to conventional
representations entails slow carry propagation that can
be avoided if the results are kept in redundant format
for later use as operands of other arithmetic
operations. Given that redundant decimal
representations, contrary to redundant binary, do not
necessarily require extra storage, we are motivated to
develop a framework for fully redundant decimal
arithmetic, where all operands and results belong to
the same redundant decimal number system and can be
stored and later used as operands of further decimal
operations. In this paper, we present a new faster
decimal signed digit add/sub unit and show how it can
be efficiently used in the design of decimal
multipliers and dividers, where all operands and
results are represented with the same redundant digit
set $ [ - 7, 7] $.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Graillat:2009:AAV,
author = "Stef Graillat and Philippe Langlois and Nicolas
Louvet",
title = "Algorithms for accurate, validated and fast polynomial
evaluation",
journal = j-JAPAN-J-INDUST-APPL-MATH,
volume = "26",
number = "2--3",
pages = "191--214",
year = "2009",
CODEN = "JAPJI7",
ISSN = "0916-7005 (print), 1868-937x (electronic)",
bibdate = "Sat Jun 4 17:41:42 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Japan Journal of Industrial and Applied Mathematics",
}
@Article{Graillat:2009:AFP,
author = "Stef Graillat",
title = "Accurate Floating-Point Product and Exponentiation",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "7",
pages = "994--1000",
month = jul,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.215",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4711041",
abstract = "Several different techniques and softwares intend to
improve the accuracy of results computed in a fixed
finite precision. Here, we focus on a method to improve
the accuracy of the product of floating-point numbers.
We show that the computed result is as accurate as if
computed in twice the working precision. The algorithm
is simple since it only requires addition, subtraction,
and multiplication of floating-point numbers in the
same working precision as the given data. Such an
algorithm can be useful for example to compute the
determinant of a triangular matrix and to evaluate a
polynomial when represented by the root product form.
It can also be used to compute the integer power of a
floating-point number.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "accurate product; computer arithmetic; error analysis;
error-free transformations; exponentiation; faithful
rounding; finite precision; floating-point arithmetic;
numerical algorithms",
}
@Article{Gu:2009:SDB,
author = "Haihua Gu and Dawu Gu",
title = "Speeding Up the Double-Base Recoding Algorithm of
Scalar Multiplication",
journal = j-CRYPTOLOGIA,
volume = "33",
number = "4",
pages = "315--320",
year = "2009",
CODEN = "CRYPE6",
ISSN = "0161-1194 (print), 1558-1586 (electronic)",
ISSN-L = "0161-1194",
bibdate = "Tue Aug 31 11:44:06 MDT 2010",
bibsource = "http://www.tandf.co.uk/journals/titles/01611194.asp;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Cryptologia",
journal-URL = "http://www.tandfonline.com/loi/ucry20",
}
@InProceedings{Guralnik:2009:ISV,
author = "Elena Guralnik and Ariel J. Birnbaum and Anatoly
Koyfman and Avi Kaplan",
title = "Implementation Specific Verification of Divide and
Square Root Instructions",
crossref = "Bruguera:2009:PIS",
pages = "114--121",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point operations such as divide and square
root are typically implemented in microcode rather than
dedicated logic. Bugs in these operations missed by
generic black-box verification tools, were analyzed.
This led to the conclusion that the corner cases, in
addition to being implementation dependent, could not
be characterized in terms of special input or output
values in a straightforward manner.\par
However, many of those cases can be easily generalized
for many known implementations. The typical
implementation uses a known iterative approximation
algorithm, such as the Newton--Raphson method, to
calculate the desired result; thus, it is sufficient to
produce the corner cases associated with the specific
algorithm.\par
We investigated the following problem: given an
iterative algorithm to compute a binary floating point
operation, the iteration number, and an interval, find
random inputs for the operation that, after the
requested iteration, yield a relative error within the
specified interval. This paper describes a method to
solve this problem. This method was implemented in a
floating-point test generator and is currently being
used to verify the floating-point units of several
processors.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Han:2009:ICS,
author = "Dong-Guk Han and Dooho Choi and Howon Kim",
title = "Improved Computation of Square Roots in Specific
Finite Fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "188--196",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.201",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663058",
abstract = "In this paper, we study exponentiation in the specific
finite fields $ F_q $ with very special exponents such
as those that occur in algorithms for computing square
roots. Here, $q$ is a prime power, $ q = p^k $, where $
k > 1 $, and $k$ is odd. Our algorithmic approach
improves the corresponding exponentiation resulted from
the better rewritten exponent. To the best of our
knowledge, it is the first major improvement to the
Tonelli--Shanks algorithm, for example, the number of
multiplications can be reduced to at least 60 percent
on the average when $ p \equiv 1 \pmod 16 $. Several
numerical examples are given that show the speedup of
the proposed methods.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "cryptography; efficient computation; finite fields;
square roots",
}
@Article{Hariri:2009:BSB,
author = "A. Hariri and A. Reyhani-Masoleh",
title = "Bit-Serial and Bit-Parallel {Montgomery}
Multiplication and Squaring over {$ \mathrm {GF}(2^m)
$}",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "10",
pages = "1332--1345",
month = oct,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.70",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4912195",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Harrison:2009:DTB,
author = "John Harrison",
title = "Decimal Transcendentals via Binary",
crossref = "Bruguera:2009:PIS",
pages = "187--194",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We describe the design and implementation of a
comprehensive library of transcendental functions for
the new IEEE decimal floating-point formats. In
principle, such functions are very much analogous to
their binary counterparts, though with a few additional
subtleties connected with `scale' (preferred exponent).
But our approach has been not to employ direct
techniques, but rather to re-use existing binary
functions as much as possible, both for greater
efficiency and ease of implementation. For some
functions the most straightforward approach (convert
from decimal to binary, perform binary operation,
convert back) works well. In many cases, however, these
are insufficiently accurate, and subtler approaches
must be used.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@InProceedings{Harrison:2009:FAB,
author = "John Harrison",
title = "Fast and Accurate {Bessel} Function Computation",
crossref = "Bruguera:2009:PIS",
pages = "104--113",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Bessel functions are considered relatively
difficult to compute. Although they have a simple power
series expansion that is everywhere convergent, they
exhibit approximately periodic behavior which makes the
direct use of the power series impractically slow and
numerically unstable. We describe an alternative method
based on systematic expansion around the zeros,
refining existing techniques based on Hankel
expansions, which mostly avoids the use of
multiprecision arithmetic while yielding accurate
results.",
acknowledgement = ack-nhfb,
keywords = "$J0(x), J1(1), Y0(x), Y1(1)$; ARITH-19; ordinary
Bessel functions of the first and second kinds",
}
@InProceedings{Hasan:2009:SSC,
author = "M. A. Hasan and C. Negre",
title = "Subquadratic Space Complexity Multiplier for a Class
of Binary Fields Using {Toeplitz} Matrix Approach",
crossref = "Bruguera:2009:PIS",
pages = "67--75",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In the recent past, subquadratic space complexity
multipliers have been proposed for binary fields
defined by irreducible trinomials and some specific
pentanomials. For such multipliers, alternative
irreducible polynomials can also be used, in
particular, nearly all one polynomials (NAOPs) seem to
be better than pentanomials (see [7]). For improved
efficiency, multiplication modulo an NAOP is performed
via modulo a quadrinomial whose degree is one more than
that of the original NAOP. In this paper, we present a
Toeplitz matrix-vector product based approach for
multiplication modulo a quadrinomial. We obtain a fully
parallel (nonsequential) multiplier with a subquadratic
space complexity, which has the same order of space
complexity as that of Fan and Hasan [4].\par
The Toeplitz matrix-vector product based approach is
also interesting in the design of sequential
multipliers. In this paper, we present two such
multipliers: one with bit serial output and the other
bit parallel output.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; binary field; double basis; multiplication;
subquadratic complexity",
}
@Article{Hinek:2009:ALS,
author = "M. Jason Hinek and Charles C. Y. Lam",
title = "Another look at some fast modular arithmetic methods",
journal = j-J-MATH-CRYPTOL,
volume = "3",
number = "2",
pages = "165--174",
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1515/JMC.2009.008",
ISSN = "1862-2976 (print), 1862-2984 (electronic)",
ISSN-L = "1862-2976",
MRclass = "68W40 (94A60)",
MRnumber = "2590262",
bibdate = "Fri Mar 17 08:36:49 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jmathcryptol.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Cryptology",
journal-URL = "http://www.degruyter.com/view/j/jmc",
}
@Article{Ho:2009:FPF,
author = "C. H. Ho and C. W. Yu and P. Leong and W. Luk and S.
J. E. Wilton",
title = "Floating-point {FPGA}: architecture and modeling",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "17",
number = "12",
pages = "1709--1718",
year = "2009",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2008.2006616",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Thu Mar 24 20:51:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@Book{ISO:2009:IIT,
author = "{International Organization for Standardization}",
title = "{ISO/IEC TR 24732:2009} Information technology ---
Programming languages, their environments and system
software interfaces --- Extension for the programming
language {C} to support decimal floating-point
arithmetic",
publisher = pub-ISO,
address = pub-ISO:adr,
year = "2009",
LCCN = "????",
bibdate = "Thu Nov 25 08:56:44 2010",
bibsource = "http://www.iso.org/iso/search.htm;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Technical report",
URL = "http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=38842",
acknowledgement = ack-nhfb,
subject = "programming languages (electronic computers)",
}
@Article{Jaberipur:2009:ISP,
author = "G. Jaberipur and A. Kaivani",
title = "Improving the Speed of Parallel Decimal
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "11",
pages = "1539--1552",
month = nov,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.110",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:44 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5184812",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Jaberipur:2009:UAD,
author = "Ghassem Jaberipur and Behrooz Parhami",
title = "Unified Approach to the Design of Modulo-$ (2^n \pm 1)
$ Adders Based on Signed-{LSB} Representation of
Residues",
crossref = "Bruguera:2009:PIS",
pages = "57--64",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Moduli of the form $ 2 n \pm 1 $, which greatly
simplify certain arithmetic operations in residue
number systems (RNS), have been of longstanding
interest. A steady stream of designs for modulo-$ 2 n
\pm 1 $ adders has rendered the latency of such adders
quite competitive with ordinary adders. The next
logical step is to approach the problem in a unified
and systematic manner that does not require each design
to be taken up from scratch and to undergo the
error-prone and labor-intensive optimization for high
speed and low power dissipation. Accordingly, we devise
a new redundant representation of mod-$ 2 n \pm 1 $
residues that allows ordinary fast adders and a small
amount of peripheral logic to be used for mod-$ 2 n \pm
1 $ addition. Advantages of the building-block approach
include shorter design time, easier exploration of the
design space (area\slash speed\slash power tradeoffs),
and greater confidence in the correctness of the
resulting circuits. Advantages of the unified design
include the possibility of fault-tolerant and
gracefully degrading RNS circuit realizations with
fairly low hardware redundancy.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@InProceedings{James:2009:HPL,
author = "R. K. James and K. P. Jacob and S. Sasi",
title = "High performance, low latency double digit decimal
multiplier on {ASIC} and {FPGA}",
crossref = "Abraham:2009:WCN",
pages = "1445--1450",
year = "2009",
DOI = "https://doi.org/10.1109/NABIC.2009.5393703",
bibdate = "Thu Feb 17 08:43:10 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Decimal multiplication is an integral part of
financial, commercial, and Internet-based computations.
This paper presents a novel double digit decimal
multiplication (DDDM) technique that offers low latency
and high throughput. This design performs two digit
multiplications simultaneously in one clock cycle.
Double digit fixed point decimal multipliers for
7digit, 16 digit and 34 digit are simulated using
Leonardo Spectrum from Mentor Graphics Corporation
using ASIC Library. The paper also presents area and
delay comparisons for these fixed point multipliers on
Xilinx, Altera, Actel and Quick logic FPGAs. This
multiplier design can be extended to support decimal
floating point multiplication for IEEE 754-2008
standard.",
acknowledgement = ack-nhfb,
}
@InProceedings{Jeannerod:2009:NBF,
author = "Claude-Pierre Jeannerod and Herv{\'e} Knochel and
Christophe Monat and Guillaume Revy and Gilles
Villard",
title = "A New Binary Floating-Point Division Algorithm and Its
Software Implementation on the {ST231} Processor",
crossref = "Bruguera:2009:PIS",
pages = "95--103",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper deals with the design and implementation of
low latency software for binary floating-point division
with correct rounding to nearest. The approach we
present here targets a VLIW integer processor of the
ST200 family, and is based on fast and accurate
programs for evaluating some particular bivariate
polynomials. We start by giving approximation and
evaluation error conditions that are sufficient to
ensure correct rounding. Then we describe the
heuristics used to generate such evaluation programs,
as well as those used to automatically validate their
accuracy. Finally, we propose, for the binary32 format,
a complete C implementation of the resulting division
algorithm. With the ST200 compiler and compared to
previous implementations, the speed-up observed with
our approach is by a factor of almost 1.8.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; binary floating-point division; code
generation and validation; correct rounding; polynomial
evaluation; VLIW integer processor",
}
@Article{Jiang:2009:FPA,
author = "D. Jiang and N. F. Stewart",
title = "Floating-Point Arithmetic for Computational Geometry
Problems with Uncertain Data",
journal = j-INT-J-COMPUT-GEOM-APPL,
volume = "19",
number = "4",
pages = "371--385",
month = aug,
year = "2009",
CODEN = "IJCAEV",
DOI = "https://doi.org/10.1142/S0218195909003015",
ISSN = "0218-1959",
bibdate = "Mon Aug 30 10:25:06 MDT 2010",
bibsource = "http://ejournals.wspc.com.sg/ijcga/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "International journal of computational geometry and
applications",
journal-URL = "http://www.worldscientific.com/loi/ijcga",
xxnote = "Check downcased title string??",
}
@InProceedings{Kaivola:2009:RTF,
author = "Roope Kaivola and Rajnish Ghughal and Naren Narasimhan
and Amber Telfer and Jesse Whittemore and Sudhindra
Pandav and Anna Slobodov{\'a} and Christopher Taylor
and Vladimir Frolov and Erik Reeber and Armaghan Naik",
title = "Replacing Testing with Formal Verification in
{Intel{\reg} Core{\TM} i7} Processor Execution Engine
Validation",
crossref = "Bouajjani:2009:CAV",
pages = "414--429",
year = "2009",
DOI = "https://doi.org/10.1007/978-3-642-02658-4_32",
ISBN = "3-642-02658-3",
ISBN-13 = "978-3-642-02658-4",
bibdate = "Fri Dec 8 13:33:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Keaton:2009:IIR,
author = "David Keaton and Thomas Plum and Robert C. Seacord and
David Svoboda and Alex Volkovitsky and Timothy Wilson",
title = "As-if Infinitely Ranged Integer Model",
type = "Technical Note",
number = "CMU/SEI-2009-TN-023",
institution = "Carnegie-Mellon University Software Engineering
Institute",
address = "Pittsburgh, PA, USA",
month = jul,
year = "2009",
bibdate = "Fri Aug 23 08:27:41 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://resources.sei.cmu.edu/asset_files/TechnicalNote/2009_004_001_15074.pdf;
https://resources.sei.cmu.edu/library/asset-view.cfm?assetid=9019",
abstract = "Integer overflow and wraparound are major causes of
software vulnerabilities in the C and C++ programming
languages. In this paper we present the as-if
infinitely ranged (AIR) integer model, which provides a
largely automated mechanism for eliminating integer
overflow and integer truncation. The AIR integer model
either produces a value equivalent to one that would
have been obtained using infinitely ranged integers or
results in a runtime constraint violation. Unlike
previous integer models, AIR integers do not require
precise traps, and consequently do not break or inhibit
most existing optimizations.",
acknowledgement = ack-nhfb,
keywords = "integer overflow; integer wraparound",
}
@Article{Kim:2009:FPU,
author = "Donghyun Kim and Lee-Sup Kim",
title = "A Floating-Point Unit for {$4$D} Vector Inner Product
with Reduced Latency",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "7",
pages = "890--901",
month = jul,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.210",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4674343",
abstract = "This paper presents the algorithm and implementation
of a new high-performance functional unit for
floating-point four-dimensional vector inner product
(4D dot product; DP4), which is most frequently
performed in 3D graphics application. The proposed
IEEE-compliant DP4 unit computes $ {\rm Z} = {\rm AB} +
{rm CD} + {\rm EF} + {\rm GH} $ in one path and keeps
the intermediate rounding by IEEE-754 rounding to
nearest even. The intermediate rounding is merged with
shift alignment, and intermediate carry-propagated
addition and normalization are omitted to reduce
latency in the proposed architecture. The proposed DP4
unit is implemented with 0.18-$ \mu $ m CMOS technology
and has 12.8-ns critical path delay, which is reduced
by 45.5 percent compared to a previous DP4
implementation using discrete multipliers and adders.
The proposed DP4 unit also reduces the cycle time of 3D
graphics applications by 12.4 percent on the average
compared to the usual 3D graphics FPU based on four-way
multiply-add-fused units.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "3D graphics; DP4; floating point arithmetic; graphics
processors; vector inner product",
}
@InProceedings{Kornerup:2009:CCR,
author = "P. Kornerup and V. Lef{\`e}vre and N. Louvet and
Jean-Michel Muller",
title = "On the Computation of Correctly-Rounded Sums",
crossref = "Bruguera:2009:PIS",
pages = "155--160",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a study of some basic blocks
needed in the design of floating-point summation
algorithms. In particular, we show that among the set
of the algorithms with no comparisons performing only
floating-point additions\slash subtractions, the 2Sum
algorithm introduced by Knuth is minimal, both in terms
of number of operations and depth of the dependency
graph. Under reasonable conditions, we also prove that
no algorithms performing only round-to-nearest
additions\slash subtractions exist to compute the
round-to-nearest sum of at least three floating-point
numbers. Starting from an algorithm due to Boldo and
Melquiond, we also present new results about the
computation of the correctly-rounded sum of three
floating-point numbers.",
acknowledgement = ack-nhfb,
keywords = "2Sum and Fast2Sum algorithms; ARITH-19; correct
rounding; floating-point arithmetic; summation
algorithms",
}
@Article{Kornerup:2009:GEI,
author = "Peter Kornerup and Paolo Montuschi and Jean-Michel
Muller and Eric Schwarz",
title = "{Guest Editors}' Introduction: Special Section on
Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "145--147",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.11",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4740165",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lang:2009:DUB,
author = "T. Lang and A. Nannarelli",
title = "Division Unit for Binary Integer Decimals",
crossref = "IEEE:2009:IICa",
pages = "1--7",
year = "2009",
DOI = "https://doi.org/10.1109/ASAP.2009.42",
bibdate = "Sat Dec 04 06:56:17 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this work, we present a radix-10 division unit that
is based on the digit-recurrence algorithm and
implements binary encodings (binary integer decimal or
BID) for significands. Recent decimal division designs
are all based on the binary coded decimal (BCD)
encoding. We adapt the radix-10 digit-recurrence
algorithm to BID representation and implement the
division unit in standard cell technology. The
implementation of the proposed BID division unit is
compared to that of a BCD based unit implementing the
same algorithm. The comparison shows that for
normalized operands the BID unit has the same latency
as the BCD unit and reduced area, but the normalization
is more expensive when implemented in BID.",
acknowledgement = ack-nhfb,
keywords = "adders; BID floating-point adder; BID floating-point
multiplier; binary coded decimal encoding; binary
integer decimals; computer arithmetic; decimal
arithmetic; decimal division designs; digit-recurrence
algorithm; digital arithmetic; division; multiplying
circuits; radix-10 digit-recurrence algorithm; radix-10
division unit",
}
@Article{Lauter:2009:ERB,
author = "C. Q. Lauter and V. Lefevre",
title = "An Efficient Rounding Boundary Test for {\tt pow(x,
y)} in Double Precision",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "197--207",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.202",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663059",
abstract = "The correct rounding of the function $ \textrm {pow} :
(x, y) \rightarrow x^y $ is currently based on Ziv's
iterative approximation process. In order to ensure its
termination, cases when $ x^y $ falls on a
rounding-boundary must be filtered out. Such
rounding-boundaries are floating-point numbers and
midpoints between two consecutive floating-point
numbers. Detecting rounding-boundaries for pow is a
difficult problem. Previous approaches use repeated
square root extraction followed by repeated square and
multiply. This paper presents a new rounding-boundary
test for pow in double precision, which reduces this to
a few comparisons with precomputed constants. These
constants are deduced from worst cases for the Table
Maker's Dilemma, searched over a small subset of the
input domain. This is a novel use of such worst-case
bounds. The resulting algorithm has been designed for a
fast-on-average correctly rounded implementation of
pow, considering the scarcity of rounding-boundary
cases. It does not stall average computations for
rounding-boundary detection. This paper includes its
correctness proof and experimental results.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "correct rounding; floating-point arithmetic; power
function.",
}
@Article{Li:2009:FAT,
author = "Xin Li and Marc Moreno Maza and {\'E}ric Schost",
title = "Fast arithmetic for triangular sets: From theory to
practice",
journal = j-J-SYMBOLIC-COMP,
volume = "44",
number = "7",
pages = "891--907",
month = jul,
year = "2009",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Wed Aug 25 20:13:19 MDT 2010",
bibsource = "http://www.sciencedirect.com/science/journal/07477171;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
}
@TechReport{Maclaren:2009:HCH,
author = "N. M. Maclaren",
title = "How Computers Handle Numbers: a.k.a. Computer
Arithmetic Uncovered",
type = "Course notes",
institution = "Cambridge University Computing Service",
address = "Cambridge, UK",
month = jul,
year = "2009",
bibdate = "Tue Apr 27 09:48:59 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www-uxsup.csx.cam.ac.uk/courses/Arithmetic/notes.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Martel:2009:PTN,
author = "Matthieu Martel",
editor = "Germ{\'a}n Puebla",
booktitle = "{Proceedings of the 2009 ACM SIGPLAN Workshop on
Partial Evaluation and Program Manipulation ---
PEPM'09: Savannah, Georgia, USA, January 19--20,
2009}",
title = "Program transformation for numerical precision",
publisher = "{ACM} Press",
pages = "101--110",
year = "2009",
DOI = "https://doi.org/10.1145/1480945.1480960",
ISBN = "1-60558-327-8",
ISBN-13 = "978-1-60558-327-3",
bibdate = "Thu Oct 17 05:52:02 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/citation.cfm?doid=1480945.1480960",
abstract = "This article introduces a new program transformation
in order to enhance the numerical accuracy of
floating-point computations. We consider that a program
would return an exact result if the computations were
carried out using real numbers. In practice, roundoff
errors due to the finite representation of values arise
during the execution. These errors are closely related
to the way formulas are evaluated. Indeed,
mathematically equivalent formulas, obtained using laws
like associativity, distributivity, etc., may lead to
very different numerical results in the computer
arithmetic. We propose a semantics-based transformation
in order to optimize the numerical accuracy of
programs. This transformation is expressed in the
abstract interpretation framework and it aims at
rewriting pieces of numerical codes in order to obtain
results closer to what the computer would output if it
used the exact arithmetic.",
acknowledgement = ack-nhfb,
}
@InProceedings{Matula:2009:HRS,
author = "David W. Matula",
title = "Higher Radix Squaring Operations Employing
Left-to-Right Dual Recoding",
crossref = "Bruguera:2009:PIS",
pages = "39--47",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We introduce a novel left-to-right leading digit first
dual recoding of an operand for the purpose of
designing the squaring operation on that operand. Our
dual recoding yields an array of non-negative partial
squares of size essentially one half that of a
comparable multiplier partial product array for both
radix-4 and radix-8 designs. For radix-8 design the
128-bit square of a 64-bit operand can be obtained from
a consolidated partial square array of just 11 rows. We
describe advantages of our left-to-right recoding
compared to a previous right-to-left Booth-folding
encoding applicable to radix-4. We also show
simplifications available to the designs of a rounded
floating point square operation and to a low precision
approximate square.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; Booth multiplier recoding; Booth-folding;
partial products; partial squares; sign extension.;
squarer",
}
@InProceedings{Mazor:2009:HPC,
author = "Stanley Mazor",
title = "A Historical Perspective on Computer Arithmetic",
crossref = "Bruguera:2009:PIS",
pages = "35--35",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; Intel 4004; Intel 8080",
remark = "Only abstract published.",
}
@Book{Miller:2009:RNR,
editor = "Frederic P. Miller and Agnes F. Vandome and John
McBrewster",
title = "Roman Numerals: Roman numeral analysis, Roman
arithmetic, Roman abacus, {Kharosthi}, {Unicode}
numerals, {Etruscan} numerals, Positional notation,
Arabic numerals, Districts of {Turku}",
publisher = "Alphascript Publishing",
address = "17 Rue Meldrum, Beau Bassin, 1713-01 Mauritius",
pages = "88 (est.)",
year = "2009",
ISBN = "613-0-06480-2",
ISBN-13 = "978-613-0-06480-8",
LCCN = "????",
bibdate = "Wed Oct 28 09:06:59 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$50",
acknowledgement = ack-nhfb,
}
@InProceedings{Minchola:2009:FID,
author = "C. Minchola and G. Sutter",
title = "A {FPGA} {IEEE-754-2008} {Decimal64} Floating-Point
Multiplier",
crossref = "Cumplido:2009:RPI",
pages = "59--64",
year = "2009",
DOI = "https://doi.org/10.1109/ReConFig.2009.34",
bibdate = "Thu Feb 17 08:36:13 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Monniaux:2009:UFPa,
author = "David Monniaux",
title = "On using floating-point computations to help an exact
linear arithmetic decision procedure",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "22",
month = apr,
year = "2009",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/0904.3525",
abstract = "We consider the decision problem for quantifier-free
formulas whose atoms are linear inequalities
interpreted over the reals or rationals. This problem
may be decided using satisfiability modulo theory
(SMT), using a mixture of a SAT solver and a
simplex-based decision procedure for conjunctions.
State-of-the-art SMT solvers use simplex
implementations over rational numbers, which perform
well for typical problems arising from model-checking
and program analysis (sparse inequalities, small
coefficients) but are slow for other applications
(denser problems, larger coefficients). We propose a
simple preprocessing phase that can be adapted on
existing SMT solvers and that may be optionally
triggered. Despite using floating-point computations,
our method is sound and complete --- it merely affects
efficiency. We implemented the method and provide
benchmarks showing that this change brings a naive and
slow decision procedure (''textbook simplex'' with
rational numbers) up to the efficiency of recent SMT
solvers, over test cases arising from model-checking,
and makes it definitely faster than state-of-the-art
SMT solvers on dense examples.",
acknowledgement = ack-nhfb,
subject = "Logic in Computer Science (cs.LO); Numerical Analysis
(cs.NA)",
}
@InProceedings{Monniaux:2009:UFPb,
author = "David Monniaux",
title = "On Using Floating-Point Computations to Help an Exact
Linear Arithmetic Decision Procedure",
crossref = "Bouajjani:2009:CAV",
pages = "570--583",
year = "2009",
DOI = "https://doi.org/10.1007/978-3-642-02658-4_42",
bibdate = "Fri Dec 8 14:29:46 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Mosbach:2009:QPI,
author = "Sebastian Mosbach and Amanda G. Turner",
title = "A quantitative probabilistic investigation into the
accumulation of rounding errors in numerical {ODE}
solution",
journal = j-COMPUT-MATH-APPL,
volume = "57",
number = "7",
pages = "1157--1167",
month = apr,
year = "2009",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:24 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122109000431",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Murakami:2009:CFT,
author = "Hiroshi Murakami",
title = "A continued fraction type method to find a rational
number in a given closed interval whose denominator is
minimal",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "43",
number = "3",
pages = "88--90",
month = sep,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1823931.1823943",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Tue Jul 6 14:14:27 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We show a fast algorithm to find a rational number in
a given real interval whose denominator is minimal. The
algorithm is similar to the regular continued fraction
expansion for a real number.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
issue = "169",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
keywords = "approximation; continued fraction; interval; rational
number",
}
@Article{Pan:2009:NEF,
author = "V. Y. Pan and B. Murphy and G. Qian and R. E.
Rosholt",
title = "A new error-free floating-point summation algorithm",
journal = j-COMPUT-MATH-APPL,
volume = "57",
number = "4",
pages = "560--564",
month = feb,
year = "2009",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/j.camwa.2008.09.051",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:22 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122108006718",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Papadantonakis:2009:PSA,
author = "K. Papadantonakis and N. Kapre and S. Chan and A.
DeHon",
title = "Pipelining Saturated Accumulation",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "208--219",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.110",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jun 12 08:51:00 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Aggressive pipelining and spatial parallelism allow
integrated circuits (e.g., custom VLSI, ASICs, and
FPGAs) to achieve high throughput on many Digital
Signal Processing applications. However, cyclic data
dependencies in the computation can limit parallelism
and reduce the efficiency and speed of an
implementation. Saturated accumulation is an important
example where such a cycle limits the throughput of
signal processing applications. We show how to
reformulate saturated addition as an associative
operation so that we can use a parallel-prefix
calculation to perform saturated accumulation at any
data rate supported by the device. This allows us, for
example, to design a 16-bit saturated accumulator which
can operate at 280 MHz on a Xilinx Spartan-3
(XC3S-5000-4) FPGA, the maximum frequency supported by
the component's DCM.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "accumulation; high-speed arithmetic; parallel prefix.;
pipeline and parallel arithmetic and logic structures;
saturated arithmetic",
remark = "Extended version of ARITH-18 article \cite{}.",
}
@InProceedings{Preiss:2009:ACS,
author = "Jochen Preiss and Maarten Boersma and Silvia Melitta
Mueller",
title = "Advanced Clockgating Schemes for
Fused-Multiply-Add-Type Floating-Point Units",
crossref = "Bruguera:2009:PIS",
pages = "48--56",
year = "2009",
DOI = "https://doi.org/10.1109/ARITH.2009.17",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper introduces fine-grain clockgating schemes
for fused multiply-add-type floating-point units (FPU).
The clockgating is based on instruction type, precision
and operand values. The presented schemes focus on
reducing the power at peak performance, where each FPU
stage is used in nearly every cycle and conventional
schemes have little impact on the power consumption.
Depending on the instruction mix, the schemes allow to
turn off 18\% to 74\% of the register bits. Even for
the worst case instruction 18\% to 37\% of the FPU are
shut down depending on the data patterns.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; clockgating; floating-point hardware; fused
multiply-add; IEEE 754 Standard; power reduction",
}
@Article{Rump:2009:CPS,
author = "Siegfried M. Rump and Paul Zimmermann and Sylvie Boldo
and Guillaume Melquiond",
title = "Computing predecessor and successor in rounding to
nearest",
journal = j-BIT-NUM-MATH,
volume = "49",
number = "2",
pages = "419--431",
month = jun,
year = "2009",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-009-0218-z",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon May 24 15:36:43 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=49&issue=2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=49&issue=2&spage=419",
abstract = "We give simple and efficient methods to compute and/or
estimate the predecessor and successor of a
floating-point number using only floating-point
operations in rounding to nearest. This may be used to
simulate interval operations, in which case the quality
in terms of the diameter of the result is significantly
improved compared to existing approaches.",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "directed rounding; floating-point arithmetic;
predecessor; rounding to nearest; successor",
}
@Article{Rump:2009:UFA,
author = "Siegfried M. Rump",
title = "Ultimately Fast Accurate Summation",
journal = j-SIAM-J-SCI-COMP,
volume = "31",
number = "5",
pages = "3466--3502",
month = "????",
year = "2009",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/080738490",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:44:20 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/5;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present two new algorithms FastAccSum and
FastPrecSum, one to compute a faithful rounding of the
sum of floating-point numbers and the other for a
result ``as if'' computed in $K$-fold precision.
Faithful rounding means the computed result either is
one of the immediate floating-point neighbors of the
exact result or is equal to the exact sum if this is a
floating-point number. The algorithms are based on our
previous algorithms AccSum and PrecSum and improve them
by up to 25\%. The first algorithm adapts to the
condition number of the sum; i.e., the computing time
is proportional to the difficulty of the problem. The
second algorithm does not need extra memory, and the
computing time depends only on the number of summands
and $K$. Both algorithms are the fastest known in terms
of flops. They allow good instruction-level parallelism
so that they are also fast in terms of measured
computing time. The algorithms require only standard
floating-point addition, subtraction, and
multiplication in one working precision, for example,
double precision.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; distillation",
}
@Article{Schwarz:2009:DFP,
author = "E. M. Schwarz and J. S. Kapernick and M. F.
Cowlishaw",
title = "Decimal floating-point support on the {IBM System z10}
processor",
journal = j-IBM-JRD,
volume = "53",
number = "1",
pages = "4:1--4:10",
month = jan # "\slash " # feb,
year = "2009",
CODEN = "IBMJAE",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Thu Jan 29 14:25:32 MST 2009",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/rd/531/schwarz.pdf",
abstract = "The latest IBM zSeries processor, the IBM System z10
processor, provides hardware support for the decimal
floating-point (DFP) facility that was introduced on
the IBM System z9 processor. The z9 processor
implements the facility with a mixture of low-level
software and hardware assists. Recently, the IBM POWER6
processor-based System p 570 server introduced a
hardware implementation of the DFP facility. The latest
zSeries processor includes a decimal floating-point
unit based on the POWER6 processor DFP unit that has
been enhanced to also support the traditional zSeries
decimal fixed-point instruction set. This paper
explains the hardware implementation to support both
decimal fixed point and DFP and the new software
support for the DFP facility, including IBM z/OS, Java
JIT, and C/C++ compilers, as well as support in IBM DB2
and middleware.",
acknowledgement = ack-nhfb,
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "ARITH-19",
remark = "Extended version of ARITH-18 article \cite{}.",
}
@InProceedings{Shaw:2009:ASM,
author = "David E. Shaw",
title = "{Anton}: a Specialized Machine for Millisecond-Scale
Molecular Dynamics Simulations of Proteins",
crossref = "Bruguera:2009:PIS",
pages = "3--3",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Shpilka:2009:IDA,
author = "Amir Shpilka",
title = "Interpolation of Depth-3 Arithmetic Circuits with Two
Multiplication Gates",
journal = j-SIAM-J-COMPUT,
volume = "38",
number = "6",
pages = "2130--2161",
month = "????",
year = "2009",
CODEN = "SMJCAT",
DOI = "",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Tue May 18 08:22:06 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/38/6;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@TechReport{Stewart:2009:FMP,
author = "G. W. Stewart",
title = "{Flap}: a {Matlab} Package for Adjustable Precision
Floating-Point Arithmetic",
type = "Report",
institution = "Department of Computer Science, University of
Maryland",
address = "College Park, MD, USA",
year = "2009",
bibdate = "Sun Jun 19 13:11:45 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.umd.edu/~stewart/flap/flap.html",
abstract = "Flap is a package to implement floating-point
arithmetic with adjustable precision. Specifically,
operations are performed on Matlab doubles but are
rounded to a user specified number of decimal digits
after each operation. The number can be changed
dynamically. Flap is intended to make it easy to
generate examples of the effects of rounding error for
classroom use.",
acknowledgement = ack-nhfb,
}
@InProceedings{Tajallipour:2009:FCD,
author = "R. Tajallipour and D. Teng and Seok-Bum Ko and K.
Wahid",
title = "On the fast computation of decimal logarithm",
crossref = "ICCIT:2009:ICC",
pages = "32--36",
year = "2009",
DOI = "https://doi.org/10.1109/ICCIT.2009.5407171",
bibdate = "Thu Feb 17 08:28:37 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper presents a new and fast algorithm to
efficiently compute radix-10 logarithm of a decimal
number. The algorithm uses 32-bit floating-point
arithmetic, and is based on a digit-by-digit iterative
computation that does not require look-up tables, curve
fitting, decimal-binary conversion, or division
operations; the number of iterations depends on the
user defined precision. The algorithm produces
error-free (infinite precision) results up to 7 decimal
digits. A numerical example is shown for the purpose of
illustration. The accuracy is analyzed for several
decimal digits showing compliance with the IEEE
754-2008 Standard. When implemented on to the Xilinx
VirtexII FPGA, the architecture costs only 1,053 logic
cells, runs at a maximum frequency of 44 MHz, and
consumes 79 mW of power.",
acknowledgement = ack-nhfb,
}
@Article{Tan:2009:LPM,
author = "D. Tan and C. E. Lemonds and Michael J. Schulte",
title = "Low-Power Multiple-Precision Iterative Floating-Point
Multiplier with {SIMD} Support",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "2",
pages = "175--187",
month = feb,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.203",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:39 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663060",
abstract = "The demand for improved SIMD floating-point
performance on general-purpose x86-compatible
microprocessors is rising. At the same time, there is a
conflicting demand in the low-power computing market
for a reduction in power consumption. Along with this,
there is the absolute necessity of backward
compatibility for x86-compatible microprocessors, which
includes the support of x87 scientific floating-point
instructions. The combined effect is that there is a
need for low-power, low-cost floating-point units that
are still capable of delivering good SIMD performance
while maintaining full x86 functionality. This paper
presents the design of an x86-compatible floating-point
multiplier (FPM) that is compliant with the IEEE-754
Standard for Binary Floating-Point Arithmetic [12] and
is specifically tailored to provide good SIMD
performance in a low-cost, low-power solution while
maintaining full x87 backward compatibility. The FPM
efficiently supports multiple precisions using an
iterative rectangular multiplier. The FPM can perform
two parallel single-precision multiplies every cycle
with a latency of two cycles, one double-precision
multiply every two cycles with a latency of four
cycles, or one extended-double-precision multiply every
three cycles with a latency of five cycles. The
iterative FPM also supports division, square-root, and
transcendental functions. Compared to a previous design
with similar functionality, the proposed iterative FPM
has 60 percent less area and 59 percent less dynamic
power dissipation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Computer arithmetic; floating-point arithmetic;
low-power; multimedia; multiplying circuits;
rectangular multiplier; very-large-scale integration",
}
@InProceedings{Tenca:2009:MOF,
author = "Alexandre F. Tenca",
title = "Multi-operand Floating-Point Addition",
crossref = "Bruguera:2009:PIS",
pages = "161--168",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The design of a component to perform parallel addition
of multiple floating-point (FP) operands is explored in
this work. In particular, a 3-input FP adder is
discussed in more detail, but the main concepts and
ideas presented in this work are valid for FP adders
with more inputs. The proposed design is more accurate
than conventional FP addition using a network of
2-operand FP adders and it may have competitive area
and delay depending on the number of input operands.
Implementation results of a 3-operand FP adder are
presented to compare its performance to a network of
2-input FP adders.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@InProceedings{Tsen:2009:CDB,
author = "Charles Tsen and Sonia Gonzalez-Navarro and Michael J.
Schulte and Brian Hickmann and Katherine Compton",
title = "A Combined Decimal and Binary Floating-Point
Multiplier",
crossref = "IEEE:2009:IICa",
pages = "8--15",
year = "2009",
DOI = "https://doi.org/10.1109/ASAP.2009.28",
bibdate = "Sat Dec 04 07:01:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, we describe the first hardware design
of a combined binary and decimal floating-point
multiplier, based on specifications in the IEEE
754-2008 floating-point standard. The multiplier design
operates on either (1) 64-bit binary encoded decimal
floating-point (DFP) numbers or (2) 64-bit binary
floating-point (BFP) numbers. It returns properly
rounded results for the rounding modes specified in
IEEE 754-2008. The design shares the following hardware
resources between the two floating-point datatypes: a
54-bit by 54-bit binary multiplier, portions of the
operand encoding/decoding, a 54-bit right shifter,
exponent calculation logic, and rounding logic. Our
synthesis results show that hardware sharing is
feasible and has a reasonable impact on area, latency,
and delay. The combined BFP and DFP multiplier occupies
only 58\% of the total area that would be required by
separate BFP and DFP units. Furthermore, the critical
path delay of a combined multiplier has a negligible
increase over a standalone DFP multiplier, without
increasing the number of cycles to perform either BFP
or DFP multiplication.",
acknowledgement = ack-nhfb,
keywords = "binary encoded decimal floating-point; binary
floating-point multiplier; combined decimal
floating-point multiplier design; Commercial
Applications; Computer Arithmetic; Decimal
Floating-point; exponent calculation logic; floating
point arithmetic; Floating-point; Hardware; hardware
design; Hardware Reuse; IEEE 754-2008; IEEE 754-2008
floating-point standard; logic design; Multiplication;
multiplying circuits; Register-Transfer-Level
Implementation; right shifter; rounding logic",
}
@TechReport{Tydeman:2009:CMC,
author = "Fred J. Tydeman",
title = "Complex Multiply and Complex Divide, taking into
account {IEEE-754 (IEC 60559)} signed zeros, signed
infinities, {NaN}, and {C99 \_Imaginary\_I}",
type = "Report",
number = "WG14 N1399",
institution = "????",
address = "????",
day = "25",
month = sep,
year = "2009",
bibdate = "Mon Sep 30 09:48:02 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1399.htm",
acknowledgement = ack-nhfb,
}
@TechReport{Usselmann:2009:FPU,
author = "R. Usselmann",
title = "Floating point unit",
type = "Web report",
institution = "Algotronix Ltd.",
address = "Edinburgh EH8 8YB, UK",
day = "20",
month = dec,
year = "2009",
bibdate = "Thu Mar 24 21:02:16 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://opencores.org/project,fpu",
abstract = "This is a single precision floating point unit. It is
fully IEEE 754 compliant. It can currently perform
Add\slash Sub, Mul and Divide operations, as well as
integer to floating point and floating point to integer
conversions. It supports four rounding modes: Round to
Nearest Even, Round to Zero, Round to +INF and Round to
INF. There is now also a separate FP compare unit. It
is located in the {\tt fpu/fcmp} directory.",
acknowledgement = ack-nhfb,
remark = "Creatred 25-Sep-2001",
}
@Article{Van:2009:PEP,
author = "Lan-Da Van and Jin-Hao Tu",
title = "Power-Efficient Pipelined Reconfigurable Fixed-Width
{Baugh--Wooley} Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "10",
pages = "1346--1355",
month = oct,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.89",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5156495",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{VanDenDries:2009:AC,
author = "Lou {Van Den Dries} and Yiannis N. Moschovakis",
title = "Arithmetic complexity",
journal = j-TOCL,
volume = "10",
number = "1",
pages = "2:1--2:??",
month = jan,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1459010.1459012",
ISSN = "1529-3785 (print), 1557-945X (electronic)",
ISSN-L = "1529-3785",
bibdate = "Mon Jan 26 18:05:23 MST 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/tocl/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We obtain {\em lower bounds\/} on the cost of
computing various arithmetic functions and deciding
various arithmetic relations from specified primitives.
This includes lower bounds for computing the greatest
common divisor and deciding coprimeness of two
integers, from primitives like addition, subtraction,
division with remainder and multiplication. Some of our
results are in terms of recursive programs, but they
generalize directly to most (plausibly all) algorithms
from the specified primitives. Our methods involve some
elementary number theory as well as the development of
some basic notions and facts about recursive
algorithms.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computational Logic",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J773",
keywords = "coprimeness; greatest common divisor; Lower bounds for
arithmetical problems; recursive programs",
}
@InProceedings{Vazquez:2009:CDT,
author = "{\'A}lvaro V{\'a}zquez and Julio Villalba and Elisardo
Antelo",
title = "Computation of Decimal Transcendental Functions Using
the {CORDIC} Algorithm",
crossref = "Bruguera:2009:PIS",
pages = "179--186",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this work we propose new decimal floating-point
CORDIC algorithms for transcendental function
evaluation. We show how these algorithms are mapped to
a state of the art Decimal Floating-Point Unit (DFPU),
both considering the use of a carry-propagate adder or
a carry-save redundant adder. We compared with previous
decimal CORDIC proposals and with table-driven
algorithms, and we concluded that our approach have
significant potential advantages for transcendental
function evaluation in state of the art DFPUs with
minor modifications of the hardware.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@InProceedings{Vazquez:2009:HPS,
author = "{\'A}lvaro V{\'a}zquez and Elisardo Antelo",
title = "A High-Performance Significand {BCD} Adder with {IEEE
754-2008} Decimal Rounding",
crossref = "Bruguera:2009:PIS",
pages = "135--144",
year = "2009",
DOI = "https://doi.org/10.1109/ARITH.2009.30",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a new method and architecture to merge
efficiently IEEE 754-2008 decimal rounding with
significand BCD addition and subtraction. This is a key
component to improve several decimal floating-point
operations such as addition, multiplication and fused
multiply-add. The decimal rounding unit is based on a
direct implementation of the IEEE 754-2008 rounding
modes. We show that the resultant implementations for
IEEE 754-2008 Decimal64 (16 precision digits) and
Decimal128 (34 precision digits) formats reduce
significantly the area and latency required for
significand BCD addition/subtraction and decimal
rounding in previous high-performance decimal
floating-point adders.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@InProceedings{Verma:2009:CAO,
author = "Ajay K. Verma and Philip Brisk and Paolo Ienne",
title = "Challenges in Automatic Optimization of Arithmetic
Circuits",
crossref = "Bruguera:2009:PIS",
pages = "213--218",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Despite the impressive progress of logic synthesis in
the past decade, finding the best architecture for a
given circuit still remains an open and largely
unsolved problem, especially for arithmetic circuits.
In many cases, the outcome of even the most advanced
synthesis techniques is highly dependent on the input
description of the circuit, and the optimizations
themselves barely modify the architecture of the
circuit itself. Once the input description is converted
to an appropriate architecture, logic synthesis
performs local optimizations quite effectively;
however, finding the best architecture up front is a
nontrivial problem. This paper reviews recent results
in arithmetic logic synthesis that the authors have
published in recent years. Progress has clearly been
made, but much further work is still needed to narrow
the gap between the effectiveness of logic synthesis
techniques for arithmetic and control-oriented
circuits.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@InProceedings{Vuillemin:2009:EDS,
author = "Jean E. Vuillemin",
title = "Efficient Data Structure and Algorithms for Sparse
Integers, Sets and Predicates",
crossref = "Bruguera:2009:PIS",
pages = "7--14",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We construct a natural number $ n > 1 $ by trichotomy
$$ n = g + x_p d, x_p = 2^{2^p}, 0 \leq g < x_p, 0 < d
< x_p $$ applied recursively, and by systematically
sharing nodes with equal integer value. The resulting
Integer Decision Diagram IDD is a directed acyclic
graph DAG which represents $n$ by $ S(n) $ nodes in
computer memory. IDDs compete with bit-arrays, which
represent the consecutive bits of $n$ within roughly $
l(n) $ contiguous bits in memory. Unlike the binary
length $ l(n) $, the size $ S(n) $ is not monotonic.
Most integers are dense: their size is near worst &
average. The IDD size of sparse integers is arbitrarily
smaller.\par
Over dense numbers, the worst\slash average time\slash
space complexity of IDDs arithmetic operations is
proportional to that of bit-arrays. Yet, equality
testing is performed in unit time with IDDs and the
time\slash space complexity of some operations (e.g. $
\textrm {sign}(n - m), n \pm 2^m, 2^{2^n} $) are (at
least) exponentially better with IDDs than with
bit-arrays, even over dense operands.
Over sparse operands, the time and space complexity of
all ALU operations $ \{ \cap, \cup, \oplus, +, - \} $
are (in general) arbitrarily better with IDDs than
bit-arrays.\par
The coding powers of integers lets IDDs implement
integer sets and predicates as well as arithmetics. The
IDD package is a one-shop alternative to 3 (and more)
successful yet rather different packages for processing
large numbers, dictionaries and Boolean functions.
Performance levels are comparable over dense
structures, and IDDs prove best in class over sparse
structures.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19; boolean functions; decision diagrams
IDD/BDD/BMD/ZDD; dictionaries; integer dichotomy and
trichotomy; sparse numbers; store/compute/code once",
}
@InProceedings{Wang:2009:DFP,
author = "Liang-Kai Wang and Michael J. Schulte",
title = "A Decimal Floating-Point Adder with Decoded Operands
and a Decimal Leading-Zero Anticipator",
crossref = "Bruguera:2009:PIS",
pages = "125--134",
year = "2009",
DOI = "https://doi.org/10.1109/ARITH.2009.9",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IEEE 754-2008 Standard for Floating-Point
Arithmetic was of officially approved this year. One of
the most important revisions to IEEE 754-1985 is the
introduction of decimal floating-point (DFP) formats
and operations. Since IEEE 754-1985 was revised, major
microprocessor vendors have been working on hardware
designs and software libraries for decimal arithmetic.
Because the new standard has been approved, many
software vendors are planning to adapt the new decimal
formats into their applications. Therefore, it is
important to investigate efficient algorithms and
hardware designs for common DFP arithmetic operations
to improve the performance of these applications. This
paper presents a novel DFP adder with decoded operands
and a decimal leading-zero anticipator (LZA). The DFP
adder is based on a previous DFP adder design with
several new features, including a new internal format,
an improved operand pre-correction stage, and a novel
decimal LZA to obtain better timing for decimal
addition and subtraction. Synthesis results show that
the new DFP adder is roughly 14\% faster than the
previous design.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Wang:2009:HDD,
author = "Liang-Kai Wang and Michael J. Schulte and J. D.
Thompson and N. Jairam",
title = "Hardware Designs for Decimal Floating-Point Addition
and Related Operations",
journal = j-IEEE-TRANS-COMPUT,
volume = "58",
number = "3",
pages = "322--335",
month = mar,
year = "2009",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2008.147",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 4 11:37:40 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4599577",
abstract = "Decimal arithmetic is often used in commercial,
financial, and Internet-based applications. Due to the
growing importance of decimal floating-point (DFP)
arithmetic, the IEEE 754-2008 Standard for
Floating-Point Arithmetic (IEEE 754-2008) includes
specifications for DFP arithmetic. IBM recently
announced adding DFP instructions to their POWER6, z9,
and z10 microprocessor architectures. As processor
support for DFP arithmetic emerges, it is important to
investigate efficient arithmetic algorithms and
hardware designs for common DFP arithmetic operations.
This paper gives an overview of DFP arithmetic in IEEE
754-2008 and discusses previous research on decimal
fixed-point and floating-point addition. It also
presents novel designs for a DFP adder and a DFP
multifunction unit (DFP MFU) that comply with IEEE
754-2008. To reduce their delay, the DFP adder and MFU
use decimal injection-based rounding, a new form of
decimal operand alignment, and a fast flag-based method
for rounding and overflow detection. Synthesis results
indicate that the proposed DFP adder is roughly 21
percent faster and 1.6 percent smaller than a previous
DFP adder design, when implemented in the same
technology. Compared to the DFP adder, the DFP MFU
provides six additional operations, yet only has 2.8
percent more delay and 9.7 percent more area. A
pipelined version of the DFP MFU has a latency of six
cycles, a throughput of one result per cycle, an
estimated critical path delay of 12.9 fanout-of-four
(FO4) inverter delays, and an estimated area of 45,681
NAND2 equivalent gates.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "addition; computer arithmetic; Decimal;
floating-point; logic design; multifunction unit;
subtraction",
}
@InProceedings{Wang:2009:RCD,
author = "Dong Wang and M. D. Ercegovac and Nanning Zheng",
title = "A radix-8 complex divider for {FPGA} implementation",
crossref = "IEEE:2009:ICF",
pages = "236--241",
year = "2009",
DOI = "https://doi.org/10.1109/FPL.2009.5272300",
bibdate = "Fri Dec 03 15:33:08 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a design of a radix-8 complex division for
fixed-point operands suitable for FPGA implementation.
The design, consisting of operands' prescaling and
digit recurrence, shares logic resources and optimizes
the use of 6-input LUTs of FPGA devices for efficient
design. An optimized single table for prescaling
factors is developed. The design is implemented in
Altera Stratix-II FPGA for several operands precisions
and compared in cost, latency and power with a design
using non-shared resources and with an IP-based design.
The results show advantages of the proposed design in
cost, delay, and power.",
acknowledgement = ack-nhfb,
keywords = "Altera Stratix-II FPGA; digit recurrence; dividing
circuits; field programmable gate arrays; IP-based
design; logic resources; non-shared resources; operand
prescaling; radix-8 complex divider",
}
@Manual{XILINX:2009:XLF,
author = "{XILINX}",
title = "{XILINX LogiCORE} floating-point operator v5.0 product
specification",
organization = "Xilinx, Inc.",
day = "24",
month = jun,
year = "2009",
bibdate = "Sat Oct 9 13:09:37 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.xilinx.com/support/documentation/ip_documentation/floating_point_ds335.pdf",
acknowledgement = ack-nhfb,
}
@Article{Zhu:2009:CRH,
author = "Yong-Kang Zhu and Wayne B. Hayes",
title = "Correct Rounding and a Hybrid Approach to Exact
Floating-Point Summation",
journal = j-SIAM-J-SCI-COMP,
volume = "31",
number = "4",
pages = "2981--3001",
month = "????",
year = "2009",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/070710020",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:44:18 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present two algorithms for computing correctly
rounded sums of arrays of floating-point numbers.
First, iFastSum improves upon our previous FastSum by
requiring no additional space beyond the original
array, which is destroyed. It runs about 20\% faster
than FastSum in the general case and two times faster
when extremely ill-conditioned data are used. The
second algorithm is HybridSum, which combines three
summation ideas together: splitting the mantissa, radix
sorting, and using iFastSum. The result is that when
the number of summands is greater than about $ 10^4 $,
for a given $n$ its running time is almost a constant,
independent of the condition number. It runs almost as
fast as iFastSum in the general case and much faster
than iFastSum when ill-conditioned data are used.
HybridSum requires only one pass through the input
array and uses constant storage, and it is thus
suitable for exact summation as an ``online''
algorithm. Neither algorithm requires extra precision
accumulators, and both work in any base. Their accuracy
is guaranteed independent of the condition number and
the number of summands.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; correct rounding;
floating-point arithmetic",
}
@InProceedings{Zimmermann:2009:DSS,
author = "Reto Zimmermann",
title = "Datapath Synthesis for Standard-Cell Design",
crossref = "Bruguera:2009:PIS",
pages = "207--211",
year = "2009",
bibdate = "Fri Jun 12 12:34:25 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Datapath synthesis for standard-cell design goes
through extraction of arithmetic operations from RTL
code, high-level arithmetic optimizations and netlist
generation. Numerous architectures and optimization
strategies exist that result in circuit implementations
with very different performance characteristics. This
work summarizes the circuit architectures and
techniques used in a commercial synthesis tool to
optimize cell-based datapath netlists for timing, area
and power.",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
}
@Article{Akbarpour:2010:VSI,
author = "Behzad Akbarpour and Amr T. Abdel-Hamid and
Sofi{\`e}ne Tahar and John Harrison",
title = "Verifying a Synthesized Implementation of {IEEE-754}
Floating-Point Exponential Function using {HOL}",
journal = j-COMP-J,
volume = "53",
number = "4",
pages = "465--488",
month = may,
year = "2010",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxp023",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Apr 28 14:33:36 MDT 2010",
bibsource = "http://comjnl.oxfordjournals.org/content/vol53/issue4/index.dtl;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/cgi/content/abstract/53/4/465;
http://comjnl.oxfordjournals.org/cgi/reprint/53/4/465",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Aldous:2010:WCO,
author = "David Aldous and Tung Phan",
title = "When Can One Test an Explanation? Compare and Contras
{Benford's Law} and the Fuzzy {CLT}",
journal = j-AMER-STAT,
volume = "64",
number = "3",
pages = "221--227",
month = aug,
year = "2010",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/tast.2010.09098",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Thu Aug 26 21:48:27 MDT 2010",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Alimohammad:2010:UAA,
author = "A. Alimohammad and S. F. Fard and B. F. Cockburn",
title = "A Unified Architecture for the Accurate and
High-Throughput Implementation of Six Key Elementary
Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "4",
pages = "449--456",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.169",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:27 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5313801",
abstract = "This paper presents a unified architecture for the
compact implementation of several key elementary
functions, including reciprocal, square root, and
logarithm, in single-precision floating-point
arithmetic. The proposed high-throughput design is
based on uniform domain segmentation and curve fitting
techniques. Numerically accurate least-squares
regression is utilized to calculate the polynomial
coefficients. The architecture is optimized by
analyzing the trade-off between the size of the
required memory and the precision of intermediate
variables to achieve the minimum 23-bit accuracy
required for single-precision floating-point
representation. The efficiency of the proposed unified
data path is demonstrated on a common
field-programmable gate array.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Amin:2010:HRM,
author = "Alaaeldin Amin and Waleed Shinwari",
title = "High-Radix Multiplier-Dividers: Theory, Design, and
Hardware",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "8",
pages = "1009--1022",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.78",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:30 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5453337",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Banescu:2010:MFP,
author = "Sebastian Banescu and Florent de Dinechin and Bogdan
Pasca and Radu Tudoran",
title = "Multipliers for floating-point double precision and
beyond on {FPGAs}",
journal = j-COMP-ARCH-NEWS,
volume = "38",
number = "4",
pages = "73--79",
month = sep,
year = "2010",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/1926367.1926380",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Thu Jan 20 14:27:03 MST 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The implementation of high-precision floating-point
applications on reconfigurable hardware requires large
multipliers. Full multipliers are the core of
floating-point multipliers. Truncated multipliers,
trading resources for a well-controlled accuracy
degradation, are useful building blocks in situations
where a full multiplier is not needed.\par
This work studies the automated generation of such
multipliers using the embedded multipliers and adders
present in the DSP blocks of current FPGAs. The
optimization of such multipliers is expressed as a
tiling problem, where a tile represents a hardware
multiplier, and super-tiles represent combinations of
several hardware multipliers and adders, making
efficient use of the DSP internal resources. This
tiling technique is shown to adapt to full or truncated
multipliers. It addresses arbitrary precisions
including single, double but also the quadruple
precision introduced by the IEEE-754-2008 standard and
currently unsupported by processor hardware. An
open-source implementation is provided in the FloPoCo
project.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Block:2010:GEB,
author = "Henry W. Block and Thomas H. Savits",
title = "A General Example for {Benford} Data",
journal = j-AMER-STAT,
volume = "64",
number = "4",
pages = "335--339",
month = nov,
year = "2010",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.1198/tast.2010.09169",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
bibdate = "Wed Nov 9 17:20:17 MST 2011",
bibsource = "http://www.amstat.org/publications/tas/;
https://www.math.utah.edu/pub/tex/bib/amstat.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Benford's Law deals, among other things, with the
proportion of numbers whose first significant digit is
a $1$ (e.g., $ 0.00131 $ and $ 19668 $ both have first
significant digit $1$) in a variety of datasets. In
these datasets, which arise in various compendiums or
as mixtures of various sets of numbers, the proportion
of numbers with first significant digit one is $ 0.3010
$ which is much higher than the commonsense value of $
1 / 9 $. The reasons for this occurrence have been
elusive. Mathematical attempts to explain this
phenomenon have been relatively fruitless. Methods
involving probability have been somewhat more
successful. In this article we give some simple reasons
for this occurrence and also give an example of a
general mixture of distributions which exactly
satisfies this Law. Various other examples and
counterexamples are also given.",
acknowledgement = ack-nhfb,
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
}
@Article{Brent:2010:PAV,
author = "Richard P. Brent",
title = "On the precision attainable with various
floating-point number systems",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "20",
month = apr,
year = "2010",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
MRclass = "65Y04",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1004.3374",
abstract = "For scientific computations on a digital computer the
set of real number is usually approximated by a finite
set $F$ of ``floating-point'' numbers. We compare the
numerical accuracy possible with difference choices of
$F$ having approximately the same range and requiring
the same word length. In particular, we compare
different choices of base (or radix) in the usual
floating-point systems. The emphasis is on the choice
of $F$, not on the details of the number representation
or the arithmetic, but both rounded and truncated
arithmetic are considered. Theoretical results are
given, and some simulations of typical floating-point
computations (forming sums, solving systems of linear
equations, finding eigenvalues) are described. If the
leading fraction bit of a normalized base 2 number is
not stored explicitly (saving a bit), and the criterion
is to minimize the mean square roundoff error, then
base 2 is best. If unnormalized numbers are allowed, so
the first bit must be stored explicitly, then base 4
(or sometimes base 8) is the best of the usual
systems.",
acknowledgement = ack-nhfb,
remark = "Published in IEEE Transactions on Computers {\bf C-22}
(1973), 601--607.",
subject = "Numerical Analysis (cs.NA); Numerical Analysis
(math.NA)",
}
@InProceedings{Brisebarre:2010:IDF,
author = "Nicolas Brisebarre and Nicolas Louvet and {\'E}rik
Martin-Dorel and Jean-Michel Muller and Adrien
Panhaleux and Milo D. Ercegovac",
editor = "Fran{\c{c}}ois Charot and Frank Hannig and J{\"u}rgen
Teich and Christophe Wolinski",
booktitle = "{ASAP 2010 --- 21st IEEE International Conference on
Application-specific Systems, Architectures and
Processors. July 7--9, 2010. Rennes, France}",
title = "Implementing decimal floating-point arithmetic through
binary: Some suggestions",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "317--320",
year = "2010",
DOI = "https://doi.org/10.1109/ASAP.2010.5540969",
ISBN = "1-4244-6967-8",
ISBN-13 = "978-1-4244-6967-3",
ISSN = "1063-6862",
ISSN-L = "1063-6862",
bibdate = "Fri Sep 29 10:41:24 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic",
}
@Article{Chapoutot:2010:ISN,
author = "Alexandre Chapoutot",
title = "Interval Slopes as Numerical Abstract Domain for
Floating-Point Variables",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "1",
month = apr,
year = "2010",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1004.0202",
abstract = "The design of embedded control systems is mainly done
with model-based tools such as Matlab/Simulink.
Numerical simulation is the central technique of
development and verification of such tools.
Floating-point arithmetic, that is well-known to only
provide approximated results, is omnipresent in this
activity. In order to validate the behaviors of
numerical simulations using abstract
interpretation-based static analysis, we present,
theoretically and with experiments, a new partially
relational abstract domain dedicated to floating-point
variables. It comes from interval expansion of
non-linear functions using slopes and it is able to
mimic all the behaviors of the floating-point
arithmetic. Hence it is adapted to prove the absence of
run-time errors or to analyze the numerical precision
of embedded control systems.",
acknowledgement = ack-nhfb,
subject = "Programming Languages (cs.PL); Numerical Analysis
(cs.NA)",
}
@Article{Cheng:2010:BSS,
author = "Qi Cheng and Xianmeng Meng and Celi Sun and Jiazhe
Chen",
title = "Bounding the sum of square roots via lattice
reduction",
journal = j-MATH-COMPUT,
volume = "79",
number = "270",
pages = "1109--1122",
month = apr,
year = "2010",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri May 14 06:21:06 MDT 2010",
bibsource = "http://www.ams.org/mcom/2010-79-270;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2010-79-270/S0025-5718-09-02304-7/home.html;
http://www.ams.org/journals/mcom/2010-79-270/S0025-5718-09-02304-7/S0025-5718-09-02304-7.pdf",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Chevillard:2010:SED,
author = "Sylvain Chevillard and Mioara Jolde and Christoph
Lauter",
title = "{Sollya}: An Environment for the Development of
Numerical Codes",
crossref = "Fukuda:2010:MSI",
pages = "28--31",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_5",
bibdate = "Sat Sep 23 06:20:46 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_5.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Cuyt:2010:VSF,
author = "Annie Cuyt and Franky Backeljauw and Stefan Becuwe and
Joris {Van Deun}",
title = "Validated Special Functions Software",
crossref = "Fukuda:2010:MSI",
pages = "32--34",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_6",
bibdate = "Sat Sep 23 06:20:46 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Daumas:2010:CBE,
author = "Marc Daumas and Guillaume Melquiond",
title = "Certification of bounds on expressions involving
rounded operators",
journal = j-TOMS,
volume = "37",
number = "1",
pages = "2:1--2:20",
month = jan,
year = "2010",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1644001.1644003",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Mar 15 10:45:33 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Gappa is a tool designed to formally verify the
correctness of numerical software and hardware. It uses
interval arithmetic and forward error analysis to bound
mathematical expressions that involve rounded as well
as exact operators. It then generates a theorem and its
proof for each verified enclosure. This proof can be
automatically checked with a proof assistant, such as
Coq or HOL Light. It relies on a large companion
library of facts that we have developed. This Coq
library provides theorems dealing with addition,
multiplication, division, and square root, for both
fixed- and floating-point arithmetics. Gappa uses
multiple-precision dyadic fractions for the endpoints
of intervals and performs forward error analysis on
rounded operators when necessary. When asked, Gappa
reports the best bounds it is able to reach for a given
expression in a given context. This feature can be used
to identify where the set of facts and automatic
techniques implemented in Gappa becomes insufficient.
Gappa handles seamlessly additional properties
expressed as interval properties or rewriting rules in
order to establish more intricate bounds. Recent work
showed that Gappa is suited to discharge proof
obligations generated for small pieces of software.
They may be produced by third-party tools and the first
applications of Gappa use proof obligations written by
designers or obtained from traces of execution.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "Coq; correct rounding; dyadic fraction; floating-point
arithmetic; Forward error analysis; HOL Light; interval
arithmetic; proof obligation; proof system; PVS",
}
@InProceedings{deDinechin:2010:AGP,
author = "Florent de Dinechin and Mioara Joldes and Bogdan
Pasca",
booktitle = "{ASAP 2010} --- {21st IEEE International Conference on
Application-specific Systems, Architectures and
Processors}",
title = "Automatic generation of polynomial-based hardware
architectures for function evaluation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "216--222",
month = jul,
year = "2010",
DOI = "https://doi.org/10.1109/asap.2010.5540952",
bibdate = "Thu Apr 10 13:04:38 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{deDinechin:2010:FGA,
author = "Florent de Dinechin and Bogdan Pasca",
title = "{FloPoCo}: generator of arithmetic cores
({Floating-Point Cores}, but not only) for {FPGAs} (but
not only)",
howpublished = "Web site and source code.",
day = "10",
month = aug,
year = "2010",
bibdate = "Sat Oct 9 14:27:50 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The purpose of the FloPoCo project is to explore the
many ways in which the flexibility of the FPGA target
can be exploited in the arithmetic realm, with a focus
on floating-point.\par
The philosophy of FloPoCo is that floating-point on
FPGAs should not rely on operators that mimick those
available in processors. By designing radically new
operators, one may obtain more accurate results with
less hardware in less time. This thesis is detailed in
this document.\par
Therefore FloPoCo focuses on exotic operators and
exotic precisions. However it also provides basic
operators (+,-,*,/ and square root) whose performance
matches vendor-supplied operators while offering more
flexibility.\par
FloPoCo is not a library of operators, but a generator
of operators written in C++. It inputs operator
specifications, and outputs synthesizable VHDL. This
approach allows much better optimization and
customization than what VHDL alone permits. In
addition, FloPoCo is to our knowledge the easiest way
to design complex operators with flexible
pipeline.\par
FloPoCo supersedes FPLibrary, and is compatible with
it.",
acknowledgement = ack-nhfb,
}
@InProceedings{deDinechin:2010:FPE,
author = "Florent de Dinechin and Bogdan Pasca",
editor = "Jinian Bian and Qiang Zhou and Kang Zhao",
booktitle = "{Proceedings 2010 International Conference on
Field-Programmable Technology, 8--10 December 2010,
Beijing, China}",
title = "Floating-point exponential functions for {DSP}-enabled
{FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "110--117",
month = dec,
year = "2010",
DOI = "https://doi.org/10.1109/FPT.2010.5681764",
bibdate = "Sat Feb 08 09:35:06 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Digeser:2010:ISE,
author = "P. Digeser and M. Tubolino and M. Klemm and D. Shapiro
and M. Bolic",
title = "Instruction set extension in the {NIOS II}: a floating
point divider for complex numbers",
crossref = "IEEE:2010:CCE",
year = "2010",
DOI = "https://doi.org/10.1109/CCECE.2010.5575173",
bibdate = "Fri Dec 03 15:43:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "As increasing the clock frequency leads to
unmanageable heat and power dissipation the search is
on for another way to get more power efficient and
faster embedded systems. Given that chip area is also a
constraint, we investigate the addition of a custom
instruction to the processor instruction set which
enables the execution of an efficient complex division.
The instruction we designed is a hardware divider for
complex numbers which receives four input values and
returns two output values. The data bandwidth
constraint of 2 inputs and 1 output is loosened by
making the instruction multicycle as described in
previous work. We uses the custom instruction interface
of the NIOS II soft processor and achieve a speedup of
up to $ 3 \tines $ over the unmodified instruction
set.",
acknowledgement = ack-nhfb,
keywords = "clock frequency; complex numbers; custom instruction;
embedded systems; floating point arithmetic; floating
point divider; instruction multicycle; instruction set
extension; instruction sets; microprocessor chips; NIOS
II soft processor; processor instruction set",
}
@Article{Dvir:2010:HRT,
author = "Zeev Dvir and Amir Shpilka and Amir Yehudayoff",
title = "Hardness-Randomness Tradeoffs for Bounded Depth
Arithmetic Circuits",
journal = j-SIAM-J-COMPUT,
volume = "39",
number = "4",
pages = "1279--1293",
month = "????",
year = "2010",
CODEN = "SMJCAT",
DOI = "",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Tue May 18 08:22:14 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/39/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
}
@Article{Emmart:2010:HPI,
author = "Niall Emmart and Charles Weems",
title = "High Precision Integer Addition, Subtraction and
Multiplication with a Graphics Processing Unit",
journal = j-PARALLEL-PROCESS-LETT,
volume = "20",
number = "4",
pages = "293--306",
month = dec,
year = "2010",
CODEN = "PPLTEE",
DOI = "https://doi.org/10.1142/S0129626410000259",
ISSN = "0129-6264 (print), 1793-642X (electronic)",
bibdate = "Tue Feb 28 11:32:05 MST 2012",
bibsource = "http://ejournals.wspc.com.sg/ppl/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/parallelprocesslett.bib",
note = "See later improvements \cite{Emmart:2011:HPI}.",
acknowledgement = ack-nhfb,
fjournal = "Parallel Processing Letters",
journal-URL = "http://www.worldscientific.com/loi/ppl",
keywords = "GNU GMP multiple precision package; graphics
processing unit; Karatsuba multiplication algorithm;
multiple precision arithmetic; parallel algorithm;
Strassen FFT multiplication algorithm",
remark = "The abstract reports improvements (GPU compared to
GMP) of 3x for multiplication, and 8x for addition and
subtraction, with very long operands (32KB or
greater).",
}
@InProceedings{Fahmy:2010:DFP,
author = "H. A. H. Fahmy and T. ElDeeb and M. Y. Hassan and Y.
Farouk and R. R. Eissa",
title = "Decimal floating point for future processors",
crossref = "IEEE:2010:ICM",
pages = "443--446",
year = "2010",
DOI = "https://doi.org/10.1109/ICM.2010.5696183",
bibdate = "Thu Feb 17 08:30:56 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Many new designs for Decimal Floating Point (DFP)
hardware units have been proposed in the last few
years. To date, only the IBM POWER6 and POWER7
processors include internal units for decimal floating
point processing. We have designed and tested several
DFP units including an adder, multiplier, divider,
square root, and fused multiply-add compliant with the
IEEE 754-2008 standard. This paper presents the results
of using our units as part of a vector co-processor and
the anticipated gains once the units are moved on chip
with the main processor.",
acknowledgement = ack-nhfb,
}
@Misc{Fiedler:2010:GGF,
author = "Glenn Fiedler",
title = "Gaffer on Games --- Floating Point Determinism",
howpublished = "Web site",
day = "24",
month = feb,
year = "2010",
bibdate = "Mon Dec 04 07:07:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Comments on the problem of reproducing game behavior
on different platforms because of floating-point
issues.",
acknowledgement = ack-nhfb,
remark = "See also \cite{Dickinson:2001:IRB}.",
}
@Article{Frey:2010:ABC,
author = "Gerhard Frey",
title = "The Arithmetic Behind Cryptography",
journal = j-NAMS,
volume = "57",
number = "3",
pages = "366--374",
month = mar,
year = "2010",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
bibdate = "Mon Feb 22 15:35:29 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ams.org/notices/201003/",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
}
@Article{Fu:2010:FDO,
author = "Haohuan Fu and O. Mencer and W. Luk",
title = "{FPGA} Designs with Optimized Logarithmic Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "7",
pages = "1000--1006",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.51",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 12:14:07 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5416693",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Ghazi:2010:WHU,
author = "Kaveh R. Ghazi and Vincent Lef{\`e}vre and Philippe
Theveny and Paul Zimmermann",
title = "Why and How to Use Arbitrary Precision",
journal = j-COMPUT-SCI-ENG,
volume = "12",
number = "3",
pages = "5",
month = may # "\slash " # jun,
year = "2010",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCSE.2010.73",
ISSN = "0740-7475 (print), 1558-1918 (electronic)",
ISSN-L = "1521-9615",
bibdate = "Thu May 13 11:08:14 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}
@InProceedings{Habegger:2010:EHI,
author = "Andreas Habegger and Andreas Stahel and Josef Goette
and Marcel Jacomet",
editor = "{IEEE}",
booktitle = "{2010 Fifth IEEE International Symposium on Electronic
Design, Test \& Applications: 13--15 January 2010 Ho
Chi Minh City, Vietnam}",
title = "An Efficient Hardware Implementation for a Reciprocal
Unit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "183--187",
year = "2010",
DOI = "https://doi.org/10.1109/delta.2010.65",
bibdate = "Thu Apr 10 13:16:33 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hemmert:2010:FEF,
author = "K. Scott Hemmert and Keith D. Underwood",
title = "Fast, Efficient Floating-Point Adders and Multipliers
for {FPGAs}",
journal = j-TRETS,
volume = "3",
number = "3",
pages = "11:1--11:??",
month = sep,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1839480.1839481",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Fri Oct 8 18:26:34 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating-point applications are a growing trend in the
FPGA community. As such, it has become critical to
create floating-point units optimized for standard FPGA
technology. Unfortunately, the FPGA design space is
very different from the VLSI design space; thus,
optimizations for FPGAs can differ significantly from
optimizations for VLSI. In particular, the FPGA
environment constrains the design space such that only
limited parallelism can be effectively exploited to
reduce latency. Obtaining the right balances between
clock speed, latency, and area in FPGAs can be
particularly challenging. This article presents
implementation details for an IEEE-754 standard
floating-point adder and multiplier for FPGAs. The
designs presented here enable a Xilinx Virtex4 FPGA
(-11 speed grade) to achieve 270 MHz IEEE compliant
double precision floating-point performance with a
9-stage adder pipeline and 14-stage multiplier
pipeline. The area requirement is approximately 500
slices for the adder and under 750 slices for the
multiplier.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
keywords = "floating point; FPGA; HPC; reconfigurable computing",
}
@InProceedings{Hsiao:2010:LCD,
author = "Shen-Fu Hsiao and Chia-Sheng Wen and Ming-Yu Tsai",
editor = "????",
booktitle = "{2010 International Symposium on Next Generation
Electronics: 18--19 November 2010}",
title = "Low-cost design of reciprocal function units using
shared multipliers and adders for polynomial
approximation and {Newton--Raphson} interpolation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "40--43",
month = nov,
year = "2010",
DOI = "https://doi.org/10.1109/isne.2010.5669204",
bibdate = "Thu Apr 10 13:30:38 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Jaberipur:2010:RDF,
author = "G. Jaberipur and B. Parhami and S. Gorgin",
title = "Redundant-Digit Floating-Point Addition Scheme Based
on a Stored Rounding Value",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "5",
pages = "694--706",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.152",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5278659",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Jiang:2010:AEP,
author = "Hao Jiang and Shengguo Li and Lizhi Cheng and Fang
Su",
title = "Accurate evaluation of a polynomial and its derivative
in {Bernstein} form",
journal = j-COMPUT-MATH-APPL,
volume = "60",
number = "3",
pages = "744--755",
month = aug,
year = "2010",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:42 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122110003706",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Misc{Kahan:2010:PUC,
author = "W. Kahan",
title = "{Pete}'s unsung contribution to {IEEE Standard 754}
for binary floating-point: a talk at a conference to
celebrate {G. W. ``Pete'' Stewart}'s 70th Birthday",
howpublished = "Lecture slides",
pages = "18",
day = "19",
month = jul,
year = "2010",
bibdate = "Wed Aug 07 15:43:36 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://people.eecs.berkeley.edu/~wkahan/19July10.pdf",
acknowledgement = ack-nhfb,
}
@Article{Kalla:2010:PIN,
author = "Ron Kalla and Balaram Sinharoy and William J. Starke
and Michael Floyd",
title = "{Power7}: {IBM}'s Next-Generation Server Processor",
journal = j-IEEE-MICRO,
volume = "30",
number = "2",
pages = "7--15",
month = mar # "\slash " # apr,
year = "2010",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2010.38",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Fri Apr 23 06:37:18 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "decimal floating-point arithmetic; fused multiply-add
(FMA); IEEE 754-2008 arithmetic; subnormal numbers in
hardware; underflow",
}
@Book{Kastner:2010:AOT,
author = "Ryan Kastner and Anup Hosangadi and Farzan Fallah",
title = "Arithmetic optimization techniques for hardware and
software design",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "vii + 187",
year = "2010",
ISBN = "0-521-88099-8",
ISBN-13 = "978-0-521-88099-2",
LCCN = "QA76.9.C62 K37 2010; QA76.9.C62 KAS 2010",
bibdate = "Mon Jul 12 14:32:42 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
library.ox.ac.uk:210/ADVANCE",
URL = "http://assets.cambridge.org/97805218/80992/cover/9780521880992.jpg",
abstract = "Obtain better system performance, lower energy
consumption, and avoid hand-coding arithmetic functions
with this concise guide to automated optimization
techniques for hardware and software design. High-level
compiler optimizations and high-speed architectures for
implementing FIR filters are covered, which can improve
performance in communications, signal processing,
computer graphics, and cryptography. Clearly explained
algorithms and illustrative examples throughout make it
easy to understand the techniques and write software
for their implementation. Background information on the
synthesis of arithmetic expressions and computer
arithmetic is also included, making the book ideal for
newcomers to the subject. This is an invaluable
resource for researchers, professionals, and graduate
students working in system level design and automation,
compilers, and VLSI CAD.",
acknowledgement = ack-nhfb,
subject = "computer arithmetic; electronic digital computers;
design and construction; computer software;
development; mathematical optimization",
tableofcontents = "1. Introduction; \\
2. Use of arithmetic expressions\\
3. Software compilation\\
4. Hardware synthesis\\
5. Fundamentals of digital arithmetic\\
6. Polynomial expressions\\
7. Linear systems",
}
@Book{Kirk:2010:PMP,
author = "David B. Kirk and Wen-mei W. Hwu",
title = "Programming Massively Parallel Processors: a Hands-on
Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xviii + 258",
year = "2010",
ISBN = "0-12-381472-3",
ISBN-13 = "978-0-12-381472-2",
LCCN = "QA76.642 .K57 2010",
bibdate = "Thu Jul 29 13:33:50 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib;
https://www.math.utah.edu/pub/tex/bib/scpe.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib;
z3950.bibsys.no:2100/BIBSYS;
z3950.loc.gov:7090/Voyager",
note = "Chapter 7 (pages 125--140) discusses GPU
floating-point considerations.",
acknowledgement = ack-nhfb,
keywords = "CUDA; nVIDIA",
libnote = "Not yet in my library.",
subject = "parallel programming (computer science); parallel
processing (electronic computers); multiprocessors;
computer architecture",
tableofcontents = "1: Introduction \\
1.1 GPUs as Parallel Computers \\
1.2 Architecture of a Modern GPU \\
1.3 Why More Speed or Parallelism? \\
1.4 Parallel Programming Languages and Models \\
1.5 Overarching Goals \\
1.6 Organization of the Book \\
2: History of GPU Computing \\
2.1. Evolution of Graphics Pipelines The Era of Fixed
Function Graphics Pipeline Evolution of Programmable
Real-Time Graphics Unified Graphics and Computing
Processors \\
2.2. GPGPU: an Intermediate Step Scalable GPUs Recent
Developments Future Trends \\
3: Introduction to CUDA \\
3.1. Data Parallelism \\
3.2. CUDA Program Structure \\
3.3. A Matrix--Matrix Multiplication Example \\
3.4. Device Memories and Data Transfer \\
3.5. Kernel Functions and Threading \\
3.6. Summary Function Declarations Kernel Launch
Predefined Variables Runtime API \\
4: CUDA Threads \\
4.1. CUDA Thread Organization \\
4.2. More on BlockIdx and ThreadIdx \\
4.3. Synchronization and Transparent Scalability \\
4.4. Thread Assignment \\
4.5. Thread Scheduling and Latency Tolerance \\
4.6. Summary \\
5: CUDA Memories \\
5.1. Importance of Memory Access Efficiency \\
5.2. CUDA Device Memory Types \\
5.3. A Strategy for Reducing Global Memory Traffic \\
5.4. Memory as a Limiting Factor to Parallelism \\
5.5. Summary \\
6: Performance Considerations \\
6.1. More on Thread Execution \\
6.2. Global Memory Bandwidth \\
6.3. Dynamic Partitioning of SM Resources \\
6.4. Data Prefetching \\
6.5. Instruction Mix \\
6.6. Thread Granularity \\
6.7. Measured Performance and Summary \\
\\
7: Floating-Point Considerations \\
7.1. Floating-Point Format Normalized representation of
M Excess encoding of E \\
7.2. Representable Numbers \\
7.3. Special Bit Patterns and Precision \\
7.4. Arithmetic Accuracy and Rounding \\
7.5. Algorithm Considerations \\
7.6. Summary \\
8: Application Case Study I \\
Advanced MRI Reconstruction \\
8.1. Application Background \\
8.2. Iterative Reconstruction \\
8.3. Computing FHd \\
Step 1: Determine the Kernel Parallelism Structure \\
Step 2: Getting Around the Memory Bandwidth Limitation
\\
Step 3: Use Hardware Trigonometry Functions \\
Step 4: Experimental Performance Testing \\
8.4. Final Evaluation \\
9: Application Case Study II \\
Molecular Visualization and Analysis \\
9.1. Application Background \\
9.2. A Simple Kernel Implementation \\
9.3. Instruction Execution Efficiency \\
9.4. Memory Coalescing \\
9.5. Additional Performance Comparisons \\
9.6. Using Multiple GPUs \\
10: Parallel Programming and Computational Thinking \\
10.1. Goals of Parallel Programming \\
10.2. Problem Decomposition \\
10.3. Algorithm Selection \\
10.4. Computational Thinking \\
11: A Brief Introduction to OpenCL? \\
11.1. Background \\
11.2. Data Parallelism Model \\
11.3. Device Architecture \\
11.4. Kernel Functions \\
11.5. Device Management and Kernel Launch \\
11.6. Electrostatic Potential Map in OpenCL \\
11.7. Summary \\
12: Conclusion and Future Outlook \\
12.1. Goals Revisited \\
12.2. Memory Architecture Evolution \\
12.3. Kernel Execution Control Evolution \\
12.4. Core Performance \\
12.5. Programming Environment \\
12.6. A Bright Outlook \\
Appendix A: Matrix Multiplication Example Code \\
Appendix B: Speed and feed of current generation CUDA
devices",
}
@Article{Knezevic:2010:FIM,
author = "M. Knezevic and F. Vercauteren and I. Verbauwhede",
title = "Faster Interleaved Modular Multiplication Based on
{Barrett} and {Montgomery} Reduction Methods",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "12",
pages = "1715--1721",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.93",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5453352",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kong:2010:RMR,
author = "Inwook Kong and E. E. Swartzlander",
title = "A Rounding Method to Reduce the Required Multiplier
Precision for {Goldschmidt} Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "12",
pages = "1703--1708",
month = dec,
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.86",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5453345",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Kornerup:2010:CCRa,
author = "Peter Kornerup and Vincent Lef{\`e}vre and Nicholas
Louvet and Jean-Michel Muller",
title = "On the computation of correctly-rounded sums",
type = "Research report",
number = "RR-7262",
institution = "INRIA",
address = "Lyon, France",
pages = "28",
month = apr,
year = "2010",
bibdate = "Tue Dec 26 14:47:39 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hal.inria.fr/inria-00475279",
abstract = "This paper presents a study of some basic blocks
needed in the design of floating-point summation
algorithms. In particular, we show that among the set
of the algorithms with no comparisons performing only
floating-point additions\slash subtractions, the 2Sum
algorithm introduced by Knuth is minimal, both in terms
of number of operations and depth of the dependency
graph. We investigate the possible use of another
algorithm, Dekker's Fast2Sum algorithm, in radix-10
arithmetic. We give methods for computing, in radix 10,
the floating-point number nearest the average value of
two floating-point numbers. Under reasonable
conditions, we also prove that no algorithms performing
only round-to-nearest additions\slash subtractions
exist to compute the round-to-nearest sum of at least
three floating-point numbers. Starting from an
algorithm due to Boldo and Melquiond, we also present
new results about the computation of the
correctly-rounded sum of three floating-point
numbers.",
acknowledgement = ack-nhfb,
}
@Article{Kornerup:2010:CCRb,
author = "Peter Kornerup and Christoph Lauter and Vincent
Lef{\`e}vre and Nicolas Louvet and Jean-Michel Muller",
title = "Computing correctly rounded integer powers in
floating-point arithmetic",
journal = j-TOMS,
volume = "37",
number = "1",
pages = "4:1--4:23",
month = jan,
year = "2010",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1644001.1644005",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Mar 15 10:45:33 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We introduce several algorithms for accurately
evaluating powers to a positive integer in
floating-point arithmetic, assuming a {\em fused
multiply-add\/} (fma) instruction is available. For
bounded, yet very large values of the exponent, we aim
at obtaining correctly rounded results in
round-to-nearest mode, that is, our algorithms return
the floating-point number that is nearest the exact
value.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "correct rounding; floating-point arithmetic; integer
power function",
}
@Book{Kornerup:2010:FPN,
author = "Peter Kornerup and David W. Matula",
title = "Finite Precision Number Systems and Arithmetic",
volume = "133",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xv + 699",
year = "2010",
ISBN = "0-521-76135-2 (hardcover)",
ISBN-13 = "978-0-521-76135-2 (hardcover)",
LCCN = "QA248 .K627 2010",
bibdate = "Sun Jun 19 14:21:37 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
series = "Encyclopedia of mathematics and its applications",
URL = "http://assets.cambridge.org/97805217/61352/cover/9780521761352.jpg;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-b.html;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-d.html;
http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-t.html",
abstract = "Fundamental arithmetic operations support virtually
all of the engineering, scientific, and financial
computations required for practical applications, from
cryptography, to financial planning, to rocket science.
This comprehensive reference provides researchers with
the thorough understanding of number representations
that is a necessary foundation for designing efficient
arithmetic algorithms. Using the elementary foundations
of radix number systems as a basis for arithmetic, the
authors develop and compare alternative algorithms for
the fundamental operations of addition, multiplication,
division, and square root with precisely defined
roundings. Various finite precision number systems are
investigated, with the focus on comparative analysis of
practically efficient algorithms for closed arithmetic
operations over these systems. Each chapter begins with
an introduction to its contents and ends with
bibliographic notes and an extensive bibliography. The
book may also be used for graduate teaching: problems
and exercises are scattered throughout the text and a
solutions manual is available for instructors.",
acknowledgement = ack-nhfb,
subject = "Arithmetic; Foundations",
tableofcontents = "Preface / xi \\
1. Radix polynomial representations / 1 \\
2. Base and digit set conversion / 59 \\
3. Addition / \\
4. Multiplication / \\
5. Division / 275 \\
6. Square root / 398 \\
7. Floating-point number systems / 447 \\
8. Modular arithmetic and residue number systems / 528
\\
9. Rational arithmetic / 63 \\
Author index / 691 \\
Index / 693",
}
@TechReport{KrusemanAretz:2010:DCP,
author = "F. E. J. {Kruseman Aretz}",
title = "Design and correctness proof of an emulation of the
floating-point operations of the {Electrologica X8}: a
case study",
type = "Computer Science Report",
number = "1002",
institution = "Technische Universiteit Eindhoven",
address = "Eindhoven, The Netherlands",
pages = "58",
day = "30",
month = mar,
year = "2010",
bibdate = "Mon Oct 17 16:37:56 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://repository.tue.nl/674735",
abstract = "Some time ago I decided to write an emulator for a
Dutch computer from the sixties of the previous
century, the Electrologica X8, in order to be able to
run its ALGOL 60 implementation and to do some
measurements with it. That emulator was written in
(standard ISO) Pascal.",
acknowledgement = ack-nhfb,
remark-1 = "From page 2: ``Electrologica was a Dutch computer
factory, founded in 1956. It produced the Electrologica
X1 (from 1958) and its successor, the Electrologica X8
(from 1965). The latter was more or less upwards
compatible with the former, about a factor of 12
faster, and in addition it had floating-point hardware:
an additional register F and instructions for
floating-point addition, subtraction, multiplication,
and division.''",
remark-2 = "From page 3: ``the floating-point operations `+', `-',
`*', and `/' all delivered the best possible result,
i.e. that floating-point number in standard form whose
value is closest to the exact result. In case that the
exact result of the operation was precisely midway two
consecutive floating-point numbers, the result was
rounded upwards for positive results and downwards for
negative results.''",
remark-3 = "From page 29: ``The number representation of the EL X8
was in one-complement, with preference for $-0$ over
$+0$ (I have not analyzed whether an implementation
directly in the one-complement representation needs
more, or perhaps less guarding bits).",
remark-4 = "Page 56 presents the four-step Newton--Raphson
algorithm used to implement the square-root operation
on the EL8, producing results with a maximum error of
0.90 bit.",
}
@Article{Lamotte:2010:CVC,
author = "Jean-Luc Lamotte and Jean-Marie Chesneaux and Fabienne
J{\'e}z{\'e}quel",
title = "{CADNA\_C}: a version of {CADNA} for use with {C} or
{C++} programs",
journal = j-COMP-PHYS-COMM,
volume = "181",
number = "11",
pages = "1925--1926",
month = nov,
year = "2010",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2010.07.006",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 11 09:54:31 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465510002353",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Lefevre:2010:LTL,
author = "Vincent Lef{\'e}vre and Philippe Th{\'e}veny and
Florent de Dinechin and Claude-Pierre Jeannerod and
Christophe Mouilleron and David Pfannholzer and
Nathalie Revol",
title = "{LEMA}: towards a language for reliable arithmetic",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "44",
number = "2",
pages = "41--52",
month = jun,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1838599.1838622",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Mon Aug 2 13:47:24 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Generating certified and efficient numerical codes
requires information ranging from the mathematical
level to the representation of numbers. Even though the
mathematical semantics can be expressed using the
content part of MathML, this language does not
encompass the implementation on computers. Indeed
various arithmetics may be involved, like
floating-point or fixed-point, in fixed precision or
arbitrary precision, and current tools do not handle
all of these.\par
Therefore we propose in this paper LEMA (Langage pour
les Expressions Math{\'e}matiques Annot{\'e}es), a
descriptive language based on MathML with additional
expressiveness. LEMA will be used during the automatic
generation of certified numerical codes. Such a
generation process typically involves several steps,
and LEMA would thus act as a glue to represent and
store the information at every stage.\par
First, we specify in the language the characteristics
of the arithmetic as described in the IEEE 754
floating-point standard: formats, exceptions, rounding
modes. This can be generalized to other arithmetics.
Then, we use annotations to attach a specific
arithmetic context to an expression tree. Finally,
considering the evaluation of the expression in this
context allows us to deduce several properties on the
result, like being exact or being an exception. Other
useful properties include numerical ranges and error
bounds.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
issue = "172",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Lima:2010:KBA,
author = "J. B. Lima and D. Panario and Qiang Wang",
title = "A {Karatsuba}-Based Algorithm for Polynomial
Multiplication in {Chebyshev} Form",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "6",
pages = "835--841",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.45",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:29 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5416688",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Loitsch:2010:PFP,
author = "Florian Loitsch",
title = "Printing floating-point numbers quickly and accurately
with integers",
journal = j-SIGPLAN,
volume = "45",
number = "6",
pages = "233--243",
month = jun,
year = "2010",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/1809028.1806623",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Fri Oct 8 17:53:18 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present algorithms for accurately converting
floating-point numbers to decimal representation. They
are fast (up to 4 times faster than commonly used
algorithms that use high-precision integers) and
correct: any printed number will evaluate to the same
number, when read again.\par
Our algorithms are fast, because they require only
fixed-size integer arithmetic. The sole requirement for
the integer type is that it has at least two more bits
than the significand of the floating-point number.
Hence, for IEEE 754 double-precision numbers (having a
53-bit significand) an integer type with 55 bits is
sufficient. Moreover we show how to exploit additional
bits to improve the generated output.\par
We present three algorithms with different properties:
the first algorithm is the most basic one, and does not
take advantage of any extra bits. It simply shows how
to perform the binary-to-decimal transformation with
the minimal number of bits. Our second algorithm
improves on the first one by using the additional bits
to produce a shorter (often the shortest)
result.\par
Finally we propose a third version that can be used
when the shortest output is a requirement. The last
algorithm either produces optimal decimal
representations (with respect to shortness and
rounding) or rejects its input. For IEEE 754
double-precision numbers and 64-bit integers roughly
99.4\% of all numbers can be processed efficiently. The
remaining 0.6\% are rejected and need to be printed by
a slower complete algorithm.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "correct rounding; dtoa; floating-point printing",
}
@InProceedings{Louvet:2010:NRA,
author = "Nicolas Louvet and Jean-Michel Muller and Adrien
Panhaleux",
title = "{Newton--Raphson} algorithms for floating-point
division using an {FMA}",
crossref = "Charot:2010:API",
pages = "200--207",
year = "2010",
DOI = "https://doi.org/10.1109/ASAP.2010.5540948",
bibdate = "Thu Feb 17 08:21:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When implementing a function $f$ in floating-point
arithmetic, if we wish correct rounding and good
performance, it is important to know if there are input
floating-point values $x$ such that $ f(x) $ is either
the middle of two consecutive floating-point numbers
(assuming rounded-to-nearest arithmetic), or a
floating-point number (assuming rounded toward $ \pm
\infty $ or toward $0$ arithmetic). In the first case,
we say that $ f(x) $ is a midpoint, and in the second
case, we say that $ f(x) $ is an exact point. For some
usual algebraic functions and various floating-point
formats, we prove whether or not there exist midpoints
or exact points. When there exist midpoints or exact
points, we characterize them or list all of them (if
there are not too many). The results and the techniques
presented in this paper can be used in particular to
deal with both the binary and the decimal formats
defined in the IEEE 754-2008 standard for
floating-point arithmetic.",
acknowledgement = ack-nhfb,
}
@Article{Maruyama:2010:SVN,
author = "Takumi Maruyama and Toshio Yoshida and Ryuji Kan and
Iwao Yamazaki and Shuji Yamamura and Noriyuki Takahashi
and Mikio Hondou and Hiroshi Okano",
title = "{Sparc64 VIIIfx}: a New-Generation Octocore Processor
for Petascale Computing",
journal = j-IEEE-MICRO,
volume = "30",
number = "2",
pages = "30--40",
month = mar # "\slash " # apr,
year = "2010",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2010.40",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Fri Apr 23 06:37:18 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "fused multiply-add (FMA); IEEE 754-2008 arithmetic",
}
@Article{Mathews:2010:AOE,
author = "Deborah Mathews",
title = "Abstract only: an empirical study of parallel big
number arithmetic",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "44",
number = "2",
pages = "25--25",
month = jun,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1838599.1838615",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Mon Aug 2 13:47:24 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "To capitalize on multi-core processing, it would be
good to perform big number arithmetic in parallel.
While a performance increase equal to the number of
processors is theoretically possible, our experiments
show that in practice the likelihood of gaining any
performance increase for big number arithmetic through
parallel processing is low. A speed-up approaching the
number of processors was not achieved for
multiplication until the operands had at least 215
bits. No performance gain was realized for addition.
The base algorithm used for multiplication was O(n2)
and, therefore, suboptimal. The expected performance
gain achieved when parallelizing a more efficient base
algorithm should be even smaller.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
issue = "172",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Mehrotra:2010:SLR,
author = "Sanjay Mehrotra and Zhifeng Li",
title = "Segment {LLL} Reduction of Lattice Bases Using Modular
Arithmetic",
journal = j-ALGORITHMS-BASEL,
volume = "3",
number = "3",
pages = "224--243",
month = sep,
year = "2010",
CODEN = "ALGOCH",
DOI = "https://doi.org/10.3390/a3030224",
ISSN = "1999-4893 (electronic)",
ISSN-L = "1999-4893",
bibdate = "Fri May 3 13:50:12 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.mdpi.com/1999-4893/3/3/224",
acknowledgement = ack-nhfb,
fjournal = "Algorithms (Basel)",
journal-URL = "https://www.mdpi.com/journal/algorithms",
pubdates = "Received: 28 May 2010 / Accepted: 29 June 2010 /
Published: 12 July 2010",
}
@Article{Meyer:2010:CGT,
author = "Quirin Meyer and Jochen S{\"u}{\ss}muth and Gerd
Su{\ss}ner and Marc Stamminger and G{\"u}nther
Greiner",
title = "Computer Graphics Theory: On Floating-Point Normal
Vectors",
journal = j-CGF,
volume = "29",
number = "4",
pages = "1405--1409",
month = jun,
year = "2010",
CODEN = "CGFODY",
DOI = "https://doi.org/10.1111/j.1467-8659.2010.01737.x",
ISSN = "0167-7055 (print), 1467-8659 (electronic)",
ISSN-L = "0167-7055",
bibdate = "Sat May 11 13:28:01 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cgf.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Com{\-}pu{\-}ter Graphics Forum",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-8659/",
onlinedate = "26 Aug 2010",
}
@TechReport{Moller:2010:IDI,
author = "Niels M{\"o}ller and Torbj{\"o}rn Granlund",
title = "Improved division by invariant integers",
type = "Report",
institution = "Centre for Industrial and Applied Mathematics, KTH",
address = "Stockholm, Sweden",
pages = "10",
day = "13",
month = apr,
year = "2010",
bibdate = "Mon Oct 14 15:57:19 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://gmplib.org/~tege/division-paper.pdf",
abstract = "This paper considers the problem of dividing a
two-word integer by a single-word integer, together
with a few extensions and applications. Due to lack of
efficient division instructions in current processors,
the division is performed as a multiplication using a
precomputed single-word approximation of the reciprocal
of the divisor, followed by a couple of adjustment
steps. There are three common types of unsigned
multiplication instructions; we define full word
multiplication (umul) which produces the two-word
product of two single-word integers, low multiplication
(umullo) which produces only the least significant word
of the product, and high multiplication (umulhi), which
produces only the most significant word. We describe an
algorithm which produces a quotient and remainder using
one umul and one umullo. This is an improvement over
earlier methods, since the new method uses cheaper
multiplication operations. It turns out we also get
some additional savings from simpler adjustment
conditions. The algorithm has been implemented in
version 4.3 of the GMP library. When applied to the
problem of dividing a large integer by a single word,
the new algorithm gives a speedup of roughly 30\%,
benchmarked on AMD and Intel processors in the x86-64
family.",
acknowledgement = ack-nhfb,
}
@Article{Morisita:2010:IEA,
author = "Hirokazu Morisita and Kenta Inakagata and Yasunori
Osana and Naoyuki Fujita and Hideharu Amano",
title = "Implementation and evaluation of an arithmetic
pipeline on {FLOPS-$2$D}: multi-{FPGA} system",
journal = j-COMP-ARCH-NEWS,
volume = "38",
number = "4",
pages = "8--13",
month = sep,
year = "2010",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/1926367.1926370",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Thu Jan 20 14:27:03 MST 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "UPACS (Unified Platform for Aerospace Computational
Simulation) is one of the practical CFD (Computational
Fluid Dynamics) packages supporting various
selectability. A custom machine for efficient execution
of MUSCL; a core functions of UPACS is implemented on
FLOPS-2D (Flexibly Linkable Object for Programmable
System); multi-FPGA reconfigurable system. The deep and
complicated pipeline structure generated from MUSCL
dataflow is divided and optimized into two FPGA boards
by using a tuning tool called RER. With optimization of
the order of operations and pipeline structure, about
60\% utilization of the pipeline is achieved even by
using serial links between two boards.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Mukherjee:2010:NAC,
author = "Manideepa Mukherjee and Amitabha Sinha",
title = "A novel architecture for conversion of binary to
single digit double base numbers",
journal = j-COMP-ARCH-NEWS,
volume = "38",
number = "5",
pages = "1--6",
month = dec,
year = "2010",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/1978907.1978909",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri May 13 11:25:46 MDT 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Double base number systems are increasingly attractive
for many compute intensive applications especially in
signal processing because of their capabilities of
handling arithmetic operations efficiently. However,
the complexity involved in converting binary to DBNS
becomes a major bottleneck and the efficiency of
performance goes down drastically due to the complexity
involved in conversion. Since complexity of multi digit
DBNS multiplications and additions increases with the
number of digits (index i,j), in this paper a novel
conversion scheme has been proposed where a given
binary number will be converted to a single digit
(index i,j) double base number. The proposed scheme not
only reduces the hardware complexity of the arithmetic
operations but also reduces the time of execution.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
keywords = "Double-Based Number System (DBNS)",
}
@Book{Muller:2010:HFP,
author = "Jean-Michel Muller and Nicolas Brisebarre and Florent
de Dinechin and Claude-Pierre Jeannerod and Vincent
Lef{\`e}vre and Guillaume Melquiond and Nathalie Revol
and Damien Stehl{\'e} and Serge Torres",
title = "Handbook of Floating-Point Arithmetic",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "xxiii + 572",
year = "2010",
DOI = "https://doi.org/10.1007/978-0-8176-4704-9;
https://doi.org/10.1007/978-0-8176-4705-6",
ISBN = "0-8176-4704-X (hardcover), 0-8176-4705-8 (e-book)",
ISBN-13 = "978-0-8176-4704-9 (hardcover), 978-0-8176-4705-6
(e-book)",
LCCN = "QA76.9.C62 H36 2010",
MRnumber = "MR2568265",
bibdate = "Thu Jan 27 16:18:58 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
price = "US\$90 (est.)",
acknowledgement = ack-nhfb,
}
@Article{Nickolls:2010:GCE,
author = "John Nickolls and William J. Dally",
title = "The {GPU} Computing Era",
journal = j-IEEE-MICRO,
volume = "30",
number = "2",
pages = "56--69",
month = mar # "\slash " # apr,
year = "2010",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2010.41",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Fri Apr 23 06:37:18 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "fused multiply-add (FMA); IEEE 754-2008 arithmetic;
subnormal numbers in hardware; underflow",
remark = "From page 64 of the article:\par
IEEE 754-2008 floating-point arithmetic\par
The Fermi CUDA core floating-point unit implements the
IEEE 754-2008 floating-point arithmetic standard for
32-bit single-precision and 64-bit double-precision
results, including fused multiply-add (FMA)
instructions. FMA computes $ D = A \times B + C $ with
no loss of precision by retaining full precision in the
intermediate product and addition, then rounding the
final sum to form the result. Using FMA enables fast
division and square-root operations with exactly
rounded results.\par
Fermi raises the throughput of 64-bit double-precision
operations to half that of single-precision operations,
a dramatic improvement over the T10 GPU. This
performance level enables broader deployment of GPUs in
high-performance computing. The floating-point
instructions handle subnormal numbers at full speed in
hardware, allowing small values to retain partial
precision rather than flushing them to zero or
calculating subnormal values in multicycle software
exception handlers as most CPUs do.\par
The SFUs execute 32-bit floating-point instructions for
fast approximations of reciprocal, reciprocal square
root, sin, cos, exp, and log functions. The
approximations are precise to better than 22 mantissa
bits.",
}
@Misc{NURCL:2010:VNV,
author = "{Northeastern University Reconfigurable Computing
Laboratory}",
title = "{Vfloat}: The {Northeastern Variable precision
FLOATing point library}",
howpublished = "Web site.",
year = "2010",
bibdate = "Sat Oct 9 12:56:05 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ece.neu.edu/groups/rcl/projects/floatingpoint/",
acknowledgement = ack-nhfb,
}
@Book{Parhami:2010:CAA,
author = "Behrooz Parhami",
title = "Computer arithmetic: algorithms and hardware designs",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
edition = "Second",
pages = "xxv + 641",
year = "2010",
ISBN = "0-19-532848-5 (hardcover)",
ISBN-13 = "978-0-19-532848-6 (hardcover)",
LCCN = "QA76.9.C62 P37 2010",
bibdate = "Sat Sep 20 16:57:27 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "The Oxford series in electrical and computer
engineering",
URL = "http://www.loc.gov/catdir/enhancements/fy1006/2009034155-d.html;
http://www.loc.gov/catdir/enhancements/fy1006/2009034155-t.html",
abstract = "Ideal for graduate and senior undergraduate courses in
computer arithmetic and advanced digital design,
Computer Arithmetic: Algorithms and Hardware Designs,
Second Edition, provides a balanced, comprehensive
treatment of computer arithmetic. It covers topics in
arithmetic unit design and circuit implementation that
complement the architectural and algorithmic speedup
techniques used in high-performance computer
architecture and parallel processing. Using a unified
and consistent framework, the text begins with number
representation and proceeds through basic arithmetic
operations, floating-point arithmetic, and function
evaluation methods. Later chapters cover broad design
and implementation topics --- including techniques for
high-throughput, low-power, fault-tolerant, and
reconfigurable arithmetic. An appendix provides a
historical view of the field and speculates on its
future. An indispensable resource for instruction,
professional development, and research, Computer
Arithmetic: Algorithms and Hardware Designs, Second
Edition, combines broad coverage of the underlying
theories of computer arithmetic with numerous examples
of practical designs, worked-out examples, and a large
collection of meaningful problems. This second edition
includes a new chapter on reconfigurable arithmetic, in
order to address the fact that arithmetic functions are
increasingly being implemented on field-programmable
gate arrays (FPGAs) and FPGA-like configurable devices.
Updated and thoroughly revised, the book offers new and
expanded coverage of saturating adders and multipliers,
truncated multipliers, fused multiply-add units,
overlapped quotient digit selection, bipartite and
multipartite tables, reversible logic, dot notation,
modular arithmetic, Montgomery modular reduction,
division by constants, IEEE floating-point standard
formats, and interval arithmetic.",
acknowledgement = ack-nhfb,
subject = "Computer arithmetic; Computer algorithms; Computer
algorithms.; Computer arithmetic.",
tableofcontents = "Part I: Number representation \\
Numbers and Arithmetic \\
Representing Signed Numbers \\
Redundant Number Systems \\
Residue Number Systems \\
Part II: Addition\slash Subtraction. Basic Addition and
Counting \\
Carry-Lookahead Adders \\
Variations in Fast Adders \\
Multioperand Addition \\
Part III: Multiplication. Basic Multiplication Schemes
\\
High-Radix Multipliers \\
Tree and Array Multipliers \\
Variations in Multipliers \\
Part IV: Division. Basic Division Schemes \\
High-Radix Dividers \\
Variations in Dividers \\
Division by Convergence \\
Part V: Real arithmetic. Floating-Point Representations
\\
Floating-Point Operations \\
Errors and Error Control \\
Precise and Certifiable Arithmetic \\
Part VI: Function evaluation. Square-Rooting Methods
\\
The CORDIC Algorithms \\
Variations in Function Evaluation \\
Arithmetic by Table Lookup \\
High-Throughput Arithmetic \\
Part VII: Implementation topics \\
Low-Power Arithmetic \\
Fault-Tolerant Arithmetic \\
Reconfigurable Arithmetic",
}
@Article{Pence:2010:OCF,
author = "W. D. Pence and R. L. White and R. Seaman",
title = "Optimal Compression of Floating-point Astronomical
Images Without Significant Loss of Information",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "7",
month = jul,
year = "2010",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in PASP {\bf 122}, 1096 (2010).",
URL = "http://arxiv.org/abs/1007.1179",
abstract = "We describe a compression method for floating-point
astronomical images that gives compression ratios of
$6$--$ 10$ while still preserving the scientifically
important information in the image. The pixel values
are first preprocessed by quantizing them into scaled
integer intensity levels, which removes some of the
uncompressible noise in the image. The integers are
then losslessly compressed using the fast and efficient
Rice algorithm and stored in a portable FITS format
file. Quantizing an image more coarsely gives greater
image compression, but it also increases the noise and
degrades the precision of the photometric and
astrometric measurements in the quantized image.
Dithering the pixel values during the quantization
process can greatly improve the precision of
measurements in the images. This is especially
important if the analysis algorithm relies on the mode
or the median which would be similarly quantized if the
pixel values are not dithered. We perform a series of
experiments on both synthetic and real astronomical CCD
images to quantitatively demonstrate that the
magnitudes and positions of stars in the quantized
images can be measured with the predicted amount of
precision. In order to encourage wider use of these
image compression methods, we have made available a
pair of general-purpose image compression programs,
called fpack and funpack, which can be used to compress
any FITS format image.",
acknowledgement = ack-nhfb,
subject = "Instrumentation and Methods for Astrophysics
(astro-ph.IM)",
}
@Article{Purohit:2010:EIA,
author = "G. N. Purohit and Asmita Singh Rawat",
title = "Efficient Implementation of Arithmetic Operations in
{ECC} over Binary Fields",
journal = j-INT-J-COMP-APPL,
volume = "6",
number = "??",
pages = "5--9",
month = sep,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.5120/1056-1376",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 08:33:30 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume6/number2/1056-1376/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "2",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@InProceedings{Qi:2010:DLC,
author = "Zichu Qi and Qi Guo and Ge Zhang and Xiangku Li and
Weiwu Hu",
title = "Design of Low-Cost High-Performance Floating-Point
Fused Multiply-Add with Reduced Power",
crossref = "IEEE:2010:ICV",
pages = "206--211",
year = "2010",
DOI = "https://doi.org/10.1109/VLSI.Design.2010.41",
bibdate = "Sun Feb 20 10:01:52 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a floating-point fused
multiply-add (FMA) unit with low-cost and low power
techniques. To improve the performance, two
single-precision operations can be performed
concurrently with one double-precision datapath, which
is very useful in multimedia and even scientific
applications. Moreover, to reduce the additional area
costs for supporting two single-precision operations in
parallel, multiple double-precision units, i.e., the
multiplier, shifter and adder, are reused as much as
possible. A modified dual-path algorithm is proposed by
classifying the exponent difference into three cases
and implementing them with close and far paths, which
can reduce latency and facilitate lowering power
consumption by enabling only one of the two paths. In
addition, in case of FADD instructions, the multiplier
in the first stage is bypassed and kept in stable mode,
which can significantly improve FADD instruction
performance and lower power consumption. The overall
FMA unit has a latency of 4 cycles while the FADD
operation has 3 cycles. Each cycle has a time delay of
about 0.66 ns in the ST 65 nm CMOS technology. Compared
with the conventional double-precision FMA, about 13\%
delay is reduced and about 22\% area is increased,
which is acceptable since two single-precision results
can be generated simultaneously.",
acknowledgement = ack-nhfb,
}
@Article{Roldao:2010:HTF,
author = "Antonio Roldao and George A. Constantinides",
title = "A High Throughput {FPGA}-Based Floating Point
Conjugate Gradient Implementation for Dense Matrices",
journal = j-TRETS,
volume = "3",
number = "1",
pages = "1:1--1:??",
month = jan,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1661438.1661439",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Tue Mar 16 09:47:03 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@InProceedings{Rummer:2010:IPI,
author = "Philipp R{\"u}mmer and Thomas Wahl",
editor = "An smt-lib theory of binary floating-point
arithmetic",
booktitle = "????",
title = "Informal proceedings of {8th International Workshop on
Satisfiability Modulo Theories (SMT) at FLoC,
Edinburgh, Scotland}",
publisher = "????",
address = "??",
pages = "??--??",
year = "2010",
DOI = "",
ISBN = "",
ISBN-13 = "",
LCCN = "",
bibdate = "Sat Apr 02 09:57:20 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "",
acknowledgement = ack-nhfb,
}
@InProceedings{Rump:2010:ARC,
author = "Siegfried M. Rump",
title = "Accurate and Reliable Computing in Floating-Point
Arithmetic",
crossref = "Fukuda:2010:MSI",
pages = "105--108",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_22",
bibdate = "Sat Sep 23 06:20:46 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_22.pdf",
acknowledgement = ack-nhfb,
}
@Article{Rump:2010:FHP,
author = "Siegfried M. Rump and T. Ogita and S. Oishi",
title = "Fast high precision summation",
journal = "Nonlinear Theory and Its Applications ({NOLTA})",
volume = "1",
number = "1",
pages = "2--24",
month = "????",
year = "2010",
DOI = "https://doi.org/10.1587/nolta.1.2",
bibdate = "Wed Oct 12 18:34:53 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate dot product; accurate summation",
}
@InProceedings{Rump:2010:VMRa,
author = "Siegfried M. Rump",
title = "Verification methods: rigorous results using
floating-point arithmetic",
crossref = "Watt:2010:IPI",
pages = "3--4",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837937",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The classical mathematical proof is performed by
pencil and paper. However, there are many ways in which
computers may be used in a mathematical proof. But
`proofs by computers' or even the use of computers in
the course of a proof are not so readily accepted (the
December 2008 issue of the Notices of the American
Mathematical Society is devoted to formal proofs by
computers).\par
In this talk we discuss how verification methods may
assist in achieving a mathematically rigorous result.
In particular we emphasize how floating-point
arithmetic is used.\par
The goal of verification methods is ambitious: For a
given problem it is proved, with the aid of a computer,
that there exists a (unique) solution within computed
bounds. The methods are constructive, and the results
are rigorous in every respect. Verification methods
apply to data with tolerances as well.\par
Rigorous results are the main goal in computer algebra.
However, verification methods use solely floating-point
arithmetic, so that the total computational effort is
not too far from that of a purely (approximate)
numerical method. Nontrivial problems have been solved
using verification methods. For example:\par
Tucker (1999) received the 2004 EMS prize awarded by
the European Mathematical Society for (citation)
`giving a rigorous proof that the Lorenz attractor
exists for the parameter values provided by Lorenz.
This was a long standing challenge to the dynamical
system community, and was included by Smale in his list
of problems for the new millennium. The proof uses
computer estimates with rigorous bounds based on higher
dimensional interval arithmetics.'\par
Sahinidis and Tawaralani (2005) received the 2006
Beale-Orchard-Hays Prize for their package BARON which
(citation) `incorporates techniques from automatic
differentiation, interval arithmetic, and other areas
to yield an automatic, modular, and relatively
efficient solver for the very difficult area of global
optimization'.\par
A main goal of this talk is to introduce the principles
of how to design verification algorithms, and how these
principles differ from those for traditional numerical
algorithms.\par
We begin with a brief discussion of the working tools
of verification methods, in particular floating-point
and interval arithmetic. In particular the development
and limits of verification methods for finite
dimensional problems are discussed in some detail;
problems include dense systems of linear equations,
sparse linear systems, systems of nonlinear equations,
semi-definite programming and other special linear and
nonlinear problems including M-matrices, simple and
multiple roots of polynomials, bounds for simple and
multiple eigenvalues or clusters, and quadrature. We
mention that automatic differentiation tools to compute
the range of gradients, Hessians, Taylor coefficients,
and slopes are necessary. If time permits, verification
methods for continuous problems, namely two-point
boundary value problems and semilinear elliptic
boundary value problems are presented.\par
Throughout the talk, a number of examples of the wrong
use of interval operations are given. In the past such
examples contributed to the dubious reputation of
interval arithmetic, whereas they are, in fact, just a
misuse.\par
Some algorithms are presented in executable
Matlab/INTLAB-code. INTLAB, the Matlab toolbox for
reliable computing and free for academic use, is
developed and written by Rump (1999). It was, for
example, used by Bornemann, Laurie, Wagon, and
Waldvogel (2004) in the solution of half of the
problems of the $ 10 \times 10 $-digit challenge by
Trefethen (2002).",
acknowledgement = ack-nhfb,
}
@Article{Rump:2010:VMRb,
author = "Siegfried M. Rump",
title = "Verification methods: Rigorous results using
floating-point arithmetic",
journal = j-ACTA-NUMERICA,
volume = "19",
pages = "287--449",
year = "2010",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S096249291000005X",
ISBN = "0-521-19284-6",
ISBN-13 = "978-0-521-19284-2",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "65G20 (03B35 68T05)",
MRnumber = "2652784 (2011j:65093)",
MRreviewer = "Ljiljana Petkovi{\'c}",
bibdate = "Sat Sep 24 10:35:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ti3.tu-harburg.de/paper/rump/Ru10.pdf",
abstract = "This review article is devoted to verification methods
and consists of three parts of similar length. In Part
1 the working tools of verification methods are
discussed, in particular floating-point and interval
arithmetic; my findings in Section 1.5 (Historical
remarks) seem new, even to experts in the field.\par
In Part 2, the development and limits of verification
methods for finite-dimensional problems are discussed
in some detail. In particular, we discuss how
verification is _not_ working. For example, we give a
probabilistic argument that the so-called interval
Gaussian elimination (IGA) does not work even for
(well-conditioned) random matrices of small size.
Verification methods are discussed for problems such as
dense systems of linear equations, sparse linear
systems, systems of nonlinear equations, semi-definite
programming and other special linear and nonlinear
problems, including M-matrices, finding simple and
multiple roots of polynomials, bounds for simple and
multiple eigenvalues or clusters, and quadrature. The
necessary automatic differentiation tools to compute
the range of gradients, Hessians, Taylor coefficients,
and slopes are also introduced.\par
Concerning the important area of optimization, Neumaier
(2004) gave in his Acta Numerica article an overview on
global optimization and constraint satisfaction
methods. In view of the thorough treatment there,
showing the essential role of interval methods in this
area, we restrict our discussion to a few recent,
complementary issues.\par
Finally, in Part 3, verification methods for
infinite-dimensional problems are presented, namely
two-point boundary value problems and semilinear
elliptic boundary value problems.\par
Throughout the article, many examples of the
inappropriate use of interval operations are given. In
the past such examples contributed to the dubious
reputation of interval arithmetic (see Section 1.3),
whereas they are, in fact, simply a misuse.\par
One main goal of this review article is to introduce
the principles of the design of verification
algorithms, and how these principles differ from those
for traditional numerical algorithms (see Section
1.4).\par
Many algorithms are presented in executable
MATLAB/INTLAB code, providing the opportunity to test
the methods directly. INTLAB, the MATLAB toolbox for
reliable computing, was, for example, used by
Bornemann, Laurie, Wagon and Waldvogel (2004) in the
solution of half of the problems of the SIAM $ 10
\times 10 $-digit challenge by Trefethen (2002).",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "10 May 2010",
}
@Article{Ryden:2010:EIR,
author = "Jesper Ryd{\'e}n and Sven Erick Alm",
title = "The effect of interaction and rounding error in
two-way {ANOVA}: example of impact on testing for
normality",
journal = j-J-APPL-STAT,
volume = "37",
number = "10",
pages = "1695--1701",
month = oct,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1080/02664760903143925",
ISSN = "0266-4763 (print), 1360-0532 (electronic)",
ISSN-L = "0266-4763",
bibdate = "Mon Sep 5 18:53:08 MDT 2011",
bibsource = "http://www.tandf.co.uk/journals/routledge/02664763.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Statistics",
journal-URL = "http://www.tandfonline.com/loi/cjas20",
onlinedate = "21 Sep 2010",
}
@Article{Saito:2010:DQP,
author = "Tsubasa Saito and Emiko Ishiwata and Hidehiko
Hasegawa",
title = "Development of quadruple precision arithmetic toolbox
{QuPAT} on {Scilab}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "6017",
pages = "60--70",
year = "2010",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-12165-4_5",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Apr 01 07:57:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-12165-4_5",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "floating-point arithmetic; QuPAT (Quadruple Precision
Arithmetic Toolbox)",
remark = "International Conference on Computational Science and
Its Applications, ICCSA 2010",
}
@InProceedings{Samy:2010:DFP,
author = "R. Samy and H. A. H. Fahmy and R. Raafat and A.
Mohamed and T. ElDeeb and Y. Farouk",
title = "A decimal floating-point fused-multiply-add unit",
crossref = "Delgado-Frias:2010:IIM",
pages = "529--532",
year = "2010",
DOI = "https://doi.org/10.1109/MWSCAS.2010.5548746",
bibdate = "Thu Feb 17 08:38:22 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents the first hardware implementation
of a fully parallel decimal floating-point
fused-multiply-add unit performing the operation $ \pm
(A \times B) \pm C $ on decimal floating-point
operands. The proposed design is fully compliant with
the IEEE 754-2008 standard and supports the two
standard formats decimal64 and decimal128. Furthermore,
the proposed design may be controlled to perform the
multiplication or the addition\slash subtraction as
standalone operations. Our decimal floating-point FMA
may be pipelined so that a complete resultant decimal
floating-point is available each clock cycle.",
acknowledgement = ack-nhfb,
}
@Article{Sasaki:2010:CFP,
author = "Tateaki Sasaki and Fujio Kako",
title = "Computing floating-point {Gr{\"o}bner} bases
accurately",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "44",
number = "3",
pages = "142--143",
month = sep,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1940475.1940504",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Thu Mar 31 10:24:16 MDT 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We propose a new method for floating-point Gr{\"o}bner
basis computation. The idea is to improve the
accuracies of the coefficients of polynomials of
intermediate bases computed by our previous method, by
reducing coefficient matrices by Gaussian
elimination.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
issue = "173",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Book{Schertz:2010:CM,
author = "Reinhard Schertz",
title = "Complex Multiplication",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xiii + 361",
year = "2010",
ISBN = "0-521-76668-0",
ISBN-13 = "978-0-521-76668-5",
LCCN = "QA564 .S294 2010",
bibdate = "Thu Mar 04 18:34:14 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "This is a self-contained account of the state of the
art in classical complex multiplication that includes
recent results on rings of integers and applications to
cryptography using elliptic curves. The author is
exhaustive in his treatment, giving a thorough
development of the theory of elliptic functions,
modular functions and quadratic number fields and
providing a concise summary of the results from class
field theory. The main results are accompanied by
numerical examples, equipping any reader with all the
tools and formulas they need. Topics covered include:
the construction of class fields over quadratic
imaginary number fields by singular values of the
modular invariant $j$ and Weber's tau-function;
explicit construction of rings of integers in ray class
fields and Galois module structure; the construction of
cryptographically relevant elliptic curves over finite
fields; proof of Berwick's congruences using division
values of the Weierstrass $p$-function; relations
between elliptic units and class numbers.",
subject = "Multiplication, Complex",
tableofcontents = "Preface \\
1. Elliptic functions \\
2. Modular functions \\
3. Basic facts from number theory \\
4. Factorisation of singular values \\
5. The reciprocity law \\
6. Generation of ring class fields and ray class fields
\\
7. Integral basis in ray class fields \\
8. Galois module structure \\
9. Berwick's congruences \\
10. Cryptographically relevant elliptic curves \\
11. The class number formulas of Curt Meyer \\
12. Arithmetic interpretation of class number formulas
\\
References \\
Index of notation \\
Index",
}
@Article{Schneeweiss:2010:SAR,
author = "H. Schneeweiss and J. Komlos and A. S. Ahmad",
title = "Symmetric and asymmetric rounding: a review and some
new results",
journal = j-ASTA-ADV-STAT-ANAL,
volume = "94",
number = "3",
pages = "247--271",
month = sep,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10182-010-0125-2",
ISSN = "1863-8171 (print), 1863-818X (electronic)",
ISSN-L = "1863-8171",
bibdate = "Thu Feb 5 09:35:46 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/asta.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/article/10.1007/s10182-010-0125-2",
acknowledgement = ack-nhfb,
fjournal = "AStA. Advances in Statistical Analysis",
journal-URL = "http://link.springer.com/journal/10182",
}
@InProceedings{Sheikh:2010:OOA,
author = "Basit Riaz Sheikh and Rajit Manohar",
editor = "IEEE",
booktitle = "{ASYNC 2010: 16th IEEE Symposium on Asynchronous
Circuits and Systems, 3--6 May 2010, Grenoble, France,
Proceedings}",
title = "An Operand-Optimized Asynchronous {IEEE 754}
Double-Precision Floating-Point Adder",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xviii + 197",
pages = "151--162",
year = "2010",
DOI = "https://doi.org/10.1109/ASYNC.2010.24",
ISBN = "0-7695-4032-5",
ISBN-13 = "978-0-7695-4032-0",
LCCN = "????",
bibdate = "Sat Apr 02 16:34:52 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5476966;
https://www.semanticscholar.org/paper/An-Operand-Optimized-Asynchronous-IEEE-754-Double-Sheikh-Manohar/3e30463d11ba059f19c5959e0acc66709390475e",
acknowledgement = ack-nhfb,
}
@Article{Shieh:2010:WBM,
author = "Ming-Der Shieh and Wen-Ching Lin",
title = "Word-Based {Montgomery} Modular Multiplication
Algorithm for Low-Latency Scalable Architectures",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "8",
pages = "1145--1151",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.72",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5441286",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Shuster:2010:ECN,
author = "John A. Shuster and Jens K{\"o}plinger",
title = "Elliptic complex numbers with dual multiplication",
journal = j-APPL-MATH-COMP,
volume = "216",
number = "12",
pages = "3497--3514",
day = "15",
month = aug,
year = "2010",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Sep 3 10:53:27 MDT 2010",
bibsource = "http://www.sciencedirect.com/science/journal/00963003;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Book{Smiley:2010:MWI,
author = "Jane Smiley",
title = "The man who invented the computer: the biography of
{John Atanasoff}, digital pioneer",
publisher = pub-DOUBLEDAY,
address = pub-DOUBLEDAY:adr,
pages = "246 + 8",
year = "2010",
ISBN = "0-385-52713-6, 0-385-53372-1 (e-book), 1-299-11995-6
(e-book)",
ISBN-13 = "978-0-385-52713-2, 978-0-385-53372-0 (e-book),
978-1-299-11995-6 (e-book)",
LCCN = "QA76.2.A75 S64 2010",
bibdate = "Mon Oct 25 10:49:42 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/t/teller-edward.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
price = "US\$25.95",
abstract = "One night in the late 1930s, in a bar on the
Illinois--Iowa border, John Vincent Atanasoff, a
professor of physics at Iowa State University, after a
frustrating day performing tedious mathematical
calculations in his lab, hit on the idea that the
binary number system and electronic switches, combined
with an array of capacitors on a moving drum to serve
as memory, could yield a computing machine that would
make his life easier. Then he went back and built the
machine. It worked, but he never patented the device,
and the developers of the far-better-known ENIAC almost
certainly stole critical ideas from him. But in 1973 a
court declared that the patent on that Sperry Rand
device was invalid, opening the gates to the computer
revolution. Biographer Jane Smiley makes the race to
develop digital computing as gripping as a real-life
techno-thriller.",
acknowledgement = ack-nhfb,
keywords = "ABC computer; Alan Turing; Charles Babbage; Clifford
Berry; J. Presper Eckert; John V (John Vincent)
Atanasoff; John von Neumann; John W. Mauchly; Konrad
Zuse; Max Newman",
remark-1 = "This book contains discussions of the patent battles
over early computer designs (pp 131--133 and Chapter
9), and some limited information about arithmetic
choices, such as on pp. 162--163 ``Howard Aiken, who
was still advocating for decimal numbers for
computers''. It also contains statements of how Konrad
Zuse's early work on electromechanical computers was
finally made known in the 1950s in the US (see p.
159).",
remark-2 = "The chapters are numbered, but without titles, so
there is no tableofcontents field in this entry.",
remark-3 = "Chapters 10--12 on the Honeywell vs Sperry lawsuit
(1968--1971) over who discovered the computer present a
strong rebuttal to the views in
\cite{McCartney:2001:ETT}.",
remark-4 = "Pages 188--189 mention Edward Teller's testimony in
August 1971 in the Honeywell vs Sperry lawsuit that the
ENIAC had been used for calculations by Los Alamos
scientists in 1945--1945, almost two years before the
Mauchly and Eckert (i.e., Sperry) patent claims on
ENIAC technology. That is `prior art' that led to
Sperry losing its patent claims for ENIAC.",
subject = "Atanasoff, John V (John Vincent); Computer scientists;
United States; Biography; Inventors; Physicists; Iowa;
College teachers; Electronic digital computers;
History; 20th century; Patents; Intellectual property",
}
@Article{Smith:2010:AFA,
author = "Alastair M. Smith and George A. Constantinides and
Peter Y. K. Cheung",
title = "An Automated Flow for Arithmetic Component Generation
in Field-Programmable Gate Arrays",
journal = j-TRETS,
volume = "3",
number = "3",
pages = "13:1--13:??",
month = sep,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1839480.1839483",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Fri Oct 8 18:26:34 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "State-of-the-art configurable logic platforms, such as
Field-Programmable Gate Arrays (FPGAs), consist of a
heterogeneous mixture of different component types.
Compared to traditional homogeneous configurable
platforms, heterogeneity provides speed and density
advantages. This is due to the replacement of
inefficient programmable logic and routing with
specialized logic and fixed interconnect in components
such as memories, embedded processor units, and fused
arithmetic units. Given the increasing complexity of
these components, this article introduces a method to
automatically propose and explore the benefits of
different types of fused arithmetic units. The methods
are based on common subgraph extraction techniques,
meaning that it is possible to explore different
subcircuits that occur frequently across a set of
benchmarks. A quantitative analysis is performed of the
various fused arithmetic circuits identified by our
tool, which are then automatically synthesized to an
ASIC process, providing a study of the speed and area
benefits of the components. The results of this study
provide bounds on the performance of heterogeneous
FPGAs: by incorporating coarse-grain components which
match the specific needs of a set of benchmarks we show
that significant improvements in circuit speed and area
can be made.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
keywords = "common subgraph; FPGA; reconfigurable logic",
}
@InProceedings{Sze:2010:TQB,
author = "Tsz-Wo Sze",
editor = "{IEEE}",
booktitle = "{2010 IEEE Second International Conference on Cloud
Computing Technology and Science (CloudCom)}",
title = "The Two Quadrillionth Bit of Pi is $0$ ! Distributed
Computation of Pi with {Apache Hadoop}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "727",
year = "2010",
DOI = "https://doi.org/10.1109/CloudCom.2010.57",
ISBN = "1-4244-9405-2",
ISBN-13 = "978-1-4244-9405-7",
LCCN = "????",
bibdate = "Mon Apr 25 18:16:05 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a new record on computing specific bits of
Pi, the mathematical constant, and discuss performing
such computations on Apache Hadoop clusters. The
specific bits represented in hexadecimal are 0E6C1294
AED40403 F56D2D76 4026265B CA98511D 0FCFFAA1 0F4D28B1
BB5392B8. These 256 bits end at the
2,000,000,000,000,252nd bit position, which doubles the
position and quadruples the precision of the previous
known record. The position of the first bit is
1,999,999,999,999,997 and the value of the two
quadrillionth bit is 0. The computation is carried out
by a MapReduce program called DistBbp. To effectively
utilize available cluster resources without
monopolizing the whole cluster, we develop an elastic
computation framework that automatically schedules
computation slices, each a DistBbp job, as either
map-side or reduce-side computation based on changing
cluster load condition. We have calculated Pi at
varying bit positions and precisions, and one of the
largest computations took 23 days of wall clock time
and 503 years of CPU time on a 1000-node cluster.",
acknowledgement = ack-nhfb,
remark = "This paper contains a good discussion of
floating-point rounding errors in the BBP algorithm,
and of the optimal way to distribute computations over
multiple independent systems sharing a common
filesystem (needed to permit restart after node
failure).",
}
@Article{Szewczak:2010:LTR,
author = "Zbigniew S. Szewczak",
title = "A limit theorem for random sums modulo $1$",
journal = j-STAT-PROB-LETT,
volume = "80",
number = "9 10",
pages = "747--751",
year = "2010",
CODEN = "SPLTDC",
DOI = "https://doi.org/10.1016/j.spl.2010.01.005",
ISSN = "0167-7152 (print), 1879-2103 (electronic)",
ISSN-L = "0167-7152",
bibdate = "Wed Jan 28 10:08:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167715210000106",
abstract = "Residues of partial sums in a class of dependent
random variables, including functionals of uniformly
recurrent Markov chains, are in the domain of
attraction of the uniform distribution. These types of
limit theorems arise for example in the multiplication
of floating-point numbers.",
acknowledgement = ack-nhfb,
fjournal = "Statistics \& Probability Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01677152",
keywords = "Benford's Law",
}
@Article{Takahashi:2010:PIM,
author = "Daisuke Takahashi",
title = "Parallel implementation of multiple-precision
arithmetic and $ 2, 576, 980, 370, 000 $ decimal digits
of $ \pi $ calculation",
journal = j-PARALLEL-COMPUTING,
volume = "36",
number = "8",
pages = "439--448",
month = aug,
year = "2010",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/j.parco.2010.02.007",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Thu Sep 2 17:51:13 MDT 2010",
bibsource = "http://www.sciencedirect.com/science/journal/01678191;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present efficient parallel algorithms for
multiple-precision arithmetic operations of more than
several million decimal digits on distributed-memory
parallel computers. A parallel implementation of
floating-point real FFT-based multiplication is used,
since the key operation for fast multiple-precision
arithmetic is multiplication. The operation for
releasing propagated carries and borrows in
multiple-precision addition, subtraction and
multiplication was also parallelized. More than 2.576
trillion decimal digits of $ \pi $ were computed on 640
nodes of Appro Xtreme-X3 (648 nodes, 147.2 GFlops/node,
95.4 TFlops peak performance) with a computing elapsed
time of 73 h 36 min which includes the time required
for verification.",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
keywords = "distributed-memory parallel computer; Fast Fourier
transform; multiple-precision arithmetic",
}
@Article{Tichy:2010:GAF,
author = "Milan Tichy and Jan Schier and David Gregg",
title = "{GSFAP} adaptive filtering using log arithmetic for
resource-constrained embedded systems",
journal = j-TECS,
volume = "9",
number = "3",
pages = "29:1--29:??",
month = feb,
year = "2010",
CODEN = "????",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Mon Mar 15 18:41:02 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "29",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}
@Article{Vazquez:2010:IDH,
author = "A. Vazquez and E. Antelo and P. Montuschi",
title = "Improved Design of High-Performance Parallel Decimal
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "5",
pages = "679--693",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2009.167",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:28 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5313798",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Vestias:2010:PDM,
author = "M. P. V{\'e}stias and H. C. Neto",
title = "Parallel decimal multipliers using binary
multipliers",
crossref = "Santos:2010:PVS",
pages = "73--78",
year = "2010",
DOI = "https://doi.org/10.1109/SPL.2010.5483001",
bibdate = "Thu Feb 17 08:10:02 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Human-centric applications, like financial and
commercial, depend on decimal arithmetic since the
results must match exactly those obtained by human
calculations. The IEEE-754 2008 standard for floating
point arithmetic has definitely recognized the
importance of decimal for computer arithmetic. A number
of hardware approaches have already been proposed for
decimal arithmetic operations, including addition,
subtraction, multiplication and division. However, few
efforts have been done to develop decimal IP cores able
to take advantage of the binary multipliers available
in most reconfigurable computing architectures. In this
paper, we analyze the tradeoffs involved in the design
of a parallel decimal multiplier, for decimal operands
with 8 and 16 digits, using existent coarse-grained
embedded binary arithmetic blocks. The proposed
circuits were implemented in a Xilinx Virtex 4 FPGA.
The results indicate that the proposed parallel
multipliers are very competitive when compared to
decimal multipliers implemented with direct
manipulation of BCD numbers.",
acknowledgement = ack-nhfb,
}
@Article{Viswanadham:2010:ULI,
author = "Y. K. Viswanadham and Ch. D. V. Subba Rao and T. V.
Subrahmanyam",
title = "Ultra Long Integer Multiplication on {GDPS}",
journal = j-INT-J-COMP-APPL,
volume = "7",
number = "??",
pages = "22--25",
month = oct,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.5120/1271-1751",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 08:33:46 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume7/number8/1271-1751/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "8",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@Article{Wang:2010:AOB,
author = "Chih-Yueh Wang and Chen-Yang Yin and Hong-Yu Chen and
Yung-Ko Chen",
title = "Arithmetic Operations Beyond Floating Point Number
Precision",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "29",
month = sep,
year = "2010",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1009.5911",
abstract = "In basic computational physics classes, students often
raise the question of how to compute a number that
exceeds the numerical limit of the machine. While
technique of avoiding overflow/underflow has practical
application in the electrical and electronics
engineering industries, it is not commonly utilized in
scientific computing, because scientific notation is
adequate in most cases. We present an undergraduate
project that deals with such calculations beyond a
machine's numerical limit, known as arbitrary precision
arithmetic. The assignment asks students to investigate
the approach of calculating the exact value of a large
number beyond the floating point number precision,
using the basic scientific programming language
Fortran. The basic concept is to utilize arrays to
decompose the number and allocate finite memory.
Examples of the successive multiplication of even
number and the multiplication and division of two
overflowing floats are presented. The multiple
precision scheme has been applied to hardware and
firmware design for digital signal processing (DSP)
systems, and is gaining importance to scientific
computing. Such basic arithmetic operations can be
integrated to solve advanced mathematical problems to
almost arbitrarily-high precision that is limited by
the memory of the host machine.",
acknowledgement = ack-nhfb,
subject = "Computational Physics (physics.comp-ph); Physics
Education (physics.ed-ph)",
}
@InProceedings{Wang:2010:DAH,
author = "Dong Wang and M. D. Ercegovac and Nanning Zheng",
title = "Design and analysis of high radix complex dividers",
crossref = "IEEE:2010:ICC",
pages = "V1--84--V1--88",
year = "2010",
DOI = "https://doi.org/10.1109/ICCET.2010.5486287",
bibdate = "Fri Dec 03 15:18:03 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper evaluates FPGA-based high radix hardware
architecture for complex division. The architecture
uses the digit-recurrence algorithm with prescaling of
complex operands. It efficiently executes the
prescaling and recurrence procedures in shared logic
resources. Thirty independent designs of different
radices from 4 to 64 and input precisions from 16 to 64
are implemented in Stratix-II FPGA and results on cost
and performance provide a broad space of design
parameters. Moreover, methods for estimating logic
resource consumption and timing performance are also
given so that one could make quick evaluations on the
design before any actual implementations. The proposed
architecture and design can be used as standalone
arithmetic units for systems-on-chip implementations,
in embedded processors, or as IP for VLSI
implementation in general.",
acknowledgement = ack-nhfb,
keywords = "design parameter; digit-recurrence algorithm; digital
arithmetic; embedded processor; field programmable gate
arrays; high radix complex dividers; IP implementation;
logic design; shared logic resource consumption;
standalone arithmetic unit; Stratix-II FPGA-based high
radix hardware architecture; system-on-chip;
systems-on-chip implementation; VLSI implementation",
}
@Article{Wang:2010:SHD,
author = "Liang-Kai Wang and Mark A. Erle and Charles Tsen and
Eric M. Schwarz and Michael J. Schulte",
title = "A survey of hardware designs for decimal arithmetic",
journal = j-IBM-JRD,
volume = "54",
number = "2",
pages = "8:1--8:15",
month = "????",
year = "2010",
CODEN = "IBMJAE",
DOI = "https://doi.org/10.1147/JRD.2010.2040930",
ISSN = "0018-8646 (print), 2151-8556 (electronic)",
ISSN-L = "0018-8646",
bibdate = "Sat May 1 17:44:14 MDT 2010",
bibsource = "http://www.research.ibm.com/journal/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.research.ibm.com/journal/abstracts/rd/542/wang-schwarz.html",
abstract = "Decimal data and decimal arithmetic operations are
ubiquitous in daily life. Although microprocessors
normally use binary arithmetic for computations,
decimal arithmetic is often required in financial and
commercial applications. Due to the increasing
importance of and demand for decimal arithmetic,
decimal floating-point (DFP) formats and operations are
specified in the revised IEEE Standard for
Floating-Point Arithmetic (IEEE 754-2008). This paper
provides a survey of hardware designs for decimal
arithmetic. It gives an overview of DFP arithmetic in
IEEE 754-2008, describes processors that provide
hardware and instruction set support for decimal
arithmetic, and provides a survey of hardware designs
for decimal addition, subtraction, multiplication, and
division. Finally, it describes potential areas for
future research.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "IBM Journal of Research and Development",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
keywords = "decimal floating-point arithmetic",
}
@Article{Wang:2010:VVP,
author = "Xiaojun Wang and Miriam Leeser",
title = "{VFloat}: a Variable Precision Fixed- and
Floating-Point Library for Reconfigurable Hardware",
journal = j-TRETS,
volume = "3",
number = "3",
pages = "16:1--16:??",
month = sep,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1839480.1839486",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Fri Oct 8 18:26:34 MDT 2010",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "Optimal reconfigurable hardware implementations may
require the use of arbitrary floating-point formats
that do not necessarily conform to IEEE specified
sizes. We present a variable precision floating-point
library (VFloat) that supports general floating-point
formats including IEEE standard formats. Most
previously published floating-point formats for use
with reconfigurable hardware are subsets of our format.
Custom datapaths with optimal bitwidths for each
operation can be built using the variable precision
hardware modules in the VFloat library, enabling a
higher level of parallelism. The VFloat library
includes three types of hardware modules for format
control, arithmetic operations, and conversions between
fixed-point and floating-point formats. The format
conversions allow for hybrid fixed- and floating-point
operations in a single design. This gives the designer
control over a large number of design possibilities
including format as well as number range within the
same application. In this article, we give an overview
of the components in the VFloat library and demonstrate
their use in an implementation of the K-means
clustering algorithm applied to multispectral satellite
images.",
acknowledgement = ack-nhfb,
articleno = "16",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
keywords = "clustering; floating-point; Reconfigurable hardware",
}
@Article{Waters:2010:RCW,
author = "Ron S. Waters and Earl E. Swartzlander",
title = "A Reduced Complexity {Wallace} Multiplier Reduction",
journal = j-IEEE-TRANS-COMPUT,
volume = "59",
number = "8",
pages = "1134--1137",
month = "????",
year = "2010",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.103",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 3 11:52:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5467045",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Zanoni:2010:ITC,
author = "Alberto Zanoni",
title = "Iterative {Toom--Cook} methods for very unbalanced
long integer multiplication",
crossref = "Watt:2010:IPI",
pages = "319--323",
year = "2010",
DOI = "https://doi.org/10.1145/1837934.1837995",
bibdate = "Fri Jun 17 08:06:37 MDT 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We consider the multiplication of long integers when
one factor is much larger than the other one. We
describe an iterative approach using Toom--Cook
unbalanced methods, which results in the evaluation of
the smaller integer only once. The particular case of
Toom-2.5 is considered in full detail. A further
optimization depending on the parity of the shortest
operand evaluation in 1 is also described. A comparison
with GMP library is also presented.",
acknowledgement = ack-nhfb,
}
@InProceedings{Zhao:2010:GMP,
author = "Kaiyong Zhao and Xiaowen Chu",
editor = "{IEEE}",
booktitle = "{IEEE 10th International Conference on Computer and
Information Technology (CIT), 2010: June 29, 2010--July
1, 2010, Bradford, West Yorkshire, UK}",
title = "{GPUMP}: a Multiple-Precision Integer Library for
{GPUs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xcix + 2987 (est.)",
pages = "1164--1168",
year = "2010",
DOI = "https://doi.org/10.1109/CIT.2010.211",
ISBN = "0-7695-4108-9 (print), 1-4244-7547-3",
ISBN-13 = "978-0-7695-4108-2 (print), 978-1-4244-7547-6",
LCCN = "????",
bibdate = "Thu Jan 16 10:33:01 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib",
note = "IEEE Computer Society Order Number E4108. BMS Part
Number: CFP10355-CDR",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5575291",
keywords = "CUDA; GPU; multiple-precision algorithm;
multiple-precision comparison; multiple-precision
division; multiple-precision exponentiation;
multiple-precision modular addition; multiple-precision
modular multiplication; multiple-precision Montgomery
exponentiation; multiple-precision Montgomery
multiplication; multiple-precision Montgomery
reduction; multiple-precision multiplication; nVidia
GT200 GPU",
}
@Article{Zhu:2010:AOE,
author = "Yong-Kang Zhu and Wayne B. Hayes",
title = "{Algorithm 908}: Online Exact Summation of
Floating-Point Streams",
journal = j-TOMS,
volume = "37",
number = "3",
pages = "37:1--37:13",
year = "2010",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1824801.1824815",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 27 10:15:50 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a novel, online algorithm for exact
summation of a stream of floating-point numbers. By
``online'' we mean that the algorithm needs to see only
one input at a time, and can take an arbitrary length
input stream of such inputs while requiring only
constant memory. By ``exact'' we mean that the sum of
the internal array of our algorithm is exactly equal to
the sum of all the inputs, and the returned result is
the correctly-rounded sum. The proof of correctness is
valid for all inputs (including nonnormalized numbers
but modulo intermediate overflow), and is independent
of the number of summands or the condition number of
the sum. The algorithm asymptotically needs only 5
FLOPs per summand, and due to instruction-level
parallelism runs only about 2--3 times slower than the
obvious, fast-but-dumb ``ordinary recursive summation''
loop when the number of summands is greater than
10,000. Thus, to our knowledge, it is the fastest, most
accurate, and most memory efficient among known
algorithms. Indeed, it is difficult to see how a faster
algorithm or one requiring significantly fewer FLOPs
could exist without hardware improvements. An
application for a large number of summands is
provided.",
acknowledgement = ack-nhfb,
articleno = "37",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accurate floating-point summation; correct rounding;
floating-point arithmetic; rounding error",
}
@InProceedings{Zimmermann:2010:RCG,
author = "Paul Zimmermann",
title = "Reliable Computing with {GNU MPFR}",
crossref = "Fukuda:2010:MSI",
pages = "42--45",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6_8",
bibdate = "Sat Sep 23 06:20:46 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Adikari:2011:HBT,
author = "Jithra Adikari and Vassil S. Dimitrov and Laurent
Imbert",
title = "Hybrid Binary-Ternary Number System for Elliptic Curve
Cryptosystems",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "254--265",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.138",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Al-Ashrafy:2011:EIF,
author = "M. Al-Ashrafy and A. Salem and W. Anis",
booktitle = "{2011 Saudi International Electronics, Communications
and Photonics Conference (SIECPC)}",
title = "An efficient implementation of floating point
multiplier",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "1--5",
year = "2011",
DOI = "https://doi.org/10.1109/SIECPC.2011.5876905",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5876905",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5783968",
}
@InProceedings{Anderson:2011:GVD,
author = "Timothy Anderson and Duc Bui and Shriram Moharil and
Soujanya Narnur and Mujibur Rahman and Anthony Lell and
Eric Biscondi and Ashish Shrivastava and Peter Dent and
Mingjian Yan and Hasan Mahmood",
title = "A {1.5 Ghz VLIW DSP CPU} with Integrated Floating
Point and Fixed Point Instructions in 40 nm {CMOS}",
crossref = "Schwarz:2011:PIS",
pages = "82--86",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.20",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992112",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Anonymous:2011:CPSa,
author = "Anonymous",
title = "Call for Papers: Special Section on Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "6",
pages = "910--910",
month = jun,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.88",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jun 29 10:26:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Antelo:2011:IIFa,
editor = "Elisardo Antelo",
title = "Industrial Implementations of Floating-Point Units",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2011",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Aug 18 08:02:12 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Filename ES0000033.",
tableofcontents = "Editor's Introduction \\
Related Videos \\
``P6 Binary Floating-Point Unit,'' by Son Dao Trong,
Martin Schmookler, Eric M. Schwarz, and Michael Kroener
\\
``FPU Implementations with Denormalized Numbers,'' by
Eric M. Schwarz, Martin Schmookler, and Son Dao Trong
\\
``1-GHz HAL SPARC64 Dual Floating Point Unit with RAS
Features,'' by Ajay Naini, Atul Dhablania, Warren
James, and Debjit Das Sarma \\
``Low-Power Multiple-Precision Iterative Floating-Point
Multiplier with SIMD Support,'' by Dimitri Tan, Carl E.
Lemonds, and Michael J. Schulte \\
``The Vector Floating-Point Unit in a Synergistic
Processor Element of a CELL Processor,'' by Silvia M.
Mueller, Christian Jacobi, Hwa-Joon Oh, Kevin D. Tran,
Scott R. Cottier, Brad W. Michael, Hiroo Nishikawa,
Yonetaro Totsuka, Tatsuya Namatame, Naoka Yano, Takashi
Machida, and Sang H. Dhong \\
``A High-Performance SIMD Floating Point Unit for
BlueGene/L: Architecture, Compilation, and Algorithm
Design,'' by Leonardo Bachega, Siddhartha Chatterjee,
Kenneth A. Dockser, John A. Gunnels, Manish Gupta, Fred
G. Gustavson, Christopher A. Lapkowski, Gary K. Liu,
Mark P. Mendell, Charles D. Wait, and T.J. Chris Ward
\\
``Design of the ARM VFP11 Divide and Square Root
Synthesisable Macrocell,'' by Neil Burgess and Chris N.
Hinds \\
``Correctness Proofs Outline for Newton-Raphson Based
Floating-Point Divide and Square Root Algorithms,'' by
Marius A. Cornea-Hasegan, Roger A. Golliver, and Peter
Markstein \\
Recommended Resources \\
About the Editor",
}
@Book{Antelo:2011:IIFb,
editor = "Elisardo Antelo",
title = "Industrial Implementations of Floating-Point Units",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2011",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Aug 18 08:02:12 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Filename ES0000034.",
tableofcontents = "Editor's Introduction \\
Related Videos \\
``A High-Performance Area-Efficient Multifunction
Interpolator,'' by Stuart F. Oberman and Michael Y. Siu
\\
``New Algorithms for Improved Transcendental Functions
on IA-64,'' by Shane Story and Ping Tak Peter Tang \\
``Energy-Delay Estimation Technique for
High-Performance Microprocessor VLSI Adders,'' by Vojin
G. Oklobdzija, Bart R. Zeydel, Hoang Dao, Sanu Mathew,
and Ram Krishnamurthy \\
``Advanced Clockgating Schemes for
Fused-Multiply-Add-Type Floating-Point Units,'' by
Jochen Preiss, Maarten Boersma, and Silvia Melitta
Mueller \\
``Design of Low-Cost High-Performance Floating-Point
Fused Multiply-Add with Reduced Power,'' by Zichu Qi,
Qi Guo, Ge Zhang, Xiangku Li, and Weiwu Hu \\
``Decimal Floating-Point: Algorism for Computers,'' by
Michael F. Cowlishaw \\
``A Software Implementation of the IEEE 754R Decimal
Floating-Point Arithmetic Using the Binary Encoding
Format,'' by Marius Cornea, John Harrison, Cristina
Anderson, Ping Tak Peter Tang, Eric Schneider, and
Evgeny Gvozdev \\
Recommended Resources \\
About the Editor",
}
@InProceedings{Arias-Garcia:2011:SFI,
author = "J. Arias-Garcia and R. Pezzuol Jacobi and C. H. Llanos
and M. Ayala-Rincon",
booktitle = "{2011 VII Southern Conference on Programmable Logic
(SPL)}",
title = "A suitable {FPGA} implementation of floating-point
matrix inversion based on {Gauss--Jordan} elimination",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "263--268",
year = "2011",
DOI = "https://doi.org/10.1109/SPL.2011.5782659",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5782659",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5771182",
}
@Article{Arnold:2011:RCL,
author = "Mark G. Arnold and Sylvain Collange",
title = "A Real\slash Complex Logarithmic Number System {ALU}",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "202--213",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.154",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Arnold:2011:TQC,
author = "Mark G. Arnold and John Cowles and Vassilis Paliouras
and Ioannis Kouretas",
title = "Towards a Quaternion Complex Logarithmic Number
System",
crossref = "Schwarz:2011:PIS",
pages = "33--42",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.14",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992106",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; logarithmic number system (LNS)",
}
@Article{Badin:2011:IAM,
author = "Matthew Badin and Lubomir Bic and Michael Dillencourt
and Alexandru Nicolau",
title = "Improving accuracy for matrix multiplications on
{GPUs}",
journal = j-SCI-PROG,
volume = "19",
number = "1",
pages = "3--11",
month = "????",
year = "2011",
CODEN = "SCIPEV",
DOI = "https://doi.org/10.3233/SPR-2011-0315",
ISSN = "1058-9244 (print), 1875-919X (electronic)",
ISSN-L = "1058-9244",
bibdate = "Tue Dec 13 19:01:37 MST 2011",
bibsource = "http://www.iospress.nl/journal/scientific-programming/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sciprogram.bib",
acknowledgement = ack-nhfb,
fjournal = "Scientific Programming",
journal-URL = "http://iospress.metapress.com/content/1058-9244",
}
@TechReport{Bailey:2011:GMD,
author = "David H. Bailey and Jonathan M. Borwein",
title = "The Greatest Mathematical Discovery?",
type = "Report",
institution = "Lawrence Berkeley National Laboratory and Centre for
Computer Assisted RMA, University of Newcastle",
address = "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
Australia",
pages = "10",
day = "8",
month = may,
year = "2011",
bibdate = "Fri Aug 12 18:29:28 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.davidhbailey.com/dhbpapers/decimal.pdf",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "decimal arithmetic history",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
}
@TechReport{Baudin:2011:EBC,
author = "M. Baudin",
title = "Error bounds of complex arithmetic",
type = "Report",
number = "??",
institution = "????",
address = "????",
month = jun,
year = "2011",
bibdate = "Sun Feb 19 07:29:34 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://forge.scilab.org/upload/compdiv/files/complexerrorbounds_v0.2.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Beebe:2011:BPAb,
author = "Nelson H. F. Beebe",
title = "A Bibliography of Publications about {Benford's Law},
{Heaps' Law}, and {Zipf's Law}",
institution = inst-CSC,
address = inst-CSC:adr,
pages = "62",
day = "12",
month = nov,
year = "2011",
bibdate = "Thu Nov 10 12:15:06 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.math.utah.edu/pub/tex/bib/index-table-b.html#benfords-law",
acknowledgement = ack-nhfb,
}
@Article{Berger:2011:FSM,
author = "Arno Berger and Theodore P. Hill and Bahar Kaynar and
Ad Ridder",
title = "Finite-state {Markov} Chains Obey {Benford's Law}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "32",
number = "3",
pages = "665--684",
month = "????",
year = "2011",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/100789890",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Wed Aug 24 11:18:18 MDT 2011",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
URL = "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "July 21, 2011",
}
@Article{Beuchat:2011:FAP,
author = "Jean-Luc Beuchat and Jeremie Detrey and Nicolas
Estibals and Eiji Okamoto and Francisco
Rodriguez-Henriquez",
title = "Fast Architectures for the {$ \eta_T $} Pairing over
Small-Characteristic Supersingular Elliptic Curves",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "266--281",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.163",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Bodrato:2011:HDT,
author = "Marco Bodrato",
title = "High Degree {Toom'n'Half} for Balanced and Unbalanced
Multiplication",
crossref = "Schwarz:2011:PIS",
pages = "15--22",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.12",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992104",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Boersma:2011:PBF,
author = "Maarten Boersma and Michael Kroner and Christophe
Layer and Petra Leber and Silvia M. Muller and Kerstin
Schelm",
title = "The {POWER7} Binary Floating-Point Unit",
crossref = "Schwarz:2011:PIS",
pages = "87--91",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.21",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992113",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Boldo:2011:EAE,
author = "Sylvie Boldo and Jean-Michel Muller",
title = "Exact and Approximated Error of the {FMA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "157--164",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.139",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The fused multiply accumulate-add (FMA) instruction,
specified by the IEEE 754-2008 Standard for
Floating-Point Arithmetic, eases some calculations, and
is already available on some current processors such as
the Power PC or the Itanium. We first extend an earlier
work on the computation of the exact error of an FMA
(by giving more general conditions and providing a
formal proof). Then, we present a new algorithm that
computes an approximation to the error of an FMA, and
provide error bounds and a formal proof for that
algorithm.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Boldo:2011:FUL,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "{Flocq}: a Unified Library for Proving Floating-Point
Algorithms in {Coq}",
crossref = "Schwarz:2011:PIS",
pages = "243--252",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.40",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992132",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Boldo:2011:FVN,
author = "Sylvie Boldo and Claude March{\'e}",
title = "Formal Verification of Numerical Programs: From {C}
Annotated Programs to Mechanical Proofs",
journal = j-MATH-COMPUT-SCI,
volume = "5",
number = "4",
pages = "377--393",
month = dec,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11786-011-0099-9",
ISSN = "1661-8270 (print), 1661-8289 (electronic)",
ISSN-L = "1661-8270",
bibdate = "Tue Nov 6 10:16:23 MST 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1661-8270&volume=5&issue=4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1661-8270&volume=5&issue=4&spage=377",
acknowledgement = ack-nhfb,
fjournal = "Mathematics in Computer Science",
journal-URL = "http://www.springerlink.com/content/1661-8270/",
keywords = "Alt-Ergo; automated reasoning; C program; Coq; CVC3;
floating-point arithmetic; formal specification;
Frama-C; Gappa; Jessie plugin; Why; Z3",
}
@InProceedings{Bos:2011:ESA,
author = "Joppe W. Bos and Thorsten Kleinjung and Arjen K.
Lenstra and Peter L. Montgomery",
title = "Efficient {SIMD} Arithmetic Modulo a {Mersenne}
Number",
crossref = "Schwarz:2011:PIS",
pages = "213--221",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.37",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992129",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Book{Brent:2011:MCA,
author = "Richard P. Brent and Paul Zimmermann",
title = "Modern Computer Arithmetic",
volume = "18",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvi + 221",
year = "2011",
DOI = "https://doi.org/10.1017/CBO9780511921698",
ISBN = "0-521-19469-5 (hardcover)",
ISBN-13 = "978-0-521-19469-3 (hardcover)",
LCCN = "QA76.9.C62 BRE 2011",
bibdate = "Sat Jan 15 12:25:22 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/sigact.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Cambridge monographs on applied and computational
mathematics",
URL = "http://www.loria.fr/~zimmerma/mca/pub226.html",
acknowledgement = ack-nhfb,
subject = "Computer arithmetic",
tableofcontents = "Preface / ix \\
Acknowledgements / xi \\
Notation / xiii \\
Integer arithmetic / 1 \\
1.1 Representation and notations / 1 \\
1.2 Addition and subtraction / 2 \\
1.3 Multiplication / J \\
i.3.1 Naive multiplication / 4 \\
1.3.2 Karatsuba's algorithm / 5 \\
1.3.3 Toom--Cook multiplication / 6 \\
1.3.4 Use of the fast Fourier transform (FFT) / 8 \\
1.3.5 Unbalanced multiplication / 8 \\
1.3.6 Squaring / 11 \\
1.3.7 Multiplication by a constant / 13 \\
1.4 Division / 14 \\
1.4.1 Naive division / 14 \\
1.4.2 Divisor preconditioning / 16 \\
1.4.3 Divide and conquer division / 18 \\
1.4.4 Newton's method / 21 \\
1.4.5 Exact division / 21 \\
1.4.6 Only quotient or remainder wanted / 22 \\
1.4.7 Division by a single word / 23 \\
1.4.8 Hensel's division / 24 \\
1.5 Roots / 25 \\
1.5.1 Square root / 25 \\
1.5.2 $k$th root / 27 \\
1.5.3 Exact root / 28 \\
1.6 Greatest common divisor / 29 \\
1.6.1 Naive GCD / 29 \\
1.6.2 Extended GCD / 32 \\
1.6.3 Half binary GCD, divide and conquer GCD / 33 \\
1.7 Base conversion / 37 \\
1.7.1 Quadratic algorithms / 37 \\
1.7.2 Subquadratic algorithms / 38 \\
1.8 Exercises / 39 \\
1.9 Notes and references / 44 \\
Modular arithmetic and the FFT / 47 \\
2.1 Representation / 47 \\
2.1.1 Classical representation / 47 \\
2.1.2 Montgomery's form / 48 \\
2.1.3 Residue number systems / 48 \\
2.1.4 MSB vs LSB algorithms / 49 \\
2.1.5 Link with Polynomials / 49 \\
2.2 Modular addition and subtraction / 50 \\
2.3 The Fourier transform / 50 \\
2.3.1 Theoretical setting / 50 \\
2.3.2 The fast Fourier transform / 51 \\
2.3.3 The Sch{\"o}nhage--Strassen algorithm / 55 \\
2.4 Modular multiplication / 58 \\
2.4.1 Barrett's algorithm / 58 \\
2.4.2 Montgomery's multiplication / 60 \\
2.4.3 McLaughlin's algorithm / 63 \\
2.4.4 Special moduli / 65 \\
2.5 Modular division and inversion / 65 \\
2.5.1 Several inversions at once / 61 \\
2.6 Modular exponentiation / 68 \\
2.6.1 Binary exponentiation / 70 \\
2.6.2 Exponentiation with a larger base / 70 \\
2.6.3 Sliding window and redundant representation / 72
\\
2.7 Chinese remainder theorem / 75 \\
2.8 Exercises / 75 \\
2.9 Notes and references / 77 \\
Floating-point arithmetic / 79 \\
3.1 Representation / 79 \\
3.1.1 Radix choice / 80 \\
3.1.2 Exponent range / 81 \\
3.1.3 Special values / 82 \\
3.1.4 Subnormal numbers / 82 \\
3.1.5 Encoding / 83 \\
3.1.6 Precision: local, global, operation, operand / 84
\\
3.1.7 Link to integers / 86 \\
3.1.8 Ziv's algorithm and error analysis / 86 \\
3.1.9 Rounding / 87 \\
3.1.10 Strategies / 90 \\
3.2 Addition, subtraction, comparison / 91 \\
3.2.1 Floating-point addition / 92 \\
3.2.2 Floating-point subtraction / 93 \\
3.3 Multiplication / 95 \\
3.3.1 Integer multiplication via complex FFT / 98 \\
3.3.2 The middle product / 99 \\
3.4 Reciprocal and division / 101 \\
3.4.1 Reciprocal / 102 \\
3.4.2 Division / 106 \\
3.5 Square root / 111 \\
3.5.1 Reciprocal square root / 112 \\
3.6 Conversion / 114 \\
3.6.1 Floating-point output / 115 \\
3.6.2 Floating-point input / 117 \\
3.7 Exercises / 118 \\
3.8 Notes and references / 120 \\
Elementary and special function evaluation / 125 \\
4.1 Introduction / 125 \\
4.2 Newton's method / 126 \\
4.2.1 Newton's method for inverse roots / 127 \\
4.2.2 Newton's method for reciprocals / 128 \\
4.2.3 Newton's method for (reciprocal) square roots /
129 \\
4.2.4 Newton's method for formal power series / 129 \\
4.2.5 Newton's method for functional inverses / 130 \\
4.2.6 Higher-order Newton-like methods / 131 \\
4.3 Argument reduction / 132 \\
4.3.1 Repeated use of a doubling formula / 134 \\
4.3.2 Loss of precision / 134 \\
4.3.3 Guard digits / 135 \\
4.3.4 Doubling versus tripling / 136 \\
4.4 Power series / 136 \\
4.4.1 Direct power series evaluation / 140 \\
4.4.2 Power series with argument reduction / 140 \\
4.4.3 Rectangular series splitting / 141 \\
4.5 Asymptotic expansions / 144 \\
4.6 Continued fractions / 150 \\
4.7 Recurrence relations / 152 \\
4.7.1 Evaluation of Bessel functions / 153 \\
4.7.2 Evaluation of Bernoulli and tangent numbers / 154
\\
4.8 Arithmetic--geometric mean / 158 \\
4.8.1 Elliptic integrals / 158 \\
4.8.2 First AGM algorithm for the logarithm / 159 \\
4.8.3 Theta functions / 160 \\
4.8.4 Second AGM algorithm for the logarithm / 162 \\
4.8.5 The complex AGM / 163 \\
4.9 Binary splitting / 163 \\
4.9.1 A binary splitting algorithm for sin, cos / 166
\\
4.9.2 The bit-burst algorithm / 161 \\
4.10 Contour integration / 169 \\
4.11 Exercises / 171 \\
4.12 Notes and references / 179 \\
Implementations and pointers / 185 \\
5.1 Software tools / 185 \\
5.1.1 CLN / 185 \\
5.1.2 GNUMP (GMP) / 185 \\
5.1.3 MPFQ / 186 \\
5.1.4 GNU MPFR / 187 \\
5.1.5 Other multiple-precision packages / 187 \\
5.1.6 Computational algebra packages / 188 \\
5.2 Mailing lists / 189 \\
5.2.1 The GMP lists / 189 \\
5.2.2 The MPFR list / 190 \\
5.3 Online documents / 190 \\
References / 191 \\
Index / 207",
}
@InProceedings{Brisebarre:2011:APS,
author = "Nicolas Brisebarre and Mioara Joldes and Peter
Kornerup and {\'E}rik Martin-Dorel and Jean-Michel
Muller",
title = "Augmented Precision Square Roots and {$2$-D} Norms,
and Discussion on Correctly Rounding $ \sqrt {x^2 +
y^2} $",
crossref = "Schwarz:2011:PIS",
pages = "23--30",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.13",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992105",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; correct rounding; floating-point arithmetic;
hypotenuse",
}
@Article{Bruguera:2011:GEI,
author = "Javier Bruguera and Marius Cornea and Debjit Das
Sarma",
title = "{Guest Editors}' Introduction: Special Section on
Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "145--147",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.15",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Brumley:2011:BSB,
author = "Billy Bob Brumley and Dan Page",
title = "Bit-Sliced Binary Normal Basis Multiplication",
crossref = "Schwarz:2011:PIS",
pages = "205--212",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.36",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992128",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; correct rounding; floating-point
arithmetic",
}
@InProceedings{Brunie:2011:MPF,
author = "Nicolas Brunie and Florent de Dinechin and Benoit de
Dinechin",
booktitle = "2011 Conference Record of the {Forty Fifth Asilomar
Conference on Signals, Systems and Computers
(ASILOMAR)}",
title = "A mixed-precision fused multiply and add",
publisher = pub-IEEE,
address = pub-IEEE:adr,
month = nov,
year = "2011",
DOI = "https://doi.org/10.1109/ACSSC.2011.6189977",
bibdate = "Wed Aug 7 14:09:53 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brusentsov:2011:TCS,
author = "Nikolay Petrovich Brusentsov and Jos{\'e} Ramil
Alvarez",
title = "Ternary Computers: The {Setun} and the {Setun 70}",
crossref = "Impagliazzo:2011:PSR",
pages = "74--80",
year = "2011",
DOI = "https://doi.org/10.1007/978-3-642-22816-2_10",
bibdate = "Sun Aug 16 19:31:45 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/openurl?genre=book%26isbn=978-3-642-22815-5",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-22816-2",
remark = "The Setun computer series was unusual in being
proposed to use base-3 (ternary) floating-point
arithmetic.",
}
@InProceedings{Burgess:2011:FRC,
author = "Neil Burgess",
title = "Fast Ripple-Carry Adders in Standard-Cell {CMOS
VLSI}",
crossref = "Schwarz:2011:PIS",
pages = "103--111",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.23",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992115",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Butts:2011:RDR,
author = "J. Adam Butts and Ping Tak Peter Tang and Ron O. Dror
and David E. Shaw",
title = "Radix-8 Digit-by-Rounding: Achieving High-Performance
Reciprocals, Square Roots, and Reciprocal Square
Roots",
crossref = "Schwarz:2011:PIS",
pages = "149--158",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.28",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992120",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Calamia:2011:CGG,
author = "J. Calamia",
title = "{China}'s {Godson} gamble",
journal = j-IEEE-SPECTRUM,
volume = "48",
number = "5",
pages = "14--16",
month = may,
year = "2011",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2011.5753229",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Fri Jan 17 18:54:05 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "American born chip; China; Chinese researcher; country
homegrown high end processor; energy conservation;
energy efficiency; floating point operation; Godson-3B;
mainframes; Mesh networks; multiprocessing systems;
supercomputer; Supercomputers; The Dawning",
}
@InProceedings{Carlough:2011:IZD,
author = "Steven Carlough and Adam Collura and Silvia Mueller
and Michael Kroener",
title = "The {IBM zEnterprise-196} Decimal Floating-Point
Accelerator",
crossref = "Schwarz:2011:PIS",
pages = "139--146",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.27",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992119",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; decimal floating-point arithmetic",
}
@Article{Cavagnino:2011:AAD,
author = "D. Cavagnino and A. E. Werbrouck",
title = "An Analysis of Associated Dividends in the {DBM}
Algorithm for Division by Constants Using
Multiplication",
journal = j-COMP-J,
volume = "54",
number = "1",
pages = "148--156",
month = jan,
year = "2011",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxp117",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 21 19:26:47 MST 2010",
bibsource = "http://comjnl.oxfordjournals.org/content/54/1.toc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/54/1/148.full.pdf+html",
abstract = "When a compiler encounters a fixed integer divisor,
which is not a power of 2, it can calculate its inverse
to be multiplied by the run-time integer dividends to
obtain the quotients, using our very efficient,
recently published [Cavagnino, D. and Werbrouck, A.E.
(2008) {\em Efficient algorithms for integer division
by constants using multiplication}. Comp. J., 51,
470--480] division by multiplication algorithms.
Essentially our algorithms permit a complete partition
of a defined number space into non-adverse and adverse
divisors on the basis of whether a dividend associated
with each divisor is, or is not, greater than the
maximum dividend size. In this paper, we demonstrate
useful relations between the dividends associated with
all divisors and with their multiples by positive
powers",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "dividend distribution; division by multiplication
(DBM); integer division; multiplicative division",
onlinedate = "December 30, 2009",
remark = "See \cite{Cavagnino:2008:EAI}.",
}
@Article{Cenk:2011:EM,
author = "Murat Cenk and Ferruh {\"O}zbudak",
title = "Efficient multiplications in {$ \mathbb {F}_{5^{5n}}
$} and {$ \mathbb {F}_{7^{7n}} $}",
journal = j-J-COMPUT-APPL-MATH,
volume = "236",
number = "2",
pages = "177--183",
day = "15",
month = aug,
year = "2011",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2011.06.016",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "11Y16 (11T99 12E20)",
MRnumber = "2827399",
bibdate = "Sat Feb 25 13:24:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042711003396",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
xxtitle = "Efficient multiplications in {[??IMAGE??]} and
{[??IMAGE??]}",
}
@Article{Chakraborty:2011:CBS,
author = "Anindita Chakraborty and Amitabha Sinha",
title = "Conversion of binary to single-term triple base
numbers for {DSP} applications",
journal = j-COMP-ARCH-NEWS,
volume = "39",
number = "5",
pages = "5--11",
month = dec,
year = "2011",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2093339.2093342",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Thu Mar 15 14:07:10 MDT 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "In this paper high speed Residue Number System (RNS)
based FIR filter using Distributed Arithmetic (DA) is
proposed. The proposed architecture uses the module set
having the value of numbers as small as possible. In
case of using Distributed Arithmetic in FIR filter; the
size of LUTs gets increased exponentially with the
increase of tap of the filter. Here care has been taken
so that sizes of LUTs do not get increased. The
proposed architecture is designed using verilog HDL; a
popular hardware description language [9]. The design
is synthesized with ISE 10.1 and implemented on
Xilinx's Virtex-4. The proposed architecture is also
compared with conventional RNS-DA FIR filter. The
results show that the proposed architecture can
implement FIR filter with high speed.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Chang:2011:CGR,
author = "Harry M. Chang",
title = "Constructing $n$-gram rules for natural language
models through exploring the limitation of the
{Zipf--Mandelbrot} law",
journal = j-COMPUTING,
volume = "91",
number = "3",
pages = "241--264",
month = mar,
year = "2011",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Sep 6 19:14:24 MDT 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
}
@Article{Chen:2011:PIM,
author = "Zhimin Chen and Patrick Schaumont",
title = "A Parallel Implementation of {Montgomery}
Multiplication on Multicore Systems: Algorithm,
Analysis, and Prototype",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "12",
pages = "1692--1703",
month = dec,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.256",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Nov 6 07:52:27 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669278",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Chen:2011:TSA,
author = "Jianxun Chen and Yongzhong Huang and Shaozhong Guo and
Shimiao Chen and Wei Wang",
booktitle = "{2011 Third International Conference on Measuring
Technology and Mechatronics Automation (ICMTMA)}",
title = "Test Standardization and Analyse Model of Mathematical
Functions for Precision",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "652--655",
year = "2011",
DOI = "https://doi.org/10.1109/ICMTMA.2011.734",
ISBN = "0-7695-4296-4",
ISBN-13 = "978-0-7695-4296-6",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5721571",
abstract = "This article describes problems of meet the
requirements to implementations of mathematical
functions working with floating-point numbers, and so
facilitate the comprehensive testing of mathematical
functions. Inconsistency and incompleteness of
available standards in the domain is demonstrated.
Correct rounding requirement is suggested to guarantee
preservation of all important properties of functions
and to support high level of interoperability between
different mathematical libraries and software using
them. The article also concerns precision analyse of
mathematical functions. Conformance test construction
method is proposed based on different sources of test
data.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5720445",
remark = "This paper contains unattributed plagiaristic copying
of material from
\url{https://www.math.utah.edu/~beebe/software/ieee/index.html}.",
}
@InProceedings{Chevillard:2011:AGC,
author = "Sylvain Chevillard",
title = "Automatic Generation of Code for the Evaluation of
Constant Expressions at Any Precision with a Guaranteed
Error Bound",
crossref = "Schwarz:2011:PIS",
pages = "225--232",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.38",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992130",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Colberg:2011:HAS,
author = "Peter H. Colberg and Felix H{\"o}fling",
title = "Highly accelerated simulations of glassy dynamics
using {GPUs}: Caveats on limited floating-point
precision",
journal = j-COMP-PHYS-COMM,
volume = "182",
number = "5",
pages = "1120--1129",
month = may,
year = "2011",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2011.01.009",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Sat Feb 11 10:10:57 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465511000294",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Corless:2011:RCA,
author = "Robert Corless and Erik Postma and David R.
Stoutemyer",
title = "Rounding coefficients and artificially underflowing
terms in non-numeric expressions",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "45",
number = "1",
pages = "17--48",
month = mar,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/2016567.2016570",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Wed Aug 17 08:55:07 MDT 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This article takes an analytical viewpoint to address
the following questions: 1. How can we justifiably
beautify an input or result sum of non-numeric terms
that has some approximate coefficients by deleting some
terms and/or rounding some coefficients to simpler
floating-point or rational numbers? 2. When we add two
expressions, how can we justifiably delete more
non-zero result terms and/or round some result
coefficients to even simpler floating-point, rational
or irrational numbers? The methods considered in this
paper provide a justifiable scale-invariant way to
attack these problems for subexpressions that are
multivariate sums of monomials with real exponents.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
issue = "175",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
keywords = "floating-point arithmetic; rounding; symbolic
algebra",
}
@InProceedings{Cui:2011:TDB,
author = "Mingyi Cui",
booktitle = "{2011 International Conference on Electronic and
Mechanical Engineering and Information Technology
(EMEIT)}",
title = "A threshold denoising based floating point
representation genetic algorithm",
volume = "7",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "3305--3308",
year = "2011",
DOI = "https://doi.org/10.1109/EMEIT.2011.6023063",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6023063",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5996364",
}
@Article{Curran:2011:ZSM,
author = "Brian W. Curran and Lee E. Eisen and Eric M. Schwarz
and Pak-kin Mak and James Warnock and Patrick J. Meaney
and Michael Fee",
title = "The {zEnterprise 196} System and Microprocessor",
journal = j-IEEE-MICRO,
volume = "31",
number = "2",
pages = "26--40",
month = mar # "\slash " # apr,
year = "2011",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2011.34",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Tue Apr 26 13:50:28 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The zEnterprise 196 is the latest IBM System zSeries
mainframe computer, which builds on IBM's 46-year
heritage of compatible enterprise-class machines. This
design advances the prior z10 processor pipeline with
out-of-order execution to achieve considerable
performance gains in legacy online transaction
processing and computationally intensive workloads.
This article describes the system structure and details
of this new high-frequency microprocessor.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
keywords = "correct rounding; floating-point arithmetic; Hot Chips
22 conference proceedings",
remark = "From page 34: ``IEEE Std 754-2008 (IEEE Standard for
Floating-Point Arithmetic) adds the requirement to
support heterogeneous operations on operands with
different precisions. In light of this standard, z196
added a new rounding mode called round to prepare for
shorter precision to all binary floating-point
instructions. Using this new rounding mode allows an
addition with a double-precision addend and a
single-precision augend to produce a single-precision
sum with correct rounding.''",
}
@Article{Daisaka:2011:GMS,
author = "Hiroshi Daisaka and Naohito Nakasato and Junichiro
Makino and Fukuko Yuasa and Tadashi Ishikawa",
title = "{GRAPE-MP}: An {SIMD} Accelerator Board for
Multi-precision Arithmetic",
journal = "Procedia Computer Science",
volume = "4",
pages = "878--887",
month = may,
year = "2011",
DOI = "https://doi.org/10.1016/j.procs.2011.04.093",
ISSN = "1877-0509",
ISSN-L = "1877-0509",
bibdate = "Wed Jun 12 16:47:38 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Proc. Comput. Sci.",
}
@Article{Das:2011:HSR,
author = "Malay Das and Amitabha Sinha and Nishant Kumar Giri",
title = "High speed residue number system ({RNS}) based {FIR}
filter using distributed arithmetic ({DA})",
journal = j-COMP-ARCH-NEWS,
volume = "39",
number = "5",
pages = "1--4",
month = dec,
year = "2011",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2093339.2093341",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Thu Mar 15 14:07:10 MDT 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@InProceedings{deDinechin:2011:AOY,
author = "Florent de Dinechin",
title = "The Arithmetic Operators You Will Never See in a
Microprocessor",
crossref = "Schwarz:2011:PIS",
pages = "189--190",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.33",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992125",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{deDinechin:2011:CFP,
author = "Florent de Dinechin and Christoph Lauter and Guillaume
Melquiond",
title = "Certifying the Floating-Point Implementation of an
Elementary Function Using {Gappa}",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "242--253",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.128",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "High confidence in floating-point programs requires
proving numerical properties of final and intermediate
values. One may need to guarantee that a value stays
within some range, or that the error relative to some
ideal value is well bounded. This certification may
require a time-consuming proof for each line of code,
and it is usually broken by the smallest change to the
code, e.g., for maintenance or optimization purpose.
Certifying floating-point programs by hand is,
therefore, very tedious and error-prone. The Gappa
proof assistant is designed to make this task both
easier and more secure, due to the following novel
features: It automates the evaluation and propagation
of rounding errors using interval arithmetic. Its input
format is very close to the actual code to validate. It
can be used incrementally to prove complex mathematical
properties pertaining to the code. It generates a
formal proof of the results, which can be checked
independently by a lower level proof assistant like
Coq. Yet it does not require any specific knowledge
about automatic theorem proving, and thus, is
accessible to a wide community. This paper demonstrates
the practical use of this tool for a widely used class
of floating-point programs: implementations of
elementary functions in a mathematical library.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{DelVento:2011:SLM,
author = "Davide {Del Vento} and Thomas Engel and Siddhartha S.
Ghosh and David L. Hart and Rory Kelly and Si Liu and
Richard Valent",
title = "System-level monitoring of floating-point performance
to improve effective system utilization",
crossref = "ACM:2011:SSP",
pages = "5:1--5:6",
year = "2011",
DOI = "https://doi.org/10.1145/2063348.2063355",
bibdate = "Fri Dec 16 11:19:26 MST 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/supercomputing2011.bib",
acknowledgement = ack-nhfb,
articleno = "5",
}
@Article{Dimitrov:2011:AEM,
author = "Vassil S. Dimitrov and Kimmo U. Jarvinen and Jithra
Adikari",
title = "Area-Efficient Multipliers Based on Multiple-Radix
Representations",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "189--201",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.200",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Dimond:2011:ALS,
author = "Rob Dimond and Sebastien Racani{\`e}re and Oliver
Pell",
title = "Accelerating Large-Scale {HPC} Applications Using
{FPGAs}",
crossref = "Schwarz:2011:PIS",
pages = "191--192",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.34",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992126",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Emmart:2011:HPI,
author = "Niall Emmart and Charles C. Weems",
title = "High Precision Integer Multiplication with a {GPU}
Using {Strassen}'s Algorithm with Multiple {FFT}
Sizes",
journal = j-PARALLEL-PROCESS-LETT,
volume = "21",
number = "3",
pages = "359--375",
month = sep,
year = "2011",
CODEN = "PPLTEE",
DOI = "https://doi.org/10.1142/S0129626411000266",
ISSN = "0129-6264 (print), 1793-642X (electronic)",
bibdate = "Tue Feb 28 11:32:08 MST 2012",
bibsource = "http://ejournals.wspc.com.sg/ppl/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/parallelprocesslett.bib",
note = "See earlier work \cite{Emmart:2010:HPI}.",
acknowledgement = ack-nhfb,
fjournal = "Parallel Processing Letters",
journal-URL = "http://www.worldscientific.com/loi/ppl",
remark = "The abstract reports an improvement (GPU compared to
GMP) of 13.9x to 19x for multiplication with operands
of 255Kbits to 16320Kbits, compared to earlier work
\cite{Emmart:2010:HPI}.",
}
@InProceedings{Fischer:2011:HIC,
author = "Ralf Fischer",
title = "High Intelligence Computing: The New Era of High
Performance Computing",
crossref = "Schwarz:2011:PIS",
pages = "3--3",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.42",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992102",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Galal:2011:EEF,
author = "Sameh Galal and Mark Horowitz",
title = "Energy-Efficient Floating-Point Unit Design",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "7",
pages = "913--922",
month = jul,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.121",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jun 29 10:26:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Galal:2011:LSF,
author = "Sameh Galal and Mark Horowitz",
title = "Latency Sensitive {FMA} Design",
crossref = "Schwarz:2011:PIS",
pages = "129--138",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.26",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992118",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Gandino:2011:GAI,
author = "Filippo Gandino and Fabrizio Lamberti and Paolo
Montuschi and Jean-Claude Bajard",
title = "A General Approach for Improving {RNS Montgomery}
Exponentiation Using Pre-processing",
crossref = "Schwarz:2011:PIS",
pages = "195--204",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.35",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992127",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; residue number system (RNS)",
}
@Article{Garofalo:2011:ACM,
author = "Valeria Garofalo and Nicola Petra and Ettore Napoli",
title = "Analytical Calculation of the Maximum Error for a
Family of Truncated Multipliers Providing Minimum Mean
Square Error",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "9",
pages = "1366--1371",
month = sep,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.236",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 22 09:18:06 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669274",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Gopikiran:2011:FIF,
author = "G. Gopikiran and R. Thilagavathy",
booktitle = "{2011 International Conference on Signal Processing,
Communication, Computing and Networking Technologies
(ICSCCN)}",
title = "{FPGA} implementation of floating-point rotation mode
{CORDIC} algorithm",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "506--508",
year = "2011",
DOI = "https://doi.org/10.1109/ICSCCN.2011.6024604",
bibdate = "Tue Sep 27 08:11:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6024604",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6016617",
}
@InProceedings{Gorgin:2011:FHR,
author = "Saeid Gorgin and Ghassem Jaberipur",
title = "A Family of High Radix Signed Digit Adders",
crossref = "Schwarz:2011:PIS",
pages = "112--120",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.24",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992116",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Goubault:2011:SAF,
author = "Eric Goubault and Sylvie Putot",
editor = "Ranjit Jhala and David A. Schmidt",
booktitle = "{VMCAI'11: Proceedings of the 12th international
conference on verification, model checking, and
abstract interpretation. Austin, TX, USA --- January
23--25, 2011}",
title = "Static Analysis of Finite Precision Computations",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "232--247",
year = "2011",
ISBN = "3-642-18274-7",
ISBN-13 = "978-3-642-18274-7",
bibdate = "Thu Oct 17 05:33:04 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/citation.cfm?id=1946284.1946301",
abstract = "We define several abstract semantics for the static
analysis of finite precision computations, that bound
not only the ranges of values taken by numerical
variables of a program, but also the difference with
the result of the same sequence of operations in an
idealized real number semantics. These domains point
out with more or less detail (control point, block,
function for instance) sources of numerical errors in
the program and the way they were propagated by further
computations, thus allowing to evaluate not only the
rounding error, but also sensitivity to inputs or
parameters of the program. We describe two classes of
abstractions, a non relational one based on intervals,
and a weakly relational one based on parametrized
zonotopic abstract domains called affine sets,
especially well suited for sensitivity analysis and
test generation. These abstract domains are implemented
in the Fluctuat static analyzer, and we finally present
some experiments.",
acknowledgement = ack-nhfb,
}
@Article{Graillat:2011:SAM,
author = "Stef Graillat and Fabienne J{\'e}z{\'e}quel and Shiyue
Wang and Yuxiang Zhu",
title = "Stochastic Arithmetic in Multiprecision",
journal = j-MATH-COMPUT-SCI,
volume = "5",
number = "4",
pages = "359--375",
month = dec,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11786-011-0103-4",
ISSN = "1661-8270 (print), 1661-8289 (electronic)",
ISSN-L = "1661-8270",
bibdate = "Tue Nov 6 10:16:23 MST 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1661-8270&volume=5&issue=4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1661-8270&volume=5&issue=4&spage=359",
acknowledgement = ack-nhfb,
fjournal = "Mathematics in Computer Science",
journal-URL = "http://www.springerlink.com/content/1661-8270/",
keywords = "interval arithmetic; MPFI; MPFR; multiprecision;
Stochastic Arithmetic in Multiprecision (SAM)",
}
@Article{Grcar:2011:JNA,
author = "Joseph F. Grcar",
title = "{John von Neumann}'s Analysis of {Gaussian}
Elimination and the Origins of Modern Numerical
Analysis",
journal = j-SIAM-REVIEW,
volume = "53",
number = "4",
pages = "607--682",
month = "????",
year = "2011",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/080734716",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "01-08, 65-03, 65F05, 65F35, 65G50, 65M12, 68-03, 65-03
(01A60 65F35 68-03)",
MRnumber = "2861262 (2012m:65001)",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/53/4;
http://epubs.siam.org/toc/siread/53/4;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sirev/resource/1/siread/v53/i4/p607_s1",
abstract = "Just when modern computers (digital, electronic, and
programmable) were being invented, John von Neumann and
Herman Goldstine wrote a paper to illustrate the
mathematical analyses that they believed would be
needed to use the new machines effectively and to guide
the development of still faster computers. Their
foresight and the congruence of historical events made
their work the first modern paper in numerical
analysis. Von Neumann once remarked that to found a
mathematical theory one had to prove the first theorem,
which he and Goldstine did for the accuracy of
mechanized Gaussian elimination --- but their paper was
about more than that. Von Neumann and Goldstine
described what they surmized would be the significant
questions once computers became available for
computational science, and they suggested enduring ways
to answer them.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "backward error, CFL condition, computer architecture,
computer arithmetic, computer programming, condition
number, decomposition paradigm, Gaussian elimination,
history, matrix norms, numerical analysis, rounding
error analysis, stability, stochastic linear algebra,
von Neumann",
onlinedate = "November 07, 2011",
}
@InProceedings{Gupta:2011:LPP,
author = "A. Gupta and S. Mandavalli and V. J. Mooney and
Keck-Voon Ling and A. Basu and H. Johan and B.
Tandianus",
booktitle = "{2011 IEEE Computer Society Annual Symposium on VLSI
(ISVLSI)}",
title = "Low Power Probabilistic Floating Point Multiplier
Design",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "182--187",
year = "2011",
DOI = "https://doi.org/10.1109/ISVLSI.2011.54",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992502",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5992458",
}
@Article{Guralnik:2011:SBV,
author = "Elena Guralnik and Merav Aharoni and Ariel J. Birnbaum
and Anatoly Koyfman",
title = "Simulation-Based Verification of Floating-Point
Division",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "176--188",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.165",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "Floating-point division is known to exhibit an
exceptionally wide array of corner cases, making its
verification a difficult challenge. Despite the
remarkable advances in formal methods, the intricacies
of this operation and its implementation often render
these inapplicable. Simulation-based methods remain the
primary means for verification of division. FPgen is a
test generation framework targeted at the floating
point datapath. It has been successfully used in the
simulation-based verification of a variety of hardware
designs. FPgen comprises a comprehensive test plan and
a powerful test generator. A proper response to the
difficulties posed by division constitutes a major part
of FPgen's capabilities. We present an overview of the
relevant verification tasks supplied with FPgen and the
underlying algorithms used to target them.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Han:2011:NDS,
author = "Liu Han and Dongdong Chen and Khan A. Wahid and
Seok-Bum Ko",
booktitle = "{2011 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "Nonspeculative decimal signed digit adder",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "1053--1056",
year = "2011",
DOI = "https://doi.org/10.1109/ISCAS.2011.5937750",
bibdate = "Tue Sep 27 08:11:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5937750",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5910713",
}
@Article{Hariri:2011:CED,
author = "Arash Hariri and Arash Reyhani-Masoleh",
title = "Concurrent Error Detection in {Montgomery}
Multiplication over Binary Extension Fields",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "9",
pages = "1341--1353",
month = sep,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.258",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 22 09:18:06 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669280",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Haron:2011:RRN,
author = "Nor Zaidi Haron and Said Hamdioui",
title = "Redundant Residue Number System Code for
Fault-Tolerant Hybrid Memories",
journal = j-JETC,
volume = "7",
number = "1",
pages = "4:1--4:??",
month = jan,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/1899390.1899394",
ISSN = "1550-4832 (print), 1550-4840 (electronic)",
ISSN-L = "1550-4832",
bibdate = "Mon Mar 28 12:17:03 MDT 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/jetc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J967",
}
@Article{Harvey:2011:FAS,
author = "David Harvey",
title = "Faster algorithms for the square root and reciprocal
of power series",
journal = j-MATH-COMPUT,
volume = "80",
number = "273",
pages = "387--394",
month = jan,
year = "2011",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Oct 13 16:46:42 MDT 2010",
bibsource = "http://www.ams.org/mcom/2011-80-273;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02392-0/home.html;
http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02392-0/S0025-5718-2010-02392-0.pdf",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Harvey:2011:SDL,
author = "David Harvey and Paul Zimmermann",
title = "Short Division of Long Integers",
crossref = "Schwarz:2011:PIS",
pages = "7--14",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.11",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992103",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Holanda:2011:FBA,
author = "B. Holanda and R. Pimentel and J. Barbosa and R.
Camarotti and A. Silva-Filho and L. Joao and V. Souza
and J. Ferraz and M. Lima",
booktitle = "{2011 IEEE International Symposium on Parallel and
Distributed Processing Workshops and Phd Forum
(IPDPSW)}",
title = "An {FPGA}-Based Accelerator to Speed-Up Matrix
Multiplication of Floating Point Operations",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "306--309",
year = "2011",
DOI = "https://doi.org/10.1109/IPDPS.2011.165",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6008910",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6008655",
}
@Article{Hong:2011:EOS,
author = "Wonhak Hong and Rajashekhar Modugu and Minsu Choi",
title = "Efficient Online Self-Checking Modulo $ 2^n + 1 $
Multiplier Design",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "9",
pages = "1354--1365",
month = sep,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.49",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 22 09:18:06 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5962404",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hsiao:2011:DLC,
author = "Shen-Fu Hsiao and Chan-Feng Chiu and Chia-Sheng Wen",
booktitle = "{2011 IEEE International Conference on IC Design \&
Technology (ICICDT)}",
title = "Design of a low-cost floating-point programmable
vertex processor for mobile graphics applications based
on hybrid number system",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "1--4",
year = "2011",
DOI = "https://doi.org/10.1109/ICICDT.2011.5783231",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5783231",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5773347",
}
@Article{Huang:2011:LCB,
author = "L. Huang and S. Ma and L. Shen and Z. Wang and N.
Xiao",
title = "Low Cost {Binary128} floating-point {FMA} Unit Design
with {SIMD} Support",
journal = j-IEEE-TRANS-COMPUT,
volume = "PP",
number = "99",
pages = "1",
month = "????",
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.77",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5740858",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Huang:2011:NHA,
author = "Miaoqing Huang and Kris Gaj and Tarek El-Ghazawi",
title = "New Hardware Architectures for {Montgomery} Modular
Multiplication Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "7",
pages = "923--936",
month = jul,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.247",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jun 29 10:26:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Huynh:2011:EAP,
author = "Thang Viet Huynh and Manfred Mucke",
booktitle = "{2011 International Conference on Advanced
Technologies for Communications (ATC)}",
title = "Error analysis and precision estimation for
floating-point dot-products using affine arithmetic",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "319--322",
year = "2011",
DOI = "https://doi.org/10.1109/ATC.2011.6027495",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6027495",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6022617",
}
@Article{Ibrahim:2011:PAA,
author = "Atef Ibrahim and Fayez Gebali and Hamed Elsimary and
Amin Nassar",
title = "Processor Array Architectures for Scalable Radix $4$
{Montgomery} Modular Multiplication Algorithm",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "22",
number = "7",
pages = "1142--1149",
month = jul,
year = "2011",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/TPDS.2010.196",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Fri Jul 22 07:54:38 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
}
@Article{Ikhile:2011:RBD,
author = "M. N. O. Ikhile",
title = "The root and {Bell}'s disk iteration methods are of
the same error propagation characteristics in the
simultaneous determination of the zeros of a
polynomial, Part {II}: Round-off error analysis by use
of interval arithmetic",
journal = j-COMPUT-MATH-APPL,
volume = "61",
number = "11",
pages = "3191--3217",
month = jun,
year = "2011",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:47 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122111002860",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InProceedings{Ismail:2011:RLL,
author = "R. Che Ismail and J. N. Coleman",
title = "{ROM}-less {LNS}",
crossref = "Schwarz:2011:PIS",
pages = "43--51",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.15",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992107",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; logarithmic number system (LNS)",
}
@Book{ISO:2011:III,
author = "{ISO}",
title = "{ISO/IEC/IEEE 60559:2011 Information technology ---
Microprocessor Systems --- Floating-Point arithmetic}",
publisher = pub-ISO,
address = pub-ISO:adr,
pages = "58",
year = "2011",
bibdate = "Fri Jul 15 12:50:32 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=57469",
abstract = "ISO/IEC/IEEE 60559:2011(E) specifies formats and
methods for floating-point arithmetic in computer
systems --- standard and extended functions with
single, double, extended, and extendable precision and
recommends formats for data interchange. Exception
conditions are defined and standard handling of these
conditions is specified. It provides a method for
computation with floating-point numbers that will yield
the same result whether the processing is done in
hardware, software, or a combination of the two. The
results of the computation will be identical,
independent of implementation, given the same input
data. Errors, and error conditions, in the mathematical
processing will be reported in a consistent manner
regardless of implementation. This first edition,
published as ISO/IEC/IEEE 60559, replaces the second
edition of IEC 60559.",
acknowledgement = ack-nhfb,
xxISBN = "????",
xxLCCN = "????",
}
@Article{Izsak:2011:CPM,
author = "Alexander Izsak and Nicholas Pippenger",
title = "Carry propagation in multiplication by constants",
journal = j-TALG,
volume = "7",
number = "4",
pages = "54:1--54:??",
month = sep,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/2000807.2000822",
ISSN = "1549-6325 (print), 1549-6333 (electronic)",
ISSN-L = "1549-6325",
bibdate = "Sat Oct 22 09:20:09 MDT 2011",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/talg.bib",
acknowledgement = ack-nhfb,
articleno = "54",
fjournal = "ACM Transactions on Algorithms (TALG)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J982",
}
@Article{Jaime:2011:HSA,
author = "F. J. Jaime and M. A. S{\'a}nchez and J. Hormigo and
J. Villalba and E. L. Zapata",
title = "High-Speed Algorithms and Architectures for Range
Reduction Computation",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "19",
number = "3",
pages = "512--516",
month = "????",
year = "2011",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2009.2033932",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5308221",
abstract = "Range reduction is a crucial step for accuracy in
trigonometric functions evaluation. This paper shows
and compares a set of algorithms for additive range
reduction computation and their corresponding
application-specific integrated circuit implementations
(ensuring an accuracy of one unit in the last place). A
word-serial architecture implementation has been used
as a reference for clearer comparisons. Besides, a new
table-based pipelined architecture for range reduction
has also been proposed.",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=92",
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@Article{Jaiswal:2011:HPF,
author = "Manish Kumar Jaiswal and Ray C. C. Cheung",
title = "High Performance {FPGA} Implementation of Double
Precision Floating Point Adder\slash Subtractor",
journal = "International Journal of Hybrid Information
Technology: IJHIT",
volume = "4",
number = "4",
pages = "71--80",
month = oct,
year = "2011",
DOI = "https://doi.org/10.14257/ijhit.2011.4.4.06",
ISSN = "1738-9968 (print), 2652-2233 (electronic)",
bibdate = "Mon Apr 20 10:04:06 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://gvpress.com/journals/IJHIT/vol4_no4/6.pdf",
acknowledgement = ack-nhfb,
journal-URL = "http://gvpress.com/journals/IJHIT/",
}
@Article{Janhunen:2011:FFP,
author = "J. Janhunen and T. Pitkanen and O. Silven and M.
Juntti",
title = "Fixed- and floating-point Processor Comparison for
{MIMO--OFDM} Detector",
journal = "IEEE Journal of Selected Topics in Signal Processing",
volume = "5",
number = "8",
pages = "1588--1598",
month = dec,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1109/JSTSP.2011.2165830",
ISSN = "1932-4553 (print), 1941-0484 (electronic)",
ISSN-L = "1932-4553",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5995137",
acknowledgement = ack-nhfb,
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4200690",
}
@InProceedings{Janhunen:2011:FVF,
author = "J. Janhunen and P. Salmela and O. Silven and M.
Juntti",
booktitle = "{2011 IEEE International Conference on Acoustics,
Speech and Signal Processing (ICASSP)}",
title = "Fixed- versus floating-point implementation of
{MIMO--OFDM} detector",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "3276--3279",
year = "2011",
DOI = "https://doi.org/10.1109/ICASSP.2011.5946721",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5946721",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5916934",
}
@Article{Jeannerod:2011:CFP,
author = "Claude-Pierr Jeannerod and Herv{\'e} Knochel and
Christophe Monat and Guillaume Revy",
title = "Computing Floating-Point Square Roots via Bivariate
Polynomial Evaluation",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "214--227",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.152",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "In this paper, we show how to reduce the computation
of correctly rounded square roots of binary
floating-point data to the fixed-point evaluation of
some particular integer polynomials in two variables.
By designing parallel and accurate evaluation schemes
for such bivariate polynomials, we show further that
this approach allows for high instruction-level
parallelism (ILP) exposure, and thus, potentially
low-latency implementations. Then, as an illustration,
we detail a C implementation of our method in the case
of IEEE 754-2008 binary32 floating-point data (formerly
called single precision in the 1985 version of the IEEE
754 standard). This software implementation, which
assumes 32-bit unsigned integer arithmetic only, is
almost complete in the sense that it supports special
operands, subnormal numbers, and all rounding-direction
attributes, but not exception handling (that is, status
flags are not set). Finally, we have carried out
experiments with this implementation on the ST231, an
integer processor from the STMicroelectronics' ST200
family, using the ST200 family VLIW compiler. The
results obtained demonstrate the practical interest of
our approach in that context: for all
rounding-direction attributes, the generated assembly
code is optimally scheduled and has indeed low latency
(23 cycles).",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Jeannerod:2011:HSF,
author = "Claude-Pierre Jeannerod and Jingyan Jourdan-Lu and
Christophe Monat and Guillaume Revy",
title = "How to Square Floats Accurately and Efficiently on the
{ST231} Integer Processor",
crossref = "Schwarz:2011:PIS",
pages = "77--81",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.19",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992111",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Jeannerod:2011:MEP,
author = "Claude-Pierre Jeannerod and Nicolas Louvet and
Jean-Michel Muller and Adrien Panhaleux",
title = "Midpoints and Exact Points of Some Algebraic Functions
in Floating-Point Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "228--241",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.144",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "When implementing a function $f$ in floating-point
arithmetic, if we wish correct rounding and good
performance, it is important to know if there are input
floating-point values $x$ such that $ f(x) $ is either
the middle of two consecutive floating-point numbers
(assuming rounded-to-nearest arithmetic), or a
floating-point number (assuming rounded toward $ \pm
\infty $ or toward $0$ arithmetic). In the first case,
we say that $ f(x) $ is a midpoint, and in the second
case, we say that $ f(x) $ is an exact point. For some
usual algebraic functions and various floating-point
formats, we prove whether or not there exist midpoints
or exact points. When there exist midpoints or exact
points, we characterize them or list all of them (if
there are not too many). The results and the techniques
presented in this paper can be used in particular to
deal with both the binary and the decimal formats
defined in the IEEE 754-2008 standard for
floating-point arithmetic.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Jiang:2011:AEP,
author = "Hao Jiang and Roberto Barrio and Housen Li and Xiangke
Liao and Lizhi Cheng and Fang Su",
title = "Accurate evaluation of a polynomial in {Chebyshev}
form",
journal = j-APPL-MATH-COMP,
volume = "217",
number = "23",
pages = "9702--9716",
day = "1",
month = aug,
year = "2011",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2011.04.054",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Oct 25 12:05:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300311006242",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@Article{Kainuma:2011:DIC,
author = "T. Kainuma and Y. Shimamura and F. Miyaoka and Y.
Yamanashi and N. Yoshikawa and A. Fujimaki and K.
Takagi and N. Takagi and S. Nagasawa",
title = "Design and Implementation of Component Circuits of an
{SFQ} Half-Precision floating-point Adder Using
{10-kA\slash cm$^2$ Nb} Process",
journal = j-IEEE-TRANS-APPL-SUPERCOND,
volume = "21",
number = "3",
pages = "827--830",
month = "????",
year = "2011",
CODEN = "ITASE9",
DOI = "https://doi.org/10.1109/TASC.2010.2096374",
ISSN = "1051-8223 (print), 1558-2515 (electronic)",
ISSN-L = "1051-8223",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5680618",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=77",
fjournal = "IEEE Transactions on Applied Superconductivity",
}
@Article{Kaivani:2011:DCR,
author = "Amir Kaivani and Ghassem Jaberipur",
title = "Decimal {CORDIC} Rotation based on Selection by
Rounding: Algorithm and Architecture",
journal = j-COMP-J,
volume = "54",
number = "11",
pages = "1798--1809",
month = nov,
year = "2011",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxr012",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Oct 28 10:35:35 MDT 2011",
bibsource = "http://comjnl.oxfordjournals.org/content/54/11.toc;
https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Hardware implementation of decimal floating-point
arithmetic is a topic of great interest among the
researchers in computer arithmetic and also the digital
processor industry. Software packages for decimal
arithmetic are actually being challenged by decimal
hardware units. This spreading trend seems to include
hardware implementation of elementary functions. The
(Coordinate Rotation Digital Computer) CORDIC
algorithm, due to its simplicity, is one of the most
efficient methods for computing elementary functions.
In this work, we develop a decimal CORDIC scheme with
almost half number of equally long cycles with respect
to the best previous design. This is achieved via
retiming of the conventional CORDIC architecture and
selection of the microrotation factors by rounding.
However, the proposed design does not lead to a
predetermined constant scaling factor. The solution
that we use is to iteratively compute the logarithm of
the scaling factor followed by a decimal
exponentiation. The same CORDIC hardware is reused for
performing the latter. The proposed CORDIC method
requires $ 2 n + 3 $ cycles for $n$-digit decimal
operands vs. $ 4 n $ cycles of the previous methods.
Evaluations with 16-digit operands based on logical
effort analysis conclude that the proposed architecture
shows 82\% speed advantage, at the cost of 60\% more
area and 2.5 KB more ROM.",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
onlinedate = "March 11, 2011",
}
@InProceedings{Kathiara:2011:AVS,
author = "J. Kathiara and M. Leeser",
booktitle = "{2011 IEEE 19th Annual International Symposium on
Field-Programmable Custom Computing Machines (FCCM)}",
title = "An Autonomous Vector\slash Scalar Floating Point
Coprocessor for {FPGAs}",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "33--36",
year = "2011",
DOI = "https://doi.org/10.1109/FCCM.2011.14",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5771244",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5771180",
}
@Article{Kim:2011:ZAS,
author = "SeongKi Kim and HaYoon Song and SangYong Han",
title = "{ZipfAllocation}: an algorithm for static allocation
of movies in a cluster of video servers",
journal = j-SPE,
volume = "41",
number = "6",
pages = "695--716",
month = may,
year = "2011",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.1027",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Tue Jun 21 17:09:57 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Software---Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "25 Nov 2010",
}
@Article{Kong:2011:GDM,
author = "Inwook Kong and Earl E. Swartzlander",
title = "A {Goldschmidt} Division Method With Faster Than
Quadratic Convergence",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "19",
number = "4",
pages = "696--700",
month = apr,
year = "2011",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/tvlsi.2009.2036926",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Mon Dec 11 08:01:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A new method to implement faster than quadratic
convergence for Goldschmidt division using simple logic
circuits is presented. While the approximate quotient
converges quadratically in conventional Goldschmidt
division, the new method achieves nearly cubic
convergence. Although division with cubic convergence
has been regarded as impractical due to its complexity,
the proposed method reduces the logic complexity and
the delay by using an approximate squarer with a simple
logic implementation and a redundant binary Booth
recoder. It is especially effective in a system that
already has a radix-8 multiplier. As a result, the
effective area for the reciprocal table can be reduced
by 25.4\%. The proposed method has been verified by
SystemC and Verilog models. The final results are
confirmed by simulation with both random double
precision numbers and an exhaustive suite of 17-bit
test vectors.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@Article{Kornerup:2011:PAO,
author = "Peter Kornerup and Jean-Michel Muller and Adrien
Panhaleux",
title = "Performing Arithmetic Operations on Round-to-Nearest
Representations",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "282--291",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.134",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "During any composite computation, there is a constant
need for rounding intermediate results before they can
participate in further processing. Recently, a class of
number representations denoted RN-Codings were
introduced, allowing an unbiased rounding-to-nearest to
take place by a simple truncation, with the property
that problems with double-roundings are avoided. In
this paper, we first investigate a particular encoding
of the binary representation. This encoding is
generalized to any radix and digit set; however, radix
complement representations for even values of the radix
turn out to be particularly feasible. The encoding is
essentially an ordinary radix complement representation
with an appended round-bit, but still allowing
rounding-to-nearest by truncation, and thus avoiding
problems with double-roundings. Conversions from radix
complement to these round-to-nearest representations
can be performed in constant time, whereas conversion
the other way, in general, takes at least logarithmic
time. Not only is rounding-to-nearest a constant time
operation, but so is also sign inversion, both of which
are at best log-time operations on ordinary two's
complement representations. Addition and multiplication
on such fixed-point representations are first analyzed
and defined in such a way that rounding information can
be carried along in a meaningful way, at minimal cost.
The analysis is carried through for a compact
(canonical) encoding using two's complement
representation, supplied with a round-bit. Based on the
fixed-point encoding, it is shown possible to define
floating-point representations, and a sketch of the
implementation of an FPU is presented.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kulisch:2011:EDP,
author = "Ulrich Kulisch and Van Snyder",
title = "The exact dot product as basic tool for long interval
arithmetic",
journal = j-COMPUTING,
volume = "91",
number = "3",
pages = "307--313",
month = mar,
year = "2011",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-010-0127-7",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Sep 6 19:14:24 MDT 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=307",
abstract = "Computing with guarantees is based on two arithmetical
features. One is fixed (double) precision interval
arithmetic. The other one is dynamic precision interval
arithmetic, here also called long interval arithmetic.
The basic tool to achieve high speed dynamic precision
arithmetic for real and interval data is an exact
multiply and accumulate operation and with it an exact
dot product. Pipelining allows to compute it at the
same high speed as vector operations on conventional
vector processors. Long interval arithmetic fully
benefits from such high speed. Exactitude brings very
high accuracy, and thereby stability into computation.
This document, which has been incorporated into the
draft standard for interval arithmetic being developed
by IEEE P1788, specifies the implementation of an exact
multiply and accumulate operation.",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "arithmetic standard; computer arithmetic; exact dot
product; floating-point arithmetic; scientific
computing",
remark = "This document is an identical copy of a motion
accepted by the international standards committee IEEE
P1788 on interval arithmetic. Its contents will be
published in a few years when the development of the
standard is completed. The new floating-point
arithmetic standard IEEE 754 (available since 2008)
provides a function for accumulation of the dot product
of two vectors with no accuracy requirement.
Manufacturers who support the dot product by hardware
should be aware that IEEE P1788 requires the exact
result. Once a weak solution has been put into hardware
it may be difficult to change it later. It is therefore
important to bring this decision to public attention as
soon as possible. Actually the simplest and fastest way
for computing a dot product is to compute it exactly
[4].",
}
@Article{Kulisch:2011:VFE,
author = "Ulrich Kulisch",
title = "Very fast and exact accumulation of products",
journal = j-COMPUTING,
volume = "91",
number = "4",
pages = "397--405",
month = apr,
year = "2011",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-010-0131-y",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Tue Sep 6 19:14:31 MDT 2011",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=4&spage=397",
abstract = "The IFIP Working Group on Numerical Software and other
scientists repeatedly requested that a future
arithmetic standard should consider and specify an
exact dot product (EDP) [The IFIP WG IEEE 754R letter,
dated September 4 (2007), The IFIP WG IEEE P1788
letter, dated September 9 (2009)]. On 18 November 2009
the IEEE standards committee P1788 on interval
arithmetic accepted a motion [Kulisch and Snyder (The
exact dot product as basic tool for long interval
arithmetic, passed on Nov 18, 2009 as official IEEE
P1788 document)] for including the EDP into a future
interval arithmetic standard. Actually the simplest and
fastest way for computing a dot product is to compute
it exactly. By pipelining, it can be computed in the
time the processor needs to read the data, i.e., it
comes with utmost speed. A hardware implementation of
the EDP exceeds any approximate computation of the dot
product in software by several orders of magnitude. By
a sample illustration the paper informally specifies
the implementation of the EDP on computers. While
[Kulisch and Snyder (The exact dot product as basic
tool for long interval arithmetic, passed on Nov 18,
2009 as official IEEE P1788 document)] defines what has
to be provided, how to embed the EDP into the new
standard IEEE 754, [IEEE Floating-Point Arithmetic
Standard 754 (2008)] and how exceptions like NaN are to
be dealt with, this article illustrates how the EDP can
be implemented on computers. There is indeed no simpler
way of accumulating a dot product. Any method that just
computes an approximation also has to consider the
relative values of the summands. This results in a more
complicated method. The hardware needed for the EDP is
comparable to that for a fast multiplier by an adder
tree, accepted years ago and now standard technology in
every modern processor. The EDP brings the same speedup
for accumulations at comparable costs. In Numerical
Analysis the dot product is ubiquitous. It is not
merely a fundamental operation in all vector and matrix
spaces. It is the EDP which makes residual correction
effective. This has a direct and positive influence on
all iterative solvers of systems of equations. The EDP
is essential for fast long real and long interval
arithmetic, as well as for assessing and managing
uncertainty in computing. By operator overloading
variable precision interval arithmetic is very easy to
use. With it the result of every arithmetic expression
can be guaranteed to a number of correct digits.",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "arithmetic standards; computer arithmetic; exact dot
product; floating-point arithmetic; scientific
computing",
}
@Article{Lamberti:2011:RCT,
author = "Fabrizio Lamberti and Nikos Andrikos and Elisardo
Antelo and Paolo Montuschi",
title = "Reducing the Computation Time in (Short Bit-Width)
Two's Complement Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "148--156",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.156",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Langhammer:2011:TFD,
author = "Martin Langhammer",
title = "Teraflop {FPGA} Design",
crossref = "Schwarz:2011:PIS",
pages = "187--188",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.32",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992124",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@TechReport{Lefevre:2011:SSI,
author = "Vincent Lef{\`e}vre",
title = "{SIPE}: Small Integer Plus Exponent",
institution = "INRIA",
address = "Lyon, France",
pages = "25",
year = "2011",
bibdate = "Tue Dec 26 14:57:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hal.inria.fr/hal-00650659",
acknowledgement = ack-nhfb,
}
@InProceedings{Lei:2011:FIV,
author = "Yuanwu Lei and Yong Dou and Song Guo and Jie Zhou",
editor = "Olivier Temam and Pen-Chung Yew and Binyu Zang",
booktitle = "Advanced Parallel Processing Technologies: {9th
International Symposium, APPT 2011, Shanghai, China,
September 26--27, 2011, Proceedings}",
title = "{FPGA} Implementation of Variable-Precision
Floating-Point Arithmetic",
volume = "6965",
publisher = pub-SV,
address = pub-SV:adr,
pages = "127--141",
year = "2011",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-24151-2_10",
ISBN = "3-642-24151-4",
ISBN-13 = "978-3-642-24151-2",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Jun 12 16:52:47 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@InProceedings{Lei:2011:VSP,
author = "Yuanwu Lei and Yong Dou and Jie Zhou and Sufeng
Wang",
editor = "Peter Athanas and Dionisios Pnevmatikatos and Nicolas
Sklavos",
booktitle = "21st International Conference on Field Programmable
Logic and Applications: {FPL 2011, 5--7 September 2011,
Chania, Greece}",
title = "{VPFPAP}: A Special-Purpose {VLIW} Processor for
Variable-Precision Floating-Point Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "252--257",
month = sep,
year = "2011",
DOI = "https://doi.org/10.1109/fpl.2011.51",
bibdate = "Wed Jun 12 16:41:42 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
book-URL = "https://ieeexplore.ieee.org/xpl/conhome/6044763/proceeding",
}
@InProceedings{Lipetz:2011:SCC,
author = "Daniel Lipetz and Eric Schwarz",
title = "Self Checking in Current Floating-Point Units",
crossref = "Schwarz:2011:PIS",
pages = "73--76",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.18",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992110",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Liu:2011:FAH,
author = "Feng Liu and Xiaoyu Song and Qingping Tan and Gang
Chen",
title = "Formal Analysis of Hybrid Prefix\slash Carry-Select
Arithmetic Systems",
journal = j-COMP-J,
volume = "54",
number = "6",
pages = "894--904",
month = jun,
year = "2011",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxq048",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed Jun 1 18:54:12 MDT 2011",
bibsource = "content/54/6.toc;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/54/6/894.full.pdf+html",
abstract = "Arithmetic circuits play an important role in
high-performance digital systems. The paper considers a
generic architecture of hybrid prefix\slash
carry-select arithmetic systems. A novel proof
methodology is proposed to model and verify hybrid
addition systems. Algebraic structures and first-order
recursive equations are harnessed in proof derivations.
Case studies on several typical classes of hybrid
prefix\slash carry-select adders and special cases with
pseudo-carries such as Ling's carry demonstrate the
effectiveness of the proposed approach.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "carry-select adders; computer arithmetic; formal
methods; parallel prefix adders",
onlinedate = "May 25, 2010",
}
@InProceedings{Liu:2011:ILC,
author = "Yuanlong Liu and Bateer and Wen Zhong",
booktitle = "{2011 International Conference on Computer Science and
Service System (CSSS)}",
title = "Implementation of a low complexity divider for
{ILUT}-based {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "464--466",
year = "2011",
DOI = "https://doi.org/10.1109/CSSS.2011.5974453",
bibdate = "Tue Sep 27 08:11:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5974453",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5959270",
}
@InProceedings{Lutz:2011:FMA,
author = "David R. Lutz",
title = "Fused Multiply-Add Microarchitecture Comprising
Separate Early-Normalizing Multiply and Add Pipelines",
crossref = "Schwarz:2011:PIS",
pages = "123--128",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.25",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992117",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Malone:2011:FBI,
author = "A. N. Malone and G. R. Morris and K. H. Abed",
booktitle = "{Southeastcon, 2011 Proceedings of IEEE}",
title = "{FPGA}-based implementation of {Horner}'s rule on a
high performance heterogeneous computer",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "277--282",
year = "2011",
DOI = "https://doi.org/10.1109/SECON.2011.5752949",
bibdate = "Tue Sep 27 08:11:09 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5752949",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5746658",
}
@Article{Masakova:2011:ANS,
author = "Z. Mas{\'a}kov{\'a} and E. Pelantov{\'a} and T.
V{\'a}vra",
title = "Arithmetics in number systems with a negative base",
journal = j-THEOR-COMP-SCI,
volume = "412",
number = "8--10",
pages = "835--845",
day = "4",
month = mar,
year = "2011",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Aug 31 10:15:30 MDT 2011",
bibsource = "http://www.sciencedirect.com/science/journal/03043975;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@InProceedings{Matula:2011:PLP,
author = "David W. Matula and Mihai T. Panu",
title = "A Prescale-Lookup-Postscale Additive Procedure for
Obtaining a Single Precision Ulp Accurate Reciprocal",
crossref = "Schwarz:2011:PIS",
pages = "177--183",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.31",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992123",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Mauer:2011:FPS,
author = "V. Mauer and M. Parker",
booktitle = "{Radar Conference (RADAR), 2011 IEEE}",
title = "Floating point {STAP} implementation on {FPGAs}",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "901--904",
year = "2011",
DOI = "https://doi.org/10.1109/RADAR.2011.5960667",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5960667",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5941184",
}
@InProceedings{Minchola:2011:FID,
author = "C. Minchola and M. Vazquez and G. Sutter",
booktitle = "{2011 VII Southern Conference on Programmable Logic
(SPL)}",
title = "A {FPGA} {IEEE-754-2008} decimal64 floating-point
adder\slash subtractor",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "251--256",
year = "2011",
DOI = "https://doi.org/10.1109/SPL.2011.5782657",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5782657",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5771182",
keywords = "decimal floating-point arithmetic",
}
@Article{Moller:2011:IDI,
author = "Niels M{\"o}ller and Torbj{\"o}rn Granlund",
title = "Improved Division by Invariant Integers",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "2",
pages = "165--175",
month = feb,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.143",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Feb 20 19:15:33 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "This paper considers the problem of dividing a
two-word integer by a single-word integer, together
with a few extensions and applications. Due to lack of
efficient division instructions in current processors,
the division is performed as a multiplication using a
precomputed single-word approximation of the reciprocal
of the divisor, followed by a couple of adjustment
steps. There are three common types of unsigned
multiplication instructions: we define full word
multiplication (umul), which produces the two-word
product of two single-word integers; low multiplication
(umullo), which produces only the least significant
word of the product; and high multiplication (umulhi),
which produces only the most significant word. We
describe an algorithm that produces a quotient and
remainder using one umul and one umullo. This is an
improvement over earlier methods, since the new method
uses cheaper multiplication operations. It turns out
that we also get some additional savings from simpler
adjustment conditions. The algorithm has been
implemented in version 4.3 of the gmp library. When
applied to the problem of dividing a large integer by a
single word, the new algorithm gives a speedup of
roughly 30 percent, benchmarked on AMD and Intel
processors in the x86\_64 family.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Mouilleron:2011:AGF,
author = "Christophe Mouilleron and Guillaume Revy",
title = "Automatic Generation of Fast and Certified Code for
Polynomial Evaluation",
crossref = "Schwarz:2011:PIS",
pages = "233--242",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.39",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992131",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Nannarelli:2011:RCD,
author = "Alberto Nannarelli",
title = "Radix-16 Combined Division and Square Root Unit",
crossref = "Schwarz:2011:PIS",
pages = "169--176",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.30",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992122",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; sqrt(x); square root",
}
@InCollection{Nguyen:2011:FSA,
author = "Hong Diep Nguyen and Bogdan Pasca and Thomas B.
Preu{\ss}er",
editor = "Peter Athanas and Dionisios Pnevmatikatos and Nicolas
Sklavos",
booktitle = "{21st International Conference on Field Programmable
Logic and Applications: FPL 2011: proceedings: 5--7
September 2011, Chania, Greece}",
title = "{FPGA}-specific arithmetic optimizations of
short-latency adders",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
bookpages = "xxviii + 560",
pages = "232--237",
year = "2011",
DOI = "https://doi.org/10.1109/FPL.2011.49",
ISBN = "0-7695-4529-7",
ISBN-13 = "978-0-7695-4529-5",
LCCN = "TK7895.G36",
bibdate = "Sat Feb 08 09:55:40 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/6044770",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=6044763",
}
@Article{Ozaki:2011:TEE,
author = "Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi
Oishi",
title = "Tight and efficient enclosure of matrix multiplication
by using optimized {BLAS}",
journal = j-NUM-LIN-ALG-APPL,
volume = "18",
number = "2",
pages = "237--248",
month = mar,
year = "2011",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.724",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Wed Mar 16 10:14:59 MDT 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper is concerned with the tight enclosure of
matrix multiplication $ A B $ for two floating-point
matrices $A$ and $B$. The aim of this paper is to
compute component-wise upper and lower bounds of the
exact result $C$ of the matrix multiplication $ A B $
by floating-point arithmetic. Namely, an interval
matrix enclosing $C$ is obtained. In this paper, new
algorithms for enclosing $C$ are proposed. The proposed
algorithms are designed to mainly exploit the level 3
operations in BLAS. Although the proposed algorithms
take around twice as much costs as a standard algorithm
promoted by Oishi and Rump, the accuracy of the result
by the proposed algorithms is better than that of the
standard algorithm. At the end of this paper, we
present numerical examples showing the efficiency of
the proposed algorithms",
acknowledgement = ack-nhfb,
fjournal = "Numerical linear algebra with applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
keywords = "interval arithmetic; matrix multiplication; verified
numerical computation",
onlinedate = "19 May 2010",
}
@InProceedings{Park:2011:LPS,
author = "Daejin Park and Tag Gon Kim and Changmin Kim and
Sungho Kwak",
title = "A low-power sync processor with a floating-point timer
and universal edge tracer for {3DTV} active shutter
glasses",
crossref = "IEEE:2011:ICC",
pages = "1--3",
year = "2011",
CODEN = "IRELAO",
DOI = "https://doi.org/10.1109/COOLCHIPS.2011.5890924",
ISSN = "0367-9950",
bibdate = "Wed Dec 21 14:34:51 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cool-chips.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5890924",
acknowledgement = ack-nhfb,
}
@InProceedings{Peay:2011:IQW,
author = "N. S. Peay and G. R. Morris and K. H. Abed",
booktitle = "{2011 Proceedings of IEEE Southeastcon}",
title = "Integrating {Quartus Wizard}-based {VHDL}
floating-point components into a high performance
heterogeneous computing environment",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "413--417",
year = "2011",
DOI = "https://doi.org/10.1109/SECON.2011.5752977",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5752977",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5746658",
}
@Article{Piso:2011:VLG,
author = "Daniel Piso and Javier D. Bruguera",
title = "Variable Latency {Goldschmidt} Algorithm Based on a
New Rounding Method and a Remainder Estimate",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "11",
pages = "1535--1546",
month = nov,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.269",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Sep 27 07:57:50 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669291",
abstract = "A new variable latency Goldschmidt algorithm is
presented. The algorithm is based on a new rounding
method for division, square root, and their reciprocals
that avoids the conventional remainder calculation in
most of cases and improves previous proposals. The
rounding decision is taken by checking the least
significant bits of the output of the last Goldschmidt
iteration without any other transformation. This helps
to reduce the number of cases which need the
calculation of the remainder. Additionally, we avoid
the calculation of the remainder for most of those
cases by using a remainder estimate that can be easily
obtained from the Goldschmidt iteration. The
calculation of the estimate is much simpler and less
time consuming than the calculation of the remainder
and this contributes to reducing the number of cases
which need a large latency. The combination of both
techniques allows us to define a variable latency
algorithm which needs to compute the remainder in just
nine percent of the total number of cases for
reciprocal and division and in 12 percent for square
root and square root reciprocal.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "accuracy; approximation algorithms; approximation
methods; computers; division; equations; Goldschmidt
algorithm; hardware; mathematical model; reciprocal;
rounding; square root; square root reciprocal; variable
latency.",
}
@InProceedings{Preusser:2011:ACF,
author = "Thomas B. Preu{\ss}er and Martin Zabel and Rainer G.
Spallek",
title = "Accelerating Computations on {FPGA} Carry Chains by
Operand Compaction",
crossref = "Schwarz:2011:PIS",
pages = "95--102",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.22",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992114",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Ramakrishnan:2011:AFP,
author = "A. Ramakrishnan and J. M. Conrad",
booktitle = "{2011 Proceedings of IEEE Southeastcon}",
title = "Analysis of floating point operations in
microcontrollers",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "97--100",
year = "2011",
DOI = "https://doi.org/10.1109/SECON.2011.5752913",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5752913",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5746658",
}
@Article{Romano:2011:NLR,
author = "Paul K. Romano and Harry McLaughlin",
title = "On Non-Linear Recursive Sequences and {Benford's
Law}",
journal = j-FIB-QUART,
volume = "49",
number = "2",
pages = "134--138",
month = may,
year = "2011",
CODEN = "FIBQAU",
ISSN = "0015-0517",
ISSN-L = "0015-0517",
bibdate = "Thu Oct 20 18:04:45 MDT 2011",
bibsource = "http://www.fq.math.ca/49-2.html;
https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.fq.math.ca/Abstracts/49-2/romano.pdf",
acknowledgement = ack-nhfb,
ajournal = "Fib. Quart",
fjournal = "The Fibonacci Quarterly",
journal-URL = "http://www.fq.math.ca/",
}
@Article{Romanovski:2011:ASS,
author = "Valery G. Romanovski and Mateja Presern",
title = "An approach to solving systems of polynomials via
modular arithmetics with applications",
journal = j-J-COMPUT-APPL-MATH,
volume = "236",
number = "2",
pages = "196--208",
day = "15",
month = aug,
year = "2011",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:24:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042711003542",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Rupp:2011:SBF,
author = "Benjamin Rupp and Howard Lovatt and Andrea Vezzini",
booktitle = "{Proceedings of the 2011 14th European Conference on
Power Electronics and Applications (EPE 2011)}",
title = "Simulink-based floating-point {DSP} Control Platform",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "1--7",
year = "2011",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6020132",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6014782",
}
@InProceedings{Samman:2011:RSP,
author = "F. A. Samman and P. Surapong and M. Glesner",
booktitle = "{2011 6th International Workshop on Reconfigurable
Communication-centric Systems-on-Chip (ReCoSoC)}",
title = "Reconfigurable streaming processor core with
interconnected floating-point arithmetic units for
multicore adaptive signal processing systems",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "1--6",
year = "2011",
DOI = "https://doi.org/10.1109/ReCoSoC.2011.5981539",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5981539",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5967008",
}
@InProceedings{Sarbishei:2011:FPA,
author = "Omid Sarbishei and Katarzyna Radecka",
title = "On the Fixed-Point Accuracy Analysis and Optimization
of {FFT} Units with {CORDIC} Multipliers",
crossref = "Schwarz:2011:PIS",
pages = "62--69",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.17",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992109",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@Article{Seidel:2011:FVI,
author = "Peter-Michael Seidel",
title = "Formal Verification of an Iterative Low-Power x86
Floating-Point Multiplier with Redundant Feedback",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "21",
month = oct,
year = "2011",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in EPTCS 70, 2011, pp. 70--83.",
URL = "http://arxiv.org/abs/1110.4675",
abstract = "We present the formal verification of a low-power x86
floating-point multiplier. The multiplier operates
iteratively and feeds back intermediate results in
redundant representation. It supports x87 and SSE
instructions in various precisions and can block the
issuing of new instructions. The design has been
optimized for low-power operation and has not been
constrained by the formal verification effort.
Additional improvements for the implementation were
identified through formal verification. The formal
verification of the design also incorporates the
implementation of clock-gating and control logic. The
core of the verification effort was based on ACL2
theorem proving. Additionally, model checking has been
used to verify some properties of the floating-point
scheduler that are relevant for the correct operation
of the unit.",
acknowledgement = ack-nhfb,
subject = "Logic in Computer Science (cs.LO); Hardware
Architecture (cs.AR); Mathematical Software (cs.MS)",
}
@Article{Seo:2011:GDP,
author = "Young-Hun Seo and Seon-Kyoo Lee and Jae-Yoon Sim",
title = "A {1-GHz} Digital {PLL} with a 3-ps resolution
floating-point-number {TDC} in a 0.18-{CMOS}",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "58",
number = "2",
pages = "70--74",
month = "????",
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1109/TCSII.2011.2106315",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5713246",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8920",
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}
@Article{Siegel:2011:LAL,
author = "Stefan Siegel and J{\"u}rgen Wolff von Gudenberg",
title = "A long accumulator like a carry-save adder",
journal = j-COMPUTING,
volume = "93",
number = "??",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-011-0164-x",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Fri Nov 18 15:08:38 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "accurate floating-point summation",
pagecount = "11",
remark = "Online on 12 November 2011, but not yet assigned to a
journal issue.",
}
@InProceedings{Singh:2011:VEF,
author = "R. R. Singh and A. Tiwari and V. K. Singh and G. S.
Tomar",
booktitle = "{2011 International Conference on Communication
Systems and Network Technologies (CSNT)}",
title = "{VHDL} Environment for Floating Point Arithmetic Logic
Unit-{ALU} Design and Simulation",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "469--472",
year = "2011",
DOI = "https://doi.org/10.1109/CSNT.2011.167",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5966491",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5963767",
}
@Article{Singha:2011:NAF,
author = "Satrughna Singha and Aniruddha Ghosh and Amitabha
Sinha",
title = "A new architecture for {FPGA} based implementation of
conversion of binary to double base number system
({DBNS}) using parallel search technique",
journal = j-COMP-ARCH-NEWS,
volume = "39",
number = "5",
pages = "12--18",
month = dec,
year = "2011",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2093339.2093343",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Thu Mar 15 14:07:10 MDT 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Non-binary number systems are increasingly gaining
popularity in signal processing applications for their
capabilities of handling arithmetic operations
efficiently. One such number system, ``Double Base
Number System (DBNS)'' has gained attention to many
researchers for it's capability of performing
multiplication operation efficiently. Recently,
``Triple Base Number System (TBNS)'' has been
introduced which shows better performance over DBNS for
higher bit operations in terms of speed, hardware
complexity and power dissipation. However, the
advantages of TBNS systems cannot be exploited due to
substantial overhead of conversion from binary to TBNS.
Keeping this issue in view, in this paper, a novel
architecture has been proposed for high performance
binary to TBNS conversion. Efficiency of this
conversion scheme has been dealt with in details and
experimental results and analysis clearly indicate the
novelty of the architecture.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@InProceedings{Tang:2011:TCT,
author = "Ping Tak Peter Tang and J. Adam Butts and Ron O. Dror
and David E. Shaw",
title = "Tight Certification Techniques for Digit-by-Rounding
Algorithms with Application to a New $ 1 / \sqrt {x} $
Design",
crossref = "Schwarz:2011:PIS",
pages = "159--168",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.29",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992121",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; reciprocal square root; rsqrt(x)",
}
@Article{Tsen:2011:HDB,
author = "Charles Tsen and Sonia Gonzalez-Navarro and Michael J.
Schulte and Katherine Compton",
title = "Hardware Designs for Binary Integer Decimal-Based
Rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "60",
number = "5",
pages = "614--627",
month = may,
year = "2011",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.268",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jun 29 10:26:18 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "Decimal floating-point (DFP) arithmetic is becoming
increasingly important, and specifications for it are
included in the revised IEEE 754 Standard for
Floating-Point Arithmetic (IEEE 754-2008). The binary
encoding of DFP numbers specified in IEEE 754-2008 is
commonly referred to as Binary-Integer Decimal (BID).
BID uses a binary integer to encode the significand,
which allows it to leverage existing high-speed binary
circuits. However, performing decimal rounding on these
binary significands is challenging. In this paper, we
propose and evaluate several approaches to perform
decimal rounding in hardware for DFP numbers that use
the BID encoding. We summarize several rounding
techniques, present the theory and design of each
proposed rounding unit, and use synthesis results to
evaluate the critical path delay, latency, and area of
rounding units for 64-bit BID numbers. Our results
indicate that the bulk of each rounder design is
occupied by a binary fixed-point multiplier that can be
shared with other integer and floating-point
operations. This is the first paper to present and
compare a variety of techniques for BID-based rounding
hardware. These techniques are valuable to designers of
BID-based DFP solutions.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Arithmetic algorithms; BID rounding; binary integer
decimal; computer arithmetic; decimal floating-point;
hardware designs; IEEE 754-2008; rounding",
}
@InProceedings{Vazquez:2011:CIA,
author = "{\'A}lvaro V{\'a}zquez and Javier D. Bruguera",
title = "Composite Iterative Algorithm and Architecture for
$q$-th Root Calculation",
crossref = "Schwarz:2011:PIS",
pages = "52--61",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH.2011.16",
bibdate = "Sat Aug 20 09:00:00 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992108",
acknowledgement = ack-nhfb,
keywords = "ARITH-20",
}
@InProceedings{Vestias:2011:IDM,
author = "M. P. Vestias and H. C. Neto",
booktitle = "{2011 VII Southern Conference on Programmable Logic
(SPL)}",
title = "Iterative decimal multiplication using binary
arithmetic",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "257--262",
year = "2011",
DOI = "https://doi.org/10.1109/SPL.2011.5782658",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5782658",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5771182",
keywords = "decimal floating-point arithmetic",
}
@InProceedings{Vigliar:2011:MFB,
author = "Mario Vigliar and Giancarlo Raiconi and Amedeo D'Auria
and Giuseppe Del Mastro",
booktitle = "{2011 IEEE 54th International Midwest Symposium on
Circuits and Systems (MWSCAS)}",
title = "Modelling a fast {BLAS} level-1 inspired vectorized
{FPU} for {ARM} devices",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "1--4",
year = "2011",
DOI = "https://doi.org/10.1109/MWSCAS.2011.6026644",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6026644",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6019810",
}
@InProceedings{Wang:2011:DFB,
author = "Mulan Wang and Xinghua Zhu and Baosheng Wang and
Xiaoxia Li",
booktitle = "{2011 International Conference on Mechatronic Science,
Electric Engineering and Computer (MEC)}",
title = "Development of {FPGA}-based arithmetic module in {CNC}
system",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "494--497",
year = "2011",
DOI = "https://doi.org/10.1109/MEC.2011.6025510",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6025510",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6020827",
}
@Article{Wang:2011:RCM,
author = "Xiaofang Wang and Pallav Gupta",
title = "Resource-constrained multiprocessor synthesis for
floating-point applications on {FPGAs}",
journal = j-TODAES,
volume = "16",
number = "4",
pages = "41:1--41:??",
month = oct,
year = "2011",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/2003695.2003701",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Sat Oct 22 09:25:48 MDT 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/todaes/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/todaes.bib",
acknowledgement = ack-nhfb,
articleno = "41",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J776",
}
@TechReport{Whitehead:2011:PPF,
author = "Nathan Whitehead and Alex Fit-Florea",
title = "Precision \& Performance: Floating Point and {IEEE
754} Compliance for {NVIDIA GPUs}",
type = "Report",
institution = "nVidia Corporation",
address = "Santa Clara, CA, USA",
pages = "7",
day = "21",
month = jun,
year = "2011",
bibdate = "Tue Sep 04 09:13:29 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://developer.download.nvidia.com/assets/cuda/files/NVIDIA-CUDA-Floating-Point.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Xu:2011:DLF,
author = "Jun Xu and Hong Wang",
booktitle = "{2011 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "Desynchronize a legacy floating-point adder with
operand-dependant delay elements",
publisher = "pub-IEEE",
address = "pub-IEEE:adr",
pages = "1427--1430",
year = "2011",
DOI = "https://doi.org/10.1109/ISCAS.2011.5937841",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5937841",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5910713",
}
@InProceedings{Yeung:2011:MCF,
author = "Jackson H. C. Yeung and Evangeline F. Y. Young and
Philip H. W. Leong",
booktitle = "{FPGA '11: Proceedings of the 19th ACM\slash SIGDA
International Symposium on Field Programmable Gate
Arrays, Monterey, CA, USA, February 27--March 01,
2011}",
title = "A {Monte-Carlo} floating-point unit for
self-validating arithmetic",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "199--208",
year = "2011",
DOI = "https://doi.org/10.1145/1950413.1950453",
ISBN = "1-4503-0554-7",
ISBN-13 = "978-1-4503-0554-9",
bibdate = "Tue Sep 27 08:57:51 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Monte-Carlo arithmetic is a form of self-validating
arithmetic that accounts for the effect of rounding
errors. We have implemented a floating point unit that
can perform either IEEE 754 or Monte-Carlo floating
point computation, allowing hardware accelerated
validation of results during execution. Experiments
show that our approach has a modest hardware overhead
and allows the propagation of rounding error to be
accurately estimated.",
acknowledgement = ack-nhfb,
keywords = "floating-point; FPGA; FPU; Monte Carlo arithmetic",
numpages = "10",
}
@Article{Yu:2011:OFP,
author = "C. Yu and A. M. Smith and W. Luk and P. H. W. Leong
and S. J. E. Wilton",
title = "Optimizing Floating Point Units in Hybrid {FPGAs}",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "PP",
number = "99",
pages = "1--10",
month = "????",
year = "2011",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2011.2153883",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Tue Sep 27 08:11:02 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5893965",
acknowledgement = ack-nhfb,
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=92",
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@Article{Zalaket:2011:PFU,
author = "Joseph Zalaket and Joseph Hajj-Boutros",
title = "Prime factorization using square root approximation",
journal = j-COMPUT-MATH-APPL,
volume = "61",
number = "9",
pages = "2463--2467",
month = may,
year = "2011",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:50:54 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122111001131",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Abbott:2012:TFA,
author = "John Abbott",
title = "Twin-float arithmetic",
journal = j-J-SYMBOLIC-COMP,
volume = "47",
number = "5",
pages = "536--551",
month = may,
year = "2012",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1016/j.jsc.2011.12.005",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Sat Feb 25 10:12:47 MST 2012",
bibsource = "http://www.sciencedirect.com/science/journal/07477171;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0747717111001970",
abstract = "We present a heuristically certified form of
floating-point arithmetic and its implementation in
CoCoALib. This arithmetic is intended to act as a fast
alternative to exact rational arithmetic, and is
developed from the idea of paired floats expounded by
Traverso and Zanoni (2002). As prerequisites we need a
source of (pseudo-)random numbers, and an underlying
floating-point arithmetic system where the user can set
the precision. Twin-float arithmetic can be used only
where the input data are exact, or can be obtained at
high enough precision. Our arithmetic includes a total
cancellation heuristic for sums and differences, and so
can be used in classical algebraic algorithms such as
Buchberger's algorithm. We also present a (new)
algorithm for recovering an exact rational value from a
twin-float, so in some cases an exact answer can be
obtained from an approximate computation.\par
The ideas presented here are implemented as a ring in
CoCoALib, called RingTwinFloat, allowing them to be
used easily in a wide variety of algebraic computations
(including Gr{\"o}bner bases).",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
}
@Article{Adam:2012:FPD,
author = "Sanda Adam and Gheorghe Adam",
title = "Floating Point Degree of Precision in Numerical
Quadrature",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7125",
pages = "189--194",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-28212-6_19",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Dec 19 15:24:39 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012b.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-28212-6_19/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-28212-6",
book-URL = "http://www.springerlink.com/content/978-3-642-28212-6",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Aharony:2012:IFP,
author = "Merav Aharony and Emanuel Gofman and Elena Guralnik
and Anatoly Koyfman",
title = "Injecting Floating-Point Testing Knowledge into Test
Generators",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7261",
pages = "234--241",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-34188-5_20",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Dec 19 15:18:42 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012d.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-34188-5_20/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-34188-5",
book-URL = "http://www.springerlink.com/content/978-3-642-34188-5",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Akleylek:2012:MRR,
author = "Sedat Akleylek and Ferruh Ozbudak",
title = "Modified Redundant Representation for Designing
Arithmetic Circuits with Small Complexity",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "3",
pages = "427--432",
month = mar,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.29",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Feb 3 07:35:03 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Al-Mohy:2012:MAB,
author = "Awad H. Al-Mohy",
title = "A more accurate {Briggs} method for the logarithm",
journal = j-NUMER-ALGORITHMS,
volume = "59",
number = "??",
pages = "??--??",
month = "????",
year = "2012",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-011-9496-z",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Nov 30 06:36:53 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/content/4110609h521kg66m/",
abstract = "A new approach for computing an expression of the form
$ a^{1 / 2^k} - 1 $ is presented that avoids the danger
of subtractive cancellation in floating point
arithmetic, where $a$ is a complex number not belonging
to the closed negative real axis and $k$ is a
nonnegative integer. We also derive a condition number
for the problem. The algorithm therefore allows highly
accurate numerical calculation of $ \log (a) $ using
Briggs' method.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Briggs' method; Briggs' tables; Inverse scaling and
squaring method; Logarithm function",
}
@Misc{Anonymous:2012:FIS,
author = "Anonymous",
title = "Fast inverse square root",
howpublished = "Wikipedia article.",
day = "20",
month = mar,
year = "2012",
bibdate = "Mon Apr 02 17:03:18 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This article describes an algorithm for the inverse
square root. The only novel feature is use of two
IEEE-754 specific magic constants for 32-bit and 64-bit
binary arithmetic that allow obtaining fast starting
estimates for Newton--Raphson iterations by
manipulating the floating-point representations as
integers. The code fails to handle signed zero,
Infinity, and NaN arguments, uses too few iterations,
and does not adjust for rounding errors to obtain
correctly-rounded results. See \cite{Blinn:1997:JBC}.",
URL = "http://en.wikipedia.org/wiki/Fast_inverse_square_root",
acknowledgement = ack-nhfb,
}
@Article{Antao:2012:RBE,
author = "Samuel Ant{\~a}o and Jean-Claude Bajard and Leonel
Sousa",
title = "{RNS}-Based Elliptic Curve Point Multiplication for
Massive Parallel Architectures",
journal = j-COMP-J,
volume = "55",
number = "5",
pages = "629--647",
month = may,
year = "2012",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxr119",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Wed May 2 11:34:42 MDT 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/55/5.toc;
https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/55/5/629.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "Residue Number System (RNS)",
onlinedate = "November 30, 2011",
}
@Article{Antelo:2012:GEI,
author = "Elisardo Antelo and David Hough and Paolo Ienne",
title = "{Guest Editors}' Introduction: Special Section on
Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "8",
pages = "1057--1058",
month = aug,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.153",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 27 08:30:49 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Antelo:2012:IIFa,
author = "Elisardo Antelo",
title = "Industrial Implementations of Floating-Point Units:
Vol. 1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "103 (est.)",
year = "2012",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Dec 06 11:34:04 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Product ID ES0000033.",
acknowledgement = ack-nhfb,
tableofcontents = "Editor's Introduction \\
Related Videos \\
P6 Binary Floating-Point Unit / Son Dao Trong, Martin
Schmookler, Eric M. Schwarz, and Michael Kroener \\
FPU Implementations with Denormalized Numbers / Eric M.
Schwarz, Martin Schmookler, and Son Dao Trong \\
1-GHz HAL SPARC64{\TM} Dual Floating Point Unit with
RAS Features / Ajay Naini, Atul Dhablania, Warren
James, and Debjit Das Sarma \\
Low-Power Multiple-Precision Iterative Floating-Point
Multiplier with SIMD Support / Dimitri Tan, Carl E.
Lemonds, and Michael J. Schulte \\
The Vector Floating-Point Unit in a Synergistic
Processor Element of a CELL Processor / Silvia M.
Mueller, Christian Jacobi, Hwa-Joon Oh, Kevin D. Tran,
Scott R. Cottier, Brad W. Michael, Hiroo Nishikawa,
Yonetaro Totsuka, Tatsuya Namatame, Naoka Yano, Takashi
Machida, and Sang H. Dhong \\
A High-Performance SIMD Floating Point Unit for
BlueGene/L: Architecture, Compilation, and Algorithm
Design / Leonardo Bachega, Siddhartha Chatterjee,
Kenneth A. Dockser, John A. Gunnels, Manish Gupta, Fred
G. Gustavson, Christopher A. Lapkowski, Gary K. Liu,
Mark P. Mendell, Charles D. Wait, and T.J. Chris Ward
\\
Design of the ARM VFP11 Divide and Square Root
Synthesisable Macrocell / Neil Burgess and Chris N.
Hinds \\
Correctness Proofs Outline for Newton--Raphson Based
Floating-Point Divide and Square Root Algorithms /
Marius A. Cornea-Hasegan, Roger A. Golliver, and Peter
Markstein \\
Recommended Resources \\
About the Editor",
}
@Book{Antelo:2012:IIFb,
author = "Elisardo Antelo",
title = "Industrial Implementations of Floating-Point Units:
Vol. 2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "79 (est.)",
year = "2012",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Dec 06 11:34:04 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Product ID ES0000034.",
acknowledgement = ack-nhfb,
tableofcontents = "Table of Contents \\
Editor Bio \\
Editor's Introduction \\
Related Videos \\
A High-Performance Area-Efficient Multifunction
Interpolator / Stuart F. Oberman and Michael Y. Siu \\
New Algorithms for Improved Transcendental Functions on
IA-64 / Shane Story and Ping Tak Peter Tang \\
Energy-Delay Estimation Technique for High-Performance
Microprocessor VLSI Adders / Vojin G. Oklobdzija, Bart
R. Zeydel, Hoang Dao, Sanu Mathew, and Ram
Krishnamurthy \\
Advanced Clockgating Schemes for
Fused-Multiply-Add-Type Floating-Point Units / Jochen
Preiss, Maarten Boersma, and Silvia Melitta Mueller \\
Design of Low-Cost High-Performance Floating-Point
Fused Multiply-Add with Reduced Power / Zichu Qi, Qi
Guo, Ge Zhang, Xiangku Li, and Weiwu Hu \\
Decimal Floating-Point: Algorism for Computers /
Michael F. Cowlishaw \\
A Software Implementation of the IEEE 754R Decimal
Floating-Point Arithmetic Using the Binary Encoding
Format / Marius Cornea, John Harrison, Cristina
Anderson, Ping Tak Peter Tang, Eric Schneider, and
Evgeny Gvozdev \\
Recommended Resources \\
About the Editor",
}
@Article{Aswal:2012:BFD,
author = "Abhilasha Aswal and M. Ganesh Perumal and G. N.
Srinivasa Prasanna",
title = "On Basic Financial Decimal Operations on Binary
Machines",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "8",
pages = "1084--1096",
month = aug,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.89",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 27 08:30:49 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Bailey:2012:AIS,
author = "David H. Bailey and Jonathan M. Borwein",
title = "Ancient {Indian} Square Roots: An Exercise in Forensic
Paleo-Mathematics",
journal = j-AMER-MATH-MONTHLY,
volume = "119",
number = "8",
pages = "646--657",
month = oct,
year = "2012",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.119.08.646",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Thu Nov 8 07:34:21 MST 2012",
bibsource = "http://www.jstor.org/journals/00029890.html;
http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8;
https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.119.08.646.pdf",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Bailey:2012:HPC,
author = "David H. Bailey and Roberto Barrio and Jonathan M.
Borwein",
title = "High-precision computation: Mathematical physics and
dynamics",
journal = j-APPL-MATH-COMP,
volume = "218",
number = "20",
pages = "10106--10121",
day = "15",
month = jun,
year = "2012",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2012.03.087",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "65Y04 (68M07)",
MRnumber = "2921767",
bibdate = "Thu Aug 11 10:27:38 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://docserver.carma.newcastle.edu.au/775/;
http://www.sciencedirect.com/science/article/pii/S0096300312003505",
abstract = "At the present time, IEEE 64-bit floating-point
arithmetic is sufficiently accurate for most scientific
applications. However, for a rapidly growing body of
important scientific computing applications, a higher
level of numeric precision is required. Such
calculations are facilitated by high-precision software
packages that include high-level language translation
modules to minimize the conversion effort. This paper
presents an overview of recent applications of these
techniques and provides some analysis of their
numerical requirements. We conclude that high-precision
arithmetic facilities are now an indispensable
component of a modern large-scale scientific computing
environment.",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
keywords = "Dynamical systems; Experimental mathematics;
High-precision computation; Mathematical physics",
ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
researcherid-numbers = "Barrio, Roberto/L-4983-2014",
}
@Article{Baudin:2012:RCD,
author = "Michael Baudin and Robert L. Smith",
title = "A Robust Complex Division in {Scilab}",
journal = "CoRR",
volume = "abs/1210.4539",
year = "2012",
bibdate = "Tue Apr 16 08:18:25 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://arxiv.org/abs/1210.4539",
abstract = "The most widely used algorithm for floating point
complex division, known as Smith's method, may fail
more often than expected. This document presents two
improved complex division algorithms. We present a
proof of the robustness of the first improved
algorithm. Numerical simulations show that this
algorithm performs well in practice and is
significantly more robust than other known
implementations. By combining additional scaling
methods with this first algorithm, we were able to
create a second algorithm, which rarely fails.",
acknowledgement = ack-nhfb,
}
@Article{Benz:2012:DPA,
author = "Florian Benz and Andreas Hildebrandt and Sebastian
Hack",
title = "A dynamic program analysis to find floating-point
accuracy problems",
journal = j-SIGPLAN,
volume = "47",
number = "6",
pages = "453--462",
month = jun,
year = "2012",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2345156.2254118",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Mon Aug 6 16:31:49 MDT 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
note = "PLDI '12 proceedings.",
abstract = "Programs using floating-point arithmetic are prone to
accuracy problems caused by rounding and catastrophic
cancellation. These phenomena provoke bugs that are
notoriously hard to track down: the program does not
necessarily crash and the results are not necessarily
obviously wrong, but often subtly inaccurate. Further
use of these values can lead to catastrophic errors. In
this paper, we present a dynamic program analysis that
supports the programmer in finding accuracy problems.
Our analysis uses binary translation to perform every
floating-point computation side by side in higher
precision. Furthermore, we use a lightweight slicing
approach to track the evolution of errors. We evaluate
our analysis by demonstrating that it catches
well-known floating-point accuracy problems and by
analyzing the Spec CFP2006 floating-point benchmark. In
the latter, we show how our tool tracks down a
catastrophic cancellation that causes a complete loss
of accuracy leading to a meaningless program result.
Finally, we apply our program to a complex, real-world
bioinformatics application in which our program
detected a serious cancellation. Correcting the
instability led not only to improved quality of the
result, but also to an improvement of the program's run
time.In this paper, we present a dynamic program
analysis that supports the programmer in finding
accuracy problems. Our analysis uses binary translation
to perform every floating-point computation side by
side in higher precision. Furthermore, we use a
lightweight slicing approach to track the evolution of
errors. We evaluate our analysis by demonstrating that
it catches well-known floating-point accuracy problems
and by analyzing the SpecfiCFP2006 floating-point
benchmark. In the latter, we show how our tool tracks
down a catastrophic cancellation that causes a complete
loss of accuracy leading to a meaningless program
result. Finally, we apply our program to a complex,
real-world bioinformatics application in which our
program detected a serious cancellation. Correcting the
instability led not only to improved quality of the
result, but also to an improvement of the program's run
time.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@InProceedings{Bohlender:2012:CFE,
author = "G. Bohlender and U. Kulisch",
title = "Comments on fast and exact accumulation of products",
crossref = "Jonasson:2012:APSb",
pages = "148--156",
year = "2012",
DOI = "https://doi.org/10.1007/978-3-642-28145-7_15",
bibdate = "Sat Oct 31 07:09:45 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Boldo:2012:AOP,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "Arithm{\'e}tique des ordinateurs et preuves formelles.
({French}) [{Computer} arithmetic and formal proofs]",
institution = "{\'E}cole des Jeunes Chercheurs en Informatique
Math{\'e}matique",
address = "????",
pages = "31",
day = "22",
month = mar,
year = "2012",
bibdate = "Fri Sep 22 17:09:39 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-00755333/file/main.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Brisebarre:2012:MPK,
author = "Nicolas Brisebarre and Milo D. Ercegovac and
Jean-Michel Muller",
editor = "{IEEE}",
booktitle = "{2012 IEEE 23rd International Conference on
Application-Specific Systems, Architectures and
Processors, 9--11 July 2012. Delft, The Netherlands}",
title = "{$ (M, p, k) $}-Friendly Points: a Table-Based Method
for Trigonometric Function Evaluation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "46--52",
year = "2012",
DOI = "https://doi.org/10.1109/ASAP.2012.17",
ISBN = "0-7695-4768-0",
ISBN-13 = "978-0-7695-4768-8",
ISSN = "1063-6862",
ISSN-L = "1063-6862",
bibdate = "Fri Sep 29 10:49:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bruintjes:2012:SLA,
author = "Tom M. Bruintjes and Karel H. G. Walters and Sabih H.
Gerez and Bert Molenkamp and Gerard J. M. Smit",
title = "{Sabrewing}: a lightweight architecture for combined
floating-point and integer arithmetic",
journal = j-TACO,
volume = "8",
number = "4",
pages = "41:1--41:??",
month = jan,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2086696.2086720",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Sat Jan 21 07:49:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
abstract = "In spite of the fact that floating-point arithmetic is
costly in terms of silicon area, the joint design of
hardware for floating-point and integer arithmetic is
seldom considered. While components like multipliers
and adders can potentially be shared, floating-point
and integer units in contemporary processors are
practically disjoint. This work presents a new
architecture which tightly integrates floating-point
and integer arithmetic in a single datapath. It is
mainly intended for use in low-power embedded digital
signal processors and therefore the following design
constraints were important: limited use of pipelining
for the convenience of the compiler; maintaining
compatibility with existing technology; minimal area
and power consumption for applicability in embedded
systems.",
acknowledgement = ack-nhfb,
articleno = "41",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J924",
}
@Article{Chen:2012:IDF,
author = "Dongdong Chen and Liu Han and Younhee Choi and
Seok-Bum Ko",
title = "Improved Decimal Floating-Point Logarithmic Converter
Based on Selection by Rounding",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "5",
pages = "607--621",
month = may,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.43",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Apr 6 18:50:40 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "This paper presents the algorithm and architecture of
the decimal floating-point (DFP) logarithmic converter,
based on the digit-recurrence algorithm with selection
by rounding. The proposed approach can compute faithful
DFP logarithm results for any one of the three DFP
formats specified in the IEEE 754-2008 standard. In
order to optimize the latency for the proposed design,
we mainly integrate the following novel features: (1)
using the redundant carry-save representation of the
data-path; (2) reducing the number of iterations by
determining the number of initial iteration; and (3)
retiming and balancing the delay of the proposed
architecture. The proposed architecture is synthesized
with STM 90-nm standard cell library and the results
show that the critical path delay and the number of
clock cycles of the proposed Decimal64 logarithmic
converter are 1.55 ns (34.4 FO4) and 19 respectively,
and the total hardware complexity is 43572 NAND2 gates.
The delay estimation results of the proposed
architecture show that its latency is close to that of
the binary radix-16 logarithmic converter, and that it
has a significant decrease on latency compared with a
recently published high performance CORDIC
implementation.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Cleemput:2012:CMT,
author = "Jeroen V. Cleemput and Bart Coppens and Bjorn {De
Sutter}",
title = "Compiler mitigations for time attacks on modern x86
processors",
journal = j-TACO,
volume = "8",
number = "4",
pages = "23:1--23:??",
month = jan,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2086696.2086702",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Sat Jan 21 07:49:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
abstract = "This paper studies and evaluates the extent to which
automated compiler techniques can defend against
timing-based side channel attacks on modern x86
processors. We study how modern x86 processors can leak
timing information through side channels that relate to
data flow. We study the efficiency, effectiveness,
portability, predictability and sensitivity of several
mitigating code transformations that eliminate or
minimize key-dependent execution time variations.
Furthermore, we discuss the extent to which compiler
backends are a suitable tool to provide automated
support for the proposed mitigations.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Archit. Code Optim.",
articleno = "23",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "https://dl.acm.org/loi/taco",
}
@Article{Das:2012:AAT,
author = "Subrata Das and Partha Sarathi Dasgupta and Samar
Sensarma",
title = "Arithmetic Algorithms for Ternary Number System",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7373",
pages = "111--120",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-31494-0_13",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Dec 19 15:21:09 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012f.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-31494-0_13/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-31494-0",
book-URL = "http://www.springerlink.com/content/978-3-642-31494-0",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{deDinechin:2012:MRC,
author = "Florent de Dinechin",
title = "Multiplication by rational constants",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "52",
number = "2",
pages = "98--102",
month = feb,
year = "2012",
DOI = "https://doi.org/10.1109/TCSII.2011.2177706",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Sat Feb 08 09:46:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/6126071",
acknowledgement = ack-nhfb,
ajournal = "IEEE trans. circuits syst., II Express briefs",
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}
@Article{deDinechin:2012:TBD,
author = "Florent de Dinechin and Laurent-St{\'e}phane Didier",
title = "Table-Based Division by Small Integer Constants",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7199",
pages = "53--63",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-28365-9_5",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Dec 19 15:26:07 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012b.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-28365-9_5/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-28365-9",
book-URL = "http://www.springerlink.com/content/978-3-642-28365-9",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Book{Deschamps:2012:GFI,
author = "Jean-Pierre Deschamps and Gustavo D. Sutter and
Enrique Cant{\'o}",
title = "Guide to {FPGA} implementation of arithmetic
functions",
volume = "95",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 469",
year = "2012",
DOI = "https://doi.org/10.1007/978-94-007-2987-2",
ISBN = "94-007-2986-3 (hardcover), 94-007-2987-1 (e-book)",
ISBN-13 = "978-94-007-2986-5 (hardcover), 978-94-007-2987-2
(e-book)",
LCCN = "TK7895.G36",
bibdate = "Wed Oct 1 10:19:58 MDT 2014",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
series = "Lecture notes in electrical engineering",
abstract = "This book is designed both for FPGA users interested
in developing new, specific components --- generally
for reducing execution times and IP core designers
interested in extending their catalog of specific
components. The main focus is circuit synthesis and the
discussion shows, for example, how a given algorithm
executing some complex function can be translated to a
synthesizable circuit description, as well as which are
the best choices the designer can make to reduce the
circuit cost, latency, or power consumption. This is
not a book on algorithms. It is a book that shows how
to translate efficiently an algorithm to a circuit,
using techniques such as parallelism, pipeline, loop
unrolling, and others. Numerous examples of FPGA
implementation are described throughout this book and
the circuits are modeled in VHDL. Complete and
synthesizable source files are available for
download.",
acknowledgement = ack-nhfb,
author-dates = "1945--",
subject = "Field programmable gate arrays; Programming;
Arithmetic functions",
tableofcontents = "Basic Building Blocks \\
Architecture of Digital Circuits \\
Special Topics of Data Path Synthesis \\
Control Unit Synthesis \\
Electronic Aspects of Digital Design \\
EDA Tools \\
Adders \\
Multipliers \\
Dividers \\
Other Operations \\
Decimal Operations \\
Floating Point Arithmetic \\
Finite-Field Arithmetic \\
Systems on Chip \\
Embedded Systems Development: Case Studies \\
Partial Reconfiguration on Xilinx FPGAs",
}
@Article{Diethelm:2012:LRN,
author = "Kai Diethelm",
title = "The Limits of Reproducibility in Numerical
Simulation",
journal = j-COMPUT-SCI-ENG,
volume = "14",
number = "1",
pages = "64--72",
month = jan # "\slash " # feb,
year = "2012",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCSE.2011.21",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Tue Jan 31 12:29:01 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
remark = "This paper discusses the problem of reproducible, and
accurate, computation of long floating-point dot
products in parallel computing environments, and how
nonreproducibility leads to user confusion.",
}
@Article{Fan:2012:EHI,
author = "Junfeng Fan and Frederik Vercauteren and Ingrid
Verbauwhede",
title = "Efficient Hardware Implementation of {FP}-Arithmetic
for Pairing-Friendly Curves",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "5",
pages = "676--685",
month = may,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.78",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Apr 6 18:50:40 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Fout:2012:APB,
author = "Nathaniel Fout and Kwan-Liu Ma",
title = "An Adaptive Prediction-Based Approach to Lossless
Compression of Floating-Point Volume Data",
journal = j-IEEE-TRANS-VIS-COMPUT-GRAPH,
volume = "18",
number = "12",
pages = "2295--2304",
month = dec,
year = "2012",
CODEN = "ITVGEA",
DOI = "https://doi.org/10.1109/TVCG.2012.194",
ISSN = "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
ISSN-L = "1077-2626",
bibdate = "Mon Oct 22 07:55:05 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransviscomputgraph.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Visualization and Computer
Graphics",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945",
}
@Article{G:2012:DOR,
author = "Rangaraju H G and Aakash Babu Suresh and Muralidhara K
N",
title = "Design and Optimization of Reversible Multiplier
Circuit",
journal = j-INT-J-COMP-APPL,
volume = "52",
number = "??",
pages = "44--50",
month = aug,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.5120/8242-1523",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 08:48:11 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume52/number10/8242-1523/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "10",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@Article{Gandino:2012:AAS,
author = "Filippo Gandino and Fabrizio Lamberti and Gianluca
Paravati and Jean-Claude Bajard and Paolo Montuschi",
title = "An Algorithmic and Architectural Study on {Montgomery}
Exponentiation in {RNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "8",
pages = "1071--1083",
month = aug,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.84",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 27 08:30:49 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gazeau:2012:NLM,
author = "Ivan Gazeau and Dale Miller and Catuscia Palamidessi",
title = "A non-local method for robustness analysis of floating
point programs",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "3",
month = feb,
year = "2012",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1202.0693",
abstract = "Robustness is a standard correctness property which
intuitively means that if the input to the program
changes less than a fixed small amount then the output
changes only slightly. This notion is useful in the
analysis of rounding error for floating point programs
because it helps to establish bounds on output errors
introduced by both measurement errors and by floating
point computation. Compositional methods often do not
work since key constructs---like the conditional and
the while-loop---are not robust. We propose a method
for proving the robustness of a while-loop. This method
is non-local in the sense that instead of breaking the
analysis down to single lines of code, it checks
certain global properties of its structure. We show the
applicability of our method on two standard algorithms:
the CORDIC computation of the cosine and Dijkstra's
shortest path algorithm.",
acknowledgement = ack-nhfb,
subject = "Programming Languages (cs.PL)",
}
@Article{Ghosh:2012:FPR,
author = "Aniruddha Ghosh and Satrughna Singha and Amitabha
Sinha",
title = "{``Floating point RNS''}: a new concept for designing
the {MAC} unit of digital signal processor",
journal = j-COMP-ARCH-NEWS,
volume = "40",
number = "2",
pages = "39--43",
month = may,
year = "2012",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2234336.2234343",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Fri Jun 1 17:06:51 MDT 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Execution of arithmetic operations at a very high
speed in real time is the major concern in compute
intensive digital signal processing (DSP) algorithms
Residue Number Systems are being considered as
alternative to binary number system because of their
capabilities of performing ``carry free'' arithmetic
operations. However, RNS systems have so far been used
to handle integer numbers only. Floating Point RNS
arithmetic units have obvious advantages over fixed
point multiply {\&} accumulate (MAC) units which are
the key units in Digital Signal Processors. Keeping
this in view, in this paper, the architecture of a
floating point MAC unit is presented.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Giessing:2012:FRB,
author = "Sarah Giessing",
title = "Flexible Rounding Based on Consistent Post-tabular
Stochastic Noise",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7556",
pages = "22--34",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-33627-0_3",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Dec 19 15:24:52 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012j.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-33627-0_3/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-33627-0",
book-URL = "http://www.springerlink.com/content/978-3-642-33627-0",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InCollection{Goldberg:2012:CA,
author = "David Goldberg",
title = "Computer Arithmetic",
crossref = "Hennessy:2012:CAQ",
chapter = "J",
pages = "J-1--J-74",
year = "2012",
bibdate = "Mon Nov 11 05:34:58 2019",
bibsource = "http://www.mkp.com/CA3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The complete Appendix J is not in the printed book; it
is available only at the book's Web site.",
URL = "http://booksite.mkp.com/9780123838728/references/appendix_j.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Goossens:2012:CTS,
author = "Bernard Goossens and Philippe [Gr{\'e}goire] Langlois
and David Parello and Kathy Porada",
booktitle = "Numerical Sofware: Design, Analysis and Verification,
Santander, Spain, 4--6 July 2012",
title = "Computing time for summation algorithm: Less hazard
and more scientific research",
publisher = "????",
address = "????",
pages = "i + 34",
year = "2012",
bibdate = "Sat Apr 01 08:09:42 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hal-lirmm.ccsd.cnrs.fr/lirmm-00835508",
abstract = "Several accurate algorithms to sum IEEE-754 floating
point numbers have been recently published. The
contributions by Rump, Ogita and Oishi [3, 4, 2] and
the newest ones proposed by Zhu and Hayes [5, 6] are
examples of accurate summation algorithms. Some of
these actually compute the correct rounding of the
exact sum, i.e., the most accurate value with respect
to the finite precision of the floating point
arithmetic. This computed sum does not suffer anymore
from the condition number of the summation. In such
cases, the run-time performances and the memory print
become the discriminant properties to decide which
algorithm to choose. In this talk we focus the problem
of presenting reliable measures of the run-time
performances of such core algorithms. As Rump writes in
[2], Measuring the computing time of summation
algorithms in a high-level language on today's
architectures is more of a hazard than scientific
research. We introduced PerPI, a software tool that
automatizes an almost machine independent analysis
based on the instruction-level parallelism of the
algorithm [1]. We analyze the previously mentioned
accurate summation algorithms. We discuss whether PerPI
provides a more reliable performance analysis and how
to improve the confidence level of future contributions
in this area.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; faithful summation; floating-point
arithmetic, accurate summation; instruction level
parallelism; performance evaluation; PerPI;
reproducibility",
remark = "Lecture slides",
}
@Article{Grcar:2012:JNA,
author = "Joseph F. Grcar",
title = "{John von Neumann}'s Analysis of {Gaussian}
Elimination and the Origins of Modern Numerical
Analysis",
journal = j-SIAM-REVIEW,
volume = "53",
number = "4",
pages = "607--682",
month = "????",
year = "2012",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/080734716",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "01-08, 65-03, 65F05, 65F35, 65G50, 65M12, 68-03",
bibdate = "Thu Jan 12 12:42:30 MST 2012",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/53/4;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://epubs.siam.org/sirev/resource/1/siread/v53/i4/p607_s1",
abstract = "Just when modern computers (digital, electronic, and
programmable) were being invented, John von Neumann and
Herman Goldstine wrote a paper to illustrate the
mathematical analyses that they believed would be
needed to use the new machines effectively and to guide
the development of still faster computers. Their
foresight and the congruence of historical events made
their work the first modern paper in numerical
analysis. Von Neumann once remarked that to found a
mathematical theory one had to prove the first theorem,
which he and Goldstine did for the accuracy of
mechanized Gaussian elimination --- but their paper was
about more than that. Von Neumann and Goldstine
described what they surmised would be the significant
questions once computers became available for
computational science, and they suggested enduring ways
to answer them.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "backward error, CFL condition, computer architecture,
computer arithmetic, computer programming, condition
number, decomposition paradigm, Gaussian elimination,
history, matrix norms, numerical analysis, rounding
error analysis, stability, stochastic linear algebra,
von Neumann",
onlinedate = "November 07, 2011",
}
@InProceedings{Haller:2012:DFP,
author = "L. Haller and A. Griggio and M. Brain and D.
Kroening",
booktitle = "{Formal Methods in Computer-Aided Design (FMCAD),
2012}",
title = "Deciding floating-point logic with systematic
abstraction",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "131--140",
month = oct,
year = "2012",
ISBN = "1-4673-4832-5",
ISBN-13 = "978-1-4673-4832-4",
bibdate = "Sat Jun 4 18:09:21 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "abstract interpretation; Abstracts; Algorithm design
and analysis; Analytical models; binary floating-point
arithmetic; bit-precise decision procedure; bit-vector
encoding; computability; conflict analysis algorithm;
conflict driven clause learning algorithm; decision
procedures; Design automation; encoding; Encoding;
floating point; floating point arithmetic;
floating-point interval abstraction; floating-point
logic; floating-point satisfiability checking;
lattice-based abstraction; Lattices; MATHSAT5;
natural-domain SMT approach; propositional solver; SAT
solver; Standards; systematic abstraction",
}
@Article{Huang:2012:LCB,
author = "Libo Huang and Sheng Ma and Li Shen and Zhiying Wang
and Nong Xiao",
title = "Low-Cost {Binary128} Floating-Point {FMA} Unit Design
with {SIMD} Support",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "5",
pages = "745--751",
month = may,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.77",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Apr 6 18:50:40 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hyman:2012:LF,
author = "Paul Hyman",
title = "Lost and found",
journal = j-CACM,
volume = "55",
number = "7",
pages = "21--21",
month = jul,
year = "2012",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/2209249.2209258",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jul 3 13:54:33 MDT 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Researchers discover computer pioneer Konrad Zuse's
long-forgotten Z9, the world's first program-controlled
binary relay calculator using floating-point
arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@TechReport{Kahan:2012:DNR,
author = "W. Kahan",
title = "Desperately Needed Remedies for the Undebuggability of
Large Floating-Point Computations in Science and
Engineering",
type = "Report",
institution = inst-BERKELEY-EECS,
address = inst-BERKELEY-EECS:adr,
pages = "90",
day = "24",
month = apr,
year = "2012",
bibdate = "Mon Aug 26 10:36:06 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://people.eecs.berkeley.edu/~wkahan/Boulder.pdf",
acknowledgement = ack-nhfb,
}
@TechReport{Katranov:2012:DRN,
author = "A. Katranov",
title = "Deterministic Reduction: a new Community Preview
Feature in {Intel Threading Building Blocks}",
type = "Report",
institution = pub-INTEL,
address = pub-INTEL:adr,
pages = "????",
year = "2012",
bibdate = "Sat Oct 31 06:58:31 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Koiran:2012:ACC,
author = "Pascal Koiran",
title = "Arithmetic circuits: the chasm at depth four gets
wider",
journal = j-THEOR-COMP-SCI,
volume = "448",
number = "1",
pages = "56--65",
day = "24",
month = aug,
year = "2012",
CODEN = "TCSCDI",
DOI = "https://doi.org/10.1016/j.tcs.2012.03.041",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Sat Jun 30 13:07:21 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tcs2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0304397512003131",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975/",
}
@Article{Kornerup:2012:CCR,
author = "Peter Kornerup and Vincent Lef{\`e}vre and Nicolas
Louvet and Jean-Michel Muller",
title = "On the Computation of Correctly Rounded Sums",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "3",
pages = "289--298",
month = mar,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.27",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Feb 3 07:35:03 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
abstract = "This paper presents a study of some basic blocks
needed in the design of floating-point summation
algorithms. In particular, in radix-2 floating-point
arithmetic, we show that among the set of the
algorithms with no comparisons performing only
floating-point additions/subtractions, the 2Sum
algorithm introduced by Knuth is minimal, both in terms
of number of operations and depth of the dependency
graph. We investigate the possible use of another
algorithm, Dekker's Fast2Sum algorithm, in radix-10
arithmetic. We give methods for computing, in radix 10,
the floating-point number nearest the average value of
two floating-point numbers. We also prove that under
reasonable conditions, an algorithm performing only
round-to-nearest additions/subtractions cannot compute
the round-to-nearest sum of at least three
floating-point numbers. Starting from an algorithm due
to Boldo and Melquiond, we also present new results
about the computation of the correctly-rounded sum of
three floating-point numbers. For a few of our
algorithms, we assume new operations defined by the
recent IEEE 754-2008 Standard are available.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "accurate floating-point summation; correct rounding;
floating-point arithmetic",
}
@Article{Kornerup:2012:FPA,
author = "Peter Kornerup and Jean-Michel Muller and Adrien
Panhaleux",
title = "Floating-Point Arithmetic on Round-to-Nearest
Representations",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "18",
month = jan,
year = "2012",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1201.3914",
abstract = "Recently we introduced a class of number
representations denoted RN-representations, allowing an
un-biased rounding-to-nearest to take place by a simple
truncation. In this paper we briefly review the binary
fixed-point representation in an encoding which is
essentially an ordinary 2's complement representation
with an appended round-bit. Not only is this rounding a
constant time operation, so is also sign inversion,
both of which are at best log-time operations on
ordinary 2's complement representations. Addition,
multiplication and division is defined in such a way
that rounding information can be carried along in a
meaningful way, at minimal cost. Based on the
fixed-point encoding we here define a floating point
representation, and describe to some detail a possible
implementation of a floating point arithmetic unit
employing this representation, including also the
directed roundings.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA)",
}
@Article{Kramer:2012:MAP,
author = "Walter Kr{\"a}mer",
title = "Multiple\slash arbitrary precision interval
computations in {C-XSC}",
journal = j-COMPUTING,
volume = "94",
number = "2--4",
pages = "229--241",
month = mar,
year = "2012",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-011-0174-8",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Mon Apr 9 16:41:18 MDT 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=94&issue=2;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=94&issue=2&spage=229",
acknowledgement = ack-nhfb,
author-dates = "1952--2014",
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
remark = "Special Issue on GAMM--IMACS International Symposium
on Scientific Computing, Computer Arithmetic and
Validated Numerics (SCAN2010).",
}
@InProceedings{Kumm:2012:RCS,
author = "Martin Kumm and Katharina Liebisch and Peter Zipf",
editor = "????",
booktitle = "{IEEE 22nd International Conference on Field
Programmable Logic and Application (FPL), 2012}",
title = "Reduced Complexity Single and Multiple Constant
Multiplication in Floating Point Precision",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "255--261",
year = "2012",
DOI = "https://doi.org/10.1109/FPL.2012.6339190",
bibdate = "Sat Feb 08 09:39:36 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/6339190/",
acknowledgement = ack-nhfb,
}
@Article{Kurka:2012:FAA,
author = "Petr K{\r{u}}rka",
title = "Fast Arithmetical Algorithms in {M{\"o}bius} Number
Systems",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "8",
pages = "1097--1109",
month = aug,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.87",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 27 08:30:49 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Langlois:2012:ACT,
author = "Philippe Langlois and Matthieu Martel and Laurent
Th{\'e}venoux",
editor = "????",
booktitle = "{Proceedings of the 15th GAMM--IMACS International
Symposium on Scientific Computing, Computer Arithmetic
and Validated Numerics, Novosibirsk, Russia}",
title = "Automatic code transformation to optimize accuracy and
speed in floating-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "??--??",
year = "2012",
bibdate = "Sat Apr 01 07:42:30 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.archives-ouvertes.fr/hal-00821667",
abstract = "We want to allow the standard software developer to
automatically transform his/her code in order to
increase the accuracy of floating-point computations.
This transformation is actually an optimization since
we aim to take into account two opposite criteria:
accuracy and execution time. A first step towards this
automatic optimization is presented in this work. We
propose to automatically introduce at the compile-time
compensation steps in (parts of) the floating-point
computations. We present a tool to parse C codes and to
insert compensated floating-point operations. This
provides a compensated computation that improves the
accuracy of specific computing patterns.",
acknowledgement = ack-nhfb,
}
@TechReport{Langlois:2012:CTS,
author = "Philippe Langlois and David Parello and Bernard
Goossens and Kathy Porada",
title = "Computing time for summation algorithm: Less hazard
and more scientific research",
type = "Research Report",
number = "RR-12021",
institution = "LIRMM, Universit{\'e} Montpellier 2",
address = "CNRS UMR 5506, France",
pages = "i + 34",
year = "2012",
bibdate = "Sat Apr 01 08:09:42 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://personales.unican.es/segurajj/numsoft12/;
https://hal-lirmm.ccsd.cnrs.fr/lirmm-00737617;
https://hal-lirmm.ccsd.cnrs.fr/lirmm-00737617/document",
abstract = "Several accurate algorithms to sum IEEE-754
floating-point numbers have been recently published.
The recent contributions by Rump, Ogita and Oishi and
the newest ones proposed by Zhu and Hayes are examples
of accurate summation algorithms. Some of these even
compute the faithful or the correct rounding of the
exact sum, i.e. the most accurate value with respect to
the finite precision of the floating-point arithmetic.
This computed sum does not suffer anymore from the
condition number of the summation. In such cases, the
run-time performances and the memory prints become the
discriminant properties to decide which algorithm is
best.\par
In this paper we focus on the reliability of the
run-time performance measure of such core algorithms.
We explain how right Rump when he writes ``Measuring
the computing time of summation algorithms in a
high-level language on today's architectures is more of
a hazard than scientific research.'' Neither the
classical flop count nor hardware counter based
measures are satisfactory here. We propose to analyze
the instruction level parallelism of these algorithms
to reliably evaluate their performance potential. We
use PerPI, a software tool that automatizes an almost
machine independent instruction-level parallelism
analysis. We study recent accurate summation algorithms
with a detailed focus on the two newest faithful ones.
We illustrate and discuss why PerPI provides a more
reliable performance analysis, the remaining weakness
and how to improve confidence for future contributions
in this area.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; faithful summation; floating-point
arithmetic, accurate summation; instruction level
parallelism; performance evaluation; PerPI;
reproducibility",
}
@Article{Lee:2012:CPS,
author = "Mun-Kyu Lee",
title = "Comments on {``Provably Sublinear Point Multiplication
on Koblitz Curves and Its Hardware Implementation''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "4",
pages = "591--592",
month = apr,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.109",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Mar 10 16:19:08 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
note = "See \cite{Dimitrov:2008:PSP}.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Lee:2012:DHP,
author = "Yong-Hwan Lee and Young-Sung Cho and Sangook Moon",
title = "Design of a high precision logarithmic converter in a
binary floating point divider",
journal = j-CCPE,
volume = "24",
number = "4",
pages = "342--353",
month = "????",
year = "2012",
CODEN = "CCPEBO",
DOI = "https://doi.org/10.1002/cpe.1569",
ISSN = "1532-0626 (print), 1532-0634 (electronic)",
ISSN-L = "1532-0626",
bibdate = "Wed Apr 4 09:18:01 MDT 2012",
bibsource = "http://www.interscience.wiley.com/jpages/1532-0626;
https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Concurrency and Computation: Prac\-tice and
Experience",
journal-URL = "http://www.interscience.wiley.com/jpages/1532-0626",
onlinedate = "1 Apr 2010",
}
@Article{Li:2012:ENE,
author = "Wenbin Li and Sven Simon and Steffen Kie{\ss}",
title = "On the estimation of numerical error bounds in linear
algebra based on discrete stochastic arithmetic",
journal = j-APPL-NUM-MATH,
volume = "62",
number = "5",
pages = "536--555",
month = may,
year = "2012",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2012.01.001",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Thu Mar 8 07:24:49 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0168927412000086",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
}
@Article{Liedel:2012:SDC,
author = "Manuel Liedel",
title = "Secure Distributed Computation of the Square Root and
Applications",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7232",
pages = "277--288",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-29101-2_19",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Dec 24 07:23:24 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012c.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-29101-2_19/;
http://link.springer.com/content/pdf/10.1007/978-3-642-29101-2_19",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-29101-2",
book-URL = "http://www.springerlink.com/content/978-3-642-29101-2",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Liu:2012:PED,
author = "Wei Liu and Alberto Nannarelli",
title = "Power Efficient Division and Square Root Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "8",
pages = "1059--1070",
month = aug,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.82",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jul 27 08:30:49 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Maitra:2012:NAC,
author = "Subhashis Maitra and Amitabha Sinha",
title = "A new algorithm for computing triple-base number
system",
journal = j-COMP-ARCH-NEWS,
volume = "40",
number = "4",
pages = "3--9",
month = sep,
year = "2012",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2411116.2411119",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Tue Dec 11 08:06:57 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "We introduce here a generalized method a new Algorithm
to find Triple-Base number system and Triple-Base chain
and hence in turn Single Digit Triple-Base number
system(SDTBNS). The proposed method is not only simpler
and faster than the Algorithms to find Double-Base
number system or Double-Base chain, experimentally it
also returns a shorter length of Triple-Base chain
which in turn reduces the size of the look-up-table to
find out SDTBNS. The complexity analysis and
experimental results shows the novelty of the proposed
Algorithm. Moreover when the proposed method is applied
to find scalar multiplication in case of Elliptic Curve
Cryptography and coefficient multiplication in case of
designing digital filter, its efficiency also proves
its novelty. Here we have used third base as $5$
because when it is multiplied by $2$ gives $ 10 $ which
can be efficiently used for decimal shifting, i.e. if
an integer '$n$' can be represented in SDTBNS form,
then $ n / 10_x $ or $ n \times 10_x $ can also
represented in SDTBNS only by diving or multiplying
'$n$' by $ 10 $.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Masotti:2012:FPN,
author = "Glauco Masotti",
title = "Floating-Point Numbers with Error Estimates
(revised)",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--45",
day = "28",
month = jan,
year = "2012",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1201.5975",
abstract = "The study addresses the problem of precision in
floating-point (FP) computations. A method for
estimating the errors which affect intermediate and
final results is proposed and a summary of many
software simulations is discussed. The basic idea
consists of representing FP numbers by means of a data
structure collecting value and estimated error
information. Under certain constraints, the estimate of
the absolute error is accurate and has a compact
statistical distribution. By monitoring the estimated
relative error during a computation (an ad-hoc
definition of relative error has been used), the
validity of results can be ensured. The error estimate
enables the implementation of robust algorithms, and
the detection of ill-conditioned problems. A dynamic
extension of number precision, under the control of
error estimates, is advocated, in order to compute
results within given error bounds. A reduced time
penalty could be achieved by a specialized FP
processor. The realization of a hardwired processor
incorporating the method, with current technology,
should not be anymore a problem and would make the
practical adoption of the method feasible for most
applications.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA)",
}
@Misc{McCalpin:2012:OSH,
author = "J. D. McCalpin",
title = "Is ``ordered summation'' a hard problem to speed up?",
howpublished = "Web document",
day = "28",
month = may,
year = "2012",
bibdate = "Sat Oct 31 07:16:11 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://blogs.utexas.edu/jdm4372/2012/02/15/is-ordered-summation-a-hard-problem-to-speed-up/",
acknowledgement = ack-nhfb,
}
@Article{Milicevic:2012:PAO,
author = "Aleksandar Milicevic and Daniel Jackson",
title = "Preventing Arithmetic Overflows in {Alloy}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7316",
pages = "108--121",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-30885-7_8",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Dec 24 07:32:30 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012e.bib",
URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-30885-7_8",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-30885-7",
book-URL = "http://www.springerlink.com/content/978-3-642-30885-7",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Mine:2012:ADB,
author = "Antoine Min{\'e}",
editor = "Gudmund Grov",
booktitle = "{WING'12 --- 4th International Workshop on Invariant
Generation, held on June 30, 2012 in Manchester, UK}",
title = "Abstract domains for bit-level machine integer and
floating-point operations",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "16",
year = "2012",
bibdate = "Sat Jun 4 17:14:37 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Mukunoki:2012:PCD,
author = "Daichi Mukunoki and Daisuke Takahashi",
editor = "????",
booktitle = "{ATIP '12: Proceedings of the ATIP\slash A*CRC
Workshop on Accelerator Technologies for
High-Performance Computing: Does Asia Lead the Way?}",
title = "Performance Comparison of Double, Triple and Quadruple
Precision Real and Complex {BLAS} Subroutines on {GPUs}
(extended abstract)",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "788--790",
year = "2012",
ISBN = "1-4503-1644-1",
ISBN-13 = "978-1-4503-1644-6",
LCCN = "????",
bibdate = "Wed Nov 14 11:07:15 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "doubled double precision; quad-double precision;
triple precision",
remark = "From page 788: ``\ldots{} the computation cost of the
quadruple precision BLAS subroutines is approximately
20 times more than the double precision
subroutines.''",
}
@Article{Muller:2012:SSV,
author = "Norbert Th. M{\"u}ller and Christian Uhrhan",
title = "Some Steps into Verification of Exact Real
Arithmetic",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7226",
pages = "168--173",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-28891-3_17",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Dec 19 15:18:01 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012c.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-28891-3_17/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-28891-3",
book-URL = "http://www.springerlink.com/content/978-3-642-28891-3",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Nehmeier:2012:SHI,
author = "M. Nehmeier and S. Siegel and J. Wolff von Gudenberg",
title = "Specification of hardware for interval arithmetic",
journal = j-COMPUTING,
volume = "94",
number = "2--4",
pages = "243--255",
month = mar,
year = "2012",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-012-0185-0",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Mon Apr 9 16:41:18 MDT 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=94&issue=2;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=94&issue=2&spage=243",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "Hardware design; Interval arithmetic; Interval
standardization",
remark = "Special Issue on GAMM--IMACS International Symposium
on Scientific Computing, Computer Arithmetic and
Validated Numerics (SCAN2010).",
}
@Article{Neron:2012:FPS,
author = "Pierre Neron",
title = "A Formal Proof of Square Root and Division Elimination
in Embedded Programs",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7679",
pages = "256--272",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-35308-6_20",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sun Dec 16 12:08:25 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012l.bib",
URL = "http://www.springerlink.com//chapter/10.1007/978-3-642-35308-6_20/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-35308-6Certified
Programs and Proofs",
book-URL = "http://www.springerlink.com/content/978-3-642-35308-6",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Oudjida:2012:NHR,
author = "A. K. Oudjida and N. Chaillet and M. L. Berrandjia and
A. Liacha",
title = "A new high radix-2 $r$ ($ r \geq 8 $) multibit
recoding algorithm for large operand size ({$ N \geq 32
$}) multipliers",
journal = j-COMP-ARCH-NEWS,
volume = "40",
number = "4",
pages = "32--43",
month = sep,
year = "2012",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2411116.2411122",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Tue Dec 11 08:06:57 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "This paper addresses the problem of multiplication
with large operand sizes ($ N \geq 32 $). We propose a
new recursive recoding algorithm that shortens the
critical path of the multiplier and reduces the
hardware complexity of partial-product-generators as
well. The new recoding algorithm provides an optimal
space/time partitioning of the multiplier architecture
for any size $N$ of the operands. As a result, the
critical path is drastically reduced to $ 3^3 \sqrt N /
2 - 3 $ with no area overhead in comparison to modified
Booth algorithm that shows a critical path of $ N / 2 $
in adder stages. For instance, only $7$ adder stages
are needed for a 64-bit two's complement multiplier.
Confronted to reference algorithms for $ N = 64 $,
important gain ratios of $ 1.62 $, $ 1.71 $, $ 2.64 $
are obtained in terms of multiply-time, energy
consumption per multiply operation, and total gate
count, respectively.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Ozaki:2012:FAF,
author = "Katsuhisa Ozaki and Takeshi Ogita and Siegfried M.
Rump and Shin'ichi Oishi",
title = "Fast algorithms for floating-point interval matrix
multiplication",
journal = j-J-COMPUT-APPL-MATH,
volume = "236",
number = "7",
pages = "1795--1814",
month = jan,
year = "2012",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:24:38 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042711005449",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@PhdThesis{Panhaleux:2012:CFP,
author = "A. Panhaleux",
title = "Contributions to floating-point arithmetic: Coding and
correct rounding of algebraic functions",
type = "{Ph.D.} dissertation",
school = "{\'E}cole Normale Sup{\'e}rieure de Lyon",
address = "Lyon, France",
year = "2012",
bibdate = "Sun Jun 19 15:08:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://theses.hal.science/tel-00744373v1",
abstract = "Efficient and reliable computer arithmetic is a key
requirement to perform fast and reliable numerical
computations. The choice of the number system and the
choice of the arithmetic algorithms are important. We
present a new representation of numbers, the
``RN-codings'', such that truncating a RN-coded number
to some position is equivalent to rounding it to the
nearest. We give some arithmetic algorithms for
manipulating RN-codings and introduce the concept of
``floating-point RN-codings''. When implementing a
function f in floating-point arithmetic, if we wish to
always return the floating-point number nearest $ f(x)
$, one must be able to determine if $ f(x) $ is above
or below the closest ``midpoint'', where a midpoint is
the middle of two consecutive floating-point numbers.
This determination is first done with some given
precision, and if it does not suffice, we start again
with higher precision, and so on. This process may not
terminate if $ f(x) $ can be a midpoint. Given an
algebraic function $f$, we try either to show that
there are no floating-point numbers $x$ such that $
f(x)$ is a midpoint, or we try to enumerate or
characterize them. Since the IBM PowerPC, binary
division has frequently been implemented using variants
of the Newton-Raphson iteration due to Peter Markstein.
This iteration is very fast, but much care is needed if
we aim at always returning the floating-point number
nearest the exact quotient. We investigate a way of
efficiently merging Markstein iterations with faster
yet less accurate iterations called Goldschmidt
iterations. We also investigate whether those
iterations can be used for decimal floating-point
arithmetic. We provide sure and tight error bounds for
these algorithms.",
acknowledgement = ack-nhfb,
}
@Article{Rodriguez:2012:RRE,
author = "Marcos Rodr{\'\i}guez and Roberto Barrio",
title = "Reducing rounding errors and achieving {Brouwer}'s law
with {Taylor Series Method}",
journal = j-APPL-NUM-MATH,
volume = "62",
number = "8",
pages = "1014--1024",
month = aug,
year = "2012",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2012.03.008",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Sat Apr 28 09:37:06 MDT 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0168927412000645",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274/",
}
@Article{Rump:2012:EEF,
author = "Siegfried M. Rump",
title = "Error estimation of floating-point summation and dot
product",
journal = j-BIT-NUM-MATH,
volume = "52",
number = "1",
pages = "201--220",
month = mar,
year = "2012",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-011-0342-4",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Apr 9 17:00:06 MDT 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=52&issue=1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=52&issue=1&spage=201",
abstract = "We improve the well-known Wilkinson-type estimates for
the error of standard floating-point recursive
summation and dot product by up to a factor 2. The
bounds are valid when computed in rounding to nearest,
no higher order terms are necessary, and they are best
possible. For summation there is no restriction on the
number of summands. The proofs are short by using a new
tool for the estimation of errors in floating-point
computations which cures drawbacks of the ``unit in the
last place (ulp)''. The presented estimates are nice
and simple, and closer to what one may expect.",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "accurate floating-point dot product; accurate
floating-point summation",
}
@Article{Rump:2012:FIM,
author = "Siegfried M. Rump",
title = "Fast interval matrix multiplication",
journal = j-NUMER-ALGORITHMS,
volume = "61",
number = "1",
pages = "1--34",
month = sep,
year = "2012",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Mar 6 09:10:18 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=61&issue=1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=61&issue=1&spage=1",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Saha:2012:DHS,
author = "Prabir Saha and Arindam Banerjee and Anup Dandapat and
Partha Bhattacharyya",
title = "Design of High Speed {Vedic} Multiplier for Decimal
Number System",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7373",
pages = "79--88",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-31494-0_10",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Dec 19 15:21:09 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012f.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-31494-0_10/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-31494-0",
book-URL = "http://www.springerlink.com/content/978-3-642-31494-0",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Saito:2012:AGM,
author = "Tsubasa Saito and Emiko Ishiwata and Hidehiko
Hasegawa",
title = "Analysis of the {GCR} method with mixed precision
arithmetic using {QuPAT}",
journal = j-J-COMPUT-SCI,
volume = "3",
number = "3",
pages = "87--91",
month = may,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.jocs.2011.05.001",
ISSN = "1877-7503 (print), 1877-7511 (electronic)",
ISSN-L = "1877-7503",
bibdate = "Tue Sep 19 13:53:15 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S1877750311000329",
acknowledgement = ack-nhfb,
ajournal = "J. Comput. Sci.",
fjournal = "Journal of Computational Science",
journal-URL = "https://www.sciencedirect.com/journal/journal-of-computational-science",
}
@Article{Seo:2012:MPM,
author = "Hwajeong Seo and Howon Kim",
title = "Multi-precision Multiplication for Public-Key
Cryptography on Embedded Microprocessors",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7690",
pages = "55--67",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-35416-8_5",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Wed Dec 19 15:18:58 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2012l.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-35416-8_5/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-35416-8",
book-URL = "http://www.springerlink.com/content/978-3-642-35416-8",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Sheikh:2012:AFP,
author = "Basit Riaz Sheikh and Rajit Manohar",
editor = "{IEEE}",
booktitle = "{2012 IEEE International Symposium on Asynchronous
Circuits and Systems: proceedings, ASYNC 2012: 7--9 May
2012, Copenhagen, Denmark}",
title = "An Asynchronous Floating-Point Multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "89--96",
year = "2012",
DOI = "https://doi.org/10.1109/ASYNC.2012.19",
ISBN = "1-4673-1360-2, 0-7695-4688-9",
ISBN-13 = "978-1-4673-1360-5, 978-0-7695-4688-9",
ISSN = "1522-8681",
ISSN-L = "1522-8681",
LCCN = "TK7868.A79",
bibdate = "Sat Apr 02 16:30:48 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=6242773",
acknowledgement = ack-nhfb,
}
@Article{Siegel:2012:LAL,
author = "Stefan Siegel and J{\"u}rgen Wolff von Gudenberg",
title = "A long accumulator like a carry-save adder",
journal = j-COMPUTING,
volume = "94",
number = "2--4",
pages = "203--213",
month = mar,
year = "2012",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/s00607-011-0164-x",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Mon Apr 9 16:41:18 MDT 2012",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=94&issue=2;
https://www.math.utah.edu/pub/tex/bib/computing.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=94&issue=2&spage=203",
acknowledgement = ack-nhfb,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
keywords = "accurate floating-point dot product; accurate
floating-point summation",
remark = "Special Issue on GAMM--IMACS International Symposium
on Scientific Computing, Computer Arithmetic and
Validated Numerics (SCAN2010).",
}
@Article{Su:2012:IIN,
author = "Chen Su and Haining Fan",
title = "Impact of {Intel}'s new instruction sets on software
implementation of {$ {\rm GF}(2)[x] $} multiplication",
journal = j-INFO-PROC-LETT,
volume = "112",
number = "12",
pages = "497--502",
day = "30",
month = jun,
year = "2012",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/j.ipl.2012.03.012",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Mon May 21 07:13:00 MDT 2012",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0020019012000804",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "AVX; Cryptography; GF(2)[x] multiplication; Karatsuba
algorithm; PCLMULQDQ; SSE",
}
@Article{Swartzlander:2012:FIF,
author = "Earl E. Swartzlander and Hani H. M. Saleh",
title = "{FFT} Implementation with Fused Floating-Point
Operations",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "2",
pages = "284--288",
month = feb,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.271",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Jan 13 17:55:10 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669293",
abstract = "This paper applies two fused floating-point operations
to the implementation of fast Fourier transform
butterfly units. The operations are a fused two-term
dot product and a fused add-subtract unit. The FFT
`butterfly' operations consist of complex
multiplications, additions and subtractions. Both
radix-2 and radix-4 butterflies are implemented
efficiently with the two fused floating-point
operations. When placed and routed using a high
performance standard cell technology, the fused FFT
butterflies are about 15\% faster and 30\% smaller than
a conventional implementation. Also the numerical
results of the fused implementations are slightly more
accurate since they use fewer rounding operations.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
book-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Thome:2012:SRA,
author = "Emmanuel Thom{\'e}",
title = "Square Root Algorithms for the Number Field Sieve",
journal = j-LECT-NOTES-COMP-SCI,
volume = "7369",
pages = "208--224",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-31662-3_15",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Mon Dec 24 07:44:06 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
URL = "http://link.springer.com/chapter/10.1007/978-3-642-31662-3_15/;
http://link.springer.com/content/pdf/10.1007/978-3-642-31662-3_15",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-642-31662-3",
book-URL = "http://www.springerlink.com/content/978-3-642-31662-3",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Vazquez:2012:RFP,
author = "Alvaro Vazquez and Julio Villalba-Moreno and Elisardo
Antelo and Emilio L. Zapata",
title = "Redundant Floating-Point Decimal {CORDIC} Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "11",
pages = "1551--1562",
month = nov,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.217",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Oct 22 08:22:47 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wang:2012:EMB,
author = "Zhen Wang and Shuqin Fan",
title = "Efficient {Montgomery}-Based Semi-Systolic Multiplier
for Even-Type {GNB} of {$ {\rm GF}(2^m) $}",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "3",
pages = "415--419",
month = mar,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2010.272",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Feb 3 07:35:03 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wang:2012:RCC,
author = "Dong Wang and Milo{\v{s}} D. Ercegovac",
title = "A Radix-16 Combined Complex Division\slash Square Root
Unit with Operand Prescaling",
journal = j-IEEE-TRANS-COMPUT,
volume = "61",
number = "9",
pages = "1243--1255",
month = sep,
year = "2012",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.143",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Aug 29 17:48:10 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Wang:2012:UBW,
author = "Xi Wang and Haogang Chen and Alvin Cheung and Zhihao
Jia and Nickolai Zeldovich and M. Frans Kaashoek",
editor = "{ACM}",
booktitle = "Proceedings of the {Asia--Pacific Workshop on Systems:
APSys '12, July 23--24, 2012, Seoul, South Korea}",
title = "Undefined Behavior: What Happened to My Code?",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "101",
year = "2012",
DOI = "https://doi.org/10.1145/2349896.2349905",
ISBN = "1-4503-1669-7",
ISBN-13 = "978-1-4503-1669-9",
LCCN = "QA75.5",
bibdate = "Thu Feb 18 06:30:11 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
URL = "http://dl.acm.org/citation.cfm?id=2349896",
abstract = "System programming languages such as C grant compiler
writers freedom to generate efficient code for a
specific instruction set by defining certain language
constructs as undefined behavior. Unfortunately, the
rules for what is undefined behavior are subtle and
programmers make mistakes that sometimes lead to
security vulnerabilities. This position paper argues
that the research community should help address the
problems that arise from undefined behavior, and not
dismiss them as esoteric C implementation issues. We
show that these errors do happen in real-world systems,
that the issues are tricky, and that current practices
to address the issues are insufficient.",
acknowledgement = ack-nhfb,
remark = "This article exhibits several small code snippets
where, because of C's rules of undefined behavior,
compilers are free to change, order, or even eliminate,
code in unexpected ways. Several of the examples are
protective code intended to detect errors, such as
division by zero and pointer dereferencing.",
}
@Article{Yan:2012:RBC,
author = "Song Yan",
title = "Review of {{\booktitle{Modern Computer Arithmetic}},
by Richard Brent and Paul Zimmermann}",
journal = j-SIGACT,
volume = "43",
number = "4",
pages = "49--51",
month = dec,
year = "2012",
CODEN = "SIGNDM",
DOI = "https://doi.org/10.1145/2421119.2421130",
ISSN = "0163-5700 (print), 1943-5827 (electronic)",
ISSN-L = "0163-5700",
bibdate = "Sun May 5 10:25:40 MDT 2013",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigact.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGACT News",
journal-URL = "http://dl.acm.org/citation.cfm?id=J697",
}
@Article{Yan:2012:RMC,
author = "Song Yan",
title = "Review of {{\booktitle{Modern Computer Arithmetic}},
by Richard Brent and Paul Zimmermann}",
journal = j-SIGACT,
volume = "43",
number = "4",
pages = "49--51",
month = dec,
year = "2012",
CODEN = "SIGNDM",
DOI = "https://doi.org/10.1145/2421119.2421130",
ISSN = "0163-5700 (print), 1943-5827 (electronic)",
ISSN-L = "0163-5700",
bibdate = "Sun May 5 10:25:40 MDT 2013",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigact.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGACT News",
journal-URL = "http://dl.acm.org/citation.cfm?id=J697",
}
@Article{Anguita:2013:EES,
author = "D. Anguita and A. Ghio and L. Oneto and X. Parra and
J. L. Reyes-Ortiz",
title = "Energy Efficient {Smartphone}-Based Activity
Recognition using Fixed-Point Arithmetic",
journal = j-J-UCS,
volume = "19",
number = "9",
pages = "1295--??",
month = "????",
year = "2013",
CODEN = "????",
ISSN = "0948-695X (print), 0948-6968 (electronic)",
ISSN-L = "0948-6968",
bibdate = "Fri Sep 13 11:19:07 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jucs.bib",
URL = "http://www.jucs.org/jucs_19_9/energy_efficient_smartphone_based",
acknowledgement = ack-nhfb,
fjournal = "J.UCS: Journal of Universal Computer Science",
journal-URL = "http://www.jucs.org/jucs",
}
@InProceedings{Anonymous:2013:DML,
author = "Anonymous",
title = "Dedication: In memory of {Luigi Ciminiera} 1954--2012
and In memory of {Luigi Dadda} 1923--2012",
crossref = "IEEE:2013:PIS",
pages = "ix--xi",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.11",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-21; Biographies; Ciminiera, Luigi; Dadda, Luigi;
Obituaries",
}
@Misc{Anonymous:2013:IOF,
author = "Anonymous",
title = "{Intel} overstates {FPU} accuracy",
howpublished = "Web document",
day = "1",
month = jun,
year = "2013",
bibdate = "Sat Jun 04 16:53:16 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.notabs.org/fpuaccuracy/",
abstract = "For nearly 20 years Intel has claimed high accuracy
for the transcendental floating point instructions in
its PC processor products. Intel documentation for the
1993 Pentium states: On the Pentium processor, the
worst case error on functions is less than 1 ulp when
rounding to the nearest-even and less than 1.5 ulps
when rounding in other modes. This claim has never been
true for the instructions fsin, fcos, fsincos, and
fptan. The red in the plots below show ranges where the
error exceeds 1.0 ulp.",
acknowledgement = ack-nhfb,
}
@Article{Antao:2013:CFA,
author = "Samuel Ant{\~a}o and Leonel Sousa",
title = "The {CRNS} framework and its application to
programmable and reconfigurable cryptography",
journal = j-TACO,
volume = "9",
number = "4",
pages = "33:1--33:??",
month = jan,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2400682.2400692",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Fri Jan 18 10:57:16 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
abstract = "This article proposes the Computing with the Residue
Number System (CRNS) framework, which aims at the
design automation of accelerators for Modular
Arithmetic (MA). The framework provides a comprehensive
set of tools ranging from a programming language and
respective compiler to back-ends targeting parallel
computation platforms such as Graphical Processing
Units (GPUs) and reconfigurable hardware. Given an
input algorithm described with a high-level programming
language, the CRNS can be used to obtain in a few
seconds the corresponding optimized Parallel Thread
Execution (PTX) program ready to be run on GPUs or the
Hardware Description Language (HDL) specification of a
fully functional accelerator suitable for
reconfigurable hardware and embedded systems. The
resulting framework's implementations benefit from the
Residue Number System (RNS) arithmetic's
parallelization properties in a fully automated way.
Designers do not need to be familiar with the
mathematical details concerning the employed
arithmetic, namely the RNS representation. In order to
thoroughly describe and evaluate the proposed
framework, experimental results obtained for the
supported back-ends (GPU and HDL) are presented
targeting the implementation of the modular
exponentiation used in the Rivest--Shamir--Adleman
(RSA) algorithm and Elliptic Curve (EC) point
multiplication. Results suggest competitive latency and
throughput with minimum design effort and overcoming
all the development issues that arise in the
specification and verification of dedicated
solutions.",
acknowledgement = ack-nhfb,
articleno = "33",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J924",
}
@InProceedings{Arnold:2013:DLN,
author = "Mark G. Arnold and Sylvain Collange",
editor = "{IEEE}",
booktitle = "{24th IEEE International Conference on
Application-Specific Systems, Architectures and
Processors (ASAP), 5--7 June 2013}",
title = "The denormal logarithmic number system",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "117--124",
year = "2013",
DOI = "https://doi.org/10.1109/ASAP.2013.6567564",
ISBN = "1-4799-0493-7, 1-4799-0494-5 (paperback),
1-4799-0492-9",
ISBN-13 = "978-1-4799-0493-8, 978-1-4799-0494-5 (paperback),
978-1-4799-0492-1",
LCCN = "QA76.5",
bibdate = "Mon May 30 07:23:44 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=6558539",
acknowledgement = ack-nhfb,
}
@Article{Bagnara:2013:EBF,
author = "Roberto Bagnara and Matthieu Carlier and Roberta Gori
and Arnaud Gotlieb",
title = "Exploiting Binary Floating-Point Representations for
Constraint Propagation: The Complete Unabridged
Version",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--51",
day = "18",
month = aug,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1308.3847",
abstract = "Floating-point computations are quickly finding their
way in the design of safety- and mission-critical
systems, despite the fact that designing floating-point
algorithms is significantly more difficult than
designing integer algorithms. For this reason,
verification and validation of floating-point
computations is a hot research topic. An important
verification technique, especially in some industrial
sectors, is testing. However, generating test data for
floating-point intensive programs proved to be a
challenging problem. Existing approaches usually resort
to random or search-based test data generation, but
without symbolic reasoning it is almost impossible to
generate test inputs that execute complex paths
controlled by floating-point computations. Moreover, as
constraint solvers over the reals or the rationals do
not natively support the handling of rounding errors,
the need arises for efficient constraint solvers over
floating-point domains. In this paper, we present and
fully justify improved algorithms for the propagation
of arithmetic IEEE 754 binary floating-point
constraints. The key point of these algorithms is a
generalization of an idea by B. Marre and C. Michel
that exploits a property of the representation of
floating-point numbers.",
acknowledgement = ack-nhfb,
subject = "Artificial Intelligence (cs.AI); Software Engineering
(cs.SE)",
}
@InProceedings{Bailey:2013:KHP,
author = "David H. Bailey",
title = "Keynote {I}: High-precision computation: Applications
and challenges",
crossref = "IEEE:2013:PIS",
pages = "3--3",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.39",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-21",
}
@InProceedings{Bajard:2013:FDR,
author = "Jean-Claude Bajard and Julien Eynard and Filippo
Gandino",
title = "Fault Detection in {RNS} {Montgomery} Modular
Multiplication",
crossref = "IEEE:2013:PIS",
pages = "119--126",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.31",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-21; Base Conversions; Computer architecture;
cryptographic functions; Cryptography; cryptography;
fault attacks; Fault detection; fault detection; Fault
Detection; fault diagnosis; fault injection; field
programmable gate arrays; FPGA; GPU; Hardware; leak
resistant arithmetic; modular arithmetic; Montgomery
Reduction; Redundancy; Residue Number System; residue
number systems; Resistance; RNS; RNS Montgomery modular
multiplication; side channel attacks; Standards",
}
@Article{Bao:2013:FDI,
author = "Tao Bao and Xiangyu Zhang",
title = "On-the-fly detection of instability problems in
floating-point program execution",
journal = j-SIGPLAN,
volume = "48",
number = "10",
pages = "817--832",
month = oct,
year = "2013",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2544173.2509526",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Mon Dec 9 09:19:33 MST 2013",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
note = "OOPSLA '13 conference proceedings.",
abstract = "The machine representation of floating point values
has limited precision such that errors may be
introduced during execution. These errors may get
propagated and magnified by the following operations,
leading to instability problems, e.g., control flow
path may be undesirably altered and faulty output may
be emitted. In this paper, we develop an on-the-fly
efficient monitoring technique that can predict if an
execution is stable. The technique does not explicitly
compute errors as doing so incurs high overhead.
Instead, it detects possible places where an error
becomes substantially inflated regarding the
corresponding value, and then tags the value with one
bit to denote that it has an inflated error. It then
tracks inflation bit propagation, taking care of
operations that may cut off such propagation. It
reports instability if any inflation bit reaches a
critical execution point, such as a predicate, where
the inflated error may induce substantial execution
difference, such as different execution paths. Our
experiment shows that with appropriate thresholds, the
technique can correctly detect that over 99.999996\% of
the inputs of all the programs we studied are stable
while a traditional technique relying solely on
inflation detection mistakenly classifies majority of
the inputs as unstable for some of the programs.
Compared to the state of the art technique that is
based on high precision computation and causes several
hundred times slowdown, our technique only causes 7.91
times slowdown on average and can report all the true
unstable executions with the appropriate thresholds.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Barr:2013:ADF,
author = "Earl T. Barr and Thanh Vo and Vu Le and Zhendong Su",
title = "Automatic detection of floating-point exceptions",
journal = j-SIGPLAN,
volume = "48",
number = "1",
pages = "549--560",
month = jan,
year = "2013",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2480359.2429133",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Mon Jul 1 17:15:03 MDT 2013",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "It is well-known that floating-point exceptions can be
disastrous and writing exception-free numerical
programs is very difficult. Thus, it is important to
automatically detect such errors. In this paper, we
present Ariadne, a practical symbolic execution system
specifically designed and implemented for detecting
floating-point exceptions. Ariadne systematically
transforms a numerical program to explicitly check each
exception triggering condition. Ariadne symbolically
executes the transformed program using real arithmetic
to find candidate real-valued inputs that can reach and
trigger an exception. Ariadne converts each candidate
input into a floating-point number, then tests it
against the original program. In general, approximating
floating-point arithmetic with real arithmetic can
change paths from feasible to infeasible and vice
versa. The key insight of this work is that, for the
problem of detecting floating-point exceptions, this
approximation works well in practice because, if one
input reaches an exception, many are likely to, and at
least one of them will do so over both floating-point
and real arithmetic. To realize Ariadne, we also
devised a novel, practical linearization technique to
solve nonlinear constraints. We extensively evaluated
Ariadne over 467 scalar functions in the widely used
GNU Scientific Library (GSL). Our results show that
Ariadne is practical and identifies a large number of
real runtime exceptions in GSL. The GSL developers
confirmed our preliminary findings and look forward to
Ariadne's public release, which we plan to do in the
near future.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "POPL '13 conference proceedings.",
}
@InProceedings{Boldo:2013:FVC,
author = "Sylvie Boldo and Jacques-Henri Jourdan and Xavier
Leroy and Guillaume Melquiond",
title = "A Formally-Verified {C} Compiler Supporting
Floating-Point Arithmetic",
crossref = "IEEE:2013:PIS",
pages = "107--115",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.30",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-21; ARM microprocessor; C compiler; Comp Cert
compilation; Computer architecture; floating point
arithmetic; floating-point arithmetic; floating-point
semantic preservation; formal proof; formal
verification; IEEE standards; IEEE-754 standard; Java;
Libraries; mathematical specification; microprocessor
chips; Optimization; PowerPC microprocessor; program
compilers; Program processors; programming language;
Semantics; Standards; verified compilation; x86-SSE2
microprocessor",
}
@InProceedings{Boldo:2013:HCA,
author = "Sylvie Boldo",
title = "How to Compute the Area of a Triangle: A Formal
Revisit",
crossref = "IEEE:2013:PIS",
pages = "91--98",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.29",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Accuracy; Algorithm design and analysis; algorithm
proof; algorithm theory; ARITH-21; Coq; Digital
arithmetic; Electronic mail; Error analysis; floating
point arithmetic; floating-point arithmetic; formal
proof; Kahan algorithm; Libraries; mathematical value;
Standards; theorem proving; triangle; triangle area;
underflow",
}
@Article{Boldo:2013:WEN,
author = "Sylvie Boldo and Fran{\c{c}}ois Cl{\'e}ment and
Jean-Christophe Filli{\^a}tre and Micaela Mayero and
Guillaume Melquiond and Pierre Weis",
title = "Wave Equation Numerical Resolution: a Comprehensive
Mechanized Proof of a {C} Program",
journal = j-J-AUTOM-REASON,
volume = "50",
number = "4",
pages = "423--456",
month = apr,
year = "2013",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-012-9255-4",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Sat Apr 2 10:51:04 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "http://link.springer.com/article/10.1007/s10817-012-9255-4",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
keywords = "floating-point error analysis",
}
@InProceedings{Brisebarre:2013:CBB,
author = "Nicolas Brisebarre and Marc Mezzarobba and Jean-Michel
Muller and Christof Lauter",
title = "Comparison between {Binary64} and {Decimal64}
Floating-Point Numbers",
crossref = "IEEE:2013:PIS",
pages = "145--152",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.23",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Accuracy; Approximation methods; ARITH-21; binary
encoding; Binary64 floating-point numbers; binary64 FP
number; Decimal Floating-Point; Decimal64
floating-point numbers; decimal64 FP number; Digital
arithmetic; Encoding; encoding; first pass; floating
point arithmetic; Floating-Point Arithmetic;
Floating-Point Comparisons; FP arithmetic; Hardware;
IEEE 754-2008 standard; IEEE standards; second pass;
software-oriented algorithm; Standards; Testing;
two-step algorithm",
}
@Article{Carter:2013:ESF,
author = "Ashley R. Carter",
title = "Evolution of the Significant Figure Rules",
journal = j-PHYS-TEACHER,
volume = "51",
number = "6",
pages = "340--343",
month = sep,
year = "2013",
CODEN = "PHTEAH",
DOI = "https://doi.org/10.1119/1.4818368",
ISSN = "0031-921X (print), 1943-4928 (electronic)",
ISSN-L = "0031-921X",
bibdate = "Mon May 21 11:31:50 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "The Physics Teacher",
journal-URL = "http://scitation.aip.org/content/aapt/journal/tpt",
}
@InProceedings{Chabrier:2013:FMB,
author = "Thomas Chabrier and Arnaud Tisserand",
title = "On-the-Fly Multi-base Recoding for {ECC} Scalar
Multiplication without Pre-computations",
crossref = "IEEE:2013:PIS",
pages = "219--228",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.17",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-21; base point multiples; cheap divisibility
tests; Clocks; Cryptography; curve-level operations;
DBNS; digital arithmetic; divisibility test;
double-base number system; ECC scalar multiplication;
elliptic curve cryptography; exact division by
constant; fast recoding methods; field programmable
gate arrays; Field programmable gate arrays; FPGA
implementation; greedy algorithm; greedy algorithms;
Hardware; MBNS; multibase number system; nonadjacent
form; off-line conversion; on-the-fly multibase
recoding; public key cryptography; scalar
multiplication; scalar recoding; Standards; Table
lookup",
}
@Article{Chen:2013:PGF,
author = "Doris Chen and Deshanand Singh",
title = "Profile-guided floating- to fixed-point conversion for
hybrid {FPGA}-processor applications",
journal = j-TACO,
volume = "9",
number = "4",
pages = "43:1--43:??",
month = jan,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2400682.2400702",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Fri Jan 18 10:57:16 MST 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
abstract = "The key to enabling widespread use of FPGAs for
algorithm acceleration is to allow programmers to
create efficient designs without the time-consuming
hardware design process. Programmers are used to
developing scientific and mathematical algorithms in
high-level languages (C/C++) using floating point data
types. Although easy to implement, the dynamic range
provided by floating point is not necessary in many
applications; more efficient implementations can be
realized using fixed point arithmetic. While this topic
has been studied previously [Han et al. 2006; Olson et
al. 1999; Gaffar et al. 2004; Aamodt and Chow 1999],
the degree of full automation has always been lacking.
We present a novel design flow for cases where FPGAs
are used to offload computations from a microprocessor.
Our LLVM-based algorithm inserts value profiling code
into an unmodified C/C++ application to guide its
automatic conversion to fixed point. This allows for
fast and accurate design space exploration on a host
microprocessor before any accelerators are mapped to
the FPGA. Through experimental results, we demonstrate
that fixed-point conversion can yield resource savings
of up to 2x--3x reductions. Embedded RAM usage is
minimized, and 13\%--22\% higher $ F_{\rm max} $ than
the original floating-point implementation is observed.
In a case study, we show that 17\% reduction in logic
and 24\% reduction in register usage can be realized by
using our algorithm in conjunction with a High-Level
Synthesis (HLS) tool.",
acknowledgement = ack-nhfb,
articleno = "43",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J924",
}
@InProceedings{Chevillard:2013:MPE,
author = "Sylvain Chevillard and Marc Mezzarobba",
title = "Multiple-Precision Evaluation of the {Airy} {Ai}
Function with Reduced Cancellation",
crossref = "IEEE:2013:PIS",
pages = "175--182",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.33",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Accuracy; Airy Ai function; algorithm; Algorithm
design and analysis; Approximation algorithms;
Approximation methods; arbitrary precision; ARITH-21;
asymptotics; cancellation reduction; classical Miller
algorithm; correct rounding; differential equations;
Equations; error bounds; ill-conditioned three-term
recurrence; linear ordinary differential equation;
Miller method; multiple-precision evaluation;
nonnegative Taylor expansions; numerical evaluation;
series (mathematics); series expansion; Shape; Special
functions; Taylor coefficients; Taylor series",
}
@Article{Cleveland:2013:OIR,
author = "Mathew A. Cleveland and Thomas A. Brunner and Nicholas
A. Gentile and Jeffrey A. Keasler",
title = "Obtaining identical results with double precision
global accuracy on different numbers of processors in
parallel particle {Monte Carlo} simulations",
journal = j-J-COMPUT-PHYS,
volume = "251",
number = "??",
pages = "223--236",
day = "15",
month = oct,
year = "2013",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2013.05.041",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Tue Aug 6 11:36:34 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999113004075",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
keywords = "accurate floating-point summation",
}
@TechReport{Corden:2013:DFP,
author = "Martyn Corden",
title = "Differences in Floating-Point Arithmetic Between
{Intel Xeon} Processors and the {Intel Xeon Phi}
Coprocessor",
type = "Report",
institution = inst-INTEL,
address = inst-INTEL:adr,
pages = "6",
year = "2013",
bibdate = "Sat Oct 31 06:56:03 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://software.intel.com/en-us/articles/differences-in-floating-point-arithmetic-between-intel-xeon-processors-and-the-intel-xeon;
https://software.intel.com/file/420203/download",
acknowledgement = ack-nhfb,
}
@InProceedings{Cornea:2013:PAR,
author = "Marius Cornea",
title = "Precision, Accuracy, and Rounding Error Propagation in
Exascale Computing",
crossref = "IEEE:2013:PIS",
pages = "231--234",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.42",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Accuracy; ARITH-21; Computational modeling; computer
architects; Digital arithmetic; exascale computing;
exascale level computers; Hardware; parallel machines;
Parallel processing; rounding error propagation;
supercomputers; Supercomputers",
}
@Article{De:2013:FIM,
author = "Anindya De and Piyush P. Kurur and Chandan Saha and
Ramprasad Saptharishi",
title = "Fast Integer Multiplication Using Modular Arithmetic",
journal = j-SIAM-J-COMPUT,
volume = "42",
number = "2",
pages = "685--699",
month = "????",
year = "2013",
CODEN = "SMJCAT",
DOI = "https://doi.org/10.1137/100811167",
ISSN = "0097-5397 (print), 1095-7111 (electronic)",
ISSN-L = "0097-5397",
bibdate = "Tue Feb 11 17:21:19 MST 2014",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/42/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Computing",
journal-URL = "http://epubs.siam.org/sicomp",
onlinedate = "January 2013",
}
@Article{deDinechin:2013:FPE,
author = "Florent de Dinechin and Pedro Echeverr{\'\i}a and
Marisa L{\'o}pez-Vallejo and Bogdan Pasca",
title = "Floating-Point Exponentiation Units for Reconfigurable
Computing",
journal = j-TRETS,
volume = "6",
number = "1",
pages = "4:1--4:??",
month = may,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2457443.2457447",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Thu Mar 13 08:09:42 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "The high performance and capacity of current FPGAs
makes them suitable as acceleration co-processors. This
article studies the implementation, for such
accelerators, of the floating-point power function $
x^y $ as defined by the C99 and IEEE 754-2008
standards, generalized here to arbitrary exponent and
mantissa sizes. Last-bit accuracy at the smallest
possible cost is obtained thanks to a careful study of
the various subcomponents: a floating-point logarithm,
a modified floating-point exponential, and a truncated
floating-point multiplier. A parameterized architecture
generator in the open-source FloPoCo project is
presented in details and evaluated.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@Article{deDinechin:2013:FPT,
author = "Florent de Dinechin and Matei Istoan and Guillaume
Sergent",
title = "Fixed-point trigonometric functions on {FPGAs}",
journal = j-COMP-ARCH-NEWS,
volume = "41",
number = "5",
pages = "83--88",
month = dec,
year = "2013",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2641361.2641375",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Mon Aug 18 17:12:43 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Three approaches for computing sines and cosines on
FPGAs are studied in this paper, with a focus of
high-throughput pipelined architecture, and
state-of-the-art implementation techniques. The first
approach is the classical CORDIC iteration, for which
we suggest a reduced iteration technique and fine
optimizations in datapath width and latency. The second
is an ad-hoc architecture specifically designed around
trigonometric identities. The third uses a generic
table- and DSP-based polynomial approximator. These
three architectures are implemented and compared in the
FloPoCo framework.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{deDinechin:2013:ZRT,
author = "Florent de Dinechin and Christoph Lauter and
Jean-Michel Muller and Serge Torres",
title = "On {Ziv}'s rounding test",
journal = j-TOMS,
volume = "39",
number = "4",
pages = "25:1--25:19",
month = jul,
year = "2013",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2491491.2491495",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Jul 19 17:20:56 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "A very simple test, introduced by Ziv, allows one to
determine if an approximation to the value f(x) of an
elementary function at a given point x suffices to
return the floating-point number nearest f(x). The same
test may be used when implementing floating-point
operations with input and output operands of different
formats, using arithmetic operators tailored for
manipulating operands of the same format. That test
depends on a ``magic constant'' e. We show how to
choose that constant e to make the test reliable and
efficient. Various cases are considered, depending on
the availability of an fma instruction, and on the
range of f(x).",
acknowledgement = ack-nhfb,
articleno = "25",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Misc{Demmel:2013:ERF,
author = "James Demmel and Hong Diep Nguyen",
title = "Efficient Reproducible Floating-Point Reduction
Operations on Large Scale Systems",
howpublished = "SIAM AN13 talk slides.",
day = "8--12",
month = jul,
year = "2013",
bibdate = "Mon Jan 04 15:49:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bebop.cs.berkeley.edu/reproblas/docs/talks/SIAM_AN13.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Demmel:2013:FRF,
author = "James Demmel and Hong Diep Nguyen",
title = "Fast Reproducible Floating-Point Summation",
crossref = "IEEE:2013:PIS",
pages = "163--172",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.9",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.eecs.berkeley.edu/~hdnguyen/public/papers/ARITH21_Fast_Sum.pdf",
acknowledgement = ack-nhfb,
keywords = "Accuracy; Algorithm design and analysis; ARITH-21;
correct rounding; correctness check; debugging; dynamic
scheduling; Educational institutions; error-free vector
transformation; floating point arithmetic; floating
point nonassociativity; floating-point; floating-point
operation; floating-point summation; Numerical
analysis; parallel computing resource; Parallel
processing; parallel processing; parallelism; Program
processors; reduction operation; reproducibility;
reproducibility property; rounding error; rounding
mode; Rump algorithm; scheduling; summation; summation
order; Vectors",
}
@InProceedings{Demmel:2013:NRA,
author = "James Demmel and Hong Diep Nguyen",
title = "Numerical Reproducibility and Accuracy at Exascale",
crossref = "IEEE:2013:PIS",
pages = "235--237",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.43",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bebop.cs.berkeley.edu/reproblas/docs/talks/ARITH21_ExaScale.pdf;
http://www.eecs.berkeley.edu/~hdnguyen/public/papers/ARITH21_ExaScale.pdf",
acknowledgement = ack-nhfb,
keywords = "Accuracy; addition; ARITH-21; Computational modeling;
Digital arithmetic; dynamic scheduling; Educational
institutions; exascale computing; floating point
arithmetic; floating point operations; Hardware;
hardware heterogeneity; hardware trends; intermittent
failures; numerical accuracy; numerical
reproducibility; parallel processing; Program
processors; Shape",
}
@Misc{Demmel:2013:RRB,
author = "James Demmel and Hong Diep Nguyen",
title = "{ReproBLAS}: Reproducible {BLAS}",
howpublished = "SC'13 talk slides.",
day = "22",
month = nov,
year = "2013",
bibdate = "Mon Jan 04 15:49:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bebop.cs.berkeley.edu/reproblas/docs/talks/SC13.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Detrey:2013:RCF,
author = "J{\'e}r{\'e}mie Detrey and Pierrick Gaudry and Marion
Videau",
title = "Relation Collection for the Function Field Sieve",
crossref = "IEEE:2013:PIS",
pages = "201--210",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.28",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "algorithmic techniques; ARITH-21; Arrays; cache
storage; cache-aware sieving algorithms; cryptographic
size; Cryptography; discrete logarithm; FFS;
finite-field arithmetic; Function Field Sieve; function
field sieve; Lattices; low-degree prime ideals;
medium-to record-sized computations; polynomial
arithmetic; polynomial arithmetic technique;
polynomials; Polynomials; public key cryptography;
record-sized discrete-logarithm computations; relation
collection step; small-characteristic finite fields;
Vectors",
}
@InProceedings{Dimitrov:2013:ALI,
author = "Vassil Dimitrov and Kimmo J{\"a}rvinen",
title = "Another Look at Inversions over Binary Fields",
crossref = "IEEE:2013:PIS",
pages = "211--218",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.25",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; ARITH-21; binary
fields; binary Galois fields; double-base
representations; Galois fields; hardware
implementations; inversion algorithms; Itoh-Tsujii
algorithm; NIST; Polynomials; Prediction algorithms;
public key cryptography; public key cryptosystems;
Signal processing algorithms; Software; Software
algorithms; software implementations; squaring
computation; triple-base representations",
}
@Article{Dingle:2013:RIT,
author = "Nicholas J. Dingle and Nicholas J. Higham",
title = "Reducing the influence of tiny normwise relative
errors on performance profiles",
journal = j-TOMS,
volume = "39",
number = "4",
pages = "24:1--24:11",
month = jul,
year = "2013",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2491491.2491494",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Jul 19 17:20:56 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "It is a widespread but little-noticed phenomenon that
the normwise relative error $ || x - y || / || x || $
of vectors $x$ and $y$ of floating point numbers of the
same precision, where $y$ is an approximation to x, can
be many orders of magnitude smaller than the unit
roundoff. We analyze this phenomenon and show that in
the $ \infty $-norm it happens precisely when $x$ has
components of widely varying magnitude and every
component of $x$ of largest magnitude agrees with the
corresponding component of $y$. Performance profiles
are a popular way to compare competing algorithms
according to particular measures of performance. We
show that performance profiles based on normwise
relative errors can give a misleading impression due to
the influence of zero or tiny normwise relative errors.
We propose a transformation that reduces the influence
of these extreme errors in a controlled manner, while
preserving the monotonicity of the underlying data and
leaving the performance profile unchanged at its left
end-point. Numerical examples with both artificial and
genuine data illustrate the benefits of the
transformation.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@TechReport{Doertel:2013:BKM,
author = "K. Doertel",
title = "Best Known Method: Avoid heterogeneous precision in
control flow calculations",
type = "Report",
institution = pub-INTEL,
address = pub-INTEL:adr,
pages = "????",
year = "2013",
bibdate = "Sat Oct 31 07:00:07 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Edmunds:2013:AME,
author = "Michael G. Edmunds",
title = "Keynote {II}: The {Antikythera Mechanism} and the
early history of mechanical computing",
crossref = "IEEE:2013:PIS",
pages = "79--79",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.40",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-21",
}
@Article{ElWazeer:2013:SVD,
author = "Khaled ElWazeer and Kapil Anand and Aparna Kotha and
Matthew Smithson and Rajeev Barua",
title = "Scalable variable and data type detection in a binary
rewriter",
journal = j-SIGPLAN,
volume = "48",
number = "6",
pages = "51--60",
month = jun,
year = "2013",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2499370.2462165",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Mon Jul 1 17:15:38 MDT 2013",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "We present scalable static analyses to recover
variables, data types, and function prototypes from
stripped x86 executables (without symbol or debug
information) and obtain a functional intermediate
representation (IR) for analysis and rewriting
purposes. Our techniques on average run $ 352 \times $
faster than current techniques and still have the same
precision. This enables analyzing executables as large
as millions of instructions in minutes which is not
possible using existing techniques. Our techniques can
recover variables allocated to the floating point
stack, unlike current techniques. We have integrated
our techniques to obtain a compiler level IR that works
correctly if recompiled and produces the same output as
the input executable. We demonstrate scalability,
precision and correctness of our proposed techniques by
evaluating them on the complete SPEC2006 benchmarks
suite.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "PLDI '13 conference proceedings.",
}
@InProceedings{Engels:2013:NLL,
author = "Susanne Engels and Elif Bilge Kavun and Christof Paar
and Tolga Yalcin and Hristina Mihajloska",
title = "A Non-Linear\slash Linear Instruction Set Extension
for Lightweight Ciphers",
crossref = "IEEE:2013:PIS",
pages = "67--75",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.36",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "algebraic normal form; ANF; ARITH-21; binary matrix
multiply-and-add form; bit permutation; Ciphers;
cryptographic operation; cryptography; embedded CPU;
embedded microcontroller; Hardware; instruction set
extension; lightweight cipher; lightweight ciphers;
lightweight cryptographic algorithm; linear instruction
set extension; linear operation; matrix algebra;
microcontrollers; modular architecture; nonlinear
instruction set extension; nonlinear operation;
Registers; s-box; Silicon; Software; Standards",
}
@InProceedings{Galal:2013:FGD,
author = "Sameh Galal and Ofer Shacham and John S. Brunhaver and
Jing Pu and Artem Vassiliev and Mark Horowitz",
title = "{FPU} Generator for Design Space Exploration",
crossref = "IEEE:2013:PIS",
pages = "25--34",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.27",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "adder; ARITH-21; Booth encoder; Booth-2 cascade
multiply-add architecture; Booth-3 fused multiply-add
architecture; Delays; design space exploration;
Encoding; energy efficiency; fair apples-to-apples
methodology; floating point; floating point arithmetic;
floating point unit; FPU generator; Fused multiply add;
Generators; latency-sensitive design; logic design;
Logic gates; multipliers; optimisation; Optimization;
optimization technique; power efficiency; Radiation
detectors; summation tree; throughput-optimized design;
Vegetation; Wallace combining tree",
}
@InProceedings{Giorgi:2013:PMM,
author = "Pascal Giorgi and Laurent Imbert and Thomas Izard",
title = "Parallel Modular Multiplication on Multi-core
Processors",
crossref = "IEEE:2013:PIS",
pages = "135--142",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.20",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; ARITH-21; Barrett;
bipartite; Complexity theory; digital arithmetic; k-ary
multipartite algorithms; k-ary multipartite
multiplication; low level arithmetic operations;
microprocessor chips; Modular multiplication;
Montgomery; multi-core; multicore processors;
multiprocessing systems; parallel arithmetic; parallel
modular multiplications; Parallel processing; parallel
processing; Program processors; Software algorithms;
software parallelism; Synchronization; tripartite",
}
@Article{Gonzalez-Navarro:2013:BID,
author = "Sonia Gonzalez-Navarro and Charles Tsen and Michael J.
Schulte",
title = "Binary Integer Decimal-Based Floating-Point
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "7",
pages = "1460--1466",
month = jul,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.79",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jun 17 15:07:53 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{Gustafson:2013:UCN,
author = "John Gustafson",
title = "Unleashed Computing: The need to right-size precision
to save energy, bandwidth, storage, and electrical
power",
howpublished = "Web slides (64).",
day = "19",
month = mar,
year = "2013",
bibdate = "Sat Apr 02 16:24:25 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://sites.ieee.org/scv-cs/files/2013/03/Right-SizingPrecision1.pdf",
acknowledgement = ack-nhfb,
}
@Article{Han:2013:HSP,
author = "Liu Han and Seok-Bum Ko",
title = "High-Speed Parallel Decimal Multiplication with
Redundant Internal Encodings",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "5",
pages = "956--968",
month = may,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.35",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jan 21 09:06:31 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
note = "See comment \cite{Gorgin:2015:CXH}.",
abstract = "The decimal multiplication is one of the most
important decimal arithmetic operations which have a
growing demand in the area of commercial, financial,
and scientific computing. In this paper, we propose a
parallel decimal multiplication algorithm with three
components, which are a partial product generation, a
partial product reduction, and a final digit-set
conversion. First, a redundant number system is applied
to recode not only the multiplier, but also multiples
of the multiplicand in signed-digit (SD) numbers.
Furthermore, we present a multioperand SD addition
algorithm to reduce the partial product array. Finally,
a digit-set conversion algorithm with a hybrid prefix
network to decrease the number of the logic gates on
the critical path is discussed. An analysis of the
timing delay and an HDL model synthesized under 90 nm
technology show that by considering the tradeoff of
designs among three components, the overall delay of
the proposed $ 16 \times 16$-digit multiplier takes
about 11 percent less timing delay with 2 percent less
area compared to the current fastest design.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Algorithm design and analysis; Arrays;
critical path; Decimal arithmetic; decimal arithmetic
operations; Delay; digit-set conversion algorithm;
Encoding; HDL model synthesis; high-speed parallel
decimal multiplication algorithm; hybrid prefix
network; logic design; logic gate number reduction;
logic gates; Logic gates; multioperand SD adder;
multioperand SD addition algorithm; multiplier
recoding; multiplying circuits; parallel
multiplication; partial-product array reduction;
partial-product generation; partial-product reduction;
redundant internal encodings; redundant number system;
redundant number systems; SD numbers; signed-digit
numbers; timing delay analysis",
}
@InProceedings{Hilaire:2013:RIL,
author = "Thibault Hilaire and Benoit Lopez",
booktitle = "{SiPS 2013} Proceedings",
title = "Reliable implementation of linear filters with
fixed-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xv + 428",
pages = "401--406",
month = oct,
year = "2013",
DOI = "https://doi.org/10.1109/sips.2013.6674540",
ISBN = "1-4673-6236-0 (print), 1-4673-6238-7 (e-book)",
ISBN-13 = "978-1-4673-6236-8 (print), 978-1-4673-6238-2
(e-book)",
LCCN = "TK5102.9 .I578 2013",
bibdate = "Sat Jun 8 08:50:15 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.gbv.de/dms/tib-ub-hannover/791452751.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Ioualalen:2013:SAF,
author = "Arnault Ioualalen and Matthieu Martel",
editor = "????",
booktitle = "{Proceedings of the 24th IEEE International Conference
on Application-Specific Systems, Architectures and
Processors, June, 2013}",
title = "Synthesizing accurate floating-point formulas",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "113--116",
year = "2013",
DOI = "https://doi.org/10.1109/ASAP.2013.6567563",
bibdate = "Sat Apr 01 08:00:40 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.archives-ouvertes.fr/hal-00835736",
acknowledgement = ack-nhfb,
}
@Article{Jaffer:2013:EAR,
author = "Aubrey Jaffer",
title = "Easy Accurate Reading and Writing of Floating-Point
Numbers",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--7",
day = "28",
month = oct,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
MRclass = "65G04",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/java2010.bib",
URL = "http://arxiv.org/abs/1310.8121",
abstract = "Presented here are algorithms for converting between
(decimal) scientific-notation and (binary) IEEE-754
double-precision floating-point numbers. By employing a
rounding integer quotient operation these algorithms
are much simpler than those previously published. The
values are stable under repeated conversions between
the formats. Unlike Java-1.6, the scientific
representations generated use only the minimum number
of mantissa digits needed to convert back to the
original binary values. Implemented in Java these
algorithms execute as fast or faster than Java's native
conversions over nearly all of the IEEE-754
double-precision range.",
acknowledgement = ack-nhfb,
keywords = "base conversion; input-output conversion; radix
conversion; round-trip base conversion",
subject = "Numerical Analysis (cs.NA)",
}
@InProceedings{Jeannerod:2013:CAC,
author = "Claude-Pierre Jeannerod and Nicolas Louvet and
Jean-Michel Muller",
title = "On the Componentwise Accuracy of Complex
Floating-Point Division with an {FMA}",
crossref = "IEEE:2013:PIS",
pages = "83--90",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.8",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
keywords = "2 determinants; absolute errors; Accuracy; Algorithm
design and analysis; Approximation algorithms;
Approximation methods; ARITH-21; compensation; complex
division; complex floating-point division;
componentwise accuracy; componentwise relative error;
Digital arithmetic; division algorithms; Error
analysis; error analysis; floating point arithmetic;
floating-point arithmetic; FMA instruction; fused
multiply-add (FMA); fused multiply-add instruction;
Kahan compensated algorithm; nonnegative products;
radix-two floating-point arithmetic; relative errors;
rounding error analysis; Standards; straight-line
program; unit roundoff",
}
@Article{Jeannerod:2013:FAK,
author = "Claude-Pierre Jeannerod and Nicolas Louvet and
Jean-Michel Muller",
title = "Further analysis of {Kahan}'s algorithm for the
accurate computation of $ 2 \times 2 $ determinants",
journal = j-MATH-COMPUT,
volume = "82",
number = "284",
pages = "2245--2264",
month = "",
year = "2013",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-2013-02679-8",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRnumber = "MR3073198",
bibdate = "Mon Jul 15 12:07:58 MDT 2013",
bibsource = "http://www.ams.org/mcom/2013-82-284;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2013-82-284/S0025-5718-2013-02679-8;
http://www.ams.org/journals/mcom/2013-82-284/S0025-5718-2013-02679-8/S0025-5718-2013-02679-8.pdf",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Jeannerod:2013:IEB,
author = "Claude-Pierre Jeannerod and Siegfried M. Rump",
title = "Improved Error Bounds for Inner Products in
Floating-Point Arithmetic",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "34",
number = "2",
pages = "338--344",
month = "????",
year = "2013",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/120894488",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Apr 5 06:24:05 MDT 2013",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/34/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2013",
}
@Article{Jiang:2013:AED,
author = "Hao Jiang and Stef Graillat and Canbin Hu and Shengguo
Li and Xiangke Liao and Lizhi Cheng and Fang Su",
title = "Accurate evaluation of the $k$-th derivative of a
polynomial and its application",
journal = j-J-COMPUT-APPL-MATH,
volume = "243",
number = "??",
pages = "28--47",
day = "1",
month = may,
year = "2013",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2012.11.008",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65D25",
MRnumber = "3003371",
MRreviewer = "Ana Maria Acu",
bibdate = "Sat Feb 25 13:26:16 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042712005018",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "compensated algorithm; derivative evaluation;
error-free transformation; floating-point arithmetic;
rounding error",
}
@InProceedings{Jiang:2013:AFE,
author = "Hao Jiang and Stef Graillat and Roberto Barrio",
title = "Accurate and Fast Evaluation of Elementary Symmetric
Functions",
crossref = "IEEE:2013:PIS",
pages = "183--190",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.18",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Accuracy; accurate algorithm; Algorithm design and
analysis; ARITH-21; compensated algorithm;
double-double library; elementary symmetric functions;
error-free transformation; error-free transformations;
floating point arithmetic; floating-point arithmetic;
forward roundoff error bound; Libraries; mathematics
computing; MATLAB poly function; Polynomials;
psychological measurement; Rasch model; roundoff error;
Roundoff errors; running error bound; shaper bound;
summation algorithm; Vectors",
}
@InProceedings{Kadric:2013:APF,
author = "Edin Kadric and Paul Gurniak and Andr{\'e} DeHon",
title = "Accurate Parallel Floating-Point Accumulation",
crossref = "IEEE:2013:PIS",
pages = "153--162",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.19",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "$O(\log N)$ depth; Accumulation; Accurate; accurate
parallel floating-point accumulation; accurate
summation; Adders; arbitrary throughput; ARITH-21;
Clocks; conservative termination detection;
Convergence; field programmable gate arrays; floating
point arithmetic; Floating-Point Arithmetic;
floating-point sums; FPGA; Hardware; IEEE standards;
IEEE-754; Indexes; iterative algorithm; iterative
methods; iterative refinement; Moore law scaling;
Parallel; parallel associative reduction; Parallel
processing; residue-preserving IEEE-754
double-precision floating-point adder; Rounding;
standard adder; streaming accurate floating-point
accumulation unit; tree reduce parallelism; Upper
bound; Virtex 6 FPGA",
}
@Article{Khanna:2013:HPN,
author = "Gaurav Khanna",
title = "High-Precision Numerical Simulations on a {CUDA GPU}:
{Kerr} Black Hole Tails",
journal = j-J-SCI-COMPUT,
volume = "56",
number = "2",
pages = "366--380",
month = aug,
year = "2013",
CODEN = "JSCOEB",
DOI = "https://doi.org/10.1007/s10915-012-9679-3",
ISSN = "0885-7474 (print), 1573-7691 (electronic)",
ISSN-L = "0885-7474",
bibdate = "Sat Mar 8 11:16:21 MST 2014",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=56&issue=2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jscicomput.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "http://link.springer.com/article/10.1007/s10915-012-9679-3;
http://link.springer.com/content/pdf/10.1007/s10915-012-9679-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Scientific Computing",
journal-URL = "http://link.springer.com/journal/10915",
}
@Article{Kouretas:2013:LPL,
author = "Ioannis Kouretas and Charalambos Basetas and Vassilis
Paliouras",
title = "Low-Power Logarithmic Number System Addition\slash
Subtraction and Their Impact on Digital Filters",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "11",
pages = "2196--2209",
month = nov,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.111",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 15 08:54:34 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Kulisch:2013:CAV,
author = "Ulrich Kulisch",
title = "Computer Arithmetic and Validity",
volume = "33",
publisher = pub-GRUYTER,
address = pub-GRUYTER:adr,
edition = "Second",
pages = "xxii + 434",
year = "2013",
DOI = "https://doi.org/10.1515/9783110301793",
ISBN = "3-11-030173-3, 3-11-030179-2 (e-book), 3-11-030180-6
(set)",
ISBN-13 = "978-3-11-030173-1, 978-3-11-030179-3 (e-book),
978-3-11-030180-9 (set)",
ISSN = "0179-0986",
ISSN-L = "0179-0986",
LCCN = "QA76.9.C62 K853 2013",
bibdate = "Sat May 18 08:56:52 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
series = "De Gruyter studies in mathematics",
abstract = "This is the revised and extended second edition of the
successful basic book on computer arithmetic. It is
consistent with the newest recent standard developments
in the field. The book shows how the arithmetic
capability of the computer can be enhanced. The work is
motivated by the desire and the need to improve the
accuracy of numerical computing and to control the
quality of the computed results (validity). The
accuracy requirements for the elementary floating-point
operations are extended to the customary product spaces
of computations including interval spaces. The
mathematical properties of these models are extracted
and lead to a general theory of computer arithmetic.
Detailed methods and circuits for the implementation of
this advanced computer arithmetic are developed in the
book. It illustrates how the extended arithmetic can be
used to compute highly accurate and mathematically
verified results. The book can be used as a high-level
undergraduate textbook but also as reference work for
research in computer arithmetic and applied
mathematics.",
acknowledgement = ack-nhfb,
subject = "computer arithmetic; computer arithmetic and logic
units; floating-point arithmetic",
tableofcontents = "Foreword to the second edition vii \\
Preface / ix \\
Introduction / 1 \\
I Theory of computer arithmetic \\
1 First concepts 13 \\
1.1 Ordered sets / 13 \\
1.2 Complete lattices and complete subnets / 18 \\
1.3 Screens and roundings / 24 \\
1.4 Arithmetic operations and roundings / 35 \\
2 Ringoids and vectoids 43 \\
2.1 Ringoids / 43 \\
2.2 Vectoids / 54 \\
3 Definition of computer arithmetic 62 \\
3.1 Introduction / 62 \\
3.2 Preliminaries / 65 \\
3.3 The traditional definition of computer arithmetic /
69 \\
3.4 Definition of computer arithmetic by semimorphisms
/ 70 \\
3.5 A remark about roundings / 78 \\
3.6 Uniqueness of the minus operator / 79 \\
3.7 Rounding near zero / 81 \\
4 Interval arithmetic 87 \\
4.1 Interval sets and arithmetic / 88 \\
4.2 Interval arithmetic over a linearly ordered set /
97 \\
4.3 Interval matrices / 101 \\
4.4 Interval vectors / 107 \\
4.5 Interval arithmetic on a screen / 110 \\
7.2 Arithmetic interval operations / 237 \\
7.2.1 Algebraic operations / 238 \\
7.2.2 Comments on the algebraic operations / 240 \\
7.3 Circuitry for the arithmetic interval operations /
241 \\
7.4 Comparisons and lattice operations / 242 \\
7.4.1 Comments on comparisons and lattice operations /
243 \\
7.4.2 Hardware support for comparisons and lattice
operations / 243 \\
7.5 Alternative circuitry for interval operations and
comparisons / 244 \\
7.5.1 Hardware support for interval arithmetic on
x86-processors 245 \\
7.5.2 Accurate evaluation of interval scalar products /
247 \\
8 Scalar products and complete arithmetic 249 \\
8.1 Introduction and motivation / 250 \\
8.2 Historical remarks / 252 \\
8.3 The ubiquity of the scalar product in numerical
analysis / 257 \\
8.4 Implementation principles / 260 \\
8.4.1 Long adder and long shift / 262 \\
8.4.2 Short adder with local memory on the arithmetic
unit / 262 \\
8.4.3 Remarks / 263 \\
8.4.4 Fast carry resolution / 265 \\
8.5 Informal sketch for computing an exact dot product
/ 267 \\
8.6 Scalar product computation units (SPUs) / 267 \\
8.6.1 SPU for computers with a 32 bit data bus / 269
\\
8.6.2 A coprocessor chip for the exact scalar product /
272 \\
8.6.3 SPU for computers with a 64 bit data bus / 275
\\
8.7 Comments / 278 \\
8.7.1 Rounding / 278 \\
8.7.2 How much local memory should be provided on an
SPU? / 279 \\
8.8 The data format complete and complete arithmetic /
281 \\
8.8.1 Low level instructions for complete arithmetic /
282 \\
8.8.2 Complete arithmetic in high level programming
languages / 283 \\
8.9 Top speed scalar product units / 287 \\
8.9.1 SPU with long adder for 64 bit data word / 287
\\
8.9.2 SPU with long adder for 32 bit data word / 292
\\
8.9.3 An FPGA coprocessor for the exact scalar product
/ 295 \\
8.9.4 SPU with short adder and complete register / 295
\\
8.9.5 Carry-free accumulation of products in redundant
arithmetic 301 \\
8.10 Hardware complete register window / 302 \\
III Principles of verified computing \\
9 Sample applications 307 \\
9.1 Basic properties of interval mathematics / 309 \\
9.1.1 Interval arithmetic, a powerful calculus to deal
with inequalities / 309 \\
9.1.2 Interval arithmetic as executable set operations
/ 310 \\
9.1.3 Enclosing the range of function values / 316 \\
9.1.4 Nonzero property of a function, global
optimization / 319 \\
9.2 Differentiation arithmetic, enclosures of
derivatives / 321 \\
9.3 The interval Newton method / 329 \\
9.4 The extended interval Newton method / 332 \\
9.5 Verified solution of systems of linear equations /
333 \\
9.6 Accurate evaluation of arithmetic expressions / 340
\\
9.6.1 Complete expressions / 341 \\
9.6.2 Accurate evaluation of polynomials / 342 \\
9.6.3 Arithmetic expressions / 346 \\
9.7 Multiple precision arithmetics / 347 \\
9.7.1 Multiple precision floating-point arithmetic /
348 \\
9.7.2 Multiple precision interval arithmetic / 351 \\
9.7.3 Applications / 356 \\
9.7.4 Adding an exponent part as a scaling factor to
complete \\
arithmetic / 358 \\
9.8 Remarks on Kaucher arithmetic / 360 \\
9.8.1 The basic operations of Kaucher arithmetic / 364
\\
A Frequently used symbols 367 \\
B On homomorphism 369 \\
Bibliography 371 \\
List of figures 421 \\
List of tables 425 \\
Index 427",
}
@Article{Kupriianova:2013:RCIa,
author = "O. Kupriianova and Ch. Lauter and Jean-Michel Muller",
title = "Radix Conversion for {IEEE754-2008} Mixed Radix
Floating-Point Arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "2",
month = dec,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1312.0455",
abstract = "Conversion between binary and decimal floating-point
representations is ubiquitous. Floating-point radix
conversion means converting both the exponent and the
mantissa. We develop an atomic operation for FP radix
conversion with simple straight-line algorithm,
suitable for hardware design. Exponent conversion is
performed with a small multiplication and a lookup
table. It yields the correct result without error.
Mantissa conversion uses a few multiplications and a
small lookup table that is shared amongst all types of
conversions. The accuracy changes by adjusting the
computing precision.",
acknowledgement = ack-nhfb,
subject = "Mathematical Software (cs.MS)",
}
@InProceedings{Kupriianova:2013:RCIb,
author = "Olga Kupriianova and Christoph Lauter and Jean-Michel
Muller",
editor = "Michael B. Matthews",
booktitle = "{The Forty-Seventh Asilomar Conference on Signals,
Systems and Computers. November 3--6, 2013. Pacific
Grove, California}",
title = "Radix conversion for {IEEE754-2008} mixed radix
floating-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1134--1138",
year = "2013",
DOI = "https://doi.org/10.1109/ACSSC.2013.6810471",
ISBN = "1-4799-2390-7",
ISBN-13 = "978-1-4799-2390-8",
bibdate = "Fri Sep 29 10:52:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kurka:2013:UAA,
author = "Petr K{\r{u}}rka and Martin Delacourt",
title = "The Unary Arithmetical Algorithm in Bimodular Number
Systems",
crossref = "IEEE:2013:PIS",
pages = "127--134",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.10",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Absorption; ARITH-21; bimodular number system; binary
signed system; computational complexity; Convergence;
Electronic mail; exact real arithmetic; expansion
subshifts; linear average time complexity; Moebius
number systems; Moebius transformation; Random
variables; residue number systems; statistical
analysis; statistical evidence; Time complexity;
Transducers; unary arithmetical algorithm; Vectors",
}
@Article{Lam:2013:DFP,
author = "Michael O. Lam and Jeffrey K. Hollingsworth and G. W.
Stewart",
title = "Dynamic floating-point cancellation detection",
journal = j-PARALLEL-COMPUTING,
volume = "39",
number = "3",
pages = "146--155",
month = mar,
year = "2013",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Wed Mar 27 07:19:15 MDT 2013",
bibsource = "http://www.sciencedirect.com/science/journal/01678191;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167819112000622",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@Misc{Lefevre:2013:HRC,
author = "Vincent Lef{\`e}vre",
title = "Hardest-to-Round Cases: Part 2",
howpublished = "Lecture slides from ENS-Lyon, France.",
pages = "30",
day = "8",
month = oct,
year = "2013",
bibdate = "Wed Oct 09 09:40:50 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "From the slides: `After 13,812,778 CPU core hours ($
\approx $ 1576 years) for the first step'', the hardest
cases for correct rounding in the IEEE 754 binary64
format were found for $ e^x $, $ 2^x $, $ 10^x $, $
\sinh $, $ \cosh $, $ \sin (2 \pi x) $, $ \cos (2 \pi
x) $, $ \tan (2 \pi x) $; for $ x^n $ for $ n \in [ -
180, - 2] $ and $ n \in [3, 5188] $; for $ \sin (x) $,
$ \cos (x) $, and $ \tan (x) $ for $ x \in [ - \pi / 2,
+ \pi / 2] $; and for their inverse functions.",
}
@TechReport{Lefevre:2013:SML,
author = "Vincent Lef{\`e}vre",
title = "{Sipe}: a mini-library for very low precision
computations with correct rounding.",
type = "Report",
number = "hal-00864580",
institution = "INRIA, LIP / CNRS / ENS Lyon / Universit{\'e} de
Lyon",
address = "Lyon, France",
pages = "13",
day = "22",
month = sep,
year = "2013",
bibdate = "Sat Dec 23 12:04:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-00864580",
abstract = "Sipe is a mini-library in the form of a C header file,
to perform radix-2 floating-point computations in very
low precisions with correct rounding, either to nearest
or toward zero. The goal of such a tool is to do proofs
of algorithms\slash properties or computations of tight
error bounds in these precisions by exhaustive tests,
in order to try to generalize them to higher
precisions. The currently supported operations are
addition, subtraction, multiplication (possibly with
the error term), fused multiply-add\slash subtract
(FMA\slash FMS), and miscellaneous comparisons and
conversions. sipe provides two implementations of these
operations, with the same API and the same behavior:
one based on integer arithmetic, and a new one based on
floating-point arithmetic. Timing comparisons have been
done with hardware IEEE-754 floating point and with GNU
MPFR.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lefevre:2013:SSI,
author = "Vincent Lef{\`e}vre",
title = "{SIPE}: Small Integer Plus Exponent",
crossref = "IEEE:2013:PIS",
pages = "99--106",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.22",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://hal.inria.fr/hal-00763954",
acknowledgement = ack-nhfb,
keywords = "addition; Algorithm design and analysis; ARITH-21;
arithmetic operations; C header file; Computers;
Context; correct rounding; floating point arithmetic;
floating-point computations; FMA; GNU MPFR; Hardware;
hardware IEEE-754 floating point; IEEE standards;
Libraries; low precision; mini-library; multiplication;
radix 2; SIPE; small integer plus exponent; Standards;
subtraction; Timing; timing comparisons",
}
@Article{Lei:2013:FIE,
author = "Yuanwu Lei and Yong Dou and Yazhuo Dong and Jie Zhou
and Fei Xia",
title = "{FPGA} implementation of an exact dot product and its
application in variable-precision floating-point
arithmetic",
journal = j-J-SUPERCOMPUTING,
volume = "64",
number = "2",
pages = "580--605",
month = may,
year = "2013",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-012-0860-0",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Sat Feb 8 10:21:14 MST 2014",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=64&issue=2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
URL = "http://link.springer.com/article/10.1007/s11227-012-0860-0",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Lei:2013:VCI,
author = "Yuanwu Lei and Yong Dou and Lei Guo and Jinbo Xu and
Jie Zhou and Yazhuo Dong and Hongjian Li",
title = "{VLIW} coprocessor for {IEEE-754} quadruple-precision
elementary functions",
journal = j-TACO,
volume = "10",
number = "3",
pages = "12:1--12:??",
month = sep,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2512430",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Mon Sep 16 17:20:12 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
abstract = "In this article, a unified VLIW coprocessor, based on
a common group of atomic operation units, for Quad
arithmetic and elementary functions (QP\_VELP) is
presented. The explicitly parallel scheme of VLIW
instruction and Estrin's evaluation scheme for
polynomials are used to improve the performance. A
two-level VLIW instruction RAM scheme is introduced to
achieve high scalability and customizability, even for
more complex key program kernels. Finally, the Quad
arithmetic accelerator (QAA) with the QP\_VELP array is
implemented on ASIC. Compared with hyper-thread
software implementation on an Intel Xeon E5620, QAA
with 8 QP\_VELP units achieves improvement by a factor
of 18X.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J924",
}
@Article{Lowery:2013:RED,
author = "Bradley R. Lowery",
title = "Relative error due to a single bit-flip in
floating-point arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--6",
day = "15",
month = apr,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1304.4292",
abstract = "We consider the error due to a single bit-flip in a
floating point number. We assume IEEE 754 double
precision arithmetic, which encodes binary floating
point numbers in a 64-bit word. We assume that the
bit-flip happens randomly so it has equi-probability
(1/64) to hit any of the 64 bits. Since we want to
mitigate the assumption on our initial floating-point
number, we assume that it is uniformly picked among all
normalized number. With this framework, we can
summarize our findings as follows. The probability for
a single bit flip to cause a relative error less than $
10^{-11} $ in a normalized floating-point number is
above 25\%; The probability for a single bit flip to
cause a relative error less than $ 10^{-6} $ in a
normalized floating-point number is above 50\%; Etc.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA)",
}
@Article{Maitra:2013:DSM,
author = "Subhashis Maitra and Amitabha Sinha",
title = "Design and simulation of {MAC} unit using
combinational circuit and adder",
journal = j-COMP-ARCH-NEWS,
volume = "41",
number = "5",
pages = "25--33",
month = dec,
year = "2013",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2641361.2641365",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Mon Aug 18 17:12:43 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Hardware and timing complexities of MAC unit to
perform arithmetic operation like addition or
multiplication especially in the field of Digital
Signal Processing (DSP) or Elliptic Curve Cryptography
(ECC) are the major issues to the designer. The
multiplication operation is essential and abundant in
DSP Applications. In order to achieve maximum
implementation efficiency and timing performance,
designing a DSP systems is critical and frequently
presents a significant challenge to hardware engineers.
There are certain multipliers that simplify this
challenge by abstracting away FPGA device specifics,
while maintaining the required maximum performance and
resource efficiency. These multipliers are able to
perform parallel multiplication and hence constant
coefficient multiplication, both with differing
implementation styles. Again with the aid of
instantaneous resource estimation, hardware engineers
can rapidly select the optimal solution for their
system. The latest additions to the IP provide fine
control over the latency using the concept of
pipelining of the multipliers that are purely
combinatorial to be fully pipelined. Here a new
compensation method that reduces both the hardware and
timing complexities of the multiplier used for DSP
application or ECC application has been proposed. The
design of the MAC unit based on the proposed
compensation method has been dealt here properly using
Xilinx 13.2 and compared with array multiplier, Booth
multiplier and Vedic multiplier to show its novelty
over them. The hardware complexity is reduced to about
60\% of the original multiplier. Design results show
that the proposed architecture has lower hardware
overhead, lower error and fast operating speed as
compared with array, Booth and Vedic multiplier.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{Maniatakos:2013:LCC,
author = "Michail Maniatakos and Prabhakar Kudva and Bruce M.
Fleischer and Yiorgos Makris",
title = "Low-Cost Concurrent Error Detection for Floating-Point
Unit ({FPU}) Controllers",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "7",
pages = "1376--1388",
month = jul,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.81",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jun 17 15:07:53 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Martin-Dorel:2013:SIR,
author = "{\'E}rik Martin-Dorel and Guillaume Melquiond and
Jean-Michel Muller",
title = "Some issues related to double rounding",
journal = j-BIT-NUM-MATH,
volume = "53",
number = "4",
pages = "897--924",
month = dec,
year = "2013",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-013-0436-2",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Dec 2 16:05:03 MST 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=53&issue=4;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/article/10.1007/s10543-013-0436-2",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Muller:2013:ADR,
author = "Jean-Michel Muller",
editor = "Michael B. Matthews",
booktitle = "{The Forty-Seventh Asilomar Conference on Signals,
Systems and Computers. November 3--6, 2013. Pacific
Grove, California}",
title = "Avoiding double roundings in scaled {Newton--Raphson}
division",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "396--399",
year = "2013",
DOI = "https://doi.org/10.1109/ACSSC.2013.6810304",
ISBN = "1-4799-2390-7",
ISBN-13 = "978-1-4799-2390-8",
bibdate = "Fri Sep 29 10:48:21 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Nathan:2013:REB,
author = "Ralph Nathan and Bryan Anthonio and Shih-Lien Lu and
Helia Naeimi and Daniel J. Sorin and Xiaobai Sun",
title = "Recycled Error Bits: Energy-Efficient Architectural
Support for Higher Precision Floating Point",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "27",
month = sep,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1309.7321",
abstract = "In this work, we provide energy-efficient
architectural support for floating point accuracy. Our
goal is to provide accuracy that is far greater than
that provided by the processor's hardware floating
point unit (FPU). Specifically, for each floating point
addition performed, we ``recycle'' that operation's
error: the difference between the finite-precision
result produced by the hardware and the result that
would have been produced by an infinite-precision FPU.
We make this error architecturally visible such that it
can be used, if desired, by software. Experimental
results on physical hardware show that software that
exploits architecturally recycled error bits can
achieve accuracy comparable to a 2B-bit FPU with
performance and energy that are comparable to a B-bit
FPU.",
acknowledgement = ack-nhfb,
subject = "Hardware Architecture (cs.AR)",
}
@Article{Nguyen:2013:SED,
author = "Trung Duc Nguyen and Rodney {Van Meter}",
title = "A Space-Efficient Design for Reversible Floating Point
Adder in Quantum Computing",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--11",
day = "17",
month = jun,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1306.3760",
abstract = "Reversible logic has applications in low-power
computing and quantum computing. However, there are few
existing designs for reversible floating-point adders
and none suitable for quantum computation. In this
paper we propose a space-efficient reversible
floating-point adder, suitable for binary quantum
computation, improving the design of Nachtigal et al.
Our work focuses on improving the reversible designs of
the alignment unit and the normalization unit, which
are the most expensive parts. By changing a few
elements of the existing algorithm, including the
circuit designs of the RLZC (reversible leading zero
counter) and converter, we have reduced the cost about
68\%. We also propose fault-tolerant designs for the
circuits. The KQ for our fault-tolerant design is
almost sixty times as expensive as for a 32-bit
fixed-point addition. We note that the floating-point
representation makes in-place, truly reversible
arithmetic impossible, requiring us to retain both
inputs, which limits the sustainability of its use for
quantum computation.",
acknowledgement = ack-nhfb,
subject = "Quantum Physics (quant-ph); Emerging Technologies
(cs.ET)",
}
@Article{Nikolajsen:2013:FSD,
author = "Jorgen L. Nikolajsen",
title = "Fractional Significant Digits",
journal = j-SIAM-J-SCI-COMP,
volume = "35",
number = "2",
pages = "A561--A576",
month = "????",
year = "2013",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/110828435",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Jul 19 07:43:46 MDT 2013",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2013",
}
@Article{Ould-Bachir:2013:SAS,
author = "Tarek Ould-Bachir and Jean Pierre David",
title = "Self-Alignment Schemes for the Implementation of
Addition-Related Floating-Point Operators",
journal = j-TRETS,
volume = "6",
number = "1",
pages = "1:1--1:??",
month = may,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2457443.2457444",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Thu Mar 13 08:09:42 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "Advances in semiconductor technology brings to the
market incredibly dense devices, capable of handling
tens to hundreds floating-point operators on a single
chip; so do the latest field programmable gate arrays
(FPGAs). In order to alleviate the complexity of
resorting to these devices in computationally intensive
applications, this article proposes hardware schemes
for the realization of addition-related floating-point
operators based on the self-alignment technique (SAT).
The article demonstrates that the schemes guarantee an
accuracy as if summation was computed accurately in the
precision of operator's internal mantissa, then
faithfully rounded to working precision. To achieve
such performance, the article adopts the redundant high
radix carry-save (HRCS) format for the rapid addition
of wide mantissas. Implementation results show that
combining the SAT and the HRCS format allows the
implementation of complex operators with reduced area
and latency, more so when a fused-path approach is
adopted. The article also proposes a new hardware
operator for performing endomorphic HRCS additions and
presents a new technique for speeding up the conversion
from the redundant HRCS to a conventional binary
format.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@Article{Ozaki:2013:GEF,
author = "Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi Oishi
and Siegfried M. Rump",
title = "Generalization of error-free transformation for matrix
multiplication and its application",
journal = j-NONLINEAR-THEORY-APPL,
volume = "4",
number = "1",
pages = "2--11",
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1587/nolta.4.2",
ISSN = "2185-4106",
ISSN-L = "2185-4106",
bibdate = "Sat Feb 8 19:02:28 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.jstage.jst.go.jp/article/nolta/4/1/4_2/_article",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Theory and Its Applications, {IEICE}",
journal-URL = "https://www.jstage.jst.go.jp/browse/nolta/",
}
@InProceedings{Pedram:2013:FPA,
author = "Ardavan Pedram and Andreas Gerstlauer and Robert A.
van de Geijn",
title = "Floating Point Architecture Extensions for Optimized
Matrix Factorization",
crossref = "IEEE:2013:PIS",
pages = "49--58",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.21",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; application specific
integrated circuits; architectural modifications;
architecture complexity; ARITH-21; Cholesky; Complexity
theory; computational complexity; Computer
architecture; custom linear algebra processor; dense
linear systems; design trade-offs; floating point;
floating point architecture extensions; floating point
arithmetic; floating point units; full-custom ASIC
designs; least mean squares methods; linear algebra;
linear least-squares problems; low power; LU
factorization; MAC units; Matrix decomposition; matrix
decomposition; matrix factorization; optimized matrix
factorization; QR factorizations; Registers; Vectors",
}
@Article{Pontarelli:2013:LCC,
author = "Salvatore Pontarelli and Pedro Reviriego and Chris J.
Bleakley and Juan Antonio Maestro",
title = "Low Complexity Concurrent Error Detection for Complex
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "9",
pages = "1899--1903",
month = sep,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.246",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 15 08:54:34 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Rodriguez-Garcia:2013:FFP,
author = "A. Rodriguez-Garcia and L. Pizano-Escalante and R.
Parra-Michel and O. Longoria-Gandara and J. Cortez",
editor = "Ren{\'e} Cumplido and Eduardo de la Torre and Mike
Wirthlin",
booktitle = "{2013 International Conference on Reconfigurable
Computing and FPGAs (ReConFig): Cancun, Mexico,
December 9--11, 2013}",
title = "Fast fixed-point divider based on {Newton--Raphson}
method and piecewise polynomial approximation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
month = dec,
year = "2013",
DOI = "https://doi.org/10.1109/reconfig.2013.6732291",
ISBN = "1-4799-2079-7",
ISBN-13 = "978-1-4799-2079-2",
bibdate = "Thu Apr 10 15:12:10 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rubio-Gonzalez:2013:PTA,
author = "Cindy Rubio-Gonz{\'a}lez and Cuong Nguyen and Hong
Diep Nguyen and James Demmel and William Kahan and
Koushik Sen and David H. Bailey and Costin Iancu and
David Hough",
booktitle = "Proceedings of the {SC13's} International Conference
on High Performance Computing, Networking, Storage and
Analysis, Denver, {CO}, {USA}",
title = "{Precimonious}: Tuning assistant for floating-point
precision",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "27",
year = "2013",
bibdate = "Sat Jun 4 17:18:19 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Rump:2013:ASDa,
author = "Siegfried M. Rump",
title = "Accurate solution of dense linear systems, {Part I}:
Algorithms in rounding to nearest",
journal = j-J-COMPUT-APPL-MATH,
volume = "242",
number = "??",
pages = "157--184",
month = apr,
year = "2013",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:26:15 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042712004360",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Rump:2013:ASDb,
author = "Siegfried M. Rump",
title = "Accurate solution of dense linear systems, Part {II}:
Algorithms using directed rounding",
journal = j-J-COMPUT-APPL-MATH,
volume = "242",
number = "??",
pages = "185--212",
month = apr,
year = "2013",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:26:15 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042712003974",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Rupley:2013:FPU,
author = "Jeff Rupley and John King and Eric Quinnell and Frank
Galloway and Ken Patton and Peter-Michael Seidel and
James Dinh and Hai Bui and Anasua Bhowmik",
title = "The Floating-Point Unit of the {Jaguar} x86 Core",
crossref = "IEEE:2013:PIS",
pages = "7--16",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.24",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Adders; AES; AES instruction set; AMD Jaguar; AMD
Jaguar x86 core; ARITH-21; arithmetic and logic unit;
AVX; AVX instruction set; bypass network; CLMUL; CLMUL
instruction set; CMOS process; complimentary metal
oxide semiconductor; coprocessor model; coprocessors;
Decoding; dedicated renamer; dual-issue scheduler;
execution pipe; F16C; F16C instruction set; floating
point arithmetic; floating-point adder; floating-point
iterative multiplier; floating-point unit; formal
verification; formal verification technique; FPU; free
list; industry implementation; instruction sets;
low-power design; Microarchitecture; MMX; native
floating-point unit; Optimization; Out of order;
physical register file; PRF; pseudorandom verification
technique; Registers; retire queue; scheduling; size 28
nm; SSE; SSE4.2 instruction set; vector integer ALU;
vector integer MUL unit; Vectors; x86 ISA extension;
x87",
}
@Article{Russinoff:2013:CFV,
author = "David M. Russinoff",
title = "Computation and Formal Verification of {SRT} Quotient
and Square Root Digit Selection Tables",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "5",
pages = "900--913",
month = may,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.40",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Apr 30 12:26:22 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Saha:2013:PAF,
author = "Amrita Saha and Manideepa Mukherjee and Debanjana
Datta and Sangita Saha and Amitabha Sinha",
title = "Performance analysis of a {FPGA} based novel binary
and {DBNS} multiplier",
journal = j-COMP-ARCH-NEWS,
volume = "41",
number = "2",
pages = "9--16",
month = may,
year = "2013",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2490302.2490305",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Sat Jun 1 11:00:26 MDT 2013",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Designing high performance Software Defined Radio
(SDR) with low power and flexibility is a major
challenge. While the high performance DSP processors
are unable to meet the speed requirements of these
SDRs, System on chips (SOCs) are also not suitable
because of their limited flexibility. Recently
dynamically reconfigurable FPGAs have emerged as high
performance programmable hardware to execute highly
parallel, computationally intensive signal processing
functions efficiently. Since basic intention of an SDR
is to implement different modulation / demodulation
schemes and basic building blocks for such schemes are
signal processing functions, FPGAs have become an
important component for implementing these. However,
the effectiveness of such an approach with respect to
cost, performance and flexibility need to be examined.
Double Base Number Systems (DBNS) have been gaining
attention for compute intensive applications in signal
processing because of their higher performance in
arithmetic operations in general and particularly
multiplication. Keeping these issues in view, this
paper aims to present a new Software defined Radio. To
Enhance the performance of the proposed architecture ,
analysis have been done employing both single index and
multiple indices DBNS multipliers. Experiments and
analysis on performance have also been done with its
binary counterpart. Both DBNS and binary based
architecture were implemented on Xilinx virtex iv FPGA
using xilinx ISE 9.1 i.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
}
@Article{SaiToh:2013:ZCL,
author = "Akira SaiToh",
title = "{ZKCM}: a {C++} library for multiprecision matrix
computation with applications in quantum information",
journal = j-COMP-PHYS-COMM,
volume = "184",
number = "8",
pages = "2005--2020",
month = aug,
year = "2013",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Wed May 15 07:02:08 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465513001306",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
keywords = "GNU GMP library; MPFR library",
}
@Article{Shen:2013:SCC,
author = "Tao Shen and Zhugang Yuan",
title = "Stability criterion for a class of fixed-point digital
filters using two's complement arithmetic",
journal = j-APPL-MATH-COMP,
volume = "219",
number = "9",
pages = "4880--4883",
day = "1",
month = jan,
year = "2013",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2012.10.064",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Mon Dec 17 14:08:35 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300312010806",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
}
@InProceedings{Sohn:2013:IAF,
author = "Jongwook Sohn and Earl E. {Swartzlander, Jr.}",
title = "Improved Architectures for a Floating-Point Fused Dot
Product Unit",
crossref = "IEEE:2013:PIS",
pages = "41--48",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.26",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Adders; alignment scheme; ARITH-21; complex
multiplication; Computer architecture; data flow
analysis; DCT butterfly operations; Digital signal
processing; digital signal processing; Digital signal
processing (DSP); discrete cosine transform butterfly
operations; DSP applications; dual-path algorithm;
early normalization; fast Fourier transform; FFT;
floating point arithmetic; floating-point arithmetic;
floating-point fused operations; floating-point fused
two-term dot product unit; four-input leading zero
anticipation; high-speed computer arithmetic;
libraries; nonpipelined dual-path design; pipeline
processing; Pipeline processing; pipelining; Power
demand; signal processing; size 45 nm; standard cell
library; Standards; two-term dot product unit;
Vectors",
}
@InProceedings{Srinivasan:2013:SPF,
author = "Suresh Srinivasan and Ketan Bhudiya and Rajaraman
Ramanarayanan and P. Sahit Babu and Tiju Jacob and Sanu
K. Mathew and Ram Krishnamurthy and Vasantha
Errgauntla",
title = "Split-Path Fused Floating Point Multiply Accumulate
({FPMAC})",
crossref = "IEEE:2013:PIS",
pages = "17--24",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.32",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Adders; ARITH-21; AVX ISA; contemporary client
microprocessor; critical path computation; Delays;
Double precision floating point multiply-accumulate;
exponent difference; floating point arithmetic; FPMAC
design; Hardware; IBM Power6; IEEE Rounding; IEEE
standard; IEEE standards; instruction set architecture;
instruction sets; ISA support; logic design; Logic
gates; microprocessor area; microprocessor chips;
microprocessor frequency; microprocessor power;
Microprocessors; near path critical logic;
Normalization; Program processors; server processor;
split-path fused floating point multiply accumulate;
SSE ISA; timing design; Wallace tree",
}
@InProceedings{Sullivan:2013:TLA,
author = "Michael B. Sullivan and Earl E. {Swartzlander, Jr.}",
title = "Truncated Logarithmic Approximation",
crossref = "IEEE:2013:PIS",
pages = "191--198",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.34",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; Analytical models;
anti-logarithm generation; Approximation algorithms;
approximation theory; ARITH-21; binary logarithm;
computer arithmetic; Delays; Linear approximation;
linear approximation algorithm; logarithm generation;
logarithmic approximation; Logic gates; Mitchell
approximation algorithm; mixed precision; resource
utilization; Truncated approximate binary logarithms;
truncated approximate logarithm",
}
@Article{Suri:2013:DHP,
author = "Lakshay Suri and Devesh Lamba and Kunwar Kritarth and
Bhavna Ghai and Geetanjali Sharma",
title = "Design of High Performance and Power Efficient 16-bit
Square Root Carry Select Adder using Hybrid {PTL\slash
CMOS} Logic",
journal = j-INT-J-COMP-APPL,
volume = "69",
number = "??",
pages = "32--35",
month = may,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.5120/11881-7696",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 08:56:30 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume69/number10/11881-7696/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "10",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@Article{Vazquez:2013:IAA,
author = "Alvaro Vazquez and Javier D. Bruguera",
title = "Iterative Algorithm and Architecture for Exponential,
Logarithm, Powering, and Root Extraction",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "9",
pages = "1721--1731",
month = sep,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2012.247",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 15 08:54:34 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Book{Warren:2013:HD,
author = "Henry S. Warren",
title = "Hacker's Delight",
publisher = pub-AW,
address = pub-AW:adr,
edition = "Second",
pages = "xvi + 494",
year = "2013",
ISBN = "0-321-84268-5 (hardcover)",
ISBN-13 = "978-0-321-84268-8 (hardcover)",
LCCN = "QA76.6 .W375 2013",
bibdate = "Mon Sep 23 11:53:48 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.pearsonhighered.com/educator/product/Hackers-Delight/9780321842688.page",
acknowledgement = ack-nhfb,
subject = "Computer programming",
tableofcontents = "Foreword / xiii \\
Preface / xv \\
Chapter 1: Introduction / 1 \\
1-1 Notation / 1 \\
1-2 Instruction Set and Execution Time Model / 5 \\
Chapter 2: Basics / 11 \\
2-1 Manipulating Rightmost Bits / 11 \\
2-2 Addition Combined with Logical Operations / 16 \\
2-3 Inequalities among Logical and Arithmetic
Expressions / 17 \\
2-4 Absolute Value Function / 18 \\
2-5 Average of Two Integers / 19 \\
2-6 Sign Extension / 19 \\
2-7 Shift Right Signed from Unsigned / 20 \\
2-8 Sign Function / 20 \\
2-9 Three-Valued Compare Function / 21 \\
2-10 Transfer of Sign Function / 22 \\
2-11 Decoding a Zero Means 2**n Field / 22 \\
2-12 Comparison Predicates / 23 \\
2-13 Overflow Detection / 28 \\
2-14 Condition Code Result of Add, Subtract, and
Multiply / 36 \\
2-15 Rotate Shifts / 37 \\
2-16 Double-Length Add/Subtract / 38 \\
2-17 Double-Length Shifts / 39 \\
2-18 Multibyte Add, Subtract, AbsoluteValue / 40 \\
2-19 Doz, Max, Min / 41 \\
2-20 Exchanging Registers / 45 \\
2-21 Alternating among Two or More Values / 48 \\
2-22 A Boolean Decomposition Formula / 51 \\
2-23 Implementing Instructions for all 16 Binary
Boolean Operations / 53 \\
Chapter 3: Power-of-2 Boundaries / 59 \\
3-1 Rounding Up/Down to a Multiple of a Known Power of
2 / 59 \\
3-2 Rounding Up/Down to the Next Power of 2 / 60 \\
3-3 Detecting a Power-of-2 Boundary Crossing / 63 \\
Chapter 4: Arithmetic Bounds / 67 \\
4-1 Checking Bounds of Integers / 67 \\
4-2 Propagating Bounds through Adds and Subtracts / 70
\\
4-3 Propagating Bounds through Logical Operations / 73
\\
Chapter 5: Counting Bits / 81 \\
5-1 Counting 1-Bits / 81 \\
5-2 Parity / 96 \\
5-3 Counting Leading 0's / 99 \\
5-4 Counting Trailing 0's / 107 \\
Chapter 6: Searching Words / 117 \\
6-1 Find First 0-Byte / 117 \\
6-2 Find First String of 1-Bits of a Given Length / 123
\\
6-3 Find Longest String of 1-Bits / 125 \\
6-4 Find Shortest String of 1-Bits / 126 \\
Chapter 7: Rearranging Bits And Bytes / 129 \\
7-1 Reversing Bits and Bytes / 129 \\
7-2 Shuffling Bits / 139 \\
7-3 Transposing a Bit Matrix / 141 \\
7-4 Compress, or GeneralizedExtract / 150 \\
7-5 Expand, or GeneralizedInsert / 156 \\
7-6 Hardware Algorithms for Compress and Expand / 157
\\
7-7 General Permutations, Sheep and Goats Operation /
161 \\
7-8 Rearrangements and Index Transformations / 165 \\
7-9 An LRU Algorithm / 166 \\
Chapter 8: Multiplication / 171 \\
8-1 Multiword Multiplication / 171 \\
8-2 High-Order Half of 64-Bit Product / 173 \\
8-3 High-Order Product Signed from/to Unsigned / 174
\\
8-4 Multiplication by Constants / 175 \\
Chapter 9: Integer Division / 181 \\
9-1 Preliminaries / 181 \\
9-2 Multiword Division / 184 \\
9-3 Unsigned Short Division from Signed Division / 189
\\
9-4 Unsigned Long Division / 192 \\
9-5 Doubleword Division from Long Division / 197 \\
Chapter 10: Integer Division by Constants / 205 \\
10-1 Signed Division by a Known Power of 2 / 205 \\
10-2 Signed Remainder from Division by a Known Power of
2 / 206 \\
10-3 Signed Division and Remainder by Non-Powers of 2 /
207 \\
10-4 Signed Division by Divisors 2 / 210 \\
10-5 Signed Division by Divisors 2 / 218 \\
10-6 Incorporation into a Compiler / 220 \\
10-7 Miscellaneous Topics / 223 \\
10-8 Unsigned Division / 227 \\
10-9 Unsigned Division by Divisors 1 / 230 \\
10-10 Incorporation into a Compiler (Unsigned) / 232
\\
10-11 Miscellaneous Topics (Unsigned) / 234 \\
10-12 Applicability to Modulus and Floor Division / 237
\\
10-13 Similar Methods / 237 \\
10-14 Sample Magic Numbers / 238 \\
10-15 Simple Code in Python / 240 \\
10-16 Exact Division by Constants / 240 \\
10-17 Test for Zero Remainder after Division by a
Constant / 248 \\
10-18 Methods Not Using Multiply High / 251 \\
10-19 Remainder by Summing Digits / 262 \\
10-20 Remainder by Multiplication and Shifting Right /
268 \\
10-21 Converting to Exact Division / 274 \\
10-22 A Timing Test / 276 \\
10-23 A Circuit for Dividing by 3 / 276 \\
Chapter 11: Some Elementary Functions / 279 \\
11-1 Integer Square Root / 279 \\
11-2 Integer Cube Root / 287 \\
11-3 Integer Exponentiation / 288 \\
11-4 Integer Logarithm / 291 \\
Chapter 12: Unusual Bases For Number Systems / 299 \\
12-1 Base 2 / 299 \\
12-2 Base 1 + i / 306 \\
12-3 Other Bases / 308 \\
12-4 What Is the Most Efficient Base? / 309 \\
Chapter 13: Gray Code / 311 \\
13-1 Gray Code / 311 \\
13-2 Incrementing a Gray-Coded Integer / 313 \\
13-3 Negabinary Gray Code / 315 \\
13-4 Brief History and Applications / 315 \\
Chapter 14: Cyclic Redundancy Check / 319 \\
14-1 Introduction / 319 \\
14-2 Theory / 320 \\
14-3 Practice / 323 \\
Chapter 15: Error-Correcting Codes / 331 \\
15-1 Introduction / 331 \\
15-2 The Hamming Code / 332 \\
15-3 Software for SEC-DED on 32 Information Bits / 337
\\
15-4 Error Correction Considered More Generally / 342
\\
Chapter 16: Hilbert's Curve / 355 \\
16-1 A Recursive Algorithm for Generating the Hilbert
Curve / 356 \\
16-2 Coordinates from Distance along the Hilbert Curve
/ 358 \\
16-3 Distance from Coordinates on the Hilbert Curve /
366 \\
16-4 Incrementing the Coordinates on the Hilbert Curve
/ 368 \\
16-5 Non-Recursive Generating Algorithms / 371 \\
16-6 Other Space-Filling Curves / 371 \\
16-7 Applications / 372 \\
Chapter 17: Floating-Point / 375 \\
17-1 IEEE Format / 375 \\
17-2 Floating-Point To/From Integer Conversions / 377
\\
17-3 Comparing Floating-Point Numbers Using Integer
Operations / 381 \\
17-4 An Approximate Reciprocal Square Root Routine /
383 \\
17-5 The Distribution of Leading Digits / 385 \\
17-6 Table of Miscellaneous Values / 387 \\
Chapter 18: Formulas for Primes / 391 \\
18-1 Introduction / 391 \\
18-2 Willans's Formulas / 393 \\
18-3 Wormell's Formula / 397 \\
18-4 Formulas for Other Difficult Functions / 398 \\
Answers to Exercises: / 405 \\
Appendix A: Arithmetic Tables for a 4-Bit Machine / 453
\\
Appendix B: Newton's Method / 457 \\
Appendix C: A Gallery of Graphs of Discrete Functions /
459 \\
C-1 Plots of Logical Operations on Integers / 459 \\
C-2 Plots of Addition, Subtraction, and Multiplication
/ 461 \\
C-3 Plots of Functions Involving Division / 463 \\
C-4 Plots of the Compress, SAG, and Rotate Left
Functions / 464 \\
C-5 2D Plots of Some Unary Functions / 466 \\
Bibliography / 471 \\
Index / 481",
}
@Article{Wiebe:2013:FPR,
author = "Nathan Wiebe and Vadym Kliuchnikov",
title = "Floating Point Representations in Quantum Circuit
Synthesis",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "23",
month = may,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1305.5528",
abstract = "We provide a non-deterministic quantum protocol that
approximates the single qubit rotations $ R_x(2 a^2
b^2) $ using $ R_x(2 a) $ and $ R_x(2 b) $ and a
constant number of Clifford and T operations. We then
use this method to construct a ``floating point''
implementation of a small rotation wherein we use the
aforementioned method to construct the exponent part of
the rotation and also to combine it with a mantissa.
This causes the cost of the synthesis to depend more
strongly on the relative (rather than absolute)
precision required. We analyze the mean and variance of
the T-count required to use our techniques and provide
new lower bounds for the T-count for ancilla free
synthesis of small single-qubit axial rotations. We
further show that our techniques can use ancillas to
beat these lower bounds with high probability. We also
discuss the T-depth of our method and see that the vast
majority of the cost of the resultant circuits can be
shifted to parallel computation paths.",
acknowledgement = ack-nhfb,
subject = "Quantum Physics (quant-ph)",
}
@Article{Yabuki:2013:DPC,
author = "Michiro Yabuki and Takashi Tsuchiya",
title = "Double Precision Computation of the Logistic Map
Depends on Computational Modes of the Floating-point
Processing Unit",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--10",
day = "14",
month = may,
year = "2013",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1305.3128",
abstract = "Today's most popular CPU can operate in two different
computational modes for double precision computations.
This fact is not very widely recognized among
scientific computer users. The present paper reports
the differences the modes bring about using the most
thoroughly studied system in chaos theory, the logistic
map. Distinct virtual periods due to finite precision
come about depending on the computational modes for the
parameter value corresponding to fully developed chaos.
For other chaotic regime various virtual periods emerge
depending on the computational modes and the
mathematical expressions of the map. Differences in the
bifurcation diagrams due to the modes and the
expressions are surveyed exhaustively. A quantity to
measure those differences is defined and calculated.",
acknowledgement = ack-nhfb,
subject = "Chaotic Dynamics (nlin.CD)",
}
@InProceedings{Yuce:2013:FCT,
author = "Bilgiday Yuce and H. Fatih Ugurdag and Sezer Goren and
Gunham Dundar",
title = "A Fast Circuit Topology for Finding the Maximum of
{$N$} $k$-bit Numbers",
crossref = "IEEE:2013:PIS",
pages = "59--66",
year = "2013",
DOI = "https://doi.org/10.1109/ARITH.2013.35",
ISSN = "1063-6889",
bibdate = "Sat Aug 1 09:38:32 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "AB; area complexity; Area-timing product; ARITH-21;
arithmetic operation; array-based maximum finder;
Arrays; binary search; Binary trees; Circuit topology;
computational complexity; Computer arithmetic; Delays;
digital arithmetic; fast circuit topology; iterative
methods; k-bit binary numbers; Logic gates; Logic
synthesis; Maximum finder; Minimum finder; network
topology; program compilers; RTL code generators;
standard-cell based iterative synthesis flow; Time
complexity; time complexity; Timing optimization;
Topology",
}
@Article{Zhang:2013:BAF,
author = "Yiwei Zhang and Joseph P. Mcgeehan and Edward M. Regan
and Stephen Kelly and Jose Luis Nunez-Yanez",
title = "Biophysically Accurate Floating Point Neuroprocessors
for Reconfigurable Logic",
journal = j-IEEE-TRANS-COMPUT,
volume = "62",
number = "3",
pages = "599--608",
month = mar,
year = "2013",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2011.257",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Apr 30 12:26:22 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Akleylek:2014:AOF,
author = "S. Akleylek and F. {\"O}zbudak and C. {\"O}zel",
title = "On the arithmetic operations over finite fields of
characteristic three with low complexity",
journal = j-J-COMPUT-APPL-MATH,
volume = "259 (part B)",
number = "??",
pages = "546--554",
day = "15",
month = mar,
year = "2014",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:34:02 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042713004160",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Misc{Anonymous:2014:CLL,
author = "Anonymous",
title = "{CR-Libm} --- a library of correctly rounded
elementary functions in double-precision",
howpublished = "Web site",
year = "2014",
bibdate = "Sat Oct 31 07:21:21 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://lipforge.ens-lyon.fr/www/crlibm/",
abstract = "CRlibm is a free mathematical library (libm) that
provides: (1) implementations of the double-precision
C99 standard elementary functions; (2) correctly
rounded in the four IEEE-754 rounding modes; (3) with a
comprehensive proof of both the algorithms used and
their implementation; (4) sufficiently efficient in
average time, worst-case time, and memory consumption
to replace existing libms transparently.",
acknowledgement = ack-nhfb,
keywords = "correct rounding; CR-Libm; floating-point arithmetic;
scslib (software carry save library)",
}
@Article{Area:2014:ACS,
author = "Iv{\'a}n Area and Dimitar K. Dimitrov and Eduardo
Godoy and Vanessa Paschoa",
title = "Approximate Calculation of Sums {I}: Bounds for the
Zeros of {Gram} Polynomials",
journal = j-SIAM-J-NUMER-ANAL,
volume = "52",
number = "4",
pages = "1867--1886",
month = "????",
year = "2014",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/120887278",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Sat Sep 13 09:22:34 MDT 2014",
bibsource = "http://epubs.siam.org/toc/sjnaam/52/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
onlinedate = "January 2014",
}
@InProceedings{Arteaga:2014:DBR,
author = "A. Arteaga and O. Fuhrer and T. Hoefler",
booktitle = "{Proceedings of the 2014 IEEE 28th International
Parallel and Distributed Processing Symposium}",
title = "Designing bit-reproducible portable high-performance
applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1235--1244",
year = "2014",
DOI = "https://doi.org/10.1109/IPDPS.2014.127",
bibdate = "Sat Oct 31 07:13:12 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Ballard:2014:CLB,
author = "G. Ballard and E. Carson and J. Demmel and M. Hoemmen
and N. Knight and O. Schwartz",
title = "Communication lower bounds and optimal algorithms for
numerical linear algebra",
journal = j-ACTA-NUMERICA,
volume = "23",
pages = "1--155",
year = "2014",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492914000038",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
bibdate = "Mon May 12 19:01:04 MDT 2014",
bibsource = "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=23&issueId=00;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
keywords = "accurate floating-point summation",
}
@Article{BasiriM:2014:EHB,
author = "Mohamed Asan {Basiri M.} and Noor Mahammad Sk",
title = "An Efficient Hardware-Based Higher Radix Floating
Point {MAC} Design",
journal = j-TODAES,
volume = "20",
number = "1",
pages = "15:1--15:??",
month = nov,
year = "2014",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/2667224",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Wed Nov 19 11:18:40 MST 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/todaes/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/todaes.bib",
abstract = "This article proposes an effective way of implementing
a multiply accumulate circuit (MAC) for high-speed
floating point arithmetic operations. The real-world
applications related to digital signal processing and
the like demand high-performance computation with
greater accuracy. In general, digital signals are
represented as a sequence of signed/unsigned
fixed/floating point numbers. The final result of a MAC
operation can be computed by feeding the mantissa of
the previous MAC result as one of the partial products
to a Wallace tree multiplier or Braun multiplier. Thus,
the separate accumulation circuit can be avoided by
keeping the circuit depth still within the bounds of
the Wallace tree multiplier, namely $ O (\log_2 n) $,
or Braun multiplier, namely $ O (n) $. In this article,
three kinds of floating point MACs are proposed. The
experimental results show 48.54\% of improvement in
worst path delay achieved by the proposed floating
point MAC using a radix-2 Wallace structure compared
with a conventional floating point MAC without a
pipeline using a 45nm technology library. The same
proposed design gives 39.92\% of improvement in worst
path delay without a pipeline using a radix-4 Braun
structure as compared with a conventional design. In
this article, a radix-32 $ Q_{32.32}$-format-based
floating point MAC is proposed using a Wallace
tree/Braun multiplier. Also this article discusses the
msb prediction problem and its solution in floating
point arithmetic that is not available in modern fused
multiply-add designs. The performance results show
comparisons between the proposed floating point MAC
with various floating point MAC designs for radix-2,
-4, -8, and -16. The proposed design has lesser depth
than a conventional floating point MAC as well as a
lower area requirement than other ways of floating
point MAC implementation, both with/without a
pipeline.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J776",
}
@PhdThesis{Boldo:2014:DFV,
author = "Sylvie Boldo",
title = "Deductive formal verification: How to make your
floating-point programs behave",
type = "Th{\`e}se d habilitation",
school = "Universit{\b{e}} Paris-Sud",
address = "Paris, France",
pages = "iv + 80",
month = oct,
year = "2014",
bibdate = "Fri Jan 31 15:49:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.lri.fr/~sboldo/files/hdr.pdf",
acknowledgement = ack-nhfb,
}
@Article{Bouvier:2014:DFB,
author = "Cyril Bouvier and Paul Zimmermann",
title = "Division-Free Binary-to-Decimal Conversion",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "1895--1901",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2315621",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "https://members.loria.fr/PZimmermann/papers/get_str.pdf",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Chiang:2014:ESI,
author = "Wei-Fan Chiang and Ganesh Gopalakrishnan and Zvonimir
Rakamari{\'c} and Alexey Solovyev",
editor = "{ACM}",
booktitle = "{PPoPP '14: Proceedings of the 19th ACM SIGPLAN
symposium on Principles and practice of parallel
programming}",
title = "Efficient Search for Inputs Causing High
Floating-point Errors",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "43--52",
year = "2014",
DOI = "https://doi.org/10.1145/2555243.2555265",
ISBN = "1-4503-2656-0",
ISBN-13 = "978-1-4503-2656-8",
LCCN = "????",
bibdate = "Tue Mar 18 14:32:45 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://dl.acm.org/citation.cfm?doid=2555243.2555265",
acknowledgement = ack-nhfb,
}
@Article{Cibikdiken:2014:CMM,
author = "Ali Osman {\c{C}}ibikdiken and Kemal Aydin",
title = "Computation of the monodromy matrix in floating point
arithmetic with the {Wilkinson} Model",
journal = j-COMPUT-MATH-APPL,
volume = "67",
number = "5",
pages = "1186--1194",
month = mar,
year = "2014",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:51:31 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122113006706",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Darulova:2014:SCR,
author = "Eva Darulova and Viktor Kuncak",
title = "Sound compilation of reals",
journal = j-SIGPLAN,
volume = "49",
number = "1",
pages = "235--248",
month = jan,
year = "2014",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2578855.2535874",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Mar 4 17:04:57 MST 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
note = "POPL '14 conference proceedings.",
abstract = "Writing accurate numerical software is hard because of
many sources of unavoidable uncertainties, including
finite numerical precision of implementations. We
present a programming model where the user writes a
program in a real-valued implementation and
specification language that explicitly includes
different types of uncertainties. We then present a
compilation algorithm that generates a finite-precision
implementation that is guaranteed to meet the desired
precision with respect to real numbers. Our compilation
performs a number of verification steps for different
candidate precisions. It generates verification
conditions that treat all sources of uncertainties in a
unified way and encode reasoning about finite-precision
roundoff errors into reasoning about real numbers. Such
verification conditions can be used as a standardized
format for verifying the precision and the correctness
of numerical programs. Due to their non-linear nature,
precise reasoning about these verification conditions
remains difficult and cannot be handled using
state-of-the art SMT solvers alone. We therefore
propose a new procedure that combines exact SMT solving
over reals with approximate and sound affine and
interval arithmetic. We show that this approach
overcomes scalability limitations of SMT solvers while
providing improved precision over affine and interval
arithmetic. Our implementation gives promising results
on several numerical models, including dynamical
systems, transcendental functions, and controller
implementations.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Darulova:2014:TCR,
author = "Eva Darulova and Viktor Kuncak",
title = "Towards a Compiler for Reals",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "1--24",
day = "1",
month = oct,
year = "2014",
bibdate = "Sat Apr 02 15:52:17 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1410.0198",
abstract = "Numerical software, common in scientific computing or
embedded systems, inevitably uses an approximation of
the real arithmetic in which most algorithms are
designed. In many domains, roundoff errors are not the
only source of inaccuracy and measurement and other
input errors further increase the uncertainty of the
computed results. Adequate tools are needed to help
users select suitable approximations, especially for
safety-critical applications. We present the
source-to-source compiler Rosa which takes as input a
real-valued program with error specifications and
synthesizes code over an appropriate floating-point or
fixed-point data type. The main challenge of such a
compiler is a fully automated, sound and yet accurate
enough numerical error estimation. We present a unified
technique for floating-point and fixed-point arithmetic
of various precisions which can handle nonlinear
arithmetic, determine closed- form symbolic invariants
for unbounded loops and quantify the effects of
discontinuities on numerical errors. We evaluate Rosa
on a number of benchmarks from scientific computing and
embedded systems and, comparing it to state-of-the-art
in automated error estimation, show it presents an
interesting trade-off between accuracy and
performance.",
acknowledgement = ack-nhfb,
}
@Article{DelBarrio:2014:ULP,
author = "Alberto A. {Del Barrio} and Nader Bagherzadeh and
Rom{\'a}n Hermida",
title = "Ultra-low-power adder stage design for exascale
floating point units",
journal = j-TECS,
volume = "13",
number = "3s",
pages = "105:1--105:??",
month = mar,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2567932",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Mon Mar 24 17:17:02 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
abstract = "Currently, the most powerful supercomputers can
provide tens of petaflops. Future many-core systems are
estimated to provide an exaflop. However, the power
budget limitation makes these machines still infeasible
and unaffordable. Floating Point Units (FPUs) are
critical from both the power consumption and
performance points of view of today's microprocessors
and supercomputers. Literature offers very different
designs. Some of them are focused on increasing
performance no matter the penalty, and others on
decreasing power at the expense of lower performance.
In this article, we propose a novel approach for
reducing the power of the FPU without degrading the
rest of parameters. Concretely, this power reduction is
also accompanied by an area reduction and a performance
improvement. Hence, an overall energy gain will be
produced. According to our experiments, our proposed
unit consumes 17.5\%, 23\% and 16.5\% less energy for
single, double and quadruple precision, with an
additional 15\%, 21.5\% and 14.5\% delay reduction,
respectively. Furthermore, area is also diminished by
4\%, 4.5\% and 5\%.",
acknowledgement = ack-nhfb,
articleno = "105",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}
@Misc{Demmel:2014:THS,
author = "James Demmel and Hong Diep Nguyen",
title = "Toward hardware support for Reproducible {BLAS}",
howpublished = "SCAN 2014 talk slides.",
day = "24",
month = sep,
year = "2014",
bibdate = "Mon Jan 04 15:49:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bebop.cs.berkeley.edu/reproblas/img/pdf.png",
acknowledgement = ack-nhfb,
}
@Article{Doerr:2014:RRP,
author = "Benjamin Doerr and Magnus Wahlstr{\"o}m",
title = "Randomized Rounding in the Presence of a Cardinality
Constraint",
journal = j-ACM-J-EXP-ALGORITHMICS,
volume = "19",
number = "1",
pages = "1.2:1--1.2:??",
month = may,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2594409",
ISSN = "1084-6654",
ISSN-L = "1084-6654",
bibdate = "Wed May 21 14:36:05 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jea.bib",
abstract = "We consider the problem of generating randomized
roundings that satisfy a single cardinality constraint
and admit Chernoff-type large deviation bounds for
weighted sums of the variables. That this can be done
efficiently was proven by Srinivasan [2001], a
different approach was later given by the first author
[Doerr 2006]. In this work, we (a) present an improved
version of the bitwise derandomization given by Doerr,
(b) give the first derandomization of Srinivasan's
tree-based randomized approach and prove its
correctness, and (c) experimentally compare the
resulting algorithms. Our experiments show that adding
a single cardinality constraint typically reduces the
rounding errors and only moderately increases the
running times. In general, our derandomization of the
tree-based approach is superior to the derandomized
bitwise one, while the two randomized versions produce
very similar rounding errors. When implementing the
derandomized tree-based approach, however, the choice
of the tree is important.",
acknowledgement = ack-nhfb,
articleno = "1.2",
fjournal = "Journal of Experimental Algorithmics (JEA)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J430",
}
@Article{Drane:2014:SCF,
author = "T. A. Drane and T. M. Rose and G. A. Constantinides",
title = "On the Systematic Creation of Faithfully Rounded
Truncated Multipliers and Arrays",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "10",
pages = "2513--2525",
month = oct,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.126",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 06 07:29:34 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "arbitrary array; bit vectors; correct rounding;
correct-by-construction; Data-path design; elemental
semiconductors; faithfully rounded truncated arrays;
faithfully rounded truncated multipliers; fixed point
arithmetic; fixed-point multiplication; floating-point
arithmetic; hardware description languages; HDL code;
heuristically inspired schemes; high-speed arithmetic;
Monte Carlo methods; Monte Carlo simulation;
multiplying circuits; parallel circuits; partial
product array; Si; silicon; silicon area; systematic
creation; truncated multiplier schemes; word length 32
bit; worst-case analysis; worst-case error",
}
@Article{Du:2014:AEP,
author = "Peibing Du and Hao Jiang and Lizhi Cheng",
title = "Accurate Evaluation of Polynomials in {Legendre}
Basis",
journal = j-J-APPL-MATH,
volume = "2014",
pages = "742538:1--742538:13",
year = "2014",
DOI = "https://doi.org/10.1155/2014/742538",
ISSN = "1110-757X (print), 1687-0042 (electronic)",
ISSN-L = "1110-757X",
bibdate = "Mon Mar 19 14:19:47 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.hindawi.com/journals/jam/2014/742538/",
acknowledgement = ack-nhfb,
fjournal = "Journal of Applied Mathematics",
journal-URL = "http://www.hindawi.com/journals/jam/",
}
@Article{Dumas:2014:NRI,
author = "Jean-Guillaume Dumas",
title = "On {Newton--Raphson} Iteration for Multiplicative
Inverses Modulo Prime Powers",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "2106--2109",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.94",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See corrections \cite{Walther:2019:VNR}.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Duracz:2014:PFI,
author = "Jan Duracz and Michal Kone{\v{c}}n{\'y}",
title = "Polynomial function intervals for floating-point
software verification",
journal = j-ANN-MATH-ARTIF-INTELL,
volume = "70",
number = "4",
pages = "351--398",
month = apr,
year = "2014",
CODEN = "AMAIEC",
DOI = "https://doi.org/10.1007/s10472-014-9409-7",
ISSN = "1012-2443 (print), 1573-7470 (electronic)",
ISSN-L = "1012-2443",
bibdate = "Sat Jun 8 08:22:14 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematics and Artificial Intelligence",
journal-URL = "http://link.springer.com/journal/10472",
keywords = "PolyPaver open-source software tool",
}
@Article{Gilani:2014:EEP,
author = "Syed Zohaib Gilani and Nam Sung Kim and Michael
Schulte",
title = "Energy-Efficient Pixel-Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "1--1",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2325827",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gladshtein:2014:DBP,
author = "Michael Gladshtein",
title = "Delay-based processing-in-wire for design of {QCA}
serial decimal arithmetic units",
journal = j-JETC,
volume = "10",
number = "2",
pages = "13:1--13:??",
month = feb,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2564927",
ISSN = "1550-4832 (print), 1550-4840 (electronic)",
ISSN-L = "1550-4832",
bibdate = "Fri Feb 28 17:06:25 MST 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/jetc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jetc.bib",
abstract = "Quantum-dot cellular automata (QCA) technology is now
considered to be one of the prospective technologies
for a nanocomputer creation. The physical properties of
QCA and its expanding range of computer applications
make it expedient to use the novel paradigm of
nanocomputer architecture: serial decimal
storage-transfer-processing. The delay-based encoding
of decimal digits allows the use a delay element as a
main element of QCA serial arithmetic units. The simple
implementation of the delay element by a short length
of QCA wire results in reduction of complexity and of
the area required for a QCA circuit. The theoretical
basics of delay-based processing-in-wire and design
examples of QCA serial decimal arithmetic units are
presented.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J967",
}
@Article{Goualard:2014:HDY,
author = "Fr{\'e}d{\'e}ric Goualard",
title = "How do you compute the midpoint of an interval?",
journal = j-TOMS,
volume = "40",
number = "2",
pages = "11:1--11:25",
month = feb,
year = "2014",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2493882",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Mar 14 06:30:41 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "The algorithm that computes the midpoint of an
interval with floating-point bounds requires some
careful devising to handle all possible inputs
correctly. We review several implementations from
prominent C/C++ interval arithmetic packages and
analyze their potential failure to deliver the expected
results. We then show how to amend them to avoid common
pitfalls. The results presented are also relevant to
noninterval arithmetic computation such as the
implementation of bisection methods. Enough background
on IEEE 754 floating-point arithmetic is provided for
this article to serve as a practical introduction to
the analysis of floating-point computation.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Graillat:2014:MRE,
author = "Stef Graillat and Vincent Lef{\`e}vre and Jean-Michel
Muller",
title = "On the maximum relative error when computing $ x^n $
in floating-point arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "11",
month = feb,
year = "2014",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1402.2991",
abstract = "In this paper, we improve the usual relative error
bound for the computation of $ x^n $ through iterated
multiplications by x in binary floating-point
arithmetic. The obtained error bound is only slightly
better than the usual one, but it is simpler. We also
discuss the more general problem of computing the
product of n terms.",
acknowledgement = ack-nhfb,
subject = "Numerical Analysis (cs.NA); Numerical Analysis
(math.NA)",
}
@InProceedings{Hormigo:2014:ODC,
author = "J. Hormigo and J. Villalba",
editor = "Michael B. Matthews",
booktitle = "{Proceedings of the 48th Asilomar Conference on
Signals, Systems, and Computers, November 2--5, 2014,
Pacific Grove, California}",
title = "Optimizing {DSP} circuits by a new family of
arithmetic operators",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "871--875",
year = "2014",
DOI = "https://doi.org/10.1109/ACSSC.2014.7094576",
ISBN = "1-4799-8297-0, 1-4799-8298-9, 1-4799-8295-4",
ISBN-13 = "978-1-4799-8297-4",
ISSN = "1058-6393",
LCCN = "TK7801",
bibdate = "Sun Jun 19 14:59:21 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Jeannerod:2014:REF,
author = "Claude-Pierre Jeannerod and Siegfried M. Rump",
title = "On relative errors of floating-point operations:
optimal bounds and applications",
type = "Preprint",
number = "??",
institution = "????",
address = "????",
month = "????",
year = "2014",
bibdate = "Mon May 30 07:31:09 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Johansson:2014:PMP,
author = "Fredrik Johansson and {The mpmath Development Team}",
title = "\pkg{mpmath}: a {Python} library for
arbitrary-precision floating-point arithmetic",
howpublished = "Web site",
year = "2014",
bibdate = "Wed Apr 24 13:50:47 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib",
URL = "http://mpmath.org/",
acknowledgement = ack-nhfb,
}
@InProceedings{Joldes:2014:CRF,
author = "Mioara Joldes and Jean-Michel Muller and Valentina
Popescu",
editor = "{IEEE}",
booktitle = "{2014 IEEE 25th International Conference on
Application-Specific Systems, Architectures and
Processors. 18-20 June 2014. Z{\"u}rich, Switzerland}",
title = "On the computation of the reciprocal of floating point
expansions using an adapted {Newton--Raphson}
iteration",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "63--67",
year = "2014",
DOI = "https://doi.org/10.1109/ASAP.2014.6868632",
ISBN = "1-4799-3608-1",
ISBN-13 = "978-1-4799-3608-3",
bibdate = "Fri Sep 29 10:47:32 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Joldes:2014:SSH,
author = "Mioara Joldes and Valentina Popescu and Warwick
Tucker",
title = "Searching for Sinks for the {H{\'e}non} Map using a
Multiple-precision {GPU} Arithmetic Library",
journal = j-COMP-ARCH-NEWS,
volume = "42",
number = "4",
pages = "63--68",
year = "2014",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2693714.2693726",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Wed Dec 3 16:18:50 MST 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Today, GPUs represent an important hardware
development platform for many problems in dynamical
systems, where massive parallel computations are
needed. Beside that, many numerical studies of chaotic
dynamical systems require a computing precision higher
than common floating point (FP) formats. One such
application is locating invariant sets for chaotic
dynamical systems. In particular, we focus on
rigorously proving the existence of stable periodic
orbits for the H{\'e}non map for parameter values close
to the classical ones. For that, we present a
multiple-precision floating-point arithmetic library in
CUDA programming language for the NVIDIA GPU platform.
Our library extends the precision using so-called FP
expansions, where a number is represented as the
unevaluated sum of standard machine precision FP
numbers. This format offers the advantage of using
directly available and highly optimized hardware FP
operations. We generalize algorithms used by
multiple-precisions libraries such as Bailey's QD, or
the analogue GPU version, GQD.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "HEART '14 conference proceedings.",
}
@Article{Korzen:2014:PPP,
author = "Marcin Korze{\'n} and Szymon Jaroszewicz",
title = "{PaCAL}: A {Python} Package for Arithmetic
Computations with Random Variables",
journal = j-J-STAT-SOFT,
volume = "57",
number = "10",
pages = "??--??",
month = may,
year = "2014",
CODEN = "JSSOBK",
ISSN = "1548-7660",
ISSN-L = "1548-7660",
bibdate = "Mon Jun 16 11:01:52 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "http://www.jstatsoft.org/v57/i10",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Software",
journal-URL = "http://www.jstatsoft.org/",
pubdates = "Submitted 2012-02-14; Accepted 2013-07-21",
}
@InProceedings{Leeser:2014:MIR,
author = "Miriam Leeser and Sayan Mukherjee and Jaideep
Ramachandran and Thomas Wahl",
editor = "{IEEE}",
booktitle = "{Design, Automation and Test in Europe Conference and
Exhibition (DATE), Dresden, Germany March 24--28,
2014}",
title = "Make it real: Effective floating-point reasoning via
exact arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--4",
year = "2014",
DOI = "https://doi.org/10.7873/DATE.2014.130",
ISBN = "1-4799-3297-3, 3-9815370-2-5",
ISBN-13 = "978-1-4799-3297-9, 978-3-9815370-2-4",
LCCN = "TK7870 .D467 2014",
bibdate = "Sat Jun 4 17:09:03 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=6784162",
acknowledgement = ack-nhfb,
}
@Article{Lei:2014:FIS,
author = "Yuanwu Lei and Lei Guo and Yong Dou and Sheng Ma and
Jinbo Xu",
title = "{FPGA} Implementation of a Special-Purpose {VLIW}
Structure for Double-Precision Elementary Function",
journal = j-TRETS,
volume = "7",
number = "2",
pages = "8:1--8:??",
month = jun,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2617594",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Mon Jun 30 18:26:23 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "In the current article, the capability and flexibility
of field programmable gate-arrays (FPGAs) to implement
IEEE-754 double-precision floating-point elementary
functions are explored. To perform various elementary
functions on the unified hardware efficiently, we
propose a special-purpose very long instruction word
(VLIW) processor, called DP_VELP. This processor is
equipped with multiple basic units, and its performance
is improved through an explicitly parallel technique.
Pipelined evaluation of polynomial approximation with
Estrin's scheme is proposed, by scheduling basic
components in an optimal order to avoid data hazard
stalls and achieve minimal latency. The custom VLIW
processor can achieve high scalability. Under the
control of specific VLIW instructions, the basic units
are combined into special-purpose hardware for
elementary functions. Common elementary functions are
presented as examples to illustrate the design of
elementary function in DP_VELP in detail. Minimax
approximation scheme is used to reduce degree of
polynomial. Compromise between the size of lookup table
and the latency is discussed, and the internal
precision is carefully planned to guarantee accuracy of
the result. Finally, we create a prototype of the
DP_VELP unit and an FPGA accelerator based on the
DP_VELP unit on a Xilinx XC6VLX760 FPGA chip to
implement the SGP4/SDP4 application. Compared with
previous researches, the proposed design can achieve
low latency with a reasonable amount of resources and
evaluate a variety of elementary functions with the
unified hardware to satisfy the demands in scientific
applications. Experimental results show that the
proposed design guarantees more than 99\% of correct
rounding. Moreover, the SGP4/SDP4 accelerator, which is
equipped with 39 DP_VELP units and runs at 200 MHz,
outperforms the parallel software approach with
hyper-thread technology on an Intel Xeon Quad E5620 CPU
at 2.40 GHz by a factor of 7X.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@Article{Lindstrom:2014:FRC,
author = "Peter Lindstrom",
title = "Fixed-Rate Compressed Floating-Point Arrays",
journal = j-IEEE-TRANS-VIS-COMPUT-GRAPH,
volume = "20",
number = "12",
pages = "2674--2683",
month = dec,
year = "2014",
CODEN = "ITVGEA",
DOI = "https://doi.org/10.1109/TVCG.2014.2346458",
ISSN = "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
ISSN-L = "1077-2626",
bibdate = "Thu Feb 12 16:40:54 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransviscomputgraph.bib",
URL = "http://csdl.computer.org/csdl/trans/tg/2014/12/06876024-abs.html",
abstract-URL = "http://csdl.computer.org/csdl/trans/tg/2014/12/06876024-abs.html",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Visualization and Computer
Graphics",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945",
}
@Article{Long:2014:SIF,
author = "Fan Long and Stelios Sidiroglou-Douskos and Deokhwan
Kim and Martin Rinard",
title = "Sound input filter generation for integer overflow
errors",
journal = j-SIGPLAN,
volume = "49",
number = "1",
pages = "439--452",
month = jan,
year = "2014",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2578855.2535888",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Mar 4 17:04:57 MST 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
note = "POPL '14 conference proceedings.",
abstract = "We present a system, SIFT, for generating input
filters that nullify integer overflow errors associated
with critical program sites such as memory allocation
or block copy sites. SIFT uses a static program
analysis to generate filters that discard inputs that
may trigger integer overflow errors in the computations
of the sizes of allocated memory blocks or the number
of copied bytes in block copy operations. Unlike all
previous techniques of which we are aware, SIFT is
sound --- if an input passes the filter, it will not
trigger an integer overflow error at any analyzed site.
Our results show that SIFT successfully analyzes (and
therefore generates sound input filters for) 56 out of
58 memory allocation and block memory copy sites in
analyzed input processing modules from five
applications (VLC, Dillo, Swfdec, Swftools, and GIMP).
These nullified errors include six known integer
overflow vulnerabilities. Our results also show that
applying these filters to 62895 real-world inputs
produces no false positives. The analysis and filter
generation times are all less than a second.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
}
@Article{Lupon:2014:SHS,
author = "Marc Lupon and Enric Gibert and Grigorios Magklis and
Sridhar Samudrala and Ra{\'u}l Mart{\'\i}nez and
Kyriakos Stavrou and David R. Ditzel",
title = "Speculative hardware\slash software co-designed
floating-point multiply-add fusion",
journal = j-COMP-ARCH-NEWS,
volume = "42",
number = "1",
pages = "623--638",
month = mar,
year = "2014",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2654822.2541978",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Thu Sep 4 07:12:13 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "A Fused Multiply-Add (FMA) instruction is currently
available in many general-purpose processors. It
increases performance by reducing latency of dependent
operations and increases precision by computing the
result as an indivisible operation with no intermediate
rounding. However, since the arithmetic behavior of a
single-rounding FMA operation is different than
independent FP multiply followed by FP add
instructions, some algorithms require significant
revalidation and rewriting efforts to work as expected
when they are compiled to operate with FMA --- a cost
that developers may not be willing to pay. Because of
that, abundant legacy applications are not able to
utilize FMA instructions. In this paper we propose a
novel HW/SW collaborative technique that is able to
efficiently execute workloads with increased
utilization of FMA, by adding the option to get the
same numerical result as separate FP multiply and FP
add pairs. In particular, we extended the host ISA of a
HW/SW co-designed processor with a new Combined
Multiply-Add (CMA) instruction that performs an FMA
operation with an intermediate rounding. This new
instruction is used by a transparent dynamic
translation software layer that uses a speculative
instruction-fusion optimization to transform FP
multiply and FP add sequences into CMA instructions.
The FMA unit has been slightly modified to support both
single-rounding and double-rounding fused instructions
without increasing their latency and to provide a
conservative fall-back path in case of misspeculation.
Evaluation on a cycle-accurate timing simulator showed
that CMA improved SPECfp performance by 6.3\% and
reduced executed instructions by 4.7\%.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "ASPLOS '14 conference proceedings.",
}
@Article{Marche:2014:VFB,
author = "Claude March{\'e}",
title = "Verification of the functional behavior of a
floating-point program: an industrial case study",
journal = j-SCI-COMPUT-PROGRAM,
volume = "96 (part 3)",
number = "??",
pages = "279--296",
day = "15",
month = dec,
year = "2014",
CODEN = "SCPGD4",
ISSN = "0167-6423 (print), 1872-7964 (electronic)",
ISSN-L = "0167-6423",
bibdate = "Fri Oct 24 05:57:57 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicomputprogram.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167642314001671",
acknowledgement = ack-nhfb,
fjournal = "Science of Computer Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/01676423/",
}
@Article{Milicevic:2014:PAO,
author = "Aleksandar Milicevic and Daniel Jackson",
title = "Preventing arithmetic overflows in {Alloy}",
journal = j-SCI-COMPUT-PROGRAM,
volume = "94 (part 2)",
number = "??",
pages = "203--216",
day = "15",
month = nov,
year = "2014",
CODEN = "SCPGD4",
DOI = "https://doi.org/10.1016/j.scico.2014.05.009",
ISSN = "0167-6423 (print), 1872-7964 (electronic)",
ISSN-L = "0167-6423",
bibdate = "Mon Sep 22 08:04:04 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicomputprogram.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167642314002470",
acknowledgement = ack-nhfb,
fjournal = "Science of Computer Programming",
journal-URL = "http://www.sciencedirect.com/science/journal/01676423/",
}
@Misc{Moler:2014:CCFa,
author = "Cleve Moler",
title = "{Cleve's Corner}: Floating Point Numbers",
howpublished = "MathWorks Web site.",
day = "7",
month = jul,
year = "2014",
bibdate = "Sat Jan 19 18:59:13 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://blogs.mathworks.com/cleve/2014/07/07/floating-point-numbers/",
acknowledgement = ack-nhfb,
}
@Misc{Moler:2014:CCFb,
author = "Cleve Moler",
title = "{Cleve's Corner}: Floating Point Denormals,
Insignificant But Controversial",
howpublished = "MathWorks Web site.",
day = "21",
month = jul,
year = "2014",
bibdate = "Sat Jan 19 18:38:12 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://blogs.mathworks.com/cleve/2014/07/21/floating-point-denormals-insignificant-but-controversial-2/",
acknowledgement = ack-nhfb,
}
@Article{Mukhopadhyay:2014:EMP,
author = "Debapriyay Mukhopadhyay and Subhas C. Nandy",
title = "Efficient multiple-precision integer division
algorithm",
journal = j-INFO-PROC-LETT,
volume = "114",
number = "3",
pages = "152--157",
month = mar,
year = "2014",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/j.ipl.2013.10.005",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Mon Dec 9 09:33:47 MST 2013",
bibsource = "http://www.sciencedirect.com/science/journal/00200190;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc2010.bib",
note = "This paper provides a correction to the algorithm
presented in \cite{Huang:2005:EMP}, and also supplies a
complicated correctness proof.",
URL = "http://www.sciencedirect.com/science/article/pii/S0020019013002627",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
keywords = "computational arithmetic; cryptography; division
algorithm; normalization",
}
@InProceedings{Muller:2014:MRE,
author = "Jean-Michel Muller",
editor = "????",
booktitle = "{INVA} Conference Proceedings, Tokyo, Japan, 2014",
title = "On the maximum relative error when computing iterated
integer powers in floating-point arithmetic",
publisher = "????",
address = "????",
pages = "??--??",
year = "2014",
bibdate = "Mon May 30 10:37:15 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "See later paper \cite{Graillat:2015:MRE}.",
}
@Article{Murakami:2014:CRN,
author = "Hiroshi Murakami",
title = "Calculation of Rational Numbers in an Interval Whose
Denominator is the Smallest by using {FP} Interval
Arithmetic",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "48",
number = "3/4",
pages = "134--136",
month = sep,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2733693.2733711",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Thu Feb 5 17:11:08 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
abstract = "The continued fraction expansion method is a fast
solver to find a rational number in a given real
interval whose denominator is the smallest. A simple
implementation of the CF expansion method which uses
floating point numbers as real numbers has a
possibility to give a wrong answer by the effect of
numerical round-off errors. In this paper, we show a
modification of the algorithm of the CF expansion
method so that it uses floating point (FP) intervals as
replacements of real numbers. By this modified
algorithm, the answer is obtained only when its
correctness is guaranteed and the possibility to give a
wrong answer is eliminated.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Nannarelli:2014:GEI,
author = "Alberto Nannarelli and Peter-Michael Seidel and Ping
Tak Peter Tang",
title = "{Guest Editors}' Introduction: Special Section on
Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "1852--1853",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2331711",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Neto:2014:PUP,
author = "Joao Carlos Neto and Alexandre Ferreira Tenca and
Wilson Vicente Ruggiero",
title = "A Parallel and Uniform $k$-Partition Method for
{Montgomery} Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "9",
pages = "2122--2133",
month = sep,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.89",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Sep 9 06:54:10 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Nguyen:2014:RED,
author = "Trung Duc Nguyen and Rodney {Van Meter}",
title = "A Resource-Efficient Design for a Reversible Floating
Point Adder in Quantum Computing",
journal = j-JETC,
volume = "11",
number = "2",
pages = "13:1--13:??",
month = nov,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2629525",
ISSN = "1550-4832 (print), 1550-4840 (electronic)",
ISSN-L = "1550-4832",
bibdate = "Wed Nov 5 18:01:28 MST 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/jetc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jetc.bib",
abstract = "Reversible logic has applications in low-power
computing and quantum computing. However, there are few
existing designs for reversible floating-point adders
and none suitable for quantum computation. In this
article, we propose a resource-efficient reversible
floating-point adder, suitable for binary quantum
computation, improving the design of Nachtigal et al.
[2011]. Our work focuses on improving the reversible
designs of the alignment unit and the normalization
unit, which are the most expensive parts. By changing a
few elements of the existing algorithm, including the
circuit designs of the RLZC (reversible leading zero
counter) and converter, we have reduced the cost by
about 68\%. We also propose quantum designs adapted to
use gates from fault-tolerant libraries. The KQ for our
fault-tolerant design is almost 60 times as expensive
as for a 32-bit fixed-point addition. We note that the
floating-point representation makes in-place, truly
reversible arithmetic impossible, requiring us to
retain both inputs, which limits the sustainability of
its use for quantum computation.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J967",
}
@Article{Pedram:2014:AAF,
author = "Ardavan Pedram and Andreas Gerstlauer and Robert A.
van de Geijn",
title = "Algorithm, Architecture, and Floating-Point Unit
Codesign of a Matrix Factorization Accelerator",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "1854--1867",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2315627",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Piso:2014:OAE,
author = "D. Piso and J. D. Bruguera",
title = "Obtaining Accurate Error Expressions and Bounds for
Floating-Point Multiplicative Algorithms",
journal = j-COMP-J,
volume = "57",
number = "2",
pages = "319--331",
month = feb,
year = "2014",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxs170",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Mon Feb 3 17:03:04 MST 2014",
bibsource = "http://comjnl.oxfordjournals.org/content/57/2.toc;
https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/57/2/319.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
onlinedate = "January 17, 2013",
}
@Misc{Regan:2014:GAD,
author = "Rick Regan",
title = "{GCC} Avoids Double Rounding Errors With
Round-To-Odd",
howpublished = "Web site",
day = "15",
month = jan,
year = "2014",
bibdate = "Fri Dec 08 14:41:07 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib",
URL = "https://www.exploringbinary.com/gcc-avoids-double-rounding-errors-with-round-to-odd/",
acknowledgement = ack-nhfb,
keywords = "correct rounding; floating-point arithmetic; round to
odd",
}
@Article{Revol:2014:NRP,
author = "Nathalie Revol and Philippe Theveny",
title = "Numerical Reproducibility and Parallel Computations:
Issues for Interval Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "1915--1924",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2322593",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "floating-point arithmetic; reproducible arithmetic",
}
@Article{Riemens:2014:TSA,
author = "Danny P. Riemens and Georgi N. Gaydadjiev and Chris I.
de Zeeuw and Christos Strydis",
title = "Towards scalable arithmetic units with graceful
degradation",
journal = j-TECS,
volume = "13",
number = "4",
pages = "87:1--87:??",
month = feb,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2499367",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Tue Mar 11 18:33:06 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
abstract = "This article presents a new family of scalable
arithmetic units (ScAUs) targeting
resource-constrained, embedded devices. We, first,
study the performance, power, area and scalability
properties of general adders. Next, suitable
error-detection schemes for low-power embedded systems
are discussed. As a result, our ScAUs are enhanced with
a suitable error-detection scheme, resulting in a
Parity-Checked ScAU (PCScAU) design. The PCScAU strikes
a flexible trade-off between space and time redundancy,
offering dependability similar to high-end techniques
for the area and power cost of low-end approaches. An
alternative design, the Precision-Scalable Arithmetic
Unit (PScAU) maintains throughput with degraded
precision in case of hardware failures. The PScAU is
targeting dependable applications where latency rather
than numerical accuracy is more important. The PScAU's
downscaled mode is also interesting for runtime thermal
management due to its advantageous power consumption.
We implemented and synthesized the PCScAU, PScAU and a
few important reference designs (double-, triple- and
quadruple-modular-redundancy adders with/without input
gating) in 90- nm UMC technology. Overall, the PC-ScAU
ranks first in 9 out of 10 power-delay-area
(PDA)-product variants. It exhibits 16\% area savings
and 12\% performance speedup for 7\% increase in total
power consumption, compared to the cheapest form of
conventional hardware replication with the same fault
coverage. The PDA product of the PCScAU is, thus,
reduced by 21\%. It is interesting that, while total
power slightly increases, the PCScAU static power in
fact decreases by 14\%. Therefore, for newer technology
nodes where the static power component is significant,
the PCScAU can also achieve-next to performance and
area --- significant power improvements.",
acknowledgement = ack-nhfb,
articleno = "87",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}
@Article{Rohn:2014:VLD,
author = "Jiri Rohn",
title = "Verification of Linear (In){Dependence} in Finite
Precision Arithmetic",
journal = j-MATH-COMPUT-SCI,
volume = "8",
number = "3--4",
pages = "323--328",
month = sep,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1007/s11786-014-0196-7",
ISSN = "1661-8270 (print), 1661-8289 (electronic)",
ISSN-L = "1661-8270",
bibdate = "Fri Feb 13 07:10:04 MST 2015",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1661-8270&volume=8&issue=3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib",
URL = "http://link.springer.com/article/10.1007/s11786-014-0196-7",
acknowledgement = ack-nhfb,
fjournal = "Mathematics in Computer Science",
journal-URL = "http://link.springer.com/journal/11786",
}
@Article{Roux:2014:IDR,
author = "Pierre Roux",
title = "Innocuous Double Rounding of Basic Arithmetic
Operations",
journal = "Journal of Formalized Reasoning",
volume = "7",
number = "1",
year = "2014",
DOI = "https://doi.org/10.6092/issn.1972-5787/4359",
ISSN = "1972-5787",
ISSN-L = "1972-5787",
bibdate = "Mon Jan 11 08:08:43 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.archives-ouvertes.fr/hal-01091186",
abstract = "Double rounding occurs when a floating-point value is
first rounded to an intermediate precision before being
rounded to a final precision. The result of two such
consecutive roundings can differ from the result
obtained when directly rounding to the final precision.
Double rounding practically happens, for instance, when
implementing the IEEE 754 binary32 format with an
arithmetic unit performing operations only in the
larger binary64 format, such as done in the PowerPC or
x87 floating-point units. It belongs to the folklore in
the floating-point arithmetic community that double
rounding is innocuous for the basic arithmetic
operations (addition, division, multiplication, and
square root) as soon as the final precision is about
twice larger than the intermediate one. This paper
addresses the formal proof of this fact considering
underflow cases and its extension to radices other than
two.",
acknowledgement = ack-nhfb,
keywords = "double rounding",
}
@Article{Schkufza:2014:SOF,
author = "Eric Schkufza and Rahul Sharma and Alex Aiken",
title = "Stochastic optimization of floating-point programs
with tunable precision",
journal = j-SIGPLAN,
volume = "49",
number = "6",
pages = "53--64",
month = jun,
year = "2014",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2666356.2594302",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Fri Sep 26 07:38:28 MDT 2014",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "The aggressive optimization of floating-point
computations is an important problem in
high-performance computing. Unfortunately,
floating-point instruction sets have complicated
semantics that often force compilers to preserve
programs as written. We present a method that treats
floating-point optimization as a stochastic search
problem. We demonstrate the ability to generate reduced
precision implementations of Intel's handwritten C
numeric library which are up to 6 times faster than the
original code, and achieve end-to-end speedups of over
30\% on a direct numeric simulation and a ray tracer by
optimizing kernels that can tolerate a loss of
precision while still remaining correct. Because these
optimizations are mostly not amenable to formal
verification using the current state of the art, we
present a stochastic search technique for
characterizing maximum error. The technique comes with
an asymptotic guarantee and provides strong evidence of
correctness.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
received = "PLDI '14 conference proceedings.",
}
@Article{Shukla:2014:LLH,
author = "R. Shukla and K. C. Ray",
title = "Low Latency Hybrid {CORDIC} Algorithm",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "12",
pages = "3066--3078",
month = dec,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.173",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Dec 4 10:36:57 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "adders; Approximation algorithms; communication
systems; Computer architecture; coordinate rotational
digital computer; CORDIC algorithm; Delays; digital
arithmetic; Digital computers; digital computers;
double step branching; fast adders; first order
hardware architecture; hardware complexity; hybrid
CORDIC algorithm; image processing; low latency; low
latency hybrid CORDIC algorithm; Mathematical model;
radix-4; redundant arithmetic; scale factor
calculation; signal processing; Signal processing
algorithms",
}
@Article{Sultana:2014:RAC,
author = "Sayeeda Sultana and Katarzyna Radecka",
title = "Reversible Architecture of Computer Arithmetic",
journal = j-INT-J-COMP-APPL,
volume = "93",
number = "??",
pages = "6--14",
month = may,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.5120/16281-5852",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 09:07:16 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume93/number14/16281-5852/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "14",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@Article{Toronto:2014:PAF,
author = "Neil Toronto and Jay McCarthy",
title = "Practically Accurate Floating-Point Math",
journal = j-COMPUT-SCI-ENG,
volume = "16",
number = "4",
pages = "80--95",
month = jul # "\slash " # aug,
year = "2014",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCSE.2014.90",
ISSN = "1521-9615 (print), 1558-366x (electronic)",
ISSN-L = "1521-9615",
bibdate = "Thu Sep 4 08:43:09 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}
@Article{Vazquez:2014:FRM,
author = "Alvaro Vazquez and Elisardo Antelo and Javier D.
Bruguera",
title = "Fast Radix-$ 10 $ Multiplication Using Redundant {BCD}
Codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "1902--1914",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2315626",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Wang:2014:CFA,
author = "Dong Wang and Milo{\v{s}} D. Ercegovac and Yang Xiao",
title = "Complex Function Approximation Using Two-Dimensional
Interpolation",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "12",
pages = "2948--2960",
month = dec,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.181",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Dec 4 10:36:57 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "2D convolution algorithm; 2D interpolation;
Approximation error; ASIC; bipartite schemes; bivariate
functions; coefficient table; complex exponential;
complex function approximation; complex function
evaluation; complex reciprocal; Complex reciprocal;
Computational complexity; cubic interpolation;
exponential functions; field programmable gate arrays;
FPGA; Function approximation; generic hardware
architecture; interpolation; interpolation degree;
interpolation kernels; Lagrange interpolation;
Lagrangian functions; linear interpolation; lookup
tables; memory requirements; multipartite schemes;
quadratic interpolation; Quadratic programming; table
lookup; tabulated function; two-dimensional
interpolation",
}
@Article{Wang:2014:RBR,
author = "PengFei Wang and JianPing Li",
title = "On the relation between reliable computation time,
float-point precision and the {Lyapunov} exponent in
chaotic systems",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--8",
day = "18",
month = oct,
year = "2014",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1410.4919",
abstract = "The relation among reliable computation time, Tc,
float-point precision, K, and the Lyapunov exponent,
{\lambda}, is obtained as Tc= (lnB/{\lambda})K+C, where
B is the base of the float-point system and C is a
constant dependent only on the chaotic equation. The
equation shows good agreement with numerical
experimental results, especially the scale factors.",
acknowledgement = ack-nhfb,
subject = "Chaotic Dynamics (nlin.CD); Numerical Analysis
(cs.NA)",
}
@Article{Yao:2014:NRP,
author = "Gavin Xiaoxu Yao and Junfeng Fan and Ray C. C. Cheung
and Ingrid Verbauwhede",
title = "Novel {RNS} Parameter Selection for Fast Modular
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "2099--2105",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.92",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Zafar:2014:HAD,
author = "Saad Zafar and Raviteja Adapa",
booktitle = "2014 International Conference on Advances in
Electrical Engineering {(ICAEE)}",
title = "Hardware architecture design and mapping of ``{Fast
Inverse Square Root}'' algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--4",
month = jan,
year = "2014",
DOI = "https://doi.org/10.1109/icaee.2014.6838433",
bibdate = "Wed Dec 20 07:29:37 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Fast Inverse Square Root algorithm has been used
in 3D games of past for lighting and reflection
calculations, because it offers up to four times
performance gains. This paper presents a hardware
implementation of the algorithm on an FPGA board by
designing the complete architecture and successfully
mapping it on Xilinx Spartan 3E after thorough
functional verification. The results show that this
implementation provides a very efficient
single-precision floating point inverse square root
calculator with practically accurate results being made
available after just 12 short clock cycles. This
performance measure is far superior to the software
counterpart of the algorithm, and is not processor
dependent like rsqrtss of x86 SSE instruction set.
Results of this work can aid FPGA based vector
processors or graphic processing units with 3D
rendering. The hardware design can also form part of a
larger floating point arithmetic unit for dedicated
reciprocal square root calculations.",
acknowledgement = ack-nhfb,
}
@Article{Ahmadifar:2015:NRN,
author = "H. Ahmadifar and G. Jaberipur",
title = "A New Residue Number System with $5$-Moduli Set: $
2^{2 q}$, $ 2^q \pm 3$, $ 2^q \pm 1$",
journal = j-COMP-J,
volume = "58",
number = "7",
pages = "1548--1565",
month = jul,
year = "2015",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxu084",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Jul 28 10:40:55 MDT 2015",
bibsource = "http://comjnl.oxfordjournals.org/content/58/7.toc;
https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/58/7/1548",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
onlinedate = "September 2, 2014",
}
@TechReport{Ahrens:2015:ERF,
author = "P. Ahrens and H. D. Nguyen and J. Demmel",
title = "Efficient Reproducible Floating Point Summation and
{BLAS}",
type = "Report",
number = "UCB/EECS-2015-229",
institution = "EECS Department, University of California, Berkeley",
address = "Berkeley, CA, USA",
day = "8",
month = dec,
year = "2015",
bibdate = "Mon Jan 04 15:39:44 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.eecs.berkeley.edu/Pubs/TechRpts/2015/EECS-2015-229.html",
abstract = "We define reproducibility to mean getting bitwise
identical results from multiple runs of the same
program, perhaps with different hardware resources or
other changes that should ideally not change the
answer. Many users depend on reproducibility for
debugging or correctness. However, dynamic scheduling
of parallel computing resources, combined with
nonassociativity of floating point addition, makes
attaining reproducibility a challenge even for simple
operations like summing a vector of numbers, or more
complicated operations like the Basic Linear Algebra
Subprograms (BLAS). We describe an algorithm that
computes a reproducible sum of floating point numbers,
independent of the order of summation. The algorithm
depends only on a subset of the IEEE Floating Point
Standard 754-2008. It is communication-optimal, in the
sense that it does just one pass over the data in the
sequential case, or one reduction operation in the
parallel case, requiring an ``accumulator'' represented
by just 6 floating point words (more can be used if
higher precision is desired). The arithmetic cost with
a 6-word accumulator is $ 7 n $ floating point
additions to sum $n$ words, and (in IEEE double
precision) the final error bound can be up to $
10^{-8}$ times smaller than the error bound for
conventional summation. We describe the basic summation
algorithm, the software infrastructure used to build
reproducible BLAS (ReproBLAS), and performance results.
For example, when computing the dot product of 4096
double precision floating point numbers, we get an $ 4
\times $ slowdown compared to Intel Math Kernel Library
(MKL) running on an Intel Core i7-2600 CPU operating at
3.4 GHz and 256 KB L2 Cache.",
acknowledgement = ack-nhfb,
keywords = "accurate dot product; accurate summation",
}
@TechReport{Ahrens:2015:RPM,
author = "Peter Ahrens",
title = "Reproducible Parallel Matrix-Vector Multiply",
type = "{CS 267} final report",
institution = "Department of Computer Science, University of
California, Berkeley",
address = "Berkeley, CA, USA",
day = "11",
month = may,
year = "2015",
bibdate = "Mon Jan 04 15:55:37 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bebop.cs.berkeley.edu/reproblas/docs/reports/PeterAhrensCS267FinalReport.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Aktan:2015:MEA,
author = "Mustafa Aktan and Dursun Baran and Vojin G.
Oklobdzija",
title = "Minimizing Energy by Achieving Optimal Sparseness in
Parallel Adders",
crossref = "Muller:2015:ISC",
pages = "10--17",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.13",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Andrysco:2015:SFP,
author = "Marc Andrysco and David Kohlbrenner and Keaton Mowery
and Ranjit Jhala and Sorin Lerner and Hovav Shacham",
title = "On subnormal floating point and abnormal timing",
crossref = "IEEE:2015:ISS",
pages = "623--639",
year = "2015",
DOI = "https://doi.org/10.1109/SP.2015.44",
bibdate = "Mon Feb 10 08:54:26 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We identify a timing channel in the floating point
instructions of modern x86 processors: the running time
of floating point addition and multiplication
instructions can vary by two orders of magnitude
depending on their operands. We develop a benchmark
measuring the timing variability of floating point
operations and report on its results. We use floating
point data timing variability to demonstrate practical
attacks on the security of the Firefox browser
(versions 23 through 27) and the Fuzz differentially
private database. Finally, we initiate the study of
mitigations to floating point data timing channels with
libfixedtimefixedpoint, a new fixed-point,
constant-time math library. Modern floating point
standards and implementations are sophisticated,
complex, and subtle, a fact that has not been
sufficiently recognized by the security community. More
work is needed to assess the implications of the use of
floating point instructions in security-relevant
software.",
acknowledgement = ack-nhfb,
URL = "https://github.com/kmowery/libfixedtimefixedpoint",
}
@InProceedings{Aneesh:2015:HHM,
author = "R. Aneesh and Patil Vinayak and M. P. Sobham and A.
David Selvakumar",
booktitle = "{2015 International Conference on VLSI Systems,
Architecture, Technology and Applications
(VLSI-SATA)}",
title = "{HMFPCC}: --- Hybrid-mode floating point conversion
co-processor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
month = jan,
year = "2015",
DOI = "https://doi.org/10.1109/vlsi-sata.2015.7050482",
bibdate = "Sat Jun 4 17:15:13 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:2015:EFP,
author = "Anonymous",
title = "The Evils of Floating Point, and the Joys of Unum",
howpublished = "Web document",
day = "24",
month = mar,
year = "2015",
bibdate = "Sat Apr 02 16:43:03 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://vrworld.com/2015/03/24/the-evils-of-floating-point-and-the-joys-of-unum/",
acknowledgement = ack-nhfb,
}
@Article{Bailey:2015:HPA,
author = "David H. Bailey and Jonathan M. Borwein",
title = "High-precision arithmetic in mathematical physics",
journal = "Mathematics",
volume = "3",
number = "2",
publisher = "Multidisciplinary Digital Publishing Institute",
pages = "337--367",
year = "2015",
bibdate = "Sat Jun 4 17:21:23 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Bailey:2015:NRH,
author = "David H. Bailey",
title = "Numerical reproducibility in high-performance
computing",
howpublished = "24 lecture slides",
day = "19",
month = nov,
year = "2015",
bibdate = "Tue Nov 05 15:38:26 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.nist.gov/sites/default/files/documents/itl/ssd/is/NRE-2015-02-dhb-num-repro.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Bajard:2015:RAA,
author = "Jean-Claude Bajard and Julien Eynard and Nabil
Merkiche and Thomas Plantard",
title = "{RNS} Arithmetic Approach in Lattice-Based
Cryptography: Accelerating the {``Rounding-off''} Core
Procedure",
crossref = "Muller:2015:ISC",
pages = "113--120",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.30",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Bankas:2015:NMA,
author = "Edem Kwedzo Bankas and Kazeem Alagbe Gbolagade",
title = "New {MRC} Adder-Based Reverse Converter for the Moduli
Set $ 2^n $, $ 2^{2 n + 1} - 1 $, $ 2^{2 n + 2} - 1 $",
journal = j-COMP-J,
volume = "58",
number = "7",
pages = "1566--1572",
month = jul,
year = "2015",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxu089",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Jul 28 10:40:55 MDT 2015",
bibsource = "http://comjnl.oxfordjournals.org/content/58/7.toc;
https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/58/7/1566",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
onlinedate = "October 9, 2014",
}
@TechReport{Biancolin:2015:HAE,
author = "David Biancolin and Jack Koenig",
title = "Hardware Accelerator for Exact Dot Product",
type = "Report",
number = "??",
institution = "ASPIRE Laboratory, University of California,
Berkeley",
address = "Berkeley, CA, USA",
day = "19",
month = jun,
year = "2015",
bibdate = "Fri Jun 19 14:30:46 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper we present a coprocessor capable of
computing a dot product exactly by use of a ``complete
register'' (CR) that encodes a fixed point
representation of the complete IEEE754 double precision
space. We explore the design space of the coprocessor
by running simulations on large numbers of distinct
configurations. Since only the accumulation register is
represented exactly, we demonstrate that EDP is
realizable in silicon, requiring additional 11\% over
Rocket's area. In addition, the accelerator showed
speedups of $3$--$ 6 \times $ over a conventional dot
product and matrix multiplication while providing both
exactness and reproducibility.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point dot product; accurate
floating-point summation",
}
@Article{Bobade:2015:SOM,
author = "Sunil Devidas Bobade and Vijay R. Mankar",
title = "Space Optimized Multiplier Architecture for Embedded
Cryptoprocessor",
journal = j-INT-J-COMP-APPL,
volume = "113",
number = "??",
pages = "26--32",
month = mar,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.5120/19897-1982",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 09:16:05 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume113/number14/19897-1982/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "14",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@InProceedings{Boldo:2015:FVP,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "Formal Verification of Programs Computing the
Floating-Point Average",
crossref = "Butler:2015:FMS",
number = "9407",
pages = "17--32",
year = "2015",
DOI = "https://doi.org/10.1007/978-3-319-25423-4_2",
bibdate = "Fri Jan 31 15:41:04 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.inria.fr/hal-01174892;
https://link.springer.com/chapter/10.1007/978-3-319-25423-4_2",
acknowledgement = ack-nhfb,
}
@Article{Boldo:2015:SSD,
author = "Sylvie Boldo",
editor = "Sergiy Bogomolov and Matthieu Martel",
booktitle = "Proceedings of the Seventh and Eighth International
Workshop on Numerical Software Verification, volume 317
of Electronic Notes in Theoretical Computer Science,
Seattle, 2015",
title = "Stupid is as Stupid Does: Taking the Square Root of
the Square of a Floating-Point Number",
journal = j-ELECT-NOTES-THEOR-COMP-SCI,
volume = "317",
pages = "50--55",
day = "18",
month = nov,
year = "2015",
DOI = "https://doi.org/10.1016/j.entcs.2015.10.004",
ISSN = "1571-0661",
ISSN-L = "1571-0661",
bibdate = "Sat Jun 04 16:01:38 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronic Notes in Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/15710661",
remark = "The author proves in Coq that the square root of the
square of a floating-point number $x$ is always $ |x|$,
and thus, that $ x / \sqrt {x^2 + y^2}$ lies in $ [ -
1, 1]$, PROVIDED that the base is $ \beta = 2$, the
precision is $ p > 1$, and rounding is either the IEEE
754 default of round-to-nearest-ties-to-even, or
round-to-nearest-ties-away-from-zero. She gives simple
examples for bases 10 and 1000 where the result lies
outside $ [ - 1, 1]$.",
}
@Article{Boldo:2015:VCF,
author = "Sylvie Boldo and Jacques-Henri Jourdan and Xavier
Leroy and Guillaume Melquiond",
title = "Verified Compilation of Floating-Point Computations",
journal = j-J-AUTOM-REASON,
volume = "54",
number = "2",
pages = "135--163",
month = feb,
year = "2015",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-014-9317-x",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Sat Apr 2 10:51:13 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "http://link.springer.com/article/10.1007/s10817-014-9317-x",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
}
@InProceedings{Brain:2015:AFS,
author = "Martin Brain and Cesare Tinelli and Philipp Ruemmer
and Thomas Wahl",
title = "An Automatable Formal Semantics for {IEEE-754}
Floating-Point Arithmetic",
crossref = "Muller:2015:ISC",
pages = "160--167",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.26",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Brunie:2015:CGM,
author = "Nicolas Brunie and Florent de Dinechin and Olga
Kupriianova and Christoph Lauter",
title = "Code Generators for Mathematical Functions",
crossref = "Muller:2015:ISC",
pages = "66--73",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.22",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Chiang:2015:UFP,
author = "Wei-Fan Chiang and Ganesh Gopalakrishnan and Zvonimir
Rakamari{\'c}",
title = "Unsafe Floating-point to Unsigned Integer Casting
Check for {GPU} Programs",
journal = j-ELECT-NOTES-THEOR-COMP-SCI,
volume = "317",
number = "??",
pages = "1--12",
day = "18",
month = nov,
year = "2015",
DOI = "https://doi.org/10.1016/j.entcs.2015.10.005",
ISSN = "1571-0661",
ISSN-L = "1571-0661",
bibdate = "Fri Apr 17 18:06:24 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also presented at NSV 2015: 8th International Workshop
on Numerical Software Verification 2015, Seattle, WA,
USA.",
URL = "http://formalverification.cs.utah.edu/papers/nsv15-unsafe-fp2ui.pdf;
http://nsv2015.informatik.uni-freiburg.de/",
acknowledgement = ack-nhfb,
fjournal = "Electronic Notes in Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/15710661",
remark = "Not yet listed at journal Web site (up to volume 311
5-Jan-2015).",
xxjournal-url = "http://www.elsevier.nl/locate/entcs",
}
@Article{Collange:2015:NRP,
author = "Sylvain Collange and David Defour and Stef Graillat
and Roman Iakymchuk",
title = "Numerical reproducibility for the parallel reduction
on multi- and many-core architectures",
journal = j-PARALLEL-COMPUTING,
volume = "49",
number = "??",
pages = "83--97",
month = nov,
year = "2015",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/j.parco.2015.09.001",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Thu Oct 29 17:53:44 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167819115001155",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191/",
keywords = "accuracy; correct rounding; correctly-rounded
floating-point sums; CPU; error-free transformations;
floating-point arithmetic; GPU; long accumulator;
multi- and many-core architectures; parallel
floating-point summation; reproducibility; Xeon Phi",
}
@Misc{Cowlishaw:2015:GDA,
author = "Mike Cowlishaw",
title = "General Decimal Arithmetic",
howpublished = "Web site.",
year = "2015",
bibdate = "Mon Apr 25 17:12:00 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://speleotrove.com/decimal/",
acknowledgement = ack-nhfb,
remark = "Previous versions 1981, 1997, 2008.",
}
@Article{Coxon:2015:MMP,
author = "Nicholas Coxon",
title = "{Montgomery}'s method of polynomial selection for the
number field sieve",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "485",
number = "??",
pages = "72--102",
day = "15",
month = nov,
year = "2015",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Sat Oct 10 17:54:20 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/linala2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0024379515004395",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Damouche:2015:TPC,
author = "N. Damouche and M. Martel and A. Chapoutot",
title = "Transformation of a {PID} Controller for Numerical
Accuracy",
journal = j-ELECT-NOTES-THEOR-COMP-SCI,
volume = "317",
pages = "47--54",
month = nov,
year = "2015",
DOI = "https://doi.org/10.1016/j.entcs.2015.10.006",
ISSN = "1571-0661",
bibdate = "Wed Oct 16 18:53:52 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Numerical programs performing floating-point
computations are very sensitive to the way formulas are
written. Several techniques have been proposed
concerning the transformation of expressions in order
to improve their accuracy and now we aim at going a
step further by automatically transforming larger
pieces of code containing several assignments and
control structures. This article presents a case study
in this direction. We consider a PID controller and we
transform its code in order to improve its accuracy.
The experimental data obtained when we compare the
different versions of the code (which are
mathematically equivalent) show that those
transformations have a significant impact on the
accuracy of the computations.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Notes in Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/15710661",
remark = "Creative Commons license.",
}
@TechReport{deDinechin:2015:FPH,
author = "Florent de Dinechin",
title = "On fixed-point hardware polynomials",
type = "Technical Report",
institution = "INSA, CITI Lab, Universit{\'e} de Lyon",
address = "Lyon, France",
month = oct,
year = "2015",
bibdate = "Mon Feb 10 07:54:27 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.inria.fr/hal-01214739",
abstract = "Polynomial approximation is a general technique for
the evaluation of numerical functions of one variable.
This article addresses the automatic construction of
fixed-point hardware polynomial evaluators. By
systematically trying to balance the accuracy of all
the steps that lead to an architecture, it simplifies
and improves the previous body of work covering
polynomial approximation, polynomial evaluation, and
range reduction. This work is supported by an
open-source implementation.",
acknowledgement = ack-nhfb,
}
@InProceedings{deDinechin:2015:HIF,
author = "Florent de Dinechin and Matei Istoan",
title = "Hardware Implementations of Fixed-Point {Atan2}",
crossref = "Muller:2015:ISC",
pages = "34--41",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.23",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Misc{Demmel:2015:CFP,
author = "James Demmel and Hong Diep Nguyen and Peter Ahrens",
title = "Cost of Floating-Point Reproducibility",
howpublished = "33 lecture slides",
day = "20",
month = nov,
year = "2015",
bibdate = "Tue Nov 05 15:43:15 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.nist.gov/sites/default/files/documents/itl/ssd/is/NRE-2015-07-Nguyen_slides.pdf",
acknowledgement = ack-nhfb,
}
@Article{Demmel:2015:PRS,
author = "J. Demmel and Hong Diep Nguyen",
title = "Parallel Reproducible Summation",
journal = j-IEEE-TRANS-COMPUT,
volume = "64",
number = "7",
pages = "2060--2070",
month = jul,
year = "2015",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2345391",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Aug 1 08:53:41 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Denis:2015:VCF,
author = "Christophe Denis and Pablo {De Oliveira Castro} and
Eric Petit",
title = "{Verificarlo}: checking floating point accuracy
through {Monte Carlo} Arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "4",
month = sep,
year = "2015",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1509.01347",
abstract = "Numerical accuracy of floating point computation is a
well studied topic, but which has not made its way to
the end-user in scientific computing. With the recent
requirements for code modernization to exploit new
highly parallel hardware and perform higher resolution
computation, this has become one of the critical issues
to address. To democratize numerical accuracy analysis,
it is important to propose tools and methodologies to
study large use cases in a reliable and automatic way.
In this paper, we propose verificarlo, an extension to
the LLVM compiler to automatically use Monte Carlo
Arithmetic in a transparent way for the end-user. It
supports all the major languages including C, C++ and
Fortran. We also illustrate the fact that unlike
source-to-source approaches, our implementation
captures the influence of compiler optimizations on the
numerical accuracy. Finally, we illustrate on various
use cases how Monte Carlo Arithmetic using the
verificarlo tool outperforms the existing approaches
and is a step toward automatic numerical analysis of
large scientific applications.",
acknowledgement = ack-nhfb,
subject = "Mathematical Software (cs.MS); Numerical Analysis
(cs.NA)",
}
@Article{Dietz:2015:UIO,
author = "Will Dietz and Peng Li and John Regehr and Vikram
Adve",
title = "Understanding Integer Overflow in {C\slash C++}",
journal = j-TOSEM,
volume = "25",
number = "1",
pages = "2:1--2:29",
month = dec,
year = "2015",
CODEN = "ATSMER",
DOI = "https://doi.org/10.1145/2743019",
ISSN = "1049-331X (print), 1557-7392 (electronic)",
ISSN-L = "1049-331X",
bibdate = "Thu Dec 3 09:54:19 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/tosem/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tosem.bib",
abstract = "Integer overflow bugs in C and C++ programs are
difficult to track down and may lead to fatal errors or
exploitable vulnerabilities. Although a number of tools
for finding these bugs exist, the situation is
complicated because not all overflows are bugs. Better
tools need to be constructed, but a thorough
understanding of the issues behind these errors does
not yet exist. We developed IOC, a dynamic checking
tool for integer overflows, and used it to conduct the
first detailed empirical study of the prevalence and
patterns of occurrence of integer overflows in C and
C++ code. Our results show that intentional uses of
wraparound behaviors are more common than is widely
believed; for example, there are over 200 distinct
locations in the SPEC CINT2000 benchmarks where
overflow occurs. Although many overflows are
intentional, a large number of accidental overflows
also occur. Orthogonal to programmers' intent,
overflows are found in both well-defined and undefined
flavors. Applications executing undefined operations
can be, and have been, broken by improvements in
compiler optimizations. Looking beyond SPEC, we found
and reported undefined integer overflows in SQLite,
PostgreSQL, SafeInt, GNU MPC and GMP, Firefox, LLVM,
Python, BIND, and OpenSSL; many of these have since
been fixed.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Software Engineering and
Methodology",
journal-URL = "https://dl.acm.org/loi/cacm0",
}
@Article{Ebergen:2015:RDA,
author = "J. Ebergen and N. Jamadagni",
title = "Radix-$2$ Division Algorithms with an Over-Redundant
Digit Set",
journal = j-IEEE-TRANS-COMPUT,
volume = "64",
number = "9",
pages = "2652--2663",
month = "????",
year = "2015",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2366738",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Sep 28 12:03:47 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{El-Razouk:2015:NBL,
author = "Hayssam El-Razouk and Arash Reyhani-Masoleh",
title = "New Bit-Level Serial {$ {\rm GF} (2^m) $}
Multiplication Using Polynomial Basis",
crossref = "Muller:2015:ISC",
pages = "129--136",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.11",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Elsayed:2015:NPE,
author = "Essam Elsayed and Hatem M. El-Boghdadi",
title = "A novel power-efficient multi-operand digit-multiplier
using reconfiguration and clock gating",
journal = j-J-SUPERCOMPUTING,
volume = "71",
number = "7",
pages = "2539--2564",
month = jul,
year = "2015",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-015-1403-2",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Sat Aug 8 12:23:11 MDT 2015",
bibsource = "http://link.springer.com/journal/11227/71/7;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
URL = "http://link.springer.com/article/10.1007/s11227-015-1403-2",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Flocke:2015:AAE,
author = "N. Flocke",
title = "{Algorithm 954}: an Accurate and Efficient Cubic and
Quartic Equation Solver for Physical Applications",
journal = j-TOMS,
volume = "41",
number = "4",
pages = "30:1--30:24",
month = oct,
year = "2015",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2699468",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 26 17:31:15 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "We report on an accurate and efficient algorithm for
obtaining all roots of general real cubic and quartic
polynomials. Both the cubic and quartic solvers give
highly accurate roots and place no restrictions on the
magnitude of the polynomial coefficients. The key to
the algorithm is a proper rescaling of both
polynomials. This puts upper bounds on the magnitude of
the roots and is very useful in stabilizing the root
finding process. The cubic solver is based on dividing
the cubic polynomial into six classes. By analyzing the
root surface for each class, a fast convergent
Newton--Raphson starting point for a real root is
obtained at a cost no higher than three additions and
four multiplications. The quartic solver uses the cubic
solver in getting information about stationary points
and, when the quartic has real roots, stable
Newton--Raphson iterations give one of the extreme real
roots. The remaining roots follow by composite
deflation to a cubic. If the quartic has only complex
roots, the present article shows that a stable
Newton--Raphson iteration on a derived symmetric sixth
degree polynomial can be formulated for the real parts
of the complex roots. The imaginary parts follow by
solving suitable quadratics.",
acknowledgement = ack-nhfb,
articleno = "30",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Frechtling:2015:MMS,
author = "Michael Frechtling and Philip H. W. Leong",
title = "{MCALIB}: Measuring Sensitivity to Rounding Error with
{Monte Carlo} Programming",
journal = j-TOPLAS,
volume = "37",
number = "2",
pages = "5:1--5:??",
month = apr,
year = "2015",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/2665073",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Thu Apr 16 18:32:12 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toplas/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toplas.bib",
abstract = "Runtime analysis provides an effective method for
measuring the sensitivity of programs to rounding
errors. To date, implementations have required
significant changes to source code, detracting from
their widespread application. In this work, we present
an open source system that automates the quantitative
analysis of floating point rounding errors through the
use of C-based source-to-source compilation and a Monte
Carlo arithmetic library. We demonstrate its
application to the comparison of algorithms, detection
of catastrophic cancellation, and determination of
whether single precision floating point provides
sufficient accuracy for a given application. Methods
for obtaining quantifiable measurements of sensitivity
to rounding error are also detailed.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
}
@Article{Froggatt:2015:EAU,
author = "Terry Froggatt",
title = "An Error in the {Ada} Universal Arithmetic Package",
journal = j-SIGADA-LETTERS,
volume = "35",
number = "2",
pages = "14--14",
month = aug,
year = "2015",
CODEN = "AALEE5",
DOI = "https://doi.org/10.1145/2903260.2903263",
ISSN = "1094-3641 (print), 1557-9476 (electronic)",
ISSN-L = "1094-3641",
bibdate = "Mon Jun 20 18:46:44 MDT 2016",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigada.bib",
note = "See \cite{Fisher:1984:UAP}. The 32-year-old error is a
test with digit $t$ that has {\tt if (t > BASE)}, but
the operator should instead be {\tt >=}.",
abstract = "An Ada Universal Arithmetic package was published over
three decades ago in Ada Letters. It was incorporated
into several Ada compilers, and it is one of the few
compiler components which will have required no change
as the Ada language has evolved. The purpose if this
note is to draw attention to an error in that package,
which may or may not have been corrected in the
compilers, but which has never subsequently been
corrected within Ada Letters.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGAda Ada Letters",
journal-URL = "http://portal.acm.org/citation.cfm?id=J32",
}
@Article{Fu:2015:ABE,
author = "Zhoulai Fu and Zhaojun Bai and Zhendong Su",
title = "Automated backward error analysis for numerical code",
journal = j-SIGPLAN,
volume = "50",
number = "10",
pages = "639--654",
month = oct,
year = "2015",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2858965.2814317",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Feb 16 12:01:43 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "Numerical code uses floating-point arithmetic and
necessarily suffers from roundoff and truncation
errors. Error analysis is the process to quantify such
uncertainty in the solution to a problem. Forward error
analysis and backward error analysis are two popular
paradigms of error analysis. Forward error analysis is
more intuitive and has been explored and automated by
the programming languages (PL) community. In contrast,
although backward error analysis is more preferred by
numerical analysts and the foundation for numerical
stability, it is less known and unexplored by the PL
community. To fill the gap, this paper presents an
automated backward error analysis for numerical code to
empower both numerical analysts and application
developers. In addition, we use the computed backward
error results to also compute the condition number, an
important quantity recognized by numerical analysts for
measuring how sensitive a function is to changes or
errors in the input. Experimental results on Intel X87
FPU functions and widely-used GNU C Library functions
demonstrate that our analysis is effective at analyzing
the accuracy of floating-point programs.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "OOPSLA '15 conference proceedings.",
}
@InProceedings{Fukushima:2015:PFCc,
author = "Toshio Fukushima",
title = "Precise and Fast Computation of Elliptic Integrals and
Functions",
crossref = "Muller:2015:ISC",
pages = "50--57",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.15",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Gerard:2015:CDR,
author = "Beno{\^\i}t G{\'e}rard and Jean-Gabriel Kammerer and
Nabil Merkiche",
title = "Contributions to the Design of Residue Number System
Architectures",
crossref = "Muller:2015:ISC",
pages = "105--112",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.25",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Gorgin:2015:CXH,
author = "S. Gorgin and G. Jaberipur",
title = "Comment on {``High-Speed Parallel Decimal
Multiplication With Redundant Internal Encodings''}",
journal = j-IEEE-TRANS-COMPUT,
volume = "64",
number = "1",
pages = "293--294",
month = jan,
year = "2015",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.160",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jan 21 08:56:46 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
note = "See \cite{Han:2013:HSP}.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Computer science; Computers; critical delay
path; Decimal arithmetic; Delays; digital arithmetic;
Educational institutions; Encoding; high speed parallel
decimal multiplication; Logic gates; matrix
multiplication; parallel decimal multiplication;
parallel processing; redundant internal encodings;
redundant partial products; redundant representation;
signed-digit partial product",
}
@InProceedings{Gouicem:2015:MMD,
author = "Mourad Gouicem",
title = "Modular Multiplication and Division Algorithms Based
on Continued Fraction Expansion",
crossref = "Muller:2015:ISC",
pages = "137--143",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.21",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Graillat:2015:ECF,
author = "Stef Graillat and Christoph Lauter and Ping Tak Peter
Tang and Naoya Yamanaka and Shin'ichi Oishi",
title = "Efficient Calculations of Faithfully Rounded $
l_2$-Norms of $n$-Vectors",
journal = j-TOMS,
volume = "41",
number = "4",
pages = "24:1--24:20",
month = oct,
year = "2015",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2699469",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 26 17:31:15 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "In this article, we present an efficient algorithm to
compute the faithful rounding of the $ l_2 $-norm of a
floating-point vector. This means that the result is
accurate to within 1 bit of the underlying
floating-point type. This algorithm does not generate
overflows or underflows spuriously, but does so when
the final result calls for such a numerical exception
to be raised. Moreover, the algorithm is well suited
for parallel implementation and vectorization. The
implementation runs up to 3 times faster than the
netlib version on current processors.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Graillat:2015:MRE,
author = "Stef Graillat and Vincent Lef{\`e}vre and Jean-Michel
Muller",
title = "On the maximum relative error when computing integer
powers by iterated multiplications in floating-point
arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "70",
number = "3",
pages = "653--667",
month = nov,
year = "2015",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-015-9967-8",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Sun Oct 25 07:27:50 MDT 2015",
bibsource = "http://link.springer.com/journal/11075/70/3;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-015-9967-8",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
remark = "The authors show via a complex multipage proof that
the iterated product for $ x^n $ in p-bit binary
arithmetic with default IEEE 754 rounding (to nearest
with ties to even) produces a worst-case relative error
in the product that is no larger than $ (n - 1) u $,
where $ u = 2^{-p} $ is the rounding unit.",
}
@Article{Graillat:2015:NVC,
author = "Stef Graillat and Fabienne J{\'e}z{\'e}quel and Romain
Picot",
title = "Numerical validation of compensated summation
algorithms with stochastic arithmetic",
journal = j-ELECT-NOTES-THEOR-COMP-SCI,
volume = "317",
pages = "55--69",
day = "18",
month = nov,
year = "2015",
DOI = "https://doi.org/10.1016/j.entcs.2015.10.007",
ISSN = "1571-0661",
ISSN-L = "1571-0661",
bibdate = "Sat Jun 4 17:40:10 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronic Notes in Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/15710661",
}
@InProceedings{Gupta:2015:DLL,
author = "Suyog Gupta and Ankur Agrawal and Kailash
Gopalakrishnan and Pritish Narayanan",
editor = "Francis Bach and David Blei",
booktitle = "{ICML'15: Proceedings of the 32nd International
Conference on International Conference on Machine
Learning: Lille, France, July 6--11, 2015}",
title = "Deep learning with limited numerical precision",
publisher = "JMLR.org",
address = "????",
pages = "1737--1746",
year = "2015",
bibdate = "Fri Sep 22 17:39:05 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Gustafson:2015:EEU,
author = "John L. Gustafson",
title = "The End of Error: Unum Computing",
publisher = pub-CHAPMAN-HALL,
address = pub-CHAPMAN-HALL:adr,
pages = "xx + 416",
year = "2015",
ISBN = "1-4822-3986-8, 1-4822-3987-6",
ISBN-13 = "978-1-4822-3986-7, 978-1-4822-3987-4",
LCCN = "QA275 .G928 2015",
bibdate = "Thu Jan 18 06:44:33 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Written by one of the foremost experts in
high-performance computing and the inventor of
Gustafson's Law, The End of Error: Unum Computing
explains a new approach to computer arithmetic: the
universal number (unum). The unum encompasses all IEEE
floating-point formats as well as fixed-point and exact
integer arithmetic. This new number type obtains more
accurate answers than floating-point arithmetic yet
uses fewer bits in many cases, saving memory,
bandwidth, energy, and power. Richly illustrated in
color, this groundbreaking book is accessible to anyone
who uses computers for technical calculations.",
acknowledgement = ack-nhfb,
xxabstract = "In this groundbreaking book, the author --- a
world-renowned expert in high-performance computing
(HPC) and inventor of Gustafson's Law --- presents his
new approach to computer arithmetic: the unum. The
universal number, or unum format, encompasses all IEEE
floating-point formats as well as fixed-point and exact
integer arithmetic. This approach obtains more accurate
answers than floating-point arithmetic yet uses fewer
bits in many cases, saving memory, bandwidth, energy,
and power. Accessible to researchers in HPC and related
areas, the book provides a Mathematica\TM{} notebook
for the code examples.",
xxtitle = "A New Number Format: The Unum",
}
@InProceedings{Gustafson:2015:KTE,
author = "John Gustafson",
title = "Keynote Talk: The End of Numerical Error",
crossref = "Muller:2015:ISC",
pages = "74--74",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.22",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Abstract only.",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InCollection{Hamming:2015:DN,
author = "R. W. Hamming",
title = "On the distribution of numbers",
crossref = "Swartzlander:2015:CAa",
pages = "321--337",
year = "2015",
DOI = "https://doi.org/10.1142/9789814651578",
bibdate = "Tue Aug 7 07:53:59 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper examines the distribution of the mantissas
of floating-point numbers and shows how the arithmetic
operations of a computer transform various
distributions toward the limiting distribution $$ r(x)
= 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
$b$ is the base of the number system). The paper also
gives a number of applications to hardware, software,
and general computing which show that this distribution
is not merely an amusing curiosity. A brief examination
of the distribution of exponents is included.",
acknowledgement = ack-nhfb,
author-dates = "Richard Wesley Hamming (1915--1998)",
keywords = "Digital arithmetic; Floating point numbers; Limiting
distributions; Number system, Application programs;
Numbering systems, Arithmetic operations",
}
@InProceedings{Hart:2015:EDC,
author = "William Bruce Hart",
title = "Efficient Divide-and-Conquer Multiprecision Integer
Division",
crossref = "Muller:2015:ISC",
pages = "90--95",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.19",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22; division; multiple-precision arithmetic",
}
@Misc{Higham:2015:MCT,
author = "Nicholas J. Higham",
title = "Matrix Computation Toolbox",
howpublished = "Web site.",
year = "2015",
bibdate = "Sat Apr 01 08:14:19 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "http://www.ma.man.ac.uk/~higham/mctoolbox",
abstract = "The Matrix Computation Toolbox is a collection of
MATLAB M-files containing functions for constructing
test matrices, computing matrix factorizations,
visualizing matrices, and carrying out direct search
optimization. Various other miscellaneous functions are
also included. This toolbox supersedes the author's
earlier Test Matrix Toolbox (final release
1995).\par
The toolbox was developed in conjunction with the book
Accuracy and Stability of Numerical Algorithms (SIAM,
Second edition, August 2002, xxx+680 pp.). That book is
the primary documentation for the toolbox: it describes
much of the underlying mathematics and many of the
algorithms and matrices (it also describes many of the
matrices provided by MATLAB's gallery function).",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; MATLAB",
}
@Article{Holzmann:2015:B,
author = "Gerard J. Holzmann",
title = "Out of Bounds",
journal = j-IEEE-SOFTWARE,
volume = "32",
number = "6",
pages = "24--26",
month = nov # "\slash " # dec,
year = "2015",
CODEN = "IESOEG",
DOI = "https://doi.org/10.1109/MS.2015.147",
ISSN = "0740-7459 (print), 1937-4194 (electronic)",
ISSN-L = "0740-7459",
bibdate = "Tue Nov 17 07:21:14 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeesoft.bib",
URL = "http://csdl.computer.org/csdl/mags/so/2015/06/mso2015060024.html",
abstract-URL = "http://csdl.computer.org/csdl/mags/so/2015/06/mso2015060024-abs.html",
acknowledgement = ack-nhfb,
fjournal = "IEEE Software",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/software",
journalabr = "IEEE Software",
remark = "This article discusses three cases of serious impact
of undetected integer overflow: (a) the loss of control
of the Deep Impact mission space probe to visit an
asteroid; (b) the Boeing 787 Dreamliner (composite
materials) generator control unit (GCU) that must now
be rebooted at least every 248 days to avoid possibly
causing a plane crash; (c) the Planetary Society's
LightSail project to test a solar sail in space. It
also discusses a failure of NASA's Mars lander, the
Curiosity rover, due to storage overflow. Reprinted in
\booktitle{Computing Edge}, January 2016, pp. 50--52.",
}
@Article{Hsiao:2015:TSR,
author = "Shen-Fu Hsiao and Po-Han Wu and Chia-Sheng Wen and
Pramod Kumar Meher",
title = "Table Size Reduction Methods for Faithfully Rounded
Lookup-Table-Based Multiplierless Function Evaluation",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "62",
number = "5",
pages = "466--470",
month = may,
year = "2015",
DOI = "https://doi.org/10.1109/TCSII.2014.2386232",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Sat Feb 08 10:23:05 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/abstract/document/6998028",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
keywords = "Accuracy; Adders; adders; Approximation methods;
Bipartite; Computer Arithmetic; computer arithmetic;
Function Evaluation; function evaluation; graph theory;
Indexes; lookup-table-based multiplierless function
evaluation; multioperand adder; Multipartite;
multipartite; multipartite method; performance
evaluation; precision width; Silicon compounds; table
decomposition; table lookup; Table lookup; table size;
table size reduction method; Table-Based Design;
table-based design; table-lookup-and-addition methods",
}
@Article{Hutter:2015:MMA,
author = "Michael Hutter and Peter Schwabe",
title = "Multiprecision multiplication on {AVR} revisited",
journal = j-J-CRYPTO-ENG,
volume = "5",
number = "3",
pages = "201--214",
month = sep,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-015-0093-2",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Sat Aug 8 10:42:46 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "http://link.springer.com/article/10.1007/s13389-015-0093-2",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
keywords = "AVR ATmega 8-bit microcontroller; Karatsuba
multiplication; microcontroller; multiprecision
multiplication",
}
@Misc{Iakymchuk:2015:EEB,
author = "Roman Iakymchuk and Sylvain Collange and David Defour
and Stef Graillat",
title = "{ExBLAS} --- Exact {BLAS}",
howpublished = "Web site.",
year = "2015",
bibdate = "Sat Oct 31 07:25:14 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://exblas.lip6.fr/;
https://www.nist.gov/sites/default/files/documents/itl/ssd/is/NRE-2015-04-iakymchuk.pdf",
abstract = "ExBLAS stands for Exact (fast, accurate, and
reproducible) Basic Linear Algebra Subprograms.\par
The increasing power of current computers enables one
to solve more and more complex problems. This,
therefore, requires to perform a high number of
floating-point operations, each one leading to a
round-off error. Because of round-off error
propagation, some problems must be solved with a longer
floating-point format.\par
As Exascale computing is likely to be reached within a
decade, getting accurate results in floating-point
arithmetic on such computers will be a challenge.
However, another challenge will be the reproducibility
of the results --- meaning getting a bitwise identical
floating-point result from multiple runs of the same
code --- due to non-associativity of floating-point
operations and dynamic scheduling on parallel
computers.\par
ExBLAS aims at providing new algorithms and
implementations for fundamental linear algebra
operations --- like those included in the BLAS library
--- that deliver reproducible and accurate results with
small or without losses to their performance on modern
parallel architectures such as Intel Xeon Phi many-core
processors and GPU accelerators. We construct our
approach in such a way that it is independent from data
partitioning, order of computations, thread scheduling,
or reduction tree schemes.",
acknowledgement = ack-nhfb,
}
@InProceedings{Iakymchuk:2015:ERA,
author = "Roman Iakymchuk and Sylvain Collange and David Defour
and Stef Graillat",
editor = "????",
booktitle = "{NRE: Numerical Reproducibility at Exascale, Austin,
TX, USA, November 2015}",
title = "{ExBLAS}: Reproducible and Accurate {BLAS} Library",
publisher = "????",
address = "????",
pages = "??--??",
year = "2015",
bibdate = "Mon Feb 10 06:22:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{IEEE:2015:ISI,
author = "{IEEE}",
title = "1788-2015 --- {IEEE} Standard for Interval
Arithmetic",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "xiv + 79",
day = "30",
month = jun,
year = "2015",
DOI = "https://doi.org/10.1109/IEEESTD.2015.7140721",
ISBN = "0-7381-9721-1 (PDF), 0-7381-9720-3 (electronic)",
ISBN-13 = "978-0-7381-9721-0 (PDF), 978-0-7381-9720-3
(electronic)",
LCCN = "????",
bibdate = "Mon Jan 16 18:28:35 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeestd.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
note = "Approved 11 June 2015 by IEEE-SA Standards Board.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7140719",
abstract = "Abstract: This standard species basic interval
arithmetic (IA) operations selecting and following one
of the commonly used mathematical interval models. This
standard supports the IEEE 755 floating-point formats
of practical use in interval computations. Exception
conditions are defined, and standard handling of these
conditions is specified. Consistency with the interval
model is tempered with practical considerations based
on input from representatives of vendors, developers
and maintainers of existing systems. The standard
provides a layer between the hardware and the
programming language levels. It does not mandate that
any operations be implemented in hardware. It does not
define any realization of the basic operations as
functions in a programming language.",
acknowledgement = ack-nhfb,
keywords = "arithmetic; computing; decoration; enclosure; hull;
IEEE 1788; interval; operation; verified",
}
@Article{Jacobsen:2015:PFP,
author = "Charles Jacobsen and Alexey Solovyev and Ganesh
Gopalakrishnan",
title = "A Parameterized Floating-Point Formalizaton in {HOL
Light}",
journal = j-ELECT-NOTES-THEOR-COMP-SCI,
volume = "317",
number = "??",
pages = "1--6",
day = "18",
month = nov,
year = "2015",
DOI = "https://doi.org/10.1016/j.entcs.2015.10.010",
ISSN = "1571-0661",
ISSN-L = "1571-0661",
bibdate = "Fri Apr 17 18:06:24 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also presented at NSV 2015: 8th International Workshop
on Numerical Software Verification 2015, Seattle, WA,
USA.",
URL = "http://formalverification.cs.utah.edu/papers/nsv15-fp-hol-light.pdf;
http://nsv2015.informatik.uni-freiburg.de/",
acknowledgement = ack-nhfb,
fjournal = "Electronic Notes in Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/15710661",
remark = "Not yet listed at journal Web site (up to volume 311
5-Jan-2015).",
xxjournal-url = "http://www.elsevier.nl/locate/entcs",
}
@TechReport{Johansson:2015:ADR,
author = "Fredrik Johansson",
title = "{Arb} Documentation Release 2.6.0",
type = "Report",
institution = "????",
address = "Softwarepark 23, Austria 4113",
day = "19",
month = apr,
year = "2015",
bibdate = "Wed Apr 22 09:04:21 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://fredrikj.net/arb/",
abstract = "Arb is a C library for arbitrary-precision
floating-point ball arithmetic, developed by Fredrik
Johansson ({\tt fredrik.[email protected]}). It
supports real and complex numbers, polynomials, power
series, matrices, and evaluation of many transcendental
functions. All is done with automatic, rigorous error
bounds.",
acknowledgement = ack-nhfb,
remark = "From the Feature Overview: ``Ball arithmetic, also
known as mid-rad interval arithmetic, is an extension
of floating-point arithmetic in which an error bound is
attached to each variable. This allows doing rigorous
computations over the real numbers, while avoiding the
overhead of traditional (inf-sup) interval arithmetic
at high precision, and eliminating much of the need for
time-consuming and bug-prone manual error analysis
associated with standard floating-point arithmetic.''",
}
@InProceedings{Johansson:2015:EIE,
author = "Fredrik Johansson",
title = "Efficient Implementation of Elementary Functions in
the Medium-Precision Range",
crossref = "Muller:2015:ISC",
pages = "83--89",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.16",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Kamm:2015:SFP,
author = "Liina Kamm and Jan Willemson",
title = "Secure floating point arithmetic and private satellite
collision analysis",
journal = j-INT-J-INFO-SEC,
volume = "14",
number = "6",
pages = "531--548",
month = nov,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10207-014-0271-8",
ISSN = "1615-5262 (print), 1615-5270 (electronic)",
ISSN-L = "1615-5262",
bibdate = "Tue Jan 23 16:01:44 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjinfosec.bib",
URL = "http://link.springer.com/article/10.1007/s10207-014-0271-8;
http://link.springer.com/content/pdf/10.1007/s10207-014-0271-8.pdf",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Information Security",
journal-URL = "https://link.springer.com/journal/10207",
}
@Article{Kornerup:2015:RHR,
author = "P. Kornerup",
title = "Reviewing High-Radix Signed-Digit Adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "64",
number = "5",
pages = "1502--1505",
month = may,
year = "2015",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2329678",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jun 4 19:46:44 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@TechReport{Kulisch:2015:HSA,
author = "Ulrich Kulisch and Gerd Bohlender",
title = "High Speed Associative Accumulation of Floating-point
Numbers and Floating-point Intervals",
type = "Report",
institution = "Institut f{\"u}r Angewandte und Numerische Mathematik,
Karlsruher Institut f{\"u}r Technologie",
address = "D-76128 Karlsruhe, Germany",
pages = "8",
day = "21",
month = dec,
year = "2015",
bibdate = "Sat Jan 02 12:26:31 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Distributed to stds-1788 mailing list on Fri, 1 Jan
2016 09:22:19 +0100; as yet unpublished.",
}
@InProceedings{Kumm:2015:ESM,
author = "Martin Kumm and Shahid Abbas and Peter Zipf",
title = "An Efficient Softcore Multiplier Architecture for
{Xilinx FPGAs}",
crossref = "Muller:2015:ISC",
pages = "18--25",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.17",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@PhdThesis{Kupriianova:2015:TMF,
author = "Olga Kupriianova",
title = "Towards a modern floating-point environment",
type = "Th{\`e}se de doctorat",
school = "Universit{\'e} Pierre et Marie Curie --- Paris VI",
address = "Paris, France",
pages = "xi + 130",
year = "2015",
bibdate = "Fri Jan 31 14:59:32 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://pdfs.semanticscholar.org/94ca/770b22739bdcf22fb9f131d9d4665dc28031.pdf",
abstract = "This work investigates two ways of enlarging the
current floating-point environment. The first is to
support several implementation versions of each
mathematical function (elementary such as $ \exp $ or $
\log $ and special such as $ \erf $ or $ \Gamma $), the
second one is to provide IEEE754 operations that mix
the inputs and the output of different radixes. As the
number of various implementations for each mathematical
function is large, this work is focused on code
generation. Our code generator supports the huge
variety of functions: it generates parametrized
implementations for the user-specified functions. So it
may be considered as a black-box function generator.
This work contains a novel algorithm for domain
splitting and an approach to replace branching on
reconstruction by a polynomial. This new domain
splitting algorithm produces less subdomains and the
polynomial degrees on adjacent subdomains do not change
much. To produce vectorizable implementations, if-else
statements on the reconstruction step have to be
avoided. Since the revision of the IEEE754 Standard in
2008 it is possible to mix numbers of different
precisions in one operation. However, there is no
mechanism that allows users to mix numbers of different
radices in one operation. This research starts an
examination of mixed-radix arithmetic with the worst
cases search for FMA. A novel algorithm to convert a
decimal character sequence of arbitrary length to a
binary floating-point number is presented. It is
independent of currently-set rounding mode and produces
correctly-rounded results.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kurka:2015:ERA,
author = "Petr K{\r{u}}rka",
title = "The Exact Real Arithmetical Algorithm in Binary
Continued Fractions",
crossref = "Muller:2015:ISC",
pages = "168--175",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.20",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Langhammer:2015:DIE,
author = "Martin Langhammer and Bogdan Pasca",
title = "Design and Implementation of an Embedded {FPGA}
Floating Point {DSP} Block",
crossref = "Muller:2015:ISC",
pages = "26--33",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.18",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Langroudi:2015:MPP,
author = "Seyed Hamed Fatemi Langroudi and Ghassem Jaberipur",
title = "Modulo-$ (2^n 2^q 1) $ Parallel Prefix Addition via
Excess-Modulo Encoding of Residues",
crossref = "Muller:2015:ISC",
pages = "121--128",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.9",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Laskar:2015:KTN,
author = "Jacques Laskar",
title = "Keynote Talk: Numerical Challenges in Long Term
Integrations of the Solar System",
crossref = "Muller:2015:ISC",
pages = "104--104",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.35",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Abstract only.",
acknowledgement = ack-nhfb,
keywords = "ARITH-22; multiple-precision arithmetic",
}
@InProceedings{Lauter:2015:SAF,
author = "Christoph Lauter and Marc Mezzarobba",
title = "Semi-Automatic Floating-Point Implementation of
Special Functions",
crossref = "Muller:2015:ISC",
pages = "58--65",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.12",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Lee:2015:RRA,
author = "Wen-Chuan Lee and Tao Bao and Yunhui Zheng and Xiangyu
Zhang and Keval Vora and Rajiv Gupta",
title = "{RAIVE}: runtime assessment of floating-point
instability by vectorization",
journal = j-SIGPLAN,
volume = "50",
number = "10",
pages = "623--638",
month = oct,
year = "2015",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2858965.2814299",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Feb 16 12:01:43 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "Floating point representation has limited precision
and inputs to floating point programs may also have
errors. Consequently, during execution, errors are
introduced, propagated, and accumulated, leading to
unreliable outputs. We call this the instability
problem. We propose RAIVE, a technique that identifies
output variations of a floating point execution in the
presence of instability. RAIVE transforms every
floating point value to a vector of multiple values ---
the values added to create the vector are obtained by
introducing artificial errors that are upper bounds of
actual errors. The propagation of artificial errors
models the propagation of actual errors. When values in
vectors result in discrete execution differences (e.g.,
following different paths), the execution is forked to
capture the resulting output variations. Our evaluation
shows that RAIVE can precisely capture output
variations. Its overhead (340\%) is 2.43 times lower
than the state of the art",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "OOPSLA '15 conference proceedings.",
}
@Article{Liu:2015:IBI,
author = "L. Liu and S. Peng and C. Zhang and R. Li and B. Wang
and C. Sun and Q. Liu and L. Dong and L. Li and Y. Shi
and Y. He and W. Zhao and G. Yang",
title = "Importance of bitwise identical reproducibility in
earth system modeling and status report",
journal = "Geoscientific Model Development Discussions",
volume = "8",
number = "6",
pages = "4375--4400",
month = jun,
year = "2015",
DOI = "https://doi.org/10.5194/gmdd-8-4375-2015",
ISSN = "1991-959X (print), 1991-9603 (electronic)",
ISSN-L = "1991-959X",
bibdate = "Mon Feb 10 17:57:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.geosci-model-dev-discuss.net/gmd-2015-83/",
abstract = "Reproducibility is a fundamental principle of
scientific research. Bitwise identical reproducibility,
i.e., bitwise computational results can be reproduced,
guarantees the reproduction of exactly the same
results. Here we show the importance of bitwise
identical reproducibility to Earth system modeling but
the importance has not yet been widely recognized.
Modeled mean climate states, variability and trends at
different scales may be significantly changed or even
lead to opposing results due to a slight change in the
original simulation setting during a reproduction. Out
of the large body of Earth system modeling
publications, few thoroughly describe the whole
original simulation setting. As a result, the
reproduction of a particular simulation experiment by
fellow scientists heavily depends on the interaction
with the original authors, which is often inconvenient
or even impossible. We anticipate bitwise identical
reproducibility to be promoted as a worldwide standard,
to guarantee the independent reproduction of simulation
results and to further improve model development and
scientific research.",
acknowledgement = ack-nhfb,
journal-URL = "https://www.geosci-model-dev.net/volumes.html",
}
@Article{Liu:2015:SSS,
author = "Weifeng Liu and Brian Vinter",
title = "Speculative segmented sum for sparse matrix-vector
multiplication on heterogeneous processors",
journal = j-PARALLEL-COMPUTING,
volume = "49",
number = "??",
pages = "179--193",
month = nov,
year = "2015",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/j.parco.2015.04.004",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Thu Oct 29 17:53:44 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167819115000770",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191/",
}
@Article{Lu:2015:REP,
author = "Xin Lu and Shufang Xu",
title = "Rounding errors of partial derivatives of simple
eigenvalues of the quadratic eigenvalue problem",
journal = j-J-COMPUT-APPL-MATH,
volume = "282",
number = "??",
pages = "268--277",
month = jul,
year = "2015",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:34:50 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042715000151",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Lutz:2015:OLZ,
author = "David Raymond Lutz",
title = "Optimized leading zero anticipators for faster fused
multiply-adds",
crossref = "Matthews:2017:CRF",
pages = "741--744",
year = "2015",
DOI = "https://doi.org/10.1109/ACSSC.2017.8335443",
bibdate = "Mon Feb 10 08:39:02 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/8335443/",
acknowledgement = ack-nhfb,
}
@Article{Martin-Dorel:2015:FVC,
author = "{\'E}rik Martin-Dorel and Guillaume Hanrot and Micaela
Mayero and Laurent Th{\'e}ry",
title = "Formally Verified Certificate Checkers for
Hardest-to-Round Computation",
journal = j-J-AUTOM-REASON,
volume = "54",
number = "1",
pages = "1--29",
month = jan,
year = "2015",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-014-9312-2",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Sat Apr 2 10:51:12 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "http://link.springer.com/article/10.1007/s10817-014-9312-2",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
}
@Article{Matula:2015:MDE,
author = "D. W. Matula and M. T. Panu and J. Y. Zhang",
title = "Multiplicative Division Employing Independent
Factors",
journal = j-IEEE-TRANS-COMPUT,
volume = "64",
number = "7",
pages = "2012--2019",
month = "????",
year = "2015",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2346206",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Aug 1 08:53:41 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{McCleeary:2015:LAA,
author = "Ryan McCleeary and Martin Brain and Aaron Stump",
title = "A lazy approach to adaptive exact real arithmetic
using floating-point operations",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "49",
number = "3",
pages = "83--86",
month = sep,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2850449.2850456",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Wed Dec 2 14:16:56 MST 2015",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
abstract = "Arithmetic operations with high degrees of precision
are needed for an increasing number of applications. We
propose an exact real arithmetic system that achieves
adaptive precision using lazy infinite lists of
floating-point values.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Meloni:2015:EDB,
author = "N. Meloni and M. A. Hasan",
title = "Efficient Double Bases for Scalar Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "64",
number = "8",
pages = "2204--2212",
month = aug,
year = "2015",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2360539",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Aug 11 08:24:23 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "double-base number system; elliptic curve",
}
@Article{Michelogiannakis:2015:ESP,
author = "George Michelogiannakis and Xiaoye S. Li",
title = "Extending Summation Precision for Network Reduction
Operations",
journal = j-INT-J-PARALLEL-PROG,
volume = "43",
number = "6",
pages = "1218--1243",
month = dec,
year = "2015",
CODEN = "IJPPE5",
DOI = "https://doi.org/10.1007/s10766-014-0326-5",
ISSN = "0885-7458 (print), 1573-7640 (electronic)",
ISSN-L = "0885-7458",
bibdate = "Tue Sep 29 10:13:48 MDT 2015",
bibsource = "http://link.springer.com/journal/10766/43/6;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjparallelprogram.bib",
URL = "http://link.springer.com/article/10.1007/s10766-014-0326-5",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Parallel Programming",
journal-URL = "http://link.springer.com/journal/10766",
keywords = "accurate floating-point summation",
}
@Article{Momeni:2015:DAA,
author = "A. Momeni and Jie Han and P. Montuschi and F.
Lombardi",
title = "Design and Analysis of Approximate Compressors for
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "64",
number = "4",
pages = "984--994",
month = apr,
year = "2015",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2014.2308214",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jun 4 19:46:38 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Morar:2015:RMT,
author = "Florin-Stefan Morar",
title = "Reinventing machines: the transmission history of the
{Leibniz} calculator",
journal = j-BRITISH-J-HIST-SCI,
volume = "48",
number = "1",
pages = "123--146",
month = mar,
year = "2015",
CODEN = "BJHSAT",
DOI = "https://doi.org/10.1017/S0007087414000429",
ISSN = "0007-0874 (print), 1474-001X (electronic)",
ISSN-L = "0007-0874",
bibdate = "Wed Feb 4 10:40:51 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bjhs2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "British J. Hist. Sci.",
fjournal = "British Journal for the History of Science",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BJH",
onlinedate = "Mon Jul 14 00:00:00 BST 2014",
}
@Article{Muller:2015:ECC,
author = "Jean-Michel Muller",
title = "On the Error of Computing $ a b + c d $ using
{Cornea}, {Harrison} and {Tang}'s Method",
journal = j-TOMS,
volume = "41",
number = "2",
pages = "7:1--7:8",
month = jan,
year = "2015",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2629615",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Feb 4 17:49:11 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "In their book, \booktitle{Scientific Computing on the
Itanium}, Cornea et al. [2002] introduce an accurate
algorithm for evaluating expressions of the form $ a b
+ c d $ in binary floating-point arithmetic, assuming
an FMA instruction is available. They show that if $p$
is the precision of the floating-point format and if $
u = 2^{-p} $, the relative error of the result is of
order $u$. We improve their proof to show that the
relative error is bounded by $ 2 u + 7 u^2 + 6 u^3 $.
Furthermore, by building an example for which the
relative error is asymptotically (as $ p \to \infty $
or, equivalently, as $ u \to 0 $) equivalent to $ 2 u
$, we show that our error bound is asymptotically
optimal.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
remark = "This article compares two algorithms (Kahan's and
Cornea / Harrison / Tang's) for computing $ a b + c d
$. It shows that the worst-case error with FMA and
round-to-nearest arithmetic is $ 2 u $ for the first,
and $ 2 u + 7 u^2 + 6 u^3 $ for the second, suggesting
that Kahan's is preferred. However, the second
guarantees that $ a b + c d = = c d + a b $, whereas
the first does not, so it may be preferred for
applications like complex multiplication and division,
in order to guarantee commutative arithmetic",
}
@TechReport{Neal:2015:FESa,
author = "Radford M. Neal",
title = "Fast exact summation using small and large
superaccumulators",
type = "Report",
institution = "Department of Statistical Sciences and Department of
Computer Science, University of Toronto",
address = "Toronto, ON, Canada",
pages = "22",
year = "2015",
bibdate = "Sat Oct 31 07:19:27 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://www.cs.toronto.edu/~radford/ftp/xsum.pdf",
acknowledgement = ack-nhfb,
}
@Article{Neal:2015:FESb,
author = "Radford M. Neal",
title = "Fast exact summation using small and large
superaccumulators",
journal = "arxiv.org",
pages = "22",
year = "2015",
bibdate = "Sat Oct 31 07:19:27 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "https://arxiv.org/pdf/1505.05571v1.pdf",
abstract = "I present two new methods for exactly summing a set of
floating-point numbers, and then correctly rounding to
the nearest floating-point number. Higher accuracy than
simple summation (rounding after each addition) is
important in many applications, such as finding the
sample mean of data. Exact summation also guarantees
identical results with parallel and serial
implementations, since the exact sum is independent of
order. The new methods use variations on the concept of
a ``superaccumulator'' --- a large fixed-point number
that can exactly represent the sum of any reasonable
number of floating-point values. One method uses a
``small'' superaccumulator with sixty-seven 64-bit
chunks, each with 32-bit overlap with the next chunk,
allowing carry propagation to be done infrequently. The
small superaccumulator is used alone when summing a
small number of terms. For big summations, a ``large''
superaccumulator is used as well. It consists of 4096
64-bit chunks, one for every possible combination of
exponent bits and sign bit, plus counts of when each
chunk needs to be transferred to the small
superaccumulator. To add a term to the large
superaccumulator, only a single chunk and its
associated count need to be updated, which takes very
few instructions if carefully implemented. On modern
64-bit processors, exactly summing a large array using
this combination of large and small superaccumulators
takes less than twice the time of simple, inexact,
ordered summation, with a serial implementation. A
parallel implementation using a small number of
processor cores can be expected to perform exact
summation of large arrays at a speed that reaches the
limit imposed by memory bandwidth. Some common methods
that attempt to improve accuracy without being exact
may therefore be pointless, at least for large
summations, since they are slower than computing the
sum exactly.",
acknowledgement = ack-nhfb,
}
@InProceedings{Negre:2015:EME,
author = "Christophe Negre and Thomas Plantard and Jean-Marc
Robert",
title = "Efficient Modular Exponentiation Based on Multiple
Multiplications by a Common Operand",
crossref = "Muller:2015:ISC",
pages = "144--151",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.24",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Nguyen:2015:RTS,
author = "Hong Diep Nguyen and James Demmel",
title = "Reproducible Tall-Skinny {QR}",
crossref = "Muller:2015:ISC",
pages = "152--159",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.28",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bebop.cs.berkeley.edu/reproblas/docs/papers/RepTSQR.pdf",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Ozaki:2015:IEF,
author = "Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi
Oishi",
title = "Improvement of error-free splitting for accurate
matrix multiplication",
journal = j-J-COMPUT-APPL-MATH,
volume = "288",
number = "??",
pages = "127--140",
month = nov,
year = "2015",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 13:34:52 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042715002289",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Palmer:2015:MBI,
author = "Tim Palmer",
title = "Modelling: Build imprecise supercomputers",
journal = j-NATURE,
volume = "526",
number = "7571",
pages = "32--33",
day = "29",
month = sep,
year = "2015",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/526032a",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Sat Mar 25 18:29:10 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
remark = "This provocative paper argues that future
supercomputers should be built with a small number of
processors that can do accurate high-precision
floating-point arithmetic, with the bulk of
computations carried out, to save energy, at lower
precision, and possibly with occasional arithmetic
errors. I [NHFB] find that a perilous approach that
would likely lead to entirely unrepeatable, and thus,
almost certainly useless, computations to which it is
impossible to apply sensible numerical analysis.!",
}
@Article{Panchekha:2015:AIA,
author = "Pavel Panchekha and Alex Sanchez-Stern and James R.
Wilcox and Zachary Tatlock",
title = "Automatically improving accuracy for floating point
expressions",
journal = j-SIGPLAN,
volume = "50",
number = "6",
pages = "1--11",
month = jun,
year = "2015",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2813885.2737959",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Tue Feb 16 12:01:41 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "Scientific and engineering applications depend on
floating point arithmetic to approximate real
arithmetic. This approximation introduces rounding
error, which can accumulate to produce unacceptable
results. While the numerical methods literature
provides techniques to mitigate rounding error,
applying these techniques requires manually rearranging
expressions and understanding the finer details of
floating point arithmetic. We introduce Herbie, a tool
which automatically discovers the rewrites experts
perform to improve accuracy. Herbie's heuristic search
estimates and localizes rounding error using sampled
points (rather than static error analysis), applies a
database of rules to generate improvements, takes
series expansions, and combines improvements for
different input regions. We evaluated Herbie on
examples from a classic numerical methods textbook, and
found that Herbie was able to improve accuracy on each
example, some by up to 60 bits, while imposing a median
performance overhead of 40\%. Colleagues in machine
learning have used Herbie to significantly improve the
results of a clustering algorithm, and a mathematical
library has accepted two patches generated using
Herbie.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "PLDI '15 conference proceedings.",
}
@Article{Parhami:2015:DAN,
author = "Behrooz Parhami",
title = "Digital Arithmetic in Nature: Continuous-Digit {RNS}",
journal = j-COMP-J,
volume = "58",
number = "5",
pages = "1214--1223",
month = may,
year = "2015",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxu060",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Sat May 2 08:05:35 MDT 2015",
bibsource = "http://comjnl.oxfordjournals.org/content/58/5.toc;
https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://comjnl.oxfordjournals.org/content/58/5/1214",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "Residue Number System (RNS)",
onlinedate = "July 17, 2014",
}
@InProceedings{Patil:2015:OFP,
author = "Vinayak Patil and Aneesh Raveendran and P. M. Sobha
and A. David Selvakumar and D. Vivian",
editor = "{IEEE}",
booktitle = "{2015 19th International Symposium on VLSI Design and
Test}",
title = "Out of order floating point coprocessor for {RISC V
ISA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--7",
year = "2015",
DOI = "https://doi.org/10.1109/ISVDAT.2015.7208116",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@Article{Peeper:2015:DDP,
author = "D. Peeper",
title = "Deep-dish peeper [The Big Picture]",
journal = j-IEEE-SPECTRUM,
volume = "52",
number = "11",
pages = "16--17",
month = nov,
year = "2015",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2015.7335888",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 07:02:09 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "FAST; five-hundred-meter aperture spherical radio
telescope; floating point operations; Puerto Rico;
radiotelescopes",
}
@InProceedings{Proust:2015:KTC,
author = "Christine Proust",
title = "Keynote Talk: Calculating in Floating Sexagesimal
Place Value Notation, 4000 years ago",
crossref = "Muller:2015:ISC",
pages = "1--1",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.33",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Abstract only.",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Renardy:2015:HIM,
author = "Antonius P. Renardy and Nur Ahmadi and Ashbir A.
Fadila and Naufal Shidqi and Trio Adiono",
editor = "{IEEE}",
booktitle = "2015 International Seminar on Intelligent Technology
and Its Applications {(ISITIA)}: proceeding: {Surabaya,
Indonesia, 20--21 May 2015}",
title = "Hardware Implementation of {Montgomery} Modular
Multiplication Algorithm Using Iterative Architecture",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "453",
pages = "99--102",
year = "2015",
DOI = "https://doi.org/10.1109/ISITIA.2015.7219961",
ISBN = "1-4799-7711-X",
ISBN-13 = "978-1-4799-7711-6",
LCCN = "TA347.A78",
bibdate = "Tue Jul 06 18:27:11 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Modular multiplication is an integral part of RSA
cryptosystems and its performance heavily determines
the performance of the encryption hardware. This paper
provides a hardware implementation of Montgomery's
modular multiplication algorithm using iterative
architecture. The proposed design is implemented in
Verilog HDL and simulated functionally using ModelSim
Altera 10.1E. The synthesis is performed using Altera
Quartus II 9.1 with target FPGA board Altera DE2-70.
The proposed design consumes 17540 logic elements with
15480 LUT and takes 2048 clock cycles to perform
multiplication process. Based on trade-off parameter
AT$^2$ measure, the proposed design offers the best
performance among other designs.",
acknowledgement = ack-nhfb,
keywords = "FPGA; Iterative Architecture; Modular Multiplication;
Montgomery's Algorithm; RSA Cryptosystem",
}
@Article{Roegel:2015:MCA,
author = "Denis Roegel",
title = "A Mechanical Calculator for Arithmetic Sequences
(1844--1852): Part 1, Historical Context and
Structure",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "37",
number = "4",
pages = "90--96",
month = "????",
year = "2015",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/MAHC.2015.79",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
bibdate = "Tue Dec 8 07:02:44 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}
@Book{Ruckert:2015:MSS,
author = "Martin Ruckert",
title = "The {MMIX} supplement: supplement to {{\booktitle{The
Art of Computer Programming, volumes 1, 2, 3}} by
Donald E. Knuth}",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xxi + 193",
year = "2015",
ISBN = "0-13-399231-4 (paperback), 0-13-399289-6",
ISBN-13 = "978-0-13-399231-1 (paperback), 978-0-13-399289-2",
LCCN = "QA76.6 .K64 2005 Suppl. 1",
bibdate = "Wed Feb 4 10:19:23 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hash.bib;
https://www.math.utah.edu/pub/tex/bib/litprog.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/string-matching.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://mmix.cs.hm.edu/",
abstract = "In the first edition of Volume 1 of The Art of
Computer Programming, Donald E. Knuth introduced the
MIX computer and its machine language: a teaching tool
that powerfully illuminated the inner workings of the
algorithms he documents. Later, with the publication of
his Fascicle 1, Knuth introduced MMIX: a modern, 64-bit
RISC replacement to the now-obsolete MIX. Now, with
Knuth's guidance and approval, Martin Ruckert has
rewritten all MIX example programs from Knuth's Volumes
1--3 for MMIX, thus completing this MMIX update to the
original classic.\par
From Donald E. Knuth's Foreword:\par
``I am thrilled to see the present book by Martin
Ruckert: It is jam-packed with goodies from which an
extraordinary amount can be learned. Martin has not
merely transcribed my early programs for MIX and recast
them in a modern idiom. He has penetrated to their
essence and rendered them anew with elegance and good
taste. His carefully checked code represents a
significant contribution to the art of pedagogy as well
as to the art of programming.''",
acknowledgement = ack-nhfb,
libnote = "Not yet in my library.",
subject = "MMIX (Computer architecture); Assembly languages
(Electronic computers); Microcomputers; Programming",
tableofcontents = "Foreword / iii \\
Preface / v \\
Style Guide / viii \\
Programming Techniques / xii \\
Basic Concepts / 1 \\
Applications to Permutations / 1 \\
Input and Output / 8 \\
Information Structures / 15 \\
Introduction / 15 \\
Sequential Allocation / 17 \\
Linked Allocation / 18 \\
Circular Lists / 25 \\
Doubly Linked Lists / 27 \\
Arrays and Orthogonal Lists / 36 \\
Traversing Binary Trees / 37 \\
Binary Tree Representation of Trees / 39 \\
Other Representations of Trees / 43 \\
Lists and Garbage Collection / 44 \\
Dynamic Storage Allocation / 45 \\
Random Numbers / 48 \\
Choice of modulus / 48 \\
Potency / 49 \\
Other Methods / 50 \\
Numerical Distributions / 51 \\
Summary / 52 \\
Arithmetic / 53 \\
Positional Number Systems / 53 \\
Single-Precision Calculations / 53 \\
Accuracy of Floating Point Arithmetic / 58 \\
Double-Precision Calculations / 58 \\
The Classical Algorithms / 62 \\
Radix Conversion / 68 \\
The Greatest Common Divisor / 70 \\
Analysis of Euclid's Algorithm / 71 \\
Factoring into Primes / 72 \\
Evaluation of Powers / 72 \\
Evaluation of Polynomials / 73 \\
Sorting / 74 \\
Internal Sorting / 74 \\
Sorting by Insertion / 76 \\
Sorting by Exchanging / 81 \\
Sorting by Selection / 87 \\
Sorting by Merging / 89 \\
Sorting by Distribution / 93 \\
Minimum-Comparison Sorting / 94 \\
Summary, History and Bibliography / 95 \\
Searching / 97 \\
Sequential Searching / 97 \\
Searching an Ordered Table / 99 \\
Binary Tree Searching / 102 \\
Balanced Trees / 103 \\
Digital Searching / 106 \\
Hashing / 108 \\
Answers to Exercises / 117 \\
The MMIX Assembly Language / 117 \\
Applications to Permutations / 120 \\
Input and Output / 120 \\
Introduction / 122 \\
Sequential Allocation / 123 \\
Linked Allocation / 124 \\
Circular Lists / 128 \\
Doubly Linked Lists / 130 \\
Arrays and Orthogonal Lists / 132 \\
Traversing Binary Trees / 134 \\
Binary Tree Representation of Trees / 136 \\
Lists and Garbage Collection / 139 \\
Dynamic Storage Allocation / 140 \\
Choice of modulus / 147 \\
Potency / 148 \\
Other Methods / 148 \\
Numerical Distributions / 149 \\
Summary / 150 \\
Positional Number Systems / 150 \\
Single-Precision Calculations / 151 \\
Accuracy of Floating Point Arithmetic / 152 \\
Double-Precision Calculations / 153 \\
The Classical Algorithms / 156 \\
Radix Conversion / 158 \\
The Greatest Common Divisor / 160 \\
Analysis of Euclid's Algorithm / 160 \\
Evaluation of Powers / 161 \\
Evaluation of Polynomials / 161 \\
Sorting / 162 \\
Internal Sorting / 162 \\
Sorting by Insertion / 165 \\
Sorting by Exchanging / 169 \\
Sorting by Selection / 174 \\
Sorting by Distribution / 179 \\
Minimum-Comparison Sorting / 180 \\
Summary, History, and Bibliography / 183 \\
Sequential Searching / 183 \\
Searching an Ordered Table / 184 \\
Binary Tree Searching / 185 \\
Balanced Trees / 185 \\
Digital Searching / 186 \\
Hashing / 186 \\
Acknowledgements / 188 \\
Index / 189",
}
@Article{Seo:2015:MMS,
author = "Hwajeong Seo and Zhe Liu and Yasuyuki Nogami and
Jongseok Choi and Howon Kim",
title = "{Montgomery} multiplication and squaring for Optimal
Prime Fields",
journal = j-COMPUT-SECUR,
volume = "52",
number = "??",
pages = "276--291",
month = jul,
year = "2015",
CODEN = "CPSEDU",
ISSN = "0167-4048 (print), 1872-6208 (electronic)",
ISSN-L = "0167-4048",
bibdate = "Mon Sep 23 09:46:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computsecur2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S0167404815000371",
acknowledgement = ack-nhfb,
fjournal = "Computers \& Security",
journal-URL = "https://www.sciencedirect.com/science/journal/01674048",
}
@TechReport{Solovyev:2015:REFa,
author = "Alexey Solovyev and Charles Jacobsen and Zvonimir
Rakamari{\'c} and Ganesh Gopalakrishnan",
title = "Rigorous Estimation of Floating-Point Round-off Errors
with Symbolic {Taylor} Expansions",
type = "Technical Report",
number = "UUCS-15-001",
institution = "School of Computing, University of Utah",
address = "Salt Lake City, UT 84112 USA",
pages = "31",
day = "6",
month = apr,
year = "2015",
bibdate = "Fri Apr 17 18:02:17 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://formalverification.cs.utah.edu/papers/fptaylor_report.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Solovyev:2015:REFb,
author = "Alexey Solovyev and Charles Jacobsen and Zvonimir
Rakamari{\'c} and Ganesh Gopalakrishnan",
booktitle = "{20th International Symposium on Formal Methods (FM
2015), Oslo, Norway}",
title = "Rigorous Estimation of Floating-Point Round-off Errors
with Symbolic {Taylor} Expansions",
publisher = pub-SV,
address = pub-SV:adr,
pages = "532--550",
day = "6",
month = jun,
year = "2015",
bibdate = "Fri Apr 17 18:02:17 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Extended version available in
\cite{Solovyev:2015:REFa}.",
URL = "http://formalverification.cs.utah.edu/papers/fptaylor_report.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Sullivan:2015:LCD,
author = "Michael B. Sullivan and Earl E. Swartzlander",
title = "Low-Cost Duplicate Multiplication",
crossref = "Muller:2015:ISC",
pages = "2--9",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.29",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Thomas:2015:GPM,
author = "David B. Thomas",
title = "A General-Purpose Method for Faithfully Rounded
Floating-Point Function Approximation in {FPGAs}",
crossref = "Muller:2015:ISC",
pages = "42--49",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.27",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Article{Trefethen:2015:CNF,
author = "Lloyd N. Trefethen",
title = "Computing numerically with functions instead of
numbers",
journal = j-CACM,
volume = "58",
number = "10",
pages = "91--97",
month = oct,
year = "2015",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/2814847",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Sep 30 07:29:42 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "http://cacm.acm.org/magazines/2015/10/192390/fulltext",
abstract = "Science and engineering depend upon computation of
functions such as flow fields, charge distributions,
and quantum states. Ultimately, such computations
require some kind of discretization, but in recent
years, it has become possible in many cases to hide the
discretizations from the user. We present the Chebfun
system for numerical computation with functions, which
is based on a key idea: an analogy of floating-point
arithmetic for functions rather than numbers.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Chebfun; Chebyshev approximation; floating-point
arithmetic; Matlab; rational arithmetic; symbolic
algebra",
}
@InProceedings{vanderHoeven:2015:FFM,
author = "Joris van der Hoeven and Gr{\'e}goire Lecerf",
title = "Faster {FFTs} in Medium Precision",
crossref = "Muller:2015:ISC",
pages = "75--82",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.10",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@InProceedings{Volkova:2015:REW,
author = "Anastasia Volkova and Thibault Hilaire and Christoph
Lauter",
title = "Reliable Evaluation of the Worst-Case Peak Gain Matrix
in Multiple Precision",
crossref = "Muller:2015:ISC",
pages = "96--103",
year = "2015",
DOI = "https://doi.org/10.1109/ARITH.2015.14",
bibdate = "Sat Aug 01 08:05:52 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-22",
}
@Misc{Wilczak:2015:CAP,
author = "Daniel Wilczak and others",
title = "Computer Assisted Proofs in Dynamics",
howpublished = "Web site and software.",
month = jun,
year = "2015",
bibdate = "Wed Jun 17 11:30:51 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://sourceforge.net/projects/capd/",
acknowledgement = ack-nhfb,
remark = "From the Web site: ``The CAPD library is a collection
of flexible C++ modules which are mainly designed to
computation of homology of sets and maps and
nonrigorous and validated numerics for dynamical
systems.'' From the announcement on the Reliable
Computing mailing list on 14-Jun-2015: ``In 2015, the
library has over 100,000 lines of code. It provides
rigorous solvers for ODEs, variational equations for
ODEs, differential inclusions, automatic computation of
Poincare maps and their derivatives, computation of
homology of spaces, maps and many other features. Its
efficiency is confirmed by several nontrivial results
in dynamics, including proving of chaos, presence of
local and global bifurcations for ODEs, existence of
attractors for ODEs, periodic orbits for PDEs, and many
other results.\par
The library comes with a comprehensive tutorial with
many examples illustrating very basic usage of CAPD as
well as quite advanced, like a complete computer
assisted proof of the existence of attractor in the
Rossler system with uniformly hyperbolic and chaotic
invariant set.''",
}
@Article{Wittmann:2015:SNC,
author = "Markus Wittmann and Thomas Zeiser and Georg Hager and
Gerhard Wellein",
title = "Short Note on Costs of Floating Point Operations on
current x86-64 Architectures: Denormals, Overflow,
Underflow, and Division by Zero",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "12",
month = jun,
year = "2015",
CODEN = "????",
ISSN = "????",
ISSN-L = "????",
bibdate = "Wed Sep 30 12:43:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1506.03997",
abstract = "Simple floating point operations like addition or
multiplication on normalized floating point values can
be computed by current AMD and Intel processors in
three to five cycles. This is different for
denormalized numbers, which appear when an underflow
occurs and the value can no longer be represented as a
normalized floating-point value. Here the costs are
about two magnitudes higher.",
acknowledgement = ack-nhfb,
subject = "Performance (cs.PF)",
}
@Article{Yamazaki:2015:MPC,
author = "Ichitaro Yamazaki and Stanimire Tomov and Jack
Dongarra",
title = "Mixed-Precision {Cholesky} {$ Q R $} Factorization and
Its Case Studies on Multicore {CPU} with Multiple
{GPUs}",
journal = j-SIAM-J-SCI-COMP,
volume = "37",
number = "3",
pages = "C307--C330",
month = "????",
year = "2015",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/14M0973773",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Sat Aug 8 06:48:44 MDT 2015",
bibsource = "http://epubs.siam.org/toc/sjoce3/37/3;
https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2015",
}
@InProceedings{Ahmed:2016:ILM,
author = "Syed Ershad Ahmed and Sanket Kadam and M. B.
Srinivas",
title = "An Iterative Logarithmic Multiplier with Improved
Precision",
crossref = "Montuschi:2016:ISC",
pages = "104--111",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.25",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@TechReport{Ahrens:2016:ERF,
author = "Peter Ahrens and Hong Diep Nguyen and James Demmel",
title = "Efficient Reproducible Floating Point Summation and
{BLAS}",
type = "Report",
number = "UCB/EECS-2016-121",
institution = "EECS Department, UC Berkeley",
address = "Berkeley, CA, USA",
day = "18",
month = jun,
year = "2016",
bibdate = "Wed Oct 12 18:31:23 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.eecs.berkeley.edu/Pubs/TechRpts/2016/EECS-2016-121.html",
acknowledgement = ack-nhfb,
keywords = "accurate dot product; accurate summation",
}
@InProceedings{Almeida:2016:VCT,
author = "Jos{\'e} Bacelar Almeida and Manuel Barbosa and Gilles
Barthe and Fran{\c{c}}ois Dupressoir and Michael Emmi",
editor = "T. Holz and S. Savage",
booktitle = "Proceedings of the {25th USENIX Security 2016, August
10--12, 2016, Austin, TX}",
title = "Verifying Constant-Time Implementations",
publisher = pub-USENIX,
address = pub-USENIX:adr,
pages = "53--70",
year = "2016",
bibdate = "Tue Aug 27 06:44:12 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://github.com/kmowery/libfixedtimefixedpoint;
https://www.usenix.org/system/files/conference/usenixsecurity16/sec16_paper_almeida.pdf",
abstract = "The constant-time programming discipline is an
effective countermeasure against timing attacks, which
can lead to complete breaks of otherwise secure
systems. However, adhering to constant-time programming
is hard on its own, and extremely hard under additional
efficiency and legacy constraints. This makes automated
verification of constant-time code an essential
component for building secure software.\par
We propose a novel approach for verifying constant-time
security of real-world code. Our approach is able to
validate implementations that locally and intentionally
violate the constant-time policy, when such violations
are benign and leak no more information than the public
outputs of the computation. Such implementations, which
are used in cryptographic libraries to obtain important
speedups or to comply with legacy APIs, would be
declared insecure by all prior solutions.\par
We implement our approach in a publicly available,
cross-platform, and fully automated prototype,
ct-verif, that leverages the SMACK and Boogie tools and
verifies optimized LLVM implementations. We present
verification results obtained over a wide range of
constant-time components from the NaCl, OpenSSL, FourQ
and other off-the-shelf libraries. The diversity and
scale of our examples, as well as the fact that we deal
with top-level APIs rather than being limited to
low-level leaf functions, distinguishes ct-verif from
prior tools.\par
Our approach is based on a simple reduction of
constant-time security of a program $P$ to safety of a
product program $Q$ that simulates two executions of
$P$. We formalize and verify the reduction for a core
high-level language using the Coq proof assistant.",
acknowledgement = ack-nhfb,
keywords = "elliptic curve arithmetic; fixed-point arithmetic;
libfixedtimefixedpoint",
}
@Article{Andrysco:2016:PFP,
author = "Marc Andrysco and Ranjit Jhala and Sorin Lerner",
title = "Printing floating-point numbers: a faster, always
correct method",
journal = j-SIGPLAN,
volume = "51",
number = "1",
pages = "555--567",
month = jan,
year = "2016",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/2914770.2837654",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Thu Jun 9 17:13:57 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "Floating-point numbers are an essential part of modern
software, recently gaining particular prominence on the
web as the exclusive numeric format of Javascript. To
use floating-point numbers, we require a way to convert
binary machine representations into human readable
decimal outputs. Existing conversion algorithms make
trade-offs between completeness and performance. The
classic Dragon4 algorithm by Steele and White and its
later refinements achieve completeness --- i.e. produce
correct and optimal outputs on all inputs --- by using
arbitrary precision integer (bignum) arithmetic which
leads to a high performance cost. On the other hand,
the recent Grisu3 algorithm by Loitsch shows how to
recover performance by using native integer arithmetic
but sacrifices optimality for 0.5\% of all inputs. We
present Errol, a new complete algorithm that is
guaranteed to produce correct and optimal results for
all inputs while simultaneously being 2x faster than
the incomplete Grisu3 and 4x faster than previous
complete methods.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "POPL '16 conference proceedings.",
}
@InProceedings{Anonymous:2016:KTS,
author = "Anonymous",
title = "{Keynote} talks and special sessions",
crossref = "Montuschi:2016:ISC",
pages = "xv--xxi",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.33",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Area:2016:ACS,
author = "Iv{\'a}n Area and Dimitar K. Dimitrov and Eduardo
Godoy and Vanessa G. Paschoa",
title = "Approximate Calculation of Sums {II}: {Gaussian} Type
Quadrature",
journal = j-SIAM-J-NUMER-ANAL,
volume = "54",
number = "4",
pages = "2210--2227",
month = "????",
year = "2016",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/140993752",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Sep 23 11:00:53 MDT 2016",
bibsource = "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/54/4;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "Chebfun",
onlinedate = "January 2016",
}
@Article{Avenel:2016:STM,
author = "Christophe Avenel and Pierre Fortin and Mourad Gouicem
and Samia Zaidi",
title = "Solving the {Table Maker}'s Dilemma on Current {SIMD}
Architectures",
journal = j-SCPE,
volume = "17",
number = "3",
pages = "237--250",
month = "????",
year = "2016",
CODEN = "????",
ISSN = "1895-1767",
ISSN-L = "1895-1767",
bibdate = "Mon Jan 7 06:46:48 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scpe.bib",
URL = "https://www.scpe.org/index.php/scpe/article/view/1183",
acknowledgement = ack-nhfb,
fjournal = "Scalable Computing: Practice and Experience",
journal-URL = "http://www.scpe.org/",
}
@Article{Bagnara:2016:EBF,
author = "Roberto Bagnara and Matthieu Carlier and Roberta Gori
and Arnaud Gotlieb",
title = "Exploiting binary floating-point representations for
constraint propagation",
journal = j-INFORMS-J-COMPUT,
volume = "28",
number = "1",
pages = "31--46",
month = "Winter",
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1287/ijoc.2015.0663",
ISSN = "1091-9856 (print), 1526-5528 (electronic)",
ISSN-L = "1091-9856",
MRclass = "68M07 (65Y04 68W40)",
MRnumber = "3461544",
bibdate = "Mon Apr 9 08:22:11 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/informs-j-comput.bib",
URL = "https://pubsonline.informs.org/doi/abs/10.1287/ijoc.2015.0663",
acknowledgement = ack-nhfb,
ajournal = "INFORMS J. Comput.",
fjournal = "INFORMS Journal on Computing",
journal-URL = "https://pubsonline.informs.org/journal/ijoc",
onlinedate = "January 21, 2016",
}
@InCollection{Bailey:2016:FRS,
author = "David H. Bailey and Jonathan M. Borwein and Victoria
Stodden",
editor = "Harald Atmanspacher and Sabine Maasen",
booktitle = "Reproducibility: Principles, Problems, Practices, and
Prospects",
title = "Facilitating Reproducibility in Scientific Computing:
Principles and Practice",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "205--231",
year = "2016",
DOI = "https://doi.org/10.1002/9781118865064.ch9",
ISBN = "1-118-86506-5",
ISBN-13 = "978-1-118-86506-4",
bibdate = "Thu Aug 11 11:01:49 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This chapter discusses the roots of the
reproducibility problem in scientific computing, and
summarizes some possible solutions that have been
suggested in the community. Statistical overfitting can
be thought of as an instance of ``selection bias'',
wherein one presents the results of only those tests
that support well one's hypothesis. The problem of
statistical overfitting in computational science is
perhaps best illustrated in the field of mathematical
finance. Present-day researchers are not as fully aware
of the potential pitfalls of performance reporting. In
any event, various high-performance computing
researchers have noted a resurrection of some of these
questionable practices. Using high-precision arithmetic
(higher than the standard IEEE 64-bit arithmetic) is
often quite useful in ameliorating numerical
difficulties and enhancing reproducibility. Very
high-precision floating-point arithmetic is essential
to obtain reproducible results in experimental
mathematics and in related mathematical physics
applications. The chapter also discusses
reproducibility in symbolic computing.",
acknowledgement = ack-nhfb,
author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
2016)",
keywords = "high-performance computing; high-precision arithmetic;
mathematical physics; numerical reproducibility;
performance reporting; scientific computing;
statistical overfitting; symbolic computing",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
xxnote = "This book was awarded the 2017 Prose Award
(``Honorable Mention'') in the category ``Textbook /
Best in Physical Sciences and Mathematics''; see
\url{https://proseawards.com/winners/2017-award-winners/}
and
\url{http://experimentalmath.org/2017/02/reproducibility-principles-problems-practices-and-prospects/}.",
}
@InProceedings{Bajard:2016:MFA,
author = "Jean-Claude Bajard and Julien Eynard and Nabil
Merkiche",
title = "Multi-fault Attack Detection for {RNS} Cryptographic
Architecture",
crossref = "Montuschi:2016:ISC",
pages = "16--23",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.16",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Ballard:2016:INS,
author = "Grey Ballard and Austin R. Benson and Alex Druinsky
and Benjamin Lipshitz and Oded Schwartz",
title = "Improving the Numerical Stability of Fast Matrix
Multiplication",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "37",
number = "4",
pages = "1382--1418",
month = "????",
year = "2016",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/15M1032168",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Aug 25 09:01:43 MDT 2017",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2016",
}
@Misc{BEBOP:2016:RRB,
author = "{Berkeley Benchmarking and OPtimization Group
(BEBOP)}",
title = "{ReproBLAS: Reproducible BLAS}",
howpublished = "Web site with software downloads.",
month = jan,
year = "2016",
bibdate = "Sat Jan 02 18:46:46 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://bebop.cs.berkeley.edu/reproblas/",
acknowledgement = ack-nhfb,
}
@Article{Bigou:2016:BTP,
author = "Karim Bigou and Arnaud Tisserand",
title = "Binary-Ternary Plus-Minus Modular Inversion in {RNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "11",
pages = "3495--3501",
month = nov,
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2016.2529625",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 11 05:14:24 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Bigou:2016:HPR,
author = "Karim Bigou and Arnaud Tisserand",
title = "Hybrid Position-Residues Number System",
crossref = "Montuschi:2016:ISC",
pages = "126--133",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.15",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Biham:2016:BA,
author = "Eli Biham and Yaniv Carmeli and Adi Shamir",
title = "Bug Attacks",
journal = j-J-CRYPTOLOGY,
volume = "29",
number = "4",
pages = "775--805",
month = oct,
year = "2016",
CODEN = "JOCREQ",
DOI = "https://doi.org/10.1007/s00145-015-9209-1",
ISSN = "0933-2790 (print), 1432-1378 (electronic)",
ISSN-L = "0933-2790",
bibdate = "Mon Sep 12 07:07:07 MDT 2016",
bibsource = "http://link.springer.com/journal/145/29/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptology.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/s00145-015-9209-1;
http://link.springer.com/article/10.1007/s00145-015-9209-1",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptology",
journal-URL = "http://link.springer.com/journal/145",
keywords = "Bug attack; ElGamal encryption; Fault attack; Pohlig
Hellman; RSA",
remark = "From the abstract: ``The best-known example of such a
bug is the Intel division bug, which resulted in
slightly inaccurate results for extremely rare inputs.
\ldots{} such bugs can be a security disaster:
decrypting ciphertexts on any computer which [sic]
multiplies even one pair of numbers incorrectly can
lead to full leakage of the secret key, sometimes with
a single well-chosen ciphertext.",
}
@TechReport{Boldo:2016:RFA,
author = "Sylvie Boldo and Stef Graillat and Jean-Michel
Muller",
title = "On the robustness of the {2Sum} and {Fast2Sum}
algorithms",
type = "Report",
number = "ensl-01310023",
institution = "Inria, LRI, CNRS \& Universit{\'e} Paris-Sud,
Universit{\'e} Paris-Saclay, France",
pages = "1 + 17",
day = "1",
month = may,
year = "2016",
bibdate = "Thu May 19 10:09:03 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal-ens-lyon.archives-ouvertes.fr/ensl-01310023",
abstract = "The 2Sum and Fast2Sum algorithms are important
building blocks in numerical computing. They are used
(implicitly or explicitly) in many compensated
algorithms (such as compensated summation or
compensated polynomial evaluation). They are also used
for manipulating floating-point expansions. We show
that these algorithms are much more robust than it is
usually believed: the returned result makes sense even
when the rounding function is not round-to-nearest, and
they are almost immune to overflow.",
acknowledgement = ack-nhfb,
}
@Article{Brisebarre:2016:CBB,
author = "Nicolas Brisebarre and Christoph Lauter and Marc
Mezzarobba and Jean-Michel Muller",
title = "Comparison between Binary and Decimal Floating-Point
Numbers",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "7",
pages = "2032--2044",
month = "????",
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2479602",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jun 15 06:49:34 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers -",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
remark = "Longer report in \cite{Brisebarre:2013:CBB}.",
}
@InProceedings{Brzicova:2016:LMD,
author = "Marta Brzicov{\'a} and Christiane Frougny and Edita
Pelantov{\'a} and Milena Svobodov{\'a}",
title = "On-line Multiplication and Division in Real and
Complex Bases",
crossref = "Montuschi:2016:ISC",
pages = "134--141",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.13",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Chen:2016:DAR,
author = "Linbin Chen and Jie Han and Weiqiang Liu and Fabrizio
Lombardi",
title = "On the Design of Approximate Restoring Dividers for
Error-Tolerant Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "8",
pages = "2522--2533",
month = aug,
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2494005",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 18:58:52 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Chen:2016:PSA,
author = "D. D. Chen and G. X. Yao and R. C. Cheung and D. Pao
and C. K. Koc",
title = "Parameter Space for the Architecture of {FFT}-Based
{Montgomery} Modular Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "1",
pages = "147--160",
month = "????",
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2417553",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Dec 15 09:36:24 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Coleman:2016:LCT,
author = "J. N. Coleman and R. Che Ismail",
title = "{LNS} with Co-Transformation Competes with
Floating-Point",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "1",
pages = "136--146",
month = "????",
year = "2016",
CODEN = "ITCOB4",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Dec 15 09:36:24 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Collange:2016:PFP,
author = "Caroline Collange and Mioara Joldes and Jean-Michel
Muller and Valentina Popescu",
editor = "{IEEE}",
booktitle = "{2016 IEEE 27th International Conference on
Application-Specific Systems, Architectures and
Processors (ASAP). July 6--8, 2016. Imperial College
London}",
title = "Parallel floating-point expansions for
extended-precision {GPU} computations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "139--146",
year = "2016",
DOI = "https://doi.org/10.1109/ASAP.2016.7760783",
ISBN = "1-5090-1503-5",
ISBN-13 = "978-1-5090-1503-0",
ISSN = "2160-0511 (print), 2160-052X (electronic)",
ISSN-L = "2160-0511",
bibdate = "Fri Sep 29 10:56:29 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cui:2016:PDM,
author = "Xiaoping Cui and Weiqiang Liu and Dong Wenwen and
Fabrizio Lombardi",
title = "A Parallel Decimal Multiplier Using Hybrid Binary
Coded Decimal {(BCD)} Codes",
crossref = "Montuschi:2016:ISC",
pages = "150--155",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.8",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@TechReport{Damouche:2016:TSB,
author = "Nasrine Damouche and Matthieu Martel and Pavel
Panchekha and Jason Qiu and Alex Sanchez-Stern and
Zachary Tatlock",
title = "Toward a Standard Benchmark Format and Suite for
Floating-Point Analysis",
type = "Report",
number = "??",
institution = "Universit{\'e} de Perpignan Via Domitia and University
of Washington",
address = "Perpignan, France and Seattle, WA, USA",
pages = "15",
month = jul,
year = "2016",
bibdate = "Thu Oct 17 05:26:46 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://fpbench.org/;
https://homes.cs.washington.edu/~ztatlock/pubs/fpbench-damouche-nsv16.pdf",
abstract = "We introduce FPBench, a standard benchmark format for
validation and optimization of numerical accuracy in
floating-point computations. FPBench is a first step
toward addressing an increasing need in our community
for comparisons and combinations of tools from
different application domains. To this end, FPBench
provides a basic floating-point benchmark format and
accuracy measures for comparing different tools. The
FPBench format and measures allow comparing and
composing different floating-point tools. We describe
the FPBench format and measures and show that FPBench
expresses benchmarks from recent papers in the
literature, by building an initial benchmark suite
drawn from these papers. We intend for FPBench to grow
into a standard benchmark suite for the members of the
floating-point tools research community",
acknowledgement = ack-nhfb,
}
@Article{DelBarrio:2016:PCS,
author = "Alberto A. {Del Barrio} and Rom{\'a}n Hermida and Seda
Ogrenci Memik",
title = "A Partial Carry-Save On-the-Fly Correction
Multispeculative Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "11",
pages = "3251--3264",
month = nov,
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2016.2529626",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 11 05:14:24 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Benchmark testing; Computer science; Delays;
Encoding; Mathematical model; Proposals",
}
@TechReport{Demmel:2016:ERF,
author = "James Demmel and Peter Ahrens and Hong Diep Nguyen",
title = "Efficient reproducible floating point summation and
{BLAS}",
type = "Technical Report",
number = "UCB/EECS-2016-121",
institution = "EECS Department, University of California, Berkeley",
address = "Berkeley, CA, USA",
year = "2016",
bibdate = "Mon Feb 10 17:49:15 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www2.eecs.berkeley.edu/Pubs/TechRpts/2016/EECS-2016-121.html",
abstract = "We define reproducibility to mean getting bitwise
identical results from multiple runs of the same
program, perhaps with different hardware resources or
other changes that should ideally not change the
answer. Many users depend on reproducibility for
debugging or correctness. However, dynamic scheduling
of parallel computing resources, combined with
nonassociativity of floating point addition, makes
attaining reproducibility a challenge even for simple
operations like summing a vector of numbers, or more
complicated operations like the Basic Linear Algebra
Subprograms (BLAS). We describe an algorithm that
computes a reproducible sum of floating point numbers,
independent of the order of summation. The algorithm
depends only on a subset of the IEEE Floating Point
Standard 754-2008. It is communication-optimal, in the
sense that it does just one pass over the data in the
sequential case, or one reduction operation in the
parallel case, requiring an ``accumulator'' represented
by just 6 floating point words (more can be used if
higher precision is desired). The arithmetic cost with
a 6-word accumulator is $ 7 n $ floating point
additions to sum $n$ words, and (in IEEE double
precision) the final error bound can be up to $ 10^( -
8)$ times smaller than the error bound for conventional
summation. We describe the basic summation algorithm,
the software infrastructure used to build reproducible
BLAS (ReproBLAS), and performance results. For example,
when computing the dot product of 4096 double precision
floating point numbers, we get a $ 4 \times $ slowdown
compared to Intel Math Kernel Library (MKL) running on
an Intel Core i7-2600 CPU operating at 3.4 GHz and 256
KB L2 Cache.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; reproducible
floating point summation",
}
@InProceedings{Denis:2016:VCF,
author = "Christophe Denis and Pablo de Oliveira Castro and Eric
Petit",
title = "{Verificarlo}: Checking Floating Point Accuracy
through {Monte Carlo} Arithmetic",
crossref = "Montuschi:2016:ISC",
pages = "55--62",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.31",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{DHollander:2016:HLS,
author = "Erik H. D'Hollander",
title = "High-Level Synthesis Optimization for Blocked
Floating-Point Matrix Multiplication",
journal = j-COMP-ARCH-NEWS,
volume = "44",
number = "4",
pages = "74--79",
month = sep,
year = "2016",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/3039902.3039916",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Mon Jun 5 18:01:57 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "In the last decade floating-point matrix
multiplication on FPGAs has been studied extensively
and efficient architectures as well as detailed
performance models have been developed. By design these
IP cores take a fixed footprint which not necessarily
optimizes the use of all available resources. Moreover,
the low-level architectures are not easily amenable to
a parameterized synthesis. In this paper high-level
synthesis is used to fine-tune the configuration
parameters in order to achieve the highest performance
with maximal resource utilization. An\ exploration
strategy is presented to optimize the use of critical
resources (DSPs, memory) for any given FPGA. To account
for the limited memory size on the FPGA, a
block-oriented matrix multiplication is organized such
that the block summation is done on the CPU while the
block multiplication occurs on the logic fabric
simultaneously. The communication overhead between the
CPU and the FPGA is minimized by streaming the blocks
in a Gray code ordering scheme which maximizes the data
reuse for consecutive block matrix product
calculations. Using highlevel synthesis optimization,
the programmable logic operates at 93\% of the
theoretical peak performance and the combined CPU-FPGA
design achieves 76\% of the available hardware
processing speed for the floating-point multiplication
of 2K by 2K matrices.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "HEART '16 conference proceedings.",
}
@InProceedings{Du:2016:AEB,
author = "Peibing Du and Hao Jiang and Housen Li and Lizhi Cheng
and Canqun Yang",
editor = "Hong Shen and Yingpeng Sang and Hui Tian",
booktitle = "Proceedings of the {Seventeenth International
Conference on Parallel and Distributed Computing,
Applications and Technologies, PDCAT 2016, Guangzhou,
China, December 16--18, 2016}",
title = "Accurate evaluation of bivariate polynomials",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "51--56",
year = "2016",
DOI = "https://doi.org/10.1109/PDCAT.2016.026",
ISBN = "1-5090-5081-7, 1-5090-5082-5 (print)",
ISBN-13 = "978-1-5090-5081-9, 978-1-5090-5082-6 (print)",
bibdate = "Mon Mar 19 14:28:19 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/document/7943331/",
acknowledgement = ack-nhfb,
remark = "IEEE Computer Society Order Number E5982.",
}
@InProceedings{Dukhan:2016:WFP,
author = "M. Dukhan and R. Vuduc and J. Riedy",
editor = "????",
booktitle = "Proceedings of the {2nd International Workshop on
Performance Modeling: Methods and Applications (PMMA16)
at ISC High Performance, Frankfurt, Germany, [June or]
July 2016}",
title = "Wanted: Floating-Point Add Round-off Error
instruction",
publisher = "????",
address = "????",
pages = "??--??",
year = "2016",
LCCN = "",
bibdate = "Wed Oct 12 18:36:50 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1603.00491",
acknowledgement = ack-nhfb,
}
@Article{El-Razouk:2016:NAD,
author = "Hayssam El-Razouk and Arash Reyhani-Masoleh",
title = "New Architectures for Digit-Level Single,
Hybrid-Double, Hybrid-Triple Field Multiplications and
Exponentiation Using {Gaussian} Normal Bases",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "8",
pages = "2495--2509",
month = aug,
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2481408",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 18:58:52 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Emmart:2016:OMM,
author = "Niall Emmart and Justin Luitjens and Charles Weems and
Cliff Woolley",
title = "Optimizing Modular Multiplication for {NVIDIA}'s
{Maxwell} {GPUs}",
crossref = "Montuschi:2016:ISC",
pages = "47--54",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.21",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Fang:2016:OSV,
author = "Xin Fang and Miriam Leeser",
title = "Open-Source Variable-Precision Floating-Point Library
for Major Commercial {FPGAs}",
journal = j-TRETS,
volume = "9",
number = "3",
pages = "1--17",
month = jul,
year = "2016",
DOI = "https://doi.org/10.1145/2851507",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Sat Feb 8 10:53:20 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/2851507",
abstract = "There is increased interest in implementing
floating-point designs for different precisions that
take advantage of the flexibility offered by
Field-Programmable Gate Arrays (FPGAs). In this
article, we present updates to the Variable-precision
FLOATing Point Library (VFLOAT) developed at
Northeastern University and highlight recent
improvements in implementations for implementing
reciprocal, division, and square root components that
scale to double precision for FPGAs from the two major
vendors: Altera and Xilinx. Our library is open source
and flexible and provides the user with many options. A
designer has many tradeoffs to consider including clock
frequency, total latency, and resource usage as well as
target architecture. We compare the generated cores to
those produced by each vendor and to another popular
open-source tool: FloPoCo. VFLOAT has the advantage of
not tying the user's design to a specific target
architecture and of providing the maximum flexibility
for all options including clock frequency and latency
compared to other alternatives. Our results show that
variable-precision as well as double-precision designs
can easily be accommodated and the resulting components
are competitive and in many cases superior to the
alternatives.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@TechReport{Fevotte:2016:VAF,
author = "Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re",
title = "{VERROU}: Assessing Floating-Point Accuracy Without
Recompiling",
type = "Working paper",
number = "??",
institution = "????",
address = "????",
month = oct,
year = "2016",
bibdate = "Thu Oct 17 05:30:32 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.archives-ouvertes.fr/hal-01383417",
acknowledgement = ack-nhfb,
}
@Article{Fritz:2016:IPM,
author = "Christopher Fritz and Adly T. Fam",
title = "Interlaced Partition Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "8",
pages = "2672--2677",
month = aug,
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2481379",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 18:58:52 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Garcia-Vega:2016:DMO,
author = "Carlos Garcia-Vega and Sonia Gonzalez-Navarro and
Pedro Balboa-La Chica and Julio Villalba-Moreno",
title = "Decimal Multiformat Online Addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "10",
pages = "3203--3209",
month = "????",
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2016.2516009",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Sep 13 06:19:58 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Garrido:2016:CIN,
author = "Mario Garrido and Petter K{\"a}llstr{\"o}m and Martin
Kumm and Oscar Gustafsson",
title = "{CORDIC II}: A New Improved {CORDIC} Algorithm",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "63",
number = "2",
pages = "186--190",
month = feb,
year = "2016",
DOI = "https://doi.org/10.1109/TCSII.2015.2483422",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Sat Feb 8 10:11:25 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
keywords = "Adders; Convergence; CORDIC; CORDIC II; digital
arithmetic; friend angles; Hardware; Kernel;
Multiplexing; nano-rotation; nanorotation; rotation;
rotation angle; Signal processing algorithms; uniformly
scaled redundant (USR) CORDIC; USR",
}
@InProceedings{Geran:2016:CBC,
author = "Amir Ali Kouzeh Geran and Arash Reyhani-Masoleh",
title = "A {CRC}-Based Concurrent Fault Detection Architecture
for {Galois\slash Counter Mode (GCM)}",
crossref = "Montuschi:2016:ISC",
pages = "24--31",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.19",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@InProceedings{Gueron:2016:ABI,
author = "Shay Gueron and Vlad Krasnov",
title = "Accelerating Big Integer Arithmetic Using {Intel}
{IFMA} Extensions",
crossref = "Montuschi:2016:ISC",
pages = "32--38",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.22",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23; integer fused multiply-add (IFMA)",
}
@InProceedings{Gueron:2016:HIA,
author = "Shay Gueron and Sanu Mathew",
title = "Hardware Implementation of {AES} Using Area-Optimal
Polynomials for Composite-Field Representation {$
\mathrm {GF}(2^4)^2 $} of {$ \mathrm {GF}(2^8) $}",
crossref = "Montuschi:2016:ISC",
pages = "112--117",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.32",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Misc{Gustafson:2016:BFP,
author = "John L. Gustafson",
title = "Beyond Floating Point: Next Generation Computer
Arithmetic",
howpublished = "Stanford seminar video.",
year = "2016",
bibdate = "Thu Dec 14 16:05:07 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.johngustafson.net/pdfs/DebateTranscription.pdf;
https://www.youtube.com/watch?v=aP0Y1uAA-2Y",
acknowledgement = ack-nhfb,
}
@Article{Gustafson:2016:RAC,
author = "John L. Gustafson",
title = "A Radical Approach to Computation with Real Numbers",
journal = j-SUPERFRI,
volume = "3",
number = "2",
pages = "38--53",
month = "????",
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.14529/jsfi160203",
ISSN = "2409-6008 (print), 2313-8734 (electronic)",
ISSN-L = "2313-8734",
bibdate = "Sat Nov 11 07:15:27 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/superfri.bib",
URL = "http://superfri.org/superfri/article/view/94",
acknowledgement = ack-nhfb,
fjournal = "Supercomputing Frontiers and Innovations",
journal-URL = "http://superfri.org/superfri/issue/archive",
}
@Misc{Gustafson:2016:TGD,
author = "John Gustafson and William Kahan",
title = "Transcription of {``The} Great Debate'': {John
Gustafson} vs. {William Kahan} on Unum Arithmetic",
howpublished = "Web document.",
pages = "50",
day = "12",
month = jul,
year = "2016",
bibdate = "Thu Jan 18 06:36:55 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.johngustafson.net/pdfs/DebateTranscription.pdf;
https://www.youtube.com/watch?v=KEAKYDyUua4",
acknowledgement = ack-nhfb,
}
@Article{Hopkins:2016:WMN,
author = "David Hopkins",
title = "Will my numbers add up correctly if {I} round them?",
journal = j-MATH-GAZ,
volume = "100",
number = "549",
pages = "396--409",
month = nov,
year = "2016",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.1017/mag.2016.104",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Thu Nov 17 10:32:54 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
note = "The probability that rounding after fixed-point
summation of $n$ terms gives the same result as
summation of rounded terms is given by $ p(n) = (2 /
\pi) \int_0^\infty (\sin (x) / x)^{n + 1} \, d x$, and
that function is always a rational number. Its values
are $ p(n) = 1, 3 / 4, 2 / 3, 115 / 192, 11 / 20, 5887
/ 11520, 151 / 315, 259723 / 573440, \ldots {}$ for $ n
= 1$ to $8$.",
URL = "https://www.cambridge.org/core/product/88F5753DFE9F0DDDEAD1F2552B0F8B22",
acknowledgement = ack-nhfb,
ajournal = "Math. Gaz.",
fjournal = "The Mathematical Gazette",
journal-URL = "http://journals.cambridge.org/action/displayIssue?jid=MAG;
http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
keywords = "correct rounding; floating-point arithmetic; rounding
in fixed-point addition",
onlinedate = "17 October 2016",
remark-1 = "See also \cite{Nelsen:1987:PSR} for an earlier
independent derivation of part of this work.",
remark-2 = "From a Maple computer-algebra session: \\
p := proc(n) return (2/Pi) * int((sin(x)/x)^(n+1), x =
0 .. infinity); end proc; \\
for k from 1 to 20 do printf({"}%2d\t%a\n{"}, k, p(k))
end do; \\
1 1 \\
2 3/4 \\
3 2/3 \\
4 115/192 \\
5 11/20 \\
6 5887/11520 \\
7 151/315 \\
8 259723/573440 \\
9 15619/36288 \\
10 381773117/928972800 \\
11 655177/1663200 \\
12 20646903199/54499737600 \\
13 27085381/74131200 \\
14 467168310097/1322526965760 \\
15 2330931341/6810804000 \\
16 75920439315929441/228532659683328000 \\
17 12157712239/37638881280 \\
18 5278968781483042969/16783438527143608320 \\
19 37307713155613/121645100408832 \\
20 9093099984535515162569/30370031620545576960000 \\
for k from 10 to 100 by 10 do printf({"}%2d\t%.4f\n{"},
k, evalf(p(k),20)) end do; \\
10 0.4110 \\
20 0.2994 \\
30 0.2470 \\
40 0.2150 \\
50 0.1929 \\
60 0.1765 \\
70 0.1637 \\
80 0.1533 \\
90 0.1446 \\
100 NaN \\
Maple evaluates p(100) as undefined / Pi.",
remark-3 = "Equivalent code in the Mathematica computer-algebra
system is \\
p = Function[n, (2 / Pi) * Integrate[(Sin[x] / x)^(n +
1), {x, 0, Infinity}]]; \\
For[k = 1, k <= 20, ++k, Print[k, {"} {"}, p[k]]]\\
\ldots{} \\
Mathematica finds p[100] = 0.137307\ldots{}",
remark-4 = "The Maxima computer-algebra system is unable to
evaluate p(n) := (2 / %pi) * int((sin(x) / x)^(n + 1),
x, 0, inf);.",
}
@Article{Hormigo:2016:MIW,
author = "Javier Hormigo and Julio Villalba-Moreno",
title = "Measuring Improvement When Using {HUB} Formats to
Implement Floating-Point Systems under
Round-to-Nearest",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "24",
number = "6",
pages = "2369--2377",
month = jun,
year = "2016",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2015.2502318",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Mon Feb 10 08:19:41 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/7349231",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
keywords = "HUB (Half-Unit-Biased) floating-point format",
}
@Article{Hormigo:2016:NFC,
author = "Javier Hormigo and Julio Villalba",
title = "New Formats for Computing with Real-Numbers under
Round-to-Nearest",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "7",
pages = "2158--2168",
month = "????",
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2479623",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jun 15 06:49:34 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers -",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Hsu:2016:TPE,
author = "J. Hsu",
title = "Three paths to exascale supercomputing",
journal = j-IEEE-SPECTRUM,
volume = "53",
number = "1",
pages = "14--15",
month = jan,
year = "2016",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2016.7367447",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 07:02:09 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "exascale computers; exascale supercomputing; floating
point arithmetic; floating-point operations;
high-performance computing; parallel machines",
}
@MastersThesis{Hunhold:2016:UNF,
author = "Laslo Hunhold",
title = "The {Unum} Number Format: Mathematical Foundations,
Implementation and Comparison to {IEEE 754}
Floating-Point Numbers",
type = "{Bachelorarbeit}",
school = "Universit{\"a}t zu K{\"o}ln",
address = "K{\"o}ln, Germany",
pages = "iv + 91",
day = "8",
month = nov,
year = "2016",
bibdate = "Fri Jan 06 19:16:38 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://frign.de/publications/2016-11-08-the_unum_number_format.pdf",
abstract = "This thesis examines a modern concept for machine
numbers based on interval arithmetic called `Unums' and
compares it to IEEE 754 floating-point arithmetic,
evaluating possible uses of this format where
floating-point numbers are inadequate. In the course of
this examination, this thesis builds theoretical
foundations for IEEE 754 floating-point numbers,
interval arithmetic based on the projectively extended
real numbers and Unums.",
acknowledgement = ack-nhfb,
advisor = "Angela Kunoth and Samuel Leweke",
keywords = "interval arithmetic; Unum",
}
@Article{Isupov:2016:AMC,
author = "Konstantin Isupov",
title = "An Algorithm for Magnitude Comparison in {RNS} based
on Mixed-Radix Conversion {II}",
journal = j-INT-J-COMP-APPL,
volume = "141",
number = "??",
pages = "1--4",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.5120/ijca2016909626",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 09:27:51 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume141/number5/24777-2016909626/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "5",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@InProceedings{Jaberipur:2016:FFC,
author = "Ghassem Jaberipur and Behrooz Parhami and Dariush
Abedi",
title = "A Formulation of Fast Carry Chains Suitable for
Efficient Implementation with Majority Elements",
crossref = "Montuschi:2016:ISC",
pages = "8--15",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.14",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Misc{Jaeger:2016:OHQ,
author = "Andreas Jaeger",
title = "{OpenLibm}: A high quality system independent,
portable, open source libm implementation",
howpublished = "Web site",
year = "2016",
bibdate = "Thu Oct 17 05:37:38 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://openlibm.org/",
abstract = "OpenLibm is an effort to have a high quality,
portable, standalone C mathematical library (libm). It
can be used standalone in applications and programming
language implementations. The project was born out of a
need to have a good libm for the Julia programming
langage that worked consistently across compilers and
operating systems, and in 32-bit and 64-bit
environments.",
acknowledgement = ack-nhfb,
}
@Article{Jeannerod:2016:RIE,
author = "Claude-Pierre Jeannerod",
title = "A Radix-Independent Error Analysis of the
{Cornea--Harrison--Tang} Method",
journal = j-TOMS,
volume = "42",
number = "3",
pages = "19:1--19:20",
month = may,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2824252",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon May 23 16:40:02 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Assuming floating-point arithmetic with a fused
multiply-add operation and rounding to nearest, the
Cornea--Harrison--Tang method aims to evaluate
expressions of the form $ a b + c d $ with high
relative accuracy. In this article, we provide a
rounding error analysis of this method, which unlike
previous studies is not restricted to binary
floating-point arithmetic but holds for any radix $
\beta $. We show first that an asymptotically optimal
bound on the relative error of this method is $ 2 \beta
u + 2 u^2 / \beta - 2 u^2 = 2 u + 2 / \beta u^2 + O
(u^3) $, where $ u = 1 / 2 \beta^{1 - p} $ is the unit
roundoff in radix $ \beta $ and precision $p$. Then we
show that the possibility of removing the $ O (u^2)$
term from this bound is governed by the radix parity
and the tie-breaking strategy used for rounding: if $
\beta $ is odd or rounding is to nearest even, then the
simpler bound $ 2 u$ is obtained, while if $ \beta $ is
even and rounding is to nearest away, then there exist
floating-point inputs $a$, $b$, $c$, $d$ that lead to a
relative error larger than $ 2 u + 2 / \beta u^2 - 4
u^3$. All these results hold provided underflows and
overflows do not occur and under some mild assumptions
on $p$ satisfied by IEEE 754-2008 formats.",
acknowledgement = ack-nhfb,
articleno = "19",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Jeannerod:2016:SEB,
author = "Claude-Pierre Jeannerod and Nicolas Louvet and
Jean-Michel Muller and Antoine Plet",
title = "Sharp error bounds for complex floating-point
inversion",
journal = j-NUMER-ALGORITHMS,
volume = "73",
number = "3",
pages = "735--760",
month = nov,
year = "2016",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-016-0115-x",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Wed Mar 1 09:12:13 MST 2017",
bibsource = "http://link.springer.com/journal/11075/73/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-016-0115-x",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Jiang:2016:ARB,
author = "Honglan Jiang and Jie Han and Fei Qiao and Fabrizio
Lombardi",
title = "Approximate Radix-8 {Booth} Multipliers for Low-Power
and High-Performance Operation",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "8",
pages = "2638--2644",
month = aug,
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2493547",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Jul 11 18:58:52 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Joldes:2016:AAE,
author = "Mioara Joldes and Olivier Marty and Jean-Michel Muller
and Valentina Popescu",
title = "Arithmetic Algorithms for Extended Precision Using
Floating-Point Expansions",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "4",
pages = "1197--1210",
month = "????",
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2441714",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Mar 19 07:47:06 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers -",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Kadric:2016:APF,
author = "Edin Kadric and Paul Gurniak and Andr{\'e} DeHon",
title = "Accurate Parallel Floating-Point Accumulation",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "11",
pages = "3224--3238",
month = nov,
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2016.2532874",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 11 05:14:24 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "accurate floating-point summation; floating-point
arithmetic; rounding errors",
}
@Book{Kneusel:2016:NC,
author = "Ronald T. Kneusel",
title = "Numbers and Computers",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 231",
year = "2016",
ISBN = "3-319-35940-1 (softcover), 3-319-17260-3 (e-book)",
ISBN-13 = "978-3-319-35940-3 (softcover), 978-3-319-17260-6
(e-book)",
LCCN = "QA241 .K54 2016",
bibdate = "Tue Aug 22 05:53:26 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This is a book about numbers and how those numbers are
represented in and operated on by computers. It is
crucial that developers understand this area because
the numerical operations allowed by computers, and the
limitations of those operations, especially in the area
of floating point math, affect virtually everything
people try to do with computers. This book aims to fill
this gap by exploring, in sufficient but not
overwhelming detail, just what it is that computers do
with numbers. Divided into two parts, the first deals
with standard representations of integers and floating
point numbers, while the second details several other
number representations. Each chapter ends with
exercises to review the key points. Topics covered
include interval arithmetic, fixed-point numbers,
floating point numbers, big integers and rational
arithmetic. This book is for anyone who develops
software including software engineering, scientists,
computer science students, engineering students and
anyone who programs for fun.",
acknowledgement = ack-nhfb,
subject = "Number theory; Numerals; Numeration; Computer science;
Mathematics",
tableofcontents = "Number Systems \\
Integers \\
Floating Point \\
Big Integers and Rational Arithmetic \\
Fixed-Point Numbers \\
Decimal Floating Point \\
Interval Arithmetic",
}
@Book{Kumm:2016:MCM,
author = "Martin Kumm",
title = "Multiple Constant Multiplication Optimizations for
Field Programmable Gate Arrays",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxiii + 206 + 47",
year = "2016",
DOI = "https://doi.org/10.1007/978-3-658-13323-8",
ISBN = "3-658-13322-8 (print), 3-658-13323-6 (e-book)",
ISBN-13 = "978-3-658-13322-1 (print), 978-3-658-13323-8
(e-book)",
LCCN = "TK7895.G36",
bibdate = "Fri Dec 8 13:11:57 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://link.springer.com/book/10.1007/978-3-658-13323-8",
abstract = "This work covers field programmable gate array
(FPGA)-specific optimizations of circuits computing the
multiplication of a variable by several constants,
commonly denoted as multiple constant multiplication
(MCM). These optimizations focus on low resource usage
but high performance. They comprise the use of fast
carry-chains in adder-based constant multiplications
including ternary (3-input) adders as well as the
integration of look-up table-based constant multipliers
and embedded multipliers to get the optimal mapping to
modern FPGAs. The proposed methods can be used for the
efficient implementation of digital filters, discrete
transforms and many other circuits in the domain of
digital signal processing, communication and image
processing.",
acknowledgement = ack-nhfb,
subject = "Engineering; Computer hardware; Applied mathematics;
Engineering mathematics; Electrical engineering;
Ing{\'e}nierie; Math{\'e}matiques de l'ing{\'e}nieur;
G{\'e}nie {\'e}lectrique; engineering.; electrical
engineering.; Electrical engineering.; Engineering.;
Engineering mathematics.",
tableofcontents = "Front Matter / i--xxxiii \\
Introduction / 1--7 \\
Background / 9--35 \\
The Pipelined Multiple Constant Multiplication Problem
\\
Front Matter / 37--37 \\
Optimal Pipelining of Precomputed Adder Graphs / 39--51
\\
The Reduced Pipelined Adder Graph Algorithm / 53--85
\\
Optimally Solving MCM Related Problems Using Integer
Linear Programming / 87--111 \\
A Heuristic for the Constant Matrix Multiplication
Problem / 113--124 \\
FPGA Specific MCM Optimizations \\
Front Matter / 125--125 \\
Combining Adder Graphs with LUT-Based Constant
Multipliers / 127--137 \\
Optimization of Hybrid Adder Graphs Containing Embedded
Multipliers / 139--152 \\
Floating Point Multiple Constant Multiplication /
153--162 \\
Optimization of Adder Graphs with Ternary (3-Input)
Adders / 163--175 \\
Conclusion and Future Work / 177--179 \\
Back Matter / 181--206",
}
@InProceedings{Langhammer:2016:SPN,
author = "Martin Langhammer and Bogdan Pasca",
title = "Single Precision Natural Logarithm Architecture for
Hard Floating-Point and {DSP}-Enabled {FPGAs}",
crossref = "Montuschi:2016:ISC",
pages = "164--171",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.20",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@InProceedings{Langlois:2016:RNR,
author = "Philippe Langlois and Rafife Nheili and Christophe
Denis",
title = "Recovering Numerical Reproducibility in Hydrodynamic
Simulations",
crossref = "Montuschi:2016:ISC",
pages = "63--70",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.27",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@TechReport{Lee:2016:VBM,
author = "Wonyeol Lee and Rahul Sharma and Alex Aiken",
title = "Verifying Bit-Manipulations of Floating-Point",
type = "Report",
institution = "Stanford University",
address = "Stanford, CA, USA",
pages = "15",
day = "15",
month = apr,
year = "2016",
bibdate = "Mon May 23 16:07:51 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://theory.stanford.edu/~aiken/publications/papers/pldi16b.pdf",
acknowledgement = ack-nhfb,
remark = "To appear in ACM PLDI'2016 conference proceedings,
usually published as an issue of \booktitle{ACM SIGPLAN
Notices}.",
}
@InProceedings{Lefevre:2016:CRA,
author = "Vincent Lef{\`e}vre",
title = "Correctly Rounded Arbitrary-Precision Floating-Point
Summation",
crossref = "Montuschi:2016:ISC",
pages = "71--78",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.9",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate summation; ARITH-23; correct rounding;
floating-point arithmetic",
}
@TechReport{Lefevre:2016:OBB,
author = "Vincent Lef{\`e}vre and Paul Zimmermann",
title = "Optimized {Binary64} and {Binary128} Arithmetic with
{GNU MPFR}",
type = "Report",
number = "hal-01502326",
institution = "Inria Grenoble --- Rh{\^o}ne-Alpes, LIP ---
Laboratoire de l'Informatique du Parall{\'e}lisme and
Inria Nancy --- Grand Est, LORIA --- ALGO ---
Department of Algorithms, Computation, Image and
Geometry",
pages = "10",
month = apr,
year = "2016",
bibdate = "Wed Apr 05 06:51:37 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib",
note = "To appear in IEEE ARITH'2016 proceedings London, UK
(24--26 July, 2016).",
URL = "https://hal.inria.fr/hal-01502326",
abstract = "We describe algorithms used to optimize the GNU MPFR
library when the operands fit into one or two words. On
modern processors, a correctly rounded addition of two
quadruple precision numbers is now performed in 22
cycles, a subtraction in 24 cycles, a multiplication in
32 cycles, a division in 64 cycles, and a square root
in 69 cycles. We also introduce a new faithful rounding
mode, which enables even faster computations. Those
optimizations will be available in version 4 of MPFR.",
acknowledgement = ack-nhfb,
}
@InProceedings{LeMaire:2016:CFP,
author = "Julien {Le Maire} and Nicolas Brunie and Florent de
Dinechin and Jean-Michel Muller",
title = "Computing floating-point logarithms with fixed-point
operations",
crossref = "Montuschi:2016:ISC",
pages = "156--163",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.24",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@InProceedings{Li:2016:SDT,
author = "Ang Li and Shuaiwen Leon Song and Mark Wijtvliet and
Akash Kumar and Henk Corporaal",
booktitle = "{ICS'16}: Proceedings of the {2016 International
Conference on Supercomputing, Istanbul Turkey, June
1--3, 2016}",
title = "{SFU}-Driven Transparent Approximation Acceleration on
{GPUs}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "1--14",
month = jun,
year = "2016",
DOI = "https://doi.org/10.1145/2925426.2926255",
ISBN = "1-4503-4361-9",
ISBN-13 = "978-1-4503-4361-9",
LCCN = "QA76.88",
bibdate = "Mon Sep 11 07:17:26 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Approximate computing, the technique that sacrifices
certain amount of accuracy in exchange for substantial
performance boost or power reduction, is one of the
most promising solutions to enable power control and
performance scaling towards exascale. Although most
existing approximation designs target the emerging
data-intensive applications that are comparatively more
error-tolerable, there is still high demand for the
acceleration of traditional scientific applications
(e.g., weather and nuclear simulation), which often
comprise intensive transcendental function calls and
are very sensitive to accuracy loss. To address this
challenge, we focus on a very important but long
ignored approximation unit on today's commercial GPUs
the special-function unit (SFU), and clarify its unique
role in performance acceleration of accuracy-sensitive
applications in the context of approximate computing.
To better understand its features, we conduct a
thorough empirical analysis on three generations of
NVIDIA GPU architectures to evaluate all the
single-precision and double-precision numeric
transcendental functions that can be accelerated by
SFUs, in terms of their performance, accuracy and power
consumption. Based on the insights from the evaluation,
we propose a transparent, tractable and portable design
framework for SFU-driven approximate acceleration on
GPUs. Our design is software-based and requires no
hardware or application modifications. Experimental
results on three NVIDIA GPU platforms demonstrate that
our proposed framework can provide fine-grained tuning
for performance and accuracy trade-offs, thus
facilitating applications to achieve the maximum
performance under certain accuracy constraints.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lichtenau:2016:QPF,
author = "Cedric Lichtenau and Steven Carlough and Silvia
Melitta Mueller",
title = "Quad Precision Floating Point on the {IBM z13}",
crossref = "Montuschi:2016:ISC",
pages = "87--94",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.26",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Liu:2016:DAI,
author = "W. Liu and L. Chen and C. Wang and M. O'Neill and F.
Lombardi",
title = "Design and Analysis of Inexact Floating-Point Adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "1",
pages = "308--314",
month = "????",
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2417549",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Dec 15 09:36:24 MST 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Martin-Dorel:2016:PTB,
author = "{\'E}rik Martin-Dorel and Guillaume Melquiond",
title = "Proving Tight Bounds on Univariate Expressions with
Elementary Functions in {Coq}",
journal = j-J-AUTOM-REASON,
volume = "57",
number = "3",
pages = "187--217",
month = oct,
year = "2016",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-015-9350-4",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Fri Sep 2 06:39:36 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/s10817-015-9350-4",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
}
@Article{Mascarenhas:2016:FPN,
author = "W. F. Mascarenhas",
title = "Floating point numbers are real numbers",
journal = "arxiv.org",
pages = "57",
month = may,
year = "2016",
bibdate = "Tue May 31 07:07:46 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1605.09202",
abstract = "Floating-point arithmetic allows us to use a finite
machine, the digital computer, to reach conclusions
about models based on continuous mathematics. In this
article we work in the other direction, that is, we
present examples in which continuous mathematics leads
to sharp, simple and new results about the evaluation
of sums, square roots and dot products in floating
point arithmetic.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "1605.09202",
keywords = "Mathematics - Numerical Analysis",
primaryclass = "math.NA",
}
@InProceedings{Meloni:2016:RDR,
author = "Nicolas M{\'e}loni and M. Anwar Hasan",
title = "Random Digit Representation of Integers",
crossref = "Montuschi:2016:ISC",
pages = "118--125",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.11",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23; modular exponentiation",
}
@Article{Montuschi:2016:MCA,
author = "Paolo Montuschi and Jean-Michel Muller",
title = "Modern Computer Arithmetic",
journal = j-IEEE-CGA,
volume = "49",
number = "9",
pages = "12--12",
month = sep,
year = "2016",
CODEN = "ICGADZ",
DOI = "https://doi.org/10.1109/MC.2016.277",
ISSN = "0272-1716 (print), 1558-1756 (electronic)",
ISSN-L = "0272-1716",
bibdate = "Tue Oct 25 06:11:19 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeecga.bib",
URL = "https://www.computer.org/csdl/mags/co/2016/09/mco2016090012.html",
acknowledgement = ack-nhfb,
fjournal = "IEEE Computer Graphics and Applications",
journal-URL = "http://www.computer.org/portal/web/csdl/magazines/cga",
remark = "This one-page editorial draws attention to three
papers on computer arithmetic in \booktitle{IEEE
Transactions on Computers}
\cite{Demmel:2015:PRS,Joldes:2016:AAE,Chen:2016:DAR}..",
}
@InProceedings{Morancho:2016:UAF,
author = "Enric Morancho",
booktitle = "{2016 Euromicro Conference on Digital System Design
(DSD)}",
title = "Unum: Adaptive Floating-Point Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "651--656",
year = "2016",
DOI = "https://doi.org/10.1109/DSD.2016.39",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Moroz:2016:FCI,
author = "Leonid V. Moroz and Cezary J. Walczyk and Andriy
Hrynchyshyn and Vijay Holimath and Jan L.
Cie{\'s}li{\'n}ski",
title = "Fast calculation of inverse square root with the use
of magic constant --- analytical approach",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--23",
day = "14",
month = mar,
year = "2016",
DOI = "https://doi.org/10.48550/arXiv.1603.04483",
bibdate = "Wed Dec 20 07:34:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/pdf/1603.04483.pdf",
abstract = "We present a mathematical analysis of transformations
used in fast calculation of inverse square root for
single-precision floating-point numbers. Optimal values
of the so called magic constants are derived in a
systematic way, minimizing either absolute or relative
errors at subsequent stages of the discussed
algorithm.",
acknowledgement = ack-nhfb,
}
@InProceedings{Muller:2016:NMA,
author = "Jean-Michel Muller and Valentina Popescu and Ping Tak
Peter Tang",
title = "A New Multiplication Algorithm for Extended Precision
Using Floating-Point Expansions",
crossref = "Montuschi:2016:ISC",
pages = "39--46",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.18",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Misc{Munshi:2016:OCS,
author = "Aaftab Munshi and Lee Howes and Bartosz Sochacki and
{Khronos OpenCL Working Group}",
title = "The {OpenCL} {C} Specification Version: 2.0 Document
Revision: 33",
howpublished = "Web document.",
pages = "205",
day = "13",
month = apr,
year = "2016",
bibdate = "Mon Apr 16 14:05:49 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "https://www.khronos.org/registry/OpenCL/specs/opencl-2.0-openclc.pdf",
acknowledgement = ack-nhfb,
remark = "Section 6.1.3.2 Math Functions, pages 74ff, defines a
function repertoire extended beyond that of ISO C,
including {\tt acospi}, {\tt asinpi}, {\tt atanpi},
{\tt atan2pi}, {\tt cospi}, {\tt sinpi}, {\tt tanpi},
{\tt cospi}, {\tt fract}, {\tt lgamma\_r}, {\tt mad}
(approximation to {\tt a * b + c}), {\tt minmag}, {\tt
pown}, {\tt rootn}, {\tt sincos}, {\tt sinpi}, and {\tt
tanpi}.",
}
@Article{Nannarelli:2016:PPS,
author = "Alberto Nannarelli",
title = "Performance\slash Power Space Exploration for
{Binary64} Division Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "5",
pages = "1671--1677",
month = may,
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2448097",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue May 31 08:56:47 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers -",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Notzli:2016:LVP,
author = "Andres N{\"o}tzli and Fraser Brown",
title = "{LifeJacket}: Verifying precise floating-point
optimizations in {LLVM}",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "??--??",
day = "30",
month = mar,
year = "2016",
bibdate = "Sat Apr 2 06:26:03 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1603.09290",
abstract = "Optimizing floating-point arithmetic is vital because
it is ubiquitous, costly, and used in compute-heavy
workloads. Implementing precise optimizations
correctly, however, is difficult, since developers must
account for all the esoteric properties of
floating-point arithmetic to ensure that their
transformations do not alter the output of a program.
Manual reasoning is error prone and stifles
incorporation of new optimizations. We present an
approach to automate reasoning about floating-point
optimizations using satisfiability modulo theories
(SMT) solvers. We implement the approach in LifeJacket,
a system for automatically verifying precise
floating-point optimizations for the LLVM assembly
language. We have used LifeJacket to verify 43 LLVM
optimizations and to discover eight incorrect ones,
including three previously unreported problems.
LifeJacket is an open source extension of the Alive
system for optimization verification.",
acknowledgement = ack-nhfb,
}
@Article{Ozaki:2016:EFT,
author = "Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi
Oishi",
title = "Error-free transformation of matrix multiplication
with a posteriori validation",
journal = j-NUM-LIN-ALG-APPL,
volume = "23",
number = "5",
pages = "931--946",
month = oct,
year = "2016",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.2061",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Thu Sep 29 08:59:10 MDT 2016",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
keywords = "accurate computing; accurate floating-point summation;
floating-point arithmetic; interval arithmetic; matrix
multiplication",
}
@Article{Ozaki:2016:SFP,
author = "Katsuhisa Ozaki and Florian B{\"u}nger and Takeshi
Ogita",
title = "Simple floating-point filters for the two-dimensional
orientation problem",
journal = j-BIT-NUM-MATH,
volume = "56",
number = "2",
pages = "729--749",
month = jun,
year = "2016",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-015-0574-9",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon May 30 06:11:11 MDT 2016",
bibsource = "http://link.springer.com/journal/10543/56/2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/article/10.1007/s10543-015-0574-9",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Paulk:2016:IFP,
author = "Mark Paulk and Lori Cameron",
title = "{IEEE} Floating Point Standard",
journal = j-COMPUTER,
volume = "49",
number = "6",
pages = "10--10",
month = jun,
year = "2016",
CODEN = "CPTRB4",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Tue Jun 21 15:00:51 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://csdl.computer.org/csdl/mags/co/2016/06/mco2016060010.html",
abstract-URL = "http://csdl.computer.org/csdl/mags/co/2016/06/mco2016060010-abs.html",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@InProceedings{Peou:2018:CSO,
author = "Kenny Peou and Alan Kelly and Joel Falcou and Cecile
Germain",
editor = "{IEEE}",
booktitle = "{2018 30th International Symposium on Computer
Architecture and High Performance Computing (SBAC-PAD):
Lyon, France, 24--27 September 2018}",
title = "A Case Study on Optimizing Accurate Half Precision
Average",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "356--363",
month = sep,
year = "2018",
DOI = "https://doi.org/10.1109/cahpc.2018.8645923",
ISBN = "1-5386-7769-5",
ISBN-13 = "978-1-5386-7769-8",
bibdate = "Fri Apr 11 08:36:46 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this work, we study the numerical performance of
various common algorithms used to calculate the average
of an array of half precision (FP16) floating point
values. While the current generation of CPUs does not
support native FP16 arithmetic, it is a planned feature
in a number of next-generation CPUs. FP16 arithmetic
was emulated via the half software library. Due to the
limitations of the FP16 data type, some algorithms
proved insufficient for arrays as small as 100
elements. We propose an algorithm that allows
numerically stable FP16 computation of the average and
compare it to the naive floating point (FP32) algorithm
in terms of both numerical precision and runtime
performance. We find that our algorithm offers
comparable robustness, numerical precision, and SIMD
performance to the higher precision computation.",
acknowledgement = ack-nhfb,
}
@Article{Phatak:2016:NDA,
author = "Dhananjay S. Phatak and Steven D. Houston",
title = "New distributed algorithms for fast sign detection in
residue number systems {(RNS)}",
journal = j-J-PAR-DIST-COMP,
volume = "97",
number = "??",
pages = "78--95",
month = nov,
year = "2016",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Aug 25 18:20:29 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0743731516300703",
acknowledgement = ack-nhfb,
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315/",
}
@InProceedings{Rane:2016:SPF,
author = "Ashey Rane and Calvin Lin and Mohit Tiwari",
editor = "T. Holz and S. Savage",
booktitle = "Proceedings of the {25th USENIX Security 2016, August
10--12, 2016, Austin, TX}",
title = "Secure, precise, and fast floating-point operations on
x86 processors",
publisher = pub-USENIX,
address = pub-USENIX:adr,
pages = "71--86",
year = "2016",
bibdate = "Mon Aug 26 17:02:50 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.usenix.org/conference/usenixsecurity16/technical-sessions/presentation/rane",
abstract = "Floating-point computations introduce several side
channels. This paper describes the first solution that
closes these side channels while preserving the
precision of non-secure executions. Our solution
exploits microarchitectural features of the x86
architecture along with novel compilation techniques to
provide low overhead.\par
Because of the details of x86 execution, the evaluation
of floating-point side channel defenses is quite
involved, but we show that our solution is secure,
precise, and fast. Our solution closes more side
channels than any prior solution. Despite the added
security, our solution does not compromise on the
precision of the floating-point operations. Finally,
for a set of microkernels, our solution is an order of
magnitude more efficient than the previous solution.",
acknowledgement = ack-nhfb,
remark = "ISBN-13 978-1-931971-32-4 from publisher Web site
BibTeX entry is incorrect: it is for an unrelated 2005
conference paper. Library catalog searches fail to find
this proceedings volume.",
xxISBN = "1-931971-32-3",
xxISBN-13 = "978-1-931971-32-4",
}
@Article{Rashidi:2016:HSH,
author = "Bahram Rashidi and Sayed Masoud Sayedi and Reza
Rezaeian Farashahi",
title = "High-speed hardware architecture of scalar
multiplication for binary elliptic curve
cryptosystems",
journal = j-MICROELECT-J,
volume = "52",
pages = "49--65",
month = jun,
year = "2016",
CODEN = "MICEB9",
DOI = "https://doi.org/10.1016/j.mejo.2016.03.006",
ISSN = "0026-2692 (print), 1879-2391 (electronic)",
ISSN-L = "0026-2692",
bibdate = "Fri Jun 24 16:29:16 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Microelectronics Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/00262692",
}
@InProceedings{Revy:2016:ADF,
author = "Guillaume Revy",
title = "Automated Design of Floating-Point Logarithm Functions
on Integer Processors",
crossref = "Montuschi:2016:ISC",
pages = "172--180",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.28",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Roux:2016:FPR,
author = "Pierre Roux",
title = "Formal Proofs of Rounding Error Bounds: With
Application to an Automatic Positive Definiteness
Check",
journal = j-J-AUTOM-REASON,
volume = "57",
number = "2",
pages = "135--156",
month = aug,
year = "2016",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-015-9339-z",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Fri Sep 2 06:39:36 MDT 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/s10817-015-9339-z",
acknowledgement = ack-nhfb,
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
keywords = "floating-point arithmetic; rounding error",
}
@InProceedings{Rubio-Gonzalez:2016:FPP,
author = "Cindy Rubio-Gonz{\'a}lez and Cuong Nguyen and Benjamin
Mehne and Koushik Sen and James Demmel and William
Kahan and Costin Iancu and Wim Lavrijsen and David H.
Bailey and David Hough",
booktitle = "Proceedings of the 38th International Conference on
Software Engineering",
title = "Floating-point precision tuning using blame analysis",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "1074--1085",
year = "2016",
bibdate = "Sat Jun 04 17:19:46 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Rump:2016:DUR,
author = "Siegfried M. Rump and Marko Lange",
title = "On the definition of unit roundoff",
journal = j-BIT-NUM-MATH,
volume = "56",
number = "1",
pages = "309--317",
month = mar,
year = "2016",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-015-0554-0",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon May 30 06:11:10 MDT 2016",
bibsource = "http://link.springer.com/journal/10543/56/1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/article/10.1007/s10543-015-0554-0",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Rump:2016:IAF,
author = "Siegfried M. Rump and Takeshi Ogita and Yusuke
Morikura and Shin'ichi Oishi",
title = "Interval arithmetic with fixed rounding mode",
journal = j-NONLINEAR-THEORY-APPL,
volume = "7",
number = "3",
pages = "362--373",
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1587/nolta.7.362",
ISSN = "2185-4106",
ISSN-L = "2185-4106",
bibdate = "Wed Jan 19 10:32:15 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We discuss several methods to simulate interval
arithmetic operations using floating-point operations
with fixed rounding mode. In particular we present
formulas using only rounding to nearest and using only
chop rounding (towards zero). The latter was the
default and only rounding on GPU (Graphics Processing
Unit) and cell processors, which in turn are very fast
and therefore attractive in scientific computations.",
acknowledgement = ack-nhfb,
fjournal = "Nonlinear Theory and Its Applications, {IEICE}",
journal-URL = "https://www.jstage.jst.go.jp/browse/nolta/",
}
@Article{Rump:2016:IEB,
author = "Siegfried M. Rump and Florian B{\"u}nger and
Claude-Pierre Jeannerod",
title = "Improved error bounds for floating-point products and
{Horner}'s scheme",
journal = j-BIT-NUM-MATH,
volume = "56",
number = "1",
pages = "293--307",
month = mar,
year = "2016",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-015-0555-z",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon May 30 06:11:10 MDT 2016",
bibsource = "http://link.springer.com/journal/10543/56/1;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/article/10.1007/s10543-015-0555-z",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Sayed:2016:WCR,
author = "Wafaa S. Sayed and Hossam A. H. Fahmy",
title = "What are the Correct Results for the Special Values of
the Operands of the Power Operation?",
journal = j-TOMS,
volume = "42",
number = "2",
pages = "14:1--14:17",
month = jun,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2809783",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Jun 3 18:52:21 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Language standards such as C99 and C11, as well as the
IEEE Standard for Floating-Point Arithmetic 754 (IEEE
Std 754-2008) specify the expected behavior of binary
and decimal floating-point arithmetic in
computer-programming environments and the handling of
special values and exception conditions. Many
researchers focus on verifying the compliance of
implementations for binary and decimal floating-point
operations with these standards. In this article, we
are concerned with the special values of the operands
of the power function Z = X$^Y$. We study how the
standards define the correct results for this
operation, propose a mathematically justified
definition for the correct results of the power
function on the occurrence of these special values as
its operands, test how different software
implementations for the power function deal with these
special values, and classify the behavior of different
programming languages from the viewpoint of how much
they conform to the standards and our proposed
mathematical definition. We present inconsistencies
between the implementations and the standards, and
discuss incompatibilities between different versions of
the same software.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Schaffner:2016:APT,
author = "Michael Schaffner and Michael Gautschi and Frank K.
G{\"u}rkaynak and Luca Benini",
title = "Accuracy and Performance Trade-Offs of Logarithmic
Number Units in Multi-Core Clusters",
crossref = "Montuschi:2016:ISC",
pages = "95--103",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.10",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@Article{Schkufza:2016:SPO,
author = "Eric Schkufza and Rahul Sharma and Alex Aiken",
title = "Stochastic program optimization",
journal = j-CACM,
volume = "59",
number = "2",
pages = "114--122",
month = feb,
year = "2016",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/2863701",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Feb 16 15:45:15 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://cacm.acm.org/magazines/2016/2/197428/fulltext",
abstract = "The optimization of short sequences of loop-free,
fixed-point assembly code sequences is an important
problem in high-performance computing. However, the
competing constraints of transformation correctness and
performance improvement often force even special
purpose compilers to produce sub-optimal code. We show
that by encoding these constraints as terms in a cost
function, and using a Markov Chain Monte Carlo sampler
to rapidly explore the space of all possible code
sequences, we are able to generate aggressively
optimized versions of a given target code sequence.
Beginning from binaries compiled by 11vm --O0, we are
able to produce provably correct code sequences that
either match or outperform the code produced by qcc
--O3, icc --O3, and in some cases expert handwritten
assembly.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
keywords = "Hacker's delight; Henry S. Warren; Montgomery
multiplication; SAXPY",
}
@Article{Seo:2016:HMR,
author = "Hwajeong Seo and Zhe Liu and Yasuyuki Nogami and
Jongseok Choi and Howon Kim",
title = "Hybrid {Montgomery} Reduction",
journal = j-TECS,
volume = "15",
number = "3",
pages = "58:1--58:??",
month = jul,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2890502",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Jul 21 17:18:13 MDT 2016",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
abstract = "In this article, we present a hybrid method to improve
the performance of the Montgomery reduction by taking
advantage of the Karatsuba technique. We divide the
Montgomery reduction into two sub-parts, including one
for the conventional Montgomery reduction and the other
one for Karatsuba-aided multiplication. This approach
reduces the multiplication complexity of $n$-limb
Montgomery reduction from $ \theta (n^2 + n)$ to
asymptotic complexity $ \theta (7 n^2 / 8 + n)$. Our
practical implementation results over an 8-bit
microcontroller also show performance enhancements by
11\%.",
acknowledgement = ack-nhfb,
articleno = "58",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J840",
}
@Article{Sohn:2016:FFP,
author = "Jongwook Sohn and Earl E. {Swartzlander, Jr.}",
title = "A Fused Floating-Point Four-Term Dot Product Unit",
journal = j-IEEE-TRANS-CIRCUITS-SYST-1,
volume = "63",
number = "3",
pages = "370--378",
month = mar,
year = "2016",
DOI = "https://doi.org/10.1109/TCSI.2016.2525042",
ISSN = "1549-8328 (print), 1558-0806 (electronic)",
ISSN-L = "1549-8328",
bibdate = "Mon Feb 10 09:06:33 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/7416176",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I: Regular
Papers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
}
@Article{Tada:2016:ESG,
author = "Jubee Tada and Maiki Hosokawa and Ryusuke Egawa and
Hiroaki Kobayashi",
title = "Effects of Stacking Granularity on {$3$-D} Stacked
Floating-point Fused Multiply-Add Units",
journal = j-COMP-ARCH-NEWS,
volume = "44",
number = "4",
pages = "62--67",
month = sep,
year = "2016",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/3039902.3039914",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Thu Jan 12 18:43:44 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Three-dimensional stacked integrated circuits
(3D-SICs) have been expected to overcome the
limitations of conventional two-dimensional (2-D)
implemented circuits. Since a stacking strategy affects
the performance and the power consumption of 3D-SICs,
this paper examines two stacking strategies for
designing the 3-D stacked floating-point fused
multiply-add (FP-FMA) module which contains four FP-FMA
units. Experimental results show that a coarse-grain
stacking strategy is suitable for reducing critical
path delay of the 3-D stacked FP-FMA module. On the
other hand, a fine-grain stacking strategy is suitable
for reducing power consumption. The 3-D stacked FP-FMA
module which is designed based on a fine-grain stacking
strategy achieves an 8.4\% critical path delay
reduction and an 18\% average power reduction compared
with the 2-D implementation.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "HEART '16 conference proceedings.",
}
@Article{Tay:2016:NIM,
author = "T. Fatt Tay and C. Chang",
title = "A Non-Iterative Multiple Residue Digit Error Detection
and Correction Algorithm in {RRNS}",
journal = j-IEEE-TRANS-COMPUT,
volume = "65",
number = "2",
pages = "396--408",
month = "????",
year = "2016",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2015.2435773",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Jan 19 07:06:51 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ugurdag:2016:ECC,
author = "H. Fatih Ugurdag and Anil Bayram and Vecdi Emre Levent
and Sezer G{\"o}ren",
title = "Efficient Combinational Circuits for Division by Small
Integer Constants",
crossref = "Montuschi:2016:ISC",
pages = "1--7",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.23",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23",
}
@InProceedings{vanderHoeven:2016:ESL,
author = "Joris van der Hoeven and Gr{\'e}goire Lecerf",
title = "Evaluating Straight-Line Programs over Balls",
crossref = "Montuschi:2016:ISC",
pages = "142--149",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.12",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23; interval arithmetic",
}
@Article{vanderHoeven:2016:MSA,
author = "Joris van der Hoeven and Gr{\'e}goire Lecerf and
Guillaume Quintin",
title = "Modular {SIMD} arithmetic in {Mathemagix}",
journal = j-TOMS,
volume = "43",
number = "1",
pages = "5:1--5:37",
month = aug,
year = "2016",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2876503",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Nov 22 17:45:25 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "http://dl.acm.org/citation.cfm?id=2876503",
abstract = "Modular integer arithmetic occurs in many algorithms
for computer algebra, cryptography, and error
correcting codes. Although recent microprocessors
typically offer a wide range of highly optimized
arithmetic functions, modular integer operations still
require dedicated implementations. In this article, we
survey existing algorithms for modular integer
arithmetic and present detailed vectorized
counterparts. We also describe several applications,
such as fast modular Fourier transforms and
multiplication of integer polynomials and matrices. The
vectorized algorithms have been implemented in C++
inside the free computer algebra and analysis system
Mathemagix. The performance of our implementation is
illustrated by various benchmarks.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://dl.acm.org/pub.cfm?id=J782",
}
@InProceedings{Villalba-Moreno:2016:DRF,
author = "Julio Villalba-Moreno",
title = "Digit Recurrence Floating-Point Division under {HUB}
Format",
crossref = "Montuschi:2016:ISC",
pages = "79--86",
year = "2016",
DOI = "https://doi.org/10.1109/ARITH.2016.17",
bibdate = "Fri Dec 16 15:17:20 MST 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-23; HUB (Half-Unit-Biased) floating-point
format",
}
@InProceedings{Wang:2016:DFP,
author = "Ran Wang and Daming Zou and Xinrui He and Yingfei
Xiong and Lu Zhang and Gang Huang",
booktitle = "{Proceedings of the 2016 24th ACM SIGSOFT
International Symposium on Foundations of Software
Engineering --- FSE 2016}",
title = "Detecting and fixing precision-specific operations for
measuring floating-point errors",
publisher = pub-ACM,
address = pub-ACM:adr,
year = "2016",
DOI = "https://doi.org/10.1145/2950290.2950355",
bibdate = "Thu Oct 17 06:42:14 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The accuracy of the floating-point calculation is
critical to many applications and different methods
have been proposed around floating-point accuracies,
such as detecting the errors in the program, verifying
the accuracy of the program, and optimizing the program
to produce more accurate results. These approaches need
a specification of the program to understand the ideal
calculation performed by the program, which is usually
approached by interpreting the program in a
precision-unspecific way.\par
However, many operations programmed in existing code
are inherently precision-specific, which cannot be
easily interpreted in a precision-unspecific way. In
fact, the semantics used in existing approaches usually
fail to interpret precision-specific operations
correctly.\par
In this paper, we present a systematic study on
precision-specific operations. First, we propose a
detection approach to detect precision-specific
operations. Second, we propose a fixing approach to
enable the tuning of precisions under the presence of
precision-specific operations. Third, we studied the
precision-specific operations in the GNU C standard
math library based on our detection and fixing
approaches. Our results show that (1) a significant
number of code fragments in the standard C math library
are precision-specific operations, and some large
inaccuracies reported in existing studies are false
positives or potential false positives due to
precision-specific operations; (2) our detection
approach has high precision and recall; (3) our fixing
approach can lead to overall more accurate result.",
acknowledgement = ack-nhfb,
}
@Article{Wilson:2016:UAA,
author = "David Wilson and Greg Stitt",
title = "The Unified Accumulator Architecture: a Configurable,
Portable, and Extensible Floating-Point Accumulator",
journal = j-TRETS,
volume = "9",
number = "3",
pages = "21:1--21:??",
month = jul,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2809432",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Thu Jul 14 16:35:43 MDT 2016",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "Applications accelerated by field-programmable gate
arrays (FPGAs) often require pipelined floating-point
accumulators with a variety of different trade-offs.
Although previous work has introduced numerous
floating-point accumulation architectures, few cores
are available for public use, which forces designers to
use fixed-point implementations or vendor-provided
cores that are not portable and are often not optimized
for the desired set of trade-offs. In this article, we
combine and extend previous floating-point accumulator
architectures into a configurable, open-source core,
referred to as the unified accumulator architecture
(UAA), which enables designers to choose between
different trade-offs for different applications. UAA is
portable across FPGAs and allows designers to
specialize the underlying adder core to take advantage
of device-specific optimizations. By providing an
extensible, open-source implementation, we hope for the
research community to extend the provided core with new
architectures and optimizations.",
acknowledgement = ack-nhfb,
articleno = "21",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@Article{Zhou:2016:PUH,
author = "Yuanyuan Zhou",
title = "Programming Uncertain {$<$T$>$ hings}",
journal = j-COMP-ARCH-NEWS,
volume = "44",
number = "2",
pages = "1--2",
month = may,
year = "2016",
CODEN = "CANED2",
DOI = "https://doi.org/10.1145/2980024.2872416",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
ISSN-L = "0163-5964",
bibdate = "Thu Jan 12 18:43:42 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
abstract = "Innovation flourishes with good abstractions. For
instance, codification of the IEEE Floating Point
standard in 1985 was critical to the subsequent success
of scientific computing. Programming languages
currently lack appropriate abstractions for uncertain
data. Applications already use estimates from sensors,
machine learning, big data, humans, and approximate
algorithms, but most programming languages do not help
developers address correctness, programmability, and
optimization problems due to estimates. To address
these problems, we propose a new programming
abstraction called Uncertain. We encourage the
community to develop and use abstractions for
estimates.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGARCH Computer Architecture News",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89",
remark = "ASPLOS'16 conference proceedings.",
}
@Article{Aliasgari:2017:SCH,
author = "Mehrdad Aliasgari and Marina Blanton and Fattaneh
Bayatbabolghani",
title = "Secure computation of hidden {Markov} models and
secure floating-point arithmetic in the malicious
model",
journal = j-INT-J-INFO-SEC,
volume = "16",
number = "6",
pages = "577--601",
month = nov,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10207-016-0350-0",
ISSN = "1615-5262 (print), 1615-5270 (electronic)",
ISSN-L = "1615-5262",
bibdate = "Tue Jan 23 16:01:49 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjinfosec.bib",
URL = "http://link.springer.com/article/10.1007/s10207-016-0350-0",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Information Security",
journal-URL = "https://link.springer.com/journal/10207",
keywords = "Floating point; Gaussian mixture models; Hidden Markov
models; Secure computation",
}
@Article{Anderson:2017:EMF,
author = "Andrew Anderson and Servesh Muralidharan and David
Gregg",
title = "Efficient Multibyte Floating Point Data Formats Using
Vectorization",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2081--2096",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2716355",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7950938/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Angerd:2017:FAC,
author = "Alexandra Angerd and Erik Sintorn and Per
Stenstr{\"o}m",
title = "A Framework for Automated and Controlled
Floating-Point Accuracy Reduction in Graphics
Applications on {GPUs}",
journal = j-TACO,
volume = "14",
number = "4",
pages = "46:1--46:??",
month = dec,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3151032",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Fri Dec 22 18:25:55 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
abstract = "Reducing the precision of floating-point values can
improve performance and/or reduce energy expenditure in
computer graphics, among other, applications. However,
reducing the precision level of floating-point values
in a controlled fashion needs support both at the
compiler and at the microarchitecture level. At the
compiler level, a method is needed to automate the
reduction of precision of each floating-point value. At
the microarchitecture level, a lower precision of each
floating-point register can allow more floating-point
values to be packed into a register file. This,
however, calls for new register file organizations.
This article proposes an automated precision-selection
method and a novel GPU register file organization that
can store floating-point register values at arbitrary
precisions densely. The automated precision-selection
method uses a data-driven approach for setting the
precision level of floating-point values, given a
quality threshold and a representative set of input
data. By allowing a small, but acceptable, degradation
in output quality, our method can remove a significant
amount of the bits needed to represent floating-point
values in the investigated kernels (between 28\% and
60\%). Our proposed register file organization exploits
these lower-precision floating-point values by packing
several of them into the same physical register. This
reduces the register pressure per thread by up to 48\%,
and by 27\% on average, for a negligible output-quality
degradation. This can enable GPUs to keep up to twice
as many threads in flight simultaneously.",
acknowledgement = ack-nhfb,
articleno = "46",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J924",
}
@InProceedings{Anonymous:2017:AI,
author = "Anonymous",
title = "Author index",
crossref = "Burgess:2017:ISC",
pages = "196--196",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.41",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents an index of the authors whose articles are
published in the conference proceedings record.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:C,
author = "Anonymous",
title = "Committees",
crossref = "Burgess:2017:ISC",
pages = "x--x",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.5",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:CN,
author = "Anonymous",
title = "{[Copyright} notice]",
crossref = "Burgess:2017:ISC",
pages = "iv--iv",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.3",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the copyright information for the conference.
May include reprint permission information.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:F,
author = "Anonymous",
title = "Foreword",
crossref = "Burgess:2017:ISC",
pages = "viii--ix",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.4",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the introductory welcome message from the
conference proceedings. May include the conference
officers' congratulations to all involved with the
conference event and publication of the proceedings
record.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:FC,
author = "Anonymous",
title = "{[Front} cover]",
crossref = "Burgess:2017:ISC",
pages = "c1--c1",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.43",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the front cover or splash screen of the
proceedings record.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:PCM,
author = "Anonymous",
title = "Program Committee Members",
crossref = "Burgess:2017:ISC",
pages = "xi--xi",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.6",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:PI,
author = "Anonymous",
title = "{[Publisher's} information]",
crossref = "Burgess:2017:ISC",
pages = "198--198",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.42",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:SC,
author = "Anonymous",
title = "Steering Committee",
crossref = "Burgess:2017:ISC",
pages = "xii--xii",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.7",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:TC,
author = "Anonymous",
title = "Table of contents",
crossref = "Burgess:2017:ISC",
pages = "v--vii",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.8",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The following topics are dealt with: multiprecision
arithmetic; computer arithmetic; DSP; floating-point
error analysis; reproducible arithmetic; FPGA; matrix
computations; and cryptography.",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic; cryptography; digital signal
processing chips; DSP; error analysis; field
programmable gate arrays; floating point arithmetic;
floating-point error analysis; FPGA; matrix algebra;
matrix computations; multiprecision arithmetic;
reproducible arithmetic",
}
@InProceedings{Anonymous:2017:TP,
author = "Anonymous",
title = "{[Title} page i]",
crossref = "Burgess:2017:ISC",
pages = "i--i",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.1",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2017:TPI,
author = "Anonymous",
title = "{[Title} page iii]",
crossref = "Burgess:2017:ISC",
pages = "iii--iii",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.2",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
}
@Article{Aurentz:2017:CCS,
author = "Jared L. Aurentz and Lloyd N. Trefethen",
title = "Chopping a {Chebyshev} Series",
journal = j-TOMS,
volume = "43",
number = "4",
pages = "33:1--33:21",
month = mar,
year = "2017",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2998442",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65G50 (65Y04)",
MRnumber = "3638570",
bibdate = "Fri Mar 24 08:51:05 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Chebfun and related software projects for numerical
computing with functions are based on the idea that at
each step of a computation, a function $ f(x) $ defined
on an interval $ [a, b] $ is ``rounded'' to a
prescribed precision by constructing a Chebyshev series
and chopping it at an appropriate point. Designing a
chopping algorithm with the right properties proves to
be a surprisingly complex and interesting problem. We
describe the chopping algorithm introduced in Chebfun
Version 5.3 in 2015 after many years of discussion and
the considerations that led to this design.",
acknowledgement = ack-nhfb,
articleno = "33",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{B:2017:GML,
author = "Sudeepa K. B. and Ganesh Aithal",
title = "Generation of maximum length non-binary key sequence
and its application for stream cipher based on residue
number system",
journal = j-J-COMPUT-SCI,
volume = "21",
pages = "379--386",
month = jul,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.jocs.2016.10.006",
ISSN = "1877-7503 (print), 1877-7511 (electronic)",
ISSN-L = "1877-7503",
MRclass = "94A60",
MRnumber = "3685019",
bibdate = "Tue Sep 19 13:54:25 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S1877750316302071",
acknowledgement = ack-nhfb,
ajournal = "J. Comput. Sci.",
fjournal = "Journal of Computational Science",
journal-URL = "https://www.sciencedirect.com/journal/journal-of-computational-science",
}
@Book{Beebe:2017:MFC,
author = "Nelson H. F. Beebe",
title = "The Mathematical-Function Computation Handbook:
Programming Using the {MathCW} Portable Software
Library",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxvi + 1114",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-64110-2",
ISBN = "3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)",
ISBN-13 = "978-3-319-64109-6 (hardcover), 978-3-319-64110-2
(e-book)",
LCCN = "QA75.5-76.95",
bibdate = "Sat Jul 15 19:34:43 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/mupad.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
URL = "http://www.springer.com/us/book/9783319641096",
acknowledgement = ack-nhfb,
ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
tableofcontents = "List of figures / xxv \\
List of tables / xxxi \\
Quick start / xxxv \\
1: Introduction / 1 \\
1.1: Programming conventions / 2 \\
1.2: Naming conventions / 4 \\
1.3: Library contributions and coverage / 5 \\
1.4: Summary / 6 \\
2: Iterative solutions and other tools / 7 \\
2.1: Polynomials and Taylor series / 7 \\
2.2: First-order Taylor series approximation / 8 \\
2.3: Second-order Taylor series approximation / 9 \\
2.4: Another second-order Taylor series approximation /
9 \\
2.5: Convergence of second-order methods / 10 \\
2.6: Taylor series for elementary functions / 10 \\
2.7: Continued fractions / 12 \\
2.8: Summation of continued fractions / 17 \\
2.9: Asymptotic expansions / 19 \\
2.10: Series inversion / 20 \\
2.11: Summary / 22 \\
3: Polynomial approximations / 23 \\
3.1: Computation of odd series / 23 \\
3.2: Computation of even series / 25 \\
3.3: Computation of general series / 25 \\
3.4: Limitations of Cody\slash Waite polynomials / 28
\\
3.5: Polynomial fits with Maple / 32 \\
3.6: Polynomial fits with Mathematica / 33 \\
3.7: Exact polynomial coefficients / 42 \\
3.8: Cody\slash Waite rational polynomials / 43 \\
3.9: Chebyshev polynomial economization / 43 \\
3.10: Evaluating Chebyshev polynomials / 48 \\
3.11: Error compensation in Chebyshev fits / 50 \\
3.12: Improving Chebyshev fits / 51 \\
3.13: Chebyshev fits in rational form / 52 \\
3.14: Chebyshev fits with Mathematica / 56 \\
3.15: Chebyshev fits for function representation / 57
\\
3.16: Extending the library / 57 \\
3.17: Summary and further reading / 58 \\
4: Implementation issues / 61 \\
4.1: Error magnification / 61 \\
4.2: Machine representation and machine epsilon / 62
\\
4.3: IEEE 754 arithmetic / 63 \\
4.4: Evaluation order in C / 64 \\
4.5: The {\tt volatile} type qualifier / 65 \\
4.6: Rounding in floating-point arithmetic / 66 \\
4.7: Signed zero / 69 \\
4.8: Floating-point zero divide / 70 \\
4.9: Floating-point overflow / 71 \\
4.10: Integer overflow / 72 \\
4.11: Floating-point underflow / 77 \\
4.12: Subnormal numbers / 78 \\
4.13: Floating-point inexact operation / 79 \\
4.14: Floating-point invalid operation / 79 \\
4.15: Remarks on NaN tests / 80 \\
4.16: Ulps --- units in the last place / 81 \\
4.17: Fused multiply-add / 85 \\
4.18: Fused multiply-add and polynomials / 88 \\
4.19: Significance loss / 89 \\
4.20: Error handling and reporting / 89 \\
4.21: Interpreting error codes / 93 \\
4.22: C99 changes to error reporting / 94 \\
4.23: Error reporting with threads / 95 \\
4.24: Comments on error reporting / 95 \\
4.25: Testing function implementations / 96 \\
4.26: Extended data types on Hewlett--Packard HP-UX
IA-64 / 100 \\
4.27: Extensions for decimal arithmetic / 101 \\
4.28: Further reading / 103 \\
4.29: Summary / 104 \\
5: The floating-point environment / 105 \\
5.1: IEEE 754 and programming languages / 105 \\
5.2: IEEE 754 and the mathcw library / 106 \\
5.3: Exceptions and traps / 106 \\
5.4: Access to exception flags and rounding control /
107 \\
5.5: The environment access pragma / 110 \\
5.6: Implementation of exception-flag and
rounding-control access / 110 \\
5.7: Using exception flags: simple cases / 112 \\
5.8: Using rounding control / 115 \\
5.9: Additional exception flag access / 116 \\
5.10: Using exception flags: complex case / 120 \\
5.11: Access to precision control / 123 \\
5.12: Using precision control / 126 \\
5.13: Summary / 127 \\
6: Converting floating-point values to integers / 129
\\
6.1: Integer conversion in programming languages / 129
\\
6.2: Programming issues for conversions to integers /
130 \\
6.3: Hardware out-of-range conversions / 131 \\
6.4: Rounding modes and integer conversions / 132 \\
6.5: Extracting integral and fractional parts / 132 \\
6.6: Truncation functions / 135 \\
6.7: Ceiling and floor functions / 136 \\
6.8: Floating-point rounding functions with fixed
rounding / 137 \\
6.9: Floating-point rounding functions: current
rounding / 138 \\
6.10: Floating-point rounding functions without {\em
inexact\/} exception / 139 \\
6.11: Integer rounding functions with fixed rounding /
140 \\
6.12: Integer rounding functions with current rounding
/ 142 \\
6.13: Remainder / 143 \\
6.14: Why the remainder functions are hard / 144 \\
6.15: Computing {\tt fmod} / 146 \\
6.16: Computing {\tt remainder} / 148 \\
6.17: Computing {\tt remquo} / 150 \\
6.18: Computing one remainder from the other / 152 \\
6.19: Computing the remainder in nonbinary bases / 155
\\
6.20: Summary / 156 \\
7: Random numbers / 157 \\
7.1: Guidelines for random-number software / 157 \\
7.2: Creating generator seeds / 158 \\
7.3: Random floating-point values / 160 \\
7.4: Random integers from floating-point generator /
165 \\
7.5: Random integers from an integer generator / 166
\\
7.6: Random integers in ascending order / 168 \\
7.7: How random numbers are generated / 169 \\
7.8: Removing generator bias / 178 \\
7.9: Improving a poor random number generator / 178 \\
7.10: Why long periods matter / 179 \\
7.11: Inversive congruential generators / 180 \\
7.12: Inversive congruential generators, revisited /
189 \\
7.13: Distributions of random numbers / 189 \\
7.14: Other distributions / 195 \\
7.15: Testing random-number generators / 196 \\
7.16: Applications of random numbers / 202 \\
7.17: The \textsf {mathcw} random number routines / 208
\\
7.18: Summary, advice, and further reading / 214 \\
8: Roots / 215 \\
8.1: Square root / 215 \\
8.2: Hypotenuse and vector norms / 222 \\
8.3: Hypotenuse by iteration / 227 \\
8.4: Reciprocal square root / 233 \\
8.5: Cube root / 237 \\
8.6: Roots in hardware / 240 \\
8.7: Summary / 242 \\
9: Argument reduction / 243 \\
9.1: Simple argument reduction / 243 \\
9.2: Exact argument reduction / 250 \\
9.3: Implementing exact argument reduction / 253 \\
9.4: Testing argument reduction / 265 \\
9.5: Retrospective on argument reduction / 265 \\
10: Exponential and logarithm / 267 \\
10.1: Exponential functions / 267 \\
10.2: Exponential near zero / 273 \\
10.3: Logarithm functions / 282 \\
10.4: Logarithm near one / 290 \\
10.5: Exponential and logarithm in hardware / 292 \\
10.6: Compound interest and annuities / 294 \\
10.7: Summary / 298 \\
11: Trigonometric functions / 299 \\
11.1: Sine and cosine properties / 299 \\
11.2: Tangent properties / 302 \\
11.3: Argument conventions and units / 304 \\
11.4: Computing the cosine and sine / 306 \\
11.5: Computing the tangent / 310 \\
11.6: Trigonometric functions in degrees / 313 \\
11.7: Trigonometric functions in units of $ \pi $ / 315
\\
11.8: Computing the cosine and sine together / 320 \\
11.9: Inverse sine and cosine / 323 \\
11.10: Inverse tangent / 331 \\
11.11: Inverse tangent, take two / 336 \\
11.12: Trigonometric functions in hardware / 338 \\
11.13: Testing trigonometric functions / 339 \\
11.14: Retrospective on trigonometric functions / 340
\\
12: Hyperbolic functions / 341 \\
12.1: Hyperbolic functions / 341 \\
12.2: Improving the hyperbolic functions / 345 \\
12.3: Computing the hyperbolic functions together / 348
\\
12.4: Inverse hyperbolic functions / 348 \\
12.5: Hyperbolic functions in hardware / 350 \\
12.6: Summary / 352 \\
13: Pair-precision arithmetic / 353 \\
13.1: Limitations of pair-precision arithmetic / 354
\\
13.2: Design of the pair-precision software interface /
355 \\
13.3: Pair-precision initialization / 356 \\
13.4: Pair-precision evaluation / 357 \\
13.5: Pair-precision high part / 357 \\
13.6: Pair-precision low part / 357 \\
13.7: Pair-precision copy / 357 \\
13.8: Pair-precision negation / 358 \\
13.9: Pair-precision absolute value / 358 \\
13.10: Pair-precision sum / 358 \\
13.11: Splitting numbers into pair sums / 359 \\
13.12: Premature overflow in splitting / 362 \\
13.13: Pair-precision addition / 365 \\
13.14: Pair-precision subtraction / 367 \\
13.15: Pair-precision comparison / 368 \\
13.16: Pair-precision multiplication / 368 \\
13.17: Pair-precision division / 371 \\
13.18: Pair-precision square root / 373 \\
13.19: Pair-precision cube root / 377 \\
13.20: Accuracy of pair-precision arithmetic / 379 \\
13.21: Pair-precision vector sum / 384 \\
13.22: Exact vector sums / 385 \\
13.23: Pair-precision dot product / 385 \\
13.24: Pair-precision product sum / 386 \\
13.25: Pair-precision decimal arithmetic / 387 \\
13.26: Fused multiply-add with pair precision / 388 \\
13.27: Higher intermediate precision and the FMA / 393
\\
13.28: Fused multiply-add without pair precision / 395
\\
13.29: Fused multiply-add with multiple precision / 401
\\
13.30: Fused multiply-add, Boldo/\penalty
\exhyphenpenalty Melquiond style / 403 \\
13.31: Error correction in fused multiply-add / 406 \\
13.32: Retrospective on pair-precision arithmetic / 407
\\
14: Power function / 411 \\
14.1: Why the power function is hard to compute / 411
\\
14.2: Special cases for the power function / 412 \\
14.3: Integer powers / 414 \\
14.4: Integer powers, revisited / 420 \\
14.5: Outline of the power-function algorithm / 421 \\
14.6: Finding $a$ and $p$ / 423 \\
14.7: Table searching / 424 \\
14.8: Computing $\log_n(g/a)$ / 426 \\
14.9: Accuracy required for $\log_n(g/a)$ / 429 \\
14.10: Exact products / 430 \\
14.11: Computing $w$, $w_1$ and $w_2$ / 433 \\
14.12: Computing $n^{w_2}$ / 437 \\
14.13: The choice of $q$ / 438 \\
14.14: Testing the power function / 438 \\
14.15: Retrospective on the power function / 440 \\
15: Complex arithmetic primitives / 441 \\
15.1: Support macros and type definitions / 442 \\
15.2: Complex absolute value / 443 \\
15.3: Complex addition / 445 \\
15.4: Complex argument / 445 \\
15.5: Complex conjugate / 446 \\
15.6: Complex conjugation symmetry / 446 \\
15.7: Complex conversion / 448 \\
15.8: Complex copy / 448 \\
15.9: Complex division: C99 style / 449 \\
15.10: Complex division: Smith style / 451 \\
15.11: Complex division: Stewart style / 452 \\
15.12: Complex division: Priest style / 453 \\
15.13: Complex division: avoiding subtraction loss /
455 \\
15.14: Complex imaginary part / 456 \\
15.15: Complex multiplication / 456 \\
15.16: Complex multiplication: error analysis / 458 \\
15.17: Complex negation / 459 \\
15.18: Complex projection / 460 \\
15.19: Complex real part / 460 \\
15.20: Complex subtraction / 461 \\
15.21: Complex infinity test / 462 \\
15.22: Complex NaN test / 462 \\
15.23: Summary / 463 \\
16: Quadratic equations / 465 \\
16.1: Solving quadratic equations / 465 \\
16.2: Root sensitivity / 471 \\
16.3: Testing a quadratic-equation solver / 472 \\
16.4: Summary / 474 \\
17: Elementary functions in complex arithmetic / 475
\\
17.1: Research on complex elementary functions / 475
\\
17.2: Principal values / 476 \\
17.3: Branch cuts / 476 \\
17.4: Software problems with negative zeros / 478 \\
17.5: Complex elementary function tree / 479 \\
17.6: Series for complex functions / 479 \\
17.7: Complex square root / 480 \\
17.8: Complex cube root / 485 \\
17.9: Complex exponential / 487 \\
17.10: Complex exponential near zero / 492 \\
17.11: Complex logarithm / 495 \\
17.12: Complex logarithm near one / 497 \\
17.13: Complex power / 500 \\
17.14: Complex trigonometric functions / 502 \\
17.15: Complex inverse trigonometric functions / 504
\\
17.16: Complex hyperbolic functions / 509 \\
17.17: Complex inverse hyperbolic functions / 514 \\
17.18: Summary / 520 \\
18: The Greek functions: gamma, psi, and zeta / 521 \\
18.1: Gamma and log-gamma functions / 521 \\
18.2: The {\tt psi} and {\tt psiln} functions / 536 \\
18.3: Polygamma functions / 547 \\
18.4: Incomplete gamma functions / 560 \\
18.5: A Swiss diversion: Bernoulli and Euler / 568 \\
18.6: An Italian excursion: Fibonacci numbers / 575 \\
18.7: A German gem: the Riemann zeta function / 579 \\
18.8: Further reading / 590 \\
18.9: Summary / 591 \\
19: Error and probability functions / 593 \\
19.1: Error functions / 593 \\
19.2: Scaled complementary error function / 598 \\
19.3: Inverse error functions / 600 \\
19.4: Normal distribution functions and inverses / 610
\\
19.5: Summary / 617 \\
20: Elliptic integral functions / 619 \\
20.1: The arithmetic-geometric mean / 619 \\
20.2: Elliptic integral functions of the first kind /
624 \\
20.3: Elliptic integral functions of the second kind /
627 \\
20.4: Elliptic integral functions of the third kind /
630 \\
20.5: Computing $K(m)$ and $K'(m)$ / 631 \\
20.6: Computing $E(m)$ and $E'(m)$ / 637 \\
20.7: Historical algorithms for elliptic integrals /
643 \\
20.8: Auxiliary functions for elliptic integrals / 645
\\
20.9: Computing the elliptic auxiliary functions / 648
\\
20.10: Historical elliptic functions / 650 \\
20.11: Elliptic functions in software / 652 \\
20.12: Applications of elliptic auxiliary functions /
653 \\
20.13: Elementary functions from elliptic auxiliary
functions / 654 \\
20.14: Computing elementary functions via $R_C(x,y)$ /
655 \\
20.15: Jacobian elliptic functions / 657 \\
20.16: Inverses of Jacobian elliptic functions / 664
\\
20.17: The modulus and the nome / 668 \\
20.18: Jacobian theta functions / 673 \\
20.19: Logarithmic derivatives of the Jacobian theta
functions / 675 \\
20.20: Neville theta functions / 678 \\
20.21: Jacobian Eta, Theta, and Zeta functions / 679
\\
20.22: Weierstrass elliptic functions / 682 \\
20.23: Weierstrass functions by duplication / 689 \\
20.24: Complete elliptic functions, revisited / 690 \\
20.25: Summary / 691 \\
21: Bessel functions / 693 \\
21.1: Cylindrical Bessel functions / 694 \\
21.2: Behavior of $J_n(x)$ and $Y_n(x)$ / 695 \\
21.3: Properties of $J_n(z)$ and $Y_n(z)$ / 697 \\
21.4: Experiments with recurrences for $J_0(x)$ / 705
\\
21.5: Computing $J_0(x)$ and $J_1(x)$ / 707 \\
21.6: Computing $J_n(x)$ / 710 \\
21.7: Computing $Y_0(x)$ and $Y_1(x)$ / 713 \\
21.8: Computing $Y_n(x)$ / 715 \\
21.9: Improving Bessel code near zeros / 716 \\
21.10: Properties of $I_n(z)$ and $K_n(z)$ / 718 \\
21.11: Computing $I_0(x)$ and $I_1(x)$ / 724 \\
21.12: Computing $K_0(x)$ and $K_1(x)$ / 726 \\
21.13: Computing $I_n(x)$ and $K_n(x)$ / 728 \\
21.14: Properties of spherical Bessel functions / 731
\\
21.15: Computing $j_n(x)$ and $y_n(x)$ / 735 \\
21.16: Improving $j_1(x)$ and $y_1(x)$ / 740 \\
21.17: Modified spherical Bessel functions / 743 \\
21.18: Software for Bessel-function sequences / 755 \\
21.19: Retrospective on Bessel functions / 761 \\
22: Testing the library / 763 \\
22.1: Testing {\tt tgamma} and {\tt lgamma} / 765 \\
22.2: Testing {\tt psi} and {\tt psiln} / 768 \\
22.3: Testing {\tt erf} and {\tt erfc} / 768 \\
22.4: Testing cylindrical Bessel functions / 769 \\
22.5: Testing exponent/\penalty \exhyphenpenalty
significand manipulation / 769 \\
22.6: Testing inline assembly code / 769 \\
22.7: Testing with Maple / 770 \\
22.8: Testing floating-point arithmetic / 773 \\
22.9: The Berkeley Elementary Functions Test Suite /
774 \\
22.10: The AT\&T floating-point test package / 775 \\
22.11: The Antwerp test suite / 776 \\
22.12: Summary / 776 \\
23: Pair-precision elementary functions / 777 \\
23.1: Pair-precision integer power / 777 \\
23.2: Pair-precision machine epsilon / 779 \\
23.3: Pair-precision exponential / 780 \\
23.4: Pair-precision logarithm / 787 \\
23.5: Pair-precision logarithm near one / 793 \\
23.6: Pair-precision exponential near zero / 793 \\
23.7: Pair-precision base-$n$ exponentials / 795 \\
23.8: Pair-precision trigonometric functions / 796 \\
23.9: Pair-precision inverse trigonometric functions /
801 \\
23.10: Pair-precision hyperbolic functions / 804 \\
23.11: Pair-precision inverse hyperbolic functions /
808 \\
23.12: Summary / 808 \\
24: Accuracy of the Cody\slash Waite algorithms / 811
\\
25: Improving upon the Cody\slash Waite algorithms /
823 \\
25.1: The Bell Labs libraries / 823 \\
25.2: The {Cephes} library / 823 \\
25.3: The {Sun} libraries / 824 \\
25.4: Mathematical functions on EPIC / 824 \\
25.5: The GNU libraries / 825 \\
25.6: The French libraries / 825 \\
25.7: The NIST effort / 826 \\
25.8: Commercial mathematical libraries / 826 \\
25.9: Mathematical libraries for decimal arithmetic /
826 \\
25.10: Mathematical library research publications / 826
\\
25.11: Books on computing mathematical functions / 827
\\
25.12: Summary / 828 \\
26: Floating-point output / 829 \\
26.1: Output character string design issues / 830 \\
26.2: Exact output conversion / 831 \\
26.3: Hexadecimal floating-point output / 832 \\
26.4: Octal floating-point output / 850 \\
26.5: Binary floating-point output / 851 \\
26.6: Decimal floating-point output / 851 \\
26.7: Accuracy of output conversion / 865 \\
26.8: Output conversion to a general base / 865 \\
26.9: Output conversion of Infinity / 866 \\
26.10: Output conversion of NaN / 866 \\
26.11: Number-to-string conversion / 867 \\
26.12: The {\tt printf} family / 867 \\
26.13: Summary / 878 \\
27: Floating-point input / 879 \\
27.1: Binary floating-point input / 879 \\
27.2: Octal floating-point input / 894 \\
27.3: Hexadecimal floating-point input / 895 \\
27.4: Decimal floating-point input / 895 \\
27.5: Based-number input / 899 \\
27.6: General floating-point input / 900 \\
27.7: The {\tt scanf} family / 901 \\
27.8: Summary / 910 \\
A: Ada interface / 911 \\
A.1: Building the Ada interface / 911 \\
A.2: Programming the Ada interface / 912 \\
A.3: Using the Ada interface / 915 \\
B: C\# interface / 917 \\
B.1: C\# on the CLI virtual machine / 917 \\
B.2: Building the C\# interface / 918 \\
B.3: Programming the C\# interface / 920 \\
B.4: Using the C\# interface / 922 \\
C: C++ interface / 923 \\
C.1: Building the C++ interface / 923 \\
C.2: Programming the C++ interface / 924 \\
C.3: Using the C++ interface / 925 \\
D: Decimal arithmetic / 927 \\
D.1: Why we need decimal floating-point arithmetic /
927 \\
D.2: Decimal floating-point arithmetic design issues /
928 \\
D.3: How decimal and binary arithmetic differ / 931 \\
D.4: Initialization of decimal floating-point storage /
935 \\
D.5: The {\tt <decfloat.h>} header file / 936 \\
D.6: Rounding in decimal arithmetic / 936 \\
D.7: Exact scaling in decimal arithmetic / 937 \\
E: Errata in the Cody\slash Waite book / 939 \\
F: Fortran interface / 941 \\
F.1: Building the Fortran interface / 943 \\
F.2: Programming the Fortran interface / 944 \\
F.3: Using the Fortran interface / 945 \\
H: Historical floating-point architectures / 947 \\
H.1: CDC family / 949 \\
H.2: Cray family / 952 \\
H.3: DEC PDP-10 / 953 \\
H.4: DEC PDP-11 and VAX / 956 \\
H.5: General Electric 600 series / 958 \\
H.6: IBM family / 959 \\
H.7: Lawrence Livermore S-1 Mark IIA / 965 \\
H.8: Unusual floating-point systems / 966 \\
H.9: Historical retrospective / 967 \\
I: Integer arithmetic / 969 \\
I.1: Memory addressing and integers / 971 \\
I.2: Representations of signed integers / 971 \\
I.3: Parity testing / 975 \\
I.4: Sign testing / 975 \\
I.5: Arithmetic exceptions / 975 \\
I.6: Notations for binary numbers / 977 \\
I.7: Summary / 978 \\
J: Java interface / 979 \\
J.1: Building the Java interface / 979 \\
J.2: Programming the Java MathCW class / 980 \\
J.3: Programming the Java C interface / 982 \\
J.4: Using the Java interface / 985 \\
L: Letter notation / 987 \\
P: Pascal interface / 989 \\
P.1: Building the Pascal interface / 989 \\
P.2: Programming the Pascal MathCW module / 990 \\
P.3: Using the Pascal module interface / 993 \\
P.4: Pascal and numeric programming / 994 \\
Bibliography / 995 \\
Author/editor index / 1039 \\
Function and macro index / 1049 \\
Subject index / 1065 \\
Colophon / 1115",
}
@InProceedings{Bocco:2017:HSU,
author = "Andrea Bocco and Yves Durand and Florent de Dinechin",
booktitle = "{2017 13th Conference on Ph.D. Research in
Microelectronics and Electronics (PRIME)}",
title = "Hardware support for {UNUM} floating point
arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "93--96",
year = "2017",
DOI = "https://doi.org/10.1109/PRIME.2017.7974115",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Boehm:2017:SDC,
author = "Hans-J. Boehm",
title = "Small-data computing: correct calculator arithmetic",
journal = j-CACM,
volume = "60",
number = "8",
pages = "44--49",
month = aug,
year = "2017",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/2911981",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Wed Jul 26 05:35:16 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Rounding errors are usually avoidable, and sometimes
we can afford to avoid them.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Book{Boldo:2017:CAF,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "Computer arithmetic and formal proofs: verifying
floating-point algorithms with the {Coq} system",
publisher = "ISTE Press",
address = "London, UK",
year = "2017",
ISBN = "1-78548-112-6, 0-08-101170-9 (e-book)",
ISBN-13 = "978-1-78548-112-3, 978-0-08-101170-6 (e-book)",
LCCN = "QA76.9.C62",
bibdate = "Tue Nov 28 08:55:56 MST 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
URL = "http://iste.co.uk/book.php?id=1238",
abstract = "Floating-point arithmetic is ubiquitous in modern
computing, as it is the tool of choice to approximate
real numbers. Due to its limited range and precision,
its use can become quite involved and potentially lead
to numerous failures. One way to greatly increase
confidence in floating-point software is by
computer-assisted verification of its correctness
proofs. This book provides a comprehensive view of how
to formally specify and verify tricky floating-point
algorithms with the Coq proof assistant. It describes
the Flocq formalization of floating-point arithmetic
and some methods to automate theorem proofs. It then
presents the specification and verification of various
algorithms, from error-free transformations to a
numerical scheme for a partial differential equation.
The examples cover not only mathematical algorithms but
also C programs as well as issues related to
compilation. Describes the notions of specification and
weakest precondition computation and their practical
use. Shows how to tackle algorithms that extend beyond
the realm of simple floating-point arithmetic. Includes
real analysis and a case study about numerical
analysis.",
acknowledgement = ack-nhfb,
subject = "Coq (Electronic resource); Computer arithmetic;
Floating-point arithmetic; Computer algorithms;
COMPUTERS / Computer Literacy; COMPUTERS / Computer
Science; COMPUTERS / Data Processing; COMPUTERS /
Hardware / General; COMPUTERS / Information Technology;
COMPUTERS / Machine Theory; COMPUTERS / Reference;
MATHEMATICS / Discrete Mathematics",
tableofcontents = "1. Floating-Point Arithmetic \\
2. The Coq System \\
3. Formalization of Formats and Basic Operators \\
4. Automated Methods \\
5. Error-Free Computations and Applications \\
6. Example Proofs of Advanced Operators \\
7. Compilation of FP Programs \\
8. Deductive Program Verification \\
9. Real and Numerical Analysis",
}
@InProceedings{Boldo:2017:REA,
author = "Sylvie Boldo and Florian Faissole and Alexandre
Chapoutot",
title = "Round-off Error Analysis of Explicit One-Step
Numerical Integration Methods",
crossref = "Burgess:2017:ISC",
pages = "82--89",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.22",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Ordinary differential equations are ubiquitous in
scientific computing. Solving exactly these equations
is usually not possible, except for special cases,
hence the use of numerical schemes to get a discretized
solution. We are interested in such numerical
integration methods, for instance Euler's method or the
Runge-Kutta methods. As they are implemented using
floating-point arithmetic, round-off errors occur. In
order to guarantee their accuracy, we aim at providing
bounds on the round-off errors of explicit one-step
numerical integration methods. Our methodology is to
apply a fine-grained analysis to these numerical
algorithms. Our originality is that our floating-point
analysis takes advantage of the linear stability of the
scheme, a mathematical property that vouches the scheme
is well-behaved.",
acknowledgement = ack-nhfb,
keywords = "differential equations; Differential equations;
explicit one-step numerical integration methods;
fine-grained analysis; floating point arithmetic;
floating-point analysis; floating-point arithmetic;
integration; linear stability; Mathematical model;
mathematical property; Numerical models; numerical
schemes; Numerical simulation; numerical stability;
Numerical stability; ordinary differential equations;
round-off error analysis; roundoff errors; scientific
computing; Stability analysis; Tools",
}
@Article{Boldo:2017:RFA,
author = "Sylvie Boldo and Stef Graillat and Jean-Michel
Muller",
title = "On the Robustness of the {2Sum} and {Fast2Sum}
Algorithms",
journal = j-TOMS,
volume = "44",
number = "1",
pages = "4:1--4:14",
month = jul,
year = "2017",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3054947",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Jul 14 16:39:28 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "The 2Sum and Fast2Sum algorithms are important
building blocks in numerical computing. They are used
(implicitly or explicitly) in many compensated
algorithms (such as compensated summation or
compensated polynomial evaluation). They are also used
for manipulating floating-point expansions. We show
that these algorithms are much more robust than it is
usually believed: The returned result makes sense even
when the rounding function is not round-to-nearest, and
they are almost immune to overflow.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Bos:2017:FAM,
author = "Joppe W. Bos and Simon Friedberger",
title = "Fast Arithmetic Modulo $ 2^x p^y \pm 1 $",
crossref = "Burgess:2017:ISC",
pages = "148--155",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.15",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We give a systematic overview of techniques to compute
arithmetic modulo $ 2^x p^y \pm 1 $ and propose
improvements. This is useful for computations in the
supersingular isogeny Diffie-Hellman (SIDH)
key-exchange protocol which is one of the more recent
contenders in the post-quantum public-key arena. One of
the main computational bottlenecks in this
cryptographic key-exchange protocol is computing
modular arithmetic in a finite field defined by a prime
of this special shape. Recent implementations already
use this special prime shape to speed up the
cryptographic implementations but it remains unclear if
the choices made are optimal or if one can do better.
Our overview shows that in the SIDH setting, where
arithmetic over a quadratic extension field is
required, the approaches based on Montgomery
multiplication are to be preferred. Based on our
results, we give selection criteria for such moduli and
the outcome of our search reveals that there exist
moduli which result in even faster implementations.",
acknowledgement = ack-nhfb,
keywords = "Barrett reduction; computational bottlenecks;
cryptographic key-exchange protocol; cryptographic
protocols; Electronic mail; Elliptic curves; fast
arithmetic modulo; finite field; modular arithmetic;
Montgomery multiplication; Optimization; post-quantum
cryptography; post-quantum public-key arena; Protocols;
Public key cryptography; public key cryptography;
quadratic extension field; quantum cryptography;
selection criteria; Shape; SIDH; SIDH key-exchange
protocol; supersingular isogeny Diffie--Hellman
key-exchange protocol",
}
@Article{Brisebarre:2017:ESC,
author = "Nicolas Brisebarre and Guillaume Hanrot and Olivier
Robert",
title = "Exponential Sums and Correctly-Rounded Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2044--2057",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2690850",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7891945/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@PhdThesis{Brisebarre:2017:PTN,
author = "Nicolas Brisebarre",
title = "Un peu de th{\'e}orie des nombres et de calcul formel
au service de l'arithm{\'e}tique des ordinateurs.
({French}) [{A} little number theory and computer
algebra in the service of computer arithmetic]",
type = "Habilitation {\`a} Diriger des Recherches",
school = "LIP --- Laboratoire de l'Informatique du
Parall{\'e}lisme",
address = "Lyon, France",
pages = "125",
year = "2017",
bibdate = "Fri Dec 08 10:49:49 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://theses.hal.science/tel-01658342v3",
acknowledgement = ack-nhfb,
}
@InProceedings{Brunie:2017:MFM,
author = "Nicolas Brunie",
title = "Modified Fused Multiply and Add for Exact Low
Precision Product Accumulation",
crossref = "Burgess:2017:ISC",
pages = "106--113",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.29",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The implementation of the Fused Multiply and Add (FMA)
operation has been extensively studied in the
literature on standard and large precisions. We suggest
re- visiting those studies for 16-bit precision. We
introduce a variation of the Mixed precision FMA
targeted for applications processing low precision
inputs (such as machine learning). We also introduce
several versions of a fixed point based floating- point
FMA which performs an exact accumulation of binary16
numbers. We study the implementation and area footprint
of those operators in comparison with standard FMAs.",
acknowledgement = ack-nhfb,
keywords = "adders; Adders; arithmetic; Complexity theory;
Computer architecture; exact low precision product
accumulation; fixed point arithmetic; fixed point based
floating- point FMA; floating-point; FMA; FPU; fused
multiply and add operation; half precision; Hardware;
Linear algebra; logic design; mixed precision FMA;
multiplying circuits; Standards",
}
@Misc{Carter:2017:PAO,
author = "John B. Carter and Bruce G. Mealey and Karthick
Rajamani and Eric E. Retter and Jeffrey A. Stuecheli",
title = "Performing arithmetic operations using both large and
small floating point values",
howpublished = "US Patent 9,665,346",
day = "30",
month = may,
year = "2017",
bibdate = "Thu Oct 17 11:38:25 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US9665346B2",
abstract = "Mechanisms are provided for performing a floating
point arithmetic operation in a data processing system.
A plurality of floating point operands of the floating
point arithmetic operation are received and bits in a
mantissa of at least one floating point operand of the
plurality of floating point operands are shifted. One
or more bits of the mantissa that are shifted outside a
range of bits of the mantissa of at least one floating
point operand are stored and a vector value is
generated based on the stored one or more bits of the
mantissa that are shifted outside of the range of bits
of the mantissa of the at least one floating point
operand. A resultant value is generated for the
floating point arithmetic operation based on the vector
value and the plurality of floating point operands.",
acknowledgement = ack-nhfb,
remark = "Patent filed 28 October 2014, granted to IBM 30 May
2017, expected expiration 22 December 2031 (in 17th
year after filing).",
}
@MastersThesis{Chapp:2017:SIN,
author = "Dylan Chapp",
title = "Study of the impact of non-determinism on numerical
reproducibility and debugging at the exascale",
type = "Master of Science in Computer Science",
school = "University of Delaware",
address = "Newark, DE, USA",
pages = "69",
month = "Spring",
year = "2017",
ISBN = "0-355-25168-X",
ISBN-13 = "978-0-355-25168-5",
LCCN = "????",
bibdate = "Mon Feb 10 06:07:39 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://udspace.udel.edu/handle/19716/24492;
https://search.proquest.com/pqdtglobal/docview/1957944576",
abstract = "Non-determinism in high performance scientific
applications has severe detrimental impacts for both
numerical reproducibility and accuracy, and debugging.
As scientific simulations are migrated to extreme-scale
platforms, the increase in platform concurrency and the
attendant increase in non-determinism is likely to
exacerbate both of these problems. In this thesis, we
address the dual challenges of non-determinism's impact
on numerical reproducibility and on debugging. To
address the numerical challenge, our work investigates
the power of mathematical methods to mitigate error
propagation at the exascale. We focus on floating-point
error accumulation over global summations where
enforcing any reduction order is expensive or
impossible. We model parallel summations with reduction
trees and identify those parameters that can be used to
estimate the reduction's sensitivity to variability in
the reduction tree. We assess the impact of these
parameters on the ability of different reduction
methods to successfully mitigate errors. Our results
illustrate the pressing need for intelligent runtime
selection of reduction operators that ensure a given
degree of reproducible accuracy. To address the
debugging challenge, our work examines the impact of
logical clock ticking policies on the Clock-Delta
Compression record-and-replay technique. We assess
three logical clock ticking policies in terms of the
number of out-of-order messages that result during
recording executions under these policies. We examine
the performance of Clock-Delta Compression when using
the three ticking policies in four distinct application
scenarios to probe the impact of floating-point
workload and communication intensity on recording
performance. Our results illustrate the pressing need
for fine-grained logical clock ticking policies that
reduce the out-of-order message rate of the Clock-Delta
Compression record-and-replay technique.",
acknowledgement = ack-nhfb,
advisor = "Michela Taufer",
}
@InProceedings{Chiang:2017:RFP,
author = "Wei-Fan Chiang and Mark Baranowski and Ian Briggs and
Alexey Solovyev and Ganesh Gopalakrishnan and Zvonimir
Rakamari{\'c}",
booktitle = "Proceedings of the {ACM SIGPLAN Symposium on
Principles of Programming Languages (POPL)}",
title = "Rigorous Floating-Point Mixed-Precision Tuning",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "300--315",
year = "2017",
DOI = "https://doi.org/10.1145/3009837.3009846",
bibdate = "Fri Mar 31 10:00:31 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Virtually all real-valued computations are carried out
using floating-point data types and operations. The
precision of these data types must be set with the
goals of reducing the overall round-off error, but also
emphasizing performance improvements. Often, a
mixed-precision allocation achieves this optimum;
unfortunately, there are no techniques available to
compute such allocations and conservatively meet a
given error target across all program inputs. In this
work, we present a rigorous approach to precision
allocation based on formal analysis via Symbolic Taylor
Expansions, and error analysis based on interval
functions. This approach is implemented in an automated
tool called FPTuner that generates and solves a
quadratically constrained quadratic program to obtain a
precision-annotated version of the given expression.
FPTuner automatically introduces all the requisite
precision up and down casting operations. It also
allows users to flexibly control precision allocation
using constraints to cap the number of high precision
operators as well as group operators to allocate the
same precision to facilitate vectorization. We evaluate
FPTuner by tuning several benchmarks and measuring the
proportion of lower precision operators allocated as we
increase the error threshold. We also measure the
reduction in energy consumption resulting from
executing mixed-precision tuned code on a real hardware
platform. We observe significant energy savings in
response to mixed-precision tuning, but also observe
situations where unexpected compiler behaviors thwart
intended optimizations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chohra:2017:RAR,
author = "Chemseddine Chohra and Philippe Langlois and David
Parello",
title = "Reproducible, accurately rounded and efficient
{BLAS}",
crossref = "Desprez:2017:EPP",
pages = "609--620",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-58943-5_49",
bibdate = "Mon Feb 10 06:36:40 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Constantinides:2017:AAC,
author = "George Anthony Constantinides",
title = "Algorithms and Arithmetic: Choose Wisely",
crossref = "Burgess:2017:ISC",
pages = "142--143",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.17",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "I will introduce a semi-formalism to allow us to
conceptually reason about the differences between
customised arithmetic design, as one might see in
FPGA-based compute, and general purpose arithmetic, as
one might find in microprocessor design. This framework
will, I hope, expose to the reader the reason that we
should be thinking carefully about appropriate data
representations when designing custom hardware for
compute, as well as clearly showing the link between
these decisions and algorithmic ones. I will then
provide a concrete example from the literature on
matrix computation where some careful algorithmic
tweaking results in the ability to use fixed-point
arithmetic and, hence, far higher performance than
would otherwise be achieved.",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; arithmetic design;
Automation; data representations; data structures;
digital arithmetic; field programmable gate arrays;
Field programmable gate arrays; fixed-point arithmetic;
FPGA; general purpose arithmetic; Hardware; Kernel;
logic design; matrix algebra; matrix computation;
microprocessor design; Microprocessors; Signal
processing algorithms",
}
@InProceedings{Cornea:2017:URE,
author = "Marius Cornea",
title = "{ULPs} and Relative Error",
crossref = "Burgess:2017:ISC",
pages = "90--97",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.30",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The paper establishes several simple, but useful
relationships between ulp (unit in the last place)
errors and the corresponding relative errors. These can
be used when converting between the two types of
errors, ensuring that the least amount of information
is lost in the process. The properties presented here
were already useful in IEEE conformance proofs for
iterative division and square root algorithms, and
should be so again to numerical analysts both in 'hand'
proofs of error bounds for floating-point computations,
and in automated tools which carry out, or support
deriving such proofs. In most cases, the properties
shown herein establish tighter bounds than found in the
literature. They also provide 'conversion' rules of
finer granularity, at floating-point value level
instead of binade level, and take into account the
special conditions which occur at binade ends. For this
reason, the paper includes a small, but non-negligible
element of novelty.",
acknowledgement = ack-nhfb,
keywords = "approximation; correctly rounded; error; floating
point arithmetic; floating-point; floating-point
computations; IEEE 754-2008; IEEE conformance proofs;
iterative division; iterative methods; numerical
analysis; quantum; relative error; square root
algorithms; ULP; ulp; ulp error; unit in the last
place",
}
@Article{Cui:2017:HPP,
author = "Xiaoping Cui and Wenwen Dong and Weiqiang Liu and Earl
E. Swartzlander and Fabrizio Lombardi",
title = "High Performance Parallel Decimal Multipliers Using
Hybrid {BCD} Codes",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "1994--2004",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2706262",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7931610/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Dai:2017:ATE,
author = "Wangchen Dai and Donald Donglong Chen and Ray C. C.
Cheung and {\c{C}}etin Kaya Ko{\c{c}}",
title = "Area-Time Efficient Architecture of {FFT}-Based
{Montgomery} Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "3",
pages = "375--388",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2016.2601334",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Feb 10 09:07:14 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Damouche:2017:INA,
author = "Nasrine Damouche and Matthieu Martel and Alexandre
Chapoutot",
title = "Improving the numerical accuracy of programs by
automatic transformation",
journal = j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
volume = "19",
number = "4",
pages = "427--448",
month = aug,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1007/s10009-016-0435-0",
ISSN = "1433-2779 (print), 1433-2787 (electronic)",
ISSN-L = "1433-2779",
bibdate = "Thu Nov 23 07:32:25 MST 2017",
bibsource = "http://link.springer.com/journal/10009/19/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sttt.bib",
URL = "https://link.springer.com/article/10.1007/s10009-016-0435-0",
acknowledgement = ack-nhfb,
fjournal = "International Journal on Software Tools for Technology
Transfer (STTT)",
journal-URL = "http://link.springer.com/journal/10009",
keywords = "Floating-point numbers; IEEE 754 standard; Numerical
accuracy; Program transformation; Static analysis",
}
@Article{Darulova:2017:TCR,
author = "Eva Darulova and Viktor Kuncak",
title = "Towards a Compiler for Reals",
journal = j-TOPLAS,
volume = "39",
number = "2",
pages = "8:1--8:??",
month = may,
year = "2017",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/3014426",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Mon Jul 24 09:44:40 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toplas/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toplas.bib",
abstract = "Numerical software, common in scientific computing or
embedded systems, inevitably uses a finite-precision
approximation of the real arithmetic in which most
algorithms are designed. In many applications, the
roundoff errors introduced by finite-precision
arithmetic are not the only source of inaccuracy, and
measurement and other input errors further increase the
uncertainty of the computed results. Adequate tools are
needed to help users select suitable data types and
evaluate the provided accuracy, especially for
safety-critical applications. We present a
source-to-source compiler called Rosa that takes as
input a real-valued program with error specifications
and synthesizes code over an appropriate floating-point
or fixed-point data type. The main challenge of such a
compiler is a fully automated, sound, and yet
accurate-enough numerical error estimation. We
introduce a unified technique for bounding roundoff
errors from floating-point and fixed-point arithmetic
of various precisions. The technique can handle
nonlinear arithmetic, determine closed-form symbolic
invariants for unbounded loops, and quantify the
effects of discontinuities on numerical errors. We
evaluate Rosa on a number of benchmarks from scientific
computing and embedded systems and, comparing it to the
state of the art in automated error estimation, show
that it presents an interesting tradeoff between
accuracy and performance.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
}
@Article{David:2017:LLD,
author = "Jean Pierre David",
title = "Low latency and division free {Gauss--Jordan} solver
in floating point arithmetic",
journal = j-J-PAR-DIST-COMP,
volume = "106",
number = "??",
pages = "185--193",
month = aug,
year = "2017",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Aug 19 13:10:31 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0743731516301897",
acknowledgement = ack-nhfb,
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
}
@Article{Dawson:2017:RVE,
author = "Andrew Dawson and Peter D. D{\"u}ben",
title = "{rpe v5}: an emulator for reduced floating-point
precision in large numerical simulations",
journal = j-GEOSCI-MODEL-DEV,
volume = "10",
number = "6",
pages = "2221--2230",
month = jun,
year = "2017",
DOI = "https://doi.org/10.5194/gmd-10-2221-2017",
ISSN = "1991-959X (print), 1991-9603 (electronic)",
ISSN-L = "1991-959X",
bibdate = "Thu Nov 7 16:40:41 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Geoscientific Model Development",
journal-URL = "http://www.geosci-model-dev.net",
}
@InProceedings{Dimitrov:2017:PMC,
author = "Vassil Dimitrov and Viduneth Ariyarathna and Diego F.
G. Coelho and Logan Rakai and Arjuna Madanayake and
Renato J. Cintra",
title = "A Parallel Method for the Computation of Matrix
Exponential Based on Truncated {Neumann} Series",
crossref = "Burgess:2017:ISC",
pages = "35--42",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.23",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper introduces a new method for computing
matrix exponential based on truncated Neumann series.
The efficiency of the method is based on smart
factorizations for evaluation of several Neumann series
that can be done in parallel and divided across
different processors with low communication overhead. A
physical realization on FPGA is provided for
proof-of-concept. The method is verified to be
advantageous over the usual Horner's rule approach for
polynomial evaluation. The hardware verification shows
a reduction of 62\% in time required for processing for
series approximations with 9 terms. Software
verification demonstrates a 30\% reduction in time
compared to Horner's rule and the trade-offs between
using a higher precision approach is illustrated.",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; approximation theory;
Eigenvalues and eigenfunctions; Error analysis; Fast
algorithms; field programmable gate arrays; FPGA;
Hardware; Horner's rule approach; low communication
overhead; matrix algebra; matrix decomposition; matrix
exponential; Matrix exponential; Neumann series;
parallel method; polynomial evaluation; polynomials;
Program processors; series (mathematics); series
approximations; smart factorizations; Software
algorithms; software verification; truncated Neumann
series; VLSI",
}
@Article{Du:2017:AQD,
author = "Peibing Du and Roberto Barrio and Hao Jiang and Lizhi
Cheng",
title = "Accurate quotient-difference algorithm: Error
analysis, improvements and applications",
journal = j-APPL-MATH-COMP,
volume = "309",
number = "??",
pages = "245--271",
day = "15",
month = sep,
year = "2017",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Aug 12 16:28:39 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300317302394",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Book{Esmay:2017:HNS,
author = "Gabriel Esmay",
title = "The History of Number Systems",
publisher = "Teacher Created Materials",
address = "Huntington Beach, CA",
pages = "32",
year = "2017",
ISBN = "0-7439-2834-2 (e-book), 1-0876-2972-1, 1-4807-5794-2
(paperback), 1-4807-5858-2 (e-book)",
ISBN-13 = "978-0-7439-2834-2 (e-book), 978-1-0876-2972-8,
978-1-4807-5794-3 (paperback), 978-1-4807-5858-2
(e-book)",
LCCN = "QA141.3 .E86 2018",
bibdate = "Fri Mar 17 08:27:53 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Learn the history of number systems with this engaging
math reader! This text combines mathematics and
literacy skills, and uses practical, real-world
examples of problem solving to teach math and language
arts content. Students will learn place value while
reading about the number systems of the Egyptians and
Romans, and also learn important vocabulary terms like
cuneiform, binary systems, roman numerals, and more!
The full-color images, math charts, and practice
problems make learning math easy and fun. The table of
contents, glossary, and index will further
understanding of math and reading concepts. The Math
Talk problems and Explore Math sidebars provide
additional learning opportunities while developing
students higher-order thinking skills.",
acknowledgement = ack-nhfb,
subject = "Numeration; History; Juvenile literature; Counting;
Calcul; Ouvrages pour la jeunesse; Counting.;
Numeration.",
tableofcontents = "Timeless need \\
Egypt \\
Babylon \\
Roman empire \\
Americas \\
Modern beginnings \\
Future of number systems \\
Problem solving \\
Glossary",
}
@Misc{Fevotte:2017:LLI,
author = "Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re",
title = "{LibEFT}: a library implementing Error-Free
transformations",
howpublished = "Web site.",
year = "2017",
bibdate = "Sat Feb 08 10:47:59 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://github.com/ffevotte/libeft",
acknowledgement = ack-nhfb,
}
@Article{Fu:2017:AHC,
author = "Zhoulai Fu and Zhendong Su",
title = "Achieving high coverage for floating-point code via
unconstrained programming",
journal = j-SIGPLAN,
volume = "52",
number = "6",
pages = "306--319",
month = jun,
year = "2017",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/3140587.3062383",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Sat Sep 16 10:18:17 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "Achieving high code coverage is essential in testing,
which gives us confidence in code quality. Testing
floating-point code usually requires painstaking
efforts in handling floating-point constraints, e.g.,
in symbolic execution. This paper turns the challenge
of testing floating-point code into the opportunity of
applying unconstrained programming --- the mathematical
solution for calculating function minimum points over
the entire search space. Our core insight is to derive
a representing function from the floating-point
program, any of whose minimum points is a test input
guaranteed to exercise a new branch of the tested
program. This guarantee allows us to achieve high
coverage of the floating-point program by repeatedly
minimizing the representing function. We have realized
this approach in a tool called CoverMe and conducted an
extensive evaluation of it on Sun's C math library. Our
evaluation results show that CoverMe achieves, on
average, 90.8\% branch coverage in 6.9 seconds,
drastically outperforming our compared tools: (1)
Random testing, (2) AFL, a highly optimized, robust
fuzzer released by Google, and (3) Austin, a
state-of-the-art coverage-based testing tool designed
to support floating-point code.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "PLDI '17 conference proceedings.",
}
@Article{Fumex:2017:AVF,
author = "Cl{\'e}ment Fumex and Claude March{\'e} and Yannick
Moy",
editor = "Andrei Paskevich and Thomas Wies",
booktitle = "Verified Software. Theories, Tools, and Experiments:
{9th International Conference, VSTTE 2017, Heidelberg,
Germany, July 22--23, 2017, Revised Selected Papers}",
title = "Automating the Verification of Floating-Point
Programs",
journal = j-LECT-NOTES-COMP-SCI,
volume = "10712",
publisher = pub-SV,
address = pub-SV:adr,
pages = "102--119",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-72308-2_7",
ISBN = "3-319-72308-1",
ISBN-13 = "978-3-319-72308-2",
ISSN = "1611-3349",
bibdate = "Sat Jun 8 09:04:13 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-319-72308-2",
}
@InProceedings{Gonzalez-Navarro:2017:NNO,
author = "Sonia Gonzalez-Navarro and Javier Hormigo",
title = "Normalizing or Not Normalizing? {An} Open Question for
Floating-Point Arithmetic in Embedded Systems",
crossref = "Burgess:2017:ISC",
pages = "188--195",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.16",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Emerging embedded applications lack of a specific
standard when they require floating-point arithmetic.
In this situation they use the IEEE-754 standard or ad
hoc variations of it. However, this standard was not
designed for this purpose. This paper aims to open a
debate to define a new extension of the standard to
cover embedded applications. In this work, we only
focus on the impact of not performing normalization. We
show how eliminating the condition of normalized
numbers, implementation costs can be dramatically
reduced, at the expense of a moderate loss of accuracy.
Several architectures to implement addition and
multiplication for non-normalized numbers are proposed
and analyzed. We show that a combined architecture
(adder-multiplier) can halve the area and power
consumption of its counterpart IEEE-754 architecture.
This saving comes at the cost of reducing an average of
about 10 dBs the Signal-to-Noise Ratio for the tested
algorithms. We think these results should encourage
researchers to perform further investigation in this
issue.",
acknowledgement = ack-nhfb,
keywords = "ad hoc variations; adder-multiplier; adders; Adders;
Computer architecture; DSP; embedded applications;
embedded systems; Embedded systems; embedded systems;
Field programmable gate arrays; floating point
arithmetic; floating-point; floating-point arithmetic;
Hardware; IEEE standards; IEEE-754 architecture;
IEEE-754 standard; Loss measurement; nonnormalized
numbers; Normalization; normalized number condition;
power consumption; signal-to-noise ratio; standard;
Standards",
}
@Article{Gorantla:2017:DAC,
author = "Anusha Gorantla and Deepa P.",
title = "Design of Approximate Compressors for Multiplication",
journal = j-JETC,
volume = "13",
number = "3",
pages = "44:1--44:??",
month = may,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3007649",
ISSN = "1550-4832 (print), 1550-4840 (electronic)",
ISSN-L = "1550-4832",
bibdate = "Tue Jul 11 17:10:31 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/jetc/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jetc.bib",
abstract = "Approximate computing is a promising technique for
energy-efficient Very Large Scale Integration (VLSI)
system design. It is best suited for error-resilient
applications such as signal processing and multimedia.
Approximate computing reduces accuracy but still
provides significant and faster results with lower
power consumption. This is attractive to arithmetic
circuits. In this article, various novel design
approaches of approximate 4-2 and 5-2 compressors have
been proposed for reduction of the partial product
stages in multiplication. Three approximate 8 $ \times
$ 8 Dadda multiplier designs using three novel
approximate 4-2 compressors and two approximate 8 $
\times $ 8 Dadda multiplier designs using two novel
approximate 5-2 compressors have proposed. The
synthesis results show that the proposed designs
achieved significant accuracy improvement together with
power and delay reductions compared to the existing
approximate designs.",
acknowledgement = ack-nhfb,
articleno = "44",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J967",
}
@TechReport{Graillat:2017:AAE,
author = "Stef Graillat",
title = "An accurate algorithm for evaluating rational
functions",
type = "Report",
number = "HAL-01578486",
institution = "Laboratoire d'Informatique de Paris 6, Universit{\'e}
Sorbonne, Campus Pierre et Marie Curie",
address = "4, place Jussieu, F-75252 Paris Cedex 05, France",
day = "29",
month = aug,
year = "2017",
MRclass = "15-04 65G99 65-04",
bibdate = "Mon Mar 19 08:17:18 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.archives-ouvertes.fr/hal-01578486",
abstract = "Several different techniques intend to improve the
accuracy of results computed in floating-point
precision. Here, we focus on a method to improve the
accuracy of the evaluation of rational functions. We
present a compensated algorithm to evaluate rational
functions. This algorithm is accurate and fast. The
accuracy of the computed result is similar to the one
given by the classical algorithm computed in twice the
working precision and then rounded to the current
working precision. This algorithm runs much more faster
than existing implementation producing the same output
accuracy.",
acknowledgement = ack-nhfb,
keywords = "accuracy; error-free transformation; floating-point;
Horner scheme; rational function; rounding errors",
}
@InProceedings{Guney:2017:OMM,
author = "Murat Efe Guney and Kazushige Goto and Timothy B.
Costa and Sarah Knepper and Louise Huot and Arthur
Mitrano and Shane Story",
title = "Optimizing Matrix Multiplication on {Intel Xeon Phi TH
x200} Architecture",
crossref = "Burgess:2017:ISC",
pages = "144--145",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.19",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Matrix multiplication is ubiquitous in scientific
computing. From computational science to machine
learning, a large and diverse set of applications rely
on the performance of general matrix-matrix
multiplication (GEMM) subroutines. The Intel Math
Kernel Library(R) provides highly optimized GEMM
subroutines that take full advantage of the available
parallelism and vectorization in both Intel Xeon and
Intel Xeon Phi(TM) processors. In this paper we discuss
the optimization of GEMM subroutines for the Intel Xeon
PhiTM x200 (code-named Knights Landing).",
acknowledgement = ack-nhfb,
keywords = "Algorithms; Bandwidth; blas; computational science;
Computer architecture; general matrix-matrix
multiplication; Intel Math Kernel Library; intel xeon
phi; Intel Xeon Phi x200 architecture; Kernel; Knights
Landing; machine learning; matrix multiplication;
microprocessor chips; Optimization; performance
optimization; Prefetching; processors; scientific
computing",
}
@Misc{Gustafson:2017:BFPa,
author = "John Gustafson",
title = "Beyond Floating Point: Next Generation Computer
Arithmetic",
howpublished = "Web video",
month = feb,
year = "2017",
bibdate = "Mon Feb 06 06:47:46 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://insidehpc.com/2017/02/john-gustafson-presents-beyond-floating-point-next-generation-computer-arithmetic",
acknowledgement = ack-nhfb,
keywords = "unum floating-point format",
}
@TechReport{Gustafson:2017:BFPb,
author = "John Gustafson and Isaac Yonemoto",
title = "Beating Floating Point at its Own Game: Posit
Arithmetic",
type = "Report",
institution = "A*STAR Computational Resources Centre and National
University of Singapore (joint appointment) [JG],
Singapore Interplanetary Robot and Electric Brain
Company, Saratoga, California USA [IY]",
pages = "16",
day = "12",
month = jun,
year = "2017",
bibdate = "Mon Sep 26 13:38:16 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.johngustafson.net/pdfs/BeatingFloatingPoint.pdf",
abstract = "A new data type called a posit is designed as a direct
drop-in replacement for IEEE Standard 754
floating-point numbers (floats). Unlike earlier forms
of universal number (unum) arithmetic, posits do not
require interval arithmetic or variable size operands;
like floats, they round if an answer is inexact.
However, they provide compelling advantages over
floats, including larger dynamic range, higher
accuracy, better closure, bitwise identical results
across systems, simpler hardware, and simpler exception
handling. Posits never overflow to infinity or
underflow to zero, and ``Not-a-Number'' (NaN) indicates
an action instead of a bit pattern. A posit processing
unit takes less circuitry than an IEEE float FPU. With
lower power use and smaller silicon footprint, the
posit operations per second (POPS) supported by a chip
can be significantly higher than the FLOPS using
similar hardware resources. GPU accelerators and Deep
Learning processors, in particular, can do more per
watt and per dollar with posits, yet deliver superior
answer quality.\par
A comprehensive series of benchmarks compares floats
and posits for decimals of accuracy produced for a set
precision. Low precision posits provide a better
solution than ``approximate computing'' methods that
try to tolerate decreased answer quality. High
precision posits provide more correct decimals than
floats of the same size; in some cases, a 32-bit posit
may safely replace a 64-bit float. In other words,
posits beat floats at their own game.",
acknowledgement = ack-nhfb,
keywords = "computer arithmetic; energy-efficient computing;
floating point; linear algebra; LINPACK; neural
networks; posits; unum computing; valid arithmetic",
}
@Article{Gustafson:2017:BFPc,
author = "John L. Gustafson and Isaac Yonemoto",
title = "Beating Floating Point at Its Own Game: Posit
Arithmetic",
journal = j-SUPERFRI,
volume = "4",
number = "2",
pages = "71--86",
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.14529/jsfi170206",
ISSN = "2313-8734 (print), 2409-6008 (electronic)",
ISSN-L = "2313-8734",
bibdate = "Sun Dec 10 14:34:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://superfri.org/index.php/superfri/article/view/137/232",
acknowledgement = ack-nhfb,
fjournal = "Supercomputing Frontiers and Innovations: an
International Journal",
journal-doi = "https://doi.org/10.14529/jsfi",
journal-URL = "https://superfri.org/index.php/superfri/",
remark = "Published at South Ural State University, Chelyabinsk,
Russia, Russia. Not in US Library of Congress or
CASSI.",
xx-journal-url = "https://superfri.org/index.php/superfri/issue/archive",
}
@Misc{Gustafson:2017:PA,
author = "John L. Gustafson",
title = "Posit Arithmetic",
howpublished = "Web PDF file.",
pages = "1--137",
day = "10",
month = oct,
year = "2017",
bibdate = "Tue Jul 09 10:34:12 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://posithub.org/docs/Posits4.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Gustafsson:2017:ANS,
author = "Oscar Gustafsson and Erik Bertilsson and Johannes
Klasson and Carl Ingemarsson",
title = "Approximate {Neumann} Series or Exact Matrix Inversion
for Massive {MIMO}?",
crossref = "Burgess:2017:ISC",
pages = "62--63",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.11",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Approximate matrix inversion based on Neumann series
has seen a recent increased interest motivated by
massive MIMO systems. There, the matrices are in many
cases diagonally dominant, and, hence, a reasonable
approximation can be obtained within a few iterations
of a Neumann series. In this work, we clarify that the
complexity of exact methods are about the same as when
three terms are used for the Neumann series, so in this
case, the complexity is not lower as often claimed. The
second common argument for Neumann series
approximation, higher parallelism, is indeed correct.
However, in most current practical use cases, such a
high degree of parallelism is not required to obtain a
low latency realization. Hence, we conclude that a
careful evaluation, based on accuracy and latency
requirements must be performed and that exact matrix
inversion is in fact viable in many more cases than the
current literature claims.",
acknowledgement = ack-nhfb,
keywords = "approximate matrix inversion; approximate Neumann
series; approximation theory; Clocks; Complexity
theory; Computer architecture; exact matrix inversion;
iterative methods; Large-scale MIMO; Latency; Massive
MIMO; massive MIMO systems; matrix algebra; Matrix
inversion; MIMO; MIMO communication; Neumann series;
Pipeline processing; Symmetric matrices",
}
@InProceedings{Gustafsson:2017:LBF,
author = "Oscar Gustafsson",
title = "On Lifting-Based Fixed-Point Complex Multiplications
and Rotations",
crossref = "Burgess:2017:ISC",
pages = "43--49",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.10",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Lifting-based complex multiplications and rotations
are integer invertible, i.e., an integer input value is
mapped to the same integer output value when rotating
forward and backward. This is an important aspect for
lossless transform based source coding, but since the
structure only require three real-valued
multiplications and three real-valued additions it is
also a potentially attractive way to perform complex
multiplications when the coefficient has unity
magnitude. In this work, we consider two aspects of
these structures. First, we show that both the
magnitude and angular error is dependent on the angle
of input value and derive both exact and approximated
expressions for these. Second, we discuss how to design
such structures without the typical separation into
three subsequent matrix multiplications. It is shown
that the proposed design method allows many more values
which are integer invertible, but can not be separated
into three subsequent matrix multiplications with
fixed-point values. The results show good
correspondence between the error approximations and the
actual error as well as a significantly increased
design space.",
acknowledgement = ack-nhfb,
keywords = "complex multiplication; complex rotation; Design
methodology; digital arithmetic; Digital arithmetic;
Discrete cosine transforms; Electrical engineering;
error analysis; error approximations; fixed-point;
lifting; lifting-based fixed-point complex
multiplications; lifting-based fixed-point complex
rotations; logic design; lossless transform based
source coding; Matrix decomposition; real-valued
additions; real-valued multiplications; rotation;
source coding; Source coding; transform coding",
}
@InProceedings{Haidar:2017:IHP,
author = "Azzam Haidar and Panruo Wu and Stanimire Tomov and
Jack Dongarra",
booktitle = "Proceedings of the {8th Workshop on Latest Advances in
Scalable Algorithms for Large-Scale Systems ---
ScalA'17}",
title = "Investigating half precision arithmetic to accelerate
dense linear system solvers",
publisher = pub-ACM,
address = pub-ACM:adr,
year = "2017",
DOI = "https://doi.org/10.1145/3148226.3148237",
ISBN = "1-4503-5125-5 (hardcover)",
ISBN-13 = "978-1-4503-5125-6 (hardcover)",
LCCN = "????",
bibdate = "Thu Nov 7 16:51:39 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ORCID-numbers = "Dongarra, Jack/0000-0003-3247-1782",
}
@Article{Hiasat:2017:ERS,
author = "Ahmad Hiasat",
title = "Efficient {RNS} Scalers for the Extended Three-Moduli
Set $ (2^n - 1, 2^{n + p}, 2^n + 1) $",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "7",
pages = "1253--1260",
month = jul,
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2652474",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jun 8 10:22:00 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "https://www.computer.org/csdl/trans/tc/2017/07/07815319-abs.html",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Residue Number System (RNS)",
}
@Book{Higham:2017:MG,
author = "Desmond J. Higham and Nicholas J. Higham",
title = "{MATLAB} guide",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxvi + 476",
year = "2017",
ISBN = "1-61197-465-8",
ISBN-13 = "978-1-61197-465-2",
MRclass = "65-00 (00A20)",
MRnumber = "3601107",
bibdate = "Sat Aug 26 17:40:10 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
abstract = "MATLAB is an interactive system for numerical
computation that is widely used for teaching and
research in industry and academia. It provides a modern
programming language and problem solving environment,
with powerful data structures, customizable graphics,
and easy-to-use editing and debugging tools. This third
edition of MATLAB Guide completely revises and updates
the best-selling second edition and is more than 25
percent longer. The book remains a lively, concise
introduction to the most popular and important features
of MATLAB and the Symbolic Math Toolbox. Key features
are a tutorial in Chapter 1 that gives a hands-on
overview of MATLAB, a thorough treatment of MATLAB
mathematics, including the linear algebra and numerical
analysis functions and the differential equation
solvers, and a web page that provides a link to example
program files, updates, and links to MATLAB resources.
The new edition contains color figures throughout,
includes pithy discussions of related topics in new
`Asides' boxes that augment the text, has new chapters
on the Parallel Computing Toolbox, object-oriented
programming, graphs, and large data sets, covers
important new MATLAB data types such as categorical
arrays, string arrays, tall arrays, tables, and
timetables, contains more on MATLAB workflow, including
the Live Editor and unit tests, and fully reflects
major updates to the MATLAB graphics system.",
acknowledgement = ack-nhfb,
remark = "Third edition of
\cite{Higham:2000:MG,Higham:2005:MG}.",
subject = "MATLAB (logiciel).; Analyse num{\'e}rique; Logiciels.;
Numerical analysis; Data processing; Data processing.",
tableofcontents = "1: A Brief Tutorial \\
2: Basics \\
3: Distinctive Features of MATLAB \\
4: Arithmetic \\
5: Matrices \\
6: Operators and Flow Control \\
7: Program Files \\
8: Graphics \\
9: Linear Algebra \\
10: More on Functions \\
11: Numerical Methods: Part I \\
12: Numerical Methods: Part II \\
13: Input and Output \\
14: Troubleshooting \\
15: Sparse Matrices \\
16: More on Coding \\
17: Advanced Graphics \\
18: Other Data Types and Multidimensional Arrays \\
19: Object-Oriented Programming \\
20: The Symbolic Math Toolbox \\
21: Graphs \\
22: Large Data Sets \\
23: Optimizing Codes \\
24: Tricks and Tips \\
25: The Parallel Computing Toolbox \\
26: Case Studies",
}
@Article{Higham:2017:MW,
author = "Nicholas J. Higham",
title = "A multiprecision world",
journal = j-SIAM-NEWS,
volume = "50",
number = "8",
pages = "??--??",
day = "2",
month = oct,
year = "2017",
ISSN = "0036-1437",
bibdate = "Wed Aug 07 15:18:43 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sinews.siam.org/Details-Page/a-multiprecision-world",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@InProceedings{Higham:2017:RMA,
author = "Nicholas John Higham",
title = "The Rise of Multiprecision Arithmetic",
crossref = "Burgess:2017:ISC",
pages = "1--1",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.24",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "There is a growing demand for and availability of
multiprecision arithmetic: floating point arithmetic
supporting multiple, possibly arbitrary, precisions.
For an increasing body of applications, including in
supernova simulations, electromagnetic scattering
theory, and computational number theory, double
precision arithmetic is insufficient to provide results
of the required accuracy. On the other hand, for
climate modelling and deep learning half precision
(about four significant decimal digits) has been shown
to be sufficient in some studies. We discuss a number
of topics involving multiprecision arithmetic,
including: The need for, availability of, and ways to
exploit, higher precision arithmetic (e.g., quadruple
precision arithmetic). How to derive linear algebra
algorithms that will run in any precision, as opposed
to be being optimized (as some key algorithms are) for
double precision. For solving linear systems with the
use of iterative refinement, the benefits of suitably
combining three different precisions of arithmetic
(say, half, single, and double). How a new form of
preconditioned iterative refinement can be used to
solve very ill conditioned sparse linear systems to
high accuracy.",
acknowledgement = ack-nhfb,
keywords = "climate modelling; Computational modeling; deep
learning half precision; Digital arithmetic; double
precision arithmetic; Electromagnetic scattering;
floating point arithmetic; Floating-point arithmetic;
iterative methods; iterative refinement; linear
algebra; linear algebra algorithms; linear systems;
Linear systems; Mathematical model; multiprecision
arithmetic; sparse linear systems",
}
@Article{Hormigo:2017:ISI,
author = "Javier Hormigo and Jean-Michel Muller and Stuart
Oberman and Nathalie Revol and Arnaud Tisserand and
Julio Villalba-Moreno",
title = "Introduction to the Special Issue on Computer
Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "1991--1993",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2761278",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Hou:2017:TGF,
author = "Junjie Hou and Yongxin Zhu and Yulan Shen and Mengjun
Li and Han Wu and Han Song",
booktitle = "{2017 IEEE 19th International Conference on High
Performance Computing and Communications; IEEE 15th
International Conference on Smart City; IEEE 3rd
International Conference on Data Science and Systems
(HPCC/SmartCity/DSS)}",
title = "Tackling Gaps in Floating-Point Arithmetic: Unum
Arithmetic Implementation on {FPGA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "615--616",
year = "2017",
DOI = "https://doi.org/10.1109/HPCC-SmartCity-DSS.2017.82",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Ishii:2017:FMA,
author = "Masahiro Ishii and J{\'e}r{\'e}mie Detrey and Pierrick
Gaudry and Atsuo Inomata and Kazutoshi Fujikawa",
title = "Fast Modular Arithmetic on the {Kalray MPPA-256}
Processor for an Energy-Efficient Implementation of
{ECM}",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2019--2030",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2704082",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7927487/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Istoan:2017:FFP,
author = "Matei Istoan and Bogdan Pasca",
title = "Flexible Fixed-Point Function Generation for {FPGAs}",
crossref = "Burgess:2017:ISC",
pages = "123--130",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.31",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Efficient fixed-point function implementation is
critical in many FPGA application domains including
convolutional neural networks, computer vision, and
communication systems. In this work we focus on
functions of the form $ x^p $, with $ p \in \{ - 1, - 1
/ 2, 1 / 2 \} $ as part of a function generator
targeting FPGAs. The generator implements architectures
based on new but also existing algorithms. In this work
we present three distinct methods implemented in this
generator that outperform state-of-the-art
implementations for certain configurations.
Traditionally, fixed-point function implementation
requires a normalization stage, compute and
denormalization (reconstruction) of the result. The
first proposed method implements the function
holistically, thus saving the logic and latency
required during the normalize and reconstruct stages.
The second proposed method is based on a novel second
order Taylor implementation. The third method is based
on the cubic convergence of Halley's method, which is
novel in this context. The proposed methods are
compared and contrasted against state-of-the art
implementations in the context of FPGA targets.",
acknowledgement = ack-nhfb,
keywords = "arithmetic; communication systems; computer vision;
convolutional neural networks; cubic convergence;
Digital signal processing; Field programmable gate
arrays; field programmable gate arrays; fixed point
arithmetic; fixed-point; flexible fixed-point function
generation; FPGA; FPGAs; generator; Generators; Halley
method; Kernel; Memory management; reciprocal;
reciprocal sqrt; second order Taylor implementation;
Signal generators; sqrt",
}
@Article{Jaiswal:2017:AEA,
author = "Manish Kumar Jaiswal and Hayden K.-H. So",
title = "Area-efficient Architecture for Dual-mode Double
Precision Floating Point Division",
journal = j-IEEE-TRANS-CIRCUITS-SYST-1,
volume = "64",
number = "2",
pages = "386--398",
month = feb,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1109/TCSI.2016.2607227",
ISSN = "1549-8328 (print), 1558-0806 (electronic)",
ISSN-L = "1549-8328",
bibdate = "Sat Feb 08 10:59:51 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/7590039",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I: Regular
Papers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
}
@InProceedings{Jeannerod:2017:CRE,
author = "Claude-Pierre Jeannerod and Jean-Michel Muller and
Antoine Plet",
title = "The Classical Relative Error Bounds for Computing $
\sqrt (a^2 + b^2) $ and $ c / \sqrt (a^2 + b^2) $ in
Binary Floating-Point Arithmetic are Asymptotically
Optimal",
crossref = "Burgess:2017:ISC",
pages = "66--73",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.40",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We study the accuracy of classical algorithms for
evaluating expressions of the form $ (a^2 + b^2) $ and
$ c (a^2 + b^2) $ in radix-2, precision-$p$
floating-point arithmetic, assuming that the elementary
arithmetic operations $ \pm $, $ \times $, $/$, $ \sqrt
$ are rounded to nearest, and assuming an unbounded
exponent range. Classical analyses show that the
relative error is bounded by $ 2 u + O(u^2)$ for $ (a^2
+ b^2)$, and by $ 3 u + O(u^2)$ for $ c / (a^2 + b^2)$,
where $ u = 2^{-p}$ is the unit roundoff. Recently, it
was observed that for $ (a^2 + b^2)$ the $ O(u^2)$ term
is in fact not needed [1]. We show here that it is not
needed either for $ c / (a^2 + b^2)$. Furthermore, we
show that these error bounds are asymptotically
optimal. Finally, we show that both the bounds and
their asymptotic optimality remain valid when an FMA
instruction is used to evaluate $ a^2 + b^2$.",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; asymptotic optimality;
binary floating-point arithmetic; classical relative
error bounds; Digital arithmetic; Error analysis;
floating point arithmetic; Floating-point arithmetic;
FMA instruction; Force; hypotenuse function; Lips;
precision-p floating-point arithmetic; relative error;
rounding error analysis; unbounded exponent range; unit
roundoff; Upper bound",
}
@Article{Jeannerod:2017:EBC,
author = "Claude-Pierre Jeannerod and Peter Kornerup and Nicolas
Louvet and Jean-Michel Muller",
title = "Error bounds on complex floating-point multiplication
with an {FMA}",
journal = j-MATH-COMPUT,
volume = "86",
number = "304",
pages = "881--898",
month = "",
year = "2017",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3123",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sat Feb 18 08:32:49 MST 2017",
bibsource = "http://www.ams.org/mcom/2017-86-304;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03123-3;
http://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03123-3/S0025-5718-2016-03123-3.pdf;
http://www.ams.org/mathscinet/search/author.html?authorName=Kornerup%2C%20Peter;
http://www.ams.org/mathscinet/search/author.html?authorName=Muller%2C%20Jean-Michel;
http://www.ams.org/mathscinet/search/author.html?mrauthid=644190;
http://www.ams.org/mathscinet/search/author.html?mrauthid=893389",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Jeannerod:2017:REC,
author = "Claude-Pierre Jeannerod and Jean-Michel Muller",
editor = "Michael B. Matthews",
booktitle = "{2017 51st Asilomar Conference on Signals, Systems,
and Computers. October 29--November 1, 2017. Pacific
Grove, California}",
title = "On the relative error of computing complex square
roots in floating-point arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "737--740",
year = "2017",
DOI = "https://doi.org/10.1109/ACSSC.2017.8335442",
ISBN = "1-5386-1823-0",
ISBN-13 = "978-1-5386-1823-3",
bibdate = "Fri Sep 29 10:59:32 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We study the accuracy of a classical approach to
computing complex square-roots in floating-point
arithmetic. Our analyses are done in binary
floating-point arithmetic in precision p, and we assume
that the (real) arithmetic operations $+$, $-$, $
\times $, $ \div $, $ \sqrt {} $ are rounded to
nearest, so the unit roundoff is $ u = 2^{-p} $. We
show that in the absence of underflow and overflow, the
componentwise and normwise relative errors of this
approach are at most $ 7 / 2 u $ and $ \sqrt {37} / 2 u
$, respectively, and this without having to neglect
terms of higher order in $u$. We then provide some
input examples showing that these bounds are reasonably
sharp for the three basic binary interchange formats
(binary32, binary64, and binary128) of the IEEE 754
standard for floating-point arithmetic.",
acknowledgement = ack-nhfb,
}
@Article{Johansson:2017:AEA,
author = "Fredrik Johansson",
title = "{Arb}: Efficient Arbitrary-Precision Midpoint--Radius
Interval Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "8",
pages = "1281--1292",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2690633",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 13 14:57:15 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7891956/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Joldes:2017:IPE,
author = "Mioara Joldes and Jean-Michel Muller and Valentina
Popescu",
title = "Implementation and Performance Evaluation of an
Extended Precision Floating-Point Arithmetic Library
for High-Accuracy Semidefinite Programming",
crossref = "Burgess:2017:ISC",
pages = "27--34",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.18",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Semidefinite programming (SDP) is widely used in
optimization problems with many applications, however,
certain SDP instances are ill-posed and need more
precision than the standard double-precision available.
Moreover, these problems are large-scale and could
benefit from parallelization on specialized
architectures such as GPUs. In this article, we
implement and evaluate the performance of a
floating-point expansion-based arithmetic library
(CAMPARY) in the context of such numerically highly
accurate SDP solvers. We plugged-in CAMPARY with the
state-of-the-art SDPA solver for both CPU and GPU-tuned
implementations. We compare and contrast both the
numerical accuracy and performance of SDPA-GMP, -QD and
-DD, which employ other multiple-precision arithmetic
libraries against SDPA-CAMPARY. We show that CAMPARY is
a very good trade-off for accuracy and speed when
solving ill-conditioned SDP problems.",
acknowledgement = ack-nhfb,
keywords = "CAMPARY; CPU; error-free transform; floating point
arithmetic; floating-point arithmetic; floating-point
expansion-based arithmetic library; floating-point
expansions; GPGPU computing; GPU; graphics processing
units; Graphics processing units; ill-posed
semidefinite programming; Libraries; mathematical
programming; mathematics computing; multiple precision
library; multiple-precision arithmetic libraries;
Optimization; Programming; SDP; SDPA-DD; SDPA-GMP;
SDPA-QD; semidefinite programming; Standards; Symmetric
matrices; Transforms",
}
@Article{Joldes:2017:TRE,
author = "Mioara Joldes and Jean-Michel Muller and Valentina
Popescu",
title = "Tight and Rigorous Error Bounds for Basic Building
Blocks of Double-Word Arithmetic",
journal = j-TOMS,
volume = "44",
number = "2",
pages = "15res:1--15res:27",
month = oct,
year = "2017",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3121432",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Oct 10 17:52:02 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3121432",
abstract = "We analyze several classical basic building blocks of
double-word arithmetic (frequently called
``double-double arithmetic'' in the literature): the
addition of a double-word number and a floating-point
number, the addition of two double-word numbers, the
multiplication of a double-word number by a
floating-point number, the multiplication of two
double-word numbers, the division of a double-word
number by a floating-point number, and the division of
two double-word numbers. For multiplication and
division we get better relative error bounds than the
ones previously published. For addition of two
double-word numbers, we show that the previously
published bound was incorrect, and we provide a new
relative error bound. We introduce new algorithms for
division. We also give examples that illustrate the
tightness of our bounds.",
acknowledgement = ack-nhfb,
articleno = "15res",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
remark = "This article is erroneously assigned the same article
number as the preceding one!",
}
@Misc{Jorgensen:2017:ACR,
author = "Alan A. Jorgensen",
title = "Apparatus for Calculating and Retaining a Bound on
Error During Floating Point Operations and Methods
Thereof",
howpublished = "US Patent 9,817,662.",
day = "14",
month = nov,
year = "2017",
bibdate = "Fri Mar 23 19:14:44 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "This patent, filed 23 October 2016, was issued despite
substantial prior art that should have resulted in its
rejection: see \cite{Trader:2018:ICS}. The inventor
does not appear to have published in the area of
floating-point arithmetic (apart from this entry, none
by him can be found in this bibliography). The only
literature references in the patent are
\cite{Monniaux:2008:PVF,Goldberg:1991:WEC,Masotti:2012:FPN,Muller:2010:HFP}.",
URL = "https://patents.google.com/patent/US9817662B2/;
https://tinyurl.com/y7ctbsez",
abstract = "The apparatus and method for calculating and retaining
a bound on error during floating point operations
inserts an additional bounding field into the standard
floating-point format that records the retained
significant bits of the calculation with notification
upon insufficient retention. The bounding field, which
accounts for both rounding and cancellation errors, has
two parts, the lost bits D Field and the accumulated
rounding error R Field. The D Field states the number
of bits in the floating point representation that are
no longer meaningful. The bounds on the real value
represented are determined from the truncated floating
point value (first bound) and the addition of the error
determined by the number of lost bits (second bound).
The true, real value is absolutely contained by the
first and second bounds. The allowed loss (optionally
programmable) of significant bits provides a fail-safe,
real-time notification of loss of significant bits.",
acknowledgement = ack-nhfb,
}
@Book{Kneusel:2017:NC,
author = "Ronald T. Kneusel",
title = "Numbers and Computers",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xiii + 346",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-50508-4",
ISBN = "3-319-50507-6, 3-319-50508-4 (e-book)",
ISBN-13 = "978-3-319-50507-7, 978-3-319-50508-4 (e-book)",
LCCN = "????",
bibdate = "Tue Aug 22 05:58:01 MDT 2017",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/10.1007/978-3-319-50508-4",
abstract = "This is a book about numbers and how those numbers are
represented in and operated on by computers. It is
crucial that developers understand this area because
the numerical operations allowed by computers, and the
limitations of those operations, especially in the area
of floating point math, affect virtually everything
people try to do with computers. This book aims to fill
this gap by exploring, in sufficient but not
overwhelming detail, just what it is that computers do
with numbers. Divided into two parts, the first deals
with standard representations of integers and floating
point numbers, while the second examines several other
number representations. Details are explained
thoroughly, with clarity and specificity. Each chapter
ends with a summary, recommendations, carefully
selected references, and exercises to review the key
points. Topics covered include interval arithmetic,
fixed-point numbers, big integers and rational
arithmetic. This new edition has three new chapters:
Pitfalls of Floating-Point Numbers (and How to Avoid
Them), Arbitrary Precision Floating Point, and Other
Number Systems. This book is for anyone who develops
software including software engineers, scientists,
computer science students, engineering students and
anyone who programs for fun.",
acknowledgement = ack-nhfb,
subject = "Number theory; Numerals; Numeration; Computer science;
Mathematics; Mathematics; Number theory; Numerals;
Numeration; Arithmetic and Logic Structures; Numeric
Computing; Arithmetik; Informatik; Software
Engineering.",
tableofcontents = "Number Systems \\
Integers \\
Floating Point \\
Pitfalls of Floating-Point Numbers (and How to Avoid
Them) \\
Big Integers and Rational Arithmetic \\
Fixed-Point Numbers \\
Decimal Floating Point \\
Interval Arithmetic \\
Arbitrary Precision Floating-Point \\
Other Number Systems",
}
@InProceedings{Koenig:2017:HAC,
author = "Jack Koenig and David Biancolin and Jonathan Bachrach
and Krste Asanovic",
title = "A Hardware Accelerator for Computing an Exact Dot
Product",
crossref = "Burgess:2017:ISC",
pages = "114--121",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.38",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We study the implementation of a hardware accelerator
that computes a dot product of IEEE-754 floating-point
numbers exactly. The accelerator uses a wide (640 or
4288 bits for single or double-precision respectively)
fixed-point representation into which intermediate
floating-point products are accumulated. We designed
the accelerator as a generator in Chisel, which can
synthesize various configurations of the accelerator
that make different area-performance trade-offs. We
integrated eight different configurations into an SoC
comprised of RISC-V in-order scalar core, split L1
instruction and data caches, and unified L2 cache. In a
TSMC 45 nm technology, the accelerator area ranges from
0.05 mm2 to 0.32 mm2, and all configurations could be
clocked at frequencies in excess of 900MHz. The
accelerator successfully saturates the SoC's memory
system, achieving the same per-element efficiency (1
cycle-per-element) as Intel MKL running on an x86
machine with a similar cache configuration.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point dot product; accurate
floating-point summation; area-performance trade-offs;
Bandwidth; cache configuration; cache storage; Chisel;
Coprocessors; data caches; exact dot product; fixed
point arithmetic; fixed-point representation; floating
point arithmetic; Generators; Hardware; hardware
accelerator; IEEE-754 floating-point numbers; Intel
MKL; intermediate floating-point products;
Microarchitecture; Registers; RISC-V in-order scalar
core; Rockets; size 45 nm; SoC memory system; split L1
instruction; system-on-chip; TSMC technology; unified
L2 cache",
}
@InProceedings{Kohlbrenner:2017:EMA,
author = "David Kohlbrenner and Hovav Shacham",
editor = "Another",
booktitle = "Proceedings of the {26th Usenix Security Symposium,
August 16--18, 2017, Vancouver, BC, Canada}",
title = "On the effectiveness of mitigations against
floating-point timing channels",
publisher = pub-USENIX,
address = pub-USENIX:adr,
pages = "69--81",
year = "2017",
ISBN = "1-931971-40-4",
ISBN-13 = "978-1-931971-40-9",
LCCN = "QA76.9.D5 P76 2005",
bibdate = "Mon Aug 26 10:26:59 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://github.com/kmowery/libfixedtimefixedpoint;
https://www.usenix.org/system/files/conference/usenixsecurity17/sec17-kohlbrenner.pdf",
abstract = "The duration of floating-point instructions is a known
timing side channel that has been used to break
Same-Origin Policy (SOP) privacy on Mozilla Firefox and
the Fuzz differentially private database. Several
defenses have been proposed to mitigate these
attacks.\par
We present detailed benchmarking of floating point
performance for various operations based on operand
values. We identify families of values that induce slow
and fast paths beyond the classes (normal, subnormal,
etc.) considered in previous work, and note that
different processors exhibit different timing
behavior.\par
We evaluate the efficacy of the defenses deployed (or
not) in Web browsers to floating point side channel
attacks on SVG filters. We find that Google Chrome,
Mozilla Firefox, and Apple's Safari have insufficiently
addressed the floating-point side channel, and we
present attacks for each that extract pixel data
cross-origin on most platforms.\par
We evaluate the vector-operation based defensive
mechanism proposed at USENIX Security 2016 by Rane, Lin
and Tiwari and find that it only reduces, not
eliminates, the floating-point side channel signal.
Together, these measurements and attacks cause us to
conclude that floating point is simply too variable to
use in a timing security sensitive context.",
acknowledgement = ack-nhfb,
keywords = "libfixedtimefixedpoint",
remark-1 = "This paper contains floating-point instruction timing
tables for the Intel i5-44609 CPU and Nvidia GeForce GT
430 GPU, with a brief table about the AMD Phenom II
X2-550. It demonstrates that timings can depend
significantly on operands, with subnormals sometimes
causing a slowdown of more than $ 20 \times $. The
scope of attacks from timing measurements is
surprisingly broad, including recovery of image pixels,
browser history, user geolocation, and browser search
strings. Several of the 18 references describe other
such attacks. One of the vulnerable graphics rendering
libraries, Skia, is used by multiple browsers and
window systems: see \url{https://skia.org/}.",
remark-2 = "From p. 80: ``Processor vendors have resisted calls to
document which of their instructions run in constant
time regardless of operands, even for operations as
basic as integer multiplication.''",
}
@Article{Kumm:2017:OCM,
author = "Martin Kumm and Martin Hardieck and Peter Zipf",
title = "Optimization of Constant Matrix Multiplication with
Low Power and High Throughput",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2072--2080",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2701365",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7919250/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Kumm:2017:ROD,
author = "Martin Kumm and Johannes Kappauf and Matei Istoan and
Peter Zipf",
title = "Resource Optimal Design of Large Multipliers for
{FPGAs}",
crossref = "Burgess:2017:ISC",
pages = "131--138",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.35",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This work presents a resource optimal approach for the
design of large multipliers for FPGAs. These are
composed of smaller multipliers which can be DSP blocks
or logic-based multipliers. A previously proposed
multiplier tiling methodology is used to describe
feasible solutions of the problem. The problem is then
formulated as an integer linear programming (ILP)
problem which can be solved by standard ILP solvers. It
can be used to minimize the total implementation cost
or to trade the LUT cost against the DSP cost. It is
demonstrated that although the problem is NP-complete,
optimal solutions can be found for most practical
multiplier sizes up to 64x64. Synthesis experiments on
relevant multiplier sizes show slice reductions of up
to 47.5\% compared to state-of-the-art heuristic
approaches.",
acknowledgement = ack-nhfb,
keywords = "Complexity theory; computational complexity; Digital
arithmetic; Digital signal processing; DSP blocks;
field programmable gate arrays; Field programmable gate
arrays; FPGA; ILP; ILP problem; ILP solvers; integer
linear programming problem; integer programming; linear
programming; logic design; logic-based multipliers;
LUT; multiplier; multiplier design; multiplier tiling
methodology; multiplying circuits; NP-complete problem;
Optimization; optimization; Shape; table lookup; Table
lookup",
}
@Article{Lai:2017:DCN,
author = "Liangzhen Lai and Naveen Suda and Vikas Chandra",
title = "Deep Convolutional Neural Network Inference with
Floating-point Weights and Fixed-point Activations",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--10",
day = "8",
month = mar,
year = "2017",
bibdate = "Fri Sep 28 06:16:02 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/pdf/1703.03073.pdf",
abstract = "Deep convolutional neural network (CNN) inference
requires significant amount of memory and computation,
which limits its deployment on embedded devices. To
alleviate these problems to some extent, prior research
utilize low precision fixed-point numbers to represent
the CNN weights and activations. However, the minimum
required data precision of fixed-point weights varies
across different networks and also across different
layers of the same network. In this work, we propose
using floating-point numbers for representing the
weights and fixed-point numbers for representing the
activations. We show that using floating-point
representation for weights is more efficient than
fixed-point representation for the same bit-width and
demonstrate it on popular large-scale CNNs such as
AlexNet, SqueezeNet, GoogLeNet and VGG-16. We also show
that such a representation scheme enables compact
hardware multiply-and-accumulate (MAC) unit design.
Experimental results show that the proposed scheme
reduces the weight storage by up to 36\% and power
consumption of the hardware multiplier by up to 50\%.",
acknowledgement = ack-nhfb,
}
@Misc{Lam:2017:FPA,
author = "Mike Lam",
title = "Floating-Point Analysis Research",
howpublished = "Web site",
year = "2017",
bibdate = "Thu May 02 17:01:37 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://w3.cs.jmu.edu/lam2mo/fpanalysis.html",
abstract = "This page is a compilation of research efforts and
software tools devoted to program analysis of
floating-point code. This research area is a community
of people from many different backgrounds: traditional
PL, high performance computing, numerical analysis, and
systems software. With this page, I am hoping to help
form connections between people and projects that might
previously have never encountered each other.",
acknowledgement = ack-nhfb,
}
@Article{Landy:2017:SAS,
author = "Aaron Landy and Greg Stitt",
title = "Serial Arithmetic Strategies for Improving {FPGA}
Throughput",
journal = j-TECS,
volume = "16",
number = "3",
pages = "84:1--84:??",
month = jul,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/2996459",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Mon Jul 24 09:51:12 MDT 2017",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
abstract = "Serial arithmetic has been shown to offer attractive
advantages in area for field-programmable gate array
(FPGA) datapaths but suffers from a significant
reduction in throughput compared to traditional
bit-parallel designs. In this work, we perform a
performance and trade-off analysis that
counterintuitively shows that, despite the decreased
throughput of individual serial operators, replication
of serial arithmetic can provide a 2.1 $ \times $
average increase in throughput compared to bit-parallel
pipelines for common FPGA applications. We complement
this analysis with a novel SerDes architecture that
enables existing FPGA pipelines to be replaced with
serial logic with potentially higher throughput. We
also present a serialized sliding-window architecture
that improves average throughput 2.4 $ \times $
compared to existing bit-parallel work.",
acknowledgement = ack-nhfb,
articleno = "84",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J840",
}
@Article{Lange:2017:EES,
author = "Marko Lange and Siegfried M. Rump",
title = "Error estimates for the summation of real numbers with
application to floating-point summation",
journal = j-BIT-NUM-MATH,
volume = "57",
number = "3",
pages = "927--941",
month = sep,
year = "2017",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-017-0658-9",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Mon Oct 2 11:20:22 MDT 2017",
bibsource = "http://link.springer.com/journal/10543/57/3;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://link.springer.com/article/10.1007/s10543-017-0658-9",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Langhammer:2017:FPT,
author = "Martin Langhammer and Bogdan Pasca",
title = "Floating Point Tangent Implementation for {FPGAs}",
crossref = "Burgess:2017:ISC",
pages = "64--65",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.25",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents an implementation of the
floating-point (FP) tangent function, optimized for an
FPGA containing hard floating point (HFP) DSP Blocks.
This function inputs values in the interval [- /2, /2],
uses the IEEE-754 single-precision (SP) format, and has
an accuracy conforming to OpenCL requirements. The
presented architecture is based on a combination of
mathematical identities and properties of the tangent
function in FP. The resultant design outperforms
generic polynomial approximation methods targeting the
same resource utilization spectrum, and provides better
resource trade-offs than classical CORDIC-based
implementations. The presented work is widely available
as part of the Intel DSP Builder Advanced Blockset.",
acknowledgement = ack-nhfb,
keywords = "Approximation methods; classical CORDIC-based
implementations; Digital arithmetic; Digital signal
processing; digital signal processing chips; field
programmable gate arrays; Field programmable gate
arrays; fixed point arithmetic; floating point
arithmetic; floating point tangent function; FPGAs;
generic polynomial approximation methods; hard floating
point DSP blocks; HFP DSP; IEEE-754 single-precision
format; Intel DSP Builder Advanced Blockset; OpenCL;
reconfigurable architectures; Resource management;
resource utilization spectrum; Table lookup",
}
@InProceedings{Langhammer:2017:QPA,
author = "Martin Langhammer",
title = "{QRD} for Parallel Arithmetic Structures",
crossref = "Burgess:2017:ISC",
pages = "146--147",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.26",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a new organization of the QR decomposition
(QRD), which is optimized for implementation on
parallel arithmetic structures, such as found in
current FPGAs. Data dependencies are hidden in the
pipeline depths of the datapaths, allowing
implementations to approach 100\% sustained to peak
throughput. The algorithm presented here is based on
the Modified Gram-Schmidt (MGS) method, and is designed
for floating point (FP) arithmetic, with a combination
of separate dot product and multiply-add datapaths. In
this short paper, we concentrate on the description of
the algorithm and architecture, rather than the
implementation, of the QRD.",
acknowledgement = ack-nhfb,
keywords = "adders; Algorithm design and analysis; Computer
architecture; data dependencies; field programmable
gate arrays; Field programmable gate arrays; floating
point arithmetic; FP arithmetic; FPGA; MGS method;
modified Gram-Schmidt method; multiply-add datapaths;
multiplying circuits; Organizations; parallel
arithmetic structures; Pipelines; QR decomposition;
QRD; Radar antennas; separate dot product; Throughput",
}
@Article{Langhammer:2017:SPL,
author = "Martin Langhammer and Bogdan Pasca",
title = "Single Precision Logarithm and Exponential
Architectures for Hard Floating-Point Enabled {FPGAs}",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2031--2043",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2703923",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7927449/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lauter:2017:ESI,
author = "Christoph Lauter",
title = "An Efficient Software Implementation of Correctly
Rounded Operations Extending {FMA}: $ a + b + c $ and $
a \times b + c \times d $",
crossref = "Matthews:2017:CRF",
pages = "452--456",
year = "2017",
DOI = "https://doi.org/10.1109/ACSSC.2017.8335379",
bibdate = "Fri Feb 16 08:24:29 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; complex multiply;
fused multiply-add; fused-add-add;
fused-multiply-twice-and-add; three-sum",
}
@Article{Lee:2017:APC,
author = "Wonyeol Lee and Rahul Sharma and Alex Aiken",
title = "On automatically proving the correctness of {\tt
math.h} implementations",
journal = j-PACMPL,
volume = "2",
number = "{POPL}",
pages = "1--32",
month = dec,
year = "2017",
DOI = "https://doi.org/10.1145/3158135",
ISSN = "2475-1421",
bibdate = "Thu May 2 17:03:44 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Industry standard implementations of {\tt math.h}
claim (often without formal proof) tight bounds on
floating-point errors. We demonstrate a novel static
analysis that proves these bounds and verifies the
correctness of these implementations. Our key insight
is a reduction of this verification task to a set of
mathematical optimization problems that can be solved
by off-the-shelf computer algebra systems. We use this
analysis to prove the correctness of implementations in
Intel's math library automatically. Prior to this work,
these implementations could only be verified with
significant manual effort",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the ACM on Programming Languages
(PACMPL)",
journal-URL = "http://pacmpl.acm.org/",
}
@Article{Lefevre:2017:CRA,
author = "Vincent Lef{\`e}vre",
title = "Correctly Rounded Arbitrary-Precision Floating-Point
Summation",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2111--2124",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2690632",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7891894/;
https://inria.hal.science/hal-01394289",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Lefevre:2017:OBB,
author = "Vincent Lef{\`e}vre and Paul Zimmermann",
title = "Optimized {Binary64} and {Binary128} Arithmetic with
{GNU MPFR}",
crossref = "Burgess:2017:ISC",
pages = "18--26",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.28",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib",
abstract = "We describe algorithms used to optimize the GNU MPFR
library when the operands fit into one or two words. On
modern processors, this gives a speedup for a correctly
rounded addition, subtraction, multiplication, division
or square root in the standard binary64 format (resp.
binary128) between 1.8 and 3.5 (resp. between 1.6 and
3.2). We also introduce a new faithful rounding mode,
which enables even faster computations. Those
optimizations will be available in version 4 of MPFR.",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; binary floating-point
formats; binary128; binary64; correct rounding;
faithful rounding; floating point arithmetic;
floating-point arithmetic; GNU MPFR; GNU MPFR library;
Libraries; Optimization; optimizations; Program
processors; Standards; Timing",
}
@InProceedings{Lesavourey:2017:ELR,
author = "Andrea Lesavourey and Christophe Negre and Thomas
Plantard",
title = "Efficient Leak Resistant Modular Exponentiation in
{RNS}",
crossref = "Burgess:2017:ISC",
pages = "156--163",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.39",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The leak resistant arithmetic in RNS was introduced in
2004 to randomize RSA modular exponentiation. This
randomization is meant to protect implementations on
embedded device from side channel analysis. We propose
in this paper a faster version of the approach of
Bajard et al. in the case of right-to-left
square-and-multiply exponentiation. We show that this
saves roughly 30\% of the computation when the
randomization is done at each loop iteration. We also
show that the level of randomization of the proposed
approach is better than the one of Bajard et al. after
a few number of loop iterations.",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; Correlation; efficient
leak resistant modular exponentiation; embedded device;
iterative methods; leak resistant arithmetic; loop
iteration; modular exponentiation; Monitoring; Public
key cryptography; public key cryptography; public key
cryptosystem; randomization; residue number system;
residue number systems; Resistance; right-to-left
square-and-multiply exponentiation; RNS; RSA; RSA
cryptosystem; RSA modular exponentiation randomization;
side channel analysis; Xenon",
}
@Article{Li:2017:MFN,
author = "Yin Li and Xingpo Ma and Yu Zhang and Chuanda Qi",
title = "{Mastrovito} Form of Non-Recursive {Karatsuba}
Multiplier for All Trinomials",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "9",
pages = "1573--1584",
month = sep,
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2677913",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 17 10:06:38 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7870679/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Liu:2017:DAR,
author = "Weiqiang Liu and Liangyu Qian and Chenghua Wang and
Honglan Jiang and Jie Han and Fabrizio Lombardi",
title = "Design of Approximate Radix-4 {Booth} Multipliers for
Error-Tolerant Computing",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "8",
pages = "1435--1441",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2672976",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 13 14:57:15 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7862783/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Liu:2017:MMA,
author = "Zhe Liu and Kimmo J{\"a}rvinen and Weiqiang Liu and
Hwajeong Seo",
title = "Multiprecision Multiplication on {ARMv8}",
crossref = "Burgess:2017:ISC",
pages = "10--17",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.27",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Multiplication of large integers is a fundamental
operation for public key cryptography. In contemporary
public key cryptography, the sizes of integers are
typically from more than one hundred bits to even
several thousands of bits. Because these sizes exceed
the bit widths of all general-purpose processors, these
multiplications must be performed with a multiprecision
multiplication algorithm which splits the operation
into multiple partial products and accumulation steps.
To ensure efficiency, multiprecision multiplication
algorithms must be designed with special care and
optimized for the instruction sets of specific
processors. Consequently, developing efficient
multiprecision multiplication algorithms and optimizing
them for specific platforms has been an active research
topic. In this paper, we optimize multiprecision
multiplication and squaring specifically for the 64-bit
ARMv8 processors which are widely used, for example, in
modern smart phones and tablets. We combine the
subtractive Karatsuba algorithm, operand-scanning
techniques (for multiplication) and
sliding-block-doubling methods (for squaring) to
accelerate the performance of the 256-bit
multiprecision multiplication and squaring by 7.6\% and
7.0\% compared to the OpenSSL implementations. We focus
particularly on the multiprecision multiplications that
are required in elliptic curve cryptography. Our
implementation supports general elliptic curves of
various sizes and all source codes are available in
public domain.",
acknowledgement = ack-nhfb,
keywords = "64-bit processor; ARMv8; ARMv8 processors; elliptic
curve cryptography; Elliptic curve cryptography;
elliptic curve cryptography; Instruction sets;
Karatsuba algorithm; microprocessor chips;
Multiprecision multiplication; multiprecision
multiplication algorithm; OpenSSL; operand-scanning
techniques; Optimization; public key cryptography;
Registers; sliding-block-doubling methods",
}
@Article{Liu:2017:UMF,
author = "S. Liu and G. Mingas and C. S. Bouganis",
title = "An Unbiased {MCMC} {FPGA}-Based Accelerator in the
Land of Custom Precision Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "5",
pages = "745--758",
month = may,
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2016.2630682",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Apr 6 07:46:06 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Approximation algorithms; Bayes methods; Computational
modeling; custom arithmetic precision; Field
programmable gate array; Field programmable gate
arrays; logistic regression; Markov chain Monte Carlo;
Markov processes; MNIST database; Monte Carlo methods;
Probability distribution",
}
@Book{Lockhart:2017:A,
author = "Paul Lockhart",
title = "Arithmetic",
publisher = "The Belknap Press of Harvard University Press",
address = "Cambridge, MA, USA",
pages = "223",
year = "2017",
ISBN = "0-674-97223-6",
ISBN-13 = "978-0-674-97223-0",
LCCN = "QA115 .L713 2017",
bibdate = "Sat Dec 22 16:04:02 MST 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
abstract = "Educator Paul Lockhart's goal is to demystify
arithmetic: to bring the subject to life in a fun and
accessible way, and to reveal its profound and simple
beauty, as seen through the eyes of a modern research
mathematician. The craft of arithmetic arises from our
natural desire to count, arrange, and compare
quantities. Over the centuries, humans have devised a
wide variety of strategies for representing and
manipulating numerical information: tally marks, rocks
and beads, marked-value and place-value systems, as
well as mechanical and electronic calculators.
\booktitle{Arithmetic} traces the history and
development of these various number languages and
calculating devices and examines their comparative
advantages and disadvantages, providing readers with an
opportunity to develop not only their computational
skills but also their own personal tastes and
preferences. The book is neither a training manual nor
an authoritative history, but rather an entertaining
survey of ideas and methods for the reader to enjoy and
appreciate. Written in a lively conversational style,
\booktitle{Arithmetic} is a fun and engaging
introduction to both practical techniques as well as
the more abstract mathematical aspects of the
subject.",
acknowledgement = ack-nhfb,
subject = "Talteori; Arithmetic; History",
tableofcontents = "Dear Reader / vii \\
Things / 1 \\
Language / 5 \\
Repetition / 10 \\
Tribes / 15 \\
Egypt / 25 \\
Rome / 32 \\
China and Japan / 41 \\
India / 48 \\
Europe / 75 \\
Multiplication / 87 \\
Division / 117 \\
Machines / 136 \\
Fractions / 151 \\
Negative numbers / 180 \\
The art of counting / 197 \\
Afterword / 215 \\
Index / 217",
}
@InProceedings{Lutz:2017:HPA,
author = "David Raymond Lutz and Christopher Neal Hinds",
title = "High-Precision Anchored Accumulators for Reproducible
Floating-Point Summation",
crossref = "Burgess:2017:ISC",
pages = "98--105",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.20",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper introduces a new datatype that allows
reproducible accumulation of floating-point (FP)
numbers in a programmer-selectable range. The new
datatype has a larger significand and a smaller range
than existing FP formats and has much better arithmetic
and computational properties. In particular, it is
associative, parallelizable, reproducible and correct.
For the modest ranges that will accommodate most
problems, it is also much faster: 3 to 12 times faster
on a single 256-bit SIMD implementation. The paper also
describes a new instruction and associated datapath
that support the proposed datatype, and discusses how a
recently published software algorithm for reproducible
FP summation could be implemented using the proposed
approach.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; arithmetic
properties; computational properties; Digital
arithmetic; floating point arithmetic; Floating-point;
floating-point summation; Hardware; high-precision;
high-precision anchored accumulators; Indexes;
Limiting; Metadata; parallel processing;
programmer-selectable range; Redundancy; Registers;
reproducibility; SIMD; software algorithm",
}
@Article{Magron:2017:CRE,
author = "Victor Magron and George Constantinides and Alastair
Donaldson",
title = "Certified Roundoff Error Bounds Using Semidefinite
Programming",
journal = j-TOMS,
volume = "43",
number = "4",
pages = "34:1--34:31",
month = mar,
year = "2017",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3015465",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Mar 24 08:51:05 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "Roundoff errors cannot be avoided when implementing
numerical programs with finite precision. The ability
to reason about rounding is especially important if one
wants to explore a range of potential representations,
for instance, for FPGAs or custom hardware
implementations. This problem becomes challenging when
the program does not employ solely linear operations as
non-linearities are inherent to many interesting
computational problems in real-world applications.
Existing solutions to reasoning possibly lead to either
inaccurate bounds or high analysis time in the presence
of nonlinear correlations between variables.
Furthermore, while it is easy to implement a
straightforward method such as interval arithmetic,
sophisticated techniques are less straightforward to
implement in a formal setting. Thus there is a need for
methods that output certificates that can be formally
validated inside a proof assistant. We present a
framework to provide upper bounds on absolute roundoff
errors of floating-point nonlinear programs. This
framework is based on optimization techniques employing
semidefinite programming and sums of squares
certificates, which can be checked inside the Coq
theorem prover to provide formal roundoff error bounds
for polynomial programs. Our tool covers a wide range
of nonlinear programs, including polynomials and
transcendental operations as well as conditional
statements. We illustrate the efficiency and precision
of this tool on non-trivial programs coming from
biology, optimization, and space control. Our tool
produces more accurate error bounds for 23\% of all
programs and yields better performance in 66\% of all
programs.",
acknowledgement = ack-nhfb,
articleno = "34",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Malaya:2017:AMP,
author = "Nicholas Malaya and Shuai Che and Joseph L. Greathouse
and Rene van Oostrum and Michael J. Schulte",
title = "Accelerating Matrix Processing with {GPUs}",
crossref = "Burgess:2017:ISC",
pages = "139--141",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.14",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Matrix operations are common and expensive
computations in a variety of applications. They occur
frequently in high-performance computing, graphics,
graph processing, and machine learning applications.
This paper discusses how to map a variety of important
matrix computations, including sparse matrix-vector
multiplication (SpMV), sparse triangle solve (SpTS),
graph processing, and dense matrix-matrix
multiplication, to GPUs. Since many emerging systems
will use heterogeneous architectures (e.g. CPUs and
GPUs) to attain the desired performance targets under
strict power constraints, this paper discusses
implications and future research for matrix processing
with heterogeneous designs. Conclusions common to the
matrix operations discussed in this paper are: (1)
Future algorithms should be written to ensure that the
essential computations fit into local memory, which may
require direct programmer management. (2) Algorithms
are needed that expose high levels of parallelism. (3)
While the scale of computation is often sufficient to
support algorithms with superior asymptotic order,
additional considerations, such as memory capacity and
bandwidth, must also be carefully managed. (4)
Libraries should be used to provide portable
performance.",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; dense matrix-matrix
multiplication; exascale; GPGPU; GPU; Graph Algorithms;
graph processing; graphics processing units; Graphics
processing units; Libraries; Linear algebra; matrix
computations; matrix multiplication; matrix processing;
Matrix-matrix multiplication; Memory management;
Parallel processing; Sparse matrices; sparse matrices;
sparse matrix-vector multiplication; sparse triangle
solve; SpMV; SpTS",
}
@Article{Martins:2017:AIR,
author = "Paulo Martins and Julien Eynard and Jean-Claude Bajard
and Leonel Sousa",
title = "Arithmetical Improvement of the Round-Off for
Cryptosystems in High-Dimensional Lattices",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2005--2018",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2690420",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7891511/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Mascarenhas:2017:ERE,
author = "Walter F. Mascarenhas and Andr{\'e} Pierro de
Camargo",
title = "The effects of rounding errors in the nodes on
barycentric interpolation",
journal = j-NUM-MATH,
volume = "135",
number = "1",
pages = "113--141",
month = jan,
year = "2017",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-016-0798-x",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Feb 18 08:20:07 MST 2017",
bibsource = "http://link.springer.com/journal/211/135/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
URL = "http://link.springer.com/accesspage/article/10.1007/s00211-016-0798-x;
http://link.springer.com/article/10.1007/s00211-016-0798-x",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Mazahir:2017:PEA,
author = "Sana Mazahir and Osman Hasan and Rehan Hafiz and
Muhammad Shafique",
title = "Probabilistic Error Analysis of Approximate Recursive
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "11",
pages = "1982--1990",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2709542",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Oct 12 06:36:58 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7935435/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Medhat:2017:MPE,
author = "Ramy Medhat and Michael O. Lam and Barry L. Rountree
and Borzoo Bonakdarpour and Sebastian Fischmeister",
title = "Managing the Performance\slash Error Tradeoff of
Floating-point Intensive Applications",
journal = j-TECS,
volume = "16",
number = "5s",
pages = "184:1--184:??",
month = oct,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3126519",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Oct 17 18:16:33 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
abstract = "Modern embedded systems are becoming more reliant on
real-valued arithmetic as they employ mathematically
complex vision algorithms and sensor signal processing.
Double-precision floating point is the most commonly
used precision in computer vision algorithm
implementations. A single-precision floating point can
provide a performance boost due to less memory
transfers, less cache occupancy, and relatively faster
mathematical operations on some architectures. However,
adopting it can result in loss of accuracy. Identifying
which parts of the program can run in single-precision
floating point with low impact on error is a manual and
tedious process. In this paper, we propose an automatic
approach to identify parts of the program that have a
low impact on error using shadow-value analysis. Our
approach provides the user with a performance/error
tradeoff, using which the user can decide how much
accuracy can be sacrificed in return for performance
improvement. We illustrate the impact of the approach
using a well known implementation of Apriltag detection
used in robotics vision. We demonstrate that an average
1.3x speedup can be achieved with no impact on tag
detection, and a 1.7x speedup with only 4\% false
negatives.",
acknowledgement = ack-nhfb,
articleno = "184",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J840",
}
@Article{Merchant:2017:ABL,
author = "Farhad Merchant and Anupam Chattopadhyay and Soumyendu
Raha and S. K. Nandy and Ranjani Narayan",
title = "Accelerating {BLAS} and {LAPACK} via Efficient
Floating Point Architecture Design",
journal = j-PARALLEL-PROCESS-LETT,
volume = "27",
number = "3--4",
pages = "1750006",
year = "2017",
CODEN = "PPLTEE",
DOI = "https://doi.org/10.1142/S0129626417500062",
ISSN = "0129-6264 (print), 1793-642X (electronic)",
ISSN-L = "0129-6264",
bibdate = "Tue May 29 09:05:31 MDT 2018",
bibsource = "http://ejournals.wspc.com.sg/ppl/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/parallelprocesslett.bib",
acknowledgement = ack-nhfb,
fjournal = "Parallel Processing Letters",
journal-URL = "http://www.worldscientific.com/loi/ppl",
}
@MastersThesis{Mian:2017:HPC,
author = "Riaz-ul-Haque Mian",
title = "High precision computation of decimal logarithm",
type = "Master of Engineering in Information and Communication
Technology",
school = "Institute of Information and Communication Technology,
Bangladesh University of Engineering and Technology",
pages = "52",
month = jan,
year = "2017",
DOI = "https://doi.org/10.13140/RG.2.2.11851.69924",
bibdate = "Tue Jul 06 18:24:02 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.researchgate.net/publication/323265326_High_precision_computation_of_decimal_logarithm",
abstract = "his report presents the design of an efficient low
power decimal logarithmic converter. The technique is
based on shift operation along with a precision unit
which is used to prevent unnecessary scan of full
memory table. Precision level is user programmable. It
does not require multiplication or division circuitry
which in turn makes it low power. Proposed decimal
logarithmic converter has been designed using Verilog
HDL and then compiled and simulated using Altera
provided Quartus II compiler and ModelSim simulator.
The synthesis results show that the proposed design
outperforms all the existing proposed decimal
logarithmic converters by other researchers. The
calculation is based on memory. Some predefined value
and their log value are stored in memory and by using
that value we calculate the logarithm of any value.
Another feature which is called precision unit is used
for controlling unnecessary scan of memory table.
According to input of precision value the algorithm
calculates logarithm value. Thus by increasing of
precision value we can increase accuracy of the result.
This algorithm does not need multiplication circuitry
and required very low memory thus it makes the
algorithm very low power.",
acknowledgement = ack-nhfb,
}
@Article{Micikevicius:2017:MPT,
author = "Paulius Micikevicius and Sharan Narang and Jonah Alben
and Gregory Diamos and Erich Elsen and David Garcia and
Boris Ginsburg and Michael Houston and Oleksii Kuchaiev
and Ganesh Venkatesh and Hao Wu",
title = "Mixed Precision Training",
journal = "arXiv.org",
day = "10",
month = oct,
year = "2017",
bibdate = "Mon Feb 10 09:21:08 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1710.03740",
abstract = "Deep neural networks have enabled progress in a wide
variety of applications. Growing the size of the neural
network typically results in improved accuracy. As
model sizes grow, the memory and compute requirements
for training these models also increases. We introduce
a technique to train deep neural networks using half
precision floating point numbers. In our technique,
weights, activations and gradients are stored in IEEE
half-precision format. Half-precision floating numbers
have limited numerical range compared to
single-precision numbers. We propose two techniques to
handle this loss of information. Firstly, we recommend
maintaining a single-precision copy of the weights that
accumulates the gradients after each optimizer step.
This single-precision copy is rounded to half-precision
format during training. Secondly, we propose scaling
the loss appropriately to handle the loss of
information with half-precision gradients. We
demonstrate that this approach works for a wide variety
of models including convolution neural networks,
recurrent neural networks and generative adversarial
networks. This technique works for large scale models
with more than 100 million parameters trained on large
datasets. Using this approach, we can reduce the memory
consumption of deep learning models by nearly $ 2
\times $. In future processors, we can also expect a
significant computation speedup using half-precision
hardware units.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
primaryclass = "cs.AI",
}
@Misc{Moler:2017:CCB,
author = "Cleve Moler",
title = "{Cleve}'s Corner: Bug in Half-Precision Floating Point
Object",
howpublished = "MathWorks Web site.",
day = "20",
month = dec,
year = "2017",
bibdate = "Sat Jan 19 18:38:12 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Moler:2017:CCH}.",
URL = "https://blogs.mathworks.com/cleve/2017/12/20/bug-in-half-precision-floating-point-object/",
acknowledgement = ack-nhfb,
}
@Misc{Moler:2017:CCH,
author = "Cleve Moler",
title = "{Cleve}'s Corner: {``Half} Precision'' 16-bit Floating
Point Arithmetic",
howpublished = "MathWorks Web site.",
day = "8",
month = may,
year = "2017",
bibdate = "Sat Jan 19 18:38:12 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See bug fix \cite{Moler:2017:CCB}.",
URL = "https://blogs.mathworks.com/cleve/2017/05/08/half-precision-16-bit-floating-point-arithmetic/",
acknowledgement = ack-nhfb,
}
@Misc{Moler:2017:CCQ,
author = "Cleve Moler",
title = "{Cleve}'s Corner: Quadruple Precision, 128-bit
Floating Point Arithmetic",
howpublished = "MathWorks Web site.",
day = "22",
month = may,
year = "2017",
bibdate = "Fri Feb 01 05:12:18 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "https://blogs.mathworks.com/cleve/2017/05/22/quadruple-precision-128-bit-floating-point-arithmetic/",
abstract = "The floating point arithmetic format that occupies 128
bits of storage is known as binary128 or quadruple
precision. This blog post describes an implementation
of quadruple precision programmed entirely in the
MATLAB language.",
acknowledgement = ack-nhfb,
}
@InProceedings{Monfared:2017:NMI,
author = "Amin Monfared and Hayssam El-Razouk and Arash
Reyhani-Masoleh",
title = "A New Multiplicative Inverse Architecture in Normal
Basis Using Novel Concurrent Serial Squaring and
Multiplication",
crossref = "Burgess:2017:ISC",
pages = "164--171",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.37",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Itoh and Tsujii proposed a fast algorithm for
computing multiplicative inverses (inversions) over
GF(2m) using normal bases by iterating single
multiplications and cyclic shifts. Recently, the
Itoh--Tsujii algorithm (ITA) has been modified to use
two digit-level single multiplications. The
improvements of the modified Itoh--Tsujii and its
variant algorithms are based on reducing the
computational latency at the expense of more area
requirements. In this paper, we propose a new inversion
architecture based on the classical IT algorithm (or
improved one) utilizing a novel interleaved
computations of two single multiplications and
squarings at the digit-level. The new inverter
outperforms previous modified Itoh--Tsujii algorithms
(such as the Ternary Itoh--Tsujii and optimal 3-chain
algorithms) in terms of its lower latency, higher
throughput, and improved hardware efficiency. The
efficiency of the proposed field inverter is
demonstrated by comparisons based on application
specific integrated circuits (ASIC) implementations
results using the standard 65nm CMOS technology
libraries.",
acknowledgement = ack-nhfb,
keywords = "application specific integrated circuits; ASIC; CMOS
technology; Computer architecture; concurrent serial
squaring; cyclic shifts; Digit-level multiplier; field
inversion; field inverter; finite field; Gaussian
processes; High definition video; hybrid-double
multiplication; Inverters; invertors; Itoh--Tsujii
algorithm; logic design; multiplicative inverse
architecture; multiplying circuits; Niobium; Standards;
two digit-level single multiplications; Two dimensional
displays",
}
@Article{Mustapha:2017:RSA,
author = "Khalid Shahabdeen Mustapha and Edem Kwedzo Bankas",
title = "{RNS} Scaling Algorithm for a New Moduli Set $ \{
2^{(2n + 1)} + 1, 2^{(2n + 1)}, 2^{(2n + 1)} - 1 \} $",
journal = j-INT-J-COMP-APPL,
volume = "165",
number = "??",
pages = "21--28",
month = may,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.5120/ijca2017913974",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 09:34:34 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume165/number10/27609-2017913974/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "10",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@Article{Numahata:2017:ASN,
author = "Dai Numahata and Hiroshi Sekigawa",
title = "An algorithm for symbolic--numeric sparse
interpolation of multivariate polynomials whose degree
bounds are unknown",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "51",
number = "1",
pages = "18--20",
month = mar,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3096730.3096734",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Tue Oct 10 16:29:29 MDT 2017",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
abstract = "We consider the problem of sparse interpolation of a
multivariate black-box polynomial in floating-point
arithmetic. More specifically, we assume that we are
given a black-box polynomial $ f(x_1, \ldots {}, x_n) =
\sum^t_{j = 1} c_j x_1^{d_j, 1} \ldots {} x_n^{d_j, n}
\in C[x_1, \ldots {}, x_n] (c_j \neq 0) $ and the
number of terms $t$, and that we can evaluate the value
of $ f(x^1, \ldots {}, x_n)$ at any point in $ C^n$ in
floating-point arithmetic. The problem is to find the
coefficients $ c_1, \ldots {}, c_t$ and the exponents $
d_{1, 1}, \ldots {}, d_{t, n}$. We propose an efficient
algorithm to solve the problem.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Rafferty:2017:ELI,
author = "Ciara Rafferty and M{\'a}ire O'Neill and Neil Hanley",
title = "Evaluation of Large Integer Multiplication Methods on
Hardware",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "8",
pages = "1369--1382",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2677426",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 13 14:57:15 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7869256/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Comba multiplication; Karatsuba multiplication;
Karatsuba--Comba multiplier; NTT--Karatsuba--Schoolbook
multiplier",
}
@InProceedings{Rieu-Helft:2017:HGE,
author = "Rapha{\"e}l Rieu-Helft and Claude March{\'e} and
Guillaume Melquiond",
editor = "Andrei Paskevich and Thomas Wies",
booktitle = "Verified Software. Theories, Tools, and Experiments:
{9th International Conference, VSTTE 2017, Heidelberg,
Germany, July 22--23, 2017}, Revised Selected Papers",
title = "How to get an efficient yet verified
arbitrary-precision integer library",
volume = "10712",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xiii + 211 + 69",
pages = "84--101",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-72308-2_6",
ISBN = "3-319-72308-1",
ISBN-13 = "978-3-319-72308-2",
LCCN = "QA76.758",
bibdate = "Sat Feb 08 09:03:15 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
URL = "https://link.springer.com/chapter/10.1007/978-3-319-72308-2_6",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-319-72308-2",
}
@InProceedings{Rioual:2017:LSN,
author = "Jean-Christophe Rioual",
title = "Large Scale Numerical Simulations of the Climate",
crossref = "Burgess:2017:ISC",
pages = "122--122",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.21",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Met Office Hadley Centre for Climate Science and
Services, based at the Met Office's Exeter HQ, provides
world-class guidance on the science of climate change
and is the primary focus in the UK for climate science.
The Hadley Centre makes significant contributions to
scientific literature and to a variety of climate
science reports, including the International Panel on
Climate Change (IPCC). In October 2014 the Government
confirmed its investment of \pounds 97 million in a new
high performance computing facility for the Met Office.
The new Cray XC40 located at Exeter Science Park is the
largest HPC system in the world dedicated to weather
and climate research. I will first give an overview of
how climate numerical experiments are organised
worldwide through the coupled model intercomparison
project (CMIP) under the auspices of the world climate
research program (WCRP). The numerical results of these
simulation campaigns are submitted to intense scrutiny
by the scientific community and policy makers.
Numerical reproducibility is therefore of paramount
importance. I will explain the parameters of what
numerical reproducibility means to our community and
how we aim to achieve it. I will present the use of
different types of floating point arithmetic in the
models. Two examples are the use double--double
precision for reproducible global sums and research on
single precision algorithms for computational
efficiency. Finally, I will look at some of the
challenges to maintain numerical reproducibility in the
exascale era.",
acknowledgement = ack-nhfb,
keywords = "climate change; Computational modeling; coupled model
intercomparison project; Cray XC40; Digital arithmetic;
floating point arithmetic; geophysics computing;
Government; Investment; large scale numerical
simulations; largest HPC system; Meteorology; Numerical
models; Numerical simulation; parallel processing;
world climate research program",
}
@InProceedings{Risse:2017:BEG,
author = "Thomas Risse",
booktitle = "{2017 8th International Conference on Information
Technology (ICIT)}",
title = "Better is the enemy of good: Unums: An alternative to
{IEEE 754} floats and doubles",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "200--204",
year = "2017",
DOI = "https://doi.org/10.1109/ICITECH.2017.8080000",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Rocca:2017:CRE,
author = "Alexandre Rocca and Victor Magron and Thao Dang",
title = "Certified Roundoff Error Bounds Using {Bernstein}
Expansions and Sparse {Krivine--Stengle}
Representations",
crossref = "Burgess:2017:ISC",
pages = "74--81",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.36",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point error is a notable drawback of embedded
systems implementation. Computing rigorous upper bounds
of roundoff errors is absolutely necessary for the
validation of critical software. This problem of
computing rigorous upper bounds is even more
challenging when addressing non-linear programs. In
this paper, we propose and compare two new methods
based on Bernstein expansions and sparse
Krivine--Stengle representations, adapted from the
field of the global optimization, to compute upper
bounds of roundoff errors for programs implementing
polynomial functions. We release two related software
package FPBern and FPKriSten, and compare them with
state of the art tools. We show that these two methods
achieve competitive performance, while computing
accurate upper bounds by comparison with other tools.",
acknowledgement = ack-nhfb,
keywords = "Algebra; Bernstein expansions; Bernstein Expansions;
certified roundoff error bounds; Computational
modeling; floating point arithmetic; Floating Point
Arithmetic; floating point error; FPBern; FPKriSten;
global optimization; Krivine-Stengle Representations;
Linear Programming Relaxations; non-linear programs;
nonlinear programming; Optimization; Polynomial
Optimization; Roundoff Error Bounds; Roundoff errors;
sparse Krivine-Stengle representations; Standards;
Tools; Upper bound",
}
@InProceedings{Rovers:2017:IPP,
author = "Kenneth C. Rovers and Sam Elliott",
title = "On Improving the Performance Per Area of {ASTC} with a
Multi-output Decoder",
crossref = "Burgess:2017:ISC",
pages = "58--59",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.32",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "ASTC is an efficient and flexible texture compression
format but it is relatively costly to implement in
hardware. By outputting multiple texels from a single
encoded ASTC block, we will show an performance per
area improvement of 25\%.",
acknowledgement = ack-nhfb,
keywords = "adaptive scalable texture compression; computer
graphics; data compression; Decoding; flexible texture
compression format; Graphics; Hardware; Image color
analysis; image texture; Indexes; Interpolation;
multioutput decoder; Performance evaluation;
performance per area; single encoded ASTC block;
texture decompression",
}
@Article{Rump:2017:IPK,
author = "Siegfried M. Rump",
title = "{IEEE754} Precision-$k$ base-$ \beta $ Arithmetic
Inherited by Precision-$m$ Base-$ \beta $ Arithmetic
for $ k < m$",
journal = j-TOMS,
volume = "43",
number = "3",
pages = "20:1--20:15",
month = jan,
year = "2017",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/2785965",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Oct 4 10:55:07 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=2785965",
abstract = "Suppose an $m$-digit floating-point arithmetic in base
$ \beta \geq 2$ following the IEEE754 arithmetic
standard is available. We show how a $k$-digit
arithmetic with $ k < m$ can be inherited solely using
$m$-digit operations. This includes the rounding into
$k$ digits, the four basic operations and the square
root, all for even or odd base $ \beta $. In
particular, we characterize the relation between $k$
and $m$ so that no double rounding occurs when
computing in $m$ digits and rounding the result into
$k$ digits. We discuss rounding to nearest as well as
directed rounding, and our approach covers exceptional
values including signed zero. For binary arithmetic, a
Matlab toolbox based on binary64 including $k$-bit
scalar, vector and matrix operations as well as $k$-bit
interval arithmetic is part of Version 8 of INTLAB, the
Matlab toolbox for reliable computing.",
acknowledgement = ack-nhfb,
articleno = "20",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Russell:2017:LBR,
author = "Brian M. Russell",
title = "Lost Bits Regained?",
journal = "Resurrection: The Journal of the Computer Conservation
Society",
volume = "??",
number = "79",
pages = "??--??",
month = "Autumn",
year = "2017",
ISSN = "0958-7403",
ISSN-L = "0958-7403",
bibdate = "Mon Jul 27 18:14:57 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://computerconservationsociety.org/resurrection/res79.htm#d",
acknowledgement = ack-nhfb,
remark = "Answers the question: ``Did the Ferranti Atlas
floating point arithmetic unit standardise its operands
before applying the requested arithmetic function or
did it risk losing accuracy if the numbers were not
standardised?''",
}
@Article{Saint-Genies:2017:ELT,
author = "Hugues de Lassus Saint-Geni{\`e}s and David Defour and
Guillaume Revy",
title = "Exact Lookup Tables for the Evaluation of
Trigonometric and Hyperbolic Functions",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2058--2071",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2703870",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7927421/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Sanchez-Stern:2017:FRC,
author = "Alex Sanchez-Stern and Pavel Panchekha and Sorin
Lerner and Zachary Tatlock",
title = "Finding Root Causes of Floating Point Error with
{Herbgrind}",
journal = "arXiv.org",
pages = "15",
year = "2017",
bibdate = "Sat Feb 8 10:38:13 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1705.10416",
abstract = "Floating-point arithmetic plays a central role in
science, engineering, and finance by enabling
developers to approximate real arithmetic. To address
numerical issues in large floating-point applications,
developers must identify root causes, which is
difficult because floating-point errors are generally
non-local, non-compositional, and non-uniform. This
paper presents Herbgrind, a tool to help developers
identify and address root causes in numerical code
written in low-level C/C++ and Fortran. Herbgrind
dynamically tracks dependencies between operations and
program outputs to avoid false positives and abstracts
erroneous computations to a simplified program fragment
whose improvement can reduce output error. We perform
several case studies applying Herbgrind to large,
expert-crafted numerical programs and show that it
scales to applications spanning hundreds of thousands
of lines, correctly handling the low-level details of
modern floating point hardware and mathematical
libraries, and tracking error across function
boundaries and through the heap.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
biburl = "https://dblp.org/rec/bib/journals/corr/Sanchez-SternPL17",
remark = "Published in PLDI 18.",
}
@Article{Sano:2017:FBS,
author = "Kentaro Sano and Satoru Yamamoto",
title = "{FPGA}-Based Scalable and Power-Efficient Fluid
Simulation using Floating-Point {DSP} Blocks",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "28",
number = "10",
pages = "2823--2837",
month = oct,
year = "2017",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/TPDS.2017.2691770",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Thu Oct 12 06:58:12 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
URL = "https://www.computer.org/csdl/trans/td/2017/10/07893769-abs.html",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "http://www.computer.org/tpds/archives.htm",
}
@Article{Schleicher:2017:NMP,
author = "Dierk Schleicher and Robin Stoll",
title = "{Newton}'s method in practice: Finding all roots of
polynomials of degree one million efficiently",
journal = j-THEOR-COMP-SCI,
volume = "681",
number = "??",
pages = "146--166",
day = "12",
month = jun,
year = "2017",
CODEN = "TCSCDI",
ISSN = "0304-3975 (print), 1879-2294 (electronic)",
ISSN-L = "0304-3975",
bibdate = "Wed Aug 9 15:42:32 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tcs2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0304397517302475",
acknowledgement = ack-nhfb,
fjournal = "Theoretical Computer Science",
journal-URL = "http://www.sciencedirect.com/science/journal/03043975",
}
@InProceedings{Serre:2017:OSL,
author = "Fran{\c{c}}ois Serre and Markus Puschel",
title = "Optimal Streamed Linear Permutations",
crossref = "Burgess:2017:ISC",
pages = "60--61",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.13",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We give an overview on optimal circuits to implement
linear permutations on FPGAs using only RAM banks and
switches. Linear means that the permutation maps
linearly the bit representation of the indices, as it
is the case with most permutations arising in digital
signal processing algorithms including those in fast
Fourier transforms, Viterbi decoders, and sorting
networks. Additionally, we assume that the data to be
permuted is streamed, i.e., input in chunks over
several cycles. The circuits are obtained from a
suitable factorization of the bit matrix representing
the permutation and achieve the minimal number of
switches possible.",
acknowledgement = ack-nhfb,
keywords = "bit representation; Bit-reversal; Complexity; Computer
science; Connection network; Data reordering; digital
signal processing algorithms; fast Fourier transforms;
field programmable gate arrays; Field programmable gate
arrays; field programmable gate arrays; FPGA; Matrix
factorization; optimal circuits; optimal streamed
linear permutations; Parallel processing; Ports
(Computers); Program processors; RAM banks; Random
access memory; random-access storage; signal
processing; Sorting; sorting networks; Streaming
datapath; Stride permutation; Viterbi decoders; Viterbi
decoding",
}
@Article{Stoutemyer:2017:APC,
author = "David R. Stoutemyer",
title = "{AskConstants} proposes concise non-floats close to
floats",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "51",
number = "1",
pages = "32--34",
month = mar,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3096730.3096739",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Tue Oct 10 16:29:29 MDT 2017",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
abstract = "This poster presentation is an opportunity to try the
downloadable AskConstants program. This copy of some
posters is a sequence of images of the program in
operation.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Thevenoux:2017:ASS,
author = "Laurent Th{\'e}venoux and Philippe Langlois and
Matthieu Martel",
title = "Automatic source-to-source error compensation of
floating-point programs: code synthesis to optimize
accuracy and time",
journal = j-CCPE,
volume = "29",
number = "7",
pages = "??--??",
day = "10",
month = apr,
year = "2017",
CODEN = "CCPEBO",
DOI = "https://doi.org/10.1002/cpe.3953",
ISSN = "1532-0626 (print), 1532-0634 (electronic)",
ISSN-L = "1532-0626",
bibdate = "Fri Mar 31 19:12:52 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Concurrency and Computation: Practice and Experience",
journal-URL = "http://www.interscience.wiley.com/jpages/1532-0626",
}
@Article{Thornes:2017:USD,
author = "Tobias Thornes and Peter D{\"u}ben and Tim Palmer",
title = "On the use of scale-dependent precision in {Earth
System} modelling",
journal = j-QUART-J-ROY-METEOROL-SOC,
volume = "143",
number = "703",
pages = "897--908",
month = jan,
year = "2017",
CODEN = "QJRMAM",
DOI = "https://doi.org/10.1002/qj.2974",
ISSN = "0035-9009 (print), 1477-870X (electronic)",
ISSN-L = "0035-9009",
bibdate = "Thu Nov 7 17:05:05 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Quarterly journal of the Royal Meteorological
Society",
journal-URL = "http://rmets.onlinelibrary.wiley.com/hub/journal/10.1002/(ISSN)1477-870X/issues/",
keywords = "half-precision floating-point arithmetic; stochastic
rounding; variable precision floating-point
arithmetic",
}
@InCollection{Titolo:2017:AIF,
author = "Laura Titolo and Marco A. Feli{\'u} and Mariano
Moscato and C{\'e}sar A. Mu{\~n}oz",
editor = "Isil Dillig and Jens Palsberg",
booktitle = "Verification, Model Checking, and Abstract
Interpretation, {19th International Conference, VMCAI
2018, Los Angeles, CA, USA, January 7--9, 2018,
Proceedings}",
title = "An Abstract Interpretation Framework for the Round-Off
Error Analysis of Floating-Point Programs",
volume = "10747",
publisher = pub-SV,
address = pub-SV:adr,
pages = "516--537",
month = dec,
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-73721-8_24",
ISBN = "3-319-73720-1 (print), 3-319-73721-X (e-book)",
ISBN-13 = "978-3-319-73720-1 (print), 978-3-319-73721-8
(e-book)",
bibdate = "Mon Sep 11 07:21:11 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
abstract = "This paper presents an abstract interpretation
framework for the round-off error analysis of
floating-point programs. This framework defines a
parametric abstract analysis that computes, for each
combination of ideal and floating-point execution path
of the program, a sound over-approximation of the
accumulated floating-point round-off error that may
occur. In addition, a Boolean expression that
characterizes the input values leading to the computed
error approximation is also computed. An abstraction on
the control flow of the program is proposed to mitigate
the explosion of the number of elements generated by
the analysis. Additionally, a widening operator is
defined to ensure the convergence of recursive
functions and loops. An instantiation of this framework
is implemented in the prototype tool PRECiSA that
generates formal proof certificates stating the
correctness of the computed round-off errors.",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/978-3-319-73721-8",
}
@Article{Ueno:2017:BCF,
author = "Tomohiro Ueno and Kentaro Sano and Satoru Yamamoto",
title = "Bandwidth Compression of Floating-Point Numerical Data
Streams for {FPGA}-Based High-Performance Computing",
journal = j-TRETS,
volume = "10",
number = "3",
pages = "18:1--18:??",
month = jul,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3053688",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Sat Dec 23 10:23:02 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
abstract = "Although computational performance is often limited by
insufficient bandwidth to/from an external memory, it
is not easy to physically increase off-chip memory
bandwidth. In this study, we propose a hardware-based
bandwidth compression technique that can be applied to
field-programmable gate array-- (FPGA) based
high-performance computation with a logically wider
effective memory bandwidth. Our proposed hardware
approach can boost the performance of FPGA-based stream
computations by applying a data compression technique
to effectively transfer more data streams. To apply
this data compression technique to bandwidth
compression via hardware, several requirements must
first be satisfied, including an acceptable level of
compression performance and a sufficiently small
hardware footprint. Our proposed hardware-based
bandwidth compressor utilizes an efficient
prediction-based data compression algorithm. Moreover,
we propose a multichannel serializer and deserializer
that enable applications to use multiple channels of
computational data with the bandwidth compression. The
serializer encodes compressed data blocks of multiple
channels into a data stream, which is efficiently
written to an external memory. Based on preliminary
evaluation, we define an encoding format considering
both high compression ratio and small hardware area. As
a result, we demonstrate that our area saving bandwidth
compressor increases performance of an FPGA-based fluid
dynamics simulation by deploying more processing
elements to exploit spatial parallelism with the
enhanced memory bandwidth.",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "http://portal.acm.org/toc.cfm?id=J1151",
}
@InProceedings{Uguen:2017:BHL,
author = "Yohann Uguen and Florent de Dinechin and Steven
Derrien",
booktitle = "{2017 27th International Conference on Field
Programmable Logic and Applications (FPL)}",
title = "Bridging high-level synthesis and application-specific
arithmetic: The case study of floating-point
summations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--8",
month = sep,
year = "2017",
DOI = "https://doi.org/10.23919/FPL.2017.8056792",
ISSN = "1946-147X (print), 1946-1488 (electronic)",
ISSN-L = "1946-147X",
bibdate = "Sat Feb 8 10:26:34 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Adders; application-specific arithmetic; C language;
C-C++ dialects; C11 standards; Field programmable gate
arrays; field programmable gate arrays; floating point
arithmetic; floating-point additions; floating-point
summations; FPGA application-specific efficiency; FPGA
programming; handcrafted HDL; Hardware; high level
synthesis; high-level C description; high-level C
language; high-level specification; high-level
synthesis; highly-customizable application-specific IP;
HLS; IEEE-754 standards; logic design; microprocessor
programming; nonstandard arithmetic formats;
nonstandard computations; Open area test sites;
Optimization; program compilers; Program processors;
source-to-source compiler; Tools; ubiquitous
floating-point summation-reduction pattern",
}
@Article{Ugurdag:2017:HDS,
author = "H. Fatih Ugurdag and Florent de Dinechin and Y. Serhan
Gener and Sezer G{\"o}ren and Laurent-St{\'e}phane
Didier",
title = "Hardware Division by Small Integer Constants",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "12",
pages = "2097--2110",
month = dec,
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2707488",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Nov 10 08:32:25 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/7933010/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{vanderHoeven:2017:MPF,
author = "Joris van der Hoeven",
title = "Multiple Precision Floating-Point Arithmetic on {SIMD}
Processors",
crossref = "Burgess:2017:ISC",
pages = "2--9",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.12",
ISSN = "1063-6889",
MRclass = "65Y04, 65T50, 68W30",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Current general purpose libraries for multiple
precision floating-point arithmetic such as MPFR suffer
from a large performance penalty with respect to
hard-wired instructions. The performance gap tends to
become even larger with the advent of wider SIMD
arithmetic in both CPUs and GPUs. In this paper, we
present efficient algorithms for multiple precision
floating-point arithmetic that are suitable for
implementations on SIMD processors. A.C.M. subject
classification: G.1.0 Computer-arithmetic A.M.S.
subject classification: 65Y04, 65T50, 68W30.",
acknowledgement = ack-nhfb,
keywords = "floating point arithmetic; floating-point arithmetic;
Frequency modulation; Hardware; Indexes; Libraries;
multiple precision; multiple precision floating-point
arithmetic; Numerical analysis; parallel processing;
Program processors; SIMD; SIMD processors; Standards",
}
@Article{VanZee:2017:IHP,
author = "Field G. {Van Zee} and Tyler M. Smith",
title = "Implementing High-performance Complex Matrix
Multiplication via the 3m and 4m Methods",
journal = j-TOMS,
volume = "44",
number = "1",
pages = "7:1--7:36",
month = jul,
year = "2017",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3086466",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Oct 4 10:55:07 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3086466",
abstract = "In this article, we explore the implementation of
complex matrix multiplication. We begin by briefly
identifying various challenges associated with the
conventional approach, which calls for a carefully
written kernel that implements complex arithmetic at
the lowest possible level (i.e., assembly language). We
then set out to develop a method of complex matrix
multiplication that avoids the need for complex kernels
altogether. This constraint promotes code reuse and
portability within libraries such as Basic Linear
Algebra Subprograms and BLAS-Like Library Instantiation
Software (BLIS) and allows kernel developers to focus
their efforts on fewer and simpler kernels. We develop
two alternative approaches --- one based on the 3m
method and one that reflects the classic 4m formulation
--- each with multiple variants, all of which rely only
on real matrix multiplication kernels. We discuss the
performance characteristics of these ``induced''
methods and observe that the assembly-level method
actually resides along the 4m spectrum of algorithmic
variants. Implementations are developed within the BLIS
framework, and testing on modern hardware confirms that
while the less numerically stable 3m method yields the
fastest runtimes, the more stable (and thus widely
applicable) 4m method's performance is somewhat limited
due to implementation challenges that appear inherent
in nature.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Vazquez:2017:SED,
author = "Alvaro V{\'a}zquez and Elisardo Antelo",
title = "A Sum Error Detection Scheme for Decimal Arithmetic",
crossref = "Burgess:2017:ISC",
pages = "172--179",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.34",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Users of financial and e-commerce services demand a
high degree of reliability and at the same time an
increasing demand of speed of processing. On the other
hand, soft errors are becoming more significant due to
the higher densities and reduced CMOS integration
technology sizes. Among the basic arithmetic
operations, addition/subtraction is the most demanded.
Although in the past, binary implementations were only
considered, today decimal implementations are becoming
important. In this context, we introduce a modular
design for fast error checking of binary and decimal
(BCD) addition/subtraction operations that avoids the
whole replication of the arithmetic units. Unlike other
error checkers based on parity prediction or residue
checking, this is a separable design that lies
completely off of the critical path of the protected
adder without incurring in important penalties in area
or performance.",
acknowledgement = ack-nhfb,
keywords = "adders; Adders; arithmetic units; CMOS; CMOS
integrated circuits; CMOS logic circuits; Combined
decimal/binary Adders; Computer architecture; decimal
arithmetic; Decimal arithmetic; Detectors; digital
arithmetic; error checking; logic design;
Microprocessors; parity prediction; radiation hardening
(electronics); Reliability; residue checking; Residue
Checking; Silicon; soft errors; sum error detection
scheme; Transient analysis",
}
@InProceedings{Volkova:2017:RVD,
author = "Anastasia Volkova and Christoph Lauter and Thibault
Hilaire",
title = "Reliable Verification of Digital Implemented Filters
Against Frequency Specifications",
crossref = "Burgess:2017:ISC",
pages = "180--187",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.9",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Reliable implementation of digital filters in finite
precision is based on accurate error analysis. However,
a small error in the time domain does not guarantee
that the implemented filter verifies the initial band
specifications in the frequency domain. We propose a
novel certified algorithm for the verification of a
filter's transfer function, or of an existing
finite-precision implementation. We show that this
problem boils down to the verification of bounds on a
rational function, and further to the positivity of a
polynomial. Our algorithm has reasonable runtime
efficiency to be used as a criterion in large
implementation space explorations. We ensure that there
are no false positives but false negative answers may
occur. For negative answers we give a tight bound on
the margin of acceptable specifications. We demonstrate
application of our algorithm to the comparison of
various finite-precision implementations of filters
already fully designed.",
acknowledgement = ack-nhfb,
keywords = "Algorithm design and analysis; digital filters;
digital implemented filters; eigendecomposition;
filters; finite-precision implementation; fixed-point
arithmetic; floating-point arithmetic; frequency
specifications; Frequency-domain analysis; interval
arithmetic; polynomials; Positivstellensatz;
reliability; Reliability; rigorous computation; Signal
processing algorithms; Software algorithms; transfer
function; transfer functions; Transfer functions;
Transforms",
}
@InProceedings{Vzquez:2017:NSA,
author = "Alvaro V{\'a}zquez and Elisardo Antelo",
title = "A Number System Approach for Adder Topologies",
crossref = "Burgess:2017:ISC",
pages = "50--57",
month = jul,
year = "2017",
DOI = "https://doi.org/10.1109/ARITH.2017.33",
ISSN = "1063-6889",
bibdate = "Fri Nov 17 09:10:14 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The design space exploration for fast and power
efficient adders is of increasing interest for
microprocessors and graphic and digital signal
processors. Recently, several methods have been
proposed to explore the design space of adders, where
well known designs appear as possible instances. These
methods are based on the identification of parameters
that lead to different hardware structures. In this
work, we go a step further by exploring the
mathematical foundation behind the trees for carry
computation. We propose an algorithm that allows to
obtain any adder topology based on design decisions.
The method is based on finding representations of
integers in a given number system. This leads to an
adder model that allows the design of any adder
structure in a compact a formal way. The proposed
formal model might be useful for a formal design
description of adders and it can be incorporated to CAD
tools.",
acknowledgement = ack-nhfb,
keywords = "Adder Topologies; adder topology; Adders; adders;
carry computation; carry logic; Computational modeling;
design space exploration; logic design; Mathematical
model; Number Systems; Prefix Adders; Solid modeling;
Space exploration; Sparse Trees; Tools; Topology",
}
@Article{Wahba:2017:AEF,
author = "Ahmed A. Wahba and Hossam A. H. Fahmy",
title = "Area Efficient and Fast Combined Binary\slash Decimal
Floating Point Fused Multiply Add Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "66",
number = "2",
pages = "226--239",
month = "????",
year = "2017",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2016.2584067",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jan 19 06:52:50 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Adams:2018:RFF,
author = "Ulf Adams",
title = "{Ry{\=u}}: fast float-to-string conversion",
journal = j-SIGPLAN,
volume = "53",
number = "4",
pages = "270--282",
month = apr,
year = "2018",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/3296979.3192369",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Wed Oct 16 14:12:57 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "We present Ry{\=u}, a new routine to convert binary
floating point numbers to their decimal representations
using only fixed-size integer operations, and prove its
correctness. Ry{\=u} is simpler and approximately three
times faster than the previously fastest
implementation.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
keywords = "base conversion; correct rounding; floating-point
arithmetic; input-output conversion; radix conversion;
round-trip base conversion",
remark = "PLDI '18 proceedings.",
}
@Article{Afriyie:2018:MBE,
author = "Yaw Afriyie and M. I. Daabo",
title = "Multiple Bits Error Detection and Correction in {RRNS}
Architecture using the {MRC} and {HD} Techniques",
journal = j-INT-J-COMP-APPL,
volume = "180",
number = "??",
pages = "18--23",
month = may,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.5120/ijca2018917030",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 09:43:10 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume180/number39/29387-2018917030/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "39",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
keywords = "Redundant Residue Number System (RRNS)",
}
@Article{Alaghi:2018:CR,
author = "A. Alaghi and J. P. Hayes",
title = "Computing with Randomness",
journal = j-IEEE-SPECTRUM,
volume = "55",
number = "3",
pages = "46--51",
month = mar,
year = "2018",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2018.8302387",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 07:02:09 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "analog numbers; analog signal; arithmetic operations;
brains-process; computer process; Computers; digital
arithmetic; Digital circuits; human hearing; human
nervous system; human vision; Image restoration;
Implants; logic circuits; Logic gates; neural impulse
sequence; Parity check codes; random binary digit
stream; Retina; stochastic bitstreams; stochastic
computing; stochastic processes; time 50 year",
}
@Article{Amanollahi:2018:ERD,
author = "Saba Amanollahi and Ghassem Jaberipur",
title = "Extended Redundant-Digit Instruction Set for
Energy-Efficient Processors",
journal = j-TECS,
volume = "17",
number = "3",
pages = "70:1--70:??",
month = jun,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3202664",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Oct 17 18:16:35 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
abstract = "The impact of extending the instruction set
architecture (ISA) of a conventional binary processor
by a set of redundant-digit arithmetic instructions is
studied. Selected binary arithmetic instructions within
a given code sequence are replaced with appropriate
redundant-digit ones. The selection criteria is so
enforced to lead to overall reduction of execution
energy and energy-delay product (EDP). A special branch
and bound algorithm is devised to modify the dataflow
graph (DFG) to a new one that takes advantage of the
extended redundant-digit instruction set. The DFG is
obtained, via an in-house tool, from the intermediate
code representation that is normally produced by the
utilized compiler. The required redundant-digit
arithmetic operations (including a multiplier, a
multiply accumulator, and three- to four-operand
redundant-digit adders specially designed for this
work) have been synthesized on 45nm NanGate technology
by a Synopsys Design Compiler. To evaluate the impact
of the proposed ISA augmentation on actual code
execution, the simulation and evaluation platform of
our choice is an MIPS processor whose ISA is extended
by the proposed redundant-digit instructions. Several
digital signal processing benchmarks are utilized as
the source of the baseline MIPS codes, which are
converted (via the aforementioned algorithm) to the
equivalent mixed binary/redundant-digit codes. Our
experiments, as such, show up to 26\% energy and 44\%
EDP savings.",
acknowledgement = ack-nhfb,
articleno = "70",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J840",
}
@InProceedings{Anderson:2018:EVM,
author = "Cristina S. Anderson and Jingwei Zhang and Marius
Cornea",
title = "Enhanced Vector Math Support on the {Intel AVX-512}
Architecture",
crossref = "Tenca:2018:PIS",
pages = "120--124",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464794",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Intel AVX-512 architecture adds new capabilities
such as masked execution, floating-point exception
suppression and static rounding modes, as well as a
small set of new instructions for mathematical library
support. These new features allow for better compliance
with floating-point or language standards (e.g. no
spurious floating-point exceptions, and faster or more
accurate code for directed rounding modes), as well as
simpler, smaller footprint implementations that
eliminate branches and special case paths. Performance
is also improved, in particular for vector mathematical
functions (which benefit from easier processing in the
main path, and fast access to small lookup tables). In
this paper, we describe the relevant new features and
their possible applications to floating-point
computation. The code examples include a few compact
implementation sequences for some common vector
mathematical functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-25; common vector mathematical functions;
directed rounding modes; enhanced vector math support;
floating-point; floating-point computation;
floating-point exception suppression; floating-point
exceptions; Instruction sets; Intel AVX-512
architecture; Libraries; masked execution; mathematical
library support; mathematics computing; Registers;
SIMD; Standards; static rounding modes; Support vector
machines; Table lookup; table lookup; vector
mathematical function; vectors",
}
@Misc{Anonymous:2018:DRD,
author = "Anonymous",
title = "Driverless racecar drives straight into a wall",
howpublished = "Web site",
year = "2018",
bibdate = "Mon Aug 26 12:09:20 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The report describes how an unanticipated
floating-point NaN caused the steering wheel to lock to
its maximum right. From the report: ``the [controller]
output values are transferred via control area network
(CAN) to the actuators, but there is no definition for
a NaN in the CAN specs, so it just transformed it into
a normal number, albeit a very large one.''",
URL = "https://www.reddit.com/r/formula1/comments/jk9jrg/comment/gai295l/",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:2018:FVF,
author = "Anonymous",
title = "Formal Verification of Floating-Point Hardware with
Assertion-Based {VIP}",
howpublished = "Web site.",
year = "2018",
bibdate = "Fri Sep 28 06:31:32 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.onespin.com/fpu/",
acknowledgement = ack-nhfb,
remark = "Sections labeled ``Nicolae Tusinschi about
Verification of Floating-Point Hardware Designs'' and
``Xilinx verifies Floating-Point Hardware IP with
OneSpin FPU App''.",
}
@Misc{Anonymous:2018:HFF,
author = "Anonymous",
title = "{Herbie}: Find and fix floating-point problems",
howpublished = "Web site and software source.",
year = "2018",
bibdate = "Thu May 02 16:59:16 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://herbie.uwplse.org/",
abstract = "Herbie detects inaccurate expressions and finds more
accurate replacements.",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:2018:OLA,
author = "Anonymous",
title = "{OneSpin} Launches {``App''} for Formal Verification
of Floating-Point Hardware Critical for Machine
Learning and Deep Learning Chips: Offers Exhaustive
Coverage of Floating-Point Arithmetic Operations
Compliant with {IEEE 754 Standard}",
howpublished = "Web site",
day = "27",
month = nov,
year = "2018",
bibdate = "Wed Nov 28 10:06:08 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://globenewswire.com/news-release/2018/11/27/1657662/0/en/OneSpin-Launches-App-for-Formal-Verification-of-Floating-Point-Hardware-Critical-for-Machine-Learning-and-Deep-Learning-Chips.html",
acknowledgement = ack-nhfb,
}
@Article{Babuska:2018:REG,
author = "Ivo Babuska and Gustaf S{\"o}derlind",
title = "On Roundoff Error Growth in Elliptic Problems",
journal = j-TOMS,
volume = "44",
number = "3",
pages = "33:1--33:22",
month = apr,
year = "2018",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3134444",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Oct 5 11:23:12 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3134444",
abstract = "Large-scale linear systems arise in finite-difference
and finite-element discretizations of elliptic
problems. With increasing computer performance, ever
larger systems are solved using direct methods. How
large can such systems be without roundoff compromising
accuracy? Here we model roundoff dynamics in standard $
L U $ and $ L D L^T $ decompositions with respect to
problem size $N$. For the one-dimensional (1D) Poisson
equation with Dirichlet boundary conditions on an
equidistant grid, we show that the relative error in
the factorized matrix grows like $ O(\epsilon \sqrt N)$
if roundoffs are modeled as independent, expectation
zero random variables. With bias, the growth rate
changes to $ O(\epsilon N)$. Subsequent back
substitution results in typical error growths of $
O(\epsilon > N \sqrt {N})$ and $ O(\epsilon N^2)$,
respectively. Error growth is governed by the dynamics
of the computational process and by the structure of
the boundary conditions rather than by the condition
number. Computational results are demonstrated in
several examples, including a few fourth-order 1D
problems and second-order 2D problems, showing that
error accumulation depends strongly on the solution
method. Thus, the same $ L U$ solver may exhibit
different growth rates for the same 2D Poisson problem,
depending on whether the five-point or nine-point FDM
operator is used.",
acknowledgement = ack-nhfb,
articleno = "33",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Bajard:2018:MRW,
author = "Jean-Claude Bajard and Julien Eynard and Nabil
Merkiche",
title = "{Montgomery} reduction within the context of residue
number system arithmetic",
journal = j-J-CRYPTO-ENG,
volume = "8",
number = "3",
pages = "189--200",
month = sep,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-017-0154-9",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Wed Oct 2 11:24:50 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "http://link.springer.com/article/10.1007/s13389-017-0154-9",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@InProceedings{Barthel:2018:HIB,
author = "Moritz B{\"a}rthel and Jochen Rust and Steffen Paul",
booktitle = "{2018 52nd Asilomar Conference on Signals, Systems,
and Computers}",
title = "Hardware Implementation of Basic Arithmetics and
Elementary Functions for Unum Computing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "125--129",
year = "2018",
DOI = "https://doi.org/10.1109/ACSSC.2018.8645453",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Becker:2018:NOS,
author = "Ruben Becker and Michael Sagraloff and Vikram Sharma
and Chee Yap",
title = "A near-optimal subdivision algorithm for complex root
isolation based on the {Pellet} test and {Newton}
iteration",
journal = j-J-SYMBOLIC-COMP,
volume = "86",
number = "??",
pages = "51--96",
month = may # "\slash " # jun,
year = "2018",
CODEN = "JSYCEH",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Wed Nov 22 16:17:19 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0747717117300378",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
}
@InProceedings{Boldo:2018:FPA,
author = "Sylvie Boldo and Florian Faissole and Vincent
Tourneur",
title = "A Formally-Proved Algorithm to Compute the Correct
Average of Decimal Floating-Point Numbers",
crossref = "Tenca:2018:PIS",
pages = "69--75",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464761",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Some modern processors include decimal floating-point
units, with a conforming implementation of the IEEE-754
2008 standard. Unfortunately, many algorithms from the
computer arithmetic literature are not correct anymore
when computations are done in radix 10. This is in
particular the case for the computation of the average
of two floating-point numbers. Several radix-2
algorithms are available, including one that provides
the correct rounding, but none hold in radix 10. This
paper presents a new radix-10 algorithm that computes
the correctly-rounded average. To guarantee a higher
level of confidence, we also provide a Coq formal proof
of our theorems, that takes gradual underflow into
account. Note that our formal proof was generalized to
ensure this algorithm is correct when computations are
done with any even radix.",
acknowledgement = ack-nhfb,
keywords = "ARITH-25; Coq formal proof; correct rounding;
correctly-rounded average; decimal floating-point
numbers; decimal floating-point units; Digital
arithmetic; floating point arithmetic; formally-proved
algorithm; Hardware; IEEE standards; IEEE-754 2008
standard; Libraries; Program processors; radix-10
algorithm; radix-2 algorithms; Software algorithms;
Standards; theorem proving",
}
@Misc{Bradbury:2018:RSR,
author = "Jonathan D. Bradbury and Steven R. Carlough and Brian
R. Prasky and Eric M. Schwarz",
title = "Reproducible stochastic rounding for out of order
processors",
howpublished = "U.S. Patent US10209958B2",
day = "23",
month = jul,
year = "2018",
bibdate = "Fri Sep 22 17:33:27 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "Patent granted 19 February 2019; expired (fee
related)",
abstract = "A method for generating a random number for use in a
stochastic rounding operation is provided. The method
includes executing an instruction that causes at least
two operands to produce an intermediate result and
incrementing a state of a random number generator. The
method further includes causing the random number
generator to generate a random number in accordance
with the state and producing a final result by
utilizing the random number to determine a rounding of
the intermediate result.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brisebarre:2018:HTP,
author = "Nicolas Brisebarre and George Constantinides and
Milo{\v{s}} Ercezovac and Silviu-Ioan Filip and Matei
Istoan and Jean-Michel Muller",
title = "A High Throughput Polynomial and Rational Function
Approximations Evaluator",
crossref = "Tenca:2018:PIS",
pages = "99--106",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464778",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present an automatic method for the evaluation of
functions via polynomial or rational approximations and
its hardware implementation, on FPGAs. These
approximations are evaluated using Ercegovac's
iterative E-method adapted for FPGA implementation. The
polynomial and rational function coefficients are
optimized such that they satisfy the constraints of the
E-method. We present several examples of practical
interest; in each case a resource-efficient
approximation is proposed and comparisons are made with
alternative approaches.",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; approximation theory;
ARITH-25; Convergence; Electronic mail; Ercegovac
iterative E-method; field programmable gate arrays;
Field programmable gate arrays; FPGA implementation;
function approximation; Hardware; hardware
implementation; Lattices; Linear systems; polynomial
function approximations evaluator; polynomials;
rational function approximations evaluator; rational
functions; resource-efficient approximation",
}
@InProceedings{Bruguera:2018:PII,
author = "J. D. Bruguera",
booktitle = "Proceedings of the {25th IEEE International Symposium
on Computer Arithmetic}",
title = "Radix-64 floating-point divider",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "87--94",
year = "2018",
bibdate = "Thu Jan 30 16:14:30 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bruguera:2018:RFP,
author = "Javier D. Bruguera",
title = "Radix-64 Floating-Point Divider",
crossref = "Tenca:2018:PIS",
pages = "84--91",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464815",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The following topics are dealt with: floating point
arithmetic; digital arithmetic; IEEE standards; field
programmable gate arrays; learning (artificial
intelligence); cryptography; parallel processing; table
lookup; multiplying circuits; mathematics computing.",
acknowledgement = ack-nhfb,
keywords = "Adders; ARITH-25; artificial intelligence;
Convergence; cryptography; digital arithmetic; Digital
arithmetic; field programmable gate arrays; floating
point arithmetic; IEEE standards; learning; learning
(artificial intelligence); Mathematical model;
mathematics computing; multiplying circuits; parallel
processing; Program processors; table lookup; Timing;
Two dimensional displays",
}
@Article{Cannizzo:2018:FVA,
author = "Fabio Cannizzo",
title = "A fast and vectorizable alternative to binary search
in {$ O(1) $} with wide applicability to arrays of
floating point numbers",
journal = j-J-PAR-DIST-COMP,
volume = "113",
number = "??",
pages = "37--54",
month = mar,
year = "2018",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Sat Jan 13 12:26:41 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0743731517302836",
acknowledgement = ack-nhfb,
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
}
@Article{Canto-Navarro:2018:FPA,
author = "E. Cant{\'o}-Navarro and M. L{\'o}pez-Garc{\'\i}a and
R. Ramos-Lara",
title = "Floating-point accelerator for biometric recognition
on {FPGA} embedded systems",
journal = j-J-PAR-DIST-COMP,
volume = "112 (part 1)",
number = "??",
pages = "20--34",
month = feb,
year = "2018",
CODEN = "JPDCER",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Fri Nov 24 17:01:13 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0743731517302642",
acknowledgement = ack-nhfb,
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
}
@InProceedings{Chatelain:2018:VCE,
author = "Yohan Chatelain and Pablo {De Oliveira Castro} and
Eric Petit and David Defour and Jordan Bieder and Marc
Torrent",
title = "{VeriTracer}: Context-enriched tracer for
floating-point arithmetic analysis",
crossref = "Tenca:2018:PIS",
pages = "61--68",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464687",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "VeriTracer automatically instruments a code and traces
the accuracy of floating-point variables over time.
VeriTracer enriches the visual traces with contextual
information such as the call site path in which a value
was modified. Contextual information is important to
understand how the floating-point errors propagate in
complex codes. VeriTracer is implemented as an LLVM
compiler tool on top of Verificarlo. We demonstrate how
VeriTracer can detect accuracy loss and quantify the
impact of using a compensated algorithm on ABINIT, an
industrial HPC application for Ab Initio quantum
computation.",
acknowledgement = ack-nhfb,
keywords = "ab initio calculations; Ab Initio quantum computation;
ABINIT; ARITH-25; complex codes; Computational
modeling; Computer bugs; Context-enriched tracer;
contextual information; floating point arithmetic;
floating-point arithmetic analysis; floating-point
errors; floating-point variables; industrial HPC
application; LLVM compiler; Numerical models; parallel
processing; Probes; program compilers; quantum
computing; Tools; Verificarlo; VeriTracer; visual
traces; Visualization",
}
@InProceedings{Chaurasiya:2018:PPA,
author = "Rohit Chaurasiya and John Gustafson and Rahul Shrestha
and Jonathan Neudorfer and Sangeeth Nambiar and Kaustav
Niyogi and Farhad Merchant and Rainer Leupers",
editor = "{IEEE}",
booktitle = "{2018 IEEE 36th International Conference on Computer
Design (ICCD)}",
title = "Parameterized Posit Arithmetic Hardware Generator",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "334--341",
year = "2018",
DOI = "https://doi.org/10.1109/ICCD.2018.00057",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2018:MMU,
author = "Jianyu Chen and Zaid Al-Ars",
title = "A Matrix-Multiply Unit for Posits in Reconfigurable
Logic Using {(OPEN)CAPI}",
crossref = "ACM:2018:CNG",
pages = "1--5",
year = "2018",
DOI = "https://doi.org/10.1145/3190339.3190340",
bibdate = "Mon Dec 11 08:58:21 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "1",
keywords = "posit arithmetic; universal number (unum) arithmetic",
}
@Misc{Cherkaev:2018:SLN,
author = "Annie Cherkaev",
title = "The secret life of {NaN}",
howpublished = "Web site",
month = mar,
year = "2018",
bibdate = "Fri Dec 01 14:21:50 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://anniecherkaev.com/the-secret-life-of-nan",
acknowledgement = ack-nhfb,
remark = "The site discusses IEEE 754 number encoding, and how
NaN payloads can be used to hold other things, like
data type codes, integers, and pointers, hidden inside
binary64 values.",
}
@InProceedings{Chung:2018:PCP,
author = "Shin Yee Chung",
title = "Provably Correct Posit Arithmetic with Fixed-Point Big
Integer",
crossref = "ACM:2018:CNG",
pages = "1--5",
year = "2018",
DOI = "https://doi.org/10.1145/3190339.3190341",
bibdate = "Mon Dec 11 09:00:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "2",
keywords = "posit arithmetic; universal number (unum) arithmetic",
}
@InProceedings{Cococcioni:2018:EPA,
author = "Marco Cococcioni and Emanuele Ruffaldi and Sergio
Saponara",
editor = "{IEEE}",
booktitle = "{2018 International Conference of Electrical and
Electronic Technologies for Automotive}",
title = "Exploiting Posit Arithmetic for Deep Neural Networks
in Autonomous Driving Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2018",
DOI = "https://doi.org/10.23919/EETA.2018.8493233",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Costello:2018:MCT,
author = "Craig Costello and Benjamin Smith",
title = "{Montgomery} curves and their arithmetic",
journal = j-J-CRYPTO-ENG,
volume = "8",
number = "3",
pages = "227--240",
month = sep,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-017-0157-6",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Wed Oct 2 11:24:50 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "http://link.springer.com/article/10.1007/s13389-017-0157-6",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@Article{Dai:2018:FBM,
author = "Wangchen Dai and Donglong Chen and Ray C. C. Cheung
and {\c{C}}etin Kaya Ko{\c{c}}",
title = "{FFT}-Based {McLaughlin}'s {Montgomery} Exponentiation
without Conditional Selections",
journal = j-IEEE-TRANS-COMPUT,
volume = "67",
number = "9",
pages = "1301--1314",
month = sep,
year = "2018",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2811466",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Mar 15 08:10:13 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "https://ieeexplore.ieee.org/document/8307235/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Dai:2018:SAM,
author = "Wangchen Dai and Ray C. C. Cheung",
title = "Spectral arithmetic in {Montgomery} modular
multiplication",
journal = j-J-CRYPTO-ENG,
volume = "8",
number = "3",
pages = "211--226",
month = sep,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-017-0151-z",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Wed Oct 2 11:24:50 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "http://link.springer.com/article/10.1007/s13389-017-0151-z",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@Article{Das:2018:MPT,
author = "Dipankar Das and Naveen Mellempudi and Dheevatsa
Mudigere and Dhiraj Kalamkar and Sasikanth Avancha and
Kunal Banerjee and Srinivas Sridharan and Karthik
Vaidyanathan and Bharat Kaul and Evangelos Georganas
and Alexander Heinecke and Pradeep Dubey and Jesus
Corbal and Nikita Shustrov and Roma Dubtsov and Evarist
Fomenko and Vadim Pirogov",
title = "Mixed Precision Training of Convolutional Neural
Networks using Integer Operations",
journal = "arXiv.org",
pages = "11",
day = "3",
month = feb,
year = "2018",
bibdate = "Mon Feb 10 09:24:48 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1802.00930",
abstract = "The state-of-the-art (SOTA) for mixed precision
training is dominated by variants of low precision
floating point operations, and in particular, FP16
accumulating into FP32 Micikevicius et al. (2017). On
the other hand, while a lot of research has also
happened in the domain of low and mixed-precision
Integer training, these works either present results
for non-SOTA networks (for instance only AlexNet for
ImageNet-1K), or relatively small datasets (like
CIFAR-10). In this work, we train state-of-the-art
visual understanding neural networks on the ImageNet-1K
dataset, with Integer operations on General Purpose
(GP) hardware. In particular, we focus on Integer
Fused-Multiply-and-Accumulate (FMA) operations which
take two pairs of INT16 operands and accumulate results
into an INT32 output.We propose a shared exponent
representation of tensors and develop a Dynamic Fixed
Point (DFP) scheme suitable for common neural network
operations. The nuances of developing an efficient
integer convolution kernel is examined, including
methods to handle overflow of the INT32 accumulator. We
implement CNN training for ResNet-50, GoogLeNet-v1,
VGG-16 and AlexNet; and these networks achieve or
exceed SOTA accuracy within the same number of
iterations as their FP32 counterparts without any
change in hyper-parameters and with a 1.8X improvement
in end-to-end training throughput. To the best of our
knowledge these results represent the first INT16
training results on GP hardware for ImageNet-1K dataset
using SOTA CNNs and achieve highest reported accuracy
using half-precision",
acknowledgement = ack-nhfb,
primaryclass = "cs.NE",
}
@InProceedings{Defour:2018:FAR,
author = "David Defour",
title = "{FP-ANR}: A representation format to handle
floating-point cancellation at run-time",
crossref = "Tenca:2018:PIS",
pages = "76--83",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464784",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When dealing with floating-point numbers, there are
several sources of error which can drastically reduce
the numerical quality of computed results. One of those
error sources is the loss of significance or
cancellation, which occurs during for example, the
subtraction of two nearly equal numbers. In this
article, we propose a representation format named
Floating-Point Adaptive Noise Reduction (FP-ANR). This
format embeds cancellation information directly into
the floating-point representation format thanks to a
dedicated pattern. With this format, insignificant
trailing bits lost during cancellation are removed from
every manipulated floating-point number. The immediate
consequence is that it increases the numerical
confidence of computed values. The proposed
representation format corresponds to a simple and
efficient implementation of significance arithmetic
based and compatible with the IEEE Standard 754
standard.",
acknowledgement = ack-nhfb,
keywords = "adaptive signal processing; ARITH-25; cancellation
information; Computers; Encoding; floating point
arithmetic; Floating-Point Adaptive Noise Reduction;
floating-point cancellation; floating-point numbers;
floating-point representation format; FP-ANR; IEEE
Standard 754 standard; IEEE standards; IEEE Standards;
interference suppression; Noise reduction; numerical
quality; signal denoising; Software; Uncertainty",
}
@Article{Demmel:2018:RBM,
author = "James Demmel and Jason Riedy and Peter Ahrens",
title = "{Reproducible BLAS}: Make Addition Associative
Again!",
journal = j-SIAM-NEWS,
volume = "51",
number = "8",
pages = "??--??",
month = oct,
year = "2018",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Oct 06 08:42:06 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sinews.siam.org/Details-Page/reproducible-blas-make-addition-associative-again",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Dolbeau:2018:TPF,
author = "Romain Dolbeau",
title = "Theoretical peak {FLOPS} per instruction set: a
tutorial",
journal = j-J-SUPERCOMPUTING,
volume = "74",
number = "3",
pages = "1341--1377",
month = mar,
year = "2018",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-017-2177-5",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Fri Mar 2 12:22:02 MST 2018",
bibsource = "http://link.springer.com/journal/11227/74/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2010.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Doliskani:2018:SCR,
author = "Javad Doliskani and Pascal Giorgi and Romain Lebreton
and Eric Schost",
title = "Simultaneous Conversions with the Residue Number
System Using Linear Algebra",
journal = j-TOMS,
volume = "44",
number = "3",
pages = "27:1--27:21",
month = apr,
year = "2018",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3145573",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Jan 22 17:49:32 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3145573",
abstract = "We present an algorithm for simultaneous conversions
between a given set of integers and their Residue
Number System representations based on linear algebra.
We provide a highly optimized implementation of the
algorithm that exploits the computational features of
modern processors. The main application of our
algorithm is matrix multiplication over integers. Our
speed-up of the conversions to and from the Residue
Number System significantly improves the overall
running time of matrix multiplication.",
acknowledgement = ack-nhfb,
articleno = "27",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Dosso:2018:EAC,
author = "Yssouf Dosso and Fabien Herbaut and Nicolas M{\'e}loni
and Pascal V{\'e}ron",
title = "{Euclidean} addition chains scalar multiplication on
curves with efficient endomorphism",
journal = j-J-CRYPTO-ENG,
volume = "8",
number = "4",
pages = "351--367",
month = nov,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-018-0190-0",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Wed Oct 2 11:24:50 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "http://link.springer.com/article/10.1007/s13389-018-0190-0",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@InProceedings{Drucker:2018:CRS,
author = "Nir Drucker and Shay Gueron and Vlad Krasnov",
title = "The Comeback of {Reed--Solomon} Codes",
crossref = "Tenca:2018:PIS",
pages = "125--129",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464690",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Distributed storage systems utilize erasure codes to
reduce their storage costs while efficiently handling
failures. Many of these codes (e.g., Reed-Solomon (RS)
codes) rely on Galois Field (GF) arithmetic, which is
considered to be fast when the field characteristic is
2. Nevertheless, some developments in the field of
erasure codes offer new efficient techniques that
require mostly XOR operations, and are thus faster than
GF operations. Recently, Intel announced [1] that its
future architecture (codename Ice Lake) will introduce
new set of instructions called Galois Field New
Instruction (GF-NI). These instructions allow software
flows to perform vector and matrix multiplications over
GF ($ 2^8$) on the wide registers that are available on
the AVX512 architectures. In this paper, we explain the
functionality of these instructions, and demonstrate
their usage for some fast computations in GF($ 2^8$).
We also use the Intel Intelligent Storage Acceleration
Library (ISA-L) in order to estimate potential future
improvement for erasure codes that are based on RS
codes. Our results predict $ 1.4 \times $ speedup for
vectorized multiplication, and $ 1.83 \times $ speedup
for the actual encoding.",
acknowledgement = ack-nhfb,
keywords = "Acceleration; ARITH-25; AVX512 architectures; codename
Ice Lake; Computer architecture; distributed storage
systems; Encoding; erasure codes; field characteristic;
Galois Field arithmetic; Galois fields; GF operations;
GF-NI; Intel; Intelligent Storage Acceleration Library;
matrix multiplication; matrix multiplications;
Reed-Solomon codes; Registers; RS codes; storage costs;
vector; vectors; Web services; XOR operations",
}
@InProceedings{Drucker:2018:FMB,
author = "Nir Drucker and Shay Gueron and Vlad Krasnov",
title = "Fast multiplication of binary polynomials with the
forthcoming vectorized {VPCLMULQDQ} instruction",
crossref = "Tenca:2018:PIS",
pages = "115--119",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464777",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Polynomial multiplication over binary fields $ \mathbb
{F}_{2^n} $ is a common primitive, used for example by
current cryptosystems such as AES-GCM (with $ n =
128$). It also turns out to be a primitive for other
cryptosystems, that are being designed for the Post
Quantum era, with values n 128. Examples from the
recent submissions to the NIST Post-Quantum
Cryptography project, are BIKE, LEDAKem, and GeMSS,
where the performance of the polynomial
multiplications, is significant. Therefore, efficient
polynomial multiplication over $ \mathbb {F}_{2^n}$,
with large $n$, is a significant emerging optimization
target. Anticipating future applications, Intel has
recently announced that its future architecture
(codename Ice Lake) will introduce a new vectorized way
to use the current VPCLMULQDQ instruction. In this
paper, we demonstrate how to use this instruction for
accelerating polynomial multiplication. Our analysis
shows a prediction for at least $ 2 \times $ speedup
for multiplications with polynomials of degree 512 or
more.",
acknowledgement = ack-nhfb,
keywords = "Acceleration; AES-GCM; ARITH-25; BIKE; binary
field-mathbbF2n; Computer architecture; Cryptography;
cryptosystems; fast binary polynomial multiplication;
fast multiplication; GeMSS; ice lake; LEDAKem; NIST;
NIST Post-Quantum Cryptography project; optimisation;
Optimization; optimization target; polynomials; post
quantum cryptography; quantum cryptography; Registers;
vectorized VPCLMULQDQ instruction; Web services",
}
@Article{Dutt:2018:ADA,
author = "Sunil Dutt and Sukumar Nandi and Gaurav Trivedi",
title = "Analysis and Design of Adders for Approximate
Computing",
journal = j-TECS,
volume = "17",
number = "2",
pages = "40:1--40:??",
month = apr,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3131274",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Oct 17 18:16:34 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
abstract = "The concept of approximate computing, that is, to
sacrifice computation quality for computation efforts,
has recently emerged as a promising design approach.
Over the past decade, several research works have
explored approximate computing at both the software
level and hardware level of abstraction with
encouraging results. At the hardware level of
abstraction, adders (being the fundamental and most
widely used data operators in digital systems) have
attracted a significant attention for approximation. In
this article, we first explain briefly the
need/significance of approximate adders. We then
propose four Approximate Full Adders (AFAs) for
high-performance energy-efficient approximate
computing. The key design objective behind the proposed
AFAs is to curtail the length of carry propagation
subjected to minimal error rate. Next, we exploit one
of the proposed AFAs (optimal one) to construct an
N-bit approximate adder that hereinafter is referred as
``ApproxADD.'' An emergent property of ApproxADD is
that carries do not propagate in it, and, consequently,
it provides bit-width-aware constant delay (O(1)).
ApproxADD also provides improvement in dynamic power
consumption by 46.31\% and in area by 28.57\% w.r.t.
Ripple Carry Adder (RCA), which exhibits the lowest
power and area. Although ApproxADD provides a
significant improvement in delay, power, and area, it
may not be preferred for some of the error-resilient
applications because its: (i) Error Distance (ED) is
too high; and (ii) Error Rate (ER) increases rapidly
with bit-width ($N$). To improve ED and ER, we exploit
the concept of carry-lifetime and Error Detection and
Correction logic, respectively. In this way, we
introduce two more (improved) versions of
ApproxADD--ApproxADD $ \upsilon $ 1 and ApproxADD. We
call these as ApproxADD $ \upsilon $ 1 and ApproxADD $
\upsilon $ 2 with existing approximate adders based on
conventional design metrics and approximate computing
design metrics. Furthermore, to inspect effectiveness
of the proposed approach in real-life applications, we
demonstrate image compression and decompression by
replacing the conventional addition operations in
Discrete Cosine Transform (DCT) and Inverse Discrete
Cosine Transform (IDCT) modules with ApproxADD $
\upsilon $ 2.",
acknowledgement = ack-nhfb,
articleno = "40",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J840",
}
@InProceedings{Emmart:2018:FME,
author = "Niall Emmart and Fangyu Zhengt and Charles Weems",
title = "Faster Modular Exponentiation Using Double Precision
Floating Point Arithmetic on the {GPU}",
crossref = "Tenca:2018:PIS",
pages = "130--137",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464792",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper presents a new approach to integer multiple
precision (MP) modular exponentiation, using
double-precision floating point (DPF) operations, that
is suitable for GPU implementation. We show speedups
ranging from 20\% to 34\% over the best prior GPU times
for sizes corresponding to common RSA cryptographic
operations (2048 to 4096 bits). Three techniques are
described. First, by adding $ 2^{104} $ to the high
half of the product, and $ 2^{52} $ to the low half, we
set the implicit leading 1 in the DPF mantissa so that
the full 52 explicit bits are available for each half
of the 104-bit products of samples. Second, the DPF
values are cast bitwise to 64-bit integers for adding
the column sums to get the MP result. Normally the cast
would require masking off the exponents, but because
they are constant, we can include them in the column
sums and correct just once for their total. Third, by
initializing the column sums with the appropriate
negative value to compensate for the exponent sums, no
corrective subtraction is needed. Our implementation on
an NVIDIA GTX Titan Black GPU achieves between 132.5K
and 161.9K modular exponentiations per second of size
1024 bits, with latencies ranging from 21.7 ms to 17.8
ms, making it practical for online RSA applications.
Proportional results are shown for 1536 and 2048 bits.
The implementation is so efficient that its maximum
sustained performance is actually bounded by the
thermal limit of the GPU.",
acknowledgement = ack-nhfb,
keywords = "appropriate negative value; ARITH-25; column sums;
common RSA cryptographic operations; Computer
architecture; cryptography; Cryptography; double
precision floating point arithmetic; DPF mantissa;
exponent sum compensation; faster modular
exponentiation; floating point arithmetic;
Floating-point arithmetic; Graphics processing units;
graphics processing units; Hardware; integer multiple
precision modular exponentiation; multiple precision
modular exponentiation; NVIDIA GTX Titan Black GPU;
online RSA applications; parallel architectures; time
17.8 ms to 21.7 ms; word length 1024.0 bit; word length
104 bit; word length 1536.0 bit; word length 2048 bit
to 4096 bit; word length 64 bit",
}
@InProceedings{Emmart:2018:NVB,
author = "Niall Emmart and Fangyu Zheng and Charles Weems",
title = "A New Variant of the {Barrett} Algorithm Applied to
Quotient Selection",
crossref = "Tenca:2018:PIS",
pages = "138--144",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464771",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Quotient Selection (QS) is a key step in the classic $
O(n^2) $ multiple precision division algorithm. On
processors with fast hardware division, it is a trivial
problem, but on GPUs, division is quite slow. In this
paper we investigate the effectiveness of Brent and
Zimmermann's variant as well as our own novel variant
of Barrett's algorithm. Our new approach is shown to be
suitable for low radix (single precision) QS. Three
highly optimized implementations, two of the Brent and
Zimmerman variant and one based on our new approach,
have been developed and we show that each is many times
faster than using the division operation built in to
the compiler. In addition, our variant is on average
22\% faster than the other two implementations. We also
sketch proofs of correctness for all of the
implementations and our new algorithm.",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; ARITH-25; Barrett algorithm;
Barrett reduction; classic $O(n^2)$ multiple precision
division algorithm; Computer security; digital
arithmetic; Digital arithmetic; division operation;
fast hardware division; GPU; graphics processing units;
Hardware; low radix QS; multiple precision division;
Newton method; O; processors; Program processors;
quotient selection; Zimmermann variant",
}
@Article{Ferguson:2018:DSM,
author = "Warren E. Ferguson and Jesse Bingham and Levent
Erk{\"o}k and John R. Harrison and Joe Leslie-Hurd",
title = "Digit Serial Methods with Applications to Division and
Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "67",
number = "3",
pages = "449--456",
month = mar,
year = "2018",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2017.2759764",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Feb 15 05:53:34 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "http://ieeexplore.ieee.org/document/8060979/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Garland:2018:LCM,
author = "James Garland and David Gregg",
title = "Low Complexity Multiply-Accumulate Units for
Convolutional Neural Networks with Weight-Sharing",
journal = j-TACO,
volume = "15",
number = "3",
pages = "31:1--31:??",
month = oct,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3233300",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Tue Jan 8 17:19:59 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
abstract = "Convolutional neural networks (CNNs) are one of the
most successful machine-learning techniques for image,
voice, and video processing. CNNs require large amounts
of processing capacity and memory bandwidth. Hardware
accelerators have been proposed for CNNs that typically
contain large numbers of multiply-accumulate (MAC)
units, the multipliers of which are large in integrated
circuit (IC) gate count and power consumption.
``Weight-sharing'' accelerators have been proposed
where the full range of weight values in a trained CNN
are compressed and put into bins, and the bin index is
used to access the weight-shared value. We reduce power
and area of the CNN by implementing parallel accumulate
shared MAC (PASM) in a weight-shared CNN. PASM
re-architects the MAC to instead count the frequency of
each weight and place it in a bin. The accumulated
value is computed in a subsequent multiply phase,
significantly reducing gate count and power consumption
of the CNN. In this article, we implement PASM in a
weight-shared CNN convolution hardware accelerator and
analyze its effectiveness. Experiments show that for a
clock speed 1GHz implemented on a 45nm ASIC process our
approach results in fewer gates, smaller logic, and
reduced power with only a slight increase in latency.
We also show that the same weight-shared-with-PASM CNN
accelerator can be implemented in resource-constrained
FPGAs, where the FPGA has limited numbers of digital
signal processor (DSP) units to accelerate the MAC
operations.",
acknowledgement = ack-nhfb,
articleno = "31",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J924",
}
@InProceedings{Glaser:2018:MMU,
author = "Florian Glaser and Stefan Mach and Abbas Rahimi and
Frank K. G{\"u}rkaynak and Qiuting Huang and Luca
Benini",
booktitle = "{2018 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "An {826 MOPS}, {210uW\slash MHz} Unum {ALU} in 65nm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2018",
DOI = "https://doi.org/10.1109/ISCAS.2018.8351546",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Graillat:2018:NVC,
author = "Stef Graillat and Fabienne J{\'e}z{\'e}quel and Romain
Picot",
title = "Numerical validation of compensated algorithms with
stochastic arithmetic",
journal = j-APPL-MATH-COMP,
volume = "329",
number = "??",
pages = "339--363",
day = "15",
month = jul,
year = "2018",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2018.02.004",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Mar 17 16:59:00 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300318300985",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "accurate floating-point dot product; accurate
floating-point summation; CADNA; compensated
algorithms; discrete stochastic arithmetic; error-free
transformations; floating-point arithmetic; numerical
validation; rounding errors",
}
@InCollection{Haidar:2018:DFE,
author = "Azzam Haidar and Ahmad Abdelfattah and Mawussi Zounon
and Panruo Wu and Srikara Pranesh and Stanimire Tomov
and Jack Dongarra",
booktitle = "Computational science---{ICCS 2018}. {Part I}",
title = "The design of fast and energy-efficient linear
solvers: on the potential of half-precision arithmetic
and iterative refinement techniques",
volume = "10860",
publisher = "Springer",
address = "Cham, Switzerland",
pages = "586--600",
year = "2018",
MRclass = "65Fxx (65Y10)",
MRnumber = "3815810",
bibdate = "Tue Jan 8 09:18:00 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
ORCID-numbers = "Dongarra, Jack/0000-0003-3247-1782",
}
@InProceedings{Haidar:2018:HGT,
author = "Azzam Haidar and Stanimire Tomov and Jack Dongarra and
Nicholas J. Higham",
editor = "{IEEE}",
booktitle = "{SC '18 Proceedings of the International Conference
for High Performance Computing, Networking, Storage,
and Analysis, Dallas, Texas, November 11--16, 2018}",
title = "Harnessing {GPU} tensor cores for fast {FP16}
arithmetic to speed up mixed-precision iterative
refinement solvers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "47:1--47:11",
year = "2018",
ISBN = "1-5386-8384-9",
ISBN-13 = "978-1-5386-8384-2",
LCCN = "????",
bibdate = "Sat Jan 19 18:51:19 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/citation.cfm?id=3291656.3291719",
abstract = "Low-precision floating-point arithmetic is a powerful
tool for accelerating scientific computing
applications, especially those in artificial
intelligence. Here, we present an investigation showing
that other high-performance computing (HPC)
applications can also harness this power. Specifically,
we use the general HPC problem, Ax = b, where A is a
large dense matrix, and a double precision (FP64)
solution is needed for accuracy. Our approach is based
on mixed-precision (FP16 $ \to $ FP64) iterative
refinement, and we generalize and extend prior advances
into a framework, for which we develop
architecture-specific algorithms and highly tuned
implementations. These new methods show how using
half-precision Tensor Cores (FP16-TC) for the
arithmetic can provide up to 4X speedup. This is due to
the performance boost that the FP16-TC provide as well
as to the improved accuracy over the classical FP16
arithmetic that is obtained because the GEMM
accumulation occurs in FP32 arithmetic.",
acknowledgement = ack-nhfb,
}
@Article{Hanson:2018:RAM,
author = "Richard J. Hanson and Tim Hopkins",
title = "Remark on {Algorithm 539: A Modern Fortran Reference
Implementation for Carefully Computing the Euclidean
Norm}",
journal = j-TOMS,
volume = "44",
number = "3",
pages = "24:1--24:23",
month = apr,
year = "2018",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3134441",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Jan 22 17:49:32 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3134441",
abstract = "We propose a set of new Fortran reference
implementations, based on an algorithm proposed by
Kahan, for the Level 1 BLAS routines *NRM2 that compute
the Euclidean norm of a real or complex input vector.
The principal advantage of these routines over the
current offerings is that, rather than losing accuracy
as the length of the vector increases, they generate
results that are accurate to almost machine precision
for vectors of length $ N < N_{\rm max} $ where $
N_{\rm max} $ depends upon the precision of the
floating point arithmetic being used. In addition, we
make use of intrinsic modules, introduced in the latest
Fortran standards, to detect occurrences of non-finite
numbers in the input data and return suitable values as
well as setting IEEE floating point status flags as
appropriate. A set of C interface routines is also
provided to allow simple, portable access to the new
routines. To improve execution speed, we advocate a
hybrid algorithm; a simple loop is used first and, only
if IEEE floating point exception flags signal, do we
fall back on Kahan's algorithm. Since most input
vectors are ``easy,'' i.e., they do not require the
sophistication of Kahan's algorithm, the simple loop
improves performance while the use of compensated
summation ensures high accuracy. We also report on a
comprehensive suite of test problems that has been
developed to test both our new implementation and
existing codes for both accuracy and the appropriate
settings of the IEEE arithmetic status flags.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
xxnote = "See \cite{Lawson:1979:ABL}.",
}
@Article{Hasanikhah:2018:EIS,
author = "Narjes Hasanikhah and Siavash Amin-Nejad and Ghafar
Darvish and M. R. Moniri",
title = "Efficient implementation of space-time adaptive
processing for adaptive weights calculation based on
floating point {FPGAs}",
journal = j-J-SUPERCOMPUTING,
volume = "74",
number = "7",
pages = "3193--3210",
month = jul,
year = "2018",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-018-2369-7",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Thu Oct 10 15:31:13 MDT 2019",
bibsource = "http://link.springer.com/journal/11227/74/7;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Misc{Higham:2018:HPA,
author = "Nicholas J. Higham",
title = "Half Precision Arithmetic: fp16 Versus bfloat16",
howpublished = "Web site.",
day = "3",
month = dec,
year = "2018",
bibdate = "Sat Jan 19 18:43:15 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://nickhigham.wordpress.com/2018/12/03/half-precision-arithmetic-fp16-versus-bfloat16/",
abstract = "The 2008 revision of the IEEE Standard for
Floating-Point Arithmetic introduced a half precision
16-bit floating point format, known as fp16, as a
storage format. Various manufacturers have adopted fp16
for computation, using the obvious extension of the
rules for the fp32 (single precision) and fp64 (double
precision) formats. For example, fp16 is supported by
the NVIDIA P100 and V100 GPUs and the AMD Radeon
Instinct MI25 GPU, as well as the A64FX Arm processor
that will power the Fujitsu Post-K exascale computer.",
acknowledgement = ack-nhfb,
}
@Article{Higham:2018:UN,
author = "Nicholas J. Higham",
title = "The Unwinding Number",
journal = j-SIAM-NEWS,
volume = "51",
number = "8",
pages = "??--??",
month = oct,
year = "2018",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Sat Oct 06 08:46:15 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sinews.siam.org/Details-Page/the-unwinding-number",
abstract = "While Fortran 66 had a complex data type, this was not
true of most other early programming languages, such as
Algol 60. As a result, programmers had to write their
own procedures to implement complex arithmetic and
transcendental functions in terms of separately stored
real and imaginary parts. They quickly realized that
this is not a trivial task; in the early 1960s, it took
five published attempts over three years to obtain a
correct implementation of the complex logarithm in
Algol 60.",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
}
@Article{Hines:2018:MPS,
author = "Jonathan Hines",
title = "Mixed Precision: A Strategy for New Science
Opportunities",
journal = j-COMPUT-SCI-ENG,
volume = "20",
number = "6",
pages = "67--71",
month = nov # "\slash " # dec,
year = "2018",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCSE.2018.2874161",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Wed Jan 30 17:58:50 MST 2019",
bibsource = "http://csdl.computer.org/comp/mags/cs/2018/06/c6toc.htm;
https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.computer.org/csdl/mags/cs/2018/06/08625902-abs.html",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}
@Article{Hou:2018:EAD,
author = "Junjie Hou and Yongxin Zhu and Sen Du and Shijin
Song",
title = "Enhancing Accuracy and Dynamic Range of Scientific
Data Analytics by Implementing Posit Arithmetic on
{FPGA}",
journal = "Journal of Signal Processing Systems",
volume = "91",
number = "10",
publisher = pub-SV,
address = pub-SV:adr,
pages = "1137--1148",
month = nov,
year = "2018",
DOI = "https://doi.org/10.1007/s11265-018-1420-5",
ISSN = "1939-8018 (print), 1939-8115 (electronic)",
ISSN-L = "1939-8115",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Hrycak:2018:ECP,
author = "Tomasz Hrycak and Sebastian Schmutzhard",
title = "Evaluation of {Chebyshev} polynomials by a three-term
recurrence in floating-point arithmetic",
journal = j-BIT-NUM-MATH,
volume = "58",
number = "2",
pages = "317--330",
month = jun,
year = "2018",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-017-0683-8",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Sep 26 07:36:57 MDT 2018",
bibsource = "http://link.springer.com/journal/10543/58/2;
https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://link.springer.com/article/10.1007/s10543-017-0683-8",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Hutter:2018:FMP,
author = "Michael Hutter and Erich Wenger",
title = "Fast Multi-precision Multiplication for Public-Key
Cryptography on Embedded Microprocessors",
journal = j-J-CRYPTOLOGY,
volume = "31",
number = "4",
pages = "1164--1182",
month = oct,
year = "2018",
CODEN = "JOCREQ",
DOI = "https://doi.org/10.1007/s00145-018-9298-8",
ISSN = "0933-2790 (print), 1432-1378 (electronic)",
ISSN-L = "0933-2790",
bibdate = "Wed Sep 26 09:58:08 MDT 2018",
bibsource = "http://link.springer.com/journal/145/31/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptology.bib",
URL = "https://link.springer.com/article/10.1007/s00145-018-9298-8",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptology",
journal-URL = "http://link.springer.com/journal/145",
}
@TechReport{Intel:2018:BHN,
author = "{Intel Corporation}",
title = "{BFLOAT16} --- Hardware Numerics Definition",
type = "White paper",
number = "338302-001US",
institution = pub-INTEL,
address = pub-INTEL:adr,
pages = "7",
month = nov,
year = "2018",
bibdate = "Sat Jan 19 18:48:10 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://software.intel.com/en-us/download/bfloat16-hardware-numerics-definition",
acknowledgement = ack-nhfb,
remark = "The BFLOAT16 (BF16) format has a 1-bit sign, 8-bit
exponent, and 7-bit stored significand, corresponding
to the top 16 bits of IEEE 754 Binary32. However,
Intel's implementation does not provide subnormal
numbers, or floating-point exceptions, and it only
supports the IEEE 754 round-to-nearest ties-to-even
rounding mode. Subnormal inputs are reduced to zero.",
}
@InProceedings{Jaiswal:2018:AGT,
author = "Manish Kumar Jaiswal and Hayden K.-H So",
editor = "{IEEE}",
booktitle = "{2018 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "Architecture Generator for {Type-3} Unum Posit
Adder\slash Subtractor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2018",
DOI = "https://doi.org/10.1109/ISCAS.2018.8351142",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jaiswal:2018:UNP,
author = "Manish Kumar Jaiswal and Hayden K.-H So",
editor = "{IEEE}",
booktitle = "{2018 Design, Automation \& Test in Europe Conference
\& Exhibition (DATE)}",
title = "Universal number posit arithmetic generator on
{FPGA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1159--1162",
year = "2018",
DOI = "https://doi.org/10.23919/DATE.2018.8342187",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jeangoudoux:2018:CRM,
author = "Clothilde Jeangoudoux and Christoph Lauter",
title = "A Correctly Rounded Mixed-Radix Fused-Multiply-Add",
crossref = "Tenca:2018:PIS",
pages = "21--28",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464818",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IEEE 754-2008 Standard governs Floating-Point
Arithmetic in all types of Computer Systems. The
Standard provides for two radices, 2 and 10. It
specifies conversion operations between these radices,
but does not allow floating-point formats of different
radices to be mixed in computational operations. In
contrast, the Standard does provide for mixing formats
of one radix in one operation. In order to enhance the
Standard and make it closed under all basic
computational operations, we propose an algorithm for a
correctly rounded mixed-radix Fused-Multiply-and-Add
(FMA). Our algorithm takes any combination of IEEE754
binary64 and decimal64 numbers in argument and provides
a result in IEEE754 binary64 and decimal64, rounded
according to any for the five IEEE754 rounding modes.
Our implementation does not require any dynamic memory
allocation; its runtime can be bounded statically. We
compare our implementation to a basic mixed-radix FMA
implementation based on the GMP Multiple Precision
library.",
acknowledgement = ack-nhfb,
keywords = "ARITH-25; basic computational operations; computer
systems; conversion operations; correctly rounded
mixed-radix Fused; decimal64 numbers; Electronic mail;
floating point arithmetic; floating-point arithmetic;
Floating-point arithmetic; floating-point formats;
Heuristic algorithms; IEEE 754-2008 Standard; IEEE
standards; IEEE754 rounding modes; Libraries;
mixed-radix FMA implementation; Software; Standards;
Systematics",
}
@Article{Jeannerod:2018:REF,
author = "Claude-Pierre Jeannerod and Siegfried M. Rump",
title = "On relative errors of floating-point operations:
{Optimal} bounds and applications",
journal = j-MATH-COMPUT,
volume = "87",
number = "310",
pages = "803--819",
month = "",
year = "2018",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Sat Jan 13 15:49:09 MST 2018",
bibsource = "http://www.ams.org/mcom/2018-87-310;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "http://www.ams.org/journals/mcom/2018-87-310/S0025-5718-2017-03234-8;
http://www.ams.org/journals/mcom/2018-87-310/S0025-5718-2017-03234-8/S0025-5718-2017-03234-8.pdf;
https://www.ams.org/mathscinet/search/authors.html?authorName=Rump%2C%20Siegfried%20M.;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=644190",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Jeannerod:2018:VWS,
author = "Claude-Pierre Jeannerod and Jean-Michel Muller and
Paul Zimmermann",
title = "On Various Ways to Split a Floating-Point Number",
crossref = "Tenca:2018:PIS",
pages = "53--60",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464793",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We review several ways to split a floating-point
number, that is, to decompose it into the exact sum of
two floating-point numbers of smaller precision. All
the methods considered here involve only a few IEEE
floating-point operations, with rounding to nearest and
including possibly the fused multiply-add (FMA).
Applications range from the implementation of integer
functions such as round and floor to the computation of
suitable scaling factors aimed, for example, at
avoiding spurious underflows and overflows when
implementing functions such as the hypotenuse.",
acknowledgement = ack-nhfb,
keywords = "ARITH-25; Computer architecture; Containers; Digital
arithmetic; floating point arithmetic; floating-point
number; Floors; IEEE floating-point operations; integer
functions; Lips; Matlab; Optimization",
}
@Article{Jeon:2018:HMP,
author = "Dong-Ik Jeon and Kyeong-Bin Park and Ki-Seok Chung",
title = "{HMC-MAC}: Processing-in Memory Architecture for
Multiply--Accumulate Operations with Hybrid Memory
Cube",
journal = j-IEEE-COMPUT-ARCHIT-LETT,
volume = "17",
number = "1",
pages = "5--8",
month = jan # "\slash " # jun,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1109/LCA.2017.2700298",
ISSN = "1556-6056 (print), 1556-6064 (electronic)",
ISSN-L = "1556-6056",
bibdate = "Tue Jun 25 07:41:05 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib",
abstract = "Many studies focus on implementing processing-in
memory (PIM) on the logic die of the hybrid memory cube
(HMC) architecture. The multiply-accumulate (MAC)
operation is heavily used in digital signal processing
(DSP) systems. In this paper, a novel PIM architecture
called HMC-MAC that implements the MAC operation in the
HMC is proposed. The vault controllers of the
conventional HMC are working independently to maximize
the parallelism, and HMC-MAC is based on the
conventional HMC without modifying the architecture
much. Therefore, a large number of MAC operations can
be processed in parallel. In HMC-MAC, the MAC operation
can be carried out simultaneously with as much as 128
KB data. The correctness on HMC-MAC is verified by
simulations, and its performance is better than the
conventional CPU-based MAC operation when the MAC
operation is consecutively executed at least six
times",
acknowledgement = ack-nhfb,
affiliation = "Chung, KS (Reprint Author), Hanyang Univ, Dept Elect
\& Comp Engn, Seoul 04763, South Korea. Jeon, Dong-Ik;
Park, Kyeong-Bin; Chung, Ki-Seok, Hanyang Univ, Dept
Elect \& Comp Engn, Seoul 04763, South Korea.",
author-email = "[email protected] [email protected]
[email protected]",
da = "2019-06-20",
doc-delivery-number = "FZ6EO",
eissn = "1556-6064",
fjournal = "IEEE Computer Architecture Letters",
funding-acknowledgement = "Basic Science Research Program through the
National Research Foundation of Korea(NRF) --- Ministry
of Education [NRF-2015R1D1A1A09061079]",
funding-text = "This research was supported by Basic Science Research
Program through the National Research Foundation of
Korea(NRF) funded by the Ministry of Education
(NRF-2015R1D1A1A09061079).",
journal-iso = "IEEE Comput. Archit. Lett.",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208",
keywords = "Computers; CPU-based MAC operation; digital signal
processing; digital signal processing systems; DRAM
chips; DSP systems; Electronic mail; HMC-MAC; hybrid
memory cube architecture; logic circuits; logic die;
memory architecture; Memory architecture; Memory
management; memory size 128.0 KByte; Memory structures;
memory used as logic; multiple data stream
architectures; multiply-accumulate operation; parallel
processing; processing-in memory architecture; Random
access memory; Registers; vault controllers",
number-of-cited-references = "11",
ORCID-numbers = "Jeon, Dong-Ik/0000-0002-8572-4184",
research-areas = "Computer Science",
times-cited = "0",
unique-id = "Jeon:2018:HMP",
web-of-science-categories = "Computer Science, Hardware \&
Architecture",
}
@Article{Jiang:2018:EFD,
author = "Xiaoyu Jiang and Kicheon Hong",
title = "Explicit form of determinants and inverse matrices of
{Tribonacci} $r$-circulant type matrices",
journal = j-J-MATH-CHEM,
volume = "56",
number = "4",
pages = "1234--1249",
month = apr,
year = "2018",
CODEN = "JMCHEG",
DOI = "https://doi.org/10.1007/s10910-017-0843-8",
ISSN = "0259-9791 (print), 1572-8897 (electronic)",
ISSN-L = "0259-9791",
bibdate = "Tue Mar 6 07:08:26 MST 2018",
bibsource = "http://link.springer.com/journal/10910/56/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
URL = "https://link.springer.com/article/10.1007/s10910-017-0843-8",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Chemistry",
journal-URL = "http://link.springer.com/journal/10910",
journalabr = "J. Math. Chem.",
}
@Article{Johnson:2018:RFP,
author = "Jeff Johnson",
title = "Rethinking floating point for deep learning",
journal = "arXiv.org",
pages = "8",
day = "1",
month = nov,
year = "2018",
bibdate = "Mon Feb 10 09:27:01 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1811.01721",
abstract = "Reducing hardware overhead of neural networks for
faster or lower power inference and training is an
active area of research. Uniform quantization using
integer multiply-add has been thoroughly investigated,
which requires learning many quantization parameters,
fine-tuning training or other prerequisites. Little
effort is made to improve floating point relative to
this baseline; it remains energy inefficient, and word
size reduction yields drastic loss in needed dynamic
range. We improve floating point to be more energy
efficient than equivalent bit width integer hardware on
a 28 nm ASIC process while retaining accuracy in 8 bits
with a novel hybrid log multiply\slash linear add,
Kulisch accumulation and tapered encodings from
Gustafson's posit format. With no network retraining,
and drop-in replacement of all math and float32
parameters via round-to-nearest-even only, this
open-sourced 8-bit log float is within 0.9\% top-1 and
0.2\% top-5 accuracy of the original float32 ResNet-50
CNN model on ImageNet. Unlike int8 quantization, it is
still a general purpose floating point arithmetic,
interpretable out-of-the-box. Our 8/38-bit log float
multiply-add is synthesized and power profiled at 28 nm
at $ 0.96 \times $ the power and $ 1.12 \times $ the
area of 8/32-bit integer multiply-add. In 16 bits, our
log float multiply-add is $ 0.59 \times $ the power and
$ 0.68 \times $ the area of IEEE 754 float16 fused
multiply-add, maintaining the same significand
precision and dynamic range, proving useful for
training ASICs as well.",
acknowledgement = ack-nhfb,
primaryclass = "cs.NA",
}
@InProceedings{Kohlbecker:2018:SNF,
author = "Ignaz Kohlbecker",
title = "The Slide Number Format",
crossref = "ACM:2018:CNG",
pages = "1--6",
year = "2018",
DOI = "https://doi.org/10.1145/3190339.3190342",
bibdate = "Mon Dec 11 09:01:38 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Slide number format divides the real number line
into connected sets. Compared to the unum format [3],
there is no ubit, no infinity, and values are placed on
a logarithmic scale with base 10. Formal definitions
for Slides and intervals composed of Slide pairs are
provided. The relative error is compared with that of
single precision floats. The performance of conversions
to and from human readable form is measured.",
acknowledgement = ack-nhfb,
articleno = "3",
keywords = "posit arithmetic; slide number format; universal
number (unum) arithmetic",
}
@Article{Kromer:2018:AQO,
author = "Pavel Kr{\"o}mer and Jan Plato{\v{s}} and Jana
Nowakov{\'a} and V{\'a}clav Sn{\'a}{\v{s}}el",
title = "An acceleration of quasigroup operations by residue
arithmetic",
journal = j-CCPE,
volume = "30",
number = "2",
pages = "??--??",
day = "25",
month = jan,
year = "2018",
CODEN = "CCPEBO",
DOI = "https://doi.org/10.1002/cpe.4239",
ISSN = "1532-0626 (print), 1532-0634 (electronic)",
ISSN-L = "1532-0626",
bibdate = "Sat Dec 30 09:12:00 MST 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Concurrency and Computation: Practice and Experience",
journal-URL = "http://www.interscience.wiley.com/jpages/1532-0626",
}
@InProceedings{Kumm:2018:KRM,
author = "Martin Kumm and Oscar Gustafsson and Florent de
Dinechin and Johannes Kappauf and Peter Zipf",
title = "{Karatsuba} with Rectangular Multipliers for {FPGAs}",
crossref = "Tenca:2018:PIS",
pages = "13--20",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464809",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This work presents an extension of Karatsuba's method
to efficiently use rectangular multipliers as a base
for larger multipliers. The rectangular multipliers
that motivate this work are the embedded $ 18 \times
25$-bit signed multipliers found in the DSP blocks of
recent Xilinx FPGAs: The traditional Karatsuba approach
must under-use them as square $ 18 \times 18 $ ones.
This work shows that rectangular multipliers can be
efficiently exploited in a modified Karatsuba method if
their input word sizes have a large greatest common
divider. In the Xilinx FPG A case, this can be obtained
by using the embedded multipliers as $ 16 \times 24 $
unsigned and as $ 17 \times 25$ signed ones. The
obtained architectures are implemented with due detail
to architectural features such as the pre-adders and
post-adders available in Xilinx DSP blocks. They are
synthesized and compared with traditional Karatsuba,
but also with (non-Karatsuba) state-of-the-art tiling
techniques that make use of the full rectangular
multipliers. The proposed technique improves resource
consumption and performance for multipliers of numbers
larger than 64 bits.",
acknowledgement = ack-nhfb,
keywords = "25-bit signed multipliers; adders; ARITH-25; Computer
architecture; Delays; Digital arithmetic; digital
arithmetic; Electrical engineering; embedded
multipliers; field programmable gate arrays; Field
programmable gate arrays; Hardware; larger multipliers;
modified Karatsuba method; multiplying circuits;
rectangular multipliers; word length 64.0 bit",
}
@Article{Kumm:2018:OSC,
author = "Martin Kumm and Oscar Gustafsson and Mario Garrido and
Peter Zipf",
title = "Optimal Single Constant Multiplication Using Ternary
Adders",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "65",
number = "7",
pages = "928--932",
month = jul,
year = "2018",
DOI = "https://doi.org/10.1109/TCSII.2016.2631630",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Sat Feb 8 09:52:23 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE trans. circuits syst., II Express briefs",
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
keywords = "adders; Adders; Arithmetic; average adder reductions;
bit shifts; circuit optimization; circuits; coefficient
word sizes; Complexity theory; digital arithmetic;
field programmable gate arrays; Field programmable gate
arrays; field-programmable gate arrays;
field-programmable gate arrays (FPGAs); fixed-point
arithmetic optimization; FPGA; mathematics; multiplying
circuits; numeric algorithms; optimal constant
multiplication circuits; optimal single constant
multiplication; Optimization; optimization methods;
Signal processing algorithms; single constant
coefficient multiplication; support efficient ternary
adders; Topology; two-input adders; word length 22.0
bit; word length 5.0 bit",
}
@Article{Lam:2018:FGF,
author = "Michael O. Lam and Jeffrey K. Hollingsworth",
title = "Fine-grained floating-point precision analysis",
journal = j-IJHPCA,
volume = "32",
number = "2",
pages = "231--245",
year = "2018",
CODEN = "IHPCFL",
DOI = "https://doi.org/10.1177/1094342016652462",
ISSN = "1094-3420 (print), 1741-2846 (electronic)",
ISSN-L = "1094-3420",
bibdate = "Mon Nov 5 17:34:16 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ijsa.bib",
URL = "http://journals.sagepub.com/doi/full/10.1177/1094342016652462",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Performance Computing
Applications",
journal-URL = "http://hpc.sagepub.com/content/by/year",
keywords = "interval arithmetic; truncating arithmetic;
variable-precision arithmetic",
xxmonth = mar,
}
@InProceedings{Langhammer:2018:HDP,
author = "Martin Langhammer and Gregg Baeckler",
title = "High Density and Performance Multiplication for
{FPGA}",
crossref = "Tenca:2018:PIS",
pages = "5--12",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464695",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Arithmetic based applications are one of the most
common use cases for modern FPGAs. Currently, machine
learning is emerging as the fastest growth area for FPG
As, renewing an interest in low precision
multiplication. There is now a new focus on
multiplication in the soft fabric --- very high-density
systems, consisting of many thousands of operations,
are the current norm. In this paper we introduce
multiplier regularization, which restructures common
multiplier algorithms into smaller, and more efficient
architectures. The multiplier structure is
parameterizable, and results are given for a continuous
range of input sizes, although the algorithm is most
efficient for small input precisions. The multiplier is
particularly effective for typical machine learning
inferencing uses, and the presented cores can be used
for dot products required for these applications.
Although the examples presented here are optimized for
Intel Stratix 10 devices, the concept of regularized
arithmetic structures are applicable to generic FPGA
LUT architectures. Results are compared to Intel
Megafunction IP as well as contrasted with normalized
representations of recently published results for
Xilinx devices. We report a 10\% to 35\% smaller area,
and a more significant latency reduction, in the range
of 25\% to 50\%, for typical inferencing use cases.",
acknowledgement = ack-nhfb,
keywords = "Adders; ARITH-25; arithmetic based applications;
common multiplier algorithms; digital arithmetic; dot
products; Field programmable gate arrays; field
programmable gate arrays; generic FPGA LUT
architectures; high-density systems; Intel Megafunction
IP; Intel Stratix devices; IP networks; latency
reduction; logic design; low precision multiplication;
Machine learning; machine learning; multiplier
regularization; multiplier structure; Performance
evaluation; performance multiplication; regularized
arithmetic structures; Routing; soft fabric-very
high-density systems; table lookup; Table lookup",
}
@InProceedings{Langroudi:2018:DLI,
author = "Seyed Hamed Fatemi Langroudi and Tej Pandit and
Dhireesha Kudithipudi",
editor = "{IEEE}",
booktitle = "{2018 1st Workshop on Energy Efficient Machine
Learning and Cognitive Computing for Embedded
Applications (EMC2)}",
title = "Deep Learning Inference on Embedded Devices:
Fixed-Point vs Posit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "19--23",
year = "2018",
DOI = "https://doi.org/10.1109/EMC2.2018.00012",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Lee:2018:APC,
author = "Wonyeol Lee and Rahul Sharma and Alex Aiken",
title = "On automatically proving the correctness of {\tt
math.h} implementations",
journal = j-PACMPL,
volume = "2",
number = "POPL",
pages = "47:1--47:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3158135",
ISSN = "2475-1421",
bibdate = "Wed Jan 10 09:45:26 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
abstract = "Industry standard implementations of {\tt math.h}
claim (often without formal proof) tight bounds on
floating-point errors. We demonstrate a novel static
analysis that proves these bounds and verifies the
correctness of these implementations. Our key insight
is a reduction of this verification task to a set of
mathematical optimization problems that can be solved
by off-the-shelf computer algebra systems. We use this
analysis to prove the correctness of implementations in
Intel's math library automatically. Prior to this work,
these implementations could only be verified with
significant manual effort.",
acknowledgement = ack-nhfb,
articleno = "47",
fjournal = "Proceedings of the ACM on Programming Languages",
journal-URL = "https://pacmpl.acm.org/",
}
@InProceedings{Lehoczky:2018:HLN,
author = "Zolt{\'a}n Leh{\'o}czky and Andr{\'a}s Retzler and
Rich{\'a}rd T{\'o}th and {\'A}lmos Szab{\'o} and
Benedek Farkas and Kriszti{\'a}n Somogyi",
title = "High-level {.NET} Software Implementations of Unum
{Type I} and Posit with Simultaneous {FPGA}
Implementation Using {Hastlayer}",
crossref = "ACM:2018:CNG",
pages = "1--7",
year = "2018",
DOI = "https://doi.org/10.1145/3190339.3190343",
bibdate = "Mon Dec 11 09:02:49 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The unum arithmetic framework has been proposed by
Gustafson, D. J. to address the short-comings of the
IEEE 754 Standard's floating-point. In this paper, we
present our software and hardware implementations of
Type I and posit unums. The software implementation is
built on the .NET platform as an open source library
written in the C\# programming language. We
automatically create hardware implementations using our
.NET to FPGA converter tool called Hastlayer. The
amount of hardware resources needed for addition
operations are quantified, and the performance of
software and prototype hardware for posits are
compared. We show that posits are significantly more
hardware friendly than Type I unums. Furthermore, our
posit FPGA implementation is about 2.04 times more
efficient per clock cycle than its software
implementation.",
acknowledgement = ack-nhfb,
articleno = "4",
keywords = "posit arithmetic; universal number arithmetic",
}
@Misc{Leong:2018:SV,
author = "Cerlane Leong",
title = "{SoftPosit} Version 0.4.1rc",
howpublished = "Web source code.",
year = "2018",
bibdate = "Sat Dec 16 15:18:01 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://gitlab.com/cerlane/SoftPosit",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2018:DEA,
author = "He Li and James J. Davis and John Wickerson and George
A. Constantinides",
title = "Digit Elision for Arbitrary-accuracy Iterative
Computation",
crossref = "Tenca:2018:PIS",
pages = "107--114",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464691",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We recently proposed the first hardware architecture
enabling the iterative solution of systems of linear
equations to accuracies limited only by the amount of
available memory. This technique, named ARCHITECT,
achieves exact numeric computation by using online
arithmetic to allow the refinement of results from
earlier iterations over time, eschewing rounding error.
ARCHITECT has a key drawback, however: often, many more
digits than strictly necessary are generated, with this
problem exacerbating the more accurate a solution is
sought. In this paper, we infer the locations of these
superfluous digits within stationary iterative
calculations by exploiting online arithmetic's digit
dependencies and using forward error analysis. We
demonstrate that their lack of computation is
guaranteed not to affect the ability to reach a
solution of any accuracy. Versus ARCHITECT, our
illustrative hardware implementation achieves a
geometric mean $ 20.1 \times $ speedup in the solution
of a set of representative linear systems through the
avoidance of redundant digit calculation. For the
computation of high-precision results, we also obtain
an up-to $ 22.4 \times $ memory requirement reduction
over the same baseline. Finally, we demonstrate that
solvers implemented following our proposals can show
superiority over conventional arithmetic
implementations by virtue of their runtime-tunable
precisions.",
acknowledgement = ack-nhfb,
keywords = "arbitrary-accuracy iterative computation; ARCHITECT;
ARITH-25; arithmetic implementations; Delays; digit
dependencies; digit elision; digital arithmetic; error
analysis; exact numeric computation; forward error
analysis; Hardware; hardware architecture; iterative
methods; Iterative methods; iterative solution;
Jacobian matrices; linear equations; Linear systems;
linear systems; memory requirement reduction; online
arithmetic; Proposals; redundant digit calculation;
rounding error; Runtime; stationary iterative
calculations; superfluous digits",
}
@Misc{Lie:2018:FPU,
author = "Sean Lie and Michael Edwin James and Michael Morrison
and Gary R. Lauterbach and Srikanth Arekapudi",
title = "Floating-point unit stochastic rounding for
accelerated deep learning",
howpublished = "U.S. Patent US11449574B2",
day = "13",
month = apr,
year = "2018",
bibdate = "Fri Sep 22 17:25:05 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Patent granted 20 September 2022; expires 29 November
2038.",
abstract = "Techniques in advanced deep learning provide
improvements in one or more of accuracy, performance,
and energy efficiency. An array of processing elements
comprising a portion of a neural network accelerator
performs flow-based computations on wavelets of data.
Each processing element has a respective compute
element and a respective routing element. Each compute
element has a respective floating-point unit enabled to
perform stochastic rounding, thus in some circumstances
enabling reducing systematic bias in long dependency
chains of floating-point computations. The long
dependency chains of floating-point computations are
performed, e.g., to train a neural network or to
perform inference with respect to a trained neural
network.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lindstrom:2018:UCR,
author = "Peter Lindstrom and Scott Lloyd and Jeffrey
Hittinger",
title = "Universal Coding of the Reals: Alternatives to {IEEE}
Floating Point",
crossref = "ACM:2018:CNG",
pages = "1--14",
year = "2018",
DOI = "https://doi.org/10.1145/3190339.3190344",
bibdate = "Sun Dec 10 14:24:09 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We propose a modular framework for representing the
real numbers that generalizes IEEE, posits, and related
floating-point number systems, and which has its roots
in universal codes for the positive integers such as
the Elias codes. This framework unifies several known
but seemingly unrelated representations within a single
schema while also introducing new representations. We
particularly focus on variable-length encoding of the
binary exponent and on the manner in which fraction
bits are mapped to values. Our framework builds upon
and shares many of the attractive properties of posits
but allows for independent experimentation with
exponent codes, fraction mappings, reciprocal closure,
rounding modes, handling of under- and overflow, and
underlying precision.",
acknowledgement = ack-nhfb,
articleno = "5",
}
@InProceedings{Liu:2018:CRA,
author = "Weiqiang Liu and Jing Li and Tao Xu and Chenghua Wang
and Paolo Montuschi and Fabrizio Lombardi",
title = "Combining Restoring Array and Logarithmic Dividers
into an Approximate Hybrid Design",
crossref = "Tenca:2018:PIS",
pages = "92--98",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464807",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper proposes a new design of an approximate
hybrid divider (AXHD), which combines the restoring
array and the logarithmic dividers to achieve an
excellent tradeoff between accuracy and hardware
performance. Exact restoring divider cells (EXDCrs) are
used to generate the MSBs of the quotient for attaining
a high accuracy; the other quotient digits are
processed by a logarithmic divider as inexact scheme to
improve figures of merit such as power consumption,
area and delay. The proposed AXHD is evaluated and
analyzed using error and hardware metrics. The proposed
design is also compared with the exact restoring
divider (EXDr) and previous approximate restoring
dividers (AXDrs). The results show that the proposed
design achieves very good performance in terms of
accuracy and hardware; case studies for image
processing also show the validity of the proposed
designs.",
acknowledgement = ack-nhfb,
keywords = "Adders; Approximate Computing; approximate hybrid
divider design; approximate restoring dividers;
ARITH-25; AXDrs; AXHD; circuit stability; dividing
circuits; Electronic mail; Error analysis; exact
restoring divider cells; EXDCrs; Hardware; hardware
metrics; hardware performance; image processing; Image
restoration; logarithmic divider; Logarithmic Divider;
logic design; Low Power; MSBs; Power demand; quotient
digit processing; restoring array; Restoring Array
Divider",
}
@Article{Loeffler:2018:WBP,
author = "John Loeffler",
title = "When Bad Programming Turns Deadly: A look at
programming disasters and how bad programming can be
deadly",
journal = "Interesting Engineering",
volume = "??",
number = "??",
pages = "??--??",
day = "22",
month = nov,
year = "2018",
bibdate = "Fri Nov 23 11:32:14 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://interestingengineering.com/when-bad-programming-turns-deadly",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; Patriot missile;
radiological equipment software malfunction",
}
@Misc{Marchese:2018:ACM,
author = "Sergio Marchese",
title = "{AI} Chips Must Get The Floating-Point Math Right:
Formal verification of {FPUs} is no longer a
prerogative of big companies spending big bucks",
howpublished = "Web site.",
day = "27",
month = sep,
year = "2018",
bibdate = "Fri Sep 28 06:12:07 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Markidis:2018:NTC,
author = "Stefano Markidis and Steven Wei Der Chien and Erwin
Laure and Ivy Bo Peng and Jeffrey S. Vetter",
booktitle = "2018 {IEEE} International Parallel and Distributed
Processing Symposium Workshops {(IPDPSW)}",
title = "{NVIDIA} Tensor Core Programmability, Performance \&
Precision",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "522--531",
month = may,
year = "2018",
DOI = "https://doi.org/10.1109/ipdpsw.2018.00091",
bibdate = "Tue Jan 28 06:32:08 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@InProceedings{Mikaitis:2018:AFP,
author = "Mantas Mikaitis and David R. Lester and Delong Shang
and Steve Furber and Gengting Liu and Jim Garside and
Stefan Scholze and Sebastian H{\"o}ppner and Andreas
Dixius",
title = "Approximate Fixed-Point Elementary Function
Accelerator for the {SpiNNaker-2} Neuromorphic Chip",
crossref = "Tenca:2018:PIS",
pages = "37--44",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464785",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Neuromorphic chips are used to model biologically
inspired Spiking-Neural-Networks (SNNs) where most
models are based on differential equations. Equations
for most SNN algorithms usually contain variables with
one or more ex components. SpiNNaker is a digital
neuromorphic chip that has so far been using
pre-calculated look-up tables for exponential function.
However this approach is limited because the memory
requirements grow as more complex neural models are
developed. To save already limited memory resources in
the next generation SpiNNaker chip, we are including a
fast exponential function in the silicon. In this paper
we analyse iterative algorithms for elementary
functions and show how to build a single hardware
accelerator for exp and natural log, for a neuromorphic
chip prototype, to be manufactured in a 22 nm FDSOI
process. We present the accelerator that has
algorithmic level approximation control, allowing it to
trade precision for latency and energy efficiency. As
an addition to neuromorphic chip application, we
provide analysis of a parameterized elementary function
unit that can be tailored for other systems with
different power, area, accuracy and latency
constraints.",
acknowledgement = ack-nhfb,
keywords = "Adders; algorithmic level approximation control;
approximate arithmetic; approximate fixed-point
elementary function accelerator; ARITH-25; Biological
system modeling; biologically inspired
spiking-neural-networks; complex neural models;
Computational modeling; Convergence; differential
equations; digital neuromorphic chip; energy
efficiency; exponential function; fast exponential
function; FDSOI process; fixed-point arithmetic;
hardware accelerators; iterative algorithms; iterative
methods; logarithm function; Mathematical model; memory
requirements; memory resources; MPSoC; neural chips;
neuromorphic chip prototype; neuromorphic computing;
Neuromorphics; next generation SpiNNaker chip;
parameterized elementary function unit; pre-calculated
look-up tables; single hardware accelerator; size 22.0
nm; SNN algorithms; SpiNNaker-2 neuromorphic chip;
SpiNNaker2; table lookup; Table lookup",
}
@Article{Moroz:2018:FCI,
author = "Leonid V. Moroz and Cezary J. Walczyk and Andriy
Hrynchyshyn and Vijay Holimath and Jan L.
Cie{\'s}li{\'n}ski",
title = "Fast calculation of inverse square root with the use
of magic constant --- analytical approach",
journal = j-APPL-MATH-COMP,
volume = "316",
number = "??",
pages = "245--255",
day = "1",
month = jan,
year = "2018",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2017.08.025",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Oct 10 15:56:03 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300317305763",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
keywords = "single-precision 32-bit IEEE 754 binary arithmetic",
}
@Book{Muller:2018:HFP,
author = "Jean-Michel Muller and Nicolas Brunie and Florent de
Dinechin and Claude-Pierre Jeannerod and Mioara Joldes
and Vincent Lef{\`e}vre and Guillaume Melquiond and
Nathalie Revol and Serge Torres",
title = "Handbook of Floating-Point Arithmetic",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
edition = "Second",
year = "2018",
DOI = "https://doi.org/10.1007/978-3-319-76526-6",
ISBN = "3-319-76525-6, 3-319-76526-4 (e-book)",
ISBN-13 = "978-3-319-76525-9, 978-3-319-76526-6 (e-book)",
LCCN = "QA76.9.C62",
bibdate = "Fri Jun 1 06:59:01 MDT 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This handbook aims to provide a complete overview of
modern floating-point arithmetic. This includes a
detailed treatment of the current (IEEE-754) and next
(preliminarily called IEEE-754R) standards for
floating-point arithmetic.",
acknowledgement = ack-nhfb,
shorttableofcontents = "Introduction / 3--14 \\
Definitions and Basic Notions / 15--45 \\
Floating-Point Formats and Environment / 47--93 \\
Basic Properties and Algorithms / 97--162 \\
Enhanced Floating-Point Sums, Dot Products, and
Polynomial Values / 163--192 \\
Languages and Compilers / 193--230 \\
Algorithms for the Basic Operations / 233--266 \\
Hardware Implementation of Floating-Point Arithmetic /
267--320 \\
Software Implementation of Floating-Point Arithmetic /
321--374 \\
Evaluating Floating-Point Elementary Functions /
375--433 \\
Complex Numbers / 437--452 \\
Interval Arithmetic / 453--477 \\
Verifying Floating-Point Algorithms / 479--511 \\
Extending the Precision / 513--552",
subject = "Floating-point arithmetic; Handbooks, manuals, etc;
Computer arithmetic; COMPUTERS / Computer Literacy;
COMPUTERS / Computer Science; COMPUTERS / Data
Processing; COMPUTERS / Hardware / General; COMPUTERS /
Information Technology; COMPUTERS / Machine Theory;
COMPUTERS / Reference.",
tableofcontents = "Intro \\
Contents \\
List of Figures \\
List of Tables \\
Preface \\
I Introduction, Basic Definitions, and Standards \\
1 Introduction \\
1.1 Some History \\
1.2 Desirable Properties \\
1.3 Some Strange Behaviors \\
1.3.1 Some famous bugs \\
1.3.2 Difficult problems \\
1.3.2.1 A sequence that seems to converge to a wrong
limit \\
1.3.2.2 The Chaotic Bank Society \\
1.3.2.3 Rump's example \\
2 Definitions and Basic Notions \\
2.1 Floating-Point Numbers \\
2.1.1 Main definitions \\
2.1.2 Normalized representations, normal and subnormal
numbers \\
2.1.3 A note on underflow \\
2.1.4 Special floating-point data \\
2.2 Rounding \\
2.2.1 Rounding functions \\
2.2.2 Useful properties \\
2.3 Tools for Manipulating Floating-Point Errors \\
2.3.1 Relative error due to rounding \\
2.3.2 The ulp function \\
2.3.3 Link between errors in ulps and relative errors
\\
2.3.3.1 Converting from errors in ulps to relative
errors \\
2.3.3.2 Converting from relative errors to errors in
ulps \\
2.3.3.3 Loss of information during these conversions
\\
2.3.4 An example: iterated products \\
2.4 The Fused Multiply-Add (FMA) Instruction \\
2.5 Exceptions \\
2.6 Lost and Preserved Properties of Real Arithmetic
\\
2.7 Note on the Choice of the Radix \\
2.7.1 Representation errors \\
2.7.2 A case for radix 10 \\
2.8 Reproducibility \\
3 Floating-Point Formats and Environment \\
3.1 The IEEE 754-2008 Standard \\
3.1.1 Formats \\
3.1.1.1 Binary interchange format encodings \\
3.1.1.2 Decimal interchange format encodings \\
3.1.1.3 Larger formats \\
3.1.1.4 Extended and extendable precisions \\
3.1.1.5 Little-endian, big-endian \\
3.1.2 Attributes and rounding \\
3.1.2.1 Rounding direction attributes \\
3.1.2.2 Alternate exception-handling attributes \\
3.1.2.3 Preferred width attributes \\
3.1.2.4 Value-changing optimization attributes \\
3.1.2.5 Reproducibility attributes \\
3.1.3 Operations specified by the standard \\
3.1.3.1 Arithmetic operations and square root \\
3.1.3.2 Remainders \\
3.1.3.3 Preferred exponent for arithmetic operations in
the decimal format \\
3.1.3.4 scaleB and logB \\
3.1.3.5 Miscellaneous \\
3.1.4 Comparisons \\
3.1.5 Conversions to/from string representations \\
3.1.6 Default exception handling \\
3.1.6.1 Invalid operation \\
3.1.6.2 Division by zero \\
3.1.6.3 Overflow \\
3.1.6.4 Underflow \\
3.1.6.5 Inexact \\
3.1.7 Special values \\
3.1.7.1 NaN: Not a Number \\
3.1.7.2 Arithmetic of infinities and zeros \\
3.1.8 Recommended functions \\
3.2 On the Possible Hidden Use of a Higher Internal
Precision \\
3.3 Revision of the IEEE 754-2008 Standard \\
3.4 Floating-Point Hardware in Current Processors \\
3.4.1 The common hardware denominator \\
3.4.2 Fused multiply-add \\
3.4.3 Extended precision and 128-bit formats \\
3.4.4 Rounding and precision control \\
3.4.5 SIMD instructions \\
3.4.6 Binary16 (half-precision) support \\
3.4.7 Decimal arithmetic \\
3.4.8 The legacy x87 processor \\
3.5 Floating-Point Hardware in Recent Graphics
Processing Units \\
3.6 IEEE Support in Programming Languages \\
3.7 Checking the Environment \\
3.7.1 MACHAR \\
3.7.2 Paranoia \\
\ldots{} \\
Basic Properties and Algorithms \\
Enhanced Floating-Point Sums, Dot Products, and
Polynomial Values \\
Languages and Compilers \\
Algorithms for the Basic Operations \\
Hardware Implementation of Floating-Point Arithmetic
\\
Software Implementation of Floating-Point Arithmetic
\\
Evaluating Floating-Point Elementary Functions \\
Complex Numbers \\
Interval Arithmetic \\
Verifying Floating-Point Algorithms \\
Extending the Precision",
}
@Article{Munoz-Coreas:2018:CQO,
author = "Edgard Mu{\~n}oz-Coreas and Himanshu Thapliyal",
title = "{T}-count and Qubit Optimized Quantum Circuit Design
of the Non-Restoring Square Root Algorithm",
journal = j-JETC,
volume = "14",
number = "3",
pages = "36:1--36:15",
month = oct,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3264816",
ISSN = "1550-4832 (print), 1550-4840 (electronic)",
ISSN-L = "1550-4832",
bibdate = "Thu Nov 1 16:44:41 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jetc.bib",
abstract = "Quantum circuits for basic mathematical functions such
as the square root are required to implement scientific
computing algorithms on quantum computers. Quantum
circuits that are based on Clifford+T gates can easily
be made fault tolerant, but the T gate is very costly
to implement. As a result, reducing T-count has become
an important optimization goal. Further, quantum
circuits with many qubits are difficult to realize,
making designs that save qubits and produce no garbage
outputs desirable. In this work, we present a T-count
optimized quantum square root circuit with only $ 2 s n
+ 1 $ qubits and no garbage output. To make a fair
comparison against existing work, the Bennett's garbage
removal scheme is used to remove garbage output from
existing works. We determined that our proposed design
achieves an average T-count savings of 43.44\%,
98.95\%, 41.06\%, and 20.28\% as well as qubit savings
of 85.46\%, 95.16\%, 90.59\%, and 86.77\% compared to
existing works.",
acknowledgement = ack-nhfb,
articleno = "36",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J967",
}
@InProceedings{Nannarelli:2018:TFP,
author = "Alberto Nannarelli",
title = "Tunable Floating-Point for Energy Efficient
Accelerators",
crossref = "Tenca:2018:PIS",
pages = "29--36",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464797",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this work, we address the design of an on-chip
accelerator for Machine Learning and other
computation-demanding applications with a Tunable
Floating-Point (TFP) precision. The precision can be
chosen for a single operation by selecting a specific
number of bits for significand and exponent in the
floating-point representation. By tuning the precision
of a given algorithm to the minimum precision achieving
an acceptable target error, we can make the computation
more power efficient. We focus on floating-point
multiplication, which is the most power demanding
arithmetic operation.",
acknowledgement = ack-nhfb,
keywords = "Adders; ARITH-25; computation-demanding applications;
Decoding; Dynamic range; electronic engineering
computing; energy efficient accelerators; floating
point arithmetic; floating-point multiplication;
floating-point representation; Hardware; learning
(artificial intelligence); Machine Learning; Machine
learning; on-chip accelerator; Standards;
System-on-chip; TFP precision; Tunable Floating-Point
precision",
}
@Article{Numahata:2018:RAS,
author = "Dai Numahata and Hiroshi Sekigawa",
title = "Robust algorithms for sparse interpolation of
multivariate polynomials",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "52",
number = "4",
pages = "145--147",
month = dec,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3338637.3338648",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Wed Oct 23 07:34:18 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
abstract = "We consider the problem of symbolic-numeric sparse
interpolation of multivariate polynomials. The problem
is to find the coefficients and the exponents of a
given black-box polynomial $ f(x_1, \ldots, x_n) =
\sum_{j = 1}^t c_j x_1^{d_{j, 1}} \ldots {} x_n^{d_{j,
n}} \in \mathbb {C}[x_1, \ldots, x_n] (c_j \neq 0) $ by
evaluating the value of $ f(x_1, \ldots, x_n) $ at any
point in $ \mathbb {C}^n $ in floating-point arithmetic
and by using the conditions of the input.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Oliveira:2018:MLB,
author = "Thomaz Oliveira and Julio L{\'o}pez and Francisco
Rodr{\'{\i}}guez-Henr{\'{\i}}quez",
title = "The {Montgomery} ladder on binary elliptic curves",
journal = j-J-CRYPTO-ENG,
volume = "8",
number = "3",
pages = "241--258",
month = sep,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-017-0163-8",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Wed Oct 2 11:24:50 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "http://link.springer.com/article/10.1007/s13389-017-0163-8",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@InProceedings{Podobas:2018:HIP,
author = "Artur Podobas and Satoshi Matsuoka",
editor = "{IEEE}",
booktitle = "{2018 IEEE International Parallel and Distributed
Processing Symposium Workshops (IPDPSW)}",
title = "Hardware Implementation of {POSITs} and Their
Application in {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "138--145",
year = "2018",
DOI = "https://doi.org/10.1109/IPDPSW.2018.00029",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Popescu:2018:FPN,
author = "Valentina Popescu and Marcel Nassar and Xin Wang and
Evren Tumer and Tristania Webb",
title = "{Flexpoint}: Predictive Numerics for Deep Learning",
crossref = "Tenca:2018:PIS",
pages = "1--4",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464801",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Deep learning has been undergoing rapid growth in
recent years thanks to its state-of-the-art performance
across a wide range of real-world applications.
Traditionally neural networks were trained in IEEE-754
binary64 or binary32 format, a common practice in
general scientific computing. However, the unique
computational requirements of deep neural network
training workloads allow for much more efficient and
inexpensive alternatives, unleashing a new wave of
numerical innovations powering specialized computing
hardware. We previously presented Flexpoint, a blocked
fixed-point data type combined with a novel predictive
exponent management algorithm designed to support
training of deep networks without modifications, aiming
at a seamless replacement of the binary32 widely in
practice today. We showed that Flexpoint with 16-bit
mantissa and 5-bit shared exponent (flex16+S) achieved
numerical parity to binary32 in training a number of
convolutional neural networks. In the current paper we
review the continuing trend of predictive numerics
enhancing deep neural network training in specialized
computing devices such as the Intel Nervana Neural
Network Processor.",
acknowledgement = ack-nhfb,
keywords = "ARITH-25; blocked fixed-point data type; convolution;
convolutional neural networks; deep learning; Deep
Learning; deep neural network training; feedforward
neural nets; Flexpoint; floating point arithmetic;
general scientific computing; Hardware; learning
(artificial intelligence); Machine learning; Market
research; Neural networks; Neural Networks; Prediction
algorithms; predictive exponent management algorithm;
Tensile stress; Training",
}
@Article{Radford:2018:FIF,
author = "Peter Radford",
title = "A {``Feature''} of {IBM 360} Floating Point",
journal = "Resurrection: The Journal of the Computer Conservation
Society",
volume = "??",
number = "82",
pages = "??--??",
month = "Summer",
year = "2018",
ISSN = "0958-7403",
ISSN-L = "0958-7403",
bibdate = "Mon Jul 27 18:19:06 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://computerconservationsociety.org/resurrection/res82.htm#f",
acknowledgement = ack-nhfb,
remark = "The short article discusses the impact of hexadecimal
normalization on representation of decimal input
values, and ends with the statement: ``32-bit floating
point remains an elephant trap for programmers to this
day.''.",
}
@InProceedings{Ram:2018:FVF,
author = "Ravi Ram and Adam Elkins and Adnan Pratama and Sasa
Stamenkovic and Sven Beyer and Sergio Marchese",
editor = "????",
booktitle = "Proceedings of {DVCon US 2018}",
title = "Formal Verification of Floating-Point Hardware with
Assertion-Based {VIP}",
publisher = "????",
address = "????",
pages = "1--9",
day = "5",
month = jun,
year = "2018",
bibdate = "Fri Sep 28 06:20:43 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.onespin.com/fileadmin/user_upload/pdf/whitepapers/Formal_Verification_of_Floating_Point_Hardware.pdf",
abstract = "Hardware for integer or fixed-point arithmetic is
relatively simple to design, at least at the
register-transfer level. If the range of values and
precision that can be represented with these formats is
not sufficient for the target application,
floating-point hardware might be required.
Unfortunately, floating-point units are complex to
design, and notoriously challenging to verify. Since
the famous 1994 Intel Pentium bug, many companies have
investigated and successfully applied formal methods to
this task. However, solutions often rely on a mix of
the following: hard-to-use formal tools; highly
specialized engineering skills; availability of a
suitable executable model of the hardware; and
significant, design-specific engineering effort. In
this paper, we present an alternative floating-point
hardware verification approach based on a reusable,
IEEE 754 compliant SystemVerilog arithmetic library.
While not addressing all verification challenges, this
method enables engineers to set up a formal testbench
and uncover deep corner-case bugs with minimal effort.
Results from industrial applications are reported.",
acknowledgement = ack-nhfb,
}
@InProceedings{Reddy:2018:DAD,
author = "K. Manikantta Reddy and M. H. Vasantha and Y. B.
Nithin Kumar and Devesh Dwivedi",
booktitle = "{2018 IEEE 61st International Midwest Symposium on
Circuits and Systems (MWSCAS)}",
title = "Design of Approximate Dividers for Error Tolerant
Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
month = aug,
year = "2018",
DOI = "https://doi.org/10.1109/mwscas.2018.8623909",
bibdate = "Wed Dec 20 07:39:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Reyhani-Masoleh:2018:NAR,
author = "Arash Reyhani-Masoleh and Mostafa Taha and Doaa
Ashmawy",
title = "New Area Record for the {AES} Combined {S}-Box\slash
Inverse {S}-Box",
crossref = "Tenca:2018:PIS",
pages = "145--152",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464780",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The AES combined S-box/inverse S-box is a single
construction that is shared between the encryption and
decryption data paths of the AES. The currently most
compact implementation of the AES combined
S-box/inverse S-box is Canright's design, introduced
back in 2005. Since then, the research community has
introduced several optimizations over the S-box only,
however the combined S-boxlinverse S-box received
little attention. In this paper, we propose a new AES
combined S-boxlinverse S-box design that is both
smaller and faster than Canright's design. We achieve
this goal by proposing to use new tower field and
optimizing each and every block inside the combined
architecture for this field. Our complexity analysis
and ASIC implementation results in the CMOS STM 65nm
and NanGate 15nm technologies show that our design
outperforms the counterparts in terms of area and
speed.",
acknowledgement = ack-nhfb,
keywords = "AES combined S-box-inverse S-box; application specific
integrated circuits; ARITH-25; Canright design; circuit
optimisation; CMOS STM; Complexity theory; Computer
architecture; cryptography; decryption data paths;
Encryption; encryption data paths; Generators; Logic
gates; Multiplexing; NanGate; Poles and towers; size
15.0 nm; size 65.0 nm",
}
@InProceedings{Riedy:2018:AAO,
author = "Jason Riedy and James Demmel",
title = "Augmented Arithmetic Operations Proposed for {IEEE-754
2018}",
crossref = "Tenca:2018:PIS",
pages = "45--52",
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464813",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Algorithms for extending arithmetic precision through
compensated summation or arithmetics like double-double
rely on operations commonly called twoSum and
twoProduct. The current draft of the IEEE 754 standard
specifies these operations under the names
augmentedAddition and augmentedMultiplication. These
operations were included after three decades of
experience because of a motivating new use: bitwise
reproducible arithmetic. Standardizing the operations
provides a hardware acceleration target that can
provide at least a 33\% speed improvements in
reproducible dot product, placing reproducible dot
product almost within a factor of two of common dot
product. This paper provides history and motivation for
standardizing these operations. We also define the
operations, explain the rationale for all the specific
choices, and provide parameterized test cases for new
boundary behaviors.",
acknowledgement = ack-nhfb,
keywords = "Acceleration; ARITH-25; arithmetic precision;
augmented arithmetic operations; bitwise reproducible
arithmetic; common dot product; floating point
arithmetic; Hardware; hardware acceleration target;
History; IEEE 754 standard; IEEE standards; IEEE-754
2018; Libraries; Magnetic heads; reproducible dot
product; Software; Standards",
}
@Article{Rodriguez-Henriquez:2018:SIH,
author = "Francisco Rodr{\'\i}guez-Henr{\'\i}quez and Erkay
Savas",
title = "Special issue in honor of {Peter Lawrence
Montgomery}",
journal = j-J-CRYPTO-ENG,
volume = "8",
number = "3",
pages = "185--187",
month = sep,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-017-0168-3",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Wed Oct 2 11:24:50 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "http://link.springer.com/article/10.1007/s13389-017-0168-3;
https://link.springer.com/content/pdf/10.1007/s13389-017-0168-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@Article{Saadat:2018:MBM,
author = "Hassaan Saadat and Haseeb Bokhari and Sri
Parameswaran",
title = "Minimally Biased Multipliers for Approximate Integer
and Floating-Point Multiplication",
journal = j-IEEE-TRANS-CAD-ICS,
volume = "37",
number = "11",
pages = "2623--2635",
month = nov,
year = "2018",
CODEN = "ITCSDI",
DOI = "https://doi.org/10.1109/tcad.2018.2857262",
ISSN = "0278-0070 (print), 1937-4151 (electronic)",
ISSN-L = "0278-0070",
bibdate = "Wed Dec 20 07:46:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computer-Aided Design of
Integrated Circuits and Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=43",
}
@Article{Sanchez-Stern:2018:FRC,
author = "Alex Sanchez-Stern and Pavel Panchekha and Sorin
Lerner and Zachary Tatlock",
title = "Finding root causes of floating point error",
journal = j-SIGPLAN,
volume = "53",
number = "4",
pages = "256--269",
month = apr,
year = "2018",
CODEN = "SINODQ",
DOI = "https://doi.org/10.1145/3296979.3192411",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
bibdate = "Wed Oct 16 14:12:57 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
abstract = "Floating-point arithmetic plays a central role in
science, engineering, and finance by enabling
developers to approximate real arithmetic. To address
numerical issues in large floating-point applications,
developers must identify root causes, which is
difficult because floating-point errors are generally
non-local, non-compositional, and non-uniform. This
paper presents Herbgrind, a tool to help developers
identify and address root causes in numerical code
written in low-level languages like C/C++ and Fortran.
Herbgrind dynamically tracks dependencies between
operations and program outputs to avoid false positives
and abstracts erroneous computations to simplified
program fragments whose improvement can reduce output
error. We perform several case studies applying
Herbgrind to large, expert-crafted numerical programs
and show that it scales to applications spanning
hundreds of thousands of lines, correctly handling the
low-level details of modern floating point hardware and
mathematical libraries and tracking error across
function boundaries and through the heap.",
acknowledgement = ack-nhfb,
fjournal = "ACM SIGPLAN Notices",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
remark = "PLDI '18 proceedings.",
}
@Article{Savas:2018:MI,
author = "Erkay Savas and {\c{C}}etin Kaya Ko{\c{c}}",
title = "{Montgomery} inversion",
journal = j-J-CRYPTO-ENG,
volume = "8",
number = "3",
pages = "201--210",
month = sep,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-017-0161-x",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Wed Oct 2 11:24:50 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "http://link.springer.com/article/10.1007/s13389-017-0161-x",
acknowledgement = ack-nhfb,
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@Article{Schneider:2018:USS,
author = "D. Schneider",
title = "{U.S.} supercomputing strikes back",
journal = j-IEEE-SPECTRUM,
volume = "55",
number = "1",
pages = "52--53",
month = jan,
year = "2018",
CODEN = "IEESAM",
DOI = "https://doi.org/10.1109/MSPEC.2018.8241739",
ISSN = "0018-9235 (print), 1939-9340 (electronic)",
ISSN-L = "0018-9235",
bibdate = "Sat Jan 18 07:02:09 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib;
https://www.math.utah.edu/pub/tex/bib/super.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Spectrum",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
keywords = "Companies; Computational modeling; floating-point
operations; Games; Hardware; parallel machines;
Payloads; petaflops; Rockets; Supercomputers; Titan
machine; U.S. high-performance computing community;
U.S. supercomputing",
}
@Article{Seo:2018:FBM,
author = "Jungjoo Seo and Kunsoo Park",
title = "Fast batch modular exponentiation with
common-multiplicand multiplication",
journal = j-INFO-PROC-LETT,
volume = "129",
number = "??",
pages = "5--10",
month = jan,
year = "2018",
CODEN = "IFPLAT",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Mon Oct 30 08:48:26 MDT 2017",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc2010.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0020019017301527",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Misc{Trader:2018:ICS,
author = "Tiffany Trader",
title = "Inventor Claims to Have Solved Floating Point Error
Problem",
howpublished = "HPC Web site.",
day = "17",
month = jan,
year = "2018",
bibdate = "Fri Mar 23 19:13:03 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "From the HPC editor: ``After this article was
published, a number of readers raised concerns about
the originality of Jorgensen's techniques, noting the
existence of prior art going back years. Specifically,
there is precedent in John Gustafson's work on unums
and interval arithmetic both at Sun and in his 2015
book, \booktitle{The End of Error}, which was published
19 months before Jorgensen's patent application was
filed. ''",
URL = "https://www.hpcwire.com/2018/01/17/inventor-claims-solved-floating-point-error-problem/",
acknowledgement = ack-nhfb,
}
@Article{Villalba-Moreno:2018:FHF,
author = "Julio Villalba-Moreno and Javier Hormigo and Sonia
Gonz{\'a}lez-Navarro",
title = "Fast {HUB} Floating-point Adder for {FPGA}",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "66",
number = "6",
pages = "1028--1032",
month = jun,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1109/TCSII.2018.2873194",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Mon Feb 10 08:25:14 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/8477084",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Circuits Syst., II Express Briefs",
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
keywords = "HUB (Half-Unit-Biased) floating-point format",
}
@Article{Villalba-Moreno:2018:URH,
author = "Julio Villalba-Moreno and Javier Hormigo and Sonia
Gonz{\'a}lez-Navarro",
title = "Unbiased Rounding for {HUB} Floating-Point Addition",
journal = j-IEEE-TRANS-COMPUT,
volume = "67",
number = "9",
pages = "1359--1365",
month = sep,
year = "2018",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2807429",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Mar 15 08:10:13 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "https://ieeexplore.ieee.org/document/8300633/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "HUB (Half-Unit-Biased) floating-point format",
}
@Article{Walczyk:2018:IAF,
author = "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
Cie{\'s}li{\'n}ski",
title = "Improving the accuracy of the fast inverse square root
algorithm",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--21",
day = "17",
month = feb,
year = "2018",
DOI = "https://doi.org/10.48550/arXiv.1802.06302",
bibdate = "Wed Dec 20 07:55:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1802.06302",
abstract = "We present improved algorithms for fast calculation of
the inverse square root for single-precision
floating-point numbers. The algorithms are much more
accurate than the famous fast inverse square root
algorithm and have the same or similar computational
cost. The main idea of our work consists in modifying
the Newton-Raphson method and demanding that the
maximal error is as small as possible. Such
modification is possible when the distribution of
Newton-Raphson corrections is not symmetric (e.g., if
they are non-positive functions).",
acknowledgement = ack-nhfb,
}
@InProceedings{Wang:2018:TDN,
author = "Naigang Wang and Jungwook Choi and Daniel Brand and
Chia-Yu Chen and Kailash Gopalakrishnan",
editor = "S. Bengio and others",
booktitle = "{Proceedings of the 32nd Conference on Neural
Information Processing Systems (NeurIPS 2018),
Montr{\'e}al, Canada}",
title = "Training {Deep Neural Networks} with 8-bit Floating
Point Numbers",
publisher = "Curran Associates, Inc.",
address = "????",
pages = "7675--7684",
year = "2018",
bibdate = "Wed Dec 19 19:17:48 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1812.08011;
https://papers.nips.cc/paper/7994-training-deep-neural-networks-with-8-bit-floating-point-numbers.pdf",
abstract = "The state-of-the-art hardware platforms for training
Deep Neural Networks (DNNs) are moving from traditional
single precision (32-bit) computations towards 16 bits
of precision in large part due to the high energy
efficiency and smaller bit storage associated with
using reduced-precision representations. However,
unlike inference, training with numbers represented
with less than 16 bits has been challenging due to the
need to maintain fidelity of the gradient computations
during back-propagation. Here we demonstrate, for the
first time, the successful training of DNNs using 8-bit
floating point numbers while fully maintaining the
accuracy on a spectrum of Deep Learning models and
datasets. In addition to reducing the data and
computation precision to 8 bits, we also successfully
reduce the arithmetic precision for additions (used in
partial product accumulation and weight updates) from
32 bits to 16 bits through the introduction of a number
of key ideas including chunk-based accumulation and
floating point stochastic rounding. The use of these
novel techniques lays the foundation for a new
generation of hardware training platforms with the
potential for 2--4 $ \times $ improved throughput over
today's systems.",
acknowledgement = ack-nhfb,
remark = "The 8-bit floating-point format, FP8, has 1 sign bit,
5 exponent bits, and 2 significand bits (1,5,2); the
16-bit format, FP16, has 1 sign bit, 6 exponent bits,
and 9 significand bits (1,6,9). There is no mention of
Infinity, NaN, signed zeros, or FMA operations",
xxpages = "1--10",
}
@InProceedings{Yang:2018:OMP,
author = "Xiong Yang and Hongbin Zhang and Tianyou Cheng and
Xuebin Ni and Chenhao Wu and Huaizhi Zong and Haojian
Lu and Zhiguo Lu and Yajing Shen",
editor = "{IEEE}",
booktitle = "{2018 IEEE International Conference on Intelligence
and Safety for Robotics (ISR)}",
title = "An Omnidirectional and Movable Palletizing Robot based
on Computer Vision Positing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "423--428",
year = "2018",
DOI = "https://doi.org/10.1109/IISR.2018.8535688",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Zhang:2018:HSA,
author = "Yunxiang Zhang and Xiaokun Yang and Lei Wu and Archit
Gajjar and Han He",
title = "Hierarchical Synthesis of Approximate Multiplier
Design for Field-programmable Gate Arrays
{(FPGA)-CSRmesh} System",
journal = j-INT-J-COMP-APPL,
volume = "180",
number = "??",
pages = "1--7",
month = feb,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.5120/ijca2018916380",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 09:43:10 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume180/number17/29021-2018916380/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "17",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@Article{Adams:2019:RRP,
author = "Ulf Adams",
title = "{Ry{\=u}} revisited: {\tt printf} floating point
conversion",
journal = j-PACMPL,
volume = "3",
number = "OOPSLA",
pages = "169:1--169:23",
month = oct,
year = "2019",
DOI = "https://doi.org/10.1145/3360595",
ISSN = "2475-1421",
bibdate = "Fri Aug 7 19:22:30 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3360595",
abstract = "Ry{\=u} Printf is a new algorithm to convert
floating-point numbers to decimal strings according to
the {\tt printf} {\tt \%f}, {\tt \%e}, and {\tt \%g}
formats: {\tt \%f} generates `full' output (integer
part of the input, dot, configurable number of digits),
{\tt \%e} generates scientific output (one leading
digit, dot, configurable number of digits, exponent),
and {\tt \%g} generates the shorter of the two.
Ry{\=u}'s Printf is based on the Ry{\=u} algorithm,
which converts binary floating-point numbers to the
shortest equivalent decimal floating-point
representation. We provide quantitative evidence that
Ry{\=u} Printf is between 3.8 and 55 times faster than
existing {\tt printf} implementations.\par
Furthermore, we show that both Ry{\=u} and Ry{\=u}
Printf generalize to arbitrary number bases. This
finding implies the existence of a fast algorithm to
convert from base-10 to base-2, as long as the maximum
precision of the input is known a priori.",
acknowledgement = ack-nhfb,
articleno = "169",
fjournal = "Proceedings of the ACM on Programming Languages",
journal-URL = "https://pacmpl.acm.org/",
keywords = "base conversion",
}
@Misc{Adams:2019:URP,
author = "Ulf Adams and Stephan T. Lavavej and Alexander Bolz
and Vinnie Falco and David Tolnay and Mitchell {Blank,
Jr.} and Mara Bos and Caleb Spare and Alexander Iljin",
title = "{ulfjack/ryu}: Printf Support",
howpublished = "Web site",
day = "12",
month = aug,
year = "2019",
DOI = "https://doi.org/10.5281/zenodo.3366212",
bibdate = "Sun Aug 16 18:37:00 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/java2010.bib",
URL = "https://github.com/ulfjack/ryu/tree/v2.0;
https://zenodo.org/record/3366212",
abstract = "This project contains C and Java implementation of
Ryu, as well as a C implementation of Ryu Printf. Ryu
converts a floating point number to its shortest
decimal representation, whereas Ryu Printf converts a
floating point number according to the printf \%f or
\%e format. At the time of this writing, these are the
fastest known float-to-string conversion algorithms. We
have tested the code on Ubuntu 19.04, MacOS Mojave, and
Windows 10.",
acknowledgement = ack-nhfb,
}
@InProceedings{Agrawal:2019:DBF,
author = "Ankur Agrawal and Silvia M. Mueller and Bruce M.
Fleischer and Xiao Sun and Naigang Wang and Jungwook
Choi and Kailash Gopalakrishnan",
title = "{DLFloat}: A 16-b Floating Point Format Designed for
Deep Learning Training and Inference",
crossref = "Takagi:2019:ISC",
pages = "92--95",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00023",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The resilience of Deep Learning (DL) training and
inference workloads to low-precision computations,
coupled with the demand for power-and area-efficient
hardware accelerators for these workloads, has led to
the emergence of 16-bit floating point formats as the
precision of choice for DL hardware accelerators. This
paper describes our optimized 16-bit format that has 6
exponent bits and 9 fraction bits, derived from a study
of the range of values encountered in DL applications.
We demonstrate that our format preserves the accuracy
of DL networks, and we compare its ease-of-use for DL
against IEEE-754 half-precision (5 exponent bits and 10
fraction bits) and bfloat16 (8 exponent bits and 7
fraction bits). Further, our format eliminated
sub-normals and simplifies rounding modes and handling
of corner cases. This streamlines floating-point unit
logic and enables realization of a compact
power-efficient computation engine.",
acknowledgement = ack-nhfb,
keywords = "16-b floating point format; 16-bit floating point
formats; Adders; ARITH-26; compact power-efficient
computation engine; Deep learning; deep learning
training; DL hardware accelerators; Dynamic range;
Engines; floating point arithmetic; floating-point unit
logic; Hardware; IEEE-754 half-precision; Image
recognition; learning (artificial intelligence);
low-precision computations; neural nets; power-and
area-efficient hardware accelerators; reduced precision
computation, floating point, machine learning, deep
learning; streamlines floating-point unit logic;
Training",
remark = "The DLFloat format has a 1-bit sign, 6-bit exponent,
and 10-bit normalized significand including the hidden
leading one-bit. Subnormals are not supported, and
underflows flush to zero. Infinity and NaN are fused
into a single value with the largest exponent and
significand; other significands with that exponent are
normal numbers. Zero and Inf-NaN are considered to be
unsigned. There is only one rounding mode:
round-nearest-up. Fused multiply-add (FMA) is
supported.",
}
@InProceedings{Anderson:2019:SAM,
author = "Andrew Anderson and Michael Doyle and David Gregg",
title = "Scalar Arithmetic Multiple Data: Customizable
Precision for Deep Neural Networks",
crossref = "Takagi:2019:ISC",
pages = "61--68",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00018",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Quantization of weights and activations in Deep Neural
Networks (DNNs) is a powerful technique for network
compression, and has enjoyed significant attention and
success. However, much of the inference-time benefit of
quantization is accessible only through customized
hardware accelerators or with an FPGA implementation of
quantized arithmetic. Building on prior work, we show
how to construct very fast implementations of arbitrary
bit-precise signed and unsigned integer operations
using a software technique which logically embeds a
vector architecture with custom bit-width lanes in
fixed-width scalar arithmetic. At the strongest level
of quantization, our approach yields a maximum speedup
of $ \approx 6 \% $ on an x86 platform, and $ \approx
10 \% $ on an ARM platform versus quantization to
native 8-bit integers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; bit-width lanes; Computer architecture;
Custom Arithmetic; Deep Neural Networks; digital
arithmetic; Field programmable gate arrays; field
programmable gate arrays; fixed-width scalar
arithmetic; FPGA implementation; Hardware; hardware
accelerators; Machine Learning; network compression;
neural nets; Program processors; quantisation (signal);
quantization; Quantization (signal); quantized
arithmetic; Registers; scalar arithmetic multiple data;
Software Performance; software technique; vectors",
}
@InProceedings{Andrlon:2019:OBF,
author = "Mak Andrlon and Peter Schachte and Harald
S{\o}ndergaard and Peter J. Stuckey",
title = "Optimal Bounds for Floating-Point Addition in Constant
Time",
crossref = "Takagi:2019:ISC",
pages = "159--166",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00038",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Reasoning about floating-point numbers is notoriously
difficult, owing to the lack of convenient algebraic
properties such as associativity. This poses a
substantial challenge for program analysis and
verification tools which rely on precise floating-point
constraint solving. Currently, interval methods in this
domain often exhibit slow convergence even on simple
examples. We present a new theorem supporting efficient
computation of exact bounds of the intersection of a
rectangle with the preimage of an interval under
floating-point addition, in any radix or rounding mode.
We thus give an efficient method of deducing optimal
bounds on the components of an addition, solving the
convergence problem.",
acknowledgement = ack-nhfb,
keywords = "addition; arbitrary radix; ARITH-26; Australia; bound
analysis; constant time; constraint handling;
convenient algebraic properties; Convergence; Digital
arithmetic; exact bounds; floating point arithmetic;
floating-point addition; Floating-point arithmetic;
floating-point numbers; Information systems; interval
methods; optimal bounds; precise floating-point
constraint solving; program analysis; radix mode;
rounding mode; Software; Standards",
}
@Article{Anonymous:2019:CPC,
author = "Anonymous",
title = "Computational `pathology' could hamper climate and
fusion simulations",
journal = j-PHYS-WORLD,
day = "26",
month = sep,
year = "2019",
CODEN = "PHWOEW",
ISSN = "0953-8585 (print), 2058-7058 (electronic)",
bibdate = "Mon Sep 30 11:21:38 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boghosian:2019:NPS}.",
URL = "https://physicsworld.com/a/computational-pathology-could-hamper-climate-and-fusion-simulations/",
acknowledgement = ack-nhfb,
fjournal = "Physics World",
journal-URL = "http://physicsworldarchive.iop.org/",
}
@Misc{Anonymous:2019:MCT,
author = "Anonymous",
title = "Multiprecision Computing Toolbox for {MATLAB}",
howpublished = "Web site",
day = "26",
month = sep,
year = "2019",
bibdate = "Tue Nov 05 15:46:16 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "https://www.advanpix.com/",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:2019:RMV,
author = "Anonymous",
title = "{Realtime Math v1.0} Open Sourced",
howpublished = "Web site",
day = "19",
month = jan,
year = "2019",
bibdate = "Tue Jan 22 16:00:13 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.gamedev.net/news/realtime-math-v10-open-sourced-r740/",
acknowledgement = ack-nhfb,
remark = "From the Web site: ``Realtime Math \ldots{} consists
entirely of C++11 headers, it runs almost everywhere,
it supports 64 bit floating point arithmetic, and it
sports a very permissive MIT license.''",
}
@Misc{Anonymous:2019:SOL,
author = "Anonymous",
title = "{SiSoftware} Official Live Ranker: Top Processor
Arithmetic Ranks",
howpublished = "Web site",
year = "2019",
bibdate = "Fri May 24 07:49:33 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Floating-point performance ranking of more than 94,500
CPU models.",
acknowledgement = ack-nhfb,
remark = "In May 2019, the top 15 entries were Intel Xeon
X-3175X and AMD Ryzen Threadripper CPUs.",
}
@Misc{Anonymous:2019:UFP,
author = "Anonymous",
title = "Universal floating-point instruction set architecture,
method, and language for computing directly with
decimal character sequences and binary formats in any
combination",
howpublished = "Attorney Docket No. 6324-5986",
pages = "136",
day = "14",
month = aug,
year = "2019",
bibdate = "Fri Aug 30 07:24:55 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://drive.google.com/file/d/1-gx_P5vBRppa6T3rdv8h6RNXz2Q_ILwg/view;
https://drive.google.com/file/d/1fOhVAwdhiebumKkgljKfLqyOaFpUDhQL/view",
abstract = "A universal floating-point Instruction Set
Architecture (ISA) and associated method and language.
Using a single instruction, the universal
floating-point ISA has the ability, in hardware, to
compute directly with dual decimal character sequences
up to IEEE 754-2008 ``H'' in length, without first
having to explicitly perform a
conversion-to-binary-format process in software before
computing with these human-readable floating-point or
integer representations. The ISA does not employ
opcodes, but rather pushes and pulls ``gobs'' of data
without the encumbering opcode fetch, decode, and
execute bottleneck. Instead, the ISA employs
stand-alone, memory-mapped operators, complete with
their own pipeline that is completely decoupled from
the processor's primary push-pull pipeline. The ISA
employs special three-port, 1024-bit wide SRAMS; a
special dual asymmetric system stack; memory-mapped
stand-alone hardware operators with private result
buffers having simultaneously readable side-A and
side-B read ports; and dual hardware
HconvertFromDecimalCharacter conversion operators.",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:2019:YAF,
author = "Anonymous",
title = "Yet another floating point tutorial",
howpublished = "Web site",
year = "2019",
bibdate = "Fri May 17 07:24:35 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://wordsandbuttons.online/yet_another_floating_point_tutorial.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Arnold:2019:UOD,
author = "Mark G. Arnold and Ioannis Kouretas and Vassilis
Paliouras and John R. Cowles",
title = "Under- and Overflow Detection in the Residue
Logarithmic Number System",
crossref = "Takagi:2019:ISC",
pages = "112--115",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00030",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Residue Number System (RNS) offers fast and cheap
carry-free integer arithmetic but has slow and
expensive overflow detection. The Logarithmic Number
System (LNS) offers fast real multiplication, division
and powers with floating-point-like relative precision.
The Residue Logarithmic Number System (RLNS) is a
combination of the two systems that offers advantages
for moderate-precision real applications where a-priori
analysis allows under-and overflow to be ignored. An
arithmetic hardware generator is essential because of
the mathematical obscurity of combining RNS and LNS.
Unfortunately, real applications often underflow. We
consider options to deal with under-and overflow using
the RLNSTool generator as a foundation.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; Arithmetic Generator; carry-free integer
arithmetic; Computational modeling; Delays; Digital
arithmetic; dividing circuits; expensive overflow
detection; fast carry-free integer arithmetic; floating
point arithmetic; floating-point-like relative
precision; Generators; Hardware; Hardware design
languages; LNS; moderate-precision real applications;
multiplying circuits; number theory; Overflow; Residue
Logarithmic Number System; residue number systems; RNS;
Wires",
}
@InProceedings{Arzelier:2019:EAE,
author = "Denis Arzelier and Florent Br{\'e}hard and Mioara
Joldes",
title = "Exchange Algorithm for Evaluation and Approximation
Error-Optimized Polynomials",
crossref = "Takagi:2019:ISC",
pages = "30--37",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00014",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Machine implementation of mathematical functions often
relies on polynomial approximations. The particularity
is that rounding errors occur both when representing
the polynomial coefficients on a finite number of bits,
and when evaluating it in finite precision. Hence, for
finding the best polynomial (for a given fixed degree,
norm and interval), one has to consider both types of
errors: approximation and evaluation. While efficient
algorithms were already developed for taking into
account the approximation error, the evaluation part is
usually a posteriori handled, in an ad-hoc manner.
Here, we formulate a semi-infinite linear optimization
problem whose solution is the best polynomial with
respect to the supremum norm of the sum of both errors.
This problem is then solved with an iterative exchange
algorithm, which can be seen as an extension of the
well-known Remez algorithm. A discussion and comparison
of the obtained results on different examples are
finally presented.",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; Approximation error;
approximation error; approximation error-optimized
polynomials; ARITH-26; Digital arithmetic; evaluation
error; exchange algorithm; function approximation;
Indexes; Input variables; iterative exchange algorithm;
iterative methods; learning (artificial intelligence);
libm; linear programming; machine implementation;
mathematical functions; mathematics computing;
optimisation; Optimization; polynomial approximation;
polynomial approximations; polynomial coefficients;
Programming; remez algorithm; Remez algorithm;
semi-infinite programming; semiinfinite linear
optimization problem",
}
@Misc{Bailey:2019:AM,
author = "David H. Bailey",
title = "An $ n \log (n) $ algorithm for multiplication",
howpublished = "Math Scholar blog",
day = "12",
month = apr,
year = "2019",
bibdate = "Fri Apr 12 14:14:40 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://mathscholar.org/2019/04/an-n-log-n-algorithm-for-multiplication/",
acknowledgement = ack-nhfb,
remark = "Description of research in \cite{Harvey:2019:IMT}.",
}
@InProceedings{Barthel:2019:SAM,
author = "Moritz B{\"a}rthel and Pascal Seidel and Jochen Rust
and Steffen Paul",
booktitle = "{2019 17th IEEE International New Circuits and Systems
Conference (NEWCAS)}",
title = "{SORN} Arithmetic for {MIMO} Symbol Detection ---
Exploration of the {Type-2} Unum Format",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--4",
year = "2019",
DOI = "https://doi.org/10.1109/NEWCAS44328.2019.8961226",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Beame:2019:TVN,
author = "Paul Beame and Vincent Liew",
title = "Toward Verifying Nonlinear Integer Arithmetic",
journal = j-J-ACM,
volume = "66",
number = "3",
pages = "22:1--22:??",
month = jun,
year = "2019",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/3319396",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
bibdate = "Wed Oct 23 06:51:06 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jacm.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3319396",
abstract = "We eliminate a key roadblock to efficient verification
of nonlinear integer arithmetic using CDCL SAT solvers,
by showing how to construct short resolution proofs for
many properties of the most widely used multiplier
circuits. Such short proofs were conjectured not to
exist. More precisely, we give $ n^{O (1)} $ size
regular resolution proofs for arbitrary degree $2$
identities on array, diagonal, and Booth multipliers
and $ n^{O(\log n)}$ size proofs for these identities
on Wallace tree multipliers.",
acknowledgement = ack-nhfb,
articleno = "22",
fjournal = "Journal of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@Article{Bellal:2019:IAA,
author = "R. Bellal and E. Lamini and H. Belbachir and S.
Tagzout and A. Belouchrani",
title = "Improved Affine Arithmetic-Based Precision Analysis
for Polynomial Function Evaluation",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "5",
pages = "702--712",
month = may,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2882537",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "affine arithmetic; affine arithmetic-based precision
analysis; Compounds; degree-n polynomial Horner's rule;
design phase; enhanced precision analysis; error
propagating formula; fixed point arithmetic;
Fixed-point arithmetic; fixed-point numbers; Hardware;
hardware function evaluation; hardware implementations;
hardware resources; Interpolation; iterative methods;
optimisation; Optimization; polynomial approximation;
polynomial function evaluation; polynomials; precision
analysis; quantisation (signal); Quantization (signal);
quantization error; Resource management; table lookup;
tighter upper bound error; Upper bound; VLSI systems;
word-length allocation; word-length optimization",
}
@TechReport{Blanchard:2019:MPB,
author = "Pierre Blanchard and Nicholas J. Higham and Florent
Lopez and Theo Mary and Srikara Pranesh",
title = "Mixed Precision Block Fused Multiply-Add: Error
Analysis and Application to {GPU} Tensor Cores",
type = "MIMS EPrint",
number = "2019.18",
institution = "Manchester Institute for Mathematical Sciences, School
of Mathematics, The University of Manchester",
address = "Manchester, UK",
day = "24",
month = sep,
year = "2019",
ISSN = "1749-9097",
bibdate = "Thu Dec 05 10:14:37 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://eprints.maths.manchester.ac.uk/2733/;
https://en.wikipedia.org/wiki/Bfloat16_floating-point_format",
abstract = "Computing units that carry out a fused multiply-add
(FMA) operation with matrix arguments, referred to as
tensor units by some vendors, have great potential for
use in scientific computing. However, these units are
inherently mixed precision and existing rounding error
analyses do not support them. We consider a mixed
precision block FMA that generalizes both the usual
scalar FMA and existing tensor units. We describe how
to exploit such a block FMA in the numerical linear
algebra kernels of matrix multiplication and LU
factorization and give rounding error analyses of both
kernels. An important application is to GMRES-based
iterative refinement with block FMAs, for which our
analysis provides new insight. Our framework is
applicable to the tensor core units in the NVIDIA Volta
and Turing GPUs. For these we compare matrix
multiplication and LU factorization with TC16 and TC32
forms of FMA, which differ in the precision used for
the output of the tensor cores. Our experiments on an
NVDIA V100 GPU confirm the predictions of the analysis
that the TC32 variant is much more accurate than the
TC16 one, while achieving almost the same
performance.",
acknowledgement = ack-nhfb,
keywords = "floating-point arithmetic; fused multiply-add; LU
factorization; matrix multiplication; rounding error
analysis, NVIDIA GPU; tensor cores",
}
@InProceedings{Bocco:2019:BAF,
author = "Andrea Bocco and Tiago T. Jost and Albert Cohen and
Florent de Dinechin and Yves Durand and Christian
Fabre",
booktitle = "{2019 IFIP/IEEE 27th International Conference on Very
Large Scale Integration (VLSI-SoC)}",
title = "Byte-Aware Floating-point Operations through a {UNUM}
Computing Unit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "323--328",
year = "2019",
DOI = "https://doi.org/10.1109/VLSI-SoC.2019.8920387",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bocco:2019:DPN,
author = "Andrea Bocco and Yves Durand and Florent de Dinechin",
title = "Dynamic Precision Numerics Using a Variable-Precision
{UNUM Type I HW} Coprocessor",
crossref = "Takagi:2019:ISC",
pages = "104--107",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00028",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A very large internal accumulation register has been
proposed to increase the accuracy of scientific code.
However, there is a general class of iterative kernels
where a vector of high-precision data must be saved
from one iteration to the next. Saving the large
internal accumulator to memory is impractical in such
cases. This work proposes a Variable Precision (VP)
Floating Point (FP) arithmetic co-processor
architecture based on RISC-V, which 1/ supports legacy
IEEE formats for input and output variables, 2/ uses
variable length internal registers (up to 512 bits of
mantissa) for inner loop multiply-add and 3/ supports
loads and stores of intermediate results to cache
memory with a dynamically adjustable precision (up to
256 bits of mantissa). It exploits the UNUM type I
floating point format, proposing solutions to address
some of its pitfalls such as the variable latency of
the internal operation, and the variable memory
footprint of the intermediate variables. This work is
integrated on FPGA and demonstrated on a representative
example.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; Arrays; cache storage; Computational
modeling; coprocessors; Coprocessors; dynamic Precision
numerics; field programmable gate arrays; floating
point arithmetic; floating point arithmetic
co-processor architecture; FPGA; internal accumulation
register; iterative kernels; iterative methods; Kernel;
Programming; reduced instruction set computing;
Registers; RISC-V; Variable Precision; Variable
precision, Floating-point, UNUM, Scientific computing,
Instruction set design, Hardware architecture, RISC-V,
Coprocessor, Multiple precision, FPGA, ASIC;
variable-precision UNUM Type I HW coprocessor",
}
@InProceedings{Bocco:2019:SSM,
author = "Andrea Bocco and Yves Durand and Florent de Dinechin",
title = "{SMURF}: {Scalar Multiple-precision Unum RISC-V
Floating-point} Accelerator for Scientific Computing",
crossref = "Gustafson:2019:CPC",
pages = "1:1--1:8",
year = "2019",
DOI = "https://doi.org/10.1145/3316279.3316280",
bibdate = "Mon Feb 10 09:31:49 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
URL = "https://hal.inria.fr/hal-02087098",
abstract = "This paper proposes an innovative Floating Point (FP)
architecture for Variable Precision (VP) computation
suitable for high precision FP computing, based on a
refined version of the UNUM type I format. This
architecture supports VP FP intervals where each
interval endpoint can have up to 512 bits of mantissa.
The proposed hardware architecture is pipelined and has
an internal word-size of 64 bits. Computations on
longer mantissas are performed iteratively on the
existing hardware. The prototype is integrated in a
RISC-V environment, it is exposed to the user through
an instruction set extension. The paper we provide an
example of software usage. The system has been
prototyped on a FPGA (Field-Programmable Gate Array)
platform and also synthesized for a 28nm FDSOI process
technology. The respective working frequency of FPGA
and ASIC implementations are 50MHz and 600MHz. The
estimated chip area is 1.5mm 2 and the estimated power
consumption is 95mW. The flops performance of this
architecture remains within the range of a regular
fixed-precision IEEE FPU while enabling arbitrary
precision computation at reasonable cost.",
acknowledgement = ack-nhfb,
articleno = "1",
keywords = "ASIC, UNUM, Floating-point, RISC-V, Coprocessor,
Instruction set design, Variable precision, Scientific
computing, Hardware architecture, Multiple precision,
FPGA",
}
@Article{Boghosian:2019:NPS,
author = "Bruce M. Boghosian and Peter V. Coveney and Hongyan
Wang",
title = "A New Pathology in the Simulation of Chaotic Dynamical
Systems on Digital Computers",
journal = j-ADV-THEORY-SIMUL,
pages = "1900125",
month = sep,
year = "2019",
CODEN = "ATSDCW",
DOI = "https://doi.org/10.1002/adts.201900125",
ISSN = "2513-0390",
bibdate = "Tue Sep 24 05:31:42 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also news releases
\cite{Caygill:2019:NLH,Caygill:2019:DCF,Silver:2019:CCN,Anonymous:2019:CPC,Dockrill:2019:CMH,Grossman:2019:CSC}.",
URL = "https://onlinelibrary.wiley.com/journal/25130390",
abstract = "Systematic distortions are uncovered in the
statistical properties of chaotic dynamical systems
when represented and simulated on digital computers
using standard IEEE floating-point numbers. This is
done by studying a model chaotic dynamical system with
a single free parameter $ \beta $, known as the
generalized Bernoulli map, many of whose exact
properties are known. Much of the structure of the
dynamical system is lost in the floating-point
representation. For even integer values of the
parameter, the long time behaviour is completely wrong,
subsuming the known anomalous behaviour for $ \beta = 2
$. For non-integer $ \beta $, relative errors in
observables can reach 14\%. For odd integer values of $
\beta $, floating-point results are more accurate, but
still produce relative errors two orders of magnitude
larger than those attributable to roundoff. The
analysis indicates that the pathology described, which
cannot be mitigated by increasing the precision of the
floating point numbers, is a representative example of
a deeper problem in the computation of expectation
values for chaotic systems. The findings sound a
warning about the uncritical application of numerical
methods in studies of the statistical properties of
chaotic dynamical systems, such as are routinely
performed throughout computational science, including
turbulence and molecular dynamics.",
acknowledgement = ack-nhfb,
ajournal = "Adv. Theory Simul.",
fjournal = "Advanced Theory and Simulations",
journal-URL = "https://onlinelibrary.wiley.com/journal/25130390",
remark = "This study demonstrates the perils of computing with
too few significant digits in the floating-point
representation. However, the authors report: ``Though
the root of this problem resides in the use of
finite-precision floating-point arithmetic, it cannot
be mitigated by increasing the precision of the
floating-point representation. Our analysis strongly
suggests that the pathology we describe will exhibit
for mantissa and exponent fields of any finite length
whatsoever, and for floating-point numbers encoded in
any radix whatsoever. Indeed, there is every reason to
anticipate that this anomalous behaviour is generic in
dissipative chaotic systems of the kind encountered in
turbulence and molecular dynamics, and that it is
entirely possible that many published results of
numerical simulation are substantially inaccurate for
this reason.''",
}
@Article{Borges:2019:IAH,
author = "Carlos F. Borges",
title = "An Improved Algorithm for {\tt hypot(a,b)}",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--15",
day = "14",
month = jun,
year = "2019",
bibdate = "Fri Apr 19 05:40:55 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1904.09481",
abstract = "We develop a fast and accurate algorithm for
evaluating $ \sqrt {x^2 + y^2} $ for two floating point
numbers $a$ and $b$. Library functions that perform
this computation are generally named {\tt hypot(a,b)}.
We will compare four approaches that we will develop in
this paper to the current resident library function
that is delivered with Julia 1.1 and to the code that
has been distributed with the C math library for
decades. We will demonstrate the performance of our
algorithms by simulation.",
acknowledgement = ack-nhfb,
}
@Article{Bos:2019:ACI,
author = "J. W. Bos and S. J. Friedberger",
title = "Arithmetic Considerations for Isogeny-Based
Cryptography",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "7",
pages = "979--990",
month = jul,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2851238",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "arithmetic; arithmetic considerations; arithmetic
techniques; Computer architecture; cryptographic
protocols; curve models; digital arithmetic; efficient
addition-subtraction chains; efficient arithmetic
modulo; efficient chains; elliptic curve scalar
multiplication; Elliptic curves; isogeny-based
cryptography; Montgomery curves; Montgomery reduction;
NIST; Optimization; post-quantum public-key arena;
Protocols; Public key cryptography; quadratic extension
field; scalar multiplication arithmetic; SIDH setting;
special shape; supersingular isogeny Diffie-Hellman
key-exchange protocol; systematic overview; twisted
Edwards curves",
}
@Misc{Bright:2019:CEN,
author = "Peter Bright",
title = "{\tt calc.exe} is now open source; there's surprising
depth in its ancient code. {The} actual calculation
engine is more than 20 years old",
howpublished = "Web site",
day = "7",
month = mar,
year = "2019",
bibdate = "Fri Mar 08 07:46:06 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arstechnica.com/gadgets/2019/03/calc-exe-is-now-open-source-theres-surprising-depth-in-its-ancient-code/;
https://github.com/Microsoft/calculator",
abstract = "Microsoft's embrace and adoption of open source
software has continued with the surprising decision to
publish the code for Windows Calculator and release it
on GitHub under the permissive MIT license.",
acknowledgement = ack-nhfb,
}
@Misc{Brown:2019:RCF,
author = "Erin Clare Brown",
title = "{Rust} and {C++} on Floating-point Intensive Code",
howpublished = "Web site.",
day = "19",
month = oct,
year = "2019",
bibdate = "Fri Oct 25 06:25:15 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://upshed.com/2019/10/24/rust-and-c-on-floating-point-intensive-code/",
acknowledgement = ack-nhfb,
}
@Article{Bruguera:2019:GEI,
author = "J. D. Bruguera and F. de Dinechin",
title = "{Guest Editors} Introduction: Special Section on
Computer Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "7",
pages = "951--952",
month = jul,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2918447",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Cryptography; Digital arithmetic; Mathematics;
Software algorithms; Special issues and sections",
}
@InProceedings{Burgess:2019:BPN,
author = "Neil Burgess and Jelena Milanovic and Nigel Stephens
and Konstantinos Monachopoulos and David Mansell",
title = "{Bfloat16} Processing for Neural Networks",
crossref = "Takagi:2019:ISC",
pages = "88--91",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00022",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Bfloat16 (``BF16'') is a new floating-point format
tailored specifically for high-performance processing
of Neural Networks and will be supported by major CPU
and GPU architectures as well as Neural Network
accelerators. This paper proposes a possible
implementation of a BF16 multiply-accumulation
operation that relaxes several IEEE Floating-Point
Standard features to afford low-cost hardware
implementations. Specifically, subnorms are flushed to
zero; only one non-standard rounding mode (Round-Odd)
is supported; NaNs are not propagated; and IEEE
exception flags are not provided. The paper shows that
this approach achieves the same network-level accuracy
as using IEEE single-precision arithmetic (``FP32'')
for less than half the datapath area cost and with
greater throughput.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; Artificial neural networks; BF16
multiply-accumulation operation; bfloat16 processing;
Computer architecture; CPU architectures; Digital
arithmetic; Error analysis; floating point arithmetic;
floating-point, rounding mode, neural networks; FP32;
GPU architectures; high-performance processing; IEEE
exception flags; IEEE floating-point standard features;
IEEE single-precision arithmetic; low-cost hardware
implementations; network-level accuracy; neural nets;
Neural Network accelerators; neural networks;
nonstandard rounding mode; Standards; Training",
}
@Article{Burgess:2019:HPA,
author = "N. Burgess and C. Goodyer and C. N. Hinds and D. R.
Lutz",
title = "High-Precision Anchored Accumulators for Reproducible
Floating-Point Summation",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "7",
pages = "967--978",
month = jul,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2855729",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "2-lane HPA accumulation; 3-lane reproducible FP
summation; accurate floating-point summation;
computational properties; Computer architecture;
datatype; double double accumulation; Electronic mail;
Encoding; existing FP formats; floating point
arithmetic; Floating-point addition; floating-point
numbers; floating-point summation; FP arithmetic; FP16
summations; FP32 summations; FP64 accumulations; FP64
operands; Hardware; high-precision anchored
accumulators; high-precision anchored number;
high-precision computing; HPA processing; Instruction
sets; modest ranges; programmer-selectable range;
Proposals; Registers; reproducibility; reproducible
accumulation; reproducible floating-point summation;
scalable vector extension; SVE; vector architecture;
vector processing",
}
@Article{Cappello:2019:UCL,
author = "Franck Cappello and Sheng Di and Sihuan Li and Xin
Liang and Ali Murat Gok and Dingwen Tao and Chun Hong
Yoon and Xin-Chuan Wu and Yuri Alexeev and Frederic T.
Chong",
title = "Use cases of lossy compression for floating-point data
in scientific data sets",
journal = j-IJHPCA,
volume = "33",
number = "6",
pages = "1201--1220",
day = "1",
month = nov,
year = "2019",
CODEN = "IHPCFL",
DOI = "https://doi.org/10.1177/1094342019853336",
ISSN = "1094-3420 (print), 1741-2846 (electronic)",
ISSN-L = "1094-3420",
bibdate = "Wed Oct 9 14:35:54 MDT 2019",
bibsource = "http://hpc.sagepub.com/;
https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ijsa.bib",
URL = "https://journals.sagepub.com/doi/full/10.1177/1094342019853336",
acknowledgement = ack-nhfb,
fjournal = "International Journal of High Performance Computing
Applications",
journal-URL = "https://journals.sagepub.com/home/hpc",
}
@Misc{Carlough:2019:DBF,
author = "Steven R. Carlough and Juergen Haess and Michael Klein
and Klaus M. Kroener and Petra Leber and Silvia M.
Mueller and Kerstin Schelm",
title = "Decimal and binary floating point arithmetic
calculations",
howpublished = "US Patent 10,416,962",
day = "17",
month = sep,
year = "2019",
bibdate = "Thu Oct 17 11:29:24 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US10416962B2",
abstract = "Logic is provided for performing decimal and binary
floating point arithmetic calculations on first and
second operands. The method includes: receiving the
first and second operands in packed format; unpacking
the first and second operands; swapping the first
operand to a fourth operand and the second operand to a
third operand, if an exponent of the first operand is
less than an exponent of the second operand, otherwise
storing the first operand to the third operand and the
second operand to the fourth operand; aligning the
third operand and the fourth operands based on the
exponent difference of the third and fourth operand and
a number of leading zeroes of the third operand;
performing an add/subtract operation on the aligned
third and fourth operands with normalizing and rounding
between the operands; and packing the result obtained
from the add/subtract.",
acknowledgement = ack-nhfb,
remark = "Patent filed 2 October 2015 based on British patent
GB1417582.2 of 6 October 2014, granted 17 September
2019 to IBM, expected expiration 11 January 2036 (in
17th year after grant).",
}
@InProceedings{Carmichael:2019:DPD,
author = "Zachariah Carmichael and Hamed F. Langroudi and Char
Khazanov and Jeffrey Lillie and John L. Gustafson and
Dhireesha Kudithipudi",
editor = "{IEEE}",
booktitle = "{2019 Design, Automation \& Test in Europe Conference
\& Exhibition (DATE)}",
title = "{Deep Positron}: a Deep Neural Network Using the Posit
Number System",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1421--1426",
year = "2019",
DOI = "https://doi.org/10.23919/DATE.2019.8715262",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Carmichael:2019:PET,
author = "Zachariah Carmichael and Hamed F. Langroudi and Char
Khazanov and Jeffrey Lillie and John L. Gustafson and
Dhireesha Kudithipudi",
title = "Performance-Efficiency Trade-off of Low-Precision
Numerical Formats in Deep Neural Networks",
crossref = "Gustafson:2019:CPC",
pages = "3:1--3:9",
year = "2019",
DOI = "https://doi.org/10.1145/3316279.3316282",
bibdate = "Mon Feb 10 12:11:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "3",
keywords = "machine learning, deep neural networks, floating
point, posit numerical format, DNN accelerators,
tapered precision, low-precision",
location = "Singapore, Singapore",
numpages = "9",
}
@Misc{Caygill:2019:DCF,
author = "Rebecca Caygill",
title = "Digital Computers Fail to Accurately Model Chaos
Because of Fundamental Numbers Limit",
howpublished = "University College London news release.",
day = "23",
month = sep,
year = "2019",
bibdate = "Tue Sep 24 05:29:26 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boghosian:2019:NPS}.",
URL = "https://scitechdaily.com/digital-computers-fail-to-accurately-model-chaos-because-of-fundamental-numbers-limit/",
acknowledgement = ack-nhfb,
}
@Misc{Caygill:2019:NLH,
author = "Rebecca Caygill",
title = "Numbers limit how accurately digital computers model
chaos",
howpublished = "University College London news release.",
day = "23",
month = sep,
year = "2019",
bibdate = "Tue Sep 24 05:29:26 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boghosian:2019:NPS}.",
URL = "https://www.eurekalert.org/pub_releases/2019-09/ucl-nlh092019.php",
acknowledgement = ack-nhfb,
}
@Article{Chen:2019:EIR,
author = "K. Chen and L. Chen and P. Reviriego and F. Lombardi",
title = "Efficient Implementations of Reduced Precision
Redundancy ({RPR}) Multiply and Accumulate ({MAC})",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "5",
pages = "784--790",
month = may,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2885044",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; arithmetic circuits; circuit overhead;
computational environments; critical systems; deep
machine learning; digital arithmetic; Discrete cosine
transforms; error correction; error correction
capabilities; error correction codes; implementation
overhead; learning (artificial intelligence); MAC
implementations; MAC operation; Machine learning;
matrix multiplication; Mean Square Error; mean square
error methods; modern computing systems; multiply and
accumulate; neural networks; Neural networks; object
recognition; precision copies; reduced precision
redundancy; redundancy; Redundancy; RPR
implementations; signed integer multiplication; soft
error; Soft errors; Tunneling magnetoresistance",
}
@Article{Cheng:2019:TCI,
author = "Xi Cheng and Min Zhou and Xiaoyu Song and Ming Gu and
Jiaguang Sun",
title = "Tolerating {C} Integer Error via Precision Elevation",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "2",
pages = "270--286",
month = feb,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2866388",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Feb 4 19:28:55 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "https://ieeexplore.ieee.org/document/8443077/",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Cornea:2019:NTI,
author = "Marius Cornea",
title = "New Technologies for Improved Computing",
crossref = "Takagi:2019:ISC",
pages = "96--96",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00024",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In recent years, we learned to live with a slow-down
in the growth rates predicted so far with remarkable
accuracy by Moore's law. However, this does not
necessarily mean that advancements in performance and
reduced power consumption are not possible anymore.
There will be more innovations and improvements in
processor and system architecture and microarchitecture
than before, which will enable continued growth - at
Intel, and in the industry. Intel has identified
several areas which deserve focused efforts and
investment, with the promise of providing in return
growth and results we came to expect. Manufacturing
processes constitute the first such area. Besides using
more advanced technologies to achieve smaller features
on our ICs, Intel is also introducing advanced
packaging solutions, which will enable exponential
scaling in computing density by extending transistor
placement in a third dimension. The second area is that
of processor and system architecture. Computing
architectures from Intel span most of the existing
compute spectrum, with scalar, vector, matrix, and
spatial architectures. These map roughly to our CPUs,
GPUs, accelerators, and FPGAs. Memory is at the center
of the third focus area. The memory hierarchy is
optimized by capacity, latency, bandwidth, cost, and
other features. Persistent memory and high-bandwidth
memory have been introduced relatively recently in
Intel systems, and will continue to influence the way
the memory system is structured. The interconnect is
the next important component, in a vastly heterogeneous
computing environment for almost all compute devices.
Communication has to keep up with computation capacity,
a true challenge when trillions of operations per
second are possible in many commonly used systems.
Security is the fifth focus area, where Intel has the
components to improve safety in computation and data
preservation in a world where threats increase in
number and sophistication, as seen too often recently.
Last but not least, software has a significant
potential in increasing computing capabilities. Intel
is aiming to offer a common set of tools that can
address the needs of developers for all the devices we
offer, from CPUs and GPUs, to accelerators and FPGAs.
Computer arithmetic is central to several of the areas
highlighted above. Advancements in this field will play
an important role in present as well as future
processor architectures and implementations. In
conclusion, we will also look at developments in this
area for future Intel processors.",
acknowledgement = ack-nhfb,
keywords = "accelerator; ARITH-26; Computer architecture; computer
arithmetic; computing architectures; Cornea; CPU; data
preservation; data security; Digital arithmetic;
digital arithmetic; Field programmable gate arrays;
field programmable gate arrays; FPGA; GPU; hardware
accelerators; heterogeneous computing environment;
improved computing; industrial economics; integrated
circuit manufacture; integrated circuit packaging;
manufacturing processes; memory hierarchy;
microprocessor chips; packaging solutions; Power
demand; security of data; semiconductor storage;
semiconductor technology; Systems architecture;
Technological innovation; three-dimensional integrated
circuits; transistor placement",
}
@Article{Courtois:2019:RRR,
author = "J. Courtois and L. Abbas-Turki and J. Bajard",
title = "Resilience of Randomized {RNS} Arithmetic with Respect
to Side-Channel Leaks of Cryptographic Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "12",
pages = "1720--1730",
month = dec,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2924630",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 7 11:20:24 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "CPA; DPA; ECC; Elliptic curve cryptography; Elliptic
curves; Hamming distance; Hamming weight; information
leakage; Maximum likelihood estimation; maximum
likelihood estimator; moduli randomization; Monte
Carlo; Multiprotocol label switching; Resilience; RNS;
side channel",
}
@Article{Covanov:2019:FIM,
author = "Svyatoslav Covanov and Emmanuel Thom{\'e}",
title = "Fast integer multiplication using generalized {Fermat}
primes",
journal = j-MATH-COMPUT,
volume = "88",
number = "317",
pages = "1449--1477",
month = jan,
year = "2019",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3367",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Jul 14 06:45:38 MDT 2020",
bibsource = "http://www.ams.org/mcom/2019-88-317;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "https://www.ams.org/journals/mcom/2019-88-317/S0025-5718-2018-03367-1;
https://www.ams.org/journals/mcom/2019-88-317/S0025-5718-2018-03367-1/S0025-5718-2018-03367-1.pdf;
https://www.ams.org/mathscinet/search/authors.html?authorName=Thome%2C%20Emmanuel;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=1105937",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Misc{Cowlishaw:2019:AIS,
author = "Mike Cowlishaw and David Hough",
title = "{ANSI/IEEE Std 754-2019}",
howpublished = "Web site",
day = "13",
month = jun,
year = "2019",
bibdate = "Fri Aug 30 07:30:45 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://754r.ucbtest.org/remote/background/",
abstract = "The IEEE 754-2008 standard expired in 2019, so a minor
revision was undertaken, to determine a set of
relatively non-controversial upward-compatible
editorial corrections and clarifications and minor
enhancements to the 2008 standard. 754-2019 was
approved by IEEE Standards Board on 13 June 2019 and
published in July 2019. David Hough was chair, Mike
Cowlishaw was editor. The base document was the
technical content of ANSI/IEEE Std 754-2008.
Some new operations have been recommended in 2019. In
particular, new min/max operations better match
application requirements, augmented addition,
subtraction, and multiplication operations support
building higher precision in software and support
reproducible reductions on arrays, and new operations
get and set NaN payloads. These recommended operations
might be required in a future edition of this
standard.",
acknowledgement = ack-nhfb,
}
@InProceedings{deDinechin:2019:PGB,
author = "Florent de Dinechin and Luc Forget and Jean-Michel
Muller and Yohann Uguen",
title = "Posits: The Good, the Bad and the Ugly",
crossref = "Gustafson:2019:CPC",
pages = "6:1--6:10",
year = "2019",
DOI = "https://doi.org/10.1145/3316279.3316285",
bibdate = "Mon Feb 10 12:11:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "6",
keywords = "numerical analysis, Posits, floating-point",
location = "Singapore, Singapore",
numpages = "10",
}
@InProceedings{deDinechin:2019:RYF,
author = "Florent de Dinechin",
title = "Reflections on 10 Years of {FloPoCo}",
crossref = "Takagi:2019:ISC",
pages = "187--189",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00042",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The FloPoCo open-source arithmetic core generator
project started modestly in 2008 with a few parametric
floating point cores. It has since then evolved to
become a framework for research on hardware arithmetic
cores at large. This article reviews some of the
choices made in this past decade, and some of the
challenges ahead for the next.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; arithmetic core generation; Computer
architecture; Digital arithmetic; Field programmable
gate arrays; floating point arithmetic; flopoco;
FloPoCo open-source arithmetic core generator project;
Generators; Hardware; hardware arithmetic cores;
parametric floating point cores; Tools; VHDL",
}
@InProceedings{deDinechin:2019:TBV,
author = "Florent de Dinechin and Silviu-Ioan Filip and Martin
Kumm and Luc Forget",
title = "Table-Based versus Shift-And-Add Constant Multipliers
for {FPGAs}",
crossref = "Takagi:2019:ISC",
pages = "151--158",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00037",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The multiplication by a constant is a frequently used
operation. To implement it on Field Programmable Gate
Arrays (FPGAs), the state of the art offers two
completely different methods: one relying on bit shifts
and additions/subtractions, and another one using
look-up tables and additions. So far, it was unclear
which method performs best for a given constant and
input/output data types. The main contribution of this
work is a thorough comparison of both methods in the
main application contexts of constant multiplication:
filters, signal-processing transforms, and elementary
functions. Most of the previous state of the art
addresses multiplication by an integer constant. This
work shows that, in most of these application contexts,
a formulation of the problem as the multiplication by a
real constant allows for more efficient architectures.
Another contribution is a novel extension of the
shift-and-add method to real constants. For that, an
integer linear programming (ILP) formulation is
proposed, which truncates each component in the
shift-and-add network to a minimum necessary word size
that is aligned with the approximation error of the
coefficient. All methods are implemented within the
open-source FloPoCo framework.",
acknowledgement = ack-nhfb,
keywords = "Adders; approximation theory; ARITH-26; Complexity
theory; constant multiplier, FPGA, optimization, ILP;
Field programmable gate arrays; Field Programmable Gate
Arrays; field programmable gate arrays; FPGAs;
Hardware; integer linear programming; integer
programming; linear programming; look-up tables;
multiplying circuits; shift-and-add network;
signal-processing transforms; Table lookup; table
lookup; table-based versus shift-and-add constant
multipliers; Throughput",
}
@InProceedings{Didier:2019:RAP,
author = "Laurent-Stephane Didier and Fangan-Yssouf Dosso and
Nadia {El Mrabet} and Jeremy Marrez and Pascal
V{\'e}ron",
title = "Randomization of Arithmetic Over Polynomial Modular
Number System",
crossref = "Takagi:2019:ISC",
pages = "199--206",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00048",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Polynomial Modular Number System (PMNS) is an
integer number system designed to speed up arithmetic
operations modulo a prime p. Such a system is defined
by a tuple B = (p, n, , , E) where E Z[X] and E() = 0
mod p. In a PMNS, an element a of Z/pZ is represented
by a polynomial A such that: A() = a mod p, deg A <; n
||A|| <; p. In [6], the authors mentioned that PMNS can
be highly redundant but they didn't really take
advantage of this possibility. In this paper we use,
for the first time, the redundancy of PMNS to protect
algorithms against Side Channel Attacks (SCA). More
precisely, we focus on elliptic curve cryptography. We
show how to randomize the modular multiplication in
order to be safe against existing SCA and we
demonstrate the resistance of our construction. We
describe the generation of a PMNS while guaranteeing,
for all elements of Z/pZ, the minimum number of
distinct representations we want. We also show how to
reach all these representations.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; arithmetic operations; digital arithmetic;
elliptic curve cryptography; Elliptic curve
cryptography; Elliptic curves; integer number system;
Lattices; Manganese; modular multiplication; PMNS;
polynomial modular number system; Polynomial Modular
Number System, Side Channel Countermeasure, Modular
Arithmetic; polynomials; Protocols; public key
cryptography; Resistance; side channel attacks;
Side-channel attacks",
}
@Article{Diffenderfer:2019:EAZ,
author = "James Diffenderfer and Alyson L. Fox and Jeffrey A.
Hittinger and Geoffrey Sanders and Peter G. Lindstrom",
title = "Error Analysis of {ZFP} Compression for Floating-Point
Data",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "3",
pages = "A1867--A1898",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1168832",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Thu Oct 10 06:58:05 MDT 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/3;
https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2019",
}
@InProceedings{Djath:2019:HAR,
author = "Libey Djath and Karim Bigou and Arnaud Tisserand",
title = "Hierarchical Approach in {RNS} Base Extension for
Asymmetric Cryptography",
crossref = "Takagi:2019:ISC",
pages = "46--53",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00016",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Base extension is a critical operation in RNS
implementations of asymmetric cryptosystems. In this
paper, we propose a new way to perform base extensions
using a hierarchical approach for computing the Chinese
remainder theorem. For well chosen parameters, it
significantly reduces the computational cost and still
ensures a high level of internal parallelism. We
illustrate the interest of the proposed approach on the
cost of typical arithmetic primitives used in
asymmetric cryptography. We also demonstrate
improvements in FPGA implementations of base extensions
on typical elliptic curve cryptography field sizes
using high-level synthesis tools.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; asymmetric cryptosystems; Cathode ray tubes;
Chinese remainder theorem; Computer architecture;
computer arithmetic; cryptography; Elliptic curve
cryptography; elliptic curve cryptography field sizes;
field programmable gate arrays; FPGA implementations;
hardware implementation; high level synthesis;
high-level synthesis tools; modular reduction; Parallel
processing; residue number system; residue number
systems; RNS base extension; RNS implementations;
Signal processing algorithms; Standards",
}
@Misc{Dockrill:2019:CMH,
author = "Peter Dockrill",
title = "Computers Are Making Huge Mistakes Because They Can't
Understand Chaos, Scientists Warn",
howpublished = "ScienceAlert Web site",
day = "27",
month = sep,
year = "2019",
bibdate = "Mon Sep 30 11:25:59 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boghosian:2019:NPS}.",
URL = "https://www.sciencealert.com/computers-are-making-huge-mistakes-because-they-can-t-understand-chaos-scientists-warn",
acknowledgement = ack-nhfb,
}
@InProceedings{Ensor:2019:BNB,
author = "Andrew Ensor",
title = "Big Numbers for a Big Universe",
crossref = "Takagi:2019:ISC",
pages = "99--99",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00026",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Square Kilometre Array is the world's largest
mega-Science project of the next decade aiming to build
enormous radio telescope arrays across Western
Australia and Southern Africa. With 160 TeraByte/sec
data generated in just stage one of the 50 year project
and over 260 PetaFLOPS compute requirements it presents
unprecedented data movement and processing challenges
in its correlators, the detection and timing of
pulsars, supercomputing pipelines for generating
images, and scalable middleware. This talk will outline
the project and its scientific goals, some of the key
data processing pipelines, and will discuss the
progress made by the design teams toward overcoming its
computing challenges.",
acknowledgement = ack-nhfb,
keywords = "Africa; ARITH-26; Arrays; Australia; big numbers; big
universe; computing challenges; design teams; Digital
arithmetic; generating images; High performance
computing; key data processing pipelines; mega-Science
project; middleware; parallel machines; PetaFLOPS
compute requirements; Pipelines; processing challenges;
Radio astronomy; radio telescope arrays;
radiotelescopes; scalable middleware; scientific goals;
Southern Africa; Square Kilometre Array; supercomputing
pipelines; time 50.0 year; unprecedented data movement;
Western Australia",
}
@Article{Fabiano:2019:ATW,
author = "Nicolas Fabiano and Jean-Michel Muller and Joris
Picot",
title = "Algorithms for Triple-Word Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "11",
pages = "1573--1583",
month = nov,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2918451",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 29 11:08:44 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
URL = "https://hal.archives-ouvertes.fr/hal-01869009v2",
abstract = "Triple-word arithmetic consists in representing
high-precision numbers as the unevaluated sum of three
floating-point numbers (with nonoverlapping constraints
that are explicited in the paper). We introduce and
analyze various algorithms for manipulating triple-word
numbers: rounding a triple-word number to a
floating-point number, adding, multiplying, dividing,
and computing square-roots of triple-word numbers, etc.
We compare our algorithms, implemented in the Campary
library, with other solutions of comparable accuracy.
It turns out that our new algorithms are significantly
faster than what one would obtain by just using the
usual floating-point expansion algorithms in the
special case of expansions of length 3.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Computer arithmetic, floating-point arithmetic,
triple-word arithmetic; Floating-point arithmetic;
Libraries; Lips; Memory management; Physics;
Programming; Standards",
}
@Misc{Feldman:2019:NAC,
author = "Michael Feldman",
title = "New Approach Could Sink Floating Point Computation",
howpublished = "Web site",
day = "8",
month = jul,
year = "2019",
bibdate = "Tue Jul 09 10:28:21 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.nextplatform.com/2019/07/08/new-approach-could-sink-floating-point-computation/",
acknowledgement = ack-nhfb,
remark = "Interview with John L. Gustafson on Posits (universal
numbers).",
}
@Article{Flegar:2019:FCL,
author = "Goran Flegar and Florian Scheidegger and Vedran
Novakovi{\'c} and Giovani Mariani and Andr{\'e}s E.
Tom{\'a}s and A. Cristiano I. Malossi and Enrique S.
Quintana-Ort{\'\i}",
title = "{FloatX}: A {C++} Library for Customized
Floating-Point Arithmetic",
journal = j-TOMS,
volume = "45",
number = "4",
pages = "40:1--40:??",
month = dec,
year = "2019",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3368086",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Dec 27 14:56:25 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3368086",
abstract = "We present FloatX (Float eXtended), a C ++ framework
to investigate the effect of leveraging customized
floating-point formats in numerical applications.
FloatX formats are based on binary IEEE 754 with
smaller significand and exponent bit counts specified
by the user. Among other properties, FloatX facilitates
an incremental transformation of the code, relies on
hardware-supported floating-point types as back-end to
preserve efficiency, and incurs no storage overhead.
The article discusses in detail the design principles,
programming interface, and datatype casting rules
behind FloatX. Furthermore, it demonstrates FloatX's
usage and benefits via several case studies from
well-known numerical dense linear algebra libraries,
such as BLAS and LAPACK; the Ginkgo library for sparse
linear systems; and two neural network applications
related with image processing and text recognition.",
acknowledgement = ack-nhfb,
articleno = "40",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Manual{Fog:2019:ITL,
author = "Agner Fog",
title = "4. {Instruction} tables: Lists of instruction
latencies, throughputs and micro-operation breakdowns
for {Intel}, {AMD}, and {VIA CPUs}",
organization = "Technical University of Denmark",
address = "Lyngby, Denmark",
pages = "367",
day = "15",
month = aug,
year = "2019",
bibdate = "Thu Jan 30 16:18:42 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.agner.org/optimize/instruction_tables.pdf",
acknowledgement = ack-nhfb,
remark = "This is the fourth in a series of five manuals: 1.
Optimizing software in C++: An optimization guide for
Windows, Linux and Mac platforms. 2. Optimizing
subroutines in assembly language: An optimization guide
for x86 platforms. 3. The microarchitecture of Intel,
AMD and VIA CPUs: An optimization guide for assembly
programmers and compiler makers. 4. Instruction tables:
Lists of instruction latencies, throughputs and
micro-operation breakdowns for Intel, AMD and VIA CPUs.
5. Calling conventions for different C++ compilers and
operating systems. The manuals are copyrighted from
1996 to 2019.",
}
@Article{Gallin:2019:GFP,
author = "G. Gallin and A. Tisserand",
title = "Generation of Finely-Pipelined {GF($P$P)} Multipliers
for Flexible Curve Based Cryptography on {FPGAs}",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "11",
pages = "1612--1622",
month = nov,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2920352",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 29 11:08:44 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "arithmetic operator generation; Clocks; Computer
architecture; Cryptography; elliptic curve
cryptography; Field programmable gate arrays; Hardware;
Modular arithmetic; Montgomery multiplication;
Pipelines; Tools",
}
@InProceedings{Gorodecky:2019:EIM,
author = "Danila Gorodecky and Tiziano Villa",
title = "Efficient Implementation of Modular Division by Input
Bit Splitting",
crossref = "Takagi:2019:ISC",
pages = "54--60",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00017",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Arithmetic operations, such as addition,
multiplication, division and modular division, impact
on the quality of arithmetic logic units and of the
whole processor, with respect to area and delay of the
circuit, power consumption, testability. In this
article we propose an algorithm to implement
efficiently the operation of modular division (X (mod
P)), where P is pre-selected. The proposed approach is
based on splitting the input operands into smaller
binary tuples and then minimizing in parallel the
two-level form of each suboperation on the tuples of
the decomposition. The experiments show gains in
performance and area of our approach vs. to circuits
synthesized by state-of-art EDA tools with an advantage
in delay and area up to 30 times.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; arithmetic logic units; Boolean functions;
Complexity theory; computer arithmetic, multiplication,
modular division, logic minimization; Delays; digital
arithmetic; dividing circuits; EDA tools; input bit
splitting; input operands; logic design; Minimization;
modular division; Partitioning algorithms; Power
demand; smaller binary tuples; Tools",
}
@Article{Graillat:2019:ATF,
author = "Stef Graillat and Fabienne J{\'e}z{\'e}quel and Romain
Picot and Fran{\c{c}}ois F{\'e}votte and Bruno
Lathuili{\`e}re",
title = "Auto-tuning for floating-point precision with
{Discrete Stochastic Arithmetic}",
journal = j-J-COMPUT-SCI,
volume = "36",
pages = "??--??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.jocs.2019.07.004",
ISSN = "1877-7503 (print), 1877-7511 (electronic)",
ISSN-L = "1877-7503",
MRclass = "65Y20 (65C50)",
MRnumber = "4007597",
bibdate = "Tue Sep 19 13:55:19 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S1877750318309475",
acknowledgement = ack-nhfb,
ajournal = "J. Comput. Sci.",
articleno = "101017",
fjournal = "Journal of Computational Science",
journal-URL = "https://www.sciencedirect.com/journal/journal-of-computational-science",
pagecount = "11",
}
@Misc{Grossman:2019:CSC,
author = "David Grossman",
title = "Computers Suck at Creating Chaos",
howpublished = "Popular Mechanics Web site",
day = "30",
month = sep,
year = "2019",
bibdate = "Tue Oct 01 08:57:55 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boghosian:2019:NPS}.",
URL = "https://www.popularmechanics.com/science/a29271351/computers-chaotic-systems/",
acknowledgement = ack-nhfb,
}
@Article{Gu:2019:GRM,
author = "Z. Gu and S. Li",
title = "A Generalized {RNS} {Mclaughlin} Modular
Multiplication with Non-Coprime Moduli Sets",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "11",
pages = "1689--1696",
month = nov,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2917433",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 29 11:08:44 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Digital arithmetic; Elliptic curve cryptography;
Indexes; McLaughlin modular multiplication;
Microelectronics; Montgomery modular multiplication;
Performance evaluation; Residue number systems",
}
@Article{Han:2019:FFE,
author = "Dong Han and Shengyuan Zhou and Tian Zhi and Yibo Wang
and Shaoli Liu",
title = "{Float-Fix}: An Efficient and Hardware-Friendly Data
Type for Deep Neural Network",
journal = j-INT-J-PARALLEL-PROG,
volume = "47",
number = "3",
pages = "345--359",
month = jun,
year = "2019",
CODEN = "IJPPE5",
DOI = "https://doi.org/10.1007/s10766-018-00626-7",
ISSN = "0885-7458 (print), 1573-7640 (electronic)",
ISSN-L = "0885-7458",
bibdate = "Fri Oct 11 08:37:52 MDT 2019",
bibsource = "http://link.springer.com/journal/10766/47/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjparallelprogram.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Parallel Programming",
journal-URL = "http://link.springer.com/journal/10766",
}
@Article{Hanuman:2019:IMP,
author = "C. R. S. Hanuman and J. Kamala and A. R. Aruna",
title = "Implementation of multi-precision floating point
divider for high speed signal processing applications",
journal = j-J-SUPERCOMPUTING,
volume = "75",
number = "9",
pages = "6038--6054",
month = sep,
year = "2019",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-019-02902-w",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Thu Oct 10 15:31:22 MDT 2019",
bibsource = "http://link.springer.com/journal/11227/75/9;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
acknowledgement = ack-nhfb,
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Misc{Harthcock:2019:BUF,
author = "Jerry D. Harthcock",
title = "{64-bit-Universal-Floating-Point-ISA-Compute-Engine}",
howpublished = "Github Web site.",
day = "8",
month = oct,
year = "2019",
bibdate = "Wed Oct 09 05:34:48 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://github.com/jerry-D/64-bit-Universal-Floating-Point-ISA-Compute-Engine",
abstract = "New 64-bit Universal Floating-Point ISA Compute Engine
computes directly with human-readable decimal character
sequences, binary64, 32, 16 or bfloat16 formatted
numbers in any combination.",
acknowledgement = ack-nhfb,
}
@Article{Harvey:2019:FIM,
author = "David Harvey and Joris van der Hoeven",
title = "Faster integer multiplication using plain vanilla
{FFT} primes",
journal = j-MATH-COMPUT,
volume = "88",
number = "315",
pages = "501--514",
month = jul,
year = "2019",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3328",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Jul 14 06:45:34 MDT 2020",
bibsource = "http://www.ams.org/mcom/2019-88-315;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "https://www.ams.org/journals/mcom/2019-88-315/S0025-5718-2018-03328-2;
https://www.ams.org/journals/mcom/2019-88-315/S0025-5718-2018-03328-2/S0025-5718-2018-03328-2.pdf;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=621578;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=734771",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@TechReport{Harvey:2019:IMT,
author = "David Harvey and Joris {Van Der Hoeven}",
title = "Integer multiplication in time {$ O(n \log n) $}",
type = "Report",
number = "hal-02070778",
institution = "School of Mathematics and Statistics, University of
New South Wales, and CNRS, Laboratoire d'informatique,
{\'E}cole polytechnique",
address = "Sydney, NSW 2052, Australia and 91128 Palaiseau,
France",
day = "18",
month = mar,
year = "2019",
bibdate = "Fri Apr 12 14:09:18 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.archives-ouvertes.fr/hal-02070778/document",
abstract = "We present an algorithm that computes the product of
two $n$-bit integers in $ O(n \log n)$ bit
operations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hayes:2019:DCB,
author = "Ari B. Hayes and Fei Hua and Jin Huang and Yanhao Chen
and Eddy Z. Zhang",
editor = "Mahmut Taylan Kandemir and Alexandra Jimborean and
Tipp Moseley",
booktitle = "{CGO'19: Proceedings of the 2019 IEEE\slash ACM
International Symposium on Code Generation and
Optimization, 16--20 February 2019, Washington, DC,
USA}",
title = "Decoding {CUDA} Binary",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xv + 287",
pages = "229--241",
year = "2019",
DOI = "https://doi.org/10.1109/cgo.2019.8661186",
ISBN = "1-72811-436-5, 1-72811-437-3",
ISBN-13 = "978-1-72811-436-1, 978-1-72811-437-8",
LCCN = "QA76.76.G46 I57 2019",
bibdate = "Mon Sep 11 06:57:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number CFP19CGO-ART.",
URL = "https://ieeexplore.ieee.org/document/8661186",
abstract = "NVIDIA's software does not offer translation of
assembly code to binary for their GPUs, since the
specifications are closed-source. This work fills that
gap. We develop a systematic method of decoding the
Instruction Set Architectures (ISAs) of NVIDIA's GPUs,
and generating assemblers for different generations of
GPUs. Our framework enables cross-architecture binary
analysis and transformation. Making the ISA accessible
in this manner opens up a world of opportunities for
developers and researchers, enabling numerous
optimizations and explorations that are unachievable at
the source-code level. Our infrastructure has already
benefited and been adopted in important applications
including performance tuning, binary instrumentation,
resource allocation, and memory protection.",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1109/CGO46174.2019",
}
@InProceedings{Henry:2019:LBA,
author = "Greg Henry and Ping Tak Peter Tang and Alexander
Heinecke",
title = "Leveraging the bfloat16 Artificial Intelligence
Datatype For Higher-Precision Computations",
crossref = "Takagi:2019:ISC",
pages = "69--76",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00019",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In recent years fused-multiply-add (FMA) units with
lower-precision multiplications and higher-precision
accumulation have proven useful in machine
learning/artificial intelligence applications, most
notably in training deep neural networks due to their
extreme computational intensity. Compared to classical
IEEE-754 32 bit (FP32) and 64 bit (FP64) arithmetic,
these reduced precision arithmetic can naturally be
sped up disproportional to their shortened width. The
common strategy of all major hardware vendors is to
aggressively further enhance their performance
disproportionately. One particular FMA operation that
multiplies two BF16 numbers while accumulating in FP32
has been found useful in deep learning, where BF16 is
the 16-bit floating point datatype with IEEE FP32
numerical range but 8 significant bits of precision. In
this paper, we examine the use this FMA unit to
implement higher-precision matrix routines in terms of
potential performance gain and implications on
accuracy. We demonstrate how a decomposition into
multiple smaller datatypes can be used to assemble a
high-precision result, leveraging the higher precision
accumulation of the FMA unit. We first demonstrate that
computations of vector inner products and by natural
extension, matrix-matrix products can be achieved by
decomposing FP32 numbers in several BF16 numbers
followed by appropriate computations that can
accommodate the dynamic range and preserve accuracy
compared to standard FP32 computations, while
projecting up to 5.2x speed-up. Furthermore, we examine
solution of linear equations formulated in the residual
form that allows for iterative refinement. We
demonstrate that the solution obtained to be comparable
to those offered by FP64 under a large range of linear
system condition numbers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; artificial intelligence datatype; bfloat16,
float16, mixed precision, combined datatypes; Deep
learning; deep learning; deep neural networks; floating
point arithmetic; floating point datatype; FMA unit;
FP32 computations; fused-multiply-add units; Hardware;
higher-precision matrix routines; IEEE-754 32 bit
arithmetic; IEEE-754 FP32 arithmetic; IEEE-754 FP64
arithmetic; iterative methods; learning (artificial
intelligence); matrix algebra; Matrix decomposition;
matrix-matrix products; neural nets; Neural networks;
Standards; Task analysis; Training",
}
@Article{Hiasat:2019:DRI,
author = "Ahmad Hiasat and Leonel Sousa",
title = "On the Design of {RNS} Inter-Modulo Processing Units
for the Arithmetic-Friendly Moduli Sets $ 2^{n + k} $,
$ 2^n - 1 $, $ 2^{n + 1} - 1 $",
journal = j-COMP-J,
volume = "62",
number = "2",
pages = "292--300",
day = "1",
month = feb,
year = "2019",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxy119",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Mon Feb 11 10:50:41 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://academic.oup.com/comjnl/article/62/2/292/5224762",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "Residue Number System (RNS)",
}
@InProceedings{Hickmann:2019:EAM,
author = "Brian Hickmann and Dennis Bradford",
title = "Experimental Analysis of Matrix Multiplication
Functional Units",
crossref = "Takagi:2019:ISC",
pages = "116--119",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00031",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The rapid growth of AI has led to the introduction of
several new hardware designs to accelerate the matrix
multiplication operation at the heart of AI
applications. Examples include NVIDIA's Tensor Core*,
Google's TPU*, and Intel's Neural Compute Stick*.
However, the IEEE 754 standard gives significant
implementation-specific flexibility in the definition
of the matrix multiplication operation and the
precision and compatibility of these new accelerators
is not well documented. This paper describes a method
exploiting the rounding modes and other features of the
IEEE 754 standard in order to gain deeper insight into
the design and functionality of matrix multiplication
units. We apply this method to the NVIDIA V100 GPU
Tensor Core* units and report our findings on the
design properties and micro-architecture.",
acknowledgement = ack-nhfb,
keywords = "AI applications; ARITH-26; Deep learning; Google TPU;
Graphics processing units; Hardware; hardware designs;
IEEE 754 standard; IEEE standards;
implementation-specific flexibility; Intel Neural
Compute Stick; learning (artificial intelligence);
Machine learning, deep learning, tensor, half
precision, single precision, Volta, matrix
multiplication; mathematics computing; matrix
multiplication; matrix multiplication functional units;
matrix multiplication units; Microarchitecture; neural
nets; NVIDIA Tensor Core; NVIDIA V100 GPU Tensor Core
units; Standards; Testing",
}
@Article{Higham:2019:NAP,
author = "Nicholas J. Higham and Theo Mary",
title = "A New Approach to Probabilistic Rounding Error
Analysis",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "5",
pages = "A2815--A2835",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1226312",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Tue Nov 5 05:24:19 MST 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/5;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "floating-point arithmetic; MATLAB; numerical linear
algebra; rounding error analysis",
onlinedate = "January 2019",
}
@Article{Higham:2019:SLP,
author = "Nicholas J. Higham and Srikara Pranesh",
title = "Simulating Low Precision Floating-Point Arithmetic",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "5",
pages = "C585--C602",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/19M1251308",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Tue Nov 5 05:24:19 MST 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/5;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "bfloat16; bit flips; directed rounding; floating-point
arithmetic; fp16; half precision; IEEE arithmetic; low
precision; MATLAB; mixed precision; round to nearest;
rounding error analysis; simulation; stochastic
rounding; subnormal numbers",
onlinedate = "January 2019",
}
@Article{Higham:2019:SMH,
author = "Nicholas J. Higham and Srikara Pranesh and Mawussi
Zounon",
title = "Squeezing a Matrix into Half Precision, with an
Application to Solving Linear Systems",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "4",
pages = "A2536--A2551",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1229511",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Thu Oct 10 06:58:08 MDT 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/4;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "diagonal scaling; fp16; GMRES; half precision
arithmetic; iterative refinement; linear system;
MATLAB; mixed precision; overflow; preconditioning;
subnormal numbers; underflow",
onlinedate = "January 2019",
}
@Article{Horyachyy:2019:SEF,
author = "Oleh Horyachyy and Leonid Moroz and Viktor Otenko",
title = "Simple Effective Fast Inverse Square Root Algorithm
with Two Magic Constants",
journal = "International Journal of Computing",
volume = "18",
number = "4",
pages = "461--470",
month = dec,
year = "2019",
ISSN = "1727-6209 (print), 2312-5381 (electronic)",
ISSN-L = "1727-6209",
bibdate = "Thu Feb 11 11:01:47 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.computingonline.net/computing/article/view/1616;
https://www.researchgate.net/publication/349173096_SIMPLE_EFFECTIVE_FAST_INVERSE_SQUARE_ROOT_ALGORITHM_WITH_TWO_MAGIC_CONSTANTS",
acknowledgement = ack-nhfb,
keywords = "FISR algorithm; floating-point arithmetic; FMA
function; Householder.; IEEE 754 standard; initial
approximation; inverse square root; magic constant;
maximum relative error; Newton-Raphson",
}
@Article{Hough:2019:ISO,
author = "David G. Hough",
title = "The {IEEE Standard 754}: One for the History Books",
journal = j-COMPUTER,
volume = "52",
number = "12",
pages = "109--112",
month = dec,
year = "2019",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/MC.2019.2926614",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Fri Nov 29 06:16:06 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/ieee-computer.pdf;
https://www.computer.org/csdl/magazine/co/2019/12/08909942/1f8KFWxbTCU",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
keywords = "Floating-point arithmetic; Hardware; History; IEEE
Standards; Microprocessors; Software",
}
@Article{Hrycak:2019:AEC,
author = "Tomasz Hrycak and Sebastian Schmutzhard",
title = "Accurate evaluation of {Chebyshev} polynomials in
floating-point arithmetic",
journal = j-BIT-NUM-MATH,
volume = "59",
number = "2",
pages = "403--416",
month = jun,
year = "2019",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-018-0738-5",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Fri Sep 6 09:16:11 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/article/10.1007/s10543-018-0738-5",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Book{IEEE-754:2019:ISF,
author = "{IEEE-754}",
title = "{IEEE 754-2019, Standard for Floating-Point
Arithmetic}",
publisher = pub-IEEE-STD,
address = pub-IEEE-STD:adr,
pages = "82",
day = "13",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/IEEESTD.2019.876622",
ISBN = "1-5044-5925-3 (print), 1-5044-5924-5 (e-PDF)",
ISBN-13 = "978-1-5044-5925-9 (print), 978-1-5044-5924-2 (e-PDF)",
bibdate = "Tue Nov 05 08:49:56 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeestd.bib",
abstract = "This standard specifies interchange and arithmetic
formats and methods for binary and decimal
floating-point arithmetic in computer programming
environments. This standard specifies exception
conditions and their default handling. An
implementation of a floating-point system conforming to
this standard may be realized entirely in software,
entirely in hardware, or in any combination of software
and hardware. For operations specified in the normative
part of this standard, numerical results and exceptions
are uniquely determined by the values of the input
data, sequence of operations, and destination formats,
all under user control.",
acknowledgement = ack-nhfb,
}
@Misc{IEEE:2019:PDA,
author = "{IEEE}",
title = "{P754/D2.50, Apr 2019 --- IEEE Approved Draft Standard
for Floating-Point Arithmetic: Revision of IEEE Std
754-2008}",
howpublished = "Web site",
month = apr,
year = "2019",
bibdate = "Thu Jun 20 15:39:16 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/document/8739150",
abstract = "This standard specifies interchange and arithmetic
formats and methods for binary and decimal
floating-point arithmetic in computer programming
environments. This standard specifies exception
conditions and their default handling. An
implementation of a floating-point system conforming to
this standard may be realized entirely in software,
entirely in hardware, or in any combination of software
and hardware. For operations specified in the normative
part of this standard, numerical results and exceptions
are uniquely determined by the values of the input
data, sequence of operations, and destination formats,
all under user control.",
acknowledgement = ack-nhfb,
}
@InProceedings{Jaberipur:2019:MPP,
author = "Ghassem Jaberipur and Sahar {Moradi Cherati}",
title = "Modulo-$ (2 n + 3) $ Parallel Prefix Addition via
Diminished-3 Representation of Residues",
crossref = "Takagi:2019:ISC",
pages = "135--142",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00035",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Diminished-1 (D1) representation of modulo-(2n + 1)
residues in [1, 2n] uses the n-bit codes [0, 2n - 1]
and maintains a zero-indicator bit. Such D1 encoding
has led to efficient parallel prefix modulo-(2n + 1)
adders that perform as fast as the companion modulo-(2n
- 1) and -2n adders with (3 + 2 log n) delay, where
denotes the delay of a simple 2-input gate. Also
similar, but slower (i.e., with one more delay) and
slightly more complex, parallel prefix architectures
have been offered for modulo-(2n - 3) adders. On the
other hand, reverse conversion schemes for 4and
5-moduli sets that include conjugate moduli pairs 2n
\pm 1 and 2n \pm 3 are already available, while we have
not encountered any efficient modulo(2n + 3) adder.
Therefore, in this paper, we offer the diminished-3
(D3) representation of modulo-(2n + 3) residues that
maps the residue interval [3, 2n + 2] to [0, 2n - 1]
and maintains a 2-bit {0,1, 2}-indicator. The
corresponding parallel prefix adder, which performs as
fast as the fastest previous modulo-(2n - 3) adder is
designed, where a 3-way compound architecture is
devised as the bulk of modular addition that yields
sum, sum+1, and sum+2. The proposed architecture is
fully synthesized via Synopsis Design Compiler and
tested for correctness, and its figures of merit
compared with modulo(2n - 3) and -(2n + 1) adders.",
acknowledgement = ack-nhfb,
keywords = "3-way compound architecture; adders; Adders; ARITH-26;
complex prefix architectures; Compounds; Computer
architecture; Computer science; D1 representation; D3
representation; Delays; Digital arithmetic;
Diminished-1 representation; diminished-3
representation; Encoding; logic design; Modulo-(2n+3)
parallel prefix addition; modulo-(2n-3) adders;
parallel prefix adder; Residue Number System, Parallel
Prefix Adder, Diminished-1, Diminished 3, 3-way
compound adder; residue number systems; simple 2-input
gate; Synopsis Design Compiler; zero-indicator bit",
}
@Article{Jaiswal:2019:PHP,
author = "Manish Kumar Jaiswal and Hayden K.-H. So",
title = "{PACoGen}: a Hardware Posit Arithmetic Core
Generator",
journal = j-IEEE-ACCESS,
volume = "7",
pages = "74586--74601",
year = "2019",
DOI = "https://doi.org/10.1109/access.2019.2920936",
ISSN = "2169-3536",
ISSN-L = "2169-3536",
bibdate = "Thu Dec 14 18:07:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Access",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}
@Article{Jia:2019:DNT,
author = "Zhe Jia and Marco Maggioni and Jeffrey Smith and
Daniele Paolo Scarpazza",
title = "Dissecting the {NVidia Turing T4 GPU} via
Microbenchmarking",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "65",
day = "18",
month = mar,
year = "2019",
DOI = "https://doi.org/10.48550/ARXIV.1903.07486",
bibdate = "Mon Sep 11 07:00:16 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/1903.07486",
abstract = "In 2019, the rapid rate at which GPU manufacturers
refresh their designs, coupled with their reluctance to
disclose microarchitectural details, is still a hurdle
for those software designers who want to extract the
highest possible performance. Last year, these very
reasons motivated us to dissect the Volta GPU
architecture using microbenchmarks.\par
The introduction in August 2018 of Turing, NVidia's
latest architecture, pressed us to update our study. In
this report, we examine Turing and compare it
quantitatively against previous NVidia GPU generations.
Specifically, we study the T4 GPU: a low-power board
aiming at inference applications. We describe its
improvements against its inference-oriented
predecessor: the P4 GPU based on the Pascal
architecture. Both T4 and P4 GPUs achieve significantly
higher frequency-per-Watt figures than their full-size
counterparts.\par
We study the performance of the T4's TensorCores,
finding a much higher throughput on low-precision
operands than on the P4 GPU. We reveal that Turing
introduces new instructions that express matrix math
more succinctly. We map Turing's instruction space,
finding the same encoding as Volta, and additional
instructions. We reveal that the Turing TU104 chip has
the same memory hierarchy depth as the Volta GV100;
cache levels sizes on the TU104 are frequently twice as
large as those found on the Pascal GP104. We benchmark
each constituent of the T4 memory hierarchy and find
substantial overall performance improvements over its
P4 predecessor. We studied how clock throttling affects
compute-intensive workloads that hit power or thermal
limits.\par
Many of our findings are novel, published here for the
first time. All of them can guide high-performance
software developers get closer to the GPU's peak
performance.",
acknowledgement = ack-nhfb,
}
@Article{Jiang:2019:LPU,
author = "H. Jiang and L. Liu and F. Lombardi and J. Han",
title = "Low-Power Unsigned Divider and Square Root Circuit
Designs Using Adaptive Approximation",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "11",
pages = "1635--1646",
month = nov,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2916817",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 29 11:08:44 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adaptive approximation; Circuit synthesis; Delays;
divider; Error correction; Hardware; image processing;
Image reconstruction; low-power; overflow; Power
dissipation; SQR circuit",
}
@InProceedings{Johansson:2019:FAP,
author = "Fredrik Johansson",
title = "Faster Arbitrary-Precision Dot Product and Matrix
Multiplication",
crossref = "Takagi:2019:ISC",
pages = "15--22",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00012",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present algorithms for real and complex dot product
and matrix multiplication in arbitrary-precision
floating-point and ball arithmetic. A low-overhead dot
product is implemented on the level of GMP limb arrays;
it is about twice as fast as previous code in MPFR and
Arb at precision up to several hundred bits. Up to 128
bits, it is 3-4 times as fast, costing 20-30 cycles per
term for floating-point evaluation and 40-50 cycles per
term for balls. We handle large matrix multiplications
even more efficiently via blocks of scaled integer
matrices. The new methods are implemented in Arb and
significantly speed up polynomial operations and linear
algebra.",
acknowledgement = ack-nhfb,
keywords = "arbitrary-precision arithmetic, ball arithmetic, dot
product, matrix multiplication; arbitrary-precision dot
product; arbitrary-precision floating-point; ARITH-26;
ball arithmetic; complex dot product; Costing; Digital
arithmetic; floating point arithmetic; floating-point
evaluation; GMP limb arrays; Indexes; Libraries; Linear
algebra; linear algebra; low-overhead dot product;
mathematics computing; matrix multiplication;
polynomial operations; polynomials; real dot product;
scaled integer matrices; Software; Upper bound; word
length 128.0 bit",
}
@InProceedings{Jugade:2019:MEE,
author = "Chaitanya Jugade and Deepak Ingole and Dayaram
Sonawane and Michal Kvasnica and John Gustafson",
editor = "{IEEE}",
booktitle = "{2019 Sixth Indian Control Conference (ICC)}",
title = "A Memory-Efficient Explicit Model Predictive Control
using Posits",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "188--193",
year = "2019",
DOI = "https://doi.org/10.1109/ICC47138.2019.9123179",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Kalamkar:2019:SBD,
author = "Dhiraj D. Kalamkar and Dheevatsa Mudigere and Naveen
Mellempudi and Dipankar Das and Kunal Banerjee and
Sasikanth Avancha and Dharma Teja Vooturi and Nataraj
Jammalamadaka and Jianyu Huang and Hector Yuen and
Jiyan Yang and Jongsoo Park and Alexander Heinecke and
Evangelos Georganas and Sudarshan Srinivasan and
Abhisek Kundu and Misha Smelyanskiy and Bharat Kaul and
Pradeep Dubey",
title = "A Study of {BFLOAT16} for Deep Learning Training",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--10",
day = "29",
month = may,
year = "2019",
bibdate = "Fri Aug 30 17:25:53 2019",
bibsource = "DBLP archive;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://arxiv.org/abs/1905.12322",
abstract = "This paper presents the first comprehensive empirical
study demonstrating the efficacy of the Brain Floating
Point (BFLOAT16) half-precision format for Deep
Learning training across image classification, speech
recognition, language modeling, generative networks and
industrial recommendation systems. BFLOAT16 is
attractive for Deep Learning training for two reasons:
the range of values it can represent is the same as
that of IEEE 754 floating-point format (FP32) and
conversion to/from FP32 is simple. Maintaining the same
range as FP32 is important to ensure that no
hyper-parameter tuning is required for convergence;
e.g., IEEE 754 compliant half-precision floating point
(FP16) requires hyper-parameter tuning. In this paper,
we discuss the flow of tensors and various key
operations in mixed precision training, and delve into
details of operations, such as the rounding modes for
converting FP32 tensors to BFLOAT16. We have
implemented a method to emulate BFLOAT16 operations in
Tensorflow, Caffe2, IntelCaffe, and Neon for our
experiments. Our results show that deep learning
training using BFLOAT16 tensors achieves the same
state-of-the-art (SOTA) results across domains as FP32
tensors in the same number of iterations and with no
changes to hyper-parameters.",
acknowledgement = ack-nhfb,
biburl = "https://dblp.org/rec/bib/journals/corr/abs-1905-12322",
eprint = "1905.12322",
timestamp = "Wed Jan 3 07:58:16 2024",
}
@InProceedings{Katajainen:2019:HMP,
author = "Jyrki Katajainen",
editor = "I. Kotsireas and P. Pardalos and K. Parsopoulos and D.
Souravlias and A. Tsokas",
booktitle = "Analysis of Experimental Algorithms. {SEA 2019}",
title = "Hacker's Multiple-Precision Integer-Division Program
in Close Scrutiny",
publisher = pub-SV,
address = pub-SV:adr,
pages = "376--391",
year = "2019",
DOI = "https://doi.org/10.1007/978-3-030-34029-2_25",
bibdate = "Thu Jan 28 19:43:12 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
URL = "http://www.cphstl.dk/Paper/Division/division.pdf",
abstract = "Before the era of ubiquitous computers, the
long-division method was presented in primary schools
as a paper-and-pencil technique to do whole-number
division. In the book \booktitle{Hacker's Delight} by
Warren [2nd edition, 2013], an implementation of this
algorithm was given using the C programming language.
In this paper we will report our experiences when
converting this program to a generic program-library
routine.\par
The highlights of the paper are as follows: (1) We
describe the long-division algorithm this is done for
educational purposes. (2) We outline its implementation
the goal is to show how to use modern C++ to achieve
flexibility, portability, and efficiency. (3) We
analyse its computational complexity by paying
attention to how the digit width affects the running
time. (4) We compare the practical performance of the
library routine against Warren's original. It is
pleasure to announce that the library routine is
faster. (5) We release the developed routine as part of
a software package that provides fixed-width integers
of arbitrary length, e.g. a number of type Open image
in new window has 2019 bits and it supports the same
operations with the same semantics as a number of type
{\tt unsigned int}",
acknowledgement = ack-nhfb,
keywords = "Algorithm; Description; Experimentation;
Implementation; Long division; Meticulous analysis;
Multiple-precision arithmetic; Software library",
ORCID-numbers = "Katajainen, Jyrki/0000-0002-7714-5588",
}
@InProceedings{Kaul:2019:OFF,
author = "Himanshu Kaul and Mark Anders and Sanu Mathew and
Seongjong Kim and Ram Krishnamurthy",
title = "Optimized Fused Floating-Point Many-Term Dot-Product
Hardware for Machine Learning Accelerators",
crossref = "Takagi:2019:ISC",
pages = "84--87",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00021",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper describes optimizations for the critical
maximum exponent and alignment operations, with
scalability for many-term fused floating-point
dot-product units. The impact of these optimizations is
quantified for up to 32-term BFloat16 weight/activation
inputs with single-precision dot-product output,
targeted for machine learning accelerators. Area and
energy efficiency results are compared across
performance targets, design parameters, and data
statistics.",
acknowledgement = ack-nhfb,
keywords = "32-term BFloat16 weight inputs; Adders; alignment
operation; ARITH-26; Computer architecture; critical
maximum exponent operation; deep neural networks;
dot-product; Energy efficiency; floating point
arithmetic; floating-point; Hardware; learning
(artificial intelligence); Machine learning; machine
learning; machine learning accelerators; neural nets;
Optimization; optimized fused floating-point many-term
dot-product hardware; single-precision dot-product
output; Throughput",
}
@InProceedings{Kim:2019:CEI,
author = "HyunJin Kim and Min Soo Kim and Alberto A. {Del
Barrio} and Nader Bagherzadeh",
title = "A Cost-Efficient Iterative Truncated Logarithmic
Multiplication for Convolutional Neural Networks",
crossref = "Takagi:2019:ISC",
pages = "108--111",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00029",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper proposes a cost-efficient approximate
logarithmic multiplication for convolutional neural
networks (CNNs), where two truncated logarithmic
multipliers are connected for error correction. The
proposed iterative logarithmic multiplication achieves
low and unbiased average error while the hardware cost
is significantly reduced by utilizing the truncated
Mitchell multiplier and approximating error terms from
the first stage. The proposed design has error
characteristics that are suitable for neural network
inferences, and the experiments on contemporary CNNs
show that the proposed multiplier does not cause
significant degradation on accuracy compared to exact
multiplication.",
acknowledgement = ack-nhfb,
keywords = "Adders; approximate multiplier; ARITH-26;
convolutional neural nets; convolutional neural
network; convolutional neural networks; Convolutional
neural networks; cost-efficient approximate logarithmic
multiplication; Delays; Detectors; Digital arithmetic;
error correction; Hardware; iterative methods;
iterative truncated logarithmic multiplication;
logarithmic multiplication; Mitchell multiplier; neural
network inferences; truncated logarithmic multipliers;
truncated Mitchell multiplier",
}
@Article{Kim:2019:EMA,
author = "M. S. Kim and A. A. D. Barrio and L. T. Oliveira and
R. Hermida and N. Bagherzadeh",
title = "Efficient {Mitchell}'s Approximate Log Multipliers for
Convolutional Neural Networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "5",
pages = "660--675",
month = may,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2880742",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "approximate log multipliers; Approximation algorithms;
approximation theory; Arithmetic and logic units; CNN;
computer vision; convolutional neural nets;
convolutional neural networks; Convolutional neural
networks; customizable design; customizable log
multiplier; Degradation; design techniques; efficient
shift amount calculation; Energy consumption; energy
consumption reduction; energy-efficient approximate
multipliers; exact zero computation; floating point
arithmetic; fully-parallel LOD; ImageNet ILSVRC2012
dataset; Logic gates; low-power design; machine
learning; multiplying circuits; object recognition;
power aware computing; probability; Training",
}
@InProceedings{Klower:2019:PAF,
author = "Milan Kl{\"o}wer and Peter D. D{\"u}ben and Tim N.
Palmer",
title = "Posits as an Alternative to Floats for Weather and
Climate Models",
crossref = "Gustafson:2019:CPC",
pages = "1:1--1:8",
year = "2019",
DOI = "https://doi.org/10.1145/3316279.3316281",
bibdate = "Mon Feb 10 12:11:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "2",
keywords = "Computational fluid dynamics, floating point, computer
arithmetic, posits, reduced precision, climate
projections, weather forecast",
location = "Singapore, Singapore",
numpages = "8",
}
@InProceedings{Kostic:2019:UNV,
author = "Dusan Kostic and Shay Gueron",
title = "Using the New {VPMADD} Instructions for the New Post
Quantum Key Encapsulation Mechanism {SIKE}",
crossref = "Takagi:2019:ISC",
pages = "215--218",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00050",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper demonstrates the use of new processor
instructions VPMADD, intended to appear in the coming
generation of Intel processors (codename ``Cannon
Lake''), in order to accelerate the newly proposed key
encapsulation mechanism (KEM) named SIKE. SIKE is one
of the submissions to the NIST standardization process
on post-quantum cryptography, and is based on
pseudo-random walks in supersingular isogeny graphs.
While very small keys are the main advantage of SIKE,
its extreme computational intensiveness makes it one of
the slowest KEM proposals. Performance optimizations
are needed. We address here the ``Level 1'' parameters
that target 64-bit quantum security, and deemed
sufficient for the NIST standardization effort. Thus,
we focus on SIKE503 that operates over Fp2 with a
503-bit prime p. These short operands pose a
significant challenge on using VPMADD effectively. We
demonstrate several optimization methods to accelerate
Fp, Fp2, and the elliptic curve arithmetic, and predict
a potential speedup by a factor of 1.72x.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; codename CannonLake; Computer architecture;
Encapsulation; extreme computational intensiveness;
Intel processors; KEM proposals; key encapsulation
mechanism; NIST; NIST standardization effort; NIST
standardization process; Optimization; post quantum key
encapsulation mechanism SIKE; post-quantum
cryptography; processor instructions VPMADD; Proposals;
pseudorandom walks; Quantum computing; quantum
cryptography; quantum security; Registers; SIKE503;
supersingular isogeny graphs; VPMADD instructions;
VPMADD processor instructions, software optimization,
post quantum cryptography, supersingular isogeny",
}
@InProceedings{Kouya:2019:PEE,
author = "Tomonori Kouya",
title = "Performance Evaluation of an Efficient Double-Double
{BLAS1} Function With Error-Free Transformation and its
Application to Explicit Extrapolation Methods",
crossref = "Takagi:2019:ISC",
pages = "120--123",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00032",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Error-free transformation (EFT) has been recently
applied to solve ill-conditioned problems. This
transformation can reduce the number of arithmetic
operations required compared to multiple precision
arithmetic. In this study, we implement double-double
(DD) BLAS1 functions with EFT and propose the
application of the approach to explicit extrapolation
methods for solving initial value problems of ordinary
differential equations (ODEs). The presented routines
can be effective for a large system of linear ODEs,
especially when a harmonic sequence is used.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; arithmetic operations; BLAS1 functions;
Convergence; differential equations; efficient
double-double BLAS1 function; EFT; error-free
transformation; error-free transformation,
extrapolation, ordinary differential equation; explicit
extrapolation methods; extrapolation; Extrapolation;
floating point arithmetic; Harmonic analysis; harmonic
sequence; ill-conditioned problems; initial value
problems; Libraries; mathematics computing; multiple
precision arithmetic; ordinary differential equations;
performance evaluation; Silicon; Standards",
}
@Article{Kulisch:2019:MSI,
author = "Ulrich Kulisch",
title = "Mathematics and Speed for Interval Arithmetic: A
Complement to {IEEE 1788}",
journal = j-TOMS,
volume = "45",
number = "1",
pages = "5:1--5:22",
month = mar,
year = "2019",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3264448",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon May 6 18:23:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3264448",
abstract = "After a short introduction, the article begins with an
axiomatic definition of rounded arithmetic. The
concepts of rounding and of rounded arithmetic
operations are defined in an axiomatic manner fully
independent of special data formats and encodings.
Basic properties of floating-point and interval
arithmetic can directly be derived from this abstract
mathematical model. Interval operations are defined as
set operations for elements of the set {\=I}R of closed
and connected sets of real numbers. As such, they form
an algebraically closed subset of the powerset of the
real numbers. This property leads to explicit formulas
for the arithmetic operations of floating-point
intervals of {\=I}F, which are executable on the
computer. Arithmetic for intervals of {\=I}F forms an
exception free calculus, i.e., arithmetic operations
for intervals of {\=I}F always lead to intervals of
{\=I}F again. Later sections are concerned with
programming support and hardware for interval
arithmetic. Both are a must and absolutely necessary to
move interval arithmetic more into the center of
scientific computing. With some minor hardware
additions, interval operations can be made as fast as
simple floating-point operations. In vector and matrix
spaces for real, complex, and interval data, the dot
product is a fundamental arithmetic operation.
Computing the dot product of two vectors with
floating-point components exactly substantially speeds
up floating-point and interval arithmetic as well as
the accuracy of the computed result. Hardware needed
for the exact dot product is very modest. The exact dot
product is essential for long real and long interval
arithmetic. Section 9 illustrates that interval
arithmetic as developed in this article already has a
long tradition. Products based on these ideas have been
available since 1980. Implementing what the article
advocates would have a profound effect on mathematical
software. Modern processor architecture from Intel, for
example, comes quite close to what is requested in this
article.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Laguna:2019:FDF,
author = "Ignacio Laguna",
editor = "IEEE\slash ACM",
booktitle = "{ASE'19: 34th IEEE\slash ACM International Conference
on Automated Software Engineering, San Diego,
California, November 10--15, 2019}",
title = "{FPChecker}: Detecting Floating-Point Exceptions in
{GPU} Applications",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "xxxv + 1296",
pages = "1126--1129",
month = nov,
year = "2019",
DOI = "https://doi.org/10.1109/ase.2019.00118",
ISBN = "1-72812-508-1",
ISBN-13 = "978-1-72812-508-4",
LCCN = "QA76.758 .Z566 2019",
bibdate = "Mon Sep 11 07:07:01 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating-point arithmetic is widely used in
applications from several fields including scientific
computing, machine learning, graphics, and finance.
Many of these applications are rapidly adopting the use
of GPUs to speedup computations. GPUs, however, have
limited support to detect floating-point exceptions,
which hinders the development of reliable applications
in GPU-based systems. We present FPCHECKER, the first
tool to automatically detect floating-point exceptions
in GPU applications. FPCHECKER uses the clang\slash
LLVM compiler to instrument GPU kernels and to detect
exceptions at runtime. Once an exception is detected,
it reports to the programmer the code location of the
exception as well as other useful information. The
programmer can then use this report to avoid the
exception, e.g., by modifying the application algorithm
or changing the input. We present the design of
FPCHECKER, an evaluation of the overhead of the tool,
and a real-world case scenario on which the tool is
used to identify a hidden exception. The slowdown of
FPCHECKER is moderate and the code is publicly
available as open source.",
acknowledgement = ack-nhfb,
}
@TechReport{Laguna:2019:GPD,
author = "Ignacio Laguna and Paul C. Wood and Ranvijay Singh and
Saurabh Bagchi",
title = "{GPUMixer}: Performance-Driven Floating-Point Tuning
for {GPU} Scientific Applications",
type = "Report",
institution = "Lawrence Livermore National Laboratory",
address = "Livermore CA 94550, USA",
year = "2019",
bibdate = "Tue Aug 06 05:54:23 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "http://lagunaresearch.org/docs/isc-2019.pdf;
https://www.hpcwire.com/2019/08/05/llnl-purdue-researchers-harness-gpu-mixed-precision-for-accuracy-performance-tradeoff/",
abstract = "We present GPUMixer, a tool to perform mixed-precision
floating-point tuning on scientific GPU applications.
While precision tuning techniques are available, they
are designed for serial programs and are
accuracy-driven, i.e., they consider configurations
that satisfy accuracy constraints, but these
configurations may degrade performance. GPUMixer, in
contrast, presents a performance-driven approach for
tuning. We introduce a novel static analysis that finds
Fast Imprecise Sets (FISets), sets of operations on low
precision that minimize type conversions, which often
yield performance speedups. To estimate the relative
error introduced by GPU mixed-precision, we propose
shadow computations analysis for GPUs, the first of
this class for multi-threaded applications. GPUMixer
obtains performance improvements of up to 46.4\% of the
ideal speedup in comparison to only 20.7\% found by
state-of-the-art methods.",
acknowledgement = ack-nhfb,
remark = "Best paper award at the 33rd ISC High Performance
conference held June 16--20, 2019.",
}
@Article{Lange:2019:SEP,
author = "Marko Lange and Siegfried M. Rump",
title = "Sharp estimates for perturbation errors in
summations",
journal = j-MATH-COMPUT,
volume = "88",
number = "315",
pages = "349--368",
month = jul,
year = "2019",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3355",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Jul 14 06:45:34 MDT 2020",
bibsource = "http://www.ams.org/mcom/2019-88-315;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
URL = "https://www.ams.org/journals/mcom/2019-88-315/S0025-5718-2018-03355-5;
https://www.ams.org/journals/mcom/2019-88-315/S0025-5718-2018-03355-5/S0025-5718-2018-03355-5.pdf;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=1082372;
https://www.ams.org/mathscinet/search/authors.html?mrauthid=151815",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput.",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "accurate floating-point summation",
}
@InProceedings{Lefevre:2019:ACM,
author = "Vincent Lef{\`e}vre and Jean-Michel Muller",
title = "Accurate Complex Multiplication in Floating-Point
Arithmetic",
crossref = "Takagi:2019:ISC",
pages = "23--29",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00013",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We deal with accurate complex multiplication in binary
floating-point arithmetic, with an emphasis on the case
where one of the operands is a ``double-word'' number.
We provide an algorithm that returns a complex product
with normwise relative error bound close to the best
possible one, i.e., the rounding unit u.",
acknowledgement = ack-nhfb,
keywords = "accurate complex multiplication; Approximation
algorithms; ARITH-26; binary floating-point arithmetic;
complex product; Digital arithmetic; double-word
number; floating point arithmetic; Floating-point
arithmetic; Floating-point arithmetic, Complex
multiplication, Rounding error analysis; Lips; Parallel
processing; Standards; Zirconium",
}
@Article{Lemire:2019:FRD,
author = "Daniel Lemire and Owen Kaser and Nathan Kurz",
title = "Faster remainder by direct computation: Applications
to compilers and software libraries",
journal = j-SPE,
volume = "49",
number = "6",
pages = "953--970",
month = jun,
year = "2019",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.2689",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Sat Oct 12 09:43:47 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
acknowledgement = ack-nhfb,
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
keywords = "integer division; integer remainder",
onlinedate = "27 February 2019",
remark = "Paul Zimmermann reported on the gmp-devel mailing list
on Tue, 15 Oct 2019 10:40:48 +0200 that the remainder
algorithm in this report was described earlier in
unpublished work in \cite{Bernstein:2004:SRT}.",
}
@InProceedings{Lindstrom:2019:UCR,
author = "Peter Lindstrom",
title = "Universal Coding of the Reals Using Bisection",
crossref = "Gustafson:2019:CPC",
pages = "7:1--7:10",
year = "2019",
DOI = "https://doi.org/10.1145/3316279.3316286",
bibdate = "Mon Feb 10 12:11:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "7",
keywords = "wobbling accuracy, floating point, bracketing, binary
search, bisection, Universal coding, posits, unbounded
search",
location = "Singapore, Singapore",
numpages = "10",
}
@Article{Liu:2019:DAA,
author = "W. Liu and T. Cao and P. Yin and Y. Zhu and C. Wang
and E. E. Swartzlander and F. Lombardi",
title = "Design and Analysis of Approximate Redundant Binary
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "6",
pages = "804--819",
month = jun,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2890222",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "adders; Adders; approximate arithmetic designs;
approximate Booth encoders; approximate circuits;
approximate computing; Approximate computing;
approximate NB Booth multipliers; approximate product
arrays; approximate RB multipliers; approximate
redundant binary multiplier design; Compressors;
Delays; Error analysis; error analysis; error
characteristics; error-resilient applications;
error-tolerant applications; exact regular partial
product arrays; Hardware; hardware simulation; logic
design; low power; low power circuits; modified Booth
encoder; multiplying circuits; partial product array;
Power demand; RB 4:2 compressors; RB adders; RB
compressor; RB compressors; RB-NB converter; RB-normal
binary converter; redundant binary (RB) multiplier",
}
@Article{Lourenco:2019:ESS,
author = "Christopher Lourenco and Adolfo R. Escobedo and Erick
Moreno-Centeno and Timothy A. Davis",
title = "Exact Solution of Sparse Linear Systems via
Left-Looking Roundoff-Error-Free {$ L U $}
Factorization in Time Proportional to Arithmetic Work",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "40",
number = "2",
pages = "609--638",
month = "????",
year = "2019",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/18M1202499",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Oct 10 08:00:32 MDT 2019",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/40/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "exact rational arithmetic; Sparse Left-looking
Integer-Preserving (SLIP) LU factorization",
onlinedate = "January 2019",
}
@InProceedings{Lu:2019:TDN,
author = "Jinming Lu and Siyuan Lu and Zhisheng Wang and Chao
Fang and Jun Lin and Zhongfeng Wang and Li Du",
editor = "{IEEE}",
booktitle = "{2019 32nd IEEE International System-on-Chip
Conference (SOCC)}",
title = "Training Deep Neural Networks Using Posit Number
System",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "62--67",
year = "2019",
DOI = "https://doi.org/10.1109/SOCC46988.2019.1570558530",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lutz:2019:AFP,
author = "David Lutz",
title = "{ARM} Floating Point 2019: Latency, Area, Power",
crossref = "Takagi:2019:ISC",
pages = "97--98",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00025",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We have had little or no speed increase from process
in the past few years, but latency continues to
decrease due to algorithmic improvements [1] and a
decision to spend more area on CPU datapaths [2]. A
binary64 floating-point (FP) add now takes two cycles
when done as part of a 2+2-cycle FMA, and even one
cycle when done as part of an in-order vector
reduction. Smaller and more specialized FP operations
(bfloat16) are even faster. Finally, the decision to
spend more area on datapath logic took a new twist this
year when we applied it to GPUs, cutting dynamic power
there by a third.",
acknowledgement = ack-nhfb,
keywords = "2+2-cycle FMA; adders; Adders; ARITH-26; ARM floating
point 2019; bfloat16; binary64 floating-point; Clocks;
CPU datapaths; datapath logic; Digital arithmetic;
floating point arithmetic; in-order vector reduction;
Microarchitecture; Pipelines; random number generation;
Security; Standards; vectors",
}
@Misc{Lutz:2019:AMP,
author = "David Raymond Lutz and Neil Burgess and Christopher
Neal Hinds and Andreas Due Engh-Halstvedt",
title = "Apparatus and method for performing arithmetic
operations to accumulate floating-point numbers",
howpublished = "US Patent 10,216,479",
day = "26",
month = feb,
year = "2019",
bibdate = "Thu Oct 17 11:34:51 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://patents.google.com/patent/US10216479B2",
abstract = "An apparatus and method are provided for performing
arithmetic operations to accumulate floating-point
numbers. The apparatus comprises execution circuitry to
perform arithmetic operations, and decoder circuitry to
decode a sequence of instructions. A convert and
accumulate instruction is provided, and the decoder
circuitry is responsive to decoding the convert and
accumulate instruction to generate one or more control
signals to control the execution circuitry to convert
at least one floating-point operand identified by the
convert and accumulate instruction into a corresponding
N-bit fixed-point operand having M fraction bits, where
M is less than N and M is dependent on a format of the
floating-point operand. The execution circuitry
accumulates each corresponding N bit fixed-point
operand and a P bit fixed-point operand identified by
the convert and accumulate instruction in order to
generate a P bit fixed-point result value, where P is
greater than N and also has M fraction bits.",
acknowledgement = ack-nhfb,
remark = "Patent filed 6 December 2016, granted to Arm Ltd. on
26 February 2019, expected expiration 2 February 2037
(in 17th year of grant).",
}
@InProceedings{Mach:2019:FSB,
author = "Stefan Mach and Fabian Schuiki and Florian Zaruba and
Luca Benini",
editor = "{IEEE}",
booktitle = "{2019 IFIP\slash IEEE 27th International Conference on
Very Large Scale Integration (VLSI-SoC)}",
title = "A {0.80pJ\slash flop, 1.24Tflop\slash sW} 8-to-64 bit
Transprecision Floating-Point Unit for a 64 bit
{RISC-V} Processor in 22nm {FD-SOI}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "95--98",
year = "2019",
DOI = "https://doi.org/10.1109/VLSI-SoC.2019.8920307",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@Article{Magron:2019:CRE,
author = "V. Magron and A. Rocca and T. Dang",
title = "Certified Roundoff Error Bounds Using {Bernstein}
Expansions and Sparse {Krivine--Stengle}
Representations",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "7",
pages = "953--966",
month = jul,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2851235",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Algebra; Bernstein expansions; Convergence; embedded
systems; embedded systems implementation; error
analysis; floating point arithmetic; FPBern software
package; FPKriSten software package; Krivine-Stengle
representations; linear programming; linear programming
relaxations; nonlinear programs; Optimization;
Polynomial optimization; polynomials; rational
functions; rigorous upper bounds; roundoff error
bounds; roundoff errors; Roundoff errors; Software
algorithms; Tools; Upper bound",
}
@InProceedings{Martins:2019:HHR,
author = "Paulo Martins and Jeremy Marrez and Jean-Claude Bajard
and Leonel Sousa",
title = "{HyPoRes}: An Hybrid Representation System for {ECC}",
crossref = "Takagi:2019:ISC",
pages = "207--214",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00049",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Residue Number System (RNS) is a numeral
representation enabling for more efficient addition and
multiplication implementations. However, due its
non-positional nature, modular reductions, required for
example by Elliptic Curve (EC) Cryptography (ECC),
become costlier. Traditional approaches to RNS modular
reduction resort to the Montgomery algorithm,
underpinned by large basis extensions. Recently,
Hybrid-Positional Residue Number Systems (HPRs) have
been proposed, providing a trade-off between the
efficiency of RNS and the flexibility of positional
number representations. Numbers are represented in a
positional representation with the coefficients
represented in RNS. By crafting primes of a special
form, the complexity of reductions modulo those primes
is mitigated, relying on extensions of smaller bases.
Due to the need of crafting special primes, this
approach is not directly extensible to group operations
over currently standardised elliptic curves. In this
paper, the Hybrid-Polynomial Residue Number System
(HyPoRes) is proposed, enabling for improved modular
reductions for any prime. Experimental results show
that the modular reduction of HyPoRes, although at most
1.4 times slower than HPR for HPR-crafted primes, is up
to 1.4 times faster than a generic RNS approach for
primes of ECC standards.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; Art; Complexity theory; Dynamic range; ECC
standards; Elliptic Curve Cryp-tography; Elliptic curve
cryptography; elliptic curve cryptography; Elliptic
curves; generic RNS approach; HPR-crafted primes;
hybrid representation system; hybrid-polynomial residue
number system; hybrid-positional residue number
systems; HyPoRes; improved modular reductions;
Lattices; Modular Arithmetic; Montgomery algorithm;
multiplication implementations; polynomials; positional
number representations; public key cryptography;
Residue Number System; residue number systems; RNS
modular reduction",
}
@InProceedings{Matula:2019:PCG,
author = "David W. Matula and Zizhen Chen",
title = "Precise and Concise Graphical Representation of the
Natural Numbers",
crossref = "Takagi:2019:ISC",
pages = "100--103",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00027",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A graphical number representation system based on the
formal logic foundation of a recursively defined
function is presented. The function exposes a
one-to-one correspondence between the natural numbers
and the set of rooted trees. Secondly, a relation
between pairs of natural numbers is shown to partition
the integers into disjoint finite sets each visualized
as a tree in the forest of all finite trees. This
relation encapsulates in visual form the natural
structure and distribution of primes in a manner not
previously investigated. These representations allow
arithmeticians to visually experience natural numbers
in a 2D graphical layout. This form is free of cultural
choices such as the number of symbols in an alphabet
and/or one-dimensional symbol strings. The fundamental
nature of these mappings is argued to be accessible to
a creative mind independent of formal schooling. This
short note includes examples illustrating the
simplicity of the constructions.",
acknowledgement = ack-nhfb,
keywords = "2D graphical layout; ARITH-26; Computer science;
disjoint finite sets; finite trees; Forestry; formal
logic foundation; graphical number representation
system; graphical representation; Labeling; natural
numbers; natural structure; number fonts;
one-dimensional symbol strings; one-to-one
correspondence; prime factorization; prime number
function; recursive function; recursive functions;
recursively defined function; rooted trees; trees
(mathematics); Two dimensional displays; Vegetation;
Visualization",
}
@Article{Maynard:2019:MPA,
author = "C. M. Maynard and D. N. Walters",
title = "Mixed-precision arithmetic in the {ENDGame} dynamical
core of the {Unified Model}, a numerical weather
prediction and climate model code",
journal = j-COMP-PHYS-COMM,
volume = "244",
number = "??",
pages = "69--75",
month = nov,
year = "2019",
CODEN = "CPHCBZ",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Sep 6 11:03:48 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S0010465519302127",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{McCullough:2019:WTS,
author = "B. D. McCullough and Taha Mokfi and Mahsa Almaeenjad",
title = "{Wilkinson}'s Tests and {SQL} Packages",
journal = j-SIGMOD,
volume = "48",
number = "3",
pages = "17--22",
month = sep,
year = "2019",
CODEN = "SRECD8",
DOI = "https://doi.org/10.1145/3377391.3377395",
ISSN = "0163-5808 (print), 1943-5835 (electronic)",
ISSN-L = "0163-5808",
bibdate = "Sat Dec 21 07:26:01 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigmod.bib",
abstract = "Wilkinson's Tests are used to benchmark the accuracy
of some statistical functions in six SQL packages:
Apache Hive, Microsoft Access, Microsoft SQL Server,
MySQL, Oracle 11g SQL, and SAP Hana. Using the best
choice of data type, we find that different packages
use different rounding schemes, two packages use
unreliable algorithms to compute the sample variance,
one package returns the population standard deviation
when the sample standard deviation is called, and one
package has an unstable algorithm for computing the
correlation coefficient. Using the wrong data type all
but guarantees inaccurate results.",
acknowledgement = ack-nhfb,
fjournal = "SIGMOD Record (ACM Special Interest Group on
Management of Data)",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J689",
remark = "This paper looks at statistical software inside six
widely-used SQL databases, and find serious errors in
most of them, and poor numerical implementations for
standard deviations and other well-understood
computational algorithms. See also earlier work
recorded in fparith.bib
\cite{McCullough:1998:ARS,McCullough:1999:ARS,McCullough:1999:NRE}.",
}
@InProceedings{Melquiond:2019:FVS,
author = "Guillaume Melquiond and Raphael Rieu-Helft",
title = "Formal Verification of a State-of-the-Art Integer
Square Root",
crossref = "Takagi:2019:ISC",
pages = "183--186",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00041",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present the automatic formal verification of a
state-of-the-art algorithm from the GMP library that
computes the square root of a 64-bit integer. Although
it uses only integer operations, the best way to
understand the program is to view it as a fixed-point
arithmetic algorithm that implements Newton's method.
The C code is short but intricate, involving magic
constants and intentional arithmetic overflows. We have
verified the algorithm using the Why3 tool and
automated solvers such as Gappa.",
acknowledgement = ack-nhfb,
keywords = "64-bit integer; Approximation algorithms; ARITH-26;
automatic formal verification; C code; C language;
Convergence; Digital arithmetic; electronic engineering
computing; fixed point arithmetic; Fixed-point
arithmetic; fixed-point arithmetic algorithm; floating
point arithmetic; Floors; Formal verification; GMP
library; integer operations; integer square root;
intentional arithmetic overflows; Libraries; Newton
method; program verification; programming; Tools; Why3
tool",
}
@PhdThesis{Melquiond:2019:NVN,
author = "Guillaume Melquiond",
title = "Normal Verification for Numerical Computations, and
the Other Way Around",
type = "{Habilitation {\`a} Diriger des Recherches}",
school = "Universit{\'e} Paris Sud, 2",
address = "Paris, France",
pages = "x + 163",
day = "25",
month = jul,
year = "2019",
bibdate = "Fri Sep 22 16:46:42 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://theses.hal.science/tel-02194683/document",
acknowledgement = ack-nhfb,
}
@InProceedings{Mian:2019:CAE,
author = "Riaz-ul-haque Mian and Michihiro Shintani and Michiko
Inoue",
editor = "{IEEE}",
booktitle = "{2019 32nd IEEE International System-on-Chip
Conference (SOCC)}",
title = "Cycle-Accurate Evaluation of Software-Hardware
Co-Design of Decimal Computation in {RISC-V}
Ecosystem",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "412--417",
year = "2019",
DOI = "https://doi.org/10.1109/SOCC46988.2019.1570559752",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "Decimal arithmetic; Decimal multiplication; Evaluation
framework; Hardware accelerator; RISC-V; RoCC; Rocket
chip",
}
@Misc{Moler:2019:CCF,
author = "Cleve Moler",
title = "{Cleve}'s Corner: Floating Point Arithmetic Before
{IEEE 754}",
howpublished = "MathWorks Web site.",
day = "18",
month = jan,
year = "2019",
bibdate = "Sat Jan 19 15:18:17 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://blogs.mathworks.com/cleve/2019/01/18/floating-point-arithmetic-before-ieee-754/",
abstract = "In a comment following my post about half-precision
arithmetic, ``Raj C'' asked how the parameters for IEEE
Standard 754 floating point arithmetic were chosen. I
replied that I didn't know but would try to find out. I
called emeritus U. C. Berkeley Professor W. (Velvel)
Kahan, who was the principle architect of 754. Here is
what I learned.",
acknowledgement = ack-nhfb,
}
@Misc{Moler:2019:CCV,
author = "Cleve Moler",
title = "{Cleve}'s Corner: Variable Format Half Precision
Floating Point Arithmetic",
howpublished = "MathWorks Web site.",
day = "16",
month = jan,
year = "2019",
bibdate = "Sat Jan 19 15:14:03 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://blogs.mathworks.com/cleve/2019/01/16/variable-format-half-precision-floating-point-arithmetic/",
abstract = "A year and a half ago I wrote a post about ``half
precision'' 16-bit floating point arithmetic, Moler on
fp16. I followed this with a bug fix, bug in fp16. Both
posts were about fp16, defined in IEEE standard 754.
This is only one of 15 possible 16-bit formats. In this
post I am going to consider all 15.",
acknowledgement = ack-nhfb,
}
@InProceedings{Moriai:2019:PPD,
author = "Shiho Moriai",
title = "Privacy-Preserving Deep Learning via Additively
Homomorphic Encryption",
crossref = "Takagi:2019:ISC",
pages = "198--198",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00047",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We aim at creating a society where we can resolve
various social challenges by incorporating the
innovations of the fourth industrial revolution (e.g.
IoT, big data, AI, robot, and the sharing economy) into
every industry and social life. By doing so the society
of the future will be one in which new values and
services are created continuously, making people's
lives more conformable and sustainable. This is Society
5.0, a super-smart society. Security and privacy are
key issues to be addressed to realize Society 5.0.
Privacy-preserving data analytics will play an
important role. In this talk we show our recent works
on privacy-preserving data analytics such as
privacy-preserving logistic regression and
privacy-preserving deep learning. Finally, we show our
ongoing research project under JST CREST AI . In this
project we are developing privacy-preserving financial
data analytics systems that can detect fraud with high
security and accuracy. To validate the systems, we will
perform demonstration tests with several financial
institutions and solve the problems necessary for their
implementation in the real world.",
acknowledgement = ack-nhfb,
keywords = "additively homomorphic encryption; ARITH-26; Big Data;
data analysis; Data analysis; data privacy; Deep
learning; Digital arithmetic; Encryption; financial
data processing; financial institutions; fourth
industrial revolution; fraud; Information and
communication technology; IoT; JST CREST AI; neural
nets; privacy issues; privacy-preserving deep learning;
privacy-preserving financial data analytics systems;
privacy-preserving logistic regression; regression
analysis; social challenges; social life; social
sciences computing; Society 5.0; super-smart society",
}
@Article{Moroz:2019:EFP,
author = "Leonid Moroz and Volodymyr Samotyy",
title = "Efficient Floating-Point Division for Digital Signal
Processing Application [Tips \& Tricks]",
journal = j-IEEE-SIGNAL-PROCESS-MAG,
volume = "36",
number = "1",
pages = "159--163",
month = jan,
year = "2019",
CODEN = "ISPRE6",
DOI = "https://doi.org/10.1109/msp.2018.2875977",
ISSN = "1053-5888 (print), 1558-0792 (electronic)",
ISSN-L = "1053-5888",
bibdate = "Thu Apr 10 15:04:29 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Signal Processing Magazine",
}
@Article{Munoz-Coreas:2019:QCD,
author = "E. Mu{\~n}oz-Coreas and H. Thapliyal",
title = "Quantum Circuit Design of a {$T$}-count Optimized
Integer Multiplier",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "5",
pages = "729--739",
month = may,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2882774",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "adders; Adders; Clifford+T gates; conditional adder;
fault tolerance; Fault tolerance; fault tolerant
implementations; Fault tolerant systems; integer
multiplication; logic design; Logic gates; quantum
arithmetic; quantum circuit design; quantum circuits;
Quantum computing; quantum conditional adder circuit;
quantum gates; quantum hardware resources; quantum
multiplier design; qubits; Registers; reliable quantum
circuits; scalable quantum circuits; T-count optimized
quantum circuit; T-count savings; Toffoli gate array",
}
@Article{Nannarelli:2019:TFP,
author = "A. Nannarelli",
title = "Tunable Floating-Point Adder",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "10",
pages = "1553--1560",
month = oct,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2906907",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 12 13:33:25 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; addition; Computer architecture; energy
efficiency; Floating-point; Google; Hardware; IEEE
rounding; Indexes; Standards; Tuning",
remark = "From the abstract: ``TFP is a variable precision
format in which a given precision can be chosen for a
single operation by selecting a specific number of bits
for significand and exponent in the floating-point
representation. By tuning the precision of an algorithm
to the minimum precision achieving an acceptable target
error, we can make the computation more power
efficient.''",
}
@InProceedings{Pandey:2019:UFP,
author = "Kumar Sambhav Pandey and Dinesh Kumar B and Neeraj
Goel and Hitesh Shrimali",
title = "An Ultra-Fast Parallel Prefix Adder",
crossref = "Takagi:2019:ISC",
pages = "125--134",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00034",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Parallel Prefix adders are arguably the most commonly
used arithmetic units. They have been extensively
investigated at architecture level, register transfer
level (RTL), gate level, circuit level as well as
layout level giving rise to a plethora of mathematical
formulations, topologies and implementations. This
paper contributes significantly to the understanding of
these parallel prefix adders in a couple of ways.
Firstly, it attempts to describe various such parallel
prefix adders in elegant and consistent formulations.
Secondly, a new family of parallel prefix adders is
proposed at architecture level. The estimates of the
area-throughput characteristics for an instance of this
family are also presented. While the speeds achieved by
this instance match those achieved by the state of the
art adders, their area characteristics exhibit upto
26\% improvement.",
acknowledgement = ack-nhfb,
keywords = "adder recurrence relations; Adders; adders;
architecture level; area-throughput characteristics;
ARITH-26; arithmetic units; Computer architecture;
Digital arithmetic; digital arithmetic; integrated
circuit layout; integrated logic circuits; logic
design; Logic gates; Microprocessors; Parallel prefix
adders; Terminology; Topology; ultrafast parallel
prefix adder",
}
@Article{Parhi:2019:CAF,
author = "Keshab K. Parhi and Yin Liu",
title = "Computing Arithmetic Functions Using Stochastic Logic
by Series Expansion",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "7",
number = "1",
pages = "44--59",
month = jan # "\slash " # mar,
year = "2019",
DOI = "https://doi.org/10.1109/TETC.2016.2618750",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
abstract = "Stochastic logic implementations of complex arithmetic
functions, such as trigonometric, exponential, and
sigmoid, are derived based on truncated versions of
their Maclaurin series expansions. This paper makes
three contributions. First, it is shown that a
polynomial can be implemented using multiple levels of
NAND gates based on Horner's rule, if the coefficients
are alternately positive and negative and their
magnitudes are monotonically decreasing. Truncated
Maclaurin series expansions of arithmetic functions are
used to generate polynomials which satisfy these
constraints. The input and output in these functions
are represented by unipolar representation. Functions
including sine, cosine, tangent hyperbolic, logarithm
and exponential can be implemented using this method.
Second, for a polynomial that does not satisfy these
constraints, it still can be implemented based on
Horner's rule if each factor of the polynomial
satisfies these constraints. It is shown that functions
such as $ \sin \pi x / \pi $, $ e^{-a x} $, $ \tanh a x
$ and $ \sigmoid (a x^3) $ (for values of $ a > 1$) can
be implemented using stochastic logic using
factorization in combination with Horner's rule. Third,
format conversion is proposed for arithmetic functions
with input and output represented in different formats,
such as $ \cos \pi x$ given $ x \in [0, 1]$ and $
\sigmoid (x)$ given $ x \in [ - 1, 1]$. Polynomials are
transformed to equivalent forms that naturally exploit
format conversions. The proposed stochastic logic
circuits outperform the well-known Bernstein polynomial
based and finite-state-machine (FSM) based
implementations. Furthermore, the hardware complexity
and the critical path of the proposed implementations
are less than the well-known Bernstein polynomial based
and FSM based implementations for most cases",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Parry:2019:PSO,
author = "Katherine Parry",
title = "A Perspective into Squarer Optimization",
crossref = "Takagi:2019:ISC",
pages = "124--124",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00033",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Artificial Intelligence applications do millions of
square calculations, such as within Gradient Descent or
Principle Component Analysis (PCA). Any time measured
or observed data is analyzed; the error, residual, or a
comparison against a norm, it is evaluated using a
square operation. Squarers are special purpose
multipliers that can be employed when the operands are
identical. Most calculations use slower multipliers,
even though squarers calculate faster, use less power,
and occupy less area. Multiplication is composed of a
series of partial products that are accumulated to
result in the multiplied product. Multiplier and
squarer propagation delay is assessed using the number
of partial products, or more their addition. The
calculation of partial products can occur in parallel,
thus does not significantly tax the propagation delay,
but carries from their addition create computational
dependencies. A standard 8-bit multiplier requires 56
partial product additions and previous work has reduced
a squarer to 22 partial products sums. This paper
reviews the previous technology and illustrates further
Boolean optimizations that minimize the number of
additions to 15 partial products.",
acknowledgement = ack-nhfb,
keywords = "8-bit multiplier; ARITH-26; Artificial intelligence;
artificial intelligence applications; Boolean
functions; Boolean optimizations; Digital arithmetic;
digital arithmetic; gradient descent; Measurement
uncertainty; multiplied product; multiplying circuits;
optimisation; Optimization; partial product additions;
partial products sums; Principal component analysis;
principle component analysis; Propagation delay;
special purpose multipliers; square calculations;
square operation; squarer optimization; squarer
propagation delay; Urban areas",
}
@InProceedings{Pasca:2019:HDP,
author = "Bogdan Pasca",
title = "Hybrid Dot-Product Design for {FP}-Enabled {FPGAs}",
crossref = "Takagi:2019:ISC",
pages = "194--196",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00045",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "FPGAs are becoming interesting solutions for neural
network training acceleration. Efficient implementation
of dot-products, as part of matrix-matrix multiply
engines, plays a key role towards this. The now de
facto standard involves the matrix multiplication on
bfloat16 inputs, with all reductions be performed in
single-precision arithmetic. We present here a generic
hybrid dot-product implementation that: (1) has a
user-defined accuracy knob and (2) targets a
user-defined logic/DSP ratio. Since our architecture is
very specialized to a given target device, we discuss
the challenges in generating this architecture
automatically.",
acknowledgement = ack-nhfb,
keywords = "Adders; ARITH-26; arithmetic; Bandwidth; bfloat16; dot
product; dot-products; Field programmable gate arrays;
field programmable gate arrays; floating point;
floating point arithmetic; FP-enabled FPGA; FPGA;
generator; hybrid; hybrid dot-product design; hybrid
dot-product implementation; Lead; logic design; matrix
multiplication; matrix-matrix multiply engines;
multiplying circuits; neural nets; neural network
training; Neural networks; single precision;
single-precision arithmetic; Tools; Training",
}
@Article{Pranesh:2019:LPF,
author = "Srikara Pranesh",
title = "Low Precision Floating-Point Formats: The {Wild West}
of Computer Arithmetic",
journal = j-SIAM-NEWS,
volume = "52",
number = "9",
pages = "12--12",
month = nov,
year = "2019",
DOI = "",
ISSN = "0036-1437",
bibdate = "Mon Nov 04 14:49:07 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sinews.siam.org/Details-Page/low-precision-floating-point-formats-the-wild-west-of-computer-arithmetic",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Reyhani-Masoleh:2019:NMI,
author = "A. Reyhani-Masoleh and H. El-Razouk and A. Monfared",
title = "New Multiplicative Inverse Architectures Using
{Gaussian} Normal Basis",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "7",
pages = "991--1006",
month = jul,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2018.2859941",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "application specific integrated circuits; arithmetic
operations; binary fields; classic inversion scheme;
classic-based addition chains; classical-interleaved
architecture; classical-interleaved inverter; CMOS
integrated circuits; Computer architecture;
cryptography; Digit-level multiplier; digital
arithmetic; field inversion; field programmable gate
arrays; finite field; FSISM; FSISM processor;
fully-serial-in square-multiply processor; Galois
fields; Gaussian normal basis; Gaussian processes;
hybrid-double multiplication; input registers;
inversion architecture; inversion architectures;
Inverters; invertors; Itoh-Tsujii algorithm; latency;
Logic gates; multiplication cycle; multiplicative
inverse architectures; multiplying circuits; NIST;
Propagation delay; size 65.0 nm; ternary Itoh-Tsujii
algorithm",
}
@InProceedings{Rohloff:2019:CAR,
author = "Kurt Rohloff",
title = "Computer Arithmetic Research to Accelerate
Privacy-Protecting Encrypted Computing Such as
Homomorphic Encryption",
crossref = "Takagi:2019:ISC",
pages = "197--197",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00046",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "One of the first major breakthroughs of computer
science in the 21st century has been the discovery and
practical demonstration of encrypted computing
technologies such as Fully Homomorphic Encryption
(FHE). Encrypted computing technologies allow sensitive
data to be encrypted such that arbitrary programs can
be securely run over the encrypted data where the
output, when decrypted, is equivalent to the result of
running the original algorithm on the unencrypted data.
In this talk we focus on the use of and potential for
computer arithmetic research to enable more practical
encrypted computing, such as to accelerate advanced
encryption implementations on custom hardware. These
technologies are ground-breaking in their ability for
privacy-preserving data science on sensitive data sets
with minimal costs in terms of engineering effort,
power, compute resources, etc. \ldots{}. We discuss
theory, design, algorithmic, hardware, software
engineering and systems research that is enabling
applications of encrypted computing in regulated data
industries, such as in medical and financial domains.
We use our work using accelerating the PALISADE
open-source homomorphic encryption software library for
practical applications in case studies.",
acknowledgement = ack-nhfb,
keywords = "Acceleration; advanced encryption implementations;
ARITH-26; computer arithmetic research; computer
science; Computer science; Computers; cryptography;
data privacy; Digital arithmetic; encrypted computing
technologies; encrypted data; Encryption; fully
homomorphic encryption; Hardware; PALISADE open-source
homomorphic encryption software library;
privacy-preserving data science; privacy-protecting
encrypted computing; public domain software; regulated
data industries; sensitive data sets; software
engineering; software libraries; unencrypted data",
}
@Article{Roughan:2019:PSS,
author = "Matthew Roughan",
title = "Practically surreal: {Surreal} arithmetic in {Julia}",
journal = j-SOFTWAREX,
volume = "9",
number = "??",
pages = "293--298",
month = jan # "\slash " # jun,
year = "2019",
CODEN = "????",
ISSN = "2352-7110",
ISSN-L = "2352-7110",
bibdate = "Mon Oct 14 09:45:43 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/softwarex.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S2352711018302152",
acknowledgement = ack-nhfb,
fjournal = "SoftwareX",
journal-URL = "https://www.sciencedirect.com/journal/softwarex/issues",
keywords = "Conway's surreal numbers",
}
@InProceedings{Rump:2019:EBC,
author = "Siegfried M. Rump",
title = "Error Bounds for Computer Arithmetics",
crossref = "Takagi:2019:ISC",
pages = "1--14",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00011",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This note summarizes recent progress in error bounds
for compound operations performed in some computer
arithmetic. Given a general set of real numbers
together with some operations satisfying the first
standard model, we identify three types A, B, and C of
weak sufficient assumptions implying new results and
sharper error estimates. Those include linearized error
estimates in the number of operations, faithfully
rounded and reproducible results. All types of
assumptions are satisfied for an IEEE-754 p-digit base-
floating-point arithmetic.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; Compounds; Computational modeling; computer
arithmetic; CREST; Digital arithmetic; error analysis;
error bounds; floating point arithmetic; IEEE-754
p-digit base- floating-point arithmetic; Japan Science
and Technology Agency; Kernel; Standards; Switches;
Vegetation",
}
@Article{Salamati:2019:MEM,
author = "Mahmoud Salamati and Rocco Salvia and Eva Darulova and
Sadegh Soudjani and Rupak Majumdar",
title = "Memory-Efficient Mixed-Precision Implementations for
Robust Explicit Model Predictive Control",
journal = j-TECS,
volume = "18",
number = "5s",
pages = "100:1--100:??",
month = oct,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3358223",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Oct 17 18:16:44 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3358223",
abstract = "We propose an optimization for space-efficient
implementations of explicit model-predictive
controllers (MPC) for robust control of linear
time-invariant (LTI) systems on embedded platforms. We
obtain an explicit-form robust model-predictive
controller as a solution to a multi-parametric linear
programming problem. The structure of the controller is
a polyhedral decomposition of the control domain, with
an affine map for each domain. While explicit MPC is
suited for embedded devices with low computational
power, the memory requirements for such controllers can
be high. We provide an optimization algorithm for a
mixed-precision implementation of the controller, where
the deviation of the implemented controller from the
original one is within the robustness margin of the
robust control problem. The core of the mixed-precision
optimization is an iterative static analysis that
co-designs a robust controller and a low-bitwidth
approximation that is statically guaranteed to always
be within the robustness margin of the original
controller. We have implemented our algorithm and show
on a set of benchmarks that our optimization can reduce
space requirements by up to 20.9\% and on average by
12.6\% compared to a minimal uniform precision
implementation of the original controller.",
acknowledgement = ack-nhfb,
articleno = "100",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J840",
}
@InProceedings{Sarkar:2019:RAP,
author = "Souradip Sarkar and Purushotham Murugappa Velayuthan
and Manil Dev Gomony",
editor = "{IEEE}",
booktitle = "{2019 22nd Euromicro Conference on Digital System
Design (DSD)}",
title = "A Reconfigurable Architecture for Posit Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "82--87",
year = "2019",
DOI = "https://doi.org/10.1109/DSD.2019.00022",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Seo:2019:HTM,
author = "Jihee Seo and Dae Hyun Kim",
title = "High-Throughput Multiplier Architectures Enabled by
Intra-Unit Fast Forwarding",
crossref = "Takagi:2019:ISC",
pages = "143--150",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00036",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, we propose a pipelined multiplier
architecture that can resolve data dependencies. The
proposed architecture generates partial results in the
pipeline stages of the multiplier and forwards the
partial results back to the pipeline stages through
so-called fast-forwarding paths, thereby enabling an
execution of dependent multiplications with a minimum
delay penalty. We apply the architecture to a normal
binary multiplier (NBBE-2) and two redundant binary
multipliers (RBBE-4 and CRBBE-4) and compare the
execution time, clock period, area, and power
consumption of the multipliers. The simulation results
show that the proposed architecture achieves up to 30\%
execution time reduction.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; Clocks; Computer architecture; data
dependencies; Delays; dependent multiplications;
digital arithmetic; execution time reduction; Fast
Forwarding; fast-forwarding paths; high-throughput
multiplier architectures; intra-unit fast forwarding;
minimum delay penalty; Multiplexing; Multiplication;
Multiplier; multiplying circuits; normal binary
multiplier; pipeline processing; Pipeline processing;
pipeline stages; pipelined multiplier architecture;
Pipelines; redundant binary multipliers; Throughput",
}
@InProceedings{Serre:2019:DBM,
author = "Fran{\c{c}}ois Serre and Markus P{\"u}schel",
title = "{DSL}-Based Modular {IP} Core Generators: Example
{FFT} and Related Structures",
crossref = "Takagi:2019:ISC",
pages = "190--191",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00043",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a hardware generator for signal processing
algorithms that consist of a network of small
processing elements, including the fast Fourier
transform and sorting networks. The generator is
implemented in Scala and uses a principled design that
leverages modern language features to generate an
entire design space of hardware implementations.
Examples include the use of embedded domain-specific
languages and staging to represent and optimize the
designs at different levels of abstraction, and the use
of Scala's type system to efficiently encode different
degrees of hardware reuse and arithmetic formats.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; arithmetic formats; Design automation;
design space; digital arithmetic; Domain specific
language; DSL; DSL-based modular IP core generators;
electronic engineering computing; embedded
domain-specific languages; embedded systems; fast
Fourier transform; fast Fourier transforms; FFT;
Generators; Hardware; hardware generator; Hardware
generator; hardware implementations; hardware reuse;
microprocessor chips; object-oriented programming;
Optimization; processing elements; Random access
memory; Scala type system; signal processing; signal
processing algorithms; Sorting; sorting; sorting
networks; specification languages; Staging; Streaming
hardware",
}
@Article{Sherman:2019:SRS,
author = "Benjamin Sherman and Jesse Michel and Michael Carbin",
title = "Sound and robust solid modeling via exact real
arithmetic and continuity",
journal = j-PACMPL,
volume = "3",
number = "ICFP",
pages = "99:1--99:29",
month = jul,
year = "2019",
DOI = "https://doi.org/10.1145/3341703",
ISSN = "2475-1421",
bibdate = "Fri Aug 7 19:22:28 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3341703",
abstract = "Algorithms for solid modeling, i.e., Computer-Aided
Design (CAD) and computer graphics, are often specified
on real numbers and then implemented with
finite-precision arithmetic, such as floating-point.
The result is that these implementations do not soundly
compute the results that are expected from their
specifications.\par
We present a new library, StoneWorks, that provides
sound and robust solid modeling primitives. We
implement StoneWorks in MarshallB, a pure functional
programming language for exact real arithmetic in which
types denote topological spaces and functions denote
continuous maps, ensuring that all programs are sound
and robust. We developed MarshallB as an extension of
the Marshall language.\par
We also define a new shape representation, compact
representation (K-rep), that enables constructions such
as Minkowski sum and analyses such as Hausdorff
distance that are not possible with traditional
representations. K-rep is a nondeterminism monad for
describing all the points in a shape.\par
With our library, language, and representation
together, we show that short StoneWorks programs can
specify and execute sound and robust solid modeling
algorithms and tasks.",
acknowledgement = ack-nhfb,
articleno = "99",
fjournal = "Proceedings of the ACM on Programming Languages",
journal-URL = "https://pacmpl.acm.org/",
}
@Misc{Silver:2019:CCN,
author = "Mike Silver and Kalimah Redd Knight",
title = "Cutting Corners on Numbers",
howpublished = "TuftsNow Web site.",
day = "24",
month = sep,
year = "2019",
bibdate = "Wed Sep 25 10:47:09 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Boghosian:2019:NPS}.",
URL = "https://now.tufts.edu/articles/cutting-corners-numbers-computation",
abstract = "Tufts mathematicians find the way we represent numbers
in computers can lead to large computational errors,
especially for modeling dynamical systems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Singh:2019:LPP,
author = "Gagandeep Singh and Dionysios Diamantopoulos and
Sander Stuijk and Christoph Hagleitner and Henk
Corporaal",
booktitle = "Embedded Computer Systems: Architectures, Modeling,
and Simulation",
title = "Low Precision Processing for High Order Stencil
Computations",
publisher = pub-SV,
address = pub-SV:adr,
pages = "403--415",
year = "2019",
DOI = "https://doi.org/10.1007/978-3-030-27562-4_29",
ISBN = "3-030-27562-0",
ISBN-13 = "978-3-030-27562-4",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Solovyev:2019:REF,
author = "Alexey Solovyev and Marek S. Baranowski and Ian Briggs
and Charles Jacobsen and Zvonimir Rakamari{\'c} and
Ganesh Gopalakrishnan",
title = "Rigorous Estimation of Floating-Point Round-Off Errors
with Symbolic {Taylor} Expansions",
journal = j-TOPLAS,
volume = "41",
number = "1",
pages = "2:1--2:??",
month = mar,
year = "2019",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/3230733",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Mon Mar 4 08:35:09 MST 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toplas.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3230733",
abstract = "Rigorous estimation of maximum floating-point
round-off errors is an important capability central to
many formal verification tools. Unfortunately,
available techniques for this task often provide very
pessimistic overestimates, causing unnecessary
verification failure. We have developed a new approach
called Symbolic Taylor Expansions that avoids these
problems, and implemented a new tool called FPTaylor
embodying this approach. Key to our approach is the use
of rigorous global optimization, instead of the more
familiar interval arithmetic, affine arithmetic, and/or
SMT solvers. FPTaylor emits per-instance analysis
certificates in the form of HOL Light proofs that can
be machine checked. In this article, we present the
basic ideas behind Symbolic Taylor Expansions in
detail. We also survey as well as thoroughly evaluate
six tool families, namely, Gappa (two tool options
studied), Fluctuat, PRECiSA, Real2Float, Rosa, and
FPTaylor (two tool options studied) on 24 examples,
running on the same machine, and taking care to find
the best options for running each of these tools. This
study demonstrates that FPTaylor estimates round-off
errors within much tighter bounds compared to other
tools on a significant number of case studies. We also
release FPTaylor along with our benchmarks, thus
contributing to future studies and tool development in
this area.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
}
@Misc{Stephens:2019:BPN,
author = "Nigel Stephens",
title = "{BFloat16} processing for Neural Networks on
{Armv8-A}",
howpublished = "Web site.",
day = "29",
month = aug,
year = "2019",
bibdate = "Mon Sep 23 07:25:21 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://community.arm.com/developer/ip-products/processors/b/ml-ip-blog/posts/bfloat16-processing-for-neural-networks-on-armv8_2d00_a",
acknowledgement = ack-nhfb,
remark = "From the article: ``The next revision of the Armv8-A
architecture will introduce Neon and SVE vector
instructions designed to accelerate certain
computations using the BFloat16 (BF16) floating-point
number format. BF16 has recently emerged as a format
tailored specifically to high-performance processing of
Neural Networks (NNs). BF16 is a truncated form of the
IEEE 754 [ieee754-2008] single-precision representation
(IEEE-FP32), which has only 7 fraction bits, instead of
23.'' IEEE FP16 has 1-bit sign, 5-bit exponent, and
10-bit significand. BF16 has 1-bit sign, 8-bit
exponent, and 7-bit significand. [This disagrees with
\cite{Verheyde:2019:BDD}, which says 5-bit exponent,
and 10-bit significand.] The article also says that two
instructions, BFDOT and BFMMLA have only one rounding
mode: Round to Odd, one type of NaN, and flush-to-zero
on underflow.",
}
@InProceedings{Takagi:2019:AI,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "Author Index",
crossref = "Takagi:2019:ISC",
pages = "219--220",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00051",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents an index of the authors whose articles are
published in the conference proceedings record.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:CN,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "{[Copyright} notice]",
crossref = "Takagi:2019:ISC",
pages = "4--4",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00003",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the copyright information for the conference.
May include reprint permission information.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:CO,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "Conference Organization",
crossref = "Takagi:2019:ISC",
pages = "11--11",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00006",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:F,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "Foreword",
crossref = "Takagi:2019:ISC",
pages = "10--10",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00005",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the introductory welcome message from the
conference proceedings. May include the conference
officers' congratulations to all involved with the
conference event and publication of the proceedings
record.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:PC,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "Program Committee",
crossref = "Takagi:2019:ISC",
pages = "12--12",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00007",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:Sa,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "Sponsors",
crossref = "Takagi:2019:ISC",
pages = "14--14",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00009",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The conference organizers greatly appreciate the
support of the various corporate sponsors listed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:Sb,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "Supporters",
crossref = "Takagi:2019:ISC",
pages = "15--15",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00010",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The conference organizers greatly appreciate the
support of the various corporate sponsors listed.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:SC,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "Steering Committee",
crossref = "Takagi:2019:ISC",
pages = "13--13",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00008",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:TC,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "Table of contents",
crossref = "Takagi:2019:ISC",
pages = "5--9",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00004",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the table of contents/splash page of the
proceedings record.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Takagi:2019:TPI,
author = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
title = "{[Title} page iii]",
crossref = "Takagi:2019:ISC",
pages = "3--3",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00002",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@InProceedings{Thibault:2019:OWL,
author = "Hilaire Thibault and Hacene Ouzia and Benoit Lopez",
title = "Optimal Word-Length Allocation for the Fixed-Point
Implementation of Linear Filters and Controllers",
crossref = "Takagi:2019:ISC",
pages = "175--182",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00040",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This article presents a word-length optimization
problem under accuracy constraints for the hardware
implementation of linear signal processing systems with
fixed-point arithmetic. For State-Space systems
(describing a linear filter or a controller), a
complete error analysis is exhibited, where the final
output error bound depends on the word-lengths and the
fixed-point formats chosen for each variable. The Most
Significant Bit of each one can be determined in order
to guarantee that no overflow occurs. Thus, it is
possible to obtain a hardware implementation minimizing
resource use. This leads to a convex nonlinear integer
optimization problem where the resources to minimize
and the accuracy constraints depend on the internal
word-lengths. This problem can then be solved with
appropriate heuristics. Finally, a global approach is
proposed and illustrated by some examples.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; convex nonlinear integer optimization
problem; convex programming; error analysis; filters;
fixed point arithmetic; fixed-point arithmetic;
Hardware; hardware implementation; integer programming;
linear filter; linear signal processing systems;
nonlinear programming; optimal word-length allocation;
Optimization; Quantization (signal); Roundoff errors;
signal processing; Signal processing algorithms;
state-space methods; state-space systems; word length
optimization; word-length optimization problem; worst
case MSB",
}
@InProceedings{Thomas:2019:CTG,
author = "David B. Thomas",
title = "Compile-Time Generation of Custom-Precision
Floating-Point {IP} using {HLS} Tools",
crossref = "Takagi:2019:ISC",
pages = "192--193",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00044",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "High-Level Synthesis (HLS) tools usually treat
floating-point operators as black-box IP cores, and
then schedule them as primitives when synthesising code
to circuits. This approach relies on a library of IP
blocks for chosen floating-point formats, which are
pre-characterised to determine latency and area
properties needed at compilation time. Two weaknesses
of this approach are that it limits the number of
floating-point formats - typically to half, single, and
double - and that it requires conservative per-cycle
scheduling of operators. Modern HLS tools have
sophisticated intra-cycle scheduling of integer
primitives, as well as C++ front-ends that can execute
substantial algorithms at compile-time. This has
enabled the creation of platform-independent C++
floating-point libraries which generate
custom-precision operators at compile-time, while
providing similar or better results as vendor-supplied
IP blocks. However, certain problems and questions
related to compilation performance and verification
remain, so it is not yet clear how widely applicable
this technique is.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26; black-box IP cores; C++; C++ languages;
chosen floating-point formats; compilation performance;
compilation time; Compile time IP; compile-time
generation; custom-precision floating-point IP;
custom-precision operators; field programmable gate
arrays; Field programmable gate arrays; Floating point;
floating point arithmetic; floating-point libraries;
floating-point operators; FPGA; High Level Synthesis;
high level synthesis; High-Level Synthesis tools; HLS;
intra-cycle scheduling; IP networks; Libraries; Meta
programming; modern HLS tools; Pipelines; Schedules;
Templates; Tools; vendor-supplied IP blocks",
}
@Article{Tiwari:2019:PPE,
author = "Sugandha Tiwari and Neel Gala and Chester Rebeiro and
V. Kamakoti",
title = "{PERI}: A Posit Enabled {RISC-V} Core",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--14",
month = nov,
year = "2019",
bibdate = "Thu Apr 09 15:06:39 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/pdf/1908.01466.pdf",
abstract = "Owing to the failure of Dennard's scaling the last
decade has seen a steep growth of prominent new
paradigms leveraging opportunities in computer
architecture. Two technologies of interest are Posit
and RISC-V. Posit was introduced in mid-2017 as a
viable alternative to IEEE 754-2008. Posit promises
more accuracy, higher dynamic range and fewer unused
states along with simpler hardware designs as compared
to IEEE 754- 2008. RISC-V, on the other hand, provides
a commercial-grade open-source ISA. It is not only
elegant and simple but also highly extensible and
customizable, thereby facilitating novel
micro-architectural research and exploration. In this
paper, we bring these two technologies together and
propose the first Posit Enabled RISC-V core. The paper
provides insights on how the current 'F' extension and
the custom op-code space of RISCV can be
leveraged/modified to support Posit arithmetic. We also
present implementation details of a parameterized and
feature-complete Posit FPU which is integrated with the
RISC-V compliant SHAKTI C-class core either as an
execution unit or as an accelerator. To fully leverage
the potential of Posit, we further enhance our Posit
FPU, with minimal overheads, to support two different
exponent sizes (with posit-size being 32-bits). This
allows applications to switch from high-accuracy
computation mode to a mode with higher dynamic-range at
run-time. In the absence of viable software tool-chain
to enable porting of applications in the Posit domain,
we present a workaround on how certain applications can
be modified minimally to exploit the existing RISC-V
tool-chain. We also provide examples of applications
which can perform better with Posit as compared to IEEE
754-2008. The proposed Posit FPU consumes 3507 slice
LUTs and 1294 slice registers on an Artix-7-100T Xilinx
FPGA while capable of operating at 100 MHz.",
acknowledgement = ack-nhfb,
keywords = "floating-point; IEEE-754; Posit; processor; RISC-V",
}
@InProceedings{Uguen:2019:EHC,
author = "Yohann Uguen and Luc Forget and Florent de Dinechin",
editor = "{IEEE}",
booktitle = "{2019 29th International Conference on Field
Programmable Logic and Applications (FPL)}",
title = "Evaluating the Hardware Cost of the Posit Number
System",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "106--113",
year = "2019",
DOI = "https://doi.org/10.1109/FPL.2019.00026",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{vanDam:2019:APA,
author = "Laurens van Dam and Johan Peltenburg and Zaid Al-Ars
and H. Peter Hofstee",
title = "An Accelerator for Posit Arithmetic Targeting Posit
Level 1 {BLAS} Routines and {Pair-HMM}",
crossref = "Gustafson:2019:CPC",
pages = "5:1--5:10",
year = "2019",
DOI = "https://doi.org/10.1145/3316279.3316284",
bibdate = "Mon Feb 10 12:11:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "5",
keywords = "pair-HMM, BLAS, decimal accuracy, arithmetic,
unum-III, accelerator, posit, unum, FPGA",
location = "Singapore, Singapore",
numpages = "10",
}
@Article{vanWyk:2019:RVT,
author = "Leonard van Wyk",
title = "Rounding versus truncation estimates in difference
calculations",
journal = j-MATH-GAZ,
volume = "103",
number = "557",
pages = "285--292",
month = jul,
year = "2019",
CODEN = "MAGAAS",
DOI = "https://doi.org/10.1017/mag.2019.60",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
ISSN-L = "0025-5572",
bibdate = "Mon Jul 22 08:44:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
URL = "https://www.cambridge.org/core/journals/mathematical-gazette/article/rounding-versus-truncation-estimates-in-difference-calculations/57BD92568C03F0FCDE63BBBDB5E6FF6D",
abstract = "Two common methods of approximating difference
problems are by rounding or truncating the minuend and
the subtrahend before calculating the difference. Since
rounding generally gives a better approximation of a
number than truncation, one might expect that rounding
also generally gives a better approximation in
difference problems. We show that intuition to be
false.",
acknowledgement = ack-nhfb,
ajournal = "Math. Gaz.",
fjournal = "The Mathematical Gazette",
journal-URL = "http://journals.cambridge.org/action/displayIssue?jid=MAG;
http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
onlinedate = "06 June 2019",
}
@InProceedings{Vazquez:2019:NPT,
author = "Alvaro V{\'a}zquez and Elisardo Antelo",
title = "New {$3$D} Projection Transformation for Point
Clouds",
crossref = "Takagi:2019:ISC",
pages = "77--83",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00020",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "3D Computer Graphics based on clouds of points is an
alternative of interest for high quality rendering of
complex scenes. For high quality graphics, the
computational requirements are significantly higher
than in the case of conventional front-end vertex
processing. One of the key computations in the graphics
pipeline is the projection transformation. Conventional
computation of the point-based projection using current
vertex processors might not be the best option for
scalable, high quality 3D graphics based on point
clouds. In this work we propose a new scalable method
that takes advantage of the special characteristics of
the point rendering model. The number of
reciprocal/division computations for perspective
correction is reduced, using instead more effective
multiply-accumulate operations. This is done by
performing a linear approximation of the reciprocal at
the cost of introducing an error in the pixel value.
There is a trade-off in the error introduced and the
exactness of the computation (linear approximation
instead of reciprocal).",
acknowledgement = ack-nhfb,
keywords = "3D computer graphics; 3D projection transformation;
ARITH-26; Cameras; complex geometry; computational
geometry; graphics processor; high quality 3D graphics;
Linear approximation; Point based rendering; point
clouds; point rendering model; point-based projection;
projection transform; Rendering (computer graphics);
rendering (computer graphics); rendering quality;
Three-dimensional displays; Upper bound; vertex
processing; VLSI graphis hardware; Zirconium",
}
@Article{Venkatachalam:2019:DAA,
author = "S. Venkatachalam and E. Adams and H. J. Lee and S.
Ko",
title = "Design and Analysis of Area and Power Efficient
Approximate {Booth} Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "11",
pages = "1697--1703",
month = nov,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2926275",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Oct 29 11:08:44 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Approximate Booth arithmetic; Complexity
theory; Computational modeling; Digital signal
processing; Encoding; Generators; inexact computing;
Integrated circuit modeling; radix-4 partial product
generators",
}
@Misc{Verheyde:2019:BDD,
author = "Arne Verheyde",
title = "{BFloat16} Deep Dive: {ARM} Brings {BF16} Deep
Learning Data Format to {ARMv8-A}",
howpublished = "Tom's Hardware Web site.",
day = "21",
month = sep,
year = "2019",
bibdate = "Mon Sep 23 07:15:36 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.tomshardware.com/news/bfloat16-deep-dive-arm-bf16-support-armv8-a,40305.html",
abstract = "RM will be adding BFloat16 support in the next
revision of the ARMv8-A architecture under its Project
Trillium ML platform. It marks a new major milestone in
the widespread adoption of the young data format that
is taking the deep learning community by storm. In this
article, we'll dive into the origins and benefits of
the format.",
acknowledgement = ack-nhfb,
remark = "The BFloat16 format has 1-bit sign, 5-bit exponent,
and 10-bit significand. From the article: ``\ldots{}
hardware area (number of transistors) scales roughly
with the square of the mantissa width. So having just
three fewer mantissa bits (7 instead of 10) means that
a bfloat16 multiplier takes up about half the area of a
conventional FP16 unit. Compared to an FP32 multiplier,
its size is eight times smaller, with an equivalent
reduction in power consumption as well. Or conversely,
within the same silicon area more useful hardware can
be put to achieve higher performance. \ldots{} Bfloat16
is called Brain Floating Point Format in full (or BF16
in short), as it is named after the Google Brain
research group where it was conceived. As Jeff Dean,
Senior Fellow of Google AI, explained in a series of
Twitter posts, Google started using the format since
the early days of TensorFlow. More specifically, it was
supported in hardware since the second version of its
Tensor Processing Units (TPUs), the TPU v2 in 2017.
\ldots{} Intel showed that an integer multiplier costs
less than half the area of a floating point multiplier
of the same number of bits. Though less relevant, the
difference is even larger for addition: while an
integer adder scales linearly with the number of bits,
a floating point adder scales quadratically,
\ldots{}''",
}
@InProceedings{Villa:2019:NDB,
author = "Oreste Villa and Mark Stephenson and David Nellans and
Stephen W. Keckler",
editor = "{IEEE\slash ACM}",
booktitle = "{MICRO '52: Proceedings of the 52nd Annual IEEE\slash
ACM International Symposium on Microarchitecture,
Columbus OH, USA, October 12--16, 2019}",
title = "{Nvbit}: A dynamic binary instrumentation framework
for {NVIDIA GPUs}",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "1104",
pages = "372--383",
year = "2019",
ISBN = "1-4503-6938-3",
ISBN-13 = "978-1-4503-6938-1",
LCCN = "QA76.6 .A568",
bibdate = "Mon Sep 11 07:23:59 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1145/3352460",
}
@InProceedings{Villalba-Moreno:2019:RSU,
author = "Julio Villalba-Moreno and Javier Hormigo and Francisco
Jaime",
title = "Reproducible Summation Under {HUB} Format",
crossref = "Takagi:2019:ISC",
pages = "38--45",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00015",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point reproducibility is a property claimed
by programmers and end users. Half-Unit-Biased (HUB) is
a new representation format in which the round to
nearest is carried out by truncation, preventing any
carry propagation and saving time and area. In this
paper we study the reproducible summation of HUB
numbers by using a error-free vector transformation
technique, providing both a specific architecture and
the usage of combined HUB/Standard floating point
adders to achieve a reproducible result.",
acknowledgement = ack-nhfb,
keywords = "adders; Adders; ARITH-26; carry propagation; Computer
architecture; Computer science; Delays; Digital
arithmetic; end users; error-free vector transformation
technique; floating point arithmetic; Half-Unit-Biased;
HUB (Half-Unit-Biased) floating-point format; HUB
format; HUB numbers; point adders; point
reproducibility; representation format; reproducible
summation; Reproducible summation, HUB format;
Standards; Terminology",
}
@InProceedings{Volkova:2019:SAI,
author = "Anastasia Volkova and Jean-Michel Muller",
title = "Semi-Automatic Implementation of the Complementary
Error Function",
crossref = "Takagi:2019:ISC",
pages = "167--174",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00039",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The normal and complementary error functions are
ubiquitous special functions for any mathematical
library. They have a wide range of applications.
Practical applications call for customized
implementations that have strict accuracy requirements.
Accurate numerical implementation of these functions
is, however, non-trivial. In particular, the
complementary error function erfc for large positive
arguments heavily suffers from cancellation, which is
largely due to its asymptotic behavior. We provide a
semi-automatic code generator for the erfc function
which is parameterized by the user-given bound on the
relative error. Our solution exploits the asymptotic
expression of erfc and leverages the automatic code
generator Metalibm that provides accurate polynomial
approximations. A fine-grained a priori error analysis
provides a libm developer with the required accuracy
for each step of the evaluation. In critical parts, we
exploit double-word arithmetic to achieve
implementations that are fast, yet accurate up to 50
bits, even for large input arguments. We demonstrate
that for high required accuracies the automatically
generated code has performance comparable to that of
the standard libm and for lower ones our code
demonstrated roughly 25\% speedup.",
acknowledgement = ack-nhfb,
keywords = "a priori error analysis; ARITH-26; asymptotic
behavior; asymptotic expression; complementary error
functions; Digital arithmetic; Error analysis; error
analysis; error function; floating-point arithmetic;
Generators; Libraries; Lips; mathematical library;
Metalibm; normal error functions; polynomial
approximation; polynomial approximations; program
compilers; semi-automated code generation;
semiautomatic code generator; semiautomatic
implementation; Standards; Tools; ubiquitous special
functions",
}
@Article{Walczyk:2019:MFI,
author = "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
Cie{\'s}li{\'n}ski",
title = "A Modification of the Fast Inverse Square Root
Algorithm",
journal = "Computation",
volume = "7",
number = "3",
pages = "41",
month = aug,
year = "2019",
DOI = "https://doi.org/10.3390/computation7030041",
ISSN = "2079-3197",
ISSN-L = "2079-3197",
bibdate = "Thu Apr 10 15:20:23 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Walther:2019:VNR,
author = "Christoph Walther",
title = "Verified {Newton--Raphson} Iteration for
Multiplicative Inverses Modulo Powers of Any Base",
journal = j-TOMS,
volume = "45",
number = "1",
pages = "9:1--9:7",
month = mar,
year = "2019",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3301317",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon May 6 18:23:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Dumas:2014:NRI}.",
URL = "https://dl.acm.org/citation.cfm?id=3301317",
abstract = "We identify two faults in a published algorithm for
fast computation of multiplicative inverses modulo
prime powers. We patch the algorithm and present
machine-assisted proofs of correctness of the repair.
Our formal proofs also reveal that being prime is an
unnecessary demand for the power base, thus attributing
a wider scope of applications to the repaired
algorithm.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Misc{Wang:2019:BSH,
author = "Shibo Wang and Pankaj Kanwar",
title = "{BFloat16}: The secret to high performance on Cloud
{TPUs}",
howpublished = "Web site",
day = "23",
month = aug,
year = "2019",
bibdate = "Fri Apr 03 09:12:39 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://cloud.google.com/blog/products/ai-machine-learning/bfloat16-the-secret-to-high-performance-on-cloud-tpus",
acknowledgement = ack-nhfb,
}
@Article{Wang:2019:PAA,
author = "Shouxiang Wang and Kai Wang and Lei Wu and Chengshan
Wang",
title = "Polar Affine Arithmetic: Optimal Affine Approximation
and Operation Development for Computation in Polar Form
Under Uncertainty",
journal = j-TOMS,
volume = "45",
number = "1",
pages = "6:1--6:29",
month = mar,
year = "2019",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3274659",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon May 6 18:23:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/citation.cfm?id=3274659",
abstract = "Uncertainties practically arise from numerous factors,
such as ambiguous information, inaccurate model, and
environment disturbance. Interval arithmetic has
emerged to solve problems with uncertain parameters,
especially in the computational process where only the
upper and lower bounds of parameters can be
ascertained. In rectangular coordinate systems, the
basic interval operations and improved interval
algorithms have been developed in the numerical
analysis. However, in polar coordinate systems,
interval arithmetic still suffers from issues of
complex computation and overestimation. This article
defines a polar affine variable and develops a polar
affine arithmetic (PAA) that extends affine arithmetic
to the polar coordinate systems, which performs better
in many aspects than the corresponding polar interval
arithmetic (PIA). Basic arithmetic operations are
developed based on the complex affine arithmetic. The
Chebyshev approximation theory and the min-range
approximation theory are used to identify the best
affine approximation. PAA can accurately keep track of
the interdependency among multiple variables throughout
the calculation procedure, which prominently reduces
the solution conservativeness. Numerical examples
implemented in MATLAB programs show that, compared with
benchmark results from the Monte Carlo method, the
proposed PAA ensures completeness of the exact solution
and presents a more compact solution region than PIA
when dependency exists in the calculation process.
Meanwhile, a comparison of affine arithmetic in polar
and rectangular coordinates is presented. An
application of PAA in circuit analysis is
quantitatively presented and potential applications in
other research fields involving complex variables in
polar form will be gradually developed.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Ye:2019:NCA,
author = "T. Ye and Y. Wei and W. Meier",
title = "A New Cube Attack on {MORUS} by Using Division
Property",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "12",
pages = "1731--1740",
month = dec,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2929137",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Nov 7 11:20:24 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Authenticated encryption algorithm; Boolean functions;
cube attack; division property; Encryption; mixed
integer linear programming; MORUS; Software algorithms;
Time complexity; time complexity",
}
@Article{Zhang:2019:EMP,
author = "H. Zhang and D. Chen and S. Ko",
title = "Efficient Multiple-Precision Floating-Point Fused
Multiply-Add with Mixed-Precision Support",
journal = j-IEEE-TRANS-COMPUT,
volume = "68",
number = "7",
pages = "1035--1048",
month = jul,
year = "2019",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2895031",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 11 09:46:20 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Clocks; Computer architecture; Deep learning;
double-precision operations; efficiency 10.6 percent;
efficiency 6.5 percent; floating point arithmetic;
floating-point arithmetics; floating-point operations;
FMA architecture; Fused multiply-add; half-precision
FMA operations; Hardware; logic design; mixed-precision
arithmetics; mixed-precision dot-product operations;
mixed-precision FMA operations; mixed-precision
operations; mixed-precision support; multiple-precision
arithmetics; multiple-precision floating-point;
multiple-precision FMA design; multiple-precision FMA
unit; multiplying circuits; normal FMA operations;
parallel half-precision operations; Pipelines;
quadruple-precision operation; single-precision
operations; Standards",
}
@InProceedings{Zhang:2019:EPM,
author = "Hao Zhang and Jiongrui He and Seok-Bum Ko",
editor = "IEEE",
booktitle = "{2019 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "Efficient Posit Multiply-Accumulate Unit Generator for
Deep Learning Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
month = may,
year = "2019",
DOI = "https://doi.org/10.1109/iscas.2019.8702349",
bibdate = "Thu Dec 14 18:03:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zorn:2019:SPD,
author = "Bill Zorn and Dan Grossman and Zach Tatlock",
title = "Sinking Point: Dynamic Precision Tracking for
Floating-Point",
crossref = "Gustafson:2019:CPC",
pages = "4:1--4:8",
year = "2019",
DOI = "https://doi.org/10.1145/3316279.3316283",
bibdate = "Mon Feb 10 12:11:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
articleno = "4",
keywords = "Floating point, numerical analysis",
location = "Singapore, Singapore",
numpages = "8",
}
@InProceedings{Abdelfattah:2020:IBF,
author = "Ahmad Abdelfattah and Stan Tomov and Jack Dongarra",
title = "Investigating the Benefit of {FP16}-Enabled
Mixed-Precision Solvers for Symmetric Positive Definite
Matrices Using {GPUs}",
crossref = "Krzhizhanovskaya:2020:CSI",
pages = "237--250",
year = "2020",
DOI = "https://doi.org/10.1007/978-3-030-50417-5_18",
bibdate = "Thu Jun 25 08:49:09 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Abdelfattah:2020:MMB,
author = "Ahmad Abdelfattah and Stanimire Tomov and Jack
Dongarra",
title = "Matrix multiplication on batches of small matrices in
half and half-complex precisions",
journal = j-J-PAR-DIST-COMP,
volume = "145",
number = "??",
pages = "188--201",
month = nov,
year = "2020",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1016/j.jpdc.2020.07.001",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Wed May 26 16:11:03 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0743731520303300",
acknowledgement = ack-nhfb,
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
}
@Article{Adams:2020:ARD,
author = "E. Adams and S. Venkatachalam and S. Ko",
title = "Approximate Restoring Dividers Using Inexact Cells and
Estimation From Partial Remainders",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "4",
pages = "468--474",
month = apr,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2953751",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Mar 12 16:58:27 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Approximate computing; error analysis; image
processing applications; low-power; restoring
division",
}
@InProceedings{Agrawal:2020:FAH,
author = "Rashmi Agrawal and Lake Bu and Michel A. Kinsy",
booktitle = "{2020 IEEE 28th Annual International Symposium on
Field-Programmable Custom Computing Machines (FCCM)}",
title = "Fast Arithmetic Hardware Library For {RLWE-Based}
Homomorphic Encryption",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "206--206",
year = "2020",
DOI = "https://doi.org/10.1109/FCCM48280.2020.00037",
bibdate = "Fri Sep 22 08:05:37 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Ahrens:2020:AER,
author = "Peter Ahrens and James Demmel and Hong Diep Nguyen",
title = "Algorithms for Efficient Reproducible Floating Point
Summation",
journal = j-TOMS,
volume = "46",
number = "3",
pages = "22:1--22:49",
month = sep,
year = "2020",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3389360",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Sep 26 07:28:19 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3389360",
abstract = "We define ``reproducibility'' as getting bitwise
identical results from multiple runs of the same
program, perhaps with different hardware resources or
other changes that should not affect the answer. Many
users depend on reproducibility for debugging or
correctness. However, dynamic scheduling of parallel
computing resources, combined with nonassociative
floating point addition, makes reproducibility
challenging even for summation, or operations like the
BLAS. We describe a ``reproducible accumulator'' data
structure (the ``binned number'') and associated
algorithms to reproducibly sum binary floating point
numbers, independent of summation order. We use a
subset of the IEEE Floating Point Standard 754-2008 and
bitwise operations on the standard representations in
memory. Our approach requires only one read-only pass
over the data, and one reduction in parallel, using a
6-word reproducible accumulator (more words can be used
for higher accuracy), enabling standard tiling
optimization techniques. Summing $n$ words with a
6-word reproducible accumulator requires approximately
$ 9 n$ floating point operations (arithmetic,
comparison, and absolute value) and approximately $ 3
n$ bitwise operations. The final error bound with a
6-word reproducible accumulator and our default
settings can be up to 229 times smaller than the error
bound for conventional (recursive) summation on
ill-conditioned double-precision inputs",
acknowledgement = ack-nhfb,
articleno = "22",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
keywords = "accurate floating-point summation",
}
@InProceedings{Anonymous:2020:ACa,
author = "Anonymous",
title = "{ARITH 2020} Committees",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00006",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2020:ACb,
author = "Anonymous",
title = "{ARITH 2020} Committees",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00007",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Provides a listing of current committee members and
society officers.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2020:ACN,
author = "Anonymous",
title = "[{ARITH 2020} Copyright notice]",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00003",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the copyright information for the conference.
May include reprint permission information.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2020:AI,
author = "Anonymous",
title = "{ARITH 2020} Index",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00030",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents an index of the authors whose articles are
published in the conference proceedings record.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2020:ALR,
author = "Anonymous",
title = "{ARITH 2020} List Reviewer Page",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00008",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The conference offers a note of thanks and lists its
reviewers.",
acknowledgement = ack-nhfb,
}
@Misc{Anonymous:2020:RVE,
author = "Anonymous",
title = "{RISC-V} embedded variant {RV32E} now fully supported
by {SEGGER}'s Floating-Point library",
howpublished = "Web site",
day = "21",
month = sep,
year = "2020",
bibdate = "Thu Jan 28 18:02:53 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.design-reuse.com/news/48672/segger-s-floating-point-library-risc-v-rv32e.html",
acknowledgement = ack-nhfb,
remark = "The story reports a significant code size reduction,
and speedup, over the GNU floating-point library.",
}
@InProceedings{Anonymous:2020:SA,
author = "Anonymous",
title = "Sponsors {ARITH 2020}",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00009",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The conference organizers greatly appreciate the
support of the various corporate sponsors listed.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2020:TC,
author = "Anonymous",
title = "Table of Contents",
crossref = "Cornea:2020:ISC",
pages = "i--iii",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00004",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the table of contents/splash page of the
proceedings record.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2020:TPa,
author = "Anonymous",
title = "{[Title} page]",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00001",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2020:TPb,
author = "Anonymous",
title = "{[Title} page]",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00002",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
}
@Article{Arnold:2020:IRL,
author = "M. G. Arnold and V. Paliouras and I. Kouretas",
title = "Implementing the Residue Logarithmic Number System
Using Interpolation and Cotransformation",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "12",
pages = "1719--1732",
month = dec,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2930514",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Nov 24 09:42:22 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Bajard:2020:AFV,
author = "Jean-Claude Bajard and Julien Eynard and Paulo Martins
and Leonel Sousa and Vincent Zucca",
title = "An asymptotically faster version of {FV} supported on
{HPR}",
crossref = "Cornea:2020:ISC",
pages = "80--87",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00020",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "State-of-the-art implementations of homomorphic
encryption exploit the Fan and Vercauteren (FV) scheme
and the Residue Number System (RNS). While the RNS
breaks down large integer arithmetic into smaller
independent channels, its non-positional nature makes
operations such as division and rounding hard to
implement, and makes the representation of small values
inefficient. In this work, we propose the application
of the Hybrid Position-Residues Number System
representation to the FV scheme. This is a positional
representation of large radix where the digits are
represented in RNS. It inherits the benefits from RNS
and allows to accelerate the critical division and
rounding operations while also making the
representation of smaller values more compact. This
directly benefits the decryption and the homomorphic
multiplication procedures, reducing their asymptotic
complexity, in dimension n, from O(n2 log n) to O(n log
n) and from O(n3 log n) to O(n3), respectively and has
resulted in noticeable speedups when experimentally
compared to related art RNS implementations.",
acknowledgement = ack-nhfb,
keywords = "Acceleration; Art; Complexity theory; Encryption;
Fan-Vercauteren scheme; Fans; Homomorphic Encryption;
Indexes; Residue Number System",
}
@InProceedings{Barthel:2020:ASA,
author = "Moritz B{\"a}rthel and Jochen Rust and Steffen Paul",
booktitle = "{2020 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "Application-Specific Analysis of Different {SORN}
Datatypes for Unum Type-2-Based Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2020",
DOI = "https://doi.org/10.1109/ISCAS45731.2020.9181182",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Boldo:2020:CRF,
author = "Sylvie Boldo and Diane Gallois-Wong and Thibault
Hilaire",
title = "A Correctly-Rounded Fixed-Point-Arithmetic Dot-Product
Algorithm",
crossref = "Cornea:2020:ISC",
pages = "9--16",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00011",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Dot products (also called sums of products) are
ubiquitous in matrix computations, for instance in
signal processing. We are especially interested in
digital filters, where they are the core operation. We
therefore focus on fixed-point arithmetic, used in
embedded systems for time and energy efficiency. Common
dot product algorithms ensure faithful rounding. For
the sake of accuracy and reproducibility, we want to
ensure correct rounding. This article describes an
algorithm that computes a correctly-rounded sum of
products from inputs whose format is known in advance.
This algorithm relies on odd rounding (that is easily
implemented in hardware) and comes with a careful proof
and some cost analysis.",
acknowledgement = ack-nhfb,
keywords = "Correct Rounding; Dot Product; Embedded systems;
Fixed-point arithmetic; Fixed-Point Arithmetic;
floating-point arithmetic; Hardware; Odd Rounding;
Runtime; Signal processing; Signal processing
algorithms; Sorting; Sum-of-Products",
}
@InProceedings{Bottcher:2020:HDL,
author = "Andreas B{\"o}ttcher and Keanu Kullmann and Martin
Kumm",
title = "Heuristics for the Design of Large Multipliers for
{FPGAs}",
crossref = "Cornea:2020:ISC",
pages = "17--24",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00012",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The following topics are dealt with: floating point
arithmetic; cryptography; field programmable gate
arrays; computational complexity; embedded systems;
public key cryptography; optimisation; probability;
fixed point arithmetic; and digital signal processing
chips.",
acknowledgement = ack-nhfb,
keywords = "Complexity theory; computer arithmetic; Digital
arithmetic; Field programmable gate arrays; heuristics;
Integer linear programming; Karatsuba multiplier; large
multiplier; Optimization; post quantum cryptography;
Shape; Table lookup; tiling",
}
@Article{Brisebarre:2020:EAS,
author = "Nicolas Brisebarre and Mioara Joldes and Jean-Michel
Muller and Ana-Maria Nanes and Joris Picot",
title = "Error Analysis of Some Operations Involved in the
{Cooley--Tukey Fast Fourier Transform}",
journal = j-TOMS,
volume = "46",
number = "2",
pages = "11:1--11:27",
month = jun,
year = "2020",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3368619",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Fri Jun 12 07:37:53 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3368619",
abstract = "We are interested in obtaining error bounds for the
classical Cooley--Tukey fast Fourier transform
algorithm in floating-point arithmetic, for the 2-norm
as well as for the infinity norm. For that purpose, we
also give some results on the relative error of the
complex multiplication by a root of unity, and on the
largest value that can take the real or imaginary part
of one term of the fast Fourier transform of a vector
$x$, assuming that all terms of $x$ have real and
imaginary parts less than some value $b$.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Bruguera:2020:LLF,
author = "J. D. Bruguera",
title = "Low Latency Floating-Point Division and Square Root
Unit",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "2",
pages = "274--287",
month = feb,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2947899",
ISSN = "2326-3814",
ISSN-L = "0018-9340",
bibdate = "Wed Jan 22 06:44:09 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Computer architecture; Convergence; Digit-recurrence
algorithms; Estimation; floating-point division, and
square root; Iterative methods; Organizations;
Registers; Timing",
}
@InProceedings{Brunie:2020:TFP,
author = "Hugo Brunie and Costin Iancu and Khaled Z. Ibrahim and
Philip Brisk and Brandon Cook",
title = "Tuning floating-point precision using dynamic program
information and temporal locality",
crossref = "IEEE:2020:SPI",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--14",
year = "2020",
bibdate = "Mon Sep 11 08:19:28 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We present a methodology for precision tuning of full
applications. These techniques must select a search
space composed of either variables or instructions and
provide a scalable search strategy. In full application
settings one cannot assume compiler support for
practical reasons. Thus, an additional important
challenge is enabling code refactoring. We argue for an
instruction-based search space and we show: (1) how to
exploit dynamic program information based on call
stacks; and (2) how to exploit the iterative nature of
scientific codes, combined with temporal locality. We
applied the methodology to tune the implementation of
scientific codes written in a combination of Python,
CUDA, C++ and Fortran, tuning calls to math exp library
functions. The iterative search refinement always
reduces the search complexity and the number of steps
to solution. Dynamic program information increases
search efficacy. Using this approach, we obtain
application runtime performance improvements up to
27\%.",
acknowledgement = ack-nhfb,
articleno = "50",
}
@InProceedings{Buoncristiani:2020:ENS,
author = "Nicholas Buoncristiani and Sanjana Shah and David
Donofrio and John Shalf",
editor = "{IEEE}",
booktitle = "{2020 IEEE International Parallel and Distributed
Processing Symposium (IPDPS)}",
title = "Evaluating the Numerical Stability of Posit
Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "612--621",
year = "2020",
DOI = "https://doi.org/10.1109/IPDPS47924.2020.00069",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Calligo:2020:PNU,
author = "{Calligo Technologies}",
title = "Posit Numeric Unit ({PNU-IP})",
howpublished = "Web software.",
year = "2020",
bibdate = "Sat Dec 16 15:24:16 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://calligotech.com/posit-numeric-unit-pnu-ip",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Cavalcante:2020:AGS,
author = "Matheus Cavalcante and Fabian Schuiki and Florian
Zaruba and Michael Schaffner and Luca Benini",
title = "{Ara}: a {1-GHz+} Scalable and Energy-Efficient
{RISC-V} Vector Processor With Multiprecision
Floating-Point Support in 22-nm {FD-SOI}",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "28",
number = "2",
pages = "530--543",
year = "2020",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2019.2950087",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@Article{Cherubin:2020:TRP,
author = "Stefano Cherubin and Giovanni Agosta",
title = "Tools for Reduced Precision Computation: a Survey",
journal = j-COMP-SURV,
volume = "53",
number = "2",
pages = "33:1--33:35",
month = jul,
year = "2020",
CODEN = "CMSVAN",
DOI = "https://doi.org/10.1145/3381039",
ISSN = "0360-0300 (print), 1557-7341 (electronic)",
ISSN-L = "0360-0300",
bibdate = "Wed Jul 8 17:24:43 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3381039",
abstract = "The use of reduced precision to improve performance
metrics such as computation latency and power
consumption is a common practice in the embedded
systems field. This practice is emerging as a new trend
in High Performance Computing (HPC), especially when
new error-tolerant applications are considered.
However, standard compiler frameworks do not support
automated precision customization, and manual tuning
and code transformation is the approach usually adopted
in most domains. In recent years, research have been
studying ways to improve the automation of this
process. This article surveys this body of work,
identifying the critical steps of this process, the
most advanced tools available, and the open challenges
in this research area. We conclude that, while several
mature tools exist, there is still a gap to close,
especially for tools based on static analysis rather
than profiling, as well as for integration within
mainstream, industry-strength compiler frameworks.",
acknowledgement = ack-nhfb,
articleno = "33",
fjournal = "ACM Computing Surveys",
journal-URL = "https://dl.acm.org/loi/csur",
}
@InProceedings{Chien:2020:PNA,
author = "Steven W. D. Chien and Ivy B. Peng and Stefano
Markidis",
title = "Posit {NPB}: Assessing the Precision Improvement in
{HPC} Scientific Applications",
crossref = "Wyrzykowski:2020:PPA",
pages = "301--310",
year = "2020",
DOI = "https://doi.org/10.1007/978-3-030-43229-4_26",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Chowdhary:2020:DDN,
author = "Sangeeta Chowdhary and Jay P. Lim and Santosh
Nagarakatte",
booktitle = "{PLDI 2020: Proceedings of the 41st ACM SIGPLAN
Conference on Programming Language Design and
Implementation}",
title = "Debugging and detecting numerical errors in
computation with posits",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "731--746",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1145/3385412.3386004",
bibdate = "Sat Dec 9 08:43:53 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Cococcioni:2020:FAH,
author = "Marco Cococcioni and Federico Rossi and Emanuele
Ruffaldi and Sergio Saponara",
booktitle = "Applications in Electronics Pervading Industry,
Environment and Society",
title = "A Fast Approximation of the Hyperbolic Tangent When
Using Posit Numbers and Its Application to Deep Neural
Networks",
publisher = pub-SV,
address = pub-SV:adr,
pages = "213--221",
year = "2020",
DOI = "https://doi.org/10.1007/978-3-030-37277-4_25",
ISBN = "3-030-37277-4",
ISBN-13 = "978-3-030-37277-4",
ISSN = "1876-1119",
ISSN-L = "1876-1100",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Cococcioni:2020:FDN,
author = "Marco Cococcioni and Federico Rossi and Emanuele
Ruffaldi and Sergio Saponara",
title = "Fast deep neural networks for image processing using
posits and {ARM} scalable vector extension",
journal = "Journal of Real-Time Image Processing",
volume = "17",
number = "3",
publisher = pub-SV,
address = pub-SV:adr,
pages = "759--771",
month = may,
year = "2020",
DOI = "https://doi.org/10.1007/s11554-020-00984-x",
ISSN = "1861-8219",
ISSN-L = "1861-8200",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Cococcioni:2020:NPB,
author = "Marco Cococcioni and Federico Rossi and Emanuele
Ruffaldi and Sergio Saponara",
editor = "{IEEE}",
booktitle = "{2020 IEEE International Conference on Smart Computing
(SMARTCOMP)}",
title = "A Novel Posit-based Fast Approximation of {ELU}
Activation Function for Deep Neural Networks",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "244--246",
year = "2020",
DOI = "https://doi.org/10.1109/SMARTCOMP50058.2020.00053",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cornea:2020:FA,
author = "Marius Cornea and Weiqiang Liu and Arnaud Tisserand",
title = "Foreword {ARITH 2020}",
crossref = "Cornea:2020:ISC",
pages = "i--i",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00005",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The 27th IEEE Symposium on Computer Arithmetic,
ARITH-2020, was initially planned to be held in
Portland, Oregon, USA on Jun 7-10, 2020. Due to the
COVID-19 crisis all around the world in 2020, the
face-to-face meeting has been canceled. The paper
selection process was completed, and the accepted
papers have been included in the ARITH-2020
proceedings. For ARITH-2020, 73 anonymous submissions
have been submitted at the beginning of February.
Following the peer-review practice of this symposium,
each paper was blind-reviewed by at least three, and up
to five, Program Committee members, and a final
decision was made by the committee in mid-April. 40 PC
members and some external reviewers were involved in
this process. The technical program of ARITH- 2020
includes 16 regular papers (8 pages) and 4 short papers
(4 pages).",
acknowledgement = ack-nhfb,
}
@InProceedings{Coward:2020:ADS,
author = "Samuel Coward and Theo Drane and Yoav Harel",
title = "Automatic Design Space Exploration for an Error
Tolerant Application",
crossref = "Cornea:2020:ISC",
pages = "117--120",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00025",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Creating optimized hardware for error tolerant
applications presents significant challenges as well as
opportunities. Many algorithms in computer graphics &
vision are error tolerant, as their application level
correctness ultimately rests on human perception. This
error tolerance can be exploited in reducing hardware
implementation cost. The challenge is how to explore
the space of application level correct designs to
determine the optimized hardware architecture. This
paper puts forward an approach to automatically explore
the space which maximally exploits the acceptable error
to minimize hardware cost for a particular graphics
algorithm --- Level-Of-Detail. Results, so far, have
shown a 26\% hardware area improvement.",
acknowledgement = ack-nhfb,
keywords = "accuracy hardware tradeoffs; approximate computing;
computer graphics; Computer graphics; Delays; design
automation; floating-point; Hardware; Logic gates;
Minimization; multiple-precision; numerical analysis;
power-efficient; Space exploration",
}
@InProceedings{Das:2020:SYR,
author = "Arnab Das and Ian Briggs and Ganesh Gopalakrishnan and
Sriram Krishnamoorthy and Pavel Panchekha",
title = "Scalable yet Rigorous Floating-Point Error Analysis",
crossref = "IEEE:2020:SPI",
pages = "1--14",
year = "2020",
bibdate = "Mon Sep 11 06:40:11 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Automated techniques for rigorous floating-point
round-off error analysis are a prerequisite to placing
important activities in HPC such as precision
allocation, verification, and code optimization on a
formal footing. Yet existing techniques cannot provide
tight bounds for expressions beyond a few dozen
operators --- barely enough for HPC. In this work, we
offer an approach embedded in a new tool called Satire
that scales error analysis by four orders of magnitude
compared to today's best-of-class tools. We explain how
three key ideas underlying Satire helps it attain such
scale: path strength reduction, bound optimization, and
abstraction. Satire provides tight bounds and rigorous
guarantees on significantly larger expressions with
well over a hundred thousand operators, covering
important examples including FFT, matrix
multiplication, and PDE stencils.",
acknowledgement = ack-nhfb,
articleno = "51",
}
@Article{deCamargo:2020:REA,
author = "Andr{\'e} Pierro de Camargo",
title = "Rounding error analysis of divided differences
schemes: {Newton}'s divided differences; {Neville}'s
algorithm; {Richardson} extrapolation; {Romberg}
quadrature; etc.",
journal = j-NUMER-ALGORITHMS,
volume = "85",
number = "2",
pages = "591--606",
month = oct,
year = "2020",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-019-00828-1",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Thu Sep 10 11:29:47 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://link.springer.com/article/10.1007/s11075-019-00828-1",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@InProceedings{Defour:2020:CPM,
author = "David Defour and Pablo de Oliveira Castro and Matei
I{\c{s}}toan and Eric Petit",
title = "Custom-Precision Mathematical Library Explorations for
Code Profiling and Optimization",
crossref = "Cornea:2020:ISC",
pages = "121--124",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00026",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The typical processors used for scientific computing
have fixed-width data-paths. This implies that
mathematical libraries were specifically developed to
target each of these fixed precisions (binary16,
binary32, binary64). However, to address the increasing
energy consumption and throughput requirements of
scientific applications, library and hardware designers
are moving beyond this one-size-fits-all approach. In
this article we propose to study the effects and
benefits of using user-defined floating-point formats
and target accuracies in calculations involving
mathematical functions. Our tool collects input-data
profiles and iteratively explores lower precisions for
each call-site of a mathematical function in user
applications. This profiling data will be a valuable
asset for specializing and fine-tuning mathematical
function implementations for a given application. We
demonstrate the tool's capabilities on SGP4, a
satellite tracking application. The profile data shows
the potential for specialization and provides insight
into answering where it is useful to provide
variable-precision designs for elementary function
evaluation.",
acknowledgement = ack-nhfb,
keywords = "custom-precision; floating-point; Hardware; HPC; libm;
Libraries; Mathematical model; Optimization;
optimization; Satellites; specialization; Standards;
Tools",
}
@InProceedings{Dinda:2020:SFP,
author = "Peter Dinda and Alex Bernat and Conor Hetland",
editor = "????",
booktitle = "Proceedings of the 29th International Symposium on
High-Performance Parallel and Distributed Computing",
title = "Spying on the floating point behavior of existing,
unmodified scientific applications",
publisher = "????",
address = "????",
pages = "5--16",
year = "2020",
bibdate = "Mon Sep 11 06:53:07 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Dolgov:2020:PCI,
author = "Sergey Dolgov and Dmitry Savostyanov",
title = "Parallel cross interpolation for high-precision
calculation of high-dimensional integrals",
journal = j-COMP-PHYS-COMM,
volume = "246",
number = "??",
pages = "Article 106869",
month = jan,
year = "2020",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2019.106869",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Tue Oct 29 14:07:57 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465519302565",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
keywords = "Cross interpolation; High precision; High-dimensional
integration; Ising integrals; Ising model; Monte Carlo
integration; Parallel algorithms; quasi Monte Carlo
integration; Tensor train format",
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
remark = "See \cite{Bailey:2006:IIC,Bailey:2015:HPA}.",
}
@InProceedings{Elkhatib:2020:HOM,
author = "Rami Elkhatib and Reza Azarderakhsh and Mehran
Mozaffari-Kermani",
title = "Highly Optimized {Montgomery} Multiplier for {SIKE}
Primes on {FPGA}",
crossref = "Cornea:2020:ISC",
pages = "64--71",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00018",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "New primes were proposed for Supersingular Isogeny Key
Encapsulation (SIKE) in NIST standardization process of
Round 2 after further cryptanalysis research showed
that the security levels of the initial primes chosen
were overestimated [1], [2]. In this paper, we develop
a highly optimized Ep Montgomery multiplication
algorithm and architecture that further utilizes the
special form of SIKE prime compared to previous
implementations available in the literature. We then
implement SIKE for all Round 2 NIST security levels
(SIKEp434 for NIST security level 1, SIKEp503 for NIST
security level 2, SIKEp610 for NIST security level 3,
and SIKEp751 for NIST security level 5) on Xilinx
Virtex 7 using the proposed multiplier. Our best
implementation (NIST security level 1) runs 29\% faster
and occupies 30\% less hardware resources in comparison
to the leading counterpart available in the literature
[3] and implementations for other security levels
achieved similar improvement.",
acknowledgement = ack-nhfb,
keywords = "Computer architecture; Elliptic curve cryptography;
Hardware; hardware architectures; isogeny-based
cryptography; Montgomery multiplication; NIST;
post-quantum cryptography; SIKE",
}
@Misc{Erickson:2020:GNF,
author = "Jack Erickson",
title = "Generate Native Floating-Point {FPGA} Implementations
for Field-Oriented Control of Motors",
howpublished = "MathWorks Web site.",
day = "17",
month = feb,
year = "2020",
bibdate = "Mon Feb 17 10:32:39 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.mathworks.com/videos/generate-native-floating-point-fpga-implementations-for-field-oriented-control-of-motors.html",
abstract = "HDL Coder now supports native floating-point code
generation, where you can implement your high-dynamic
range operations in single-precision floating point,
and generate VHDL or Verilog code directly without
converting to fixed-point types and operations.",
acknowledgement = ack-nhfb,
}
@TechReport{Fog:2020:FPE,
author = "Agner Fog",
title = "Floating point exception tracking and {NAN}
propagation",
type = "Report",
institution = "Technical University of Denmark",
address = "Lyngby, Denmark",
pages = "10",
day = "27",
month = apr,
year = "2020",
bibdate = "Wed May 17 11:52:28 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.agner.org/optimize/nan_propagation.pdf",
abstract = "The most common methods for detecting floating point
errors are based on exception trapping or a global
status register. These methods are inefficient in
modern systems that use out-of-order parallelism and
single-instruction-multiple-data (SIMD) parallelism for
improving performance. It is argued that a method based
on NAN propagation is more efficient and deterministic.
Problems with NAN propagation in current systems are
discussed. Examples of implementation in the C++ vector
class library and in an experimental instruction set
named ForwardCom are presented. The IEEE-754 standard
for floating point arithmetic may need adjustment to
accommodate the needs of modern forms of parallelism.",
acknowledgement = ack-nhfb,
remark = "See also later revisions \cite{Fog:2023:FPE} and
\cite{Fog:2024:FPE}.",
}
@Article{Gallois-Wong:2020:OIP,
author = "Diane Gallois-Wong and Sylvie Boldo and Pascal Cuoq",
title = "Optimal inverse projection of floating-point
addition",
journal = j-NUMER-ALGORITHMS,
volume = "83",
number = "3",
pages = "957--986",
month = mar,
year = "2020",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-019-00711-z",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Tue Feb 18 08:09:21 MST 2020",
bibsource = "http://link.springer.com/journal/11075/83/3;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "floating-point arithmetic; interval arithmetic",
}
@Article{Godunov:2020:ACC,
author = "A. Godunov",
title = "Algorithms for Calculating Correctly Rounded
Exponential Function in Double-Precision Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "9",
pages = "1388--1400",
month = sep,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2020.2972901",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Aug 12 14:58:16 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
abstract = "Correct rounding provides the best approximation of
the exponential function by double-precision numbers.
To obtain the correctly rounded exponential of some
arguments, the exponential should be calculated with
high accuracy. For small arguments, even higher
accuracy is required. This article presents simple and
very fast algorithms for small arguments. Yet another
algorithm presented here demonstrates a good maximum
execution time, which may be important for critical
applications. This algorithm can be combined with some
other already existing algorithms to achieve the best
maximum and average execution times. All proposed
algorithms calculate the correctly rounded exponential
function for all rounding modes and use only
double-precision arithmetic for computation. In the
argument reduction step, precalculated tables are used.
Test implementations of these algorithms were developed
in C language and are portable. Full proofs are
presented either in this article itself or in its
appendices.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Gonzalez-Navarro:2020:NRN,
author = "S. Gonz{\'a}lez-Navarro and J. Hormigo",
title = "New Results on Non-Normalized Floating-Point Formats",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "12",
pages = "1733--1744",
month = dec,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2929039",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Nov 24 09:42:22 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Goualard:2020:GRF,
author = "Fr{\'e}d{\'e}ric Goualard",
title = "Generating Random Floating-Point Numbers by Dividing
Integers: a Case Study",
crossref = "Krzhizhanovskaya:2020:CSI",
pages = "15--28",
year = "2020",
DOI = "https://doi.org/10.1007/978-3-030-50417-5_2",
bibdate = "Thu Jun 25 07:31:47 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/julia.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
acknowledgement = ack-nhfb,
keywords = "error analysis; floating-point number; GMP; Julia;
Matlab; Mersenne Twister; PRNG; pseudo-random numbers;
random number",
}
@InProceedings{Graillat:2020:ASF,
author = "Stef Graillat and Vincent Lef{\`e}vre and Jean-Michel
Muller",
title = "Alternative Split Functions and {Dekker}'s Product",
crossref = "Cornea:2020:ISC",
pages = "41--47",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00015",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We introduce algorithms for splitting a positive
binary floating-point number into two numbers of around
half the system precision, using arithmetic operations
all rounded either toward $-$ or toward $+$. We use
these algorithms to compute exact products (i.e., to
express the product of two floating-point numbers as
the unevaluated sum of two floating-point numbers, the
rounded product and an error term). This is similar to
the classical Dekker product, adapted here to directed
roundings.",
acknowledgement = ack-nhfb,
keywords = "accurate products; Approximation algorithms;
Cognition; Digital arithmetic; Floating-point
arithmetic; Indexes; Lips; split functions; Standards;
Switches",
}
@Article{Grutzmacher:2020:APC,
author = "Thomas Gr{\"u}tzmacher and Terry Cojean and Goran
Flegar and Hartwig Anzt and Enrique S.
Quintana-Ort{\'\i}",
title = "Acceleration of {PageRank} with Customized Precision
Based on Mantissa Segmentation",
journal = j-TOPC,
volume = "7",
number = "1",
pages = "4:1--4:19",
month = apr,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3380934",
ISSN = "2329-4949 (print), 2329-4957 (electronic)",
ISSN-L = "2329-4949",
bibdate = "Mon Apr 6 08:56:55 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pagerank.bib;
https://www.math.utah.edu/pub/tex/bib/topc.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3380934",
abstract = "We describe the application of a
communication-reduction technique for the PageRank
algorithm that dynamically adapts the precision of the
data access to the numerical requirements of the
algorithm as the iteration converges. Our
variable-precision strategy, using a customized
precision format based on mantissa segmentation (CPMS),
abandons the IEEE 754 single- and double-precision
number representation formats employed in the standard
implementation of PageRank, and instead handles the
data in memory using a customized floating-point
format. The customized format enables fast data access
in different accuracy, prevents overflow/underflow by
preserving the IEEE 754 double-precision exponent, and
efficiently avoids data duplication, since all bits of
the original IEEE 754 double-precision mantissa are
preserved in memory, but re-organized for efficient
reduced precision access. With this approach, the
truncated values (omitting significand bits), as well
as the original IEEE double-precision values, can be
retrieved without duplicating the data in different
formats.\par
Our numerical experiments on an NVIDIA V100 GPU (Volta
architecture) and a server equipped with two Intel Xeon
Platinum 8168 CPUs (48 cores in total) expose that,
compared with a standard IEEE double-precision
implementation, the CPMS-based PageRank completes about
10\% faster if high-accuracy output is needed, and
about 30\% faster if reduced output accuracy is
acceptable.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Parallel Computing",
journal-URL = "https://dl.acm.org/loi/topc",
}
@InProceedings{Gu:2020:NMM,
author = "Zhen Gu and Shuguo Li",
title = "A Novel Method of Modular Multiplication Based on
{Karatsuba}-like Multiplication",
crossref = "Cornea:2020:ISC",
pages = "33--40",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00014",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this paper, we propose a novel method of modular
multiplication which embeds the modular reduction in
the evaluation and interpolation parts of the
Karatsuba-like multiplication. Before, the modular
reduction can only be performed independently between
multiplication. However, applying our method, the
interpolation of the previous multiplication, modular
reduction and evaluation of the next multiplication are
merged as a whole step, which leads to the
simplification of computations and improvement of
parallelism. This method can be applied to the modular
multiplication with simple moduli like NIST primes, and
for general moduli, we can apply this method by using
Montgomery modular multiplication instead.",
acknowledgement = ack-nhfb,
keywords = "Digital arithmetic; Interpolation; Karatsuba-like
multiplication; Microelectronics; Modular
multiplication; Montgomery modular multiplication;
NIST; Public key cryptography; Transforms",
}
@InProceedings{Guo:2020:EGE,
author = "Hui Guo and Cindy Rubio-Gonz{\'a}lez",
booktitle = "Proceedings of the {ACM/IEEE 42nd International
Conference on Software Engineering}",
title = "Efficient generation of error-inducing floating-point
inputs via symbolic execution",
publisher = pub-ACM,
address = pub-ACM:adr,
month = jun,
year = "2020",
DOI = "https://doi.org/10.1145/3377811.3380359",
bibdate = "Sat Dec 9 08:57:26 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Floating point is widely used in software to emulate
arithmetic over reals. Unfortunately, floating point
leads to rounding errors that propagate and accumulate
during execution. Generating inputs to maximize the
numerical error is critical when evaluating the
accuracy of floating-point code. In this paper, we
formulate the problem of generating high error-inducing
floating-point inputs as a code coverage maximization
problem solved using symbolic execution. Specifically,
we define inaccuracy checks to detect large precision
loss and cancellation. We inject these checks at
strategic program locations to construct specialized
branches that, when covered by a given input, are
likely to lead to large errors in the result. We apply
symbolic execution to generate inputs that exercise
these specialized branches, and describe optimizations
that make our approach practical. We implement a tool
named FPGen and present an evaluation on 21 numerical
programs including matrix computation and statistics
libraries. We show that FPGen exposes errors for 20 of
these programs and triggers errors that are, on
average, over 2 orders of magnitude larger than the
state of the art.",
acknowledgement = ack-nhfb,
}
@InProceedings{Guo:2020:PIL,
author = "Hui Guo and Ignacio Laguna and Cindy
Rubio-Gonz{\'a}lez",
title = "{pLiner}: isolating lines of floating-point code for
compiler-induced variability",
crossref = "IEEE:2020:SPI",
pages = "1--14",
year = "2020",
bibdate = "Mon Sep 11 08:22:13 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Scientific applications are often impacted by
numerical inconsistencies when using different
compilers or when a compiler is used with different
optimization levels; such inconsistencies hinder
reproducibility and can be hard to diagnose. We present
pLiner, a tool to automatically pinpoint code lines
that trigger compiler-induced variability. pLiner uses
a novel approach to enhance floating-point precision at
different levels of code granularity, and performs a
guided search to identify locations affected by
numerical inconsistencies. We demonstrate pLiner on a
real-world numerical inconsistency that required weeks
to diagnose, which pLiner isolates in minutes. We also
evaluate pLiner on 100 synthetic programs, and the NAS
Parallel Benchmarks (NPB). On the synthetic programs,
pLiner detects the affected lines of code 87\% of the
time while the state-of-the-art approach only detects
the affected lines 6\% of the time. Furthermore, pLiner
successfully isolates all numerical inconsistencies
found in the NPB.",
acknowledgement = ack-nhfb,
articleno = "49",
}
@Article{Harris:2020:APN,
author = "Charles R. Harris and K. Jarrod Millman and St{\'e}fan
J. van der Walt and Ralf Gommers and Pauli Virtanen and
David Cournapeau and Eric Wieser and Julian Taylor and
Sebastian Berg and Nathaniel J. Smith and Robert Kern
and Matti Picus and Stephan Hoyer and Marten H. van
Kerkwijk and Matthew Brett and Allan Haldane and Jaime
Fern{\'a}ndez del R{\'\i}o and Mark Wiebe and Pearu
Peterson and Pierre G{\'e}rard-Marchant and Kevin
Sheppard and Tyler Reddy and Warren Weckesser and
Hameer Abbasi and Christoph Gohlke and Travis E.
Oliphant",
title = "Array programming with {NumPy}",
journal = j-NATURE,
volume = "585",
number = "7825",
pages = "357--362",
month = sep,
year = "2020",
CODEN = "NATUAS",
DOI = "https://doi.org/10.1038/s41586-020-2649-2",
ISSN = "0028-0836 (print), 1476-4687 (electronic)",
ISSN-L = "0028-0836",
bibdate = "Tue Jan 28 06:28:18 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Nature",
journal-URL = "http://www.nature.com/nature/archive/",
keywords = "accurate floating-point summation",
}
@TechReport{Harvey:2020:IMT,
author = "David Harvey and Joris van der Hoeven",
title = "Integer multiplication in time {$ O(n \log n) $}",
type = "Report",
number = "hal-02070778",
institution = "School of Mathematics and Statistics, University of
New South Wales",
address = "Sydney NSW 2052, Australia",
pages = "45",
day = "28",
month = nov,
year = "2020",
bibdate = "Thu May 16 15:51:09 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.science/hal-02070778v2",
abstract = "We present an algorithm that computes the product of
two $n$-bit integers in $ O(n \log n)$ bit operations,
thus confirming a conjecture of Sch{\"o}nhage and
Strassen from 1971. Our complexity analysis takes place
in the multitape Turing machine model, with integers
encoded in the usual binary representation. Central to
the new algorithm is a novel Gaussian resampling
technique that enables us to reduce the integer
multiplication problem to a collection of
multidimensional discrete Fourier transforms over the
complex numbers, whose dimensions are all powers of
two. These transforms may then be evaluated rapidly by
means of Nussbaumer's fast polynomial transforms.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hickmann:2020:INN,
author = "Brian Hickmann and Jieasheng Chen and Michael Rotzin
and Andrew Yang and Maciej Urbanski and Sasikanth
Avancha",
title = "{Intel Nervana Neural Network Processor-T (NNP-T)}
Fused Floating Point Many-Term Dot Product",
crossref = "Cornea:2020:ISC",
pages = "133--136",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00029",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Intel's Nervana Neural Network Processor for Training
(NNP-T) contains at its core an advanced floating point
dot product design to accelerate the matrix
multiplication operations found in many AI
applications. Each Matrix Processing Unit (MPU) on the
Intel NNP-T can process a 32x32 BFloat16 matrix
multiplication every 32 cycles, accumulating the result
in single precision (FP32). To reduce hardware costs,
the MPU uses a fused many-term floating point dot
product design with block alignment of the many input
terms during addition, resulting in a unique datapath
with several interesting design trade-offs. In this
paper, we describe the details of the MPU pipeline,
discuss the trade-offs made in the design, and present
information on the accuracy of the computation as
compared to traditional FMA implementations.",
acknowledgement = ack-nhfb,
keywords = "Adders; Artificial neural networks; deep learning;
floating point dot product; Hardware; Machine learning;
matrix multiplication; Tensile stress; tensor;
Training",
}
@Article{Hopkins:2020:SRR,
author = "Michael Hopkins and Mantas Mikaitis and Dave R. Lester
and Steve Furber",
title = "Stochastic rounding and reduced-precision fixed-point
arithmetic for solving neural ordinary differential
equations",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "378",
number = "2166",
pages = "20190052",
month = jan,
year = "2020",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.2019.0052",
ISSN = "1364-503X (print), 1471-2962 (electronic)",
ISSN-L = "1364-503X",
bibdate = "Fri Sep 22 17:51:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Transactions of the Royal Society A:
Mathematical, Physical, and Engineering Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
}
@InProceedings{Hormigo:2020:FPF,
author = "Javier Hormigo and Julio Villalba-Moreno and Sonia
Gonzalez-Navarro",
title = "Floating Point Fused Multiply Add under {HUB} Format",
crossref = "Cornea:2020:ISC",
pages = "1--8",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00010",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The Half-Unit-Biased (HUB) format has interesting
advantages for implementing floating-point arithmetic
which has been proved for the four basic arithmetic
operations as well as square root. Nevertheless,
although Floating-point Fused Multiply-add (FMA)
operation ($ A \times B + C$) is one of the most
important and complex arithmetic instructions in modern
processors, FMA operation for HUB numbers has not been
confronted yet. In this paper, we present a design to
deal with this operation under HUB format. The key
points to turn the conventional FMA architecture into a
HUB unit are explained. Comparing the ASIC
implementation of a HUB FMA unit with the conventional
one, the former reduces the required area and power up
to 38\% and 35\%, respectively, for single-precision.
For BFloat16, the HUB FMA increases the speed a 15\%,
and even then, reduces the area and power by 26\% and
12\%, respectively.",
acknowledgement = ack-nhfb,
keywords = "Computer architecture; Deep-learning; Delays; Digital
arithmetic; DSP applications; Fused
multiplication-addition; Hardware; HUB format;
Inverters; Program processors; Standards",
}
@Article{Hrycak:2020:ELP,
author = "Tomasz Hrycak and Sebastian Schmutzhard",
title = "Evaluation of {Legendre} polynomials by a three-term
recurrence in floating-point arithmetic",
journal = j-IMA-J-NUMER-ANAL,
volume = "40",
number = "1",
pages = "587--605",
month = jan,
year = "2020",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/dry079",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Sat Feb 29 14:22:43 MST 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
URL = "http://academic.oup.com/imajna/article/40/1/587/5162990",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Ipsen:2020:PEA,
author = "Ilse C. F. Ipsen and Hua Zhou",
title = "Probabilistic Error Analysis for Inner Products",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "41",
number = "4",
pages = "1726--1741",
month = "????",
year = "2020",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/19M1270434",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Mar 12 10:18:05 MST 2021",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/41/4;
https://www.math.utah.edu/pub/bibnet/authors/i/ipsen-ilse-c-f.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "January 2020",
}
@Book{ISO:2020:III,
author = "{ISO}",
title = "{ISO\slash IEC 60559:2020} Information technology ---
Microprocessor Systems --- Floating-Point arithmetic",
publisher = pub-ISO,
address = pub-ISO:adr,
pages = "74",
year = "2020",
bibdate = "Thu Jan 28 07:09:28 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/isostd.bib",
URL = "https://www.iso.org/standard/80985.html",
abstract = "This standard specifies interchange and arithmetic
formats and methods for binary and decimal
floating-point arithmetic in computer programming
environments. This standard specifies exception
conditions and their default handling. An
implementation of a floating-point system conforming to
this standard may be realized entirely in software,
entirely in hardware, or in any combination of software
and hardware. For operations specified in the normative
part of this standard, numerical results and exceptions
are uniquely determined by the values of the input
data, sequence of operations, and destination formats,
all under user control.",
acknowledgement = ack-nhfb,
remark = "This is the international version of IEEE 754-2019. It
replaces ISO/IEC/IEEE 60559:2011.",
}
@Article{Isupov:2020:DIM,
author = "Konstantin Isupov and Vladimir Knyazkov and Alexander
Kuvaev",
title = "Design and implementation of multiple-precision {BLAS
Level 1} functions for graphics processing units",
journal = j-J-PAR-DIST-COMP,
volume = "140",
number = "??",
pages = "25--36",
month = jun,
year = "2020",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1016/j.jpdc.2020.02.006",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Wed May 26 16:11:01 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0743731519303302",
acknowledgement = ack-nhfb,
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
}
@Misc{Isupov:2020:MPB,
author = "Konstantin Isupov and Vladimir Knyazkov",
title = "Multiple-Precision {BLAS} Library for Graphics
Processing Units",
howpublished = "TechRxiv preprint.",
day = "30",
month = jun,
year = "2020",
DOI = "https://doi.org/10.36227/techrxiv.12580301.v1",
bibdate = "Fri Sep 29 14:30:54 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The binary32 and binary64 floating-point formats
provide good performance on current hardware, but also
introduce a rounding error in almost every arithmetic
operation. Consequently, the accumulation of rounding
errors in large computations can cause accuracy issues.
One way to prevent these issues is to use
multiple-precision floating-point arithmetic. This
preprint, submitted to Russian Supercomputing Days
2020, presents a new library of basic linear algebra
operations with multiple precision for graphics
processing units. The library is written in CUDA C/C++
and uses the residue number system to represent
multiple-precision significands of floating-point
numbers. The supported data types, memory layout, and
main features of the library are considered.
Experimental results are presented showing the
performance of the library.",
acknowledgement = ack-nhfb,
remark = "Preprint submitted to Russian Supercomputing Days
2020.",
}
@Article{Jeannerod:2020:RAX,
author = "Claude-Pierre Jeannerod",
title = "The relative accuracy of $ (x + y) * (x - y) $",
journal = j-J-COMPUT-APPL-MATH,
volume = "369",
number = "??",
pages = "Article 112613",
day = "1",
month = may,
year = "2020",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2019.112613",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Wed May 13 06:58:31 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042719306181",
acknowledgement = ack-nhfb,
articleno = "112613",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Johnson:2020:EAHa,
author = "Jeff Johnson",
title = "Efficient, arbitrarily high precision hardware
logarithmic arithmetic for linear algebra",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "1--8",
day = "14",
month = may,
year = "2020",
bibdate = "Tue Jul 06 18:17:13 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/pdf/2004.09313.pdf",
abstract = "The logarithmic number system (LNS) is arguably not
broadly used due to exponential circuit overheads for
summation tables relative to arithmetic precision.
Methods to reduce this overhead have been proposed, yet
still yield designs with high chip area and power
requirements. Use remains limited to lower precision or
high multiply/add ratio cases, while much of linear
algebra (near 1:1 multiply/add ratio) does not
qualify.\par
We present a dual-base approximate logarithmic
arithmetic comparable to floating point in use, yet
unlike LNS it is easily fully pipelined, extendable to
arbitrary precision with $ O(n^2) $ overhead, and
energy efficient at a 1:1 multiply/add ratio.Compared
to float32 or float64 vector inner product with FMA,
our design is respectively $ 2.3 \times $ and $ 4.6
\times $ more energy efficient in 7 nm CMOS. It depends
on exp and log evaluation $ 5.4 \times $ and $ 3.2
\times $ more energy efficient, at $ 0.23 \times $ and
$ 0.37 \times $ the chip area for equivalent accuracy
versus standard hyperbolic CORDIC using shift-and-add
and approximated ODE integration in the style of Revol
and Yakoubsohn. This technique is a novel alternative
for low power, high precision hardened linear algebra
in computer vision, graphics and machine learning
applications.",
acknowledgement = ack-nhfb,
keywords = "approximate arithmetic; elementary function
evaluation; hardware linear algebra; logarithmic
arithmetic",
remark = "Published in \cite{Johnson:2020:EAHb}.",
}
@InProceedings{Johnson:2020:EAHb,
author = "Jeff Johnson",
title = "Efficient, arbitrarily high precision hardware
logarithmic arithmetic for linear algebra",
crossref = "Cornea:2020:ISC",
pages = "25--32",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00013",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The logarithmic number system (LNS) is arguably not
broadly used due to exponential circuit overheads for
summation tables relative to arithmetic precision.
Methods to reduce this overhead have been proposed, yet
still yield designs with high chip area and power
requirements. Use remains limited to lower precision or
high multiply/add ratio cases, while much of linear
algebra (near 1:1 multiply/add ratio) does not qualify.
We present a dual-base approximate logarithmic
arithmetic comparable to floating point in use, yet
unlike LNS it is easily fully pipelined, extendable to
arbitrary precision with $ O(n^2) $ overhead, and
energy efficient at a 1:1 multiply/add ratio. Compared
to float32 or float64 vector inner product with FMA,
our design is respectively $ 2.3 \times $ and $ 4.6
\times $ more energy efficient in 7 nm CMOS. It depends
on exp and log evaluation 5.4 and $ 3.2 \times $ more
energy efficient, at $ 0.23 \times $ and $ 0.37 \times
$ the chip area for equivalent accuracy versus standard
hyperbolic CORDIC using shift-and-add and approximated
ODE integration in the style of Revol and Yakoubsohn.
This technique is a novel alternative for low power,
high precision hardened linear algebra in computer
vision, graphics and machine learning applications.",
acknowledgement = ack-nhfb,
keywords = "Adders; approximate arithmetic; Clocks; elementary
function evaluation; Hardware; hardware linear algebra;
Linear algebra; logarithmic arithmetic; Pipeline
processing; Read only memory; Switches",
}
@InProceedings{Joldes:2020:AMQ,
author = "Mioara Jolde{\c{s}} and Jean-Michel Muller",
title = "Algorithms for Manipulating Quaternions in
Floating-Point Arithmetic",
crossref = "Cornea:2020:ISC",
pages = "48--55",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00016",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Quaternions form a set of four global but not unique
parameters, which can represent three-dimensional
rotations in a non-singular way. They are frequently
used in computer graphics, drone and aerospace vehicle
control. Floating-point quaternion operations
(addition, multiplication, reciprocal, norm) are often
implemented by the book . Although all usual
implementations are algebraically equivalent, their
numerical behavior can be quite different. For
instance, the arithmetic operations on quaternions as
well as conversion algorithms to/from rotation matrices
are subject to spurious under/overflow (an intermediate
calculation underflows or overflows, making the
computed final result irrelevant, although the exact
result is in the domain of the representable numbers).
The goal of this paper is to analyze and then propose
workarounds and better accuracy alternatives for such
algorithms.",
acknowledgement = ack-nhfb,
keywords = "Aerospace control; Algebra; Computer graphics; Drones;
Error analysis; Floating-point arithmetic; Quaternions;
quaternions; rounding error analysis; Standards",
}
@InProceedings{Jugade:2020:FEM,
author = "Chaitanya Jugade and Deepak Ingole and Dayaram
Sonawane and Michal Kvasnica and John Gustafson",
editor = "{IEEE}",
booktitle = "{2020 59th IEEE Conference on Decision and Control
(CDC)}",
title = "A Framework for Embedded Model Predictive Control
using Posits",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "2509--2514",
year = "2020",
DOI = "https://doi.org/10.1109/CDC42340.2020.9304262",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Klarreich:2020:NMH,
author = "Erica Klarreich",
title = "News: Multiplication hits the speed limit",
journal = j-CACM,
volume = "63",
number = "1",
pages = "11--13",
month = jan,
year = "2020",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/3371387",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Thu Jan 2 16:41:05 MST 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3371387",
abstract = "A problem ``around since antiquity'' may have been
resolved by a new algorithm.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@Article{Klower:2020:NFE,
author = "Milan Kl{\"o}wer and Peter D. D{\"u}ben and Tim N.
Palmer",
title = "Number Formats, Error Mitigation, and Scope for 16-Bit
Arithmetics in Weather and Climate Modeling Analyzed
With a Shallow Water Model",
journal = j-J-ADV-MODEL-EARTH-SYST,
volume = "12",
number = "10",
pages = "1--17",
month = oct,
year = "2020",
DOI = "https://doi.org/10.1029/2020MS002246",
ISSN = "1942-2466 (print), 1942-2466 (electronic)",
ISSN-L = "1942-2466",
bibdate = "Fri Dec 15 11:03:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Adv. Model. Earth Syst. [JAMES]",
fjournal = "Journal of Advances in Modeling Earth Systems",
journal-URL = "https://agupubs.onlinelibrary.wiley.com/journal/19422466",
}
@InProceedings{Knobbe:2020:CRS,
author = "Simon Knobbe and Moritz B{\"a}rthel and Steffen Paul
and Jochen Rust",
booktitle = "{2020 9th International Conference on Modern Circuits
and Systems Technologies (MOCAST)}",
title = "Complexity Reduction for Sphere Decoding using
{Unum-Type-II}-Based {SORN}-Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--4",
year = "2020",
DOI = "https://doi.org/10.1109/MOCAST49295.2020.9200263",
bibdate = "Fri Dec 15 07:38:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Koc:2020:AIM,
author = "{\c{C}}etin Kaya Ko{\c{c}}",
title = "Algorithms for Inversion Mod $ p^k $",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "6",
pages = "907--913",
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2020.2970411",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 23 16:03:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
abstract = "This article describes and analyzes all existing
algorithms for computing $ x = a^{-1} (\bmod p^k) $ for
a prime $p$, and also introduces a new algorithm based
on the exact solution of linear equations using
$p$-adic expansions. The algorithm starts with the
initial value $ c = a^{-1} (\bmod p)$ and iteratively
computes the digits of the inverse $ x = a^{-1} (\bmod
p^k)$ in base $p$. The $ \bmod 2$ version of the
algorithm is more efficient than all existing
algorithms for small values of $k$. Moreover, it stands
out as being the only one that works for any $p$, any
$k$, and digit-by-digit. While the new algorithm is
asymptotically worse off, it requires the minimal
number of arithmetic operations (just a single
addition) per step, as compared to all existing
algorithms.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Laguna:2020:VQF,
author = "Ignacio Laguna",
booktitle = "2020 {IEEE} International Parallel and Distributed
Processing Symposium {(IPDPS)}",
title = "{Varity}: Quantifying Floating-Point Variations in
{HPC} Systems Through Randomized Testing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "622--633",
month = may,
year = "2020",
DOI = "https://doi.org/10.1109/ipdps47924.2020.00070",
bibdate = "Tue Jan 28 06:34:18 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Lange:2020:FRF,
author = "Marko Lange and Siegfried M. Rump",
title = "Faithfully Rounded Floating-point Computations",
journal = j-TOMS,
volume = "46",
number = "3",
pages = "21:1--21:20",
month = sep,
year = "2020",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3290955",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Sep 26 07:28:19 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3290955",
abstract = "We present a pair arithmetic for the four basic
operations and square root. It can be regarded as a
simplified, more-efficient double-double arithmetic.
The central assumption on the underlying arithmetic is
the first standard model for error analysis for
operations on a discrete set of real numbers. Neither
do we require a floating-point grid nor a rounding to
nearest property. Based on that, we define a relative
rounding error unit $u$ and prove rigorous error bounds
for the computed result of an arbitrary arithmetic
expression depending on $u$, the size of the
expression, and possibly a condition measure. In the
second part of this note, we extend the error analysis
by examining requirements to ensure faithfully rounded
outputs and apply our results to IEEE 754 standard
conform floating-point systems. For a class of
mathematical expressions, using an IEEE 754 standard
conform arithmetic with base $ \beta $, the result is
proved to be faithfully rounded for up to $ 1 / \sqrt
{\beta u - 2}$ operations. Our findings cover a number
of previously published algorithms to compute
faithfully rounded results, among them Horner's scheme,
products, sums, dot products, or Euclidean norm. Beyond
that, several other problems can be analyzed, such as
polynomial interpolation, orientation problems,
Householder transformations, or the smallest singular
value of Hilbert matrices of large size.",
acknowledgement = ack-nhfb,
articleno = "21",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Lange:2020:NDF,
author = "Marko Lange and Shin'ichi Oishi",
title = "A note on {Dekker}'s {FastTwoSum} algorithm",
journal = j-NUM-MATH,
volume = "145",
number = "2",
pages = "383--403",
month = jun,
year = "2020",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-020-01114-2",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Thu Jun 4 12:18:54 MDT 2020",
bibsource = "http://link.springer.com/journal/211/145/2;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
note = "See correction \cite{Lange:2021:CND}.",
URL = "https://link.springer.com/article/10.1007/s00211-020-01114-2",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Langroudi:2020:APP,
author = "Hamed F. Langroudi and Vedant Karia and John L.
Gustafson and Dhireesha Kudithipudi",
editor = "{IEEE}",
booktitle = "{2020 IEEE/CVF Conference on Computer Vision and
Pattern Recognition Workshops (CVPRW)}",
title = "Adaptive Posit: Parameter aware numerical format for
deep learning inference on the edge",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3123--3131",
year = "2020",
DOI = "https://doi.org/10.1109/CVPRW50498.2020.00371",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lauter:2020:FSA,
author = "Christoph Lauter and Anastasia Volkova",
title = "A Framework for Semi-Automatic Precision and Accuracy
Analysis for Fast and Rigorous Deep Learning",
crossref = "Cornea:2020:ISC",
pages = "103--110",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00023",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Deep Neural Networks (DNN) represent a
performance-hungry application. Floating-Point (FP) and
custom floating-point-like arithmetic satisfies this
hunger. While there is need for speed, inference in
DNNs does not seem to have any need for precision. Many
papers experimentally observe that DNNs can
successfully run at almost ridiculously low precision.
The aim of this paper is two-fold: first, to shed some
theoretical light upon why a DNN's FP accuracy stays
high for low FP precision. We observe that the loss of
relative accuracy in the convolutional steps is
recovered by the activation layers, which are extremely
well-conditioned. We give an interpretation for the
link between precision and accuracy in DNNs. Second,
the paper presents a software framework for
semi-automatic FP error analysis for the inference
phase of deep-learning. Compatible with common
Tensorflow/Keras models, it leverages the frugally-deep
Python/C++ library to transform a neural network into
C++ code in order to analyze the network's need for
precision. This rigorous analysis is based an Interval
and Affine arithmetics to compute absolute and relative
error bounds for a DNN. We demonstrate our tool with
several examples.",
acknowledgement = ack-nhfb,
keywords = "affine arithmetic; Analytical models; Biological
neural networks; Computational modeling; deep learning;
Digital arithmetic; error analysis; floating-point
arithmetic; interval arithmetic; Machine learning;
Neurons; Tools",
}
@InProceedings{Lindstrom:2020:VRC,
author = "Peter Lindstrom",
title = "Variable-Radix Coding of the Reals",
crossref = "Cornea:2020:ISC",
pages = "111--116",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00024",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently proposed real number systems like Posits and
Elias codes make use of tapered accuracy resulting from
variable-length coding of exponents and significands.
Several quite different interpretations of these number
systems have been provided, though most often these
rely on some combination of fixed- and variable-length
codes for exponent and significand. We provide a new
perspective on these number systems that unifies known
representations while suggesting new ones. Our
framework is based on multibit radix representations
that encode the exponent in unary, the leading nonzero
digit in a variable-length code, and the remaining
digits in fixed-length binary code. We show how Posits,
the various Elias codes, and IEEE 754 like
representations can be expressed in this framework.
Moreover, we show that Posits and the Elias and codes
represent the leading digit using the canonical Huffman
code for a probability distribution given by Benford's
law, which governs the probability of leading digits.
We further show that Posits correspond to the use of a
fixed radix while Elias and codes are based on simple
sequences of increasing radix. Our approach provides
for an intuitive and uniform framework for representing
numbers that reveals a visual mapping between codewords
and the binary representation of real numbers obscured
by prior frameworks. This new interpretation suggests a
generalization of Posits and other number systems and
provides simple rules for designing
information-theoretically optimal codes.",
acknowledgement = ack-nhfb,
keywords = "Benford's law; Binary codes; Digital arithmetic; Elias
codes; Encoding; floating point; Huffman code; Indexes;
posits; Probability distribution; Proposals; real
number systems; tapered accuracy; Visualization",
}
@Article{Luo:2020:ADN,
author = "Y. Luo and S. Yu",
title = "Accelerating Deep Neural Network In-Situ Training With
Non-Volatile and Volatile Memory Based Hybrid Precision
Synapses",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "8",
pages = "1113--1127",
year = "2020",
CODEN = "ITCOB4",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jul 23 16:03:24 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Marquer:2020:HLI,
author = "Yoann Marquer and Tania Richmond",
title = "A Hole in the Ladder: Interleaved Variables in
Iterative Conditional Branching",
crossref = "Cornea:2020:ISC",
pages = "56--63",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00017",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The modular exponentiation is crucial to the RSA
cryptographic protocol, and variants inspired by the
Montgomery ladder have been studied to provide more
secure algorithms. In this paper, we abstract away the
iterative conditional branching used in the Montgomery
ladder, and formalize systems of equations necessary to
obtain what we call the semi-interleaved and
fully-interleaved ladder properties. In particular, we
design fault-injection attacks able to obtain bits of
the secret against semi-interleaved ladders, including
the Montgomery ladder, but not against
fully-interleaved ladders that are more secure. We also
apply these equations to extend the Montgomery ladder
for both the semi- and fully-interleaved cases, thus
proposing novel and more secure algorithms to compute
the modular exponentiation.",
acknowledgement = ack-nhfb,
keywords = "Countermeasures (computer); Cryptography; Fault
detection; Iterative algorithms; Mathematical model;
Public-key cryptography; Registers; Security;
Side-channel attacks; Space exploration",
}
@TechReport{Meurant:2020:PFM,
author = "G{\'e}rard Meurant",
title = "\pkg{FLOATP\_toolbox}, {Matlab} software, variable
precision floating point arithmetic.",
type = "Report",
number = "????",
institution = "Commissariat a l'{\'E}nergie Atomique (CEA)",
address = "????, France",
year = "2020",
bibdate = "Sat Dec 23 12:13:27 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "https://gerard-meurant.pagesperso-orange.fr/soft_meurant_n.html",
acknowledgement = ack-nhfb,
remark = "URL links to almost-empty home page.",
}
@InProceedings{Mikaitis:2020:IRG,
author = "Mantas Mikaitis",
title = "Issues with rounding in the {GCC} implementation of
the {ISO 18037:2008} standard fixed-point arithmetic",
crossref = "Cornea:2020:ISC",
pages = "129--132",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00028",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib",
abstract = "We describe various issues caused by the lack of
round-to-nearest mode in the gcc compiler
implementation of the fixed-point arithmetic data types
and operations. We demonstrate that round-to-nearest is
not performed in the conversion of constants,
conversion from one numerical type to a less precise
type and results of multiplications. Furthermore, we
show that mixed-precision operations in fixed-point
arithmetic lose precision on arguments, even before
carrying out arithmetic operations. The ISO 18037:2008
standard was created to standardize C language
extensions, including fixed-point arithmetic, for
embedded systems. Embedded systems are usually based on
ARM processors, of which approximately 100 billion have
been manufactured by now. Therefore, the observations
about numerical issues that we discuss in this paper
can be rather dangerous and are important to address,
given the wide ranging type of applications that these
embedded systems are running.",
acknowledgement = ack-nhfb,
keywords = "Computer languages; Embedded systems; fixed-point
arithmetic; Hardware; ISO 18037:2008; ISO Standards;
Libraries; Program processors; rounding",
}
@Article{Mikaitis:2020:SRA,
author = "Mantas Mikaitis",
title = "Stochastic Rounding: Algorithms and Hardware
Accelerator",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--6",
day = "29",
month = jun,
year = "2020",
DOI = "https://doi.org/10.48550/arXiv.2001.01501",
bibdate = "Wed Aug 07 16:03:40 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
URL = "https://arxiv.org/abs/2001.01501#",
abstract = "Algorithms and a hardware accelerator for performing
stochastic rounding (SR) are presented. The main goal
is to augment the ARM M4F based multi-core processor
SpiNNaker2 with a more flexible rounding functionality
than is available in the ARM processor itself. The
motivation of adding such an accelerator in hardware is
based on our previous results showing improvements in
numerical accuracy of ODE solvers in fixed-point
arithmetic with SR, compared to standard round to
nearest or bit truncation rounding modes. Furthermore,
performing SR purely in software can be expensive, due
to requirement of a pseudorandom number generator
(PRNG), multiple masking and shifting instructions, and
an addition operation. Also, saturation of the rounded
values is included, since rounding is usually followed
by saturation, which is especially important in
fixed-point arithmetic due to a narrow dynamic range of
representable values. The main intended use of the
accelerator is to round fixed-point multiplier outputs,
which are returned unrounded by the ARM processor in a
wider fixed-point format than the arguments.",
acknowledgement = ack-nhfb,
}
@Article{Muller:2020:EFA,
author = "Jean-Michel Muller",
title = "Elementary Functions and Approximate Computing",
journal = j-PROC-IEEE,
volume = "108",
number = "12",
pages = "2136--2149",
month = dec,
year = "2020",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1109/jproc.2020.2991885",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Tue Mar 1 06:07:02 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "In this article, we review some of the classical
methods used for quickly obtaining low-precision
approximations to the elementary functions. Then, for
each of the three main classes of elementary function
algorithms (shift-and-add algorithms, polynomial or
rational approximations, and table-based methods) and
for the additional, specific to approximate computing,
``bit-manipulation'' techniques, we examine what can be
done for obtaining very fast estimates of a function,
at the cost of a (controlled) loss in terms of
accuracy.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}
@InProceedings{Murillo:2020:CPA,
author = "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
Botella",
editor = "{IEEE}",
booktitle = "{IEEE International Symposium on Circuits and Systems
(ISCAS): Seville, Spain, October 11--14, 2020}",
title = "Customized Posit Adders and Multipliers using the
{FloPoCo} Core Generator",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2020",
DOI = "https://doi.org/10.1109/ISCAS45731.2020.9180771",
ISBN = "1-72813-320-3",
ISBN-13 = "978-1-72813-320-1",
ISSN = "0271-4302 (print), 2158-1525 (electronic)",
ISSN-L = "0271-4302",
bibdate = "Thu Dec 14 17:18:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1109/ISCAS45731.2020",
}
@Article{Murillo:2020:DPD,
author = "R. Murillo and A. A. {Del Barrio} and G. Botella",
title = "{Deep PeNSieve}: a deep learning framework based on
the posit number system",
journal = j-DIGIT-SIGNAL-PROCESS,
volume = "102",
pages = "1--8",
month = jul,
year = "2020",
CODEN = "DSPREJ",
DOI = "https://doi.org/10.1016/j.dsp.2020.102762",
ISSN = "1051-2004 (print), 1095-4333 (electronic)",
ISSN-L = "1051-2004",
bibdate = "Thu Dec 14 17:04:34 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S105120042030107X",
acknowledgement = ack-nhfb,
articleno = "102762",
fjournal = "Digital Signal Processing",
journal-URL = "https://www.sciencedirect.com/journal/digital-signal-processing",
}
@InProceedings{Nannarelli:2020:VPB,
author = "Alberto Nannarelli",
title = "Variable Precision 16-Bit Floating-Point Vector Unit
for Embedded Processors",
crossref = "Cornea:2020:ISC",
pages = "96--102",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00022",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The increasing demand of computation at the edge and
the tight power budgets push designers to migrate
double and single-precision calculations to formats of
reduced precision and dynamic range for applications
that can tolerate some inaccuracy.In this context, we
introduce a variable format for reduced precision
floating-point with storage limited to 16 bits. This
format is suitable for applications in signal
processing, machine learning and other applications in
embedded systems. We present the hardware
implementations for multiplication and division units
that can sustain a throughput of one result per clock
cycle designed for vector processing. We also show some
examples of applications that can benefit from the
proposed format.",
acknowledgement = ack-nhfb,
keywords = "Adders; customizable bias; Dynamic range; Encoding;
Floating-point; Hardware; Program processors; Signal
processing; Standards; variable precision",
}
@Misc{Nass:2020:GUL,
author = "Rich Nass",
title = "{GreenWaves} Ultra-Low Power {GAP9} {IoT} Apps
Processor Suits Intelligence at the Edge",
howpublished = "Web site",
day = "21",
month = jan,
year = "2020",
bibdate = "Wed Jan 22 07:07:03 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "GAP9 offers vectorized 2-bit and 4-bit fixed-point
arithmetic, and 8-, 16-, and 32-bit floating-point
arithmetic.",
URL = "https://www.embedded-computing.com/guest-blogs/greenwaves-ultra-low-power-gap9-iot-apps-processor-suits-intelligence-at-the-edge",
acknowledgement = ack-nhfb,
}
@InProceedings{Neves:2020:DFM,
author = "Nuno Neves and Pedro Tom{\'a}s and Nuno Roma",
editor = "{IEEE}",
booktitle = "{2020 IEEE Workshop on Signal Processing Systems
(SiPS)}",
title = "Dynamic Fused Multiply-Accumulate Posit Unit with
Variable Exponent Size for Low-Precision {DSP}
Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2020",
DOI = "https://doi.org/10.1109/SiPS50750.2020.9195256",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Neves:2020:RSB,
author = "Nuno Neves and Pedro Tom{\'a}s and Nuno Roma",
editor = "{IEEE}",
booktitle = "{2020 IEEE 31st International Conference on
Application-specific Systems, Architectures and
Processors (ASAP)}",
title = "Reconfigurable Stream-based Tensor Unit with
Variable-Precision Posit Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "149--156",
year = "2020",
DOI = "https://doi.org/10.1109/ASAP49362.2020.00033",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Niasar:2020:FSA,
author = "Mojtaba Bisheh Niasar and Rami {El Khatib} and Reza
Azarderakhsh and Mehran Mozaffari-Kermani",
title = "Fast, Small, and Area-Time Efficient Architectures for
Key-Exchange on {Curve25519}",
crossref = "Cornea:2020:ISC",
pages = "72--79",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00019",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper demonstrates fast and compact
implementations of Elliptic Curve Cryptography (ECC)
for efficient key agreement over Curve25519. Curve25519
has been recently adopted as a key exchange method for
several applications and included in the National
Institute of Standards and Technology (NIST)
recommendations for public key cryptography. This paper
presents three different performance level designs
including lightweight, area-time efficient, and
high-performance architectures. Lightweight hardware
implementations are used for several Internet of Things
(IoT) applications due to their resources being at
premium. Our lightweight architecture utilizes 90\%
less resources compared to the best previous work while
it is still more optimized in term of A $ \cdot $ T
(area $ \times $ time). For efficient implementation
from either time or utilized resources, our area-time
efficient architecture can establish almost 7,000 key
sessions per second which is 64\% faster than the
previous works. The area-time efficient architecture
uses well scheduled interleaved multiplication combined
with a reduction algorithm. Additionally, we offer a
fast architecture for high performance applications
based on the 4-level Karatsuba method and Carry-Compact
Addition (CCA). Our high-performance architecture also
outperforms previous work in terms of A middot; T. The
results show 9\% and 29\% improvement in A middot; T
and Admiddot; T (DSP\_count $ \times $ time),
respectively. All architectures are variable-base-point
implemented on the Xilinx Zynq-7020 FPGA family where
performance and implementation metrics are reported and
compared. Finally, various side-channel attack
countermeasures are embedded in the proposed
architectures.",
acknowledgement = ack-nhfb,
keywords = "Computer architecture; Curve25519; Elliptic curve
cryptography; elliptic curve Diffie-Hellman (ECDH);
Elliptic curves; Field programmable gate arrays;
field-programmable gate array (FPGA); Hardware; NIST;
point multiplication; Random access memory",
}
@InProceedings{Papachatzopoulos:2020:MDM,
author = "Kleanthis Papachatzopoulos and Vassilis Paliouras",
title = "Maximum Delay Models for Parallel-Prefix Adders in the
Presence of Threshold Voltage Variations",
crossref = "Cornea:2020:ISC",
pages = "88--95",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00021",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This paper introduces a delay modeling formulation for
several Parallel-Prefix Adders in the presence of
threshold voltage variability. A path-based model is
derived for the delay variability of Kogge-Stone,
Knowles, Sklansky, Brent-Kung, Han-Carlson,
Ladner-Fischer, and New Adder architectures. The delay
model accuracy is evaluated for the specific adders on
the basis of SPICE Monte-Carlo Simulations at 45 nm and
16 nm nodes. The presented analysis reveals that the
proposed path-based model estimates the maximum delay
Probability Density Function of the particular adder
architectures with sufficient accuracy, assuming 3
intra-die threshold voltage variations as high as 10\%
of nominal value. Delay yield estimations produced by
the proposed model are found to agree with those of
Monte-Carlo Simulations for a number of highly probable
critical paths, presenting an error less than 2\%. For
the particular adders and technology nodes, an
approximately 10-fold reduction in simulation time is
obtained when exploiting the proposed model. The
particular observation indicates that the computational
time for delay yield estimation of Parallel-Prefix
Adders can be exponentially reduced with negligible
accuracy loss when the analysis focuses solely on the
Nominal-Maximum Delay critical path. Finally, a
quantitative comparison of prefix adders to the
Borrow-Save Adder is offered, in terms of complexity
and susceptibility to variations.",
acknowledgement = ack-nhfb,
keywords = "Adders; critical path; delay yield; Delays; Gaussian
distribution; Monte Carlo methods; parallel-prefix
adders; SPICE; Threshold voltage; threshold voltage
variations; variability",
}
@InProceedings{Payer:2020:SMF,
author = "Stefan Payer and Cedric Lichtenau and Michael Klein
and Kerstin Schelm and Petra Leber and Nicol Hofmann
and Tina Babinsky",
title = "{SIMD} Multi Format Floating-Point Unit on the {IBM
z15}",
crossref = "Cornea:2020:ISC",
pages = "125--128",
month = jun,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020.00027",
ISSN = "2576-2265",
bibdate = "Wed Jul 7 06:24:52 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The IBM z Systems(TM) is the backbone of the
insurance, banking, and retail industry. Innovation in
these markets is driving the demand for new and
additional applications to better serve the customers.
These workloads like machine learning, data analytics,
AI, etc. require a rapidly increasing number of
computations in smaller precision formats. With IBM
z15(TM) we completely redesigned the binary and
hexadecimal floating-point unit to efficiently
implement SIMD operations at 5.2GHz while maintaining
the industry leading reliability, availability and
serviceability standard. This paper describes the new
design and special techniques used to achieve these
goals like reusing the existing double precision unit
pipeline for lower precision parallel SIMD, new
approaches to formally verify the design, and improving
error detection for the 14nm technology node.",
acknowledgement = ack-nhfb,
keywords = "AI; Binary; Digital arithmetic; Floating Point Unit;
Formal Verification; Hafnium; Hexadecimal; IBM z15(TM);
Machine Learning; Multi Format; SIMD",
}
@InProceedings{Raveendran:2020:NPF,
author = "Aneesh Raveendran and Sandra Jean and J. Mervin and D.
Vivian and David Selvakumar",
editor = "{IEEE}",
booktitle = "{2020 33rd International Conference on VLSI Design and
2020 19th International Conference on Embedded Systems
(VLSID), Bengaluru, India, 4--8 January 2020}",
title = "A Novel Parametrized Fused Division and Square-Root
{POSIT} Arithmetic Architecture",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "207--212",
month = jan,
year = "2020",
DOI = "https://doi.org/10.1109/vlsid49098.2020.00053",
ISBN = "1-72815-701-3",
ISBN-13 = "978-1-72815-701-6",
ISSN = "1063-9667 (print), 2380-6923 (electronic)",
ISSN-L = "1063-9667",
bibdate = "Fri Dec 15 07:29:26 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Saadat:2020:WWC,
author = "Hassaan Saadat and Haris Javaid and Aleksandar
Ignjatovic and Sri Parameswaran",
booktitle = "{2020 25th Asia and South Pacific Design Automation
Conference (ASP-DAC)}",
title = "{WEID}: Worst-case Error Improvement in Approximate
Dividers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "8D-1--8D-6",
month = jan,
year = "2020",
DOI = "https://doi.org/10.1109/asp-dac47756.2020.9045504",
bibdate = "Wed Dec 20 08:02:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Approximate integer dividers suffer from unreasonably
high worst-case relative errors (such as 50\% or
100\%), which can adversely affect the
application-level output. In this paper, we propose
WEID, which is a novel lightweight method to improve
the worst-case relative errors in approximate integer
dividers. We first present an in-depth analysis to gain
insights into the cause of the high worst-case relative
error. Based on our insights, we propose a novel method
to detect when an error occurs in an approximate
divider, and modify the output to reduce the error.
Further, we present the hardware realization of WEID
method and demonstrate that it can be generically
coupled with several state-of-the-art approximate
dividers. Our results show that for 32-by-16 dividers,
WEID reduces worst-case relative errors from 100\% to $
\approx 20 $ \%, while still achieving $ \approx 80 \%
$ and $ \approx 70 \% $ reduction in delay and energy
compared to an accurate array divider.",
acknowledgement = ack-nhfb,
}
@Misc{SEGGER:2020:SFP,
author = "{SEGGER Microcontroller}",
title = "{SEGGER} Floating-Point Library",
howpublished = "Web site.",
month = jan,
year = "2020",
bibdate = "Fri Feb 07 06:02:26 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.segger.com/products/development-tools/runtime-library/technology/floating-point-library/",
abstract = "The floating-point library contains complete, fully
optimized and verified floating point functionality,
which is required for devices without an FPU. The
floating-point emulator, a crucial part of the
floating-point library, of the Arm and RISC-V variants
are written in assembly language, optimized either for
small code size or increased execution speed. For other
processor architectures the library has a portable C
implementation. \ldots{} The SEGGER Floating-Point
Library is delivered in source code, with optional
rights for redistribution in object code form. All
source files, a mix of C code and assembly, are fully
commented. The floating-point emulator, providing the
low-level functions, is entirely written in assembly.
Higher level functions are implemented as a mix of
primarily C code with some assembly routines. The code
can be compiled with any ANSO-compliant C compiler,
such as GCC, Clang, or IAR.",
acknowledgement = ack-nhfb,
}
@Article{Sharma:2020:CRV,
author = "Niraj Sharma and Riya Jain and Madhumita Mohan and
Sachin Patkar and Rainer Leupers and Nikhil Rishiyur
and Farhad Merchant",
title = "{CLARINET}: A {RISC-V} Based Framework for Posit
Arithmetic Empiricism",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--20",
day = "30",
month = may,
year = "2020",
DOI = "https://doi.org/10.48550/arXiv.2006.00364",
bibdate = "Sat Dec 16 10:27:27 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
URL = "https://arxiv.org/abs/2006.00364",
abstract = "Many engineering and scientific applications require
high precision arithmetic. IEEE~754-2008 compliant
(floating-point) arithmetic is the de facto standard
for performing these computations. Recently, posit
arithmetic has been proposed as a drop-in replacement
for floating-point arithmetic. The posit{\TM} data
representation and arithmetic claim several absolute
advantages over the floating-point format and
arithmetic, including higher dynamic range, better
accuracy, and superior performance-area trade-offs.
However, there does not exist any accessible, holistic
framework that facilitates the validation of these
claims of posit arithmetic, especially when the claims
involve long accumulations (quire).\par
In this paper, we present a consolidated
general-purpose processor-based framework to support
posit arithmetic empiricism. The end-users of the
framework have the liberty to seamlessly experiment
with their applications using posit and floating-point
arithmetic since the framework is designed for the two
number systems to coexist. Melodica is a posit
arithmetic core that implements parametric fused
operations that uniquely involve the quire data type.
Clarinet is a Melodica-enabled processor based on the
RISC-V ISA. To the best of our knowledge, this is the
first-ever integration of quire with a RISC-V core. To
show the effectiveness of the Clarinet platform, we
perform an extensive application study and benchmark
some of the common linear algebra and computer vision
kernels. We emulate Clarinet on a Xilinx FPGA and
present utilization and timing data. Clarinet and
Melodica remain actively under development and are
available in open-source for posit arithmetic
empiricism.",
acknowledgement = ack-nhfb,
}
@Article{Shibata:2020:SPV,
author = "Naoki Shibata and Francesco Petrogalli",
title = "{SLEEF}: A Portable Vectorized Library of {C} Standard
Mathematical Functions",
journal = j-IEEE-TRANS-PAR-DIST-SYS,
volume = "31",
number = "6",
pages = "1316--1327",
month = jun,
year = "2020",
CODEN = "ITDSEO",
DOI = "https://doi.org/10.1109/TPDS.2019.2960333",
ISSN = "1045-9219 (print), 1558-2183 (electronic)",
ISSN-L = "1045-9219",
bibdate = "Thu Feb 20 10:08:58 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Parallel and Distributed
Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
keywords = "elementary functions; floating-point arithmetic;
Parallel and vector implementations; SIMD processors",
}
@Misc{Smith:2020:HMC,
author = "Ernie Smith",
title = "How a Minor Calculation Error Cost {Intel} Half a
Billion Dollars: How one of the most famous computer
bugs of all time, the {Intel Pentium} floating-point
division glitch, blew out of proportion into a {PR}
crisis",
howpublished = "Web site.",
day = "14",
month = sep,
year = "2020",
bibdate = "Thu Jan 28 17:58:10 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.vice.com/en/article/dyzqdj/how-a-minor-calculation-error-cost-intel-half-a-billion-dollars",
acknowledgement = ack-nhfb,
remark = "This is a retrospective on the infamous Pentium divide
flaw of the 1990s. Near the end, it remarks about the
discoverer of the bug ``[Thomas] Nicely, who died last
year and was largely seen as legendary by his peers,
spent roughly three decades at the University of
Lynchburg before retiring in 2000.''",
}
@InProceedings{Sommer:2020:CAN,
author = "Lukas Sommer and Lukas Weber and Martin Kumm and
Andreas Koch",
booktitle = "{2020 IEEE 28th Annual International Symposium on
Field-Programmable Custom Computing Machines (FCCM)}",
title = "Comparison of Arithmetic Number Formats for Inference
in Sum--Product Networks on {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "75--83",
year = "2020",
DOI = "https://doi.org/10.1109/FCCM48280.2020.00020",
bibdate = "Fri Sep 22 08:07:44 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sousa:2020:TIR,
author = "L. Sousa and R. Paludo and P. Martins and H.
Pettenghi",
title = "Towards the Integration of Reverse Converters into the
{RNS} Channels",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "3",
pages = "342--348",
month = mar,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2948335",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Mar 5 13:54:11 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; arithmetic units; Computer architecture;
Delays; Logic gates; modular arithmetic; Power demand;
Program processors; Proposals; Residue number systems;
reverse conversion",
}
@InProceedings{Stine:2020:AIV,
author = "James E. Stine and Milo D. Ercegovac and Jean-Michel
Muller",
editor = "Michael B. Matthews",
booktitle = "{2020 54th Asilomar Conference on Signals, Systems,
and Computers. November 1--5, 2020. Pacific Grove,
California}",
title = "An Architecture for Improving Variable Radix Real and
Complex Division Using Recurrence Division",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "529--533",
year = "2020",
DOI = "https://doi.org/10.1109/IEEECONF51394.2020.9443498",
ISBN = "0-7381-3126-1",
ISBN-13 = "978-0-7381-3126-9",
bibdate = "Fri Sep 29 11:01:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sun:2020:ULP,
author = "Xiao Sun and Naigang Wang and Chia-Yu Chen and Jiamin
Ni and Ankur Agrawal and Xiaodong Cui and Swagath
Venkataramani and Kaoutar El Maghraoui and
Vijayalakshmi (Viji) Srinivasan and Kailash
Gopalakrishnan",
editor = "H. Larochelle and M. Ranzato and R. Hadsell and M. F.
Balcan and H. Lin",
booktitle = "Advances in Neural Information Processing Systems
{(NeurIPS 2020)}",
title = "Ultra-low precision 4-bit training of deep neural
networks",
publisher = "Curran Associates, Inc.",
address = "Red Hook, NY, USA",
pages = "1796--1807",
year = "2020",
ISBN = "1-71382-954-1",
ISBN-13 = "978-1-71382-954-6",
LCCN = "????",
bibdate = "Wed Aug 07 16:44:01 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://proceedings.neurips.cc/paper_files/paper/2020/file/13b919438259814cd5be8cb45877d577-Paper.pdf",
abstract = "In this paper, we propose a number of novel techniques
and numerical representation formats that enable, for
the very first time, the precision of training systems
to be aggressively scaled from 8-bits to 4-bits. To
enable this advance, we explore a novel adaptive
Gradient Scaling technique (Gradscale) that addresses
the challenges of insufficient range and resolution in
quantized gradients as well as explores the impact of
quantization errors observed during model training. We
theoretically analyze the role of bias in gradient
quantization and propose solutions that mitigate the
impact of this bias on model convergence. Finally, we
examine our techniques on a spectrum of deep learning
models in computer vision, speech, and NLP. In
combination with previously proposed solutions for
4-bit quantization of weight and activation tensors,
4-bit training shows a non-significant loss in accuracy
across application domains while enabling significant
hardware acceleration (> 7X over state-of-the-art FP16
systems).",
acknowledgement = ack-nhfb,
}
@InProceedings{Ternovoy:2020:CAF,
author = "E. Ternovoy and Mikhail G. Popov and Dmitrii V. Kaleev
and Yurii V. Savchenko and Alexey L. Pereverzev",
editor = "{IEEE}",
booktitle = "{2020 IEEE Conference of Russian Young Researchers in
Electrical and Electronic Engineering (EIConRus)}",
title = "Comparative Analysis of Floating-Point Accuracy of
{IEEE 754} and Posit Standards",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1883--186",
year = "2020",
DOI = "https://doi.org/10.1109/EIConRus49466.2020.9039521",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{ThoughtWorks:2020:PER,
author = "{ThoughtWorks}",
title = "{Posit Enhanced Rocket Chip (PERC)}",
howpublished = "Web software.",
year = "2020",
bibdate = "Sat Dec 16 15:25:19 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.thoughtworks.com/engineering-research/perc",
acknowledgement = ack-nhfb,
}
@Misc{Turley:2020:WBA,
author = "Jim Turley",
title = "What Is bfloat16, Anyway? {New} Floating-Point Format
is Suddenly Popular for Machine Learning",
howpublished = "Electronic Engineering journal Web site",
day = "23",
month = mar,
year = "2020",
bibdate = "Fri Apr 03 09:07:54 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.eejournal.com/article/what-is-bfloat16-anyway/",
acknowledgement = ack-nhfb,
}
@Article{Uguen:2020:ASA,
author = "Yohann Uguen and Florent {De Dinechin} and Victor
Lezaud and Steven Derrien",
title = "Application-Specific Arithmetic in High-Level
Synthesis Tools",
journal = j-TACO,
volume = "17",
number = "1",
pages = "5:1--5:23",
month = mar,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3377403",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Tue Mar 10 08:30:23 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3377403",
abstract = "This work studies hardware-specific optimization
opportunities currently unexploited by high-level
synthesis compilers. Some of these optimizations are
specializations of floating-point operations that
respect the usual semantics of the input program
without changing the numerical result. Some other
optimizations, locally triggered by the programmer
thanks to a pragma, assume a different semantics, where
floating-point code is interpreted as the specification
of computation with real numbers. The compiler is then
in charge to ensure an application-level accuracy
constraint expressed in the pragma and has the freedom
to use non-standard arithmetic hardware when more
efficient. These two classes of optimizations are
prototyped in the GeCoS source-to-source compiler and
evaluated on the Polybench and EEMBC benchmark suites.
Latency is reduced by up to 93\%, and resource usage is
reduced by up to 58\%.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "https://dl.acm.org/loi/taco",
}
@Article{Volkova:2020:AAR,
author = "A. Volkova and T. Hilaire and C. Lauter",
title = "Arithmetic Approaches for Rigorous Design of Reliable
Fixed-Point {LTI} Filters",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "4",
pages = "489--504",
month = apr,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2950658",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Mar 12 16:58:27 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "digital filters; eigendecomposition; Error analysis;
fixed-point arithmetic; Floating-point arithmetic;
Gershgorin circles; Heuristic algorithms; interval
arithmetic; Linear matrix inequalities; Linear systems;
Mathematical model; multiple precision; Reliability;
reliable computations; Signal processing algorithms;
table maker's dilemma",
}
@Article{Ward-Foxton:2020:AIG,
author = "Sally Ward-Foxton",
title = "Artificial Intelligence Gets Its Own System of
Numbers",
journal = "EE Times",
volume = "??",
number = "??",
pages = "??--??",
day = "14",
month = feb,
year = "2020",
bibdate = "Wed May 19 11:58:46 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.eetimes.com/artificial-intelligence-gets-its-own-system-of-numbers/",
acknowledgement = ack-nhfb,
keywords = "BF16 (1 + 8 + 7); FP16 (1 + 5 + 10); Nervana
Flexpoint",
}
@Article{Xiao:2020:PAH,
author = "Feibao Xiao and Feng Liang and Bin Wu and Junzhe Liang
and Shuting Cheng and Guohe Zhang",
title = "Posit Arithmetic Hardware Implementations with The
Minimum Cost Divider and Square Root",
journal = j-ELECTRONICS,
volume = "9",
number = "10",
pages = "1622:1--1622:16",
month = oct,
year = "2020",
DOI = "https://doi.org/10.3390/electronics9101622",
ISSN = "2079-9292",
ISSN-L = "2079-9292",
bibdate = "Fri Dec 15 07:25:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@InProceedings{Zaruba:2020:CRV,
author = "Florian Zaruba and Fabian Schuiki and Luca Benini",
editor = "{IEEE}",
booktitle = "{2020 IEEE Hot Chips 32 Symposium (HCS)}",
title = "A 4096-core {RISC-V} Chiplet Architecture for
Ultra-efficient Floating-point Computing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--24",
year = "2020",
DOI = "https://doi.org/10.1109/HCS49909.2020.9220474",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
remark = "This article consists only of a collection of slides
from the author's conference presentation",
}
@Article{Zhang:2020:DPE,
author = "Hao Zhang and Seok-Bum Ko",
title = "Design of Power Efficient Posit Multiplier",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "67",
number = "5",
pages = "861--865",
year = "2020",
DOI = "https://doi.org/10.1109/TCSII.2020.2980531",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}
@Article{Zhang:2020:NAE,
author = "N. Zhang and Q. Qin and H. Yuan and C. Zhou and S. Yin
and S. Wei and L. Liu",
title = "{NTTU}: An Area-Efficient Low-Power {NTT}-Uncoupled
Architecture for {NTT}-Based Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "4",
pages = "520--533",
month = apr,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2958334",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Mar 12 16:58:27 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Clocks; Cloud computing; Complexity theory; Computer
architecture; Encryption; Fully homomorphic encryption;
large integer multiplication; number theoretical
conversion; polynomial multiplication; Random access
memory; Transforms",
}
@Article{Zhang:2020:NFM,
author = "H. Zhang and D. Chen and S. Ko",
title = "New Flexible Multiple-Precision Multiply-Accumulate
Unit for Deep Neural Network Training and Inference",
journal = j-IEEE-TRANS-COMPUT,
volume = "69",
number = "1",
pages = "26--38",
month = jan,
year = "2020",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2019.2936192",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jan 9 07:48:57 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; computer arithmetic; Deep learning; deep
neural network computing; flexible precision
arithmetic; Hardware; multiple-precision arithmetic;
Multiply-accumulate unit; Neural networks; Pipelines;
Standards; Training",
}
@TechReport{Zimmermann:2020:AMFa,
author = "Paul Zimmermann",
title = "Accuracy of Mathematical Functions in Single
Precision",
institution = "????",
pages = "2",
day = "3",
month = feb,
year = "2020",
bibdate = "Mon Aug 17 15:41:19 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Previous versions dated 4 February 2020, 10 May 2020,
26 May 2020, 7 August 2020, 25 August 2020, 28 August
2020, 15 September 2020, 17 September 2020.",
URL = "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
acknowledgement = ack-nhfb,
remark = "Tabular comparison of GNU and Intel -lm libraries for
correct rounding, versus results from MPFR.",
}
@TechReport{Zimmermann:2020:AMFb,
author = "Paul Zimmermann",
title = "Accuracy of Mathematical Functions in Single, Double,
and Quadruple Precision",
institution = "????",
pages = "14",
day = "4",
month = dec,
year = "2020",
bibdate = "Fri Dec 04 11:52:43 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Revised February 4, May 10, May 26 and August 7
[2020].",
URL = "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
acknowledgement = ack-nhfb,
remark = "Tabular comparison of AMD, GNU, Intel, RedHat,
OpenLibm, and Musl -lm libraries for correct rounding,
versus results from MPFR.",
}
@Article{Zou:2020:DFP,
author = "Daming Zou and Muhan Zeng and Yingfei Xiong and
Zhoulai Fu and Lu Zhang and Zhendong Su",
title = "Detecting floating-point errors via atomic
conditions",
journal = j-PACMPL,
volume = "4",
number = "POPL",
pages = "60:1--60:27",
month = jan,
year = "2020",
DOI = "https://doi.org/10.1145/3371128",
ISSN = "2475-1421",
bibdate = "Fri Aug 7 18:46:52 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3371128",
abstract = "This paper tackles the important, difficult problem of
detecting program inputs that trigger large
floating-point errors in numerical code. It introduces
a novel, principled {\em dynamic analysis\/} that
leverages the mathematically rigorously analyzed {\em
condition numbers\/} for atomic numerical operations,
which we call {\em atomic conditions}, to effectively
guide the search for large floating-point errors.
Compared with existing approaches, our work based on
atomic conditions has several distinctive benefits: (1)
it does not rely on high-precision implementations to
act as approximate oracles, which are difficult to
obtain in general and computationally costly; and (2)
atomic conditions provide accurate, modular search
guidance. These benefits in combination lead to a
highly effective approach that detects more significant
errors in real-world code (e.g., widely-used numerical
library functions) and achieves several orders of
speedups over the state-of-the-art, thus making error
analysis significantly more practical. We expect the
methodology and principles behind our approach to
benefit other floating-point program analysis tasks
such as debugging, repair and synthesis. To facilitate
the reproduction of our work, we have made our
implementation, evaluation data and results publicly
available on GitHub at
\url{https://github.com/FP-Analysis/atomic-condition}",
acknowledgement = ack-nhfb,
articleno = "60",
fjournal = "Proceedings of the ACM on Programming Languages",
journal-URL = "https://pacmpl.acm.org/",
}
@Article{Ahn:2021:KSK,
author = "Dong H. Ahn and Allison H. Baker and Michael Bentley
and Ian Briggs and Ganesh Gopalakrishnan and Dorit M.
Hammerling and Ignacio Laguna and Gregory L. Lee and
Daniel J. Milroy and Mariana Vertenstein",
title = "Keeping science on keel when software moves",
journal = j-CACM,
volume = "64",
number = "2",
pages = "66--74",
month = feb,
year = "2021",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/3382037",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jan 26 14:34:25 MST 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cacm2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/doi/10.1145/3382037",
abstract = "An approach to reproducibility problems related to
porting software across machines and compilers.",
acknowledgement = ack-nhfb,
ajournal = "Commun. ACM",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
}
@InProceedings{Alouani:2021:IIR,
author = "Ihsen Alouani and Anouar {Ben Khalifa} and Farhad
Merchant and Rainer Leupers",
editor = "{IEEE}",
booktitle = "{2021 34th International Conference on VLSI Design and
2021 20th International Conference on Embedded Systems
(VLSID)}",
title = "An Investigation on Inherent Robustness of Posit Data
Representation",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "276--281",
year = "2021",
DOI = "https://doi.org/10.1109/VLSID51830.2021.00052",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Andrysco:2021:SFP,
author = "Marc Andrysco and David Kohlbrenner and Keaton Mowery
and Ranjit Jhala and Sorin Lerner and Hovav Shacham",
title = "On Subnormal Floating Point and Abnormal Timing",
type = "Report",
institution = "Department of Computer Science and Engineering
University of California, San Diego",
address = "La Jolla, California, USA",
pages = "17",
day = "2",
month = jan,
year = "2021",
bibdate = "Fri Sep 06 10:04:19 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We identify a timing channel in the floating point
instructions of modern x86 processors: the running time
of floating point addition and multiplication
instructions can vary by two orders of magnitude
depending on their operands. We develop a benchmark
measuring the timing variability of floating point
operations and report on its results. We use floating
point data timing variability to demonstrate practical
attacks on the security of the Firefox browser
(versions 23 through 27) and the Fuzz differentially
private database. Finally, we initiate the study of
mitigations to floating point data timing channels with
libfixedtimefixedpoint, a new fixed-point,
constant-time math library.\par
Modern floating point standards and implementations are
sophisticated, complex, and subtle, a fact that has not
been sufficiently recognized by the security community.
More work is needed to assess the implications of the
use of floating point instructions in security-relevant
software.",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:2021:AI,
author = "Anonymous",
title = "Author Index",
crossref = "IEEE:2021:ISC",
pages = "141--141",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00037",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Anonymous:2021:CN,
author = "Anonymous",
title = "[{Copyright} notice]",
crossref = "IEEE:2021:ISC",
pages = "1--1",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00003",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Anonymous:2021:FC,
author = "Anonymous",
title = "[{Front} cover]",
crossref = "IEEE:2021:ISC",
pages = "1--1",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00002",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Anonymous:2021:IPA,
author = "Anonymous",
title = "Industry Panel {ARITH 2021}: Processors for the
Computing of the 2020s",
crossref = "IEEE:2021:ISC",
pages = "xv--xv",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00010",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Anonymous:2021:PCA,
author = "Anonymous",
title = "Program Committee {ARITH 2021}",
crossref = "IEEE:2021:ISC",
pages = "xii--xii",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00007",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Anonymous:2021:SA,
author = "Anonymous",
title = "Sponsors {ARITH 2021}",
crossref = "IEEE:2021:ISC",
pages = "xviii--xviii",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00012",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Anonymous:2021:SCA,
author = "Anonymous",
title = "Steering Committee {ARITH 2021}",
crossref = "IEEE:2021:ISC",
pages = "xiii--xiii",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00008",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Anonymous:2021:TC,
author = "Anonymous",
title = "Table of Contents",
crossref = "IEEE:2021:ISC",
pages = "v--viii",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00004",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Anonymous:2021:TP,
author = "Anonymous",
title = "[{Title} page]",
crossref = "IEEE:2021:ISC",
pages = "1--1",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00001",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Ashmawy:2021:FHI,
author = "Doaa Ashmawy and Arash Reyhani-Masoleh",
title = "A Faster Hardware Implementation of the {AES}
{S}-box",
crossref = "IEEE:2021:ISC",
pages = "123--130",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00034",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Bagnara:2021:PAV,
author = "Roberto Bagnara and Michele Chiari and Roberta Gori
and Abramo Bagnara",
title = "A Practical Approach to Verification of Floating-Point
{C\slash C++} Programs with {\tt math.h}\slash {\tt
cmath} Functions",
journal = j-TOSEM,
volume = "30",
number = "1",
pages = "9:1--9:53",
month = jan,
year = "2021",
CODEN = "ATSMER",
DOI = "https://doi.org/10.1145/3410875",
ISSN = "1049-331X (print), 1557-7392 (electronic)",
ISSN-L = "1049-331X",
bibdate = "Fri Jan 22 07:02:14 MST 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tosem.bib",
URL = "https://dl.acm.org/doi/10.1145/3410875",
abstract = "Verification of C/C++ programs has seen considerable
progress in several areas, but not for programs that
use these languages' mathematical libraries. The reason
is that all libraries in widespread use come with no
guarantees about the computed results. This would seem
to prevent any attempt at formal verification of
programs that use them: without a specification for the
functions, no conclusion can be drawn statically about
the behavior of the program. We propose an alternative
to surrender. We introduce a pragmatic approach that
leverages the fact that most {\tt math.h}\slash {\tt
cmath} functions are almost piecewise monotonic: as we
discovered through exhaustive testing, they may have
glitches, often of very small size and in small
numbers. We develop interval refinement techniques for
such functions based on a modified dichotomic search,
which enable verification via symbolic execution based
model checking, abstract interpretation, and test data
generation. To the best of our knowledge, our
refinement algorithms are the first in the literature
to be able to handle non-correctly rounded function
implementations, enabling verification in the presence
of the most common implementations. We experimentally
evaluate our approach on real-world code, showing its
ability to detect or rule out anomalous behaviors.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Software Engineering and
Methodology",
journal-URL = "https://dl.acm.org/loi/tosem",
}
@Misc{Bailey:2021:PMN,
author = "David H. Bailey",
title = "\pkg{MPFUN2020}: A new thread-safe arbitrary precision
package",
howpublished = "Web document",
pages = "54",
day = "18",
month = may,
year = "2021",
bibdate = "Mon Dec 05 07:32:16 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.davidhbailey.com/dhbpapers/mpfun2020.pdf",
abstract = "Numerous research studies have arisen, particularly in
mathematical physics and experimental mathematics, that
require extremely high numeric precision. Such
precision greatly magnifies computer run times, so
software packages to support high-precision computing
must be designed for thread-based parallel
processing.
This paper describes a new arbitrary precision software
package (``MPFUN2020'') that features several
significant improvements over an earlier package. It
comes in two versions: a self-contained all-Fortran
version, and a version based on the MPFR package, which
is even faster. Both versions feature: (a) a completely
thread-safe design, so user codes can be converted for
parallel execution at the application level; (b) a
full-featured high-level Fortran interface, so that
most applications can be converted to multiprecision
with relatively minor changes to source code; (c) full
support for both real and complex datatypes; (d) a wide
variety of transcendental functions and special
functions; (e) run-time checking and other facilities
to overcome problems with converting double precision
constants and data; (f) a medium precision datatype,
which improves performance and reduces memory cost on
large variable precision applications; and (g)
interoperability --- with a simple restriction,
application codes written for one version can be run
with the other without change.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bajard:2021:GRN,
author = "Jean-Claude Bajard and Kazuhide Fukushima and Shinsaku
Kiyomoto and Thomas Plantard and Arnaud Sipasseuth and
Willy Susilo",
title = "Generating Residue Number System Bases",
crossref = "IEEE:2021:ISC",
pages = "86--93",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00027",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Bertaccini:2021:TFL,
author = "Luca Bertaccini and Matteo Perotti and Stefan Mach and
Pasquale Davide Schiavone and Florian Zaruba and Luca
Benini",
editor = "{IEEE}",
booktitle = "{2021 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "{Tiny-FPU}: Low-Cost Floating-Point Support for Small
{RISC-V MCU} Cores",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2021",
DOI = "https://doi.org/10.1109/ISCAS51556.2021.9401149",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bigou:2021:ERA,
author = "Karim Bigou and Mojtaba Bisheh Niasar and Lu{\'\i}s
Fiolhais and Rogerio Paludo and Hwajeong Seo",
title = "External Reviewers {ARITH 2021}",
crossref = "IEEE:2021:ISC",
pages = "xiv--xiv",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00009",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Bisheh-Niasar:2021:HSN,
author = "Mojtaba Bisheh-Niasar and Reza Azarderakhsh and Mehran
Mozaffari-Kermani",
title = "High-Speed {NTT}-based Polynomial Multiplication
Accelerator for Post-Quantum Cryptography",
crossref = "IEEE:2021:ISC",
pages = "94--101",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00028",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Boldo:2021:ERN,
author = "Sylvie Boldo and Christoph Quirin Lauter and
Jean-Michel Muller",
title = "Emulating Round-to-Nearest-Ties-to-Zero ``augmented''
Floating-Point Operations Using
Round-to-Nearest-Ties-to-Even Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "70",
number = "7",
pages = "1046--1058",
month = jul,
year = "2021",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2020.3002702",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jun 10 15:51:57 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Boldo:2021:SFT,
author = "Sylvie Boldo and Guillaume Melquiond",
title = "Some Formal Tools for Computer Arithmetic: {Flocq} and
{Gappa}",
crossref = "IEEE:2021:ISC",
pages = "111--114",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00031",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Borges:2021:AIA,
author = "Carlos F. Borges",
title = "{Algorithm 1014}: an Improved Algorithm for {\tt
hypot(x,y)}",
journal = j-TOMS,
volume = "47",
number = "1",
pages = "9:1--9:12",
month = jan,
year = "2021",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3428446",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Jan 7 10:31:04 MST 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/julia.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3428446",
abstract = "We develop fast and accurate algorithms for evaluating
$ \sqrt {x^2 + y^2} $ for two floating-point numbers
$x$ and $y$. Library functions that perform this
computation are generally named {\tt hypot(x,y)}. We
compare five approaches that we will develop in this
article to the current resident library function that
is delivered with Julia 1.1 and to the code that has
been distributed with the C math library for decades.
We will investigate the accuracy of our algorithms by
simulation.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Borges:2021:CRN,
author = "Carlos F. Borges",
title = "A Correctly Rounded {Newton} Step for the Reciprocal
Square Root",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--8",
day = "28",
month = dec,
year = "2021",
bibdate = "Fri Sep 22 16:08:53 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2112.14321",
abstract = "The reciprocal square root is an important computation
for which many sophisticated algorithms exist (see for
example \cite{Moroz,863046,863031} and the references
therein). A common theme is the use of Newton's method
to refine the estimates. In this paper we develop a
correctly rounded Newton step that can be used to
improve the accuracy of a naive calculation (using
methods similar to those developed in \cite{borges})
The approach relies on the use of the fused
multiply-add (FMA) which is widely available in
hardware on a variety of modern computer architectures.
We then introduce the notion of {\em weak rounding} and
prove that our proposed algorithm meets this standard.
We then show how to leverage the exact Newton step to
get a Halley's method compensation which requires one
additional FMA and one additional multiplication. This
method appears to give correctly rounded results
experimentally and we show that it can be combined with
a square root free method for estimating the reciprocal
square root to get a method that is both very fast (in
computing environments with a slow square root) and,
experimentally, highly accurate.",
acknowledgement = ack-nhfb,
}
@Article{Borges:2021:FCA,
author = "Carlos F. Borges",
title = "Fast compensated algorithms for the reciprocal square
root, the reciprocal hypotenuse, and {Givens}
rotations",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--11",
day = "23",
month = feb,
year = "2021",
bibdate = "Fri Sep 22 16:05:47 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2103.08694",
abstract = "The reciprocal square root is an important computation
for which many very sophisticated algorithms exist (see
for example \cite{863046,863031} and the references
therein). In this paper we develop a simple
differential compensation (much like those developed in
\cite{borges}) that can be used to improve the accuracy
of a naive calculation. The approach relies on the use
of the fused multiply-add (FMA) which is widely
available in hardware on a variety of modern computer
architectures. We then demonstrate how to combine this
approach with a somewhat inaccurate but fast square
root free method for estimating the reciprocal square
root to get a method that is both fast (in computing
environments with a slow square root) and,
experimentally, highly accurate. Finally, we show how
this same approach can be extended to the reciprocal
hypotenuse calculation and, most importantly, to the
construction of Givens rotations.",
acknowledgement = ack-nhfb,
}
@Article{Bos:2021:MPM,
author = "Joppe W. Bos and Kristin E. Lauter",
title = "In Memoriam: {Peter L. Montgomery} (1947--2020)",
journal = j-NAMS,
volume = "68",
number = "4",
pages = "538--545",
month = apr,
year = "2021",
CODEN = "AMNOAN",
DOI = "https://doi.org/10.1090/noti2258",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "01A70 (11-03 11Yxx 94A60)",
MRnumber = "4228130",
bibdate = "Sat May 29 18:37:36 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/nams2020.bib",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
}
@InProceedings{Bottcher:2021:ROT,
author = "Andreas B{\"o}ttcher and Martin Kumm and Florent de
Dinechin",
title = "Resource Optimal Truncated Multipliers for {FPGAs}",
crossref = "IEEE:2021:ISC",
pages = "102--109",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00029",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Brun:2021:SEBa,
author = "Emeric Brun and David Defour and Pablo {de Oliveira
Castro} and Matei I{\c{s}}toan and Davide Mancusi and
Eric Petit and Alan Vaquet",
title = "A Study of the Effects and Benefits of
Custom-Precision Mathematical Libraries for {HPC}
Codes",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "9",
number = "3",
pages = "1467--1478",
month = jul # "\slash " # sep,
year = "2021",
DOI = "https://doi.org/10.1109/TETC.2021.3070422",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
note = "See \cite{Brun:2021:SEBb}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
keywords = "ARITH-28",
}
@InProceedings{Brun:2021:SEBb,
author = "Emeric Brun and David Defour and Pablo {De Oliveira
Castro} and Matei Istoan and Davide Mancusi and Eric
Petit and Alan Vaquet",
title = "A Study of the Effects and Benefits of
Custom-Precision Mathematical Libraries for {HPC}
Codes",
crossref = "IEEE:2021:ISC",
pages = "62--62",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00022",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Brun:2021:SEBa}.",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
remark = "Published in IEEE Transactions on Emerging Topics in
Computing, Volume: 9, Issue: 3, July--September 2021,
and orally presented at ARITH 2021.",
}
@InProceedings{Brunie:2021:MAE,
author = "Nicolas Brunie",
title = "Manifest for an Approximation Exchange Format",
crossref = "IEEE:2021:ISC",
pages = "63--68",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00023",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We introduce AXF, Approximation eXchange Format, a
file format dedicated to the description of basic
constructs for function approximation, such as
numerical description of piecewise polynomial
approximations. AXF is designed as a numerical
intermediate representation between approximation
generation and approximation implementation tools.",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Ciocirlan:2021:AEPa,
author = "Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya
Ramapantulu and Nicolae Tapus and Yong Meng Teo",
title = "The Accuracy and Efficiency of Posit Arithmetic",
journal = "arXiv.org",
volume = "??",
number = "??",
day = "16",
month = sep,
year = "2021",
bibdate = "Sat Dec 16 15:13:00 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
abstract = "Motivated by the increasing interest in the posit
numeric format, in this paper we evaluate the accuracy
and efficiency of posit arithmetic in contrast to the
traditional IEEE 754 32-bit floating-point (FP32)
arithmetic. We first design and implement a Posit
Arithmetic Unit (PAU), called POSAR, with flexible
bit-sized arithmetic suitable for applications that can
trade accuracy for savings in chip area. Next, we
analyze the accuracy and efficiency of POSAR with a
series of benchmarks including mathematical
computations, ML kernels, NAS Parallel Benchmarks
(NPB), and Cifar-10 CNN. This analysis is done on our
implementation of POSAR integrated into a RISC-V Rocket
Chip core in comparison with the IEEE 754-based
Floating Point Unit (FPU) of Rocket Chip. Our analysis
shows that POSAR can outperform the FPU, but the
results are not spectacular. For NPB, 32-bit posit
achieves better accuracy than FP32 and improves the
execution by up to 2\%. However, POSAR with 32-bit
posit needs 30\% more FPGA resources compared to the
FPU. For classic ML algorithms, we find that 8-bit
posits are not suitable to replace FP32 because they
exhibit low accuracy leading to wrong results. Instead,
16-bit posit offers the best option in terms of
accuracy and efficiency. For example, 16-bit posit
achieves the same Top-1 accuracy as FP32 on a Cifar-10
CNN with a speedup of 18\%.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "2109.08225",
primaryclass = "cs.AR",
}
@InProceedings{Ciocirlan:2021:AEPb,
author = "Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya
Ramapantulu and Nicolae {pu } and Yong Meng Teo",
editor = "{IEEE}",
booktitle = "{2021 IEEE 39th International Conference on Computer
Design (ICCD)}",
title = "The Accuracy and Efficiency of Posit Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "83--87",
year = "2021",
DOI = "https://doi.org/10.1109/ICCD53106.2021.00024",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic; RISC-V",
}
@Article{Cococcioni:2021:VPO,
author = "Marco Cococcioni and Federico Rossi and Emanuele
Ruffaldi and Sergio Saponara",
title = "Vectorizing posit operations on {RISC-V} for faster
deep neural networks: experiments and comparison with
{ARM SVE}",
journal = "Neural Computing and Applications",
volume = "33",
number = "16",
publisher = pub-SV,
address = pub-SV:adr,
pages = "10575--10585",
month = feb,
year = "2021",
DOI = "https://doi.org/10.1007/s00521-021-05814-0",
ISSN = "1433-3058",
ISSN-L = "0941-0643",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Coladon:2021:MFR,
author = "Titouan Coladon and Philippe Elbaz-Vincent and Cyril
Hugounenq",
title = "{MPHELL}: a fast and robust library with unified and
versatile arithmetics for elliptic curves
cryptography",
crossref = "IEEE:2021:ISC",
pages = "78--85",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00026",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Connolly:2021:SRP,
author = "Michael P. Connolly and Nicholas J. Higham and Theo
Mary",
title = "Stochastic Rounding and Its Probabilistic Backward
Error Analysis",
journal = j-SIAM-J-SCI-COMP,
volume = "43",
number = "1",
pages = "A566--A585",
month = "????",
year = "2021",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/20M1334796",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Mar 12 11:40:06 MST 2021",
bibsource = "http://epubs.siam.org/toc/sjoce3/43/1;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2021",
}
@Article{Czachor:2021:NNM,
author = "Marek Czachor",
title = "Non-{Newtonian} Mathematics Instead of Non-{Newtonian}
Physics: Dark Matter and Dark Energy from a Mismatch of
Arithmetics",
journal = j-FOUND-SCI,
volume = "26",
number = "1",
pages = "75--95",
month = mar,
year = "2021",
CODEN = "FOSCFI",
DOI = "https://doi.org/10.1007/s10699-020-09687-9",
ISSN = "1233-1821 (print), 1572-8471 (electronic)",
ISSN-L = "1233-1821",
bibdate = "Mon Apr 19 10:16:53 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/foundsci.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://link.springer.com/article/10.1007/s10699-020-09687-9",
acknowledgement = ack-nhfb,
ajournal = "Found. Sci.",
fjournal = "Foundations of Science",
journal-URL = "http://link.springer.com/journal/10699",
online-date = "Published: 28 July 2020 Pages: 75 - 95",
}
@Misc{Darcy:2021:FPA,
author = "Joseph D. Darcy",
title = "Floating-Point Arithmetic: What Every {Java}
Programmer Should Know!",
howpublished = "Web site 29m37s video.",
year = "2021",
bibdate = "Tue Feb 27 11:53:09 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/java2020.bib",
URL = "https://youtu.be/ajaHQ9S4uTA",
acknowledgement = ack-nhfb,
}
@InProceedings{deDinechin:2021:TAC,
author = "Florent de Dinechin and Silviu-Ioan Filip and Martin
Kumm and Anastasia Volkova",
title = "Towards Arithmetic-Centered Filter Design",
crossref = "IEEE:2021:ISC",
pages = "115--118",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00032",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Defour:2021:SCB,
author = "David Defour and Pablo de Oliveira Castro and Matei
I{\c{s}}toan and Eric Petit",
title = "Shadow computation with {BFloat16} to estimate the
numerical accuracy of summations",
crossref = "IEEE:2021:ISC",
pages = "33--36",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00017",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{delaFraga:2021:DEU,
author = "Luis Gerardo de la Fraga",
title = "Differential Evolution under Fixed Point Arithmetic
and {FP16} Numbers",
journal = j-MATH-COMPUT-APPL,
volume = "26",
number = "1",
pages = "13--??",
month = mar,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.3390/mca26010013",
ISSN = "2297-8747",
ISSN-L = "2297-8747",
bibdate = "Sun Feb 18 06:28:40 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
URL = "https://www.mdpi.com/2297-8747/26/1/13",
acknowledgement = ack-nhfb,
fjournal = "Mathematical and Computational Applications",
journal-URL = "https://www.mdpi.com/journal/mca",
}
@InProceedings{Demeure:2021:TET,
author = "Nestor Demeure and C{\'e}dric Chevalier and Christophe
Denis and Pierre Dossantos-Uzarralde",
title = "Tagged error: tracing numerical error through
computations",
crossref = "IEEE:2021:ISC",
pages = "9--16",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00014",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Demmel:2021:NIS,
author = "James Demmel and Jason Riedy",
title = "A New {IEEE 754} Standard for Floating-Point
Arithmetic in an Ever-Changing World",
journal = j-SIAM-NEWS,
volume = "54",
number = "6",
pages = "??--??",
month = jul # "\slash " # aug,
year = "2021",
ISSN = "0036-1437",
bibdate = "Tue Nov 16 08:21:39 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://sinews.siam.org/Details-Page/a-new-ieee-754-standard-for-floating-point-arithmetic-in-an-ever-changing-world",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
}
@Article{Dimitrakopoulos:2021:SPAa,
author = "Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos
and Vassilis Paliouras",
title = "Sum Propagate Adders",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "9",
number = "3",
pages = "1479--1488",
month = jul # "\slash " # sep,
year = "2021",
DOI = "https://doi.org/10.1109/TETC.2021.3068729",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
note = "See \cite{Dimitrakopoulos:2021:SPAb}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Dimitrakopoulos:2021:SPAb,
author = "Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos
and Vassilis Paliouras",
title = "Sum Propagate Adders",
crossref = "IEEE:2021:ISC",
pages = "110--110",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00030",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Dimitrakopoulos:2021:SPAa}.",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
remark = "Published in IEEE Transactions on Emerging Topics in
Computing, Volume: 9, Issue: 3, July--September 2021,
and orally presented at ARITH 2021.",
}
@Misc{Druck:2021:NSB,
author = "Philip Druck",
title = "A Novel Set of Base-Prime Floating Point Numbers",
howpublished = "TechRxiv preprint.",
day = "16",
month = feb,
year = "2021",
DOI = "https://doi.org/10.36227/techrxiv.13960829.v1",
bibdate = "Fri Sep 29 14:28:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "A novel set is presented that generalizes the usual
base representations of floating point real numbers. It
uses base-prime numbers instead of the usual base 2
(binary), base 3 (for the Cantor set), base 10
(decimal), base 16 (hexadecimal) and the like. This
base-prime set, denoted DS, is essentially an
experimental finding, identified in unrelated patented
research on nonuniform signal data sampling [1] and
self-stabilizing computer arithmetic [2].",
acknowledgement = ack-nhfb,
}
@Article{Eliahu:2021:MME,
author = "Adi Eliahu and Ronny Ronen and Pierre-Emmanuel
Gaillardon and Shahar Kvatinsky",
title = "{multiPULPly}: a Multiplication Engine for
Accelerating Neural Networks on Ultra-low-power
Architectures",
journal = j-JETC,
volume = "17",
number = "2",
pages = "24:1--24:27",
month = apr,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.1145/3432815",
ISSN = "1550-4832 (print), 1550-4840 (electronic)",
ISSN-L = "1550-4832",
bibdate = "Fri Apr 30 06:39:29 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jetc.bib",
URL = "https://dl.acm.org/doi/10.1145/3432815",
abstract = "Computationally intensive neural network applications
often need to run on resource-limited low-power
devices. Numerous hardware accelerators have been
developed to speed up the performance of neural network
applications and reduce power consumption; however,
most focus on data centers and full-fledged systems.
Acceleration in ultra-low-power systems has been only
partially addressed. In this article, we present
multiPULPly, an accelerator that integrates memristive
technologies within standard low-power CMOS technology,
to accelerate multiplication in neural network
inference on ultra-low-power systems. This accelerator
was designated for PULP, an open-source microcontroller
system that uses low-power RISC-V processors.
Memristors were integrated into the accelerator to
enable power consumption only when the memory is
active, to continue the task with no context-restoring
overhead, and to enable highly parallel analog
multiplication. To reduce the energy consumption, we
propose novel dataflows that handle common
multiplication scenarios and are tailored for our
architecture. The accelerator was tested on FPGA and
achieved a peak energy efficiency of 19.5 TOPS/W,
outperforming state-of-the-art accelerators by $ 1.5
\times $ to $ 4.5 \times $.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "https://dl.acm.org/loi/jetc",
}
@InProceedings{Elkhatib:2021:ARV,
author = "Rami Elkhatib and Reza Azarderakhsh and Mehran
Mozaffari-Kermani",
title = "Accelerated {RISC-V} for {SIKE}",
crossref = "IEEE:2021:ISC",
pages = "131--138",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00035",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Fasi:2021:ASRa,
author = "Massimiliano Fasi and Mantas Mikaitis",
title = "Algorithms for Stochastically Rounded Elementary
Arithmetic Operations in {IEEE 754} Floating-Point
Arithmetic",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "9",
number = "3",
pages = "1451--1466",
month = jul # "\slash " # sep,
year = "2021",
DOI = "https://doi.org/10.1109/TETC.2021.3069165",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
note = "See \cite{Fasi:2021:ASRb}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
keywords = "ARITH-28",
}
@InProceedings{Fasi:2021:ASRb,
author = "Massimiliano Fasi and Mantas Mikaitis",
title = "Algorithms for Stochastically Rounded Elementary
Arithmetic Operations in {IEEE 754} Floating-Point
Arithmetic",
crossref = "IEEE:2021:ISC",
pages = "69--69",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00024",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Fasi:2021:ASRa}.",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
remark = "Published in IEEE Transactions on Emerging Topics in
Computing, Volume: 9, Issue: 3, July--September 2021,
and orally presented at ARITH 2021.",
}
@Article{Fasi:2021:NBN,
author = "Massimiliano Fasi and Nicholas J. Higham and Mantas
Mikaitis and Srikara Pranesh",
title = "Numerical behavior of {NVIDIA} tensor cores",
journal = "PeerJ Computer Science",
volume = "7",
pages = "e330:1--e330:19",
month = feb,
year = "2021",
DOI = "https://doi.org/10.7717/peerj-cs.330",
ISSN = "2376-5992",
bibdate = "Mon Apr 22 14:18:25 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
journal-URL = "https://peerj.com/cs/",
}
@Article{Fortin:2021:HPS,
author = "Pierre Fortin and Ambroise Fleury and Fran{\c{c}}ois
Lemaire and Michael Monagan",
title = "High-performance {SIMD} modular arithmetic for
polynomial evaluation",
journal = j-CCPE,
volume = "33",
number = "16",
pages = "e6270:1--e6270:??",
day = "25",
month = aug,
year = "2021",
CODEN = "CCPEBO",
DOI = "https://doi.org/10.1002/cpe.6270",
ISSN = "1532-0626 (print), 1532-0634 (electronic)",
ISSN-L = "1532-0626",
bibdate = "Tue Feb 22 09:49:56 MST 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Concurr. Comput.",
fjournal = "Concurrency and Computation: Practice and Experience",
journal-URL = "http://www.interscience.wiley.com/jpages/1532-0626",
onlinedate = "25 May 2021",
}
@Article{Garofalo:2021:XEEa,
author = "Angelo Garofalo and Giuseppe Tagliavini and Francesco
Conti and Luca Benini and Davide Rossi",
title = "{XpulpNN}: Enabling Energy Efficient and Flexible
Inference of Quantized Neural Networks on {RISC-V}
Based {IoT} End Nodes",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "9",
number = "3",
pages = "1489--1505",
month = jul # "\slash " # sep,
year = "2021",
DOI = "https://doi.org/10.1109/TETC.2021.3072337",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
note = "See \cite{Garofalo:2021:XEEb}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Garofalo:2021:XEEb,
author = "Angelo Garofalo and Giuseppe Tagliavini and Francesco
Conti and Luca Benini and Davide Rossi",
title = "{XpulpNN}: Enabling Energy Efficient and Flexible
Inference of Quantized Neural Networks on {RISC-V}
based {IoT} End Nodes",
crossref = "IEEE:2021:ISC",
pages = "53--53",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00020",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Garofalo:2021:XEEa}.",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
remark = "Published in IEEE Transactions on Emerging Topics in
Computing, Volume: 9, Issue: 3, July--September 2021,
and orally presented at ARITH 2021.",
}
@Article{Gohil:2021:FPF,
author = "Varun Gohil and Sumit Walia and Joycee Mekie and Manu
Awasthi",
title = "Fixed-Posit: a Floating-Point Representation for
Error-Resilient Applications",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "68",
number = "10",
pages = "3341--3345",
year = "2021",
DOI = "https://doi.org/10.1109/TCSII.2021.3072217",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}
@InProceedings{Gopalakrishnan:2021:GNA,
author = "Ganesh Gopalakrishnan and Ignacio Laguna and Ang Li
and Pavel Panchekha and Cindy Rubio-Gonz{\'a}lez and
Zachary Tatlock",
editor = "????",
booktitle = "{Correctness 2021: Fifth International Workshop on
Software Correctness for HPC Applications, November 19,
2021, America's Center Convention Complex St. Louis,
MO, USA}",
title = "Guarding Numerics Amidst Rising Heterogeneity",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2021",
bibdate = "Mon Sep 11 06:54:23 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://correctness-workshop.github.io/2021/",
acknowledgement = ack-nhfb,
}
@InProceedings{Gustafsson:2021:AFP,
author = "Oscar Gustafsson and Noah Hellman",
title = "Approximate Floating-Point Operations with Integer
Units by Processing in the Logarithmic Domain",
crossref = "IEEE:2021:ISC",
pages = "45--52",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00019",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Held:2021:KRP,
author = "James P. Held and Th{\'e}o Mary",
title = "Keynote 1: Realizing the Promise of Quantum
Computing",
crossref = "IEEE:2021:ISC",
pages = "xvi--xvi",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00011",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@MastersThesis{Hellman:2021:MBA,
author = "Noah Hellman",
title = "{Mitchell}-Based Approximate Operations on
Floating-Point Numbers",
type = "{Master of Science Thesis in Electrical Engineering}",
school = "Department of Electrical Engineering, Link{\"o}ping
University",
address = "Link{\"o}ping, Sweden",
pages = "56",
day = "19",
month = jun,
year = "2021",
bibdate = "Wed Dec 20 07:05:10 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://liu.diva-portal.org/smash/get/diva2:1590166/FULLTEXT01.pdf;
http://liu.diva-portal.org/smash/record.jsf?pid=diva2%3A1590166&dswid=5128",
abstract = "By adapting Mitchell's algorithm for floating-point
numbers, one can efficiently perform arithmetic
floating-point operations in an approximate logarithmic
domain in order to perform approximate computations of
functions such as multiplication, division, square root
and others. This work examines how this algorithm can
be improved in terms of accuracy and hardware
complexity by applying a set of various methods that
are parametrized and offer a large design space.
Optimal coefficients for a large portion of this space
is determined and used to synthesize circuits for both
ASIC and FPGA circuits using the bfloat16 format.
Optimal configurations are then extracted to create an
optimal curve where one can select an acceptable error
range and obtain a circuit with a minimal hardware
cost.",
acknowledgement = ack-nhfb,
advisor = "Oscar Gustafsson",
remark = "See \cite{Mitchell:1962:CMD}.",
}
@Article{Ho:2021:GFD,
author = "Nhut-Minh Ho and Himeshi {De Silva} and Weng-Fai
Wong",
title = "{GRAM}: a Framework for Dynamically Mixing Precisions
in {GPU} Applications",
journal = j-TACO,
volume = "18",
number = "2",
pages = "19:1--19:24",
month = mar,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.1145/3441830",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Sat Mar 20 17:25:10 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
URL = "https://dl.acm.org/doi/10.1145/3441830",
abstract = "This article presents GRAM (GPU-based Runtime Adaption
for Mixed-precision) a framework for the effective use
of mixed precision arithmetic for CUDA programs. Our
method provides a fine-grain tradeoff between output
error and performance. It can create many variants that
satisfy different accuracy requirements by assigning
different groups of threads to different precision
levels adaptively at runtime. To widen the range of
applications that can benefit from its approximation,
GRAM comes with an optional half-precision approximate
math library. Using GRAM, we can trade off precision
for any performance improvement of up to 540\%,
depending on the application and accuracy
requirement.",
acknowledgement = ack-nhfb,
articleno = "19",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "https://dl.acm.org/loi/taco",
}
@InProceedings{Ho:2021:PAT,
author = "Nhut-Minh Ho and Duy-Thanh Nguyen and Himeshi {De
Silva} and John L. Gustafson and Weng-Fai Wong and Ik
Joon Chang",
editor = "{IEEE}",
booktitle = "{2021 Design, Automation \& Test in Europe Conference
\& Exhibition (DATE)}",
title = "Posit Arithmetic for the Training and Deployment of
Generative Adversarial Networks",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1350--1355",
year = "2021",
DOI = "https://doi.org/10.23919/DATE51398.2021.9473933",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hormigo:2021:FAB,
author = "Javier Hormigo and Gabriel Caffarena",
title = "{FPGA} acceleration of bit-true simulations for
word-length optimization",
crossref = "IEEE:2021:ISC",
pages = "119--122",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00033",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Hough:2021:ISO,
author = "David G. Hough",
title = "The {IEEE Standard 754}: One for the History Books",
journal = j-COMPUT-EDGE,
volume = "??",
number = "4",
pages = "42--46",
month = aug,
year = "2021",
DOI = "https://doi.org/10.1109/MC.2019.2926614",
ISSN = "2469-7087",
bibdate = "Thu Aug 19 14:23:25 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/ieee-computer.pdf;
https://www.computer.org/csdl/magazine/co/2019/12/08909942/1f8KFWxbTCU",
acknowledgement = ack-nhfb,
fjournal = "Computing Edge",
journal-URL = "http://www.computer.org/web/computingedge",
keywords = "Floating-point arithmetic; Hardware; History; IEEE
Standards; Microprocessors; Software",
remark = "Reprint of \cite{Hough:2019:ISO}.",
xxISSN = "2376-113X",
}
@Misc{Jain:2021:M,
author = "Riya Jain and Niraj Nayan Sharma",
title = "{Melodica}",
howpublished = "Web software.",
year = "2021",
bibdate = "Sat Dec 16 15:21:57 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://github.com/HPC-Lab-IITB/Melodica",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Jean:2021:PFN,
author = "Sandra Jean and Aneesh Raveendran and A. David
Selvakumar and Gagandeep Kaur and Shankar G Dharani and
Shashikala Gunderao Pattanshetty and Vivian
Desalphine",
editor = "{IEEE}",
booktitle = "{2021 34th International Conference on VLSI Design and
2021 20th International Conference on Embedded Systems
(VLSID)}",
title = "{P-FMA}: a Novel Parameterized Posit Fused
Multiply-Accumulate Arithmetic Processor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "282--287",
year = "2021",
DOI = "https://doi.org/10.1109/VLSID51830.2021.00053",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Joldes:2021:FA,
author = "Mioara Joldes and Fabrizio Lambert",
title = "Foreword {ARITH 2021}",
crossref = "IEEE:2021:ISC",
pages = "ix--x",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00005",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Joldes:2021:SSE,
author = "Mioara Joldes and Fabrizio Lamberti and Alberto
Nannarelli",
title = "Special Section on Emerging and Impacting Trends on
Computer Arithmetic",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "9",
number = "3",
pages = "1449--1450",
month = jul # "\slash " # sep,
year = "2021",
DOI = "https://doi.org/10.1109/TETC.2021.3096698",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Kant:2021:IPI,
author = "Manash Kant and Rajeev Thakur",
editor = "{IEEE}",
booktitle = "{2021 Fifth International Conference on I-SMAC (IoT in
Social, Mobile, Analytics and Cloud) (I-SMAC)}",
title = "Implementation and Performance Improvement of {POSIT}
Multiplier for Advance {DSP} Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1730--1736",
year = "2021",
DOI = "https://doi.org/10.1109/I-SMAC52330.2021.9640999",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kouya:2021:ALD,
author = "Tomonori Kouya",
title = "Acceleration of {$ L U $} decomposition supporting
double--double, triple--double, and quadruple--double
precision floating-point arithmetic with {AVX2}",
crossref = "IEEE:2021:ISC",
pages = "54--61",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00021",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Kulkarni:2021:PVS,
author = "Annarao Kulkarni and Shashikala Pattanshetty and
Aneesh Raveendran and David Selvakumar and Sandra Jean
and Vivian Desalphine",
editor = "{IEEE}",
booktitle = "{2021 34th International Conference on VLSI Design and
2021 20th International Conference on Embedded Systems
(VLSID)}",
title = "{PositGen} --- a Verification Suite for Posit
Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "204--209",
year = "2021",
DOI = "https://doi.org/10.1109/VLSID51830.2021.00040",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Lange:2021:CND,
author = "Marko Lange and Shin'ichi Oishi",
title = "Correction to: {A note on Dekker's FastTwoSum
algorithm}",
journal = j-NUM-MATH,
volume = "149",
number = "1",
pages = "227--228",
month = sep,
year = "2021",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-021-01213-8",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Wed Sep 15 05:50:42 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
note = "See \cite{Lange:2020:NDF}.",
URL = "http://link.springer.com/article/10.1007/s00211-021-01213-8;
https://link.springer.com/content/pdf/10.1007/s00211-021-01213-8.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Langroudi:2021:AAQ,
author = "Hamed F. Langroudi and Vedant Karia and Zachariah
Carmichael and Abdullah Zyarah and Tej Pandit and John
L. Gustafson and Dhireesha Kudithipudi",
editor = "{IEEE}",
booktitle = "{2021 IEEE/CVF Conference on Computer Vision and
Pattern Recognition Workshops (CVPRW)}",
title = "Alps: Adaptive Quantization of Deep Neural Networks
with {GeneraLized} {PositS}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3094--3103",
year = "2021",
DOI = "https://doi.org/10.1109/CVPRW53098.2021.00346",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Lemire:2021:NPG,
author = "Daniel Lemire",
title = "Number parsing at a gigabyte per second",
journal = j-SPE,
volume = "51",
number = "8",
pages = "1700--1727",
month = aug,
year = "2021",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.2984",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Fri Jul 23 09:04:36 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/go.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
note = "See improvement \cite{Mushtak:2023:FNP}.",
abstract = "With disks and networks providing gigabytes per
second, parsing decimal numbers from strings becomes a
bottleneck. We consider the problem of parsing decimal
numbers to the nearest binary floating-point value. The
general problem requires variable-precision arithmetic.
However, we need at most 17 digits to represent 64-bit
standard floating-point numbers (IEEE 754). Thus, we
can represent the decimal significand with a single
64-bit word. By combining the significand and
precomputed tables, we can compute the nearest
floating-point number using as few as one or two 64-bit
multiplications. Our implementation can be several
times faster than conventional functions present in
standard C libraries on modern 64-bit systems (Intel,
AMD, ARM, and POWER9). Our work is available as open
source software used by major systems such as Apache
Arrow and Yandex ClickHouse. The Go standard library
has adopted a version of our approach.",
acknowledgement = ack-nhfb,
ajournal = "Softw. Pract. Exp.",
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "11 May 2021",
}
@Article{Leon:2021:IPD,
author = "Vasileios Leon and Theodora Paparouni and Evangelos
Petrongonas and Dimitrios Soudris and Kiamal
Pekmestzi",
title = "Improving Power of {DSP} and {CNN} Hardware
Accelerators Using Approximate Floating-point
Multipliers",
journal = j-TECS,
volume = "20",
number = "5",
pages = "39:1--39:21",
month = jul,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.1145/3448980",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Tue Aug 10 13:35:00 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
URL = "https://dl.acm.org/doi/10.1145/3448980",
abstract = "Approximate computing has emerged as a promising
design alternative for delivering power-efficient
systems and circuits by exploiting the inherent error
resiliency of numerous applications. The current
article aims to tackle the increased hardware cost of
floating-point multiplication units, which prohibits
their usage in embedded computing. We introduce AFMU
(Approximate Floating-point MUltiplier), an
area/power-efficient family of multipliers, which apply
two approximation techniques in the resource-hungry
mantissa multiplication and can be seamlessly extended
to support dynamic configuration of the approximation
levels via gating signals. AFMU offers large accuracy
configuration margins, provides negligible logic
overhead for dynamic configuration, and detects
unexpected results that may arise due to the
approximations. Our evaluation shows that AFMU delivers
energy gains in the range 3.6\%--53.5\% for
half-precision and 37.2\%--82.4\% for single-precision,
in exchange for mean relative error around
0.05\%--3.33\% and 0.01\%--2.20\%, respectively. In
comparison with state-of-the-art multipliers, AFMU
exhibits up to 4--6 $ \times $ smaller error on average
while delivering more energy-efficient computing. The
evaluation in image processing shows that AFMU provides
sufficient quality of service, i.e., more than 50db
PSNR and near 1 SSIM values, and up to 57.4\% power
reduction. When used in floating-point CNNs, the
accuracy loss is small (or zero), i.e., up to 5.4\% for
MNIST and CIFAR-10, in exchange for up to 63.8\% power
gain.",
acknowledgement = ack-nhfb,
articleno = "39",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "https://dl.acm.org/loi/tecs",
}
@InProceedings{Lim:2021:HPC,
author = "Jay P. Lim and Santosh Nagarakatte",
editor = "Stephen N. Freund and Eran Yahav",
booktitle = "{PLDI '21: Proceedings of the 42nd ACM SIGPLAN
International Conference on Programming Language Design
and Implementation, June 20--25, 2021 [virtual
meeting]}",
title = "High performance correctly rounded math libraries for
32-bit floating point representations",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
month = jun,
year = "2021",
DOI = "978-1-4503-8391-2",
DOI = "https://doi.org/10.1145/3453483.3454049",
bibdate = "Thu Sep 19 15:15:02 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Liu:2021:DAM,
author = "Weiqiang Liu and Tingting Zhang and Emma McLarnon and
Maire O'Neill and Paolo Montuschi and Fabrizio
Lombardi",
title = "Design and Analysis of Majority Logic-Based
Approximate Adders and Multipliers",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "9",
number = "3",
pages = "1609--1624",
month = jul # "\slash " # sep,
year = "2021",
DOI = "https://doi.org/10.1109/TETC.2019.2929100",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Lu:2021:EDN,
author = "Jinming Lu and Chao Fang and Mingyang Xu and Jun Lin
and Zhongfeng Wang",
title = "Evaluations on Deep Neural Networks Training Using
Posit Number System",
journal = j-IEEE-TRANS-COMPUT,
volume = "70",
number = "2",
pages = "174--187",
year = "2021",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2020.2985971",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Mary:2021:KOM,
author = "Th{\'e}o Mary",
title = "Keynote 2: Opportunities for Mixed Precision
Arithmetic in Numerical Linear Algebra",
crossref = "IEEE:2021:ISC",
pages = "xvii--xvii",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00011",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Matos:2021:EFP,
author = "Jos{\'e} A. O. Matos and Paulo B. Vasconcelos",
title = "Effectiveness of Floating-Point Precision on the
Numerical Approximation by Spectral Methods",
journal = j-MATH-COMPUT-APPL,
volume = "26",
number = "2",
pages = "42--??",
month = jun,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.3390/mca26020042",
ISSN = "2297-8747",
ISSN-L = "2297-8747",
bibdate = "Sun Feb 18 06:28:40 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
URL = "https://www.mdpi.com/2297-8747/26/2/42",
acknowledgement = ack-nhfb,
fjournal = "Mathematical and Computational Applications",
journal-URL = "https://www.mdpi.com/journal/mca",
}
@TechReport{MPFR:2021:MLA,
author = "{The MPFR Team}",
title = "The {MPFR} Library: Algorithms and Proofs",
type = "Report",
institution = "????",
address = "????",
pages = "69",
day = "5",
month = nov,
year = "2021",
bibdate = "Tue Mar 14 13:13:13 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.mpfr.org/algorithms.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Muller:2021:X,
author = "Jean-Michel Muller",
title = "$ a \cdot (x \cdot \ x) $ or $ (a \cdot x) \cdot x?
$",
crossref = "IEEE:2021:ISC",
pages = "17--24",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00015",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Expressions such as $ a x^2 $, $ a x y $, or $ a x^3
$, where $a$ is a constant, are not infrequent in
computing. There are several ways of parenthesizing
them (and therefore, choosing the order of evaluation).
Depending on the value of $a$, is there a more accurate
evaluation order? We discuss this point (with a small
digression on spurious underflows and overflows).",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Muntean:2021:IIR,
author = "Paul Muntean and Martin Monperrus and Hao Sun and Jens
Grossklags and Claudia Eckert",
title = "{IntRepair}: Informed Repairing of Integer Overflows",
journal = j-IEEE-TRANS-SOFTW-ENG,
volume = "47",
number = "10",
pages = "2225--2241",
month = oct,
year = "2021",
CODEN = "IESEDJ",
DOI = "https://doi.org/10.1109/TSE.2019.2946148",
ISSN = "0098-5589 (print), 1939-3520 (electronic)",
ISSN-L = "0098-5589",
bibdate = "Thu Oct 21 10:49:15 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranssoftweng2020.bib",
abstract = "Integer overflows have threatened software
applications for decades. Thus, in this paper, we
propose a novel technique to provide automatic repairs
of integer overflows in C source code. Our technique,
based on static symbolic execution, fuses detection ,
repair generation and validation. This technique is
implemented in a prototype named IntRepair. We applied
IntRepair to 2,052 C programs (approx. 1 million lines
of code) contained in SAMATE's Juliet test suite and 50
synthesized programs that range up to 20 KLOC. Our
experimental results show that IntRepair is able to
effectively detect integer overflows and successfully
repair them, while only increasing the source code
(LOC) and binary (Kb) size by around 1 percent,
respectively. Further, we present the results of a user
study with 30 participants which shows that IntRepair
repairs are more than 10x efficient as compared to
manually generated code repairs.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Software Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
keywords = "integer overflow detection and repair",
}
@InProceedings{Murillo:2021:EEM,
author = "Raul Murillo and David Mallasen and Alberto A. {Del
Barrio} and Guillermo Botella",
editor = "{IEEE}",
booktitle = "{2021 IEEE 39th International Conference on Computer
Design (ICCD): 24--27 October 2021, Storrs, CT, USA}",
title = "Energy-Efficient {MAC} Units for Fused Posit
Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "138--145",
month = oct,
year = "2021",
DOI = "https://doi.org/10.1109/iccd53106.2021.00032",
bibdate = "Thu Dec 14 18:10:59 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Nambi:2021:EDE,
author = "Suresh Nambi and Salim Ullah and Siva Satyendra Sahoo
and Aditya Lohana and Farhad Merchant and Akash Kumar",
title = "{ExPAN(N)D}: Exploring Posits for Efficient Artificial
Neural Network Design in {FPGA}-Based Systems",
journal = j-IEEE-ACCESS,
volume = "9",
pages = "103691--103708",
year = "2021",
DOI = "https://doi.org/10.1109/ACCESS.2021.3098730",
ISSN = "2169-3536",
ISSN-L = "2169-3536",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Access",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}
@InProceedings{Nannarelli:2021:OCA,
author = "Alberto Nannarelli and Mioara Joldes and Fabrizio
Lamberti and Flemming Stassen and Daniele Jahier
Pagliari and Alberto Cannav{\`o}",
title = "Organizing Committee {ARITH 2021}",
crossref = "IEEE:2021:ISC",
pages = "xi--xi",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00006",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Norris:2021:AIP,
author = "Cameron James Norris and Sunwoong Kim",
editor = "{IEEE}",
booktitle = "{2021 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "An Approximate and Iterative Posit Multiplier
Architecture for {FPGAs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2021",
DOI = "https://doi.org/10.1109/ISCAS51556.2021.9401158",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Parrot:2021:POU,
author = "R{\'e}mi Parrot and Mika{\"e}l Briday and Olivier H.
Roux",
title = "Pipeline Optimization using a Cost Extension of Timed
Petri Nets",
crossref = "IEEE:2021:ISC",
pages = "37--44",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00018",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Patankar:2021:RBC,
author = "Udayan S. Patankar and Ants Koel",
title = "Review of Basic Classes of Dividers Based on Division
Algorithm",
journal = j-IEEE-ACCESS,
volume = "9",
pages = "23035--23069",
year = "2021",
DOI = "https://doi.org/10.1109/access.2021.3055735",
ISSN = "2169-3536",
ISSN-L = "2169-3536",
bibdate = "Thu Apr 10 15:08:12 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Access",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}
@Article{Plantard:2021:EWSa,
author = "Thomas Plantard",
title = "Efficient Word Size Modular Arithmetic",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "9",
number = "3",
pages = "1506--1518",
month = jul # "\slash " # sep,
year = "2021",
DOI = "https://doi.org/10.1109/TETC.2021.3073475",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
note = "See \cite{Plantard:2021:EWSb}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
keywords = "ARITH-28",
}
@InProceedings{Plantard:2021:EWSb,
author = "Thomas Plantard",
title = "Efficient Word Size Modular Arithmetic",
crossref = "IEEE:2021:ISC",
pages = "139--139",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00036",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Plantard:2021:EWSa}.",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
remark = "Published in IEEE Transactions on Emerging Topics in
Computing, Volume: 9, Issue: 3, July--September 2021,
and orally presented at ARITH 2021.",
}
@InProceedings{Rao:2021:PND,
author = "Dhage Navaneet Rao and Ganne Sai Charan and Degala
Veera Venkata Sairam and Kamatchi S.",
booktitle = "{2021 International Conference on Advances in
Electrical, Computing, Communication and Sustainable
Technologies (ICAECT)}",
title = "Posit Number Division using {Newton--Raphson} method",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
month = feb,
year = "2021",
DOI = "https://doi.org/10.1109/icaect49130.2021.9392582",
bibdate = "Fri Dec 15 06:57:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Raposo:2021:PTD,
author = "Gon{\c{c}}alo Raposo and Pedro Tom{\'a}s and Nuno
Roma",
editor = "{IEEE}",
booktitle = "{ICASSP 2021 - 2021 IEEE International Conference on
Acoustics, Speech and Signal Processing (ICASSP)}",
title = "Positnn: Training Deep Neural Networks with Mixed
Low-Precision Posit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "7908--7912",
year = "2021",
DOI = "https://doi.org/10.1109/ICASSP39728.2021.9413919",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Reichenbach:2021:RVR,
author = "Marc Reichenbach and Johannes Kn{\"o}dtel and
Sebastian Rachuj and Dietmar Fey",
title = "{RISC-V3}: a {RISC-V} Compatible {CPU} With a Data
Path Based on Redundant Number Systems",
journal = j-IEEE-ACCESS,
volume = "9",
number = "",
pages = "43684--43700",
year = "2021",
DOI = "https://doi.org/10.1109/ACCESS.2021.3063238",
ISSN = "2169-3536",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Access",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}
@InProceedings{Revy:2021:AIF,
author = "Guillaume Revy",
title = "Analyzing the impact of floating-point precision
adaptation in iterative programs",
crossref = "IEEE:2021:ISC",
pages = "25--32",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00016",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Book{Rodriguez:2021:DLS,
author = "Andres Rodriguez",
title = "Deep Learning Systems: Algorithms, Compilers, and
Processors for Large-Scale Production",
publisher = pub-SV,
address = pub-SV:adr,
year = "2021",
DOI = "https://doi.org/10.1007/978-3-031-01769-8",
ISBN = "3-031-01769-2",
ISBN-13 = "978-3-031-01769-8",
ISSN = "1935-3243",
ISSN-L = "1935-3235",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Synthesis Lectures on Computer Architecture",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Romanov:2021:APB,
author = "Aleksandr Yu. Romanov and Alexander L. Stempkovsky and
Ilia V. Lariushkin and Georgy E. Novoselov and Roman A.
Solovyev and Vladimir A. Starykh and Irina I. Romanova
and Dmitry V. Telpukhov and Ilya A. Mkrtchan",
title = "Analysis of Posit and {Bfloat} Arithmetic of Real
Numbers for Machine Learning",
journal = j-IEEE-ACCESS,
volume = "9",
pages = "82318--82324",
year = "2021",
DOI = "https://doi.org/10.1109/ACCESS.2021.3086669",
ISSN = "2169-3536",
ISSN-L = "2169-3536",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Access",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}
@InProceedings{Saiki:2021:CPT,
author = "Brett Saiki and Oliver Flatt and Chandrakana Nandi and
Pavel Panchekha and Zachary Tatlock",
title = "Combining Precision Tuning and Rewriting",
crossref = "IEEE:2021:ISC",
pages = "1--8",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00013",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@InProceedings{Saxena:2021:BOF,
author = "Vinay Saxena and Ankitha Reddy and Jonathan Neudorfer
and John Gustafson and Sangeeth Nambiar and Rainer
Leupers and Farhad Merchant",
editor = "{IEEE}",
booktitle = "{2021 22nd International Symposium on Quality
Electronic Design (ISQED)}",
title = "Brightening the Optical Flow through Posit
Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "463--468",
year = "2021",
DOI = "https://doi.org/10.1109/ISQED51717.2021.9424360",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Shah:2021:PWS,
author = "Nimish Shah and Laura Isabel Galindez Olascoaga and
Shirui Zhao and Wannes Meert and Marian Verhelst",
editor = "{IEEE}",
booktitle = "{2021 IEEE International Solid-State Circuits
Conference (ISSCC)}",
title = "{9.4 PIU}: a {248GOPS/W} Stream-Based Processor for
Irregular Probabilistic Inference Networks Using
Precision-Scalable Posit Arithmetic in 28nm",
volume = "64",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "150--152",
year = "2021",
DOI = "https://doi.org/10.1109/ISSCC42613.2021.9366061",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Shekhawat:2021:HGP,
author = "Diksha Shekhawat and Apoorva Jangir and Jai Gopal
Pandey",
editor = "{IEEE}",
booktitle = "{2021 25th International Symposium on VLSI Design and
Test (VDAT)}",
title = "A Hardware Generator for Posit Arithmetic and its
{FPGA} Prototyping",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2021",
DOI = "https://doi.org/10.1109/VDAT53777.2021.9601025",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{SmallPositHDL:2021:CBS,
author = "{SmallPositHDL}",
title = "Chisel-based {SmallPositHDL}",
howpublished = "Web software",
year = "2021",
bibdate = "Sat Dec 16 15:23:17 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://github.com/starbrilliance/SmallPositHDL",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Sohier:2021:CIS,
author = "Devan Sohier and Pablo {De Oliveira Castro} and
Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re
and Eric Petit and Olivier Jamond",
title = "Confidence Intervals for Stochastic Arithmetic",
journal = j-TOMS,
volume = "47",
number = "2",
pages = "10:1--10:33",
month = apr,
year = "2021",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3432184",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Apr 27 08:23:28 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3432184",
abstract = "Quantifying errors and losses due to the use of
Floating-point (FP) calculations in industrial
scientific computing codes is an important part of the
Verification, Validation, and Uncertainty
Quantification process. Stochastic Arithmetic is one
way to model and estimate FP losses of accuracy, which
scales well to large, industrial codes. It exists in
different flavors, such as CESTAC or MCA, implemented
in various tools such as CADNA, Verificarlo, or Verrou.
These methodologies and tools are based on the idea
that FP losses of accuracy can be modeled via
randomness. Therefore, they share the same need to
perform a statistical analysis of programs results to
estimate the significance of the results.\par
In this article, we propose a framework to perform a
solid statistical analysis of Stochastic Arithmetic.
This framework unifies all existing definitions of the
number of significant digits (CESTAC and MCA), and also
proposes a new quantity of interest: the number of
digits contributing to the accuracy of the results.
Sound confidence intervals are provided for all
estimators, both in the case of normally distributed
results, and in the general case. The use of this
framework is demonstrated by two case studies of
industrial codes: Europlexus and code\aster.",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Soylu:2021:IAC,
author = "G{\"u}ltekin Soylu",
title = "Improved Arithmetic of Complex Fans",
journal = j-TOMS,
volume = "47",
number = "2",
pages = "11:1--11:10",
month = apr,
year = "2021",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3434400",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Apr 27 08:23:28 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3434400",
abstract = "Complex fans are sets of complex numbers whose
magnitudes and angles range in closed intervals. The
fact that the sum of two fans is a disordered shape
gives rise to the need for computational methods to
find the minimal enclosing fan. Cases where the sum of
two fans contains the origin of the complex plane as a
boundary point are of special interest. The result of
the addition is then enclosed by circles in current
methods, but under certain circumstances this turns out
to be an overestimate. The focus of this article is the
diagnosis and treatment of such cases.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Thapliyal:2021:QCD,
author = "Himanshu Thapliyal and Edgard Mu{\~n}oz-Coreas and T.
S. S. Varun and Travis S. Humble",
title = "Quantum Circuit Designs of Integer Division Optimizing
{T}-count and {T}-depth",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "9",
number = "2",
pages = "1045--1056",
month = apr # "\slash " # jun,
year = "2021",
DOI = "https://doi.org/10.1109/TETC.2019.2910870",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Tiwari:2021:PCP,
author = "Sugandha Tiwari and Neel Gala and Chester Rebeiro and
V. Kamakoti",
title = "{PERI}: a Configurable Posit Enabled {RISC-V} Core",
journal = j-TACO,
volume = "18",
number = "3",
pages = "25:1--25:26",
month = jun,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.1145/3446210",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Tue Jun 29 08:21:11 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
URL = "https://dl.acm.org/doi/10.1145/3446210",
abstract = "Owing to the failure of Dennard's scaling, the past
decade has seen a steep growth of prominent new
paradigms leveraging opportunities in computer
architecture. Two technologies of interest are Posit
and RISC-V. Posit was introduced in mid-2017 as a
\ldots{}",
acknowledgement = ack-nhfb,
articleno = "25",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "https://dl.acm.org/loi/taco",
}
@Article{Ullah:2021:AOA,
author = "S. Ullah and H. Schmidl and S. S. Sahoo and S. Rehman
and A. Kumar",
title = "Area-Optimized Accurate and Approximate Softcore
Signed Multiplier Architectures",
journal = j-IEEE-TRANS-COMPUT,
volume = "70",
number = "3",
pages = "384--392",
year = "2021",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2020.2988404",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Tue Feb 23 12:51:19 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{VanZee:2021:SMD,
author = "Field G. {Van Zee} and Devangi N. Parikh and Robert A.
{Van De Geijn}",
title = "Supporting Mixed-domain Mixed-precision Matrix
Multiplication within the {BLIS} Framework",
journal = j-TOMS,
volume = "47",
number = "2",
pages = "12:1--12:26",
month = apr,
year = "2021",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3402225",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Apr 27 08:23:28 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3402225",
abstract = "We approach the problem of implementing mixed-datatype
support within the general matrix multiplication (gemm)
operation of the BLAS-like Library Instantiation
Software framework, whereby each matrix operand A, B,
and C may be stored as single- or double-precision real
or complex values. Another factor of complexity,
whereby the matrix product and accumulation are allowed
to take place in a precision different from the storage
precisions of either A or B, is also discussed. We
first break the problem into orthogonal dimensions,
considering the mixing of domains separately from
mixing precisions. Support for all combinations of
matrix operands stored in either the real or complex
domain is mapped out by enumerating the cases and
describing an implementation approach for each.
Supporting all combinations of storage and computation
precisions is handled by typecasting the matrices at
key stages of the computation --- during packing and/or
accumulation, as needed. Several optional optimizations
are also documented. Performance results gathered on a
56-core Marvell ThunderX2 and a 52-core Intel Xeon
Platinum demonstrate that high performance is mostly
preserved, with modest slowdowns incurred from
unavoidable typecast instructions. The mixed-datatype
implementation confirms that combinatorial
intractability is avoided, with the framework relying
on only two assembly microkernels to implement 128
datatype combinations.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Vestias:2021:DMF,
author = "M{\'a}rio P. V{\'e}stias and Hor{\'a}cio C. Neto",
title = "Decimal Multiplication in {FPGA} with a Novel Decimal
Adder\slash Subtractor",
journal = j-ALGORITHMS-BASEL,
volume = "14",
number = "7",
month = jul,
year = "2021",
CODEN = "ALGOCH",
DOI = "https://doi.org/10.3390/a14070198",
ISSN = "1999-4893 (electronic)",
ISSN-L = "1999-4893",
bibdate = "Fri Jul 23 15:05:28 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.mdpi.com/1999-4893/14/7/198",
acknowledgement = ack-nhfb,
articleno = "198",
fjournal = "Algorithms (Basel)",
journal-URL = "https://www.mdpi.com/journal/algorithms",
pagecount = "??",
}
@Article{Walczyk:2021:IAF,
author = "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
Cie{\'s}li{\'n}ski",
title = "Improving the Accuracy of the Fast Inverse Square Root
by Modifying {Newton--Raphson} Corrections",
journal = j-ENTROPY,
volume = "23",
number = "1",
pages = "86:1--86:20",
month = jan,
year = "2021",
CODEN = "ENTRFG",
DOI = "https://doi.org/10.3390/e23010086",
ISSN = "1099-4300",
ISSN-L = "1099-4300",
bibdate = "Wed Dec 20 07:52:39 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Entropy",
journal-URL = "https://www.mdpi.com/journal/entropy/",
}
@InProceedings{Wang:2021:LLP,
author = "Yang Wang and Dazheng Deng and Leibo Liu and Shaojun
Wei and Shouyi Yin",
editor = "{IEEE}",
booktitle = "{2021 IEEE 3rd International Conference on Artificial
Intelligence Circuits and Systems (AICAS)}",
title = "{LPE}: Logarithm Posit Processing Element for
Energy-Efficient Edge-Device Training",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--4",
year = "2021",
DOI = "https://doi.org/10.1109/AICAS51828.2021.9458421",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{Ward-Foxton:2021:BBT,
author = "Sally Ward-Foxton",
title = "Bringing 8-Bit Training Breakthroughs to {AI}
Hardware",
howpublished = "EET Asia Web site",
day = "2",
month = mar,
year = "2021",
bibdate = "Wed May 19 12:05:25 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.eetasia.com/bringing-8-bit-training-breakthroughs-to-ai-hardware/",
acknowledgement = ack-nhfb,
keywords = "FP8",
}
@InProceedings{Wu:2021:DCH,
author = "Chai Wah Wu",
title = "Dither computing: a hybrid deterministic-stochastic
computing framework",
crossref = "IEEE:2021:ISC",
pages = "70--77",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021.00025",
bibdate = "Thu Sep 21 10:36:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
}
@Article{Xia:2021:EDA,
author = "Yuanyuan Xia and Shaozhong Guo and Jinchen Xu",
title = "Error detection of arithmetic expressions",
journal = j-J-SUPERCOMPUTING,
volume = "77",
number = "6",
pages = "5492--5509",
month = jun,
year = "2021",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-020-03469-7",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Fri May 14 09:20:01 MDT 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-020-03469-7",
abstract = "Inspecting floating-point errors is essential to
floating-point operations. In this paper, we present
floating-point error detector (FPED), an inspector of
floating-point errors for arithmetic expressions. FPED
can pick a suitable benchmark generation approach by
analyzing the distribution of the expression of a
floating-point operation, thereby minimizing the
possibilities of underreporting floating-point errors.
FPED is also able to determine the significant sources
of errors in a floating-point operation according to
the frequencies of computation building blocks that
contribute most to the floating-point errors,
benefiting the follow-up optimizations of computation
accuracies. We validate the correctness and
functionalities of FPED by conducting experiments on
the FPBench benchmark suite. The experimental results
demonstrate that FPED can obtain more accurate
detection results than the random detecting approach
with respect to floating-point error detection. We also
compare FPED with the existing dynamic error detection
tools. The experimental results show that in most of
the 33 test benchmarks, the maximum error results of
FPED are greater than Herbgrind and the detection
performance is higher than Herbgrind.",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
online-date = "Published: 09 November 2020 Pages: 5492--5509",
}
@Article{Zaruba:2021:MCR,
author = "Florian Zaruba and Fabian Schuiki and Luca Benini",
title = "{Manticore}: A 4096-Core {RISC-V} Chiplet Architecture
for Ultraefficient Floating-Point Computing",
journal = j-IEEE-MICRO,
volume = "41",
number = "2",
pages = "36--42",
month = mar # "\slash " # apr,
year = "2021",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2020.3045564",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hot-chips.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
}
@Article{Zaruba:2021:STP,
author = "Florian Zaruba and Fabian Schuiki and Torsten Hoefler
and Luca Benini",
title = "{Snitch}: A Tiny Pseudo Dual-Issue Processor for Area
and Energy Efficient Execution of Floating-Point
Intensive Workloads",
journal = j-IEEE-TRANS-COMPUT,
volume = "70",
number = "11",
pages = "1845--1860",
month = nov,
year = "2021",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2020.3027900",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Oct 14 10:04:00 2021",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Zhang:2021:EMP,
author = "Hao Zhang and Seok-Bum Ko",
editor = "{IEEE}",
booktitle = "{2021 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "Efficient Multiple-Precision Posit Multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2021",
DOI = "https://doi.org/10.1109/ISCAS51556.2021.9401213",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Zhu:2021:PBP,
author = "Yongwen Zhu",
title = "The Plum-Blossom Product Method of Large Digit
Multiplication and Its Application to Computer
Science",
journal = j-INT-J-COMP-APPL,
volume = "183",
number = "??",
pages = "17--23",
month = dec,
year = "2021",
CODEN = "????",
DOI = "https://doi.org/10.5120/ijca2021921805",
ISSN = "0975-8887",
ISSN-L = "0975-8887",
bibdate = "Fri Jan 24 09:46:40 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
URL = "https://www.ijcaonline.org/archives/volume183/number41/32202-2021921805/",
acknowledgement = ack-nhfb,
ajournal = "Intern. J. of Computer Applications",
articleno = "41",
fjournal = "International Journal of Computer Applications",
journal-URL = "https://www.ijcaonline.org/",
}
@Article{Ziols:2021:HPB,
author = "Ryan Ziols and Kathryn L. Kirchgasler",
title = "Health and pathology: a brief history of the
biopolitics of {US} mathematics education",
journal = j-EDUC-STUD-MATH,
volume = "108",
number = "1--2",
publisher = pub-SV,
address = pub-SV:adr,
pages = "123--142",
month = oct,
year = "2021",
CODEN = "EDSMAN",
DOI = "https://doi.org/10.1007/s10649-021-10110-8",
ISSN = "1573-0816",
ISSN-L = "0013-1954",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Educational Studies in Mathematics",
journal-URL = "http://link.springer.com/journal/10649",
keywords = "posit arithmetic",
}
@Article{Zlatopolski:2021:MES,
author = "Dmitry M. Zlatopolski",
title = "Method for extracting square and cubic roots in the
binary number system. ({Russian})",
journal = "Inform. School",
volume = "1",
number = "??",
pages = "42--45",
month = "????",
year = "2021",
DOI = "https://doi.org/10.32517/2221-1993-2021-1-42-45",
bibdate = "Fri Mar 17 09:03:18 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "Russian",
remark = "DOI does not resolve; cited as final reference in
\cite{Zlatopolski:2023:PAV}.",
}
@Article{Ahmadinejad:2022:EQE,
author = "Mohammad Ahmadinejad and Mohammad Hossein Moaiyeri",
title = "Energy- and Quality-Efficient Approximate Multipliers
for Neural Network and Image Processing Applications",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "2",
pages = "1105--1116",
month = apr # "\slash " # jun,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2021.3072666",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
abstract = "Approximate computing is a new trend that trades off
computational accuracy for lower energy dissipation and
design complexity in various applications, where high
precision is not a critical need. In this paper,
energy- and quality- efficient approximate multipliers
based on new approximate compressors are proposed. We
use NAND gates for generating the complemented partial
products, which reduces the number of transistors.
Furthermore, new approximate compressors with different
accuracy and performance characteristics are designed.
Accordingly, three hybrid approximate multipliers
offering different trade-offs between accuracy and
hardware efficiency are proposed. The proposed designs
are simulated using HSPICE with the 7nm FinFET model as
a modern technology. Furthermore, the efficacies of the
approximate multipliers in the neural network and image
processing applications are evaluated using MATLAB.
According to the results, the proposed designs provide
far better compromises between the quality and energy
metrics in comparison with the previous designs and can
be considered as efficient alternatives for the exact
multipliers in neural network and image processing
applications.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Ahmadpour:2022:BMM,
author = "Zabihollah Ahmadpour and Ghassem Jaberipur",
title = "Up to $ 8 k $-bit Modular {Montgomery} Multiplication
in Residue Number Systems With Fast 16-bit Residue
Channels",
journal = j-IEEE-TRANS-COMPUT,
volume = "71",
number = "6",
pages = "1399--1410",
month = jun,
year = "2022",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2021.3086071",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed May 25 09:41:19 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Alder:2022:FPU,
author = "Fritz Alder and Jo {Van Bulck} and Jesse Spielman and
David Oswald and Frank Piessens",
title = "Faulty Point Unit: {ABI} Poisoning Attacks on Trusted
Execution Environments",
journal = j-DTRAP,
volume = "3",
number = "2",
pages = "13:1--13:26",
month = jun,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1145/3491264",
ISSN = "2692-1626 (print), 2576-5337 (electronic)",
ISSN-L = "2576-5337",
bibdate = "Sat Jul 30 07:34:14 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/dtrap.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/doi/10.1145/3491264",
abstract = "This article analyzes a previously overlooked attack
surface that allows unprivileged adversaries to impact
floating-point computations in enclaves through the
Application Binary Interface (ABI). In a comprehensive
study across 7 industry-standard and esearch enclave
shielding runtimes for Intel Software Guard Extensions
(SGX), we show that control and state registers of the
x87 Floating-Point Unit (FPU) and Intel Streaming SIMD
Extensions are not always properly sanitized on enclave
entry. We furthermore show that this attack goes beyond
the x86 architecture and can also affect RISC-V
enclaves. Focusing on SGX, we abuse the adversary's
control over precision and rounding modes as an ABI
fault injection primitive to corrupt enclaved
floating-point operations. Our analysis reveals that
this is especially relevant for applications that use
the older x87 FPU, which is still under certain
conditions used by modern compilers. We exemplify the
potential impact of ABI quality-degradation attacks for
enclaved machine learning and for the SPEC benchmarks.
We then explore the impact on confidentiality, showing
that control over exception masks can be abused as a
controlled channel to recover enclaved multiplication
operands. Our findings, affecting 5 of 7 studied SGX
runtimes and one RISC-V runtime, demonstrate the
challenges of implementing high-assurance trusted
execution across computing architectures.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "Digital Threats: Research and Practice (DTRAP)",
journal-URL = "https://dl.acm.org/loi/dtrap",
}
@Misc{AMD:2022:AIM,
author = "{AMD Corporation}",
title = "{``AMD Instinct MI200''} Instruction Set Architecture
Reference Guide",
howpublished = "Web document",
pages = "viii + 267",
day = "4",
month = feb,
year = "2022",
bibdate = "Fri Dec 01 14:05:58 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.amd.com/content/dam/amd/en/documents/instinct-tech-docs/instruction-set-architectures/instinct-mi200-cdna2-instruction-set-architecture.pdf",
acknowledgement = ack-nhfb,
remark = "This document describes the AMD GPUs in the
``Instinct'' product line, which replaces the earlier
FirePro and Radeon products. The new CPUs support 8-,
16-, 32-, and 64-bit signed and unsigned integers, the
binary32 and binary64 IEEE 754 floating-point formats,
and the BF16 (Bfloat16) 16-bit floating-point values.
However, it appears that fused multiply-add is only
supported in the vector instruction set.",
}
@InProceedings{Anonymous:2022:AI,
author = "Anonymous",
title = "Author Index",
crossref = "IEEE:2022:ISC",
pages = "133--134",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00033",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Anonymous:2022:C,
author = "Anonymous",
title = "Copyright",
crossref = "IEEE:2022:ISC",
pages = "1--1",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00003",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Anonymous:2022:PCA,
author = "Anonymous",
title = "Program Committee: {ARITH 2022}",
crossref = "IEEE:2022:ISC",
pages = "ix--ix",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00007",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Anonymous:2022:SA,
author = "Anonymous",
title = "Sponsors: {ARITH 2022}",
crossref = "IEEE:2022:ISC",
pages = "xi--xi",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00009",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Anonymous:2022:SCA,
author = "Anonymous",
title = "Steering Committee: {ARITH 2022}",
crossref = "IEEE:2022:ISC",
pages = "x--x",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00008",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Anonymous:2022:TC,
author = "Anonymous",
title = "Table of Contents",
crossref = "IEEE:2022:ISC",
pages = "iv--vi",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00004",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Anonymous:2022:TP,
author = "Anonymous",
title = "Title Page {I}",
crossref = "IEEE:2022:ISC",
pages = "1--1",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00001",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Anonymous:2022:TPI,
author = "Anonymous",
title = "Title Page {III}",
crossref = "IEEE:2022:ISC",
pages = "1--1",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00002",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Aoki:2022:EWS,
author = "Daichi Aoki and Kazuhiko Minematsu and Toshihiko
Okamura and Tsuyoshi Takagi",
title = "Efficient Word Size Modular Multiplication over Signed
Integers",
crossref = "IEEE:2022:ISC",
pages = "94--101",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00026",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Arnold:2022:TQL,
author = "Mark G. Arnold",
title = "Towards Quantum Logarithm Number Systems",
crossref = "IEEE:2022:ISC",
pages = "76--83",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00022",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Bajard:2022:GVL,
author = "Jean-Claude Bajard and Kazuhide Fukushima and Thomas
Plantard and Arnaud Sipasseuth",
title = "Generating Very Large {RNS} Bases",
crossref = "IEEE:2022:ISC",
pages = "102--102",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00027",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29; Residue Number System (RNS)",
}
@InProceedings{Barthel:2022:TIO,
author = "Moritz B{\"a}rthel and Nils H{\"u}lsmeier and Jochen
Rust and Steffen Paul",
title = "On the Implementation of Edge Detection Algorithms
with {SORN} Arithmetic",
crossref = "Gustafson:2022:NGA",
pages = "1--13",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9_1",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic; Sets-Of-Real-Numbers (SORN)
arithmetic",
}
@InProceedings{Benmouhoub:2022:ESA,
author = "Farah Benmouhoub and Pierre-Loic Garoche and Matthieu
Martel",
booktitle = "Software Verification: {13th International Conference,
VSTTE 2021, New Haven, CT, USA, October 18--19, 2021,
and 14th International Workshop, NSV 2021, Los Angeles,
CA, USA, July 18--19, 2021}",
title = "An Efficient Summation Algorithm for the Accuracy,
Convergence and Reproducibility of Parallel Numerical
Methods",
publisher = pub-SV,
address = pub-SV:adr,
pages = "165--181",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-030-95561-8_10",
ISBN = "3-030-95561-3",
ISBN-13 = "978-3-030-95561-8",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Dec 9 08:51:02 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Nowadays, parallel computing is ubiquitous in several
application fields, both in engineering and science.
The computations rely on the floating-point arithmetic
specified by the IEEE 754 Standard. In this context, an
elementary brick of computation, used everywhere, is
the sum of a sequence of numbers. This sum is subject
to many numerical errors in floating-point arithmetic.
To alleviate this issue, we have introduced a new
parallel algorithm for summing a sequence of
floating-point numbers. This algorithm which scales up
easily with the number of processors, adds numbers of
the same exponents first. In this article, our main
contribution is an extensive analysis of its efficiency
with respect to several properties: accuracy,
convergence and reproducibility. In order to show the
usefulness of our algorithm, we have chosen a set of
representative numerical methods which are Simpson,
Jacobi, LU factorization and the Iterated power
method.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation; floating-point
arithmetic",
}
@InProceedings{BenSalem-Knapp:2022:BRE,
author = "Louise {Ben Salem-Knapp} and Sylvie Boldo and William
Weens",
title = "Bounding the Round-Off Error of the Upwind Scheme for
Advection",
crossref = "IEEE:2022:ISC",
pages = "127--127",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00031",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Bertaccini:2022:MNE,
author = "Luca Bertaccini and Gianna Paulin and Tim Fischer and
Stefan Mach and Luca Benini",
title = "{MiniFloat-NN} and {ExSdotp}: an {ISA} Extension and a
Modular Open Hardware Unit for Low-Precision Training
on {RISC-V} Cores",
crossref = "IEEE:2022:ISC",
pages = "1--8",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00010",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Borges:2022:HLA,
author = "Carlos F. Borges and Claude-Pierre Jeannerod and
Jean-Michel Muller",
title = "High-level algorithms for correctly-rounded reciprocal
square roots",
crossref = "IEEE:2022:ISC",
pages = "18--25",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00013",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29; correct rounding; floating-point
arithmetic",
}
@InProceedings{Bruguera:2022:LLH,
author = "Javier D. Bruguera",
title = "Low-Latency and High-Bandwidth Pipelined Radix-64
Division and Square Root Unit",
crossref = "IEEE:2022:ISC",
pages = "10--17",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00012",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Buhrow:2022:PMM,
author = "Benjamin Buhrow and Barry Gilbert and Clifton Haider",
title = "Parallel modular multiplication using 512-bit advanced
vector instructions",
journal = j-J-CRYPTO-ENG,
volume = "12",
number = "1",
pages = "95--105",
month = apr,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-021-00256-9",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Sat Apr 16 13:18:32 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "https://link.springer.com/article/10.1007/s13389-021-00256-9",
acknowledgement = ack-nhfb,
ajournal = "J. Crypto. Eng.",
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@Article{Cardarilli:2022:DSE,
author = "Gian Carlo Cardarilli and Luca {Di Nunzio} and Rocco
Fazzolari and Alberto Nannarelli and Massimo Petricca
and Marco Re",
title = "Design Space Exploration Based Methodology for Residue
Number System Digital Filters Implementation",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "1",
pages = "186--198",
month = jan # "\slash " # mar,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2020.2997067",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Chen:2022:PPL,
author = "Chuangtao Chen and Weikang Qian and Mohsen Imani and
Xunzhao Yin and Cheng Zhuo",
title = "{PAM}: a Piecewise-Linearly-Approximated
Floating-Point Multiplier With Unbiasedness and
Configurability",
journal = j-IEEE-TRANS-COMPUT,
volume = "71",
number = "10",
pages = "2473--2486",
month = oct,
year = "2022",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2021.3131850",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 8 07:59:47 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Cococcioni:2022:ERO,
author = "Marco Cococcioni and Federico Rossi and Emanuele
Ruffaldi and Sergio Saponara",
booktitle = "Applications in Electronics Pervading Industry,
Environment and Society",
title = "Experimental Results of Vectorized Posit-Based {DNNs}
on a Real {ARM SVE} High Performance Computing
Machine",
publisher = pub-SV,
address = pub-SV:adr,
pages = "61--68",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-030-95498-7_9",
ISBN = "3-030-95498-6",
ISBN-13 = "978-3-030-95498-7",
ISSN = "1876-1119",
ISSN-L = "1876-1100",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Cococcioni:2022:LPP,
author = "Marco Cococcioni and Federico Rossi and Emanuele
Ruffaldi and Sergio Saponara",
title = "A Lightweight Posit Processing Unit for {RISC-V}
Processors in Deep Neural Network Applications",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "4",
pages = "1898--1908",
month = oct # "\slash " # dec,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2021.3120538",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Cococcioni:2022:SRR,
author = "Marco Cococcioni and Federico Rossi and Emanuele
Ruffaldi and Sergio Saponara",
title = "Small Reals Representations for Deep Learning at the
Edge: a Comparison",
crossref = "Gustafson:2022:NGA",
pages = "117--133",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9_8",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Coward:2022:ADO,
author = "Samuel Coward and George A. Constantinides and Theo
Drane",
title = "Automatic Datapath Optimization using E-Graphs",
crossref = "IEEE:2022:ISC",
pages = "43--50",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00016",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Misc{Cowlishaw:2022:DAFa,
author = "Mike Cowlishaw",
title = "Decimal Arithmetic {FAQ}: {Part} 1 --- General
Questions",
howpublished = "Web site.",
day = "21",
month = apr,
year = "2022",
bibdate = "Mon Apr 25 17:12:00 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://speleotrove.com/decimal/decifaq1.html",
acknowledgement = ack-nhfb,
remark = "Previous versions 2000, 2007.",
}
@Misc{Cowlishaw:2022:DAFb,
author = "Mike Cowlishaw",
title = "Decimal Arithmetic {FAQ}: {Part} 2 --- Definitions",
howpublished = "Web site.",
day = "25",
month = apr,
year = "2022",
bibdate = "Mon Apr 25 17:12:00 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://speleotrove.com/decimal/decifaq2.html",
acknowledgement = ack-nhfb,
remark = "Previous versions 2000, 2007.",
}
@Misc{Cowlishaw:2022:DAFc,
author = "Mike Cowlishaw",
title = "Decimal Arithmetic {FAQ}: {Part} 3 --- Hardware
Questions",
howpublished = "Web site.",
day = "25",
month = apr,
year = "2022",
bibdate = "Mon Apr 25 17:12:00 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://speleotrove.com/decimal/decifaq3.html",
acknowledgement = ack-nhfb,
remark = "Previous versions 2000, 2007.",
}
@Misc{Cowlishaw:2022:DAFd,
author = "Mike Cowlishaw",
title = "Decimal Arithmetic {FAQ}: {Part} 4 --- Arithmetic
Specification Questions",
howpublished = "Web site.",
day = "25",
month = apr,
year = "2022",
bibdate = "Mon Apr 25 17:12:00 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://speleotrove.com/decimal/decifaq4.html",
acknowledgement = ack-nhfb,
remark = "Previous versions 2000, 2007.",
}
@Misc{Cowlishaw:2022:DAFe,
author = "Mike Cowlishaw",
title = "Decimal Arithmetic {FAQ}: {Part} 5 --- Encoding
Questions",
howpublished = "Web site.",
day = "25",
month = apr,
year = "2022",
bibdate = "Mon Apr 25 17:12:00 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://speleotrove.com/decimal/decifaq1.html",
acknowledgement = ack-nhfb,
remark = "Previous versions 2000, 2007.",
}
@Misc{Cowlishaw:2022:DAFf,
author = "Mike Cowlishaw",
title = "Decimal Arithmetic {FAQ}: {Part} 5 --- Miscellaneous
Questions",
howpublished = "Web site.",
day = "25",
month = apr,
year = "2022",
bibdate = "Mon Apr 25 17:12:00 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://speleotrove.com/decimal/decifaq6.html",
acknowledgement = ack-nhfb,
remark = "Previous versions 2000, 2007.",
}
@Article{Crespo:2022:UPI,
author = "Lu{\'\i}s Crespo and Pedro Tom{\'a}s and Nuno Roma and
Nuno Neves",
title = "Unified Posit\slash {IEEE-754} Vector {MAC} Unit for
Transprecision Computing",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "69",
number = "5",
pages = "2478--2482",
year = "2022",
DOI = "https://doi.org/10.1109/TCSII.2022.3160191",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}
@InProceedings{deDinechin:2022:FA,
author = "Florent de Dinechin and Stuart Oberman and Bogdan
Pasca and Leonel Sousa",
title = "Foreword: {ARITH 2022}",
crossref = "IEEE:2022:ISC",
pages = "vii--vii",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00005",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{deDinechin:2022:OCA,
author = "Florent de Dinechin and Stuart Oberman and Bogdan
Pasca and Leonel Sousa and Guillaume Melquiond and Marc
Mezzarobba and Vojin G. Oklobdzija",
title = "Organizing Committee: {ARITH 2022}",
crossref = "IEEE:2022:ISC",
pages = "viii--viii",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00006",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Demmel:2022:PCEa,
author = "James Demmel and Jack Dongarra and Mark Gates and Greg
Henry and Julien Langou and Xiaoye Li and Piotr
Luszczek and Weslley Pereira and Jason Riedy and Cindy
Rubio-Gonz{\'a}lez",
title = "Proposed Consistent Exception Handling for the {BLAS}
and {LAPACK}",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "92",
day = "19",
month = jul,
year = "2022",
bibdate = "Mon Sep 11 06:47:01 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2207.09281",
abstract = "Numerical exceptions, which may be caused by overflow,
operations like division by 0 or sqrt(-1), or
convergence failures, are unavoidable in many cases, in
particular when software is used on unforeseen and
difficult inputs. As more aspects of society become
automated, e.g., self-driving cars, health monitors,
and cyber-physical systems more generally, it is
becoming increasingly important to design software that
is resilient to exceptions, and that responds to them
in a consistent way. Consistency is needed to allow
users to build higher-level software that is also
resilient and consistent (and so on recursively). In
this paper we explore the design space of consistent
exception handling for the widely used BLAS and LAPACK
linear algebra libraries, pointing out a variety of
instances of inconsistent exception handling in the
current versions, and propose a new design that
balances consistency, complexity, ease of use, and
performance. Some compromises are needed, because there
are preexisting inconsistencies that are outside our
control, including in or between existing vendor BLAS
implementations, different programming languages, and
even compilers for the same programming language. And
user requests from our surveys are quite diverse. We
also propose our design as a possible model for other
numerical software, and welcome comments on our design
choices",
acknowledgement = ack-nhfb,
}
@InProceedings{Demmel:2022:PCEb,
author = "James Demmel and Jack Dongarra and Mark Gates and Greg
Henry and Julien Langou and Xiaoye Li and Piotr
Luszczek and Weslley Pereira and Jason Riedy and Cindy
Rubio-Gonz{\'a}lez",
editor = "{IEEE}",
booktitle = "{Correctness 2022: Sixth International Workshop on
Software Correctness for HPC Applications: Held in
conjunction with SC22: The International Conference for
High Performance Computing, Networking, Storage and
Analysis. Dallas, Texas, USA, November 13-18, 2022}",
title = "Proposed Consistent Exception Handling for the {BLAS}
and {LAPACK}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "??--??",
year = "2022",
DOI = "https://doi.org/10.1109/Correctness56720.2022.00006",
ISBN = "1-66546-335-X",
ISBN-13 = "978-1-66546-335-5",
LCCN = "????",
bibdate = "Wed Aug 07 14:39:23 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Desrentes:2022:PDO,
author = "Or{\'e}gane Desrentes and Diana Resmerita and
Beno{\^\i}t Dupont de Dinechin",
title = "A {Posit8} Decompression Operator for Deep Neural
Network Inference",
crossref = "Gustafson:2022:NGA",
pages = "14--30",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9_2",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Didier:2022:SCR,
author = "Laurent-St{\'e}phane Didier and Jean-Marc Robert and
Fangan Yssouf Dosso and Nadia {El Mrabet}",
title = "A software comparison of {RNS} and {PMNS}",
crossref = "IEEE:2022:ISC",
pages = "86--93",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00025",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29; Polynomial Modular Number System (PMNS);
Residue Number System (RNS)",
}
@Article{Dieguez:2022:EHP,
author = "Adrian P. Dieguez and Margarita Amor and Ram{\'o}n
Doallo and Akira Nukada and Satoshi Matsuoka",
title = "Efficient high-precision integer multiplication on the
{GPU}",
journal = j-IJHPCA,
volume = "36",
number = "3",
pages = "356--369",
day = "1",
month = may,
year = "2022",
CODEN = "IHPCFL",
DOI = "https://doi.org/10.1177/10943420221077964",
ISSN = "1094-3420 (print), 1741-2846 (electronic)",
ISSN-L = "1094-3420",
bibdate = "Thu May 30 07:31:45 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ijsa.bib",
URL = "https://journals.sagepub.com/doi/abs/10.1177/10943420221077964",
acknowledgement = ack-nhfb,
ajournal = "????",
fjournal = "International Journal of High Performance Computing
Applications",
journal-URL = "https://journals.sagepub.com/home/hpc",
ORCID-numbers = "https://orcid.org/0000-0001-7168-9050",
}
@Article{DiMeo:2022:AFP,
author = "Gennaro {Di Meo} and Gerardo Saggese and Antonio G. M.
Strollo and Davide {De Caro} and Nicola Petra",
title = "Approximate Floating-Point Multiplier based on Static
Segmentation",
journal = j-ELECTRONICS,
volume = "11",
number = "11",
pages = "3005:1--3005:23",
year = "2022",
DOI = "https://doi.org/10.3390/electronics1119",
ISSN = "2079-9292",
ISSN-L = "2079-9292",
bibdate = "Wed Dec 20 07:43:28 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://mdpi-res.com/d_attachment/electronics/electronics-11-03005/article_deploy/electronics-11-03005.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronics",
journal-URL = "https://www.mdpi.com/journal/electronics",
}
@InProceedings{Dosso:2022:PEA,
author = "Fangan Yssouf Dosso and Jean-Marc Robert and Pascal
V{\'e}ron",
title = "{PMNS} for efficient arithmetic and small memory
cost",
crossref = "IEEE:2022:ISC",
pages = "84--84",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00023",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Dross:2022:MPF,
author = "Claire Dross and Johannes Kanig",
editor = "R. Bloem and R. Dimitrova and C. Fan and N.
Sharygina",
booktitle = "Software Verification: {NSV VSTTE 2021}",
title = "Making Proofs of Floating-Point Programs Accessible to
Regular Developers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "13124",
pages = "7--24",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-030-95561-8_2",
ISBN = "3-030-95561-3",
ISBN-13 = "978-3-030-95561-8",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Jun 8 09:07:55 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Durand:2022:AVC,
author = "Yves Durand and Eric Guthmuller and Cesar Fuguet and
J{\'e}r{\^o}me Fereyre and Andrea Bocco and Riccardo
Alidori",
title = "Accelerating Variants of the Conjugate Gradient with
the Variable Precision Processor",
crossref = "IEEE:2022:ISC",
pages = "51--57",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00017",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{ElArar:2022:PES,
author = "El-Mehdi {El Arar} and Devan Sohier and Pablo {de
Oliveira Castro} and Eric Petit",
title = "The Positive Effects of Stochastic Rounding in
Numerical Algorithms",
crossref = "IEEE:2022:ISC",
pages = "58--65",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00018",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Recently, stochastic rounding (SR) has been
implemented in specialized hardware but most current
computing nodes do not yet support this rounding mode.
Several works empirically illustrate the benefit of
stochastic rounding in various fields such as neural
networks and ordinary differential equations. For some
algorithms, such as summation, inner product or
matrix-vector multiplication, it has been proved that
SR provides probabilistic error bounds better than the
traditional deterministic bounds.\par
In this paper, we extend this theoretical ground for a
wider adoption of SR in computer architecture. First,
we analyze the biases of the two SR modes: SR-nearness
and SR-up-or-down. We demonstrate on a case-study of
Euler's forward method that IEEE-754 default rounding
modes and SR-up-or-down accumulate rounding errors
across iterations and that SR-nearness, being unbiased,
does not. Second, we prove a $ O(\sqrt {n}) $
probabilistic bound on the forward error of Horner's
polynomial evaluation method with SR, improving on the
known deterministic $ O(n) $ bound.",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Elsaid:2022:OFA,
author = "Kareem Elsaid and Mona Safar and M. Watheq
El-Kharashi",
editor = "{IEEE}",
booktitle = "{2022 International Conference on Microelectronics
(ICM)}",
title = "Optimized {FPGA} Architecture for Machine Learning
Applications using Posit Multipliers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "50--53",
year = "2022",
DOI = "https://doi.org/10.1109/ICM56065.2022.10005431",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ene:2022:PTS,
author = "Teodor Dumitru Ene and James E. Stine",
title = "Point-Targeted Sparseness and {Ling} Transforms on
Parallel Prefix Adder Trees",
crossref = "IEEE:2022:ISC",
pages = "68--75",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00021",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Essam:2022:DIL,
author = "Mohammed Essam and Ahmed Shalaby and Mohamed Taher",
editor = "{IEEE}",
booktitle = "{2022 10th International Japan-Africa Conference on
Electronics, Communications, and Computations
(JAC-ECC)}",
title = "Design and Implementation of Low Power Posit
Arithmetic Unit for Efficient Hardware Accelerators",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "68--71",
year = "2022",
DOI = "https://doi.org/10.1109/JAC-ECC56395.2022.10043893",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Evstigneev:2022:CSD,
author = "N. M. Evstigneev and O. I. Ryabkov and A. N. Bocharov
and V. P. Petrovskiy and I. O. Teplyakov",
title = "Compensated summation and dot product algorithms for
floating-point vectors on parallel architectures: Error
bounds, implementation and application in the {Krylov}
subspace methods",
journal = j-J-COMPUT-APPL-MATH,
volume = "414",
number = "??",
pages = "??--??",
month = nov,
year = "2022",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2022.114434",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Tue Jun 14 16:20:17 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042722002047",
acknowledgement = ack-nhfb,
articleno = "114434",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Gao:2022:TFI,
author = "Zhanyuan Gao and Laiping Zhao and Haonan Chen",
editor = "{IEEE}",
booktitle = "{2022 IEEE\slash ACIS 22nd International Conference on
Computer and Information Science (ICIS)}",
title = "A Trigonometric Function Instruction Set Extension
Method Based on {RISC-V}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "119--126",
year = "2022",
DOI = "https://doi.org/10.1109/ICIS54925.2022.9882453",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@Misc{Genkina:2022:PNK,
author = "Dina Genkina",
title = "Posits, a New Kind of Number, Improves the Math of
{AI}: The first posit-based processor core gave a
ten-thousandfold accuracy boost",
howpublished = "IEEE Spectrum Web site",
day = "26",
month = sep,
year = "2022",
bibdate = "Wed Sep 28 10:46:38 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://spectrum.ieee.org/floating-point-numbers-posits-processor",
acknowledgement = ack-nhfb,
}
@InProceedings{Greuet:2022:QAM,
author = "Aur{\'e}lien Greuet and Simon Montoya and Cl{\'e}mence
Vermeersch",
title = "Quotient Approximation Modular Reduction",
crossref = "IEEE:2022:ISC",
pages = "103--110",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00028",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Gudivada:2022:NOL,
author = "A. Arunkumar Gudivada and Gnanou Florence Sudha",
title = "Novel optimized low power design of single-precision
floating-point adder using Quantum-dot Cellular
Automata",
journal = j-J-SUPERCOMPUTING,
volume = "78",
number = "4",
pages = "6035--6053",
month = mar,
year = "2022",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-021-04089-5",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Fri Feb 21 15:59:35 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-021-04089-5",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Higham:2022:MPA,
author = "Nicholas J. Higham and Theo Mary",
title = "Mixed precision algorithms in numerical linear
algebra",
journal = j-ACTA-NUMERICA,
volume = "31",
pages = "347--414",
month = may,
year = "2022",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492922000022",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
bibdate = "Wed Jun 15 09:10:34 MDT 2022",
bibsource = "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=31&issueId=00;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.cambridge.org/core/journals/acta-numerica/article/mixed-precision-algorithms-in-numerical-linear-algebra/43CA701BA29251B5790C653E66F46197",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
author-dates = "Nicholas John Higham (25 December 1961--20 January
2024)",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "09 June 2022",
}
@InProceedings{Ho:2022:QNG,
author = "Nhut-Minh Ho and Himeshi De Silva and John L.
Gustafson and Weng-Fai Wong",
title = "{Qtorch+}: Next Generation Arithmetic for {Pytorch}
Machine Learning",
crossref = "Gustafson:2022:NGA",
pages = "31--49",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9_3",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Immaneni:2022:PEO,
author = "Amritha Immaneni and Salim Ullah and Suresh Nambi and
Siva Satyendra Sahoo and Akash Kumar",
editor = "{IEEE}",
booktitle = "{2022 25th Euromicro Conference on Digital System
Design (DSD)}",
title = "{PosAx-O}: Exploring Operator-level Approximations for
Posit Arithmetic in Embedded {AI\slash ML}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "214--223",
year = "2022",
DOI = "https://doi.org/10.1109/DSD57027.2022.00037",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Isupov:2022:MPS,
author = "Konstantin Isupov",
title = "Multiple-precision sparse matrix--vector
multiplication on {GPUs}",
journal = j-J-COMPUT-SCI,
volume = "61",
pages = "??--??",
month = may,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1016/j.jocs.2022.101609",
ISSN = "1877-7503 (print), 1877-7511 (electronic)",
ISSN-L = "1877-7503",
bibdate = "Tue Sep 19 13:56:09 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S1877750322000382",
acknowledgement = ack-nhfb,
ajournal = "J. Comput. Sci.",
articleno = "101609",
fjournal = "Journal of Computational Science",
journal-URL = "https://www.sciencedirect.com/journal/journal-of-computational-science",
}
@InProceedings{Keerthi:2022:DIM,
author = "T Keerthi and Yashu Swami",
editor = "{IEEE}",
booktitle = "{2022 IEEE 3rd International Conference on VLSI
Systems, Architecture, Technology and Applications
(VLSI SATA)}",
title = "Design and Implementation of {MAC} by Using Efficient
Posit Multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--4",
year = "2022",
DOI = "https://doi.org/10.1109/VLSISATA54927.2022.10046599",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Kim:2022:EAM,
author = "Min Soo Kim and Alberto A. {Del Barrio} and HyunJin
Kim and Nader Bagherzadeh",
title = "The Effects of Approximate Multiplication on
Convolutional Neural Networks",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "2",
pages = "904--916",
month = apr # "\slash " # jun,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2021.3050989",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
abstract = "This article analyzes the effects of approximate
multiplication when performing inferences on deep
convolutional neural networks (CNNs). The approximate
multiplication can reduce the cost of the underlying
circuits so that CNN inferences can be performed more
efficiently in hardware accelerators. The study
identifies the critical factors in the convolution,
fully-connected, and batch normalization layers that
allow more accurate CNN predictions despite the errors
from approximate multiplication. The same factors also
provide an arithmetic explanation of why bfloat16
multiplication performs well on CNNs. The experiments
are performed with recognized network architectures to
show that the approximate multipliers can produce
predictions that are nearly as accurate as the FP32
references, without additional training. For example,
the ResNet and Inception-v4 models with Mitch-$w$ 6
multiplication produces Top-5 errors that are within
0.2 percent compared to the FP32 references. A brief
cost comparison of Mitch-$w$ 6 against bfloat16 is
presented where a MAC operation saves up to 80 percent
of energy compared to the bfloat16 arithmetic. The most
far-reaching contribution of this article is the
analytical justification that multiplications can be
approximated while additions need to be exact in CNN
MAC operations.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Knodtel:2022:SID,
author = "Johannes Kn{\"o}dtel and Sebastian Rachuj and Marc
Reichenbach",
editor = "{IEEE}",
booktitle = "{2022 25th Euromicro Conference on Digital System
Design (DSD)}",
title = "Suitability of {ISAs} for Data Paths Based on
Redundant Number Systems: Is {RISC-V} the best?",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "247--253",
year = "2022",
DOI = "https://doi.org/10.1109/DSD57027.2022.00041",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kuang:2022:HSN,
author = "Honglin Kuang and Yifan Zhao and Jun Han",
editor = "{IEEE}",
booktitle = "{2022 IEEE Asia Pacific Conference on Circuits and
Systems (APCCAS)}",
title = "A High-Speed {NTT}-Based Polynomial Multiplication
Accelerator with Vector Extension of {RISC-V} for
{Saber} Algorithm",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "592--595",
year = "2022",
DOI = "https://doi.org/10.1109/APCCAS55924.2022.10090293",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Laguna:2022:BAF,
author = "Ignacio Laguna and Xinyi Li and Ganesh
Gopalakrishnan",
editor = "????",
booktitle = "{SOAP 2022: Proceedings of the 11th ACM SIGPLAN
International Workshop on the State Of the Art in
Program Analysis, San Diego, CA, USA, 14 June 2022}",
title = "{BinFPE}: Accurate Floating-Point Exception Detection
for {GPU} Applications",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "50",
pages = "1--8",
year = "2022",
DOI = "https://doi.org/10.1145/3520313.3534655",
ISBN = "1-4503-9274-1",
ISBN-13 = "978-1-4503-9274-7",
bibdate = "Mon Sep 11 07:11:11 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "When modern heterogeneous HPC systems perform
numerical computations, floating-point exceptional
quantities such as NaN and infinity in the GPU context,
remain insufficiently handled. This is because commonly
used GPUs and the CUDA language have no inherent
exception detection capabilities. Existing
compiler-based approaches for this problem are tied to
a given compiler and cannot detect exceptions generated
by binaries and precompiled libraries. This paper
contributes BinFPE, a unique tool that addresses these
challenges. BinFPE uses the NVBit dynamic binary
instrumentation framework to check the machine
registers after each calculation to recognize
exceptions, and conveys this information to the CPU for
final reporting. We demonstrate the effectiveness of
BinFPE on 42 CUDA programs, reporting previously
unreported exceptions. We also present the limitations
of BinFPE and our perspective on building GPU tools via
binary instrumentation.",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1145/3520313",
}
@InProceedings{Laguna:2022:FIT,
author = "Ignacio Laguna and Ganesh Gopalakrishnan",
editor = "{ACM}",
booktitle = "{SC '22: Proceedings of the International Conference
on High Performance Computing, Networking, Storage and
Analysis, Dallas, Texas, November 13--18, 2022}",
title = "Finding Inputs that Trigger Floating-Point Exceptions
in {GPUs} via {Bayesian} Optimization",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "464--475",
year = "2022",
ISBN = "1-66545-444-X",
ISBN-13 = "978-1-66545-444-5",
ISSN = "2167-4329 (print), 2167-4337 (electronic)",
ISSN-L = "2167-4337",
bibdate = "Mon Sep 11 07:09:51 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Testing code for floating-point exceptions is crucial
as exceptions can quickly propagate and produce
unreliable numerical answers. The state-of-the-art to
test for floating-point exceptions in GPUs is quite
limited and solutions require the application's source
code, which precludes their use in accelerated
libraries where the source is not publicly available.
We present an approach to find inputs that trigger
floating-point exceptions in black-box GPU functions,
i.e., functions where the source code and information
about input bounds are unavailable. Our approach is the
first to use Bayesian optimization (BO) to identify
such inputs and uses novel strategies to overcome the
challenges that arise in applying BO to this problem.
We implement our approach in the Xscope framework and
demonstrate it on 58 functions from the CUDA Math
Library and functions from ten HPC programs. Xscope is
able to identify inputs that trigger exceptions in
about 72\% of the tested functions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Langroudi:2022:AAH,
author = "Hamed F. Langroudi and Vedant Karia and Tej Pandit and
Becky Mashaido and Dhireesha Kudithipudi",
title = "{ACTION}: {Automated Hardware--Software Codesign
Framework for Low-precision Numerical Format SelecTION}
in {TinyML}",
crossref = "Gustafson:2022:NGA",
pages = "50--65",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9_4",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Lim:2022:OPA,
author = "Jay P. Lim and Santosh Nagarakatte",
title = "One polynomial approximation to produce correctly
rounded results of an elementary function for multiple
representations and rounding modes",
journal = j-PACMPL,
volume = "6",
number = "POPL",
pages = "3:1--3:28",
month = jan,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1145/3498664",
ISSN = "2475-1421 (electronic)",
ISSN-L = "2475-1421",
bibdate = "Thu May 26 06:32:48 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
URL = "https://dl.acm.org/doi/10.1145/3498664",
abstract = "Mainstream math libraries for floating point (FP) do
not produce correctly rounded results for all inputs.
In contrast, CR-LIBM and RLIBM provide correctly
rounded implementations for a specific FP
representation with one rounding mode. Using such
libraries for a representation with a new rounding mode
or with different precision will result in wrong
results due to double rounding. This paper proposes a
novel method to generate a single polynomial
approximation that produces correctly rounded results
for all inputs for multiple rounding modes and multiple
precision configurations. To generate a correctly
rounded library for n-bits, our key idea is to generate
a polynomial approximation for a representation with
n+2-bits using the round-to-odd mode. We prove that the
resulting polynomial approximation will produce
correctly rounded results for all five rounding modes
in the standard and for multiple representations with
k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $
is the number of exponent bits in the representation.
Similar to our prior work in the RLIBM project, we
approximate the correctly rounded result when we
generate the library with n+2-bits using the
round-to-odd mode. We also generate polynomial
approximations by structuring it as a linear
programming problem but propose enhancements to
polynomial generation to handle the round-to-odd mode.
Our prototype is the first 32-bit float library that
produces correctly rounded results with all rounding
modes in the IEEE standard for all inputs with a single
polynomial approximation. It also produces correctly
rounded results for any FP configuration ranging from
10-bits to 32-bits while also being faster than
mainstream libraries.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "Proceedings of the ACM on Programming Languages
(PACMPL)",
journal-URL = "https://dl.acm.org/loi/pacmpl",
keywords = "correct rounding; elementary functions",
}
@InProceedings{Lindstrom:2022:MUC,
author = "Peter Lindstrom",
title = "{MultiPosits}: Universal Coding of $ \mathbb {R}^n $",
crossref = "Gustafson:2022:NGA",
pages = "66--83",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9_5",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Liu:2022:DUA,
author = "Weiqiang Liu and Tao Xu and Jing Li and Chenghua Wang
and Paolo Montuschi and Fabrizio Lombardi",
title = "Design of Unsigned Approximate Hybrid Dividers Based
on Restoring Array and Logarithmic Dividers",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "1",
pages = "339--350",
month = jan # "\slash " # mar,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2020.3022290",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
abstract = "Approximate computer arithmetic has been extensively
studied due to its advantages to further reduce power
consumption and increase performance at reduced
accuracy. Although a number of approximate adders and
multipliers have been studied, only a few approximate
dividers have been proposed. A logarithmic divider (LD)
has low complexity and accuracy, while an exact array
divider (EXD) has a high complexity. Therefore, in this
article, an approximate hybrid divider (AXHD) is
proposed. It takes advantage of both LD and EXD to
achieve a tradeoff between hardware performance and
accuracy. Exact restoring divider cells are used to
generate the most significant bits (MSBs) of the
quotient for attaining a high accuracy while the other
quotient digits are generated by using a LD as an
approximate scheme to improve figures of merit such as
power consumption, area and delay. To further save
hardware resources, a so-called eliminated approximate
hybrid divider (E-AXHD) based on AXHD is also proposed.
In this improved design, a reduced width divider is
used to replace the EXD in AXHD. Specifically, for a
16-by-8 design, $ n / (n + 1) $ array division is used
to replace the $ n / 8 $ array division ($ n < 8$). The
proposed AXHD and E-AXHD are evaluated and analyzed
using error and hardware metrics. The proposed designs
are also compared with EXD, LD and previous approximate
dividers. The results show that the proposed designs
outperform previous approximate dividers by considering
both energy and error. The proposed hybrid dividers are
of particular interest for error tolerant applications
such as image processing and machine learning.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Mallasen:2022:CCR,
author = "David Mallas{\'e}n and Raul Murillo and Alberto A.
{Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
and Manuel Prieto Matias",
editor = "{IEEE}",
booktitle = "{2022 37th Conference on Design of Circuits and
Integrated Circuits (DCIS)}",
title = "Customizing the {CVA6 RISC-V} Core to Integrate Posit
and Quire Instructions",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "01--06",
year = "2022",
DOI = "https://doi.org/10.1109/DCIS55711.2022.9970026",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@Article{Mallasen:2022:POSa,
author = "David Mallas{\'e}n and Raul Murillo and Alberto A.
{Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
and Manuel Prieto-Matias",
title = "{PERCIVAL}: Open-Source Posit {RISC-V} Core With Quire
Capability",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "3",
pages = "1241--1252",
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2022.3187199",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Mallasen:2022:POSb,
author = "David Mallas{\'e}n and Raul Murillo and Alberto A.
{Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
and Manuel Prieto-Matias",
title = "{PERCIVAL}: Open-Source Posit {RISC-V} Core With Quire
Capability",
crossref = "IEEE:2022:ISC",
pages = "66--66",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00019",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
note = "Authors and title only.",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{Mathis:2022:IHP,
author = "Brett Mathis and James E. Stine",
editor = "{IEEE}",
booktitle = "{2022 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "Implementation of High Performance {IEEE 754}-Posit
Conversion Hardware",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "934--937",
year = "2022",
DOI = "https://doi.org/10.1109/ISCAS48785.2022.9937426",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Mccoid:2022:PRA,
author = "Conor Mccoid and Martin J. Gander",
title = "A Provably Robust Algorithm for Triangle--triangle
Intersections in Floating-point Arithmetic",
journal = j-TOMS,
volume = "48",
number = "2",
pages = "17:1--17:30",
month = jun,
year = "2022",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3513264",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Jul 20 07:04:17 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3513264",
abstract = "Motivated by the unexpected failure of the triangle
intersection component of the Projection Algorithm for
Nonmatching Grids (PANG), this article provides a
robust version with proof of backward stability. The
new triangle intersection algorithm ensures consistency
and parsimony across three types of calculations. The
set of intersections produced by the algorithm, called
representations, is shown to match the set of geometric
intersections, called models. The article concludes
with a comparison between the old and new intersection
algorithms for PANG using an example found to reliably
generate failures in the former.",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Meloni:2022:AAP,
author = "Nicolas Meloni",
title = "An Alternative Approach to Polynomial Modular Number
System Internal Reduction",
crossref = "IEEE:2022:ISC",
pages = "85--85",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00024",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Micikevicius:2022:FFD,
author = "Paulius Micikevicius and Dusan Stosic and Neil Burgess
and Marius Cornea and Pradeep Dubey and Richard
Grisenthwaite and Sangwon Ha and Alexander Heinecke and
Patrick Judd and John Kamalu and Naveen Mellempudi and
Stuart Oberman and Mohammad Shoeybi and Michael Siu and
Hao Wu",
title = "{FP8} Formats for Deep Learning",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--9",
year = "2022",
bibdate = "Wed Aug 7 16:23:07 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2209.05433",
abstract = "FP8 is a natural progression for accelerating deep
learning training inference beyond the 16-bit formats
common in modern processors. In this paper we propose
an 8-bit floating point (FP8) binary interchange format
consisting of two encodings - E4M3 (4-bit exponent and
3-bit mantissa) and E5M2 (5-bit exponent and 2-bit
mantissa). While E5M2 follows IEEE 754 conventions for
representation of special values, E4M3's dynamic range
is extended by not representing infinities and having
only one mantissa bit-pattern for NaNs. We demonstrate
the efficacy of the FP8 format on a variety of image
and language tasks, effectively matching the result
quality achieved by 16-bit training sessions. Our study
covers the main modern neural network architectures -
CNNs, RNNs, and Transformer-based models, leaving all
the hyperparameters unchanged from the 16-bit baseline
training sessions. Our training experiments include
large, up to 175B parameter, language models. We also
examine FP8 post-training-quantization of language
models trained using 16-bit formats that resisted fixed
point int8 quantization.",
acknowledgement = ack-nhfb,
archiveprefix = "arXiv",
eprint = "2209.05433",
primaryclass = "cs.LG",
}
@InProceedings{Monniaux:2022:FVB,
author = "David Monniaux and Alice Pain",
title = "Formally verified 32- and 64-bit integer division
using double-precision floating-point arithmetic",
crossref = "IEEE:2022:ISC",
pages = "128--132",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00032",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.science/hal-03722203/",
abstract = "Some recent processors are not equipped with an
integer division unit. Compilers then implement
division by a call to a special function supplied by
the processor designers, which implements division by a
loop producing one bit of quotient per iteration. This
hinders compiler optimizations and results in
non-constant time computation, which is a problem in
some applications. We advocate instead using the
processor's floating-point unit, and propose code that
the compiler can easily interleave with other
computations. We fully proved the correctness of our
algorithm, which mixes floating-point and
fixed-bitwidth integer computations, using the Coq
proof assistant and successfully integrated it into the
CompCert formally verified compiler.",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Montuschi:2022:CAC,
author = "Paolo Montuschi and Jean-Michel Muller and Florent de
Dinechin",
title = "Computer Arithmetic: Continuing a Long and Steady
Emergence",
journal = j-COMPUTER,
volume = "55",
number = "10",
pages = "4--6",
month = oct,
year = "2022",
CODEN = "CPTRB4",
DOI = "https://doi.org/10.1109/MC.2022.3193206",
ISSN = "0018-9162 (print), 1558-0814 (electronic)",
ISSN-L = "0018-9162",
bibdate = "Thu Oct 27 08:20:29 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/computer2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}
@Article{Muller:2022:FDW,
author = "Jean-Michel Muller and Laurence Rideau",
title = "Formalization of Double-Word Arithmetic, and Comments
on {``Tight and Rigorous Error Bounds for Basic
Building Blocks of Double-Word Arithmetic''}",
journal = j-TOMS,
volume = "48",
number = "1",
pages = "9:1--9:24",
month = mar,
year = "2022",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3484514",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Feb 17 08:00:57 MST 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3484514",
abstract = "Recently, a complete set of algorithms for
manipulating double-word numbers (some classical, some
new) was analyzed [16]. We have formally proven all the
theorems given in that article, using the Coq proof
assistant. The formal proof work led us to: (i) locate
mistakes in some of the original paper proofs (mistakes
that, however, do not hinder the validity of the
algorithms), (ii) significantly improve some error
bounds, and (iii) generalize some results by showing
that they are still valid if we slightly change the
rounding mode. The consequence is that the algorithms
presented in [16] can be used with high confidence, and
that some of them are even more accurate than what was
believed before. This illustrates what formal proof can
bring to computer arithmetic: beyond mere (yet
extremely useful) verification, correction, and
consolidation of already known results, it can help to
find new properties. All our formal proofs are freely
available.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Murillo:2022:CDD,
author = "Raul Murillo and David Mallas{\'e}n and Alberto A.
{Del Barrio} and Guillermo Botella",
title = "Comparing Different Decodings for Posit Arithmetic",
crossref = "Gustafson:2022:NGA",
pages = "84--99",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9_6",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Murillo:2022:PPL,
author = "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
Botella and Min Soo Kim and HyunJin Kim and Nader
Bagherzadeh",
title = "{PLAM}: a Posit Logarithm-Approximate Multiplier",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "4",
pages = "2079--2085",
month = oct # "\slash " # dec,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2021.3109127",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
abstract = "The Posit{\TM} Number System was introduced in 2017 as
a replacement for floating-point numbers. Since then,
the community has explored its application in several
areas, such as deep learning, and produced some unit
designs which are still far from being competitive with
their floating-point counterparts. This article
proposes a Posit Logarithm-Approximate Multiplication
(PLAM) scheme to significantly reduce the complexity of
posit multipliers, one of the most power-hungry
arithmetic units. The impact of this approach is
evaluated in deep neural network inference, where there
are no significant accuracy drops. Compared with
state-of-the-art posit multipliers, experiments show
that the proposed technique reduces the area, power,
and delay of 32-bit hardware multipliers up to 72.86\%,
81.79\%, and 17.01\%, respectively.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Nath:2022:KVM,
author = "Kaushik Nath and Palash Sarkar",
title = "{Kummer} versus {Montgomery} Face-off over Prime Order
Fields",
journal = j-TOMS,
volume = "48",
number = "2",
pages = "13:1--13:28",
month = jun,
year = "2022",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3503536",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Wed Jul 20 07:04:17 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3503536",
abstract = "This paper makes a comprehensive comparison of the
efficiencies of vectorized implementations of Kummer
lines and Montgomery curves at various security levels.
For the comparison, nine Kummer lines are considered,
out of which eight are new, and new assembly
implementations of all nine Kummer lines have been
made. Seven previously proposed Montgomery curves are
considered and new vectorized assembly implementations
have been made for three of them. Our comparisons show
that for all security levels, Kummer lines are
consistently faster than Montgomery curves, though the
speed-up gap is not much.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Noune:2022:BNF,
author = "B. Noune and P. Jones and D. Justus and D. Masters and
C. Luschi",
title = "8-bit numerical formats for deep neural networks",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--30",
year = "2022",
bibdate = "Thu Nov 30 05:46:05 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2206.02915",
abstract = "Given the current trend of increasing size and
complexity of machine learning architectures, it has
become of critical importance to identify new
approaches to improve the computational efficiency of
model training. In this context, we address the
advantages of floating-point over fixed-point
representation, and present an in-depth study on the
use of 8-bit floating-point number formats for
activations, weights, and gradients for both training
and inference. We explore the effect of different
bit-widths for exponents and significands and different
exponent biases. The experimental results demonstrate
that a suitable choice of these low-precision formats
enables faster training and reduced power consumption
without any degradation in accuracy for a range of deep
learning models for image classification and language
processing.",
acknowledgement = ack-nhfb,
}
@Article{Nunez-Yanez:2022:FAD,
author = "Jose Nunez-Yanez",
title = "Fused Architecture for Dense and Sparse Matrix
Processing in {TensorFlow Lite}",
journal = j-IEEE-MICRO,
volume = "42",
number = "6",
pages = "55--66",
month = nov # "\slash " # dec,
year = "2022",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2022.3196705",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Nov 03 05:37:10 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@Article{Oaks:2022:ZNM,
author = "Jeffrey Oaks",
title = "Zero and nothing in medieval {Arabic} arithmetic",
journal = j-BRITISH-J-HIST-MATH,
volume = "37",
number = "3",
pages = "179--211",
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1080/26375451.2022.2115745",
ISSN = "1749-8430 (print), 1749-8341 (electronic)",
ISSN-L = "1749-8341",
bibdate = "Tue Feb 28 07:20:03 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bshm.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/26375451.2022.2115745",
abstract = "Whether explaining calculations with decimal or
sexagesimal notation, arithmetic books composed in
Arabic beginning in the ninth century CE consistently
describe the zero ({\d{s}}ifr) as a sign indicating an
empty place where there is no number. And yet we find
that some arithmeticians explicitly performed
operations on this zero. To understand how the zero was
conceived and manipulated in medieval Arabic texts we
first address the way that numbers themselves were
conceived and how `nothing' entered into arithmetical
problem-solving. From there we examine arithmetic books
for their treatment of zero. We find that there is no
inconsistency in operating on what is literally
nothing, and thus there was no motive for
arithmeticians to regard zero as a number.",
acknowledgement = ack-nhfb,
ajournal = "BSHM Bull.",
fjournal = "BSHM Bulletin: Journal of the British Society for the
History of Mathematics",
journal-URL = "http://www.tandfonline.com/loi/tbsh20",
onlinedate = "25 Sep 2022",
}
@Article{Oberman:2022:GES,
author = "Stuart Oberman and Leonel Sousa and Bogdan Pasca and
Alberto Nannarelli",
title = "Guest Editorial: Special Section on Emerging and
Impacting Trends on Computer Arithmetic",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "3",
pages = "1239--1240",
month = jul # "\slash " # sep,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2022.3195414",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Oh:2022:EPA,
author = "Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee",
editor = "{IEEE}",
booktitle = "{2022 19th International SoC Design Conference
(ISOCC)}",
title = "Evaluation of Posit Arithmetic on Machine Learning
based on Approximate Exponential Functions",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "358--359",
year = "2022",
DOI = "https://doi.org/10.1109/ISOCC56007.2022.10031524",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Ollivier:2022:PRB,
author = "S{\'e}bastien Ollivier and Xinyi Zhang and Yue Tang
and Chayanika Choudhuri and Jingtong Hu and Alex K.
Jones",
title = "Pod-racing: bulk-bitwise to floating-point compute in
racetrack memory for machine learning at the edge",
journal = j-IEEE-MICRO,
volume = "42",
number = "6",
pages = "9--16",
month = nov # "\slash " # dec,
year = "2022",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2022.3195761",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Nov 03 05:37:10 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "http://www.computer.org/csdl/mags/mi/index.html",
}
@InProceedings{Omtzigt:2022:URR,
author = "E. Theodore L. Omtzigt and James Quinlan",
title = "Universal: Reliable, Reproducible, and
Energy-Efficient Numerics",
crossref = "Gustafson:2022:NGA",
pages = "100--116",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9_7",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Osorio:2022:BFA,
author = "John Osorio and Adri{\`a} Armejach and Eric Petit and
Greg Henry and Marc Casas",
title = "A {BF16 FMA} is All You Need for {DNN} Training",
crossref = "IEEE:2022:ISC",
pages = "9--9",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00011",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Authors and title only.",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Park:2022:RCR,
author = "Kangkyu Park and Seungkyu Choi and Yeongjae Choi and
Lee-Sup Kim",
title = "Rare Computing: Removing Redundant Multiplications
From Sparse and Repetitive Data in Deep Neural
Networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "71",
number = "4",
pages = "795--808",
month = apr,
year = "2022",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2021.3063269",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Mar 17 06:38:17 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Peng:2022:DNN,
author = "Jiaxin Peng and Yousra Alkabani and Krunal Puri and
Xiaoxuan Ma and Volker Sorger and Tarek El-Ghazawi",
title = "A Deep Neural Network Accelerator using Residue
Arithmetic in a Hybrid Optoelectronic System",
journal = j-JETC,
volume = "18",
number = "4",
pages = "81:1--81:??",
month = oct,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1145/3550273",
ISSN = "1550-4832 (print), 1550-4840 (electronic)",
ISSN-L = "1550-4832",
bibdate = "Sat Oct 29 07:30:43 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jetc.bib",
URL = "https://dl.acm.org/doi/10.1145/3550273",
abstract = "The acceleration of Deep Neural Networks (DNNs) has
attracted much attention in research. Many critical
real-time applications benefit from DNN accelerators
but are limited by their compute-intensive nature. This
work introduces an accelerator for \ldots{}",
acknowledgement = ack-nhfb,
articleno = "81",
fjournal = "ACM Journal on Emerging Technologies in Computing
Systems (JETC)",
journal-URL = "https://dl.acm.org/loi/jetc",
}
@TechReport{PWG:2022:SPA,
author = "{Posit Working Group}",
title = "Standard for Posit{\TM} Arithmetic (2022)",
type = "Report",
institution = "National Supercomputing Centre (NSCC)",
address = "Singapore",
pages = "12",
day = "2",
month = mar,
year = "2022",
bibdate = "Fri Dec 15 11:16:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://posithub.org/docs/posit_standard-2.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Ramachandran:2022:PCP,
author = "Akshat Ramachandran and John Gustafson and Anusua Roy
and Rizwan Ahmed Ansari and Rohin Daruwala",
editor = "{IEEE}",
booktitle = "{2022 25th Euromicro Conference on Digital System
Design (DSD)}",
title = "{PositIV}: a Configurable Posit Processor Architecture
for Image and Video Processing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "93--100",
year = "2022",
DOI = "https://doi.org/10.1109/DSD57027.2022.00022",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Roy:2022:AAC,
author = "Avishek Sinha Roy and Hardik Agrawal and Anindya
Sundar Dhar",
title = "{ACBAM}-Accuracy-Configurable Sign Inclusive Broken
Array {Booth} Multiplier Design",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "4",
pages = "2072--2078",
month = oct # "\slash " # dec,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2021.3107509",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Russinoff:2022:FVC,
author = "David Russinoff and Javier Bruguera and Cuong Chau and
Mayank Manjrekar and Nicholas Pfister and Harsha
Valsaraju",
title = "Formal Verification of a Chained Multiply-Add Design:
Combining Theorem Proving and Equivalence Checking",
crossref = "IEEE:2022:ISC",
pages = "120--126",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00030",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@InProceedings{S:2022:IRP,
author = "Sathyavathi N S and Augusta Sophy Beulet P",
editor = "{IEEE}",
booktitle = "{2022 Third International Conference on Intelligent
Computing Instrumentation and Control Technologies
(ICICICT)}",
title = "Implementation of {Regime-5} Posit adder",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1040--1043",
year = "2022",
DOI = "https://doi.org/10.1109/ICICICT54557.2022.9917949",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Sadeghimanesh:2022:SSN,
author = "AmirHosein Sadeghimanesh and Matthew England",
title = "An {SMT} solver for non-linear real arithmetic inside
{Maple}",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "56",
number = "2",
pages = "76--79",
month = jun,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1145/3572867.3572880",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Mon Aug 21 16:58:02 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
URL = "https://dl.acm.org/doi/10.1145/3572867.3572880",
abstract = "We report on work-in-progress to create an SMT-solver
inside Maple for non-linear real arithmetic (NRA). We
give background information on the algorithm being
implemented: cylindrical algebraic coverings as a
theory solver in the lazy SMT paradigm. We then present
some new work on the identification of minimal
conflicting cores from the coverings.",
acknowledgement = ack-nhfb,
ajournal = "ACM Commun. Computer Algebr.",
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "https://dl.acm.org/loi/sigsam-cca",
}
@InProceedings{Safieh:2022:ERA,
author = "Malek Safieh and Fabrizio {De Santis}",
title = "Efficient Reduction Algorithms for Special {Gaussian}
Integer Moduli",
crossref = "IEEE:2022:ISC",
pages = "111--119",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00029",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Schober:2022:HAM,
author = "Peter Schober and M. Hassan Najafi and Nima
TaheriNejad",
title = "High-Accuracy Multiply-Accumulate ({MAC}) Technique
for Unary Stochastic Computing",
journal = j-IEEE-TRANS-COMPUT,
volume = "71",
number = "6",
pages = "1425--1439",
month = jun,
year = "2022",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2021.3087027",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed May 25 09:41:19 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Shah:2022:DDP,
author = "Nimish Shah and Laura Isabel Galindez Olascoaga and
Shirui Zhao and Wannes Meert and Marian Verhelst",
title = "{DPU}: {DAG} Processing Unit for Irregular Graphs With
Precision-Scalable Posit Arithmetic in 28 nm",
journal = j-IEEE-J-SOLID-STATE-CIRCUITS,
volume = "57",
number = "8",
pages = "2586--2596",
year = "2022",
CODEN = "IJSCBC",
DOI = "https://doi.org/10.1109/JSSC.2021.3134897",
ISSN = "0018-9200 (print), 1558-173X (electronic)",
ISSN-L = "0018-9200",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal of Solid-State Circuits",
}
@InProceedings{Sibidanov:2022:CMP,
author = "Alexei Sibidanov and Paul Zimmermann and St{\'e}phane
Glondu",
title = "The {CORE-MATH} Project",
crossref = "IEEE:2022:ISC",
pages = "26--34",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00014",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "The CORE-MATH project aims at providing open-source
mathematical functions with correct rounding that can
be integrated into current mathematical libraries. This
article demonstrates the CORE-MATH methodology on two
functions: the binary32 power function (powf) and the
binary64 cube root function (cbrt). CORE-MATH already
provides a full set of correctly rounded C99 functions
for single precision (binary32). These functions
provide similar or in some cases up to threefold
speedups with respect to the GNU libc mathematic
library, which is not correctly rounded. This work
offers a prospect of the mandatory requirement of
correct rounding for mathematical functions in the next
revision of the IEEE-754 standard.",
acknowledgement = ack-nhfb,
keywords = "ARITH-29; correct rounding; floating-point
arithmetic",
}
@InProceedings{Siddamshetty:2022:EHA,
author = "Susheel Ujwal Siddamshetty and Srinivas Boppu and
Debapratim Ghosh",
editor = "{IEEE}",
booktitle = "{2022 IEEE 15th International Symposium on Embedded
Multicore/Many-core Systems-on-Chip (MCSoC)}",
title = "Efficient Hardware Architecture for Posit
Addition\slash Subtraction",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "387--394",
year = "2022",
DOI = "https://doi.org/10.1109/MCSoC57363.2022.00068",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sohn:2022:EFP,
author = "Jongwook Sohn and David K. Dean and Eric Quintana and
Wing Shek Wong",
title = "Enhanced Floating-Point Adder with Full Denormal
Support",
crossref = "IEEE:2022:ISC",
pages = "01--08",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00015",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Misc{Spiridonov:2022:ABE,
author = "Iouri Spiridonov",
title = "Arithmetic of binary equivalents of decimal numbers",
howpublished = "TechRxiv preprint.",
day = "23",
month = nov,
year = "2022",
DOI = "https://doi.org/10.36227/techrxiv.19294511.v4",
bibdate = "Fri Sep 29 14:24:39 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.techrxiv.org/articles/preprint/The_arithmetic_of_binary_equivalents_of_decimal_numbers/19294511",
abstract = "Within the framework of the concept of decimal
calculations proposed in the article using binary
arithmetic, a theory of binary equivalents of decimal
floating-point numbers has been developed. According to
this theory, basic decimal arithmetic operations on
finite decimal numbers are performed with decimal
precision by a binary processor according to the rules
of binary arithmetic on the binary equivalents of
decimal numbers. These calculation results are entirely
consistent with the classical decimal finite number
arithmetic and do not require the use of test programs.
The identity of calculation results in decimal and
binary equivalent arithmetics guarantees the
repeatability of results on any platform. The article
shows that implementing binary equivalents arithmetic
with an acceptable decimal calculation error requires
significantly fewer bits of binary processor registers
than in modern computers. Because of the uniqueness of
binary decimal equivalents, the difference between
equal, properly rounded binary decimal equivalents is
strictly zero. The presence of an explicit zero in the
arithmetic of binary equivalents of decimal numbers
makes it possible to implement a bitwise comparison of
such numbers and introduce the concept of an
infinitesimal number when the significand of a
floating-point number is equal to zero.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sravya:2022:HPN,
author = "Alapati Madhu Sravya and N. Swetha and Asisa Kumar
Panigrahy",
editor = "{IEEE}",
booktitle = "{2022 3rd International Conference for Emerging
Technology (INCET)}",
title = "Hardware Posit Numeration System primarily based on
Arithmetic Operations",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--8",
year = "2022",
DOI = "https://doi.org/10.1109/INCET54531.2022.9825011",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Srivastava:2022:FSC,
author = "Nitish Srivastava and Gai Liu and Yi-Hsiang Lai and
Zhiru Zhang",
booktitle = "Handbook of Computer Architecture",
title = "{FPGA}-Specific Compilers",
publisher = "Springer Nature",
address = "Singapore",
pages = "1--37",
year = "2022",
DOI = "https://doi.org/10.1007/978-981-15-6401-7_25-1",
ISBN = "981-15-6401-9",
ISBN-13 = "978-981-15-6401-7",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Book{Strickland:2022:LBI,
author = "Lloyd Strickland and Harry R. Lewis",
title = "{Leibniz} on Binary: The Invention of Computer
Arithmetic",
publisher = "MIT Press",
address = "Wheaton, MA, USA",
pages = "413",
year = "2022",
ISBN = "0-262-37212-6 (e-book), 0-262-54434-2",
ISBN-13 = "978-0-262-37212-1 (e-book), 978-0-262-54434-4",
LCCN = "QA141.4",
bibdate = "Fri Mar 17 08:38:41 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "Leibniz, Gottfried Wilhelm, Freiherr von; Translations
into English; Mathematics, German; Binary system
(Mathematics); History",
subject-dates = "1646--1716",
tableofcontents = "Intro \\
Title Page \\
Copyright Page \\
Dedication \\
Epigraph \\
Table of Contents \\
List of Figures \\
Abbreviations \\
Preface \\
Acknowledgments \\
Introduction \\
1. Notes on Algebra, Arithmetic, and Geometric Series
(October 1674) \\
2. The Series of All Numbers, and on Binary Progression
(before 15/25 March 1679) \\
3. Binary Progression (before 15/25 March 1679) \\
4. Geometric Progressions and Positional Notation
(before 15/25 March 1679) \\
5. Binary Arithmetic Machine (before 15/25 March 1679)
\\
6. On the Binary Progression (15/25 March 1679)7.
Attempted Expression of the Circle in Binary
Progression (c. 1679) \\
8. Sedecimal Progression (1679) \\
9. Binary Progression Is for Theory, Sedecimal for
Practice (c. 1679) \\
10. On the Organon or Great Art of Thinking (first half
[?] of 1679) \\
11. Binary Ancestral Calculations (early 1680s [?]) \\
12. Sedecimal on an Envelope (c. 1682--1685) \\
13. Remarks on Weigel (1694--mid-March 1695) \\
14. Leibniz to Duke Rudolph August (7/17--8/18 May
1696)15. A Wonderful Expression of All Numbers by 1 and
0 Representing the Origin of Things from God and
Nothing, or the Mystery of Creation (7/17 May 1696) \\
16. Wonderful Origin of All Numbers from 1 and 0, Which
Serves as a Beautiful Representation of the Mystery of
Creation, since Everything Arises from God and Nothing
Else (8/18 May 1696) \\
17. Leibniz to Duke Rudolph August (2/12 January 1697)
\\
18. Duke Rudolph August to Johann Urban M{\"u}ller
(5/15 January 1697) \\
19. Leibniz to Claudio Filippo Grimaldi
(mid-January-early February 1697) \\
20. Periods (May 1698--first half of January 1701)21.
Leibniz to Philippe Naud{\'e} (15 January 1701) \\
22. Leibniz to Joachim Bouvet (15 February 1701) \\
23. Essay on a New Science of Numbers (26 February
1701) \\
24. Binary Addition (spring-summer 1701 [?]) \\
25. Periods in Binary (spring-fall 1701) \\
26. Periods and Powers (mid-to-late June 1701 [?]) \\
27. Demonstration That Columns of Sequences Exhibiting
Powers of Arithmetic Progressions, or Numbers Composed
from These, Are Periodic (November 1701) \\
28. Joachim Bouvet to Leibniz (4 November 1701) \\
29. Leibniz to Bouvet (early April [?] 1703)30.
Explanation of Binary Arithmetic, Which Uses Only the
Digits 0 and 1, with Some Remarks on Its Usefulness,
and on the Light It Throws on the Ancient Chinese
Figures of Fuxi (7 April 1703) \\
31. Leibniz to C{\'e}sar Caze (23 June 1705) \\
32. On Binary (late June 1705) \\
Bibliography \\
Index",
}
@Article{Tan:2022:SRT,
author = "Bryan Tan and Benjamin Mariano and Shuvendu K. Lahiri
and Isil Dillig and Yu Feng",
title = "{SolType}: refinement types for arithmetic overflow in
{Solidity}",
journal = j-PACMPL,
volume = "6",
number = "POPL",
pages = "4:1--4:29",
month = jan,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1145/3498665",
ISSN = "2475-1421 (electronic)",
ISSN-L = "2475-1421",
bibdate = "Thu May 26 06:32:48 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
URL = "https://dl.acm.org/doi/10.1145/3498665",
abstract = "As smart contracts gain adoption in financial
transactions, it becomes increasingly important to
ensure that they are free of bugs and security
vulnerabilities. Of particular relevance in this
context are arithmetic overflow bugs, as integers are
often used to represent financial assets like account
balances. Motivated by this observation, this paper
presents SolType, a refinement type system for Solidity
that can be used to prevent arithmetic over- and
under-flows in smart contracts. SolType allows
developers to add refinement type annotations and uses
them to prove that arithmetic operations do not lead to
over- and under-flows. SolType incorporates a rich
vocabulary of refinement terms that allow expressing
relationships between integer values and aggregate
properties of complex data structures. Furthermore, our
implementation, called Solid, incorporates a type
inference engine and can automatically infer useful
type annotations, including non-trivial contract
invariants.\par
To evaluate the usefulness of our type system, we use
Solid to prove arithmetic safety of a total of 120
smart contracts. When used in its fully automated mode
(i.e., using Solid's type inference capabilities),
Solid is able to eliminate 86.3\% of redundant runtime
checks used to guard against overflows. We also compare
Solid against a state-of-the-art arithmetic safety
verifier called VeriSmart and show that Solid has a
significantly lower false positive rate, while being
significantly faster in terms of verification time.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "Proceedings of the ACM on Programming Languages
(PACMPL)",
journal-URL = "https://dl.acm.org/loi/pacmpl",
}
@InProceedings{Tortorella:2022:RCF,
author = "Yvan Tortorella and Luca Bertaccini and Davide Rossi
and Luca Benini and Francesco Conti",
editor = "{IEEE}",
booktitle = "{2022 Design, Automation \& Test in Europe Conference
\& Exhibition (DATE)}",
title = "{RedMulE}: a Compact {FP16} Matrix-Multiplication
Accelerator for Adaptive Deep Learning on
{RISC-V}-Based Ultra-Low-Power {SoCs}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1099--1102",
year = "2022",
DOI = "https://doi.org/10.23919/DATE54114.2022.9774759",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Verma:2022:RVC,
author = "Anu Verma and Priyamvada Sharma and Bishnu Prasad
Das",
editor = "{IEEE}",
booktitle = "{2022 25th Euromicro Conference on Digital System
Design (DSD)}",
title = "{RISC-V} Core with Approximate Multiplier for
Error-Tolerant Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "239--246",
year = "2022",
DOI = "https://doi.org/10.1109/DSD57027.2022.00040",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@Article{Walia:2022:FLP,
author = "Sumit Walia and Bachu Varun Tej and Arpita Kabra and
Joydeep Devnath and Joycee Mekie",
title = "Fast and Low-Power Quantized Fixed Posit High-Accuracy
{DNN} Implementation",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "30",
number = "1",
pages = "108--111",
year = "2022",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2021.3131609",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@Article{Wang:2022:PNE,
author = "Yang Wang and Dazheng Deng and Leibo Liu and Shaojun
Wei and Shouyi Yin",
title = "{PL-NPU}: an Energy-Efficient Edge-Device {DNN}
Training Processor With Posit-Based Logarithm-Domain
Computing",
journal = j-IEEE-TRANS-CIRCUITS-SYST-1,
volume = "69",
number = "10",
pages = "4042--4055",
year = "2022",
DOI = "https://doi.org/10.1109/TCSI.2022.3184115",
ISSN = "1549-8328 (print), 1558-0806 (electronic)",
ISSN-L = "1549-8328",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I: Regular
Papers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
}
@Article{Waris:2022:AAR,
author = "Haroon Waris and Chenghua Wang and Chenyu Xu and
Weiqiang Liu",
title = "{AxRMs}: Approximate Recursive Multipliers Using
High-Performance Building Blocks",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "2",
pages = "1229--1235",
month = apr # "\slash " # jun,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2021.3096515",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Waris:2022:HPP,
author = "Haroon Waris and Chenghua Wang and Weiqiang Liu and
Jie Han and Fabrizio Lombardi",
title = "Hybrid Partial Product-Based High-Performance
Approximate Recursive Multipliers",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "1",
pages = "507--513",
month = jan # "\slash " # mar,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2020.3013977",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Xie:2022:EHI,
author = "Jiafeng Xie and Pengzhou He and Xiaofang Wang and
Jos{\'e} L. Ima{\~n}a",
title = "Efficient Hardware Implementation of Finite Field
Arithmetic {$ A B + C A B + C $} for Binary Ring-{LWE}
Based Post-Quantum Cryptography",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "10",
number = "2",
pages = "1222--1228",
month = apr # "\slash " # jun,
year = "2022",
DOI = "https://doi.org/10.1109/TETC.2021.3091982",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{You:2022:RVP,
author = "Chao-Xing You and Qi-Tong Wang and Han Zhong and Cheng
Liu",
editor = "{IEEE}",
booktitle = "{2022 4th International Academic Exchange Conference
on Science and Technology Innovation (IAECST)}",
title = "{RISC-V} processor-based automatic access
floating-point computing accelerated dataflow
co-processor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "647--650",
year = "2022",
DOI = "https://doi.org/10.1109/IAECST57965.2022.10061878",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zacharelos:2022:ARM,
author = "Efstratios Zacharelos and Italo Nunziata and Gerardo
Saggese and Antonio G. M. Strollo and Ettore Napoli",
title = "Approximate Recursive Multipliers Using Low Power
Building Blocks",
crossref = "IEEE:2022:ISC",
pages = "67--67",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022.00020",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
}
@Article{Zhang:2022:HRD,
author = "Bo Zhang and Zeming Cheng and Massoud Pedram",
title = "High-Radix Design of a Scalable {Montgomery} Modular
Multiplier With Low Latency",
journal = j-IEEE-TRANS-COMPUT,
volume = "71",
number = "2",
pages = "436--449",
month = feb,
year = "2022",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2021.3052999",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Jan 20 07:18:16 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Zhang:2022:SDF,
author = "Yi Zhang and Mengdi Sun and Xin Qi",
title = "Speedup of discrete {Fourier} transform by efficient
modular arithmetic",
journal = j-CCPE,
volume = "34",
number = "3",
pages = "e6564:1--e6564:??",
day = "1",
month = feb,
year = "2022",
CODEN = "CCPEBO",
DOI = "https://doi.org/10.1002/cpe.6564",
ISSN = "1532-0626 (print), 1532-0634 (electronic)",
ISSN-L = "1532-0626",
bibdate = "Tue Feb 22 09:50:06 MST 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Concurr. Comput.",
fjournal = "Concurrency and Computation: Practice and Experience",
journal-URL = "http://www.interscience.wiley.com/jpages/1532-0626",
onlinedate = "15 September 2021",
}
@Article{Zolfagharinejad:2022:PPE,
author = "Mohamadreza Zolfagharinejad and Mehdi Kamal and Ali
Afzali-Khusha and Massoud Pedram",
title = "Posit Process Element for Using in Energy-Efficient
{DNN} Accelerators",
journal = j-IEEE-TRANS-VLSI-SYST,
volume = "30",
number = "6",
pages = "844--848",
year = "2022",
CODEN = "IEVSE9",
DOI = "https://doi.org/10.1109/TVLSI.2022.3165510",
ISSN = "1063-8210 (print), 1557-9999 (electronic)",
ISSN-L = "1063-8210",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Very Large Scale Integration
(VLSI) Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}
@Article{Zou:2022:OFR,
author = "Daming Zou and Yuchen Gu and Yuanfeng Shi and MingZhe
Wang and Yingfei Xiong and Zhendong Su",
title = "Oracle-free repair synthesis for floating-point
programs",
journal = j-PACMPL,
volume = "6",
number = "OOPSLA2",
pages = "159:1--159:??",
month = oct,
year = "2022",
CODEN = "????",
DOI = "https://doi.org/10.1145/3563322",
ISSN = "2475-1421 (electronic)",
ISSN-L = "2475-1421",
bibdate = "Sat Mar 11 09:08:36 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
URL = "https://dl.acm.org/doi/10.1145/3563322",
abstract = "The floating-point representation provides widely-used
data types (such as ``float'' and ``double'') for
modern numerical software. Numerical errors are
inherent due to floating-point's approximate nature,
and pose an important, well-known challenge. It is
nontrivial to fix/repair numerical code to reduce
numerical errors --- it requires either numerical
expertise (for manual fixing) or high-precision oracles
(for automatic repair); both are difficult
requirements. To tackle this challenge, this paper
introduces a principled dynamic approach that is fully
automated and oracle-free for effectively repairing
floating-point errors. The key of our approach is the
novel notion of micro-structure that characterizes
structural patterns of floating-point errors. We
leverage micro-structures' statistical information on
floating-point errors to effectively guide repair
synthesis and validation. Compared with existing
state-of-the-art repair approaches, our work is fully
automatic and has the distinctive benefit of not
relying on the difficult to obtain high-precision
oracles. Evaluation results on 36 commonly-used
numerical programs show that our approach is highly
efficient and effective: (1) it is able to synthesize
repairs instantaneously, and (2) versus the original
programs, the repaired programs have orders of
magnitude smaller floating-point errors, while having
faster runtime performance",
acknowledgement = ack-nhfb,
articleno = "159",
fjournal = "Proceedings of the ACM on Programming Languages
(PACMPL)",
journal-URL = "https://dl.acm.org/loi/pacmpl",
}
@Article{Abad:2023:HAT,
author = "Sudeh Shirkavand Saleh Abad and Mohammad Hossein
Moaiyeri",
title = "Hardware-accuracy trade-offs for error-resilient
applications using an ultra-efficient hybrid
approximate multiplier",
journal = j-J-SUPERCOMPUTING,
volume = "79",
number = "3",
pages = "3357--3372",
month = feb,
year = "2023",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-022-04789-6",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Sat Feb 18 09:20:28 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-022-04789-6",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Abdi:2023:FEF,
author = "Athena Abdi and Sina Shahoveisi",
title = "{FT-EALU}: fault-tolerant arithmetic and logic unit
for critical embedded and real-time systems",
journal = j-J-SUPERCOMPUTING,
volume = "79",
number = "1",
pages = "626--649",
month = jan,
year = "2023",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-022-04698-8",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Sat Feb 18 09:20:27 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-022-04698-8",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@InProceedings{Adela:2023:DIS,
author = "Noor Alhuda Saad Adela and Amani Najeeb {Ben Yousuf}
and Mohamed Muftah Eljhani",
booktitle = "{2023 IEEE 3rd International Maghreb Meeting of the
Conference on Sciences and Techniques of Automatic
Control and Computer Engineering (MI-STA)}",
title = "Design and Implementation of Single Precision
Floating-point Arithmetic Logic Unit for {RISC}
Processor on {FPGA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "130--134",
month = may,
year = "2023",
DOI = "https://doi.org/10.1109/mi-sta57575.2023.10169623",
bibdate = "Thu Dec 7 11:55:39 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Alapati:2023:HIP,
author = "Madhu Sravya Alapati and Raghunandan Swain and Asisa
Kumar Panigrahy",
editor = "{IEEE}",
booktitle = "{2023 7th International Conference on Trends in
Electronics and Informatics (ICOEI)}",
title = "Hardware Implementation of Posit Numeration System
using {FPGA} for Signal Processing Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "278--282",
year = "2023",
DOI = "https://doi.org/10.1109/ICOEI56765.2023.10125920",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Allred:2023:FNT,
author = "Taylor Allred and Xinyi Li and Ashton Wiersdorf and
Ben Greenman and Ganesh Gopalakrishnan",
editor = "????",
booktitle = "Julia Conference 2023",
title = "{FlowFPX}: Nimble Tools for Debugging Floating-Point
Exceptions",
publisher = "????",
address = "????",
pages = "8",
year = "2023",
bibdate = "Mon Sep 11 06:29:11 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/julia.bib",
URL = "https://live.juliacon.org/talk/A3LVDS",
abstract = "Reliable numerical computations are central to
scientific computing, but the floating-point arithmetic
that enables large-scale models is error-prone. Numeric
exceptions are a common occurrence and can propagate
through code, leading to flawed results. This paper
presents FlowFPX, a toolkit for systematically
debugging floating-point exceptions by recording their
flow, coalescing exception contexts, and fuzzing in
select locations. These tools help scientists discover
when exceptions happen and track down their origin,
smoothing the way to a reliable codebase.",
acknowledgement = ack-nhfb,
keywords = "Julia programming language",
}
@Article{Andrlon:2023:FNB,
author = "Mak Andrlon",
title = "Finding Normal Binary Floating-Point Factors
Efficiently",
journal = j-J-AUTOM-REASON,
volume = "67",
number = "1",
pages = "??--??",
month = mar,
year = "2023",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-023-09659-1",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Mon Nov 27 10:20:09 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "https://link.springer.com/article/10.1007/s10817-023-09659-1",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
articleno = "11",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
}
@Misc{Anonymous:2023:IWG,
author = "Anonymous",
title = "{IEEE Working Group P3109} Interim Report on 8-bit
Binary Floating-Point Formats",
howpublished = "IEEE Web document.",
pages = "18",
day = "18",
month = sep,
year = "2023",
bibdate = "Thu Nov 30 05:10:41 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Version 0.5.1: 24 November 2023.",
URL = "https://github.com/P3109/Public/blob/main/Shared%20Reports/P3109%20WG%20Interim%20report.pdf",
acknowledgement = ack-nhfb,
remark = "The draft specifies encodings of unsigned zero,
+/-Infinity, and quiet NaN, with precision 3, 4, and 5
bits (including the implicit not-stored leading bit),
and subnormals.",
}
@TechReport{Anonymous:2023:TDT,
author = "Anonymous",
title = "{Tesla Dojo Technology}: a guide to {Tesla}'s
configurable floating point formats and arithmetic:
{Tesla Configurable Float8 (CFloat8) \& Float16
(CFloat16)} Formats",
type = "Report",
institution = "Tesla. Inc.",
pages = "9",
year = "2023",
bibdate = "Thu Nov 30 05:53:41 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://tesla-cdn.thron.com/static/MXMU3S_tesla-dojo-technology_1WDVZN.pdf",
abstract = "This standard specifies Tesla arithmetic formats and
methods for the new 8-bit and 16-bit binary
floating-point arithmetic in computer programming
environments for deep learning neural network training.
This standard also specifies exception conditions and
the status flags thereof. An implementation of a
floating-point system conforming to this standard may
be realized entirely in software, entirely in hardware,
or in any combination of software and hardware",
acknowledgement = ack-nhfb,
}
@Misc{ARM:2023:ACA,
author = "{ARM Corporation}",
title = "{ARM} Compiler {ARM C} and {C++} Libraries and
Floating-Point Support User Guide Version 6.00",
howpublished = "Web site",
year = "2023",
bibdate = "Fri Dec 01 12:34:49 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://developer.arm.com/documentation/dui0808/a/floating-point-support/exception-types-recognized-by-the-arm-floating-point-environment",
acknowledgement = ack-nhfb,
}
@Article{Awais:2023:TOS,
author = "Muhammad Awais and Ali Zahir and Syed Ayaz Ali Shah
and Pedro Reviriego and Anees Ullah and Nasim Ullah and
Adam Khan and Hazrat Ali",
title = "Toward Optimal Softcore Carry-aware Approximate
Multipliers on {Xilinx} {FPGAs}",
journal = j-TECS,
volume = "22",
number = "4",
pages = "76:1--76:??",
month = jul,
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.1145/3564243",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Aug 10 07:21:24 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
URL = "https://dl.acm.org/doi/10.1145/3564243",
abstract = "Domain-specific accelerators for signal processing,
image processing, and machine learning are increasingly
being implemented on SRAM-based field-programmable gate
arrays (FPGAs). Owing to the inherent error tolerance
of such applications, approximate arithmetic
operations, in particular, the design of approximate
multipliers, have become an important research problem.
Truncation of lower bits is a widely used approximation
approach; however, analyzing and limiting the effects
of carry-propagation due to this approximation has not
been explored in detail yet. In this article, an
optimized carry-aware approximate radix-4 Booth
multiplier design is presented that leverages the
built-in slice look-up tables (LUTs) and carry-chain
resources in a novel configuration. The proposed
multiplier simplifies the computation of the upper and
lower bits and provides significant benefits in terms
of FPGA resource usage (LUTs saving 38.5\%--42.9\%),
Power Delay Product (PDP saving 49.4\%--53\%),
performance metric (LUTs $ \times $ critical path delay
(CPD) $ \times $ PDP saving 68.9\%--73.1\%) and errors
(70\% improvement in mean relative error distance)
compared to the latest state-of-the-art designs.
Therefore, the proposed designs are an attractive
choice to implement multiplication on FPGA-based
accelerators.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Embed. Comput. Syst.",
articleno = "76",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "https://dl.acm.org/loi/tecs",
}
@InProceedings{Badizadegan:2023:NRI,
author = "Nima Badizadegan",
title = "{Newton--Raphson} Integer Division for
Area-Constrained Microcontrollers",
crossref = "IEEE:2023:PIS",
pages = "9--15",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00024",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; Approximation methods;
ARITH-30; Costs; Digital arithmetic; Division;
Hardware; Integer Division; Iterative algorithms; Logic
gates; Microarchitecture; Microcontrollers; Newton
Raphson division; Newton Raphson method",
}
@Article{Bahoo:2023:EEG,
author = "Ali Akbar Bahoo and Omid Akbari and Muhammad
Shafique",
title = "An Energy-Efficient Generic Accuracy Configurable
Multiplier Based on Block-Level Voltage Overscaling",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "11",
number = "4",
pages = "851--867",
month = oct # "\slash " # dec,
year = "2023",
DOI = "https://doi.org/10.1109/TETC.2023.3279419",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Fri Apr 12 08:11:23 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
keywords = "Adders; Aging; Approximate computing; Complexity
theory; Energy efficiency; energy efficiency;
multiplier; Voltage; Voltage control; voltage
overscaling",
}
@Article{Bartels:2023:FFP,
author = "Tinko Bartels and Vissarion Fisikopoulos and Martin
Weiser",
title = "Fast floating-point filters for robust predicates",
journal = j-BIT-NUM-MATH,
volume = "63",
number = "2",
pages = "??--??",
month = jun,
year = "2023",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-023-00975-x",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Thu Aug 10 14:23:15 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://link.springer.com/article/10.1007/s10543-023-00975-x",
abstract = "Geometric predicates are at the core of many
algorithms, such as the construction of Delaunay
triangulations, mesh processing and spatial relation
tests. These algorithms have applications in scientific
computing, geographic information systems and
computer-aided design. With floating-point arithmetic,
these geometric predicates can incur round-off errors
that may lead to incorrect results and inconsistencies,
causing computations to fail. This issue has been
addressed using a combination of exact arithmetic for
robustness and floating-point filters to mitigate the
computational cost of exact computations. The
implementation of exact computations and floating-point
filters can be a difficult task, and code generation
tools have been proposed to address this. We present a
new C++ meta-programming framework for the generation
of fast, robust predicates for arbitrary geometric
predicates based on polynomial expressions. We combine
and extend different approaches to filtering, branch
reduction, and overflow avoidance that have previously
been proposed. We show examples of how this approach
produces correct results for data sets that could lead
to incorrect predicate results with naive
implementations. Our benchmark results demonstrate that
our implementation surpasses state-of-the-art
implementations.",
acknowledgement = ack-nhfb,
ajournal = "Bit Num. Math.",
articleno = "31",
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "correct rounding; exact computation; floating-point
arithmetic; rounding errors",
}
@InProceedings{Bavier:2023:VNF,
author = "Eric Bavier and Nicholas Knight and Hugues de Lassus
Saint-Geni{\`e}s and Eric Love",
title = "Vectorized Nonlinear Functions with the {RISC-V}
Vector Extension",
crossref = "IEEE:2023:PIS",
pages = "127--130",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00032",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; floating point; Instruction sets; Libraries;
Pipelines; RISC-V vectors; scalable vectors; Software;
Software algorithms; vector mathematical functions;
Vectors; Writing",
}
@Article{Belorgey:2023:MFE,
author = "Mariya Georgieva Belorgey and Sergiu Carpov and Kevin
Deforth and Dimitar Jetchev and Abson Sae-Tang and
Marius Vuille and Nicolas Gama and Jon Katz and Iraklis
Leontiadis and Mohsen Mohammadi",
title = "{Manticore}: A Framework for Efficient Multiparty
Computation Supporting Real Number and {Boolean}
Arithmetic",
journal = j-J-CRYPTOLOGY,
volume = "36",
number = "3",
pages = "??--??",
month = jul,
year = "2023",
CODEN = "JOCREQ",
DOI = "https://doi.org/10.1007/s00145-023-09464-4",
ISSN = "0933-2790 (print), 1432-1378 (electronic)",
ISSN-L = "0933-2790",
bibdate = "Tue Aug 1 08:28:21 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptology.bib",
URL = "https://link.springer.com/article/10.1007/s00145-023-09464-4",
acknowledgement = ack-nhfb,
ajournal = "J. Cryptology",
articleno = "31",
fjournal = "Journal of Cryptology",
journal-URL = "http://link.springer.com/journal/145",
}
@InProceedings{Beutel:2023:PFA,
author = "Moritz Beutel and Robert Strzodka",
title = "A Paradigm for Interval-Aware Programming",
crossref = "Gustafson:2023:NGA",
pages = "38--60",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_3",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Blanchard:2023:NMD,
author = "Jeffrey D. Blanchard and Marc Chamberland",
title = "{Newton}'s Method Without Division",
journal = j-AMER-MATH-MONTHLY,
volume = "130",
number = "7",
pages = "606--617",
year = "2023",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.1080/00029890.2022.2093573",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Fri Aug 25 08:24:37 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html;
https://www.tandfonline.com/loi/uamm20",
onlinedate = "04 Aug 2023",
}
@Article{Boldo:2023:FPA,
author = "Sylvie Boldo and Claude-Pierre Jeannerod and Guillaume
Melquiond and Jean-Michel Muller",
title = "Floating-point arithmetic",
journal = j-ACTA-NUMERICA,
volume = "32",
pages = "203--290",
month = may,
year = "2023",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492922000101",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
bibdate = "Sat May 13 08:10:16 MDT 2023",
bibsource = "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=32&issueId=00;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.cambridge.org/core/journals/acta-numerica/article/floatingpoint-arithmetic/287C4D5F6D4A43FBEEB1ABED2A405AAF",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "11 May 2023",
}
@Article{Bommana:2023:DST,
author = "Ashish Reddy Bommana and Susheel Ujwal Siddamshetty
and Dhilleswararao Pudi and Arvind Thumatti K. R. and
Srinivas Boppu and M. Sabarimalai Manikandan and Linga
Reddy Cenkeramaddi",
title = "Design of Synthesis-time Vectorized Arithmetic
Hardware for Tapered Floating-point Addition and
Subtraction",
journal = j-TODAES,
volume = "28",
number = "3",
pages = "32:1--32:??",
month = may,
year = "2023",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/3567423",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Wed May 17 08:06:20 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/todaes.bib",
URL = "https://dl.acm.org/doi/10.1145/3567423",
abstract = "Energy efficiency has become the new performance
criterion in this era of pervasive embedded computing;
thus, accelerator-rich multi-processor system-on-chips
are commonly used in embedded computing hardware. Once
computationally intensive machine learning applications
gained much traction, they are now deployed in many
application domains due to abundant and cheaply
available computational capacity. In addition, there is
a growing trend toward developing hardware accelerators
for machine learning applications for embedded edge
devices where performance and energy efficiency are
critical. Although these hardware accelerators
frequently use floating-point operations for accuracy,
reduced-width floating-point formats are also used to
reduce hardware complexity; thus, power consumption
while maintaining accuracy. Vectorization concepts can
also be used to improve performance, energy efficiency,
and memory bandwidth. We propose the design of a
vectorized floating-point adder/subtractor that
supports arbitrary length floating-point formats with
varying exponent and mantissa widths in this article.
In comparison to existing designs in the literature,
the proposed design is 2.57$ \times $ area- and 1.56$
\times $ power-efficient, and it supports true
vectorization with no restrictions on exponent and
mantissa widths.",
acknowledgement = ack-nhfb,
articleno = "32",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems",
journal-URL = "https://dl.acm.org/loi/todaes",
}
@Article{Bottcher:2023:TGO,
author = "Andreas B{\"o}ttcher and Martin Kumm",
title = "Towards Globally Optimal Design of Multipliers for
{FPGAs}",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "5",
pages = "1261--1273",
month = may,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2023.3238128",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Apr 28 11:15:52 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Brisebarre:2023:EUMa,
author = "Nicolas Brisebarre and Jean-Michel Muller and Joris
Picot",
title = "Error in ulps of the multiplication or division by a
correctly-rounded function or constant in binary
floating-point arithmetic",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "??",
number = "??",
pages = "1--11",
year = "2023",
DOI = "https://doi.org/10.1109/TETC.2023.3294986",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Fri Sep 29 10:36:37 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
abstract = "Assume we use a binary floating-point arithmetic and
that RN is the round-to-nearest function. Also assume
that c is a constant or a real function of one or more
variables, and that we have at our disposal a correctly
rounded implementation of c, say c' = RN(c) . For
evaluating xc(resp.x / corc / x), the natural way is to
replace it by RN(x.c') (resp.RN(x / c') or RN(c' / x)),
that is, to call function c' and to perform a
floating-point multiplication or division. This can be
generalized to the approximation of n / d by RN(n' /
d') and the approximation of n d by RN(n'.d'), where n'
= RN(n) and d' = RN(d), and n and d are functions for
which we have at our disposal a correctly rounded
implementation. We discuss tight error bounds in ulps
of such approximations. From our results, one
immediately obtains tight error bounds for calculations
such as x * pi, ln(2) / x, x / (y + z), (x + y) * z, x
/ sqrt(y), sqrt(x) / y, (x + y)(z + t), (x + y) / (z +
t), (x + y) / (zt), etc. in floating-point
arithmetic.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
remark = "Early access: not yet published [29-Sep-2023].",
}
@InProceedings{Brisebarre:2023:EUMb,
author = "Nicolas Brisebarre and Jean-Michel Muller and Joris
Picot",
title = "Error in ulps of the multiplication or division by a
correctly-rounded function or constant in binary
floating-point arithmetic",
crossref = "IEEE:2023:PIS",
pages = "88--88",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00036",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in ``IEEE Transactions on Emerging Topics in
Computing, Volume: {\bf 11}, Issue: 4, 01
October--December 2023'' and orally presented at ARITH
2023.",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Digital arithmetic; Floating-point
arithmetic",
}
@TechReport{Brisebarre:2023:IPC,
author = "Nicolas Brisebarre and Guillaume Hanrot",
title = "Integer points close to a transcendental curve and
correctly-rounded evaluation of a function",
type = "Preprint",
institution = "LIP --- Laboratoire de l'Informatique du
Parall{\'e}lisme",
address = "Lyon, France",
pages = "66",
year = "2023",
bibdate = "Fri Dec 08 10:07:21 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.science/hal-03240179v4/file/tmd-hal-V4.pdf",
abstract = "Despite several significant advances over the last 30
years, guaranteeing the correctly rounded evaluation of
elementary functions, such as $ \sqrt {} $, $ \cos $, $
\exp $, $ \sqrt [3]{} $ for instance, is still a
difficult issue. This can be formulated as a
Diophantine approximation problem, called the Table
Maker's Dilemma, which reduces to determining points
with integer coordinates that are close to a curve. In
this article, we propose two algorithmic approaches to
tackle this problem, closely related to a celebrated
work by Bombieri and Pila and to the so-called
Coppersmith's method. We establish the underlying
theoretical foundations, prove the algorithms, study
their complexity and present practical experiments; we
also compare our approach with previously existing
ones. In particular, our results show that the
development of a correctly rounded mathematical library
for the binary128 format is now possible at a much
smaller cost than with previously existing approaches",
acknowledgement = ack-nhfb,
keywords = "correct rounding; floating-point arithmetic",
}
@InProceedings{Brisebarre:2023:TME,
author = "Nicolas Brisebarre and Silviu-Ioan Filip",
title = "Towards Machine-Efficient Rational {$ L^\infty
$}-Approximations of Mathematical Functions",
crossref = "IEEE:2023:PIS",
pages = "119--126",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00029",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Approximation algorithms; ARITH-30; Behavioral
sciences; Digital arithmetic; Software",
}
@InProceedings{Brisebarre:2023:TSK,
author = "Nicolas Brisebarre and Jean-Michel Muller and Joris
Picot",
title = "Testing the Sharpness of Known Error Bounds on the
{Fast Fourier Transform}",
crossref = "IEEE:2023:PIS",
pages = "89--92",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00027",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Digital arithmetic; Error analysis; Fast
Fourier Transform (FFT); Fast Fourier transforms;
Floating-point arithmetic; Floating-Point arithmetic;
Libraries; Testing",
}
@InProceedings{Brthel:2023:FTI,
author = "Moritz B{\"a}rthel and Chen Yuxing and Nils
H{\"u}lsmeier and Jochen Rust and Steffen Paul",
title = "Fused Three-Input {SORN} Arithmetic",
crossref = "Gustafson:2023:NGA",
pages = "101--113",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_7",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Bruguera:2023:RFP,
author = "Javier D. Bruguera",
title = "Radix-64 Floating-Point Division and Square Root:
Iterative and Pipelined Units",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "10",
pages = "2990--3001",
month = oct,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2023.3280136",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Sep 14 07:25:14 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
abstract = "Digit-recurrence algorithms are widely used in actual
microprocessors to compute floating-point division and
square root. These iterative algorithms present a good
trade-off in terms of performance, area and power.
Traditionally, commercial processors have iterative
division and square root units where the iteration
logic is used over several cycles. The main drawbacks
of these iterative units are long latency and low
throughput due to the reuse of part of the logic over
several cycles, and its hardware complexity with
separated logic for division and square root. We
present a radix-64 floating-point division and square
root algorithm with a common iteration for division and
square root and where, to have an affordable
implementation, each radix-64 iteration is made of two
simpler radix-8 iterations. The radix-64 algorithm
allows to get low-latency operations, and the common
division and square root radix-64 iteration results in
some area reduction. The algorithm is mapped into two
different microarchitectures: a low-latency and low
area iterative unit, and a low-latency and
high-throughput pipelined unit. In both units
speculation between consecutive radix-8 iterations is
used to reduce the timing.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Buckle:2023:HEY,
author = "David Buckle",
title = "How the estimate of $ \sqrt {2} $ on {YBC 7289} may
have been calculated",
journal = j-HIST-MATH,
volume = "62",
number = "??",
pages = "3--18",
month = feb,
year = "2023",
CODEN = "HIMADS",
DOI = "https://doi.org/10.1016/j.hm.2022.08.002",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Mar 15 09:40:56 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086022000477",
abstract = "It remains unknown how the approximation of $ \sqrt
{2} $ scribed on Babylonian tablet YBC 7289 was
calculated. In this article I show how it can be
straightforwardly computed using a well-known regular
number as the input for the Babylonian method of
estimating square roots. My objective is to demonstrate
that Babylonian mathematics was sufficiently evolved
for the approximation to be easily derived and thus
propose an approach that may have been used to
calculate it.",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860",
keywords = "Babylonian tablet YBC 7289",
}
@Article{Chen:2023:TLM,
author = "Benjamin Chen and Yu Li and Eugene Zima",
title = "On a Two-Layer Modular Arithmetic",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "57",
number = "3",
pages = "133--136",
month = sep,
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.1145/3637529.3637534",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Thu Dec 14 15:54:00 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
URL = "https://dl.acm.org/doi/10.1145/3637529.3637534",
abstract = "Two-layer organization of modular arithmetic is
considered. Lower layer uses many moduli at hardware
precision and simultaneous conversion to/from RNS as
described in [2]. Upper layer uses specially selected
large moduli allowing for fast reduction and\slash or
reconstruction. Implementation of two different
strategies for selecting moduli on the upper layer
confirms practicality of proposed approach.",
acknowledgement = ack-nhfb,
ajournal = "ACM Commun. Computer Algebr.",
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "https://dl.acm.org/loi/sigsam-cca",
}
@InProceedings{Crespo:2023:TPP,
author = "Lu{\'\i}s Crespo and Pedro Tom{\'a}s and Nuno Roma and
Nuno Neves",
editor = "{IEEE}",
booktitle = "{2023 IEEE 35th International Symposium on Computer
Architecture and High Performance Computing
(SBAC-PAD)}",
title = "Trading Performance, Power, and Area on Low-Precision
Posit {MAC} Units for {CNN} Training",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "46--56",
year = "2023",
DOI = "https://doi.org/10.1109/SBAC-PAD59825.2023.00014",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{deDinechin:2023:ASA,
author = "Florent de Dinechin and Martin Kumm",
title = "Application-specific Arithmetic: Computing Just Right
for the Reconfigurable Computer and the Dark Silicon
Era",
publisher = pub-SV,
address = pub-SV:adr,
pages = "????",
year = "2023",
ISBN = "3-031-42807-2",
ISBN-13 = "978-3-031-42807-4",
LCCN = "????",
bibdate = "Fri Dec 8 13:09:29 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://link.springer.com/book/10.1007/978-3-031-42807-4",
acknowledgement = ack-nhfb,
remark = "TO DO: URL not yet resolvable, and DOI unknown.",
}
@InProceedings{Defour:2023:CAN,
author = "David Defour and Franck Vedrine",
title = "Chromatic Analysis of Numerical Programs",
crossref = "IEEE:2023:PIS",
pages = "97--100",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00012",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Additives; ARITH-30; Artificial neural networks;
automatic differentiation; Digital arithmetic; Error
analysis; IEEE-754; rounding error analysis;
sensitivity analysis; Sensitivity analysis",
}
@InProceedings{deLamarliere:2023:SFP,
author = "Paul Geneau de Lamarli{\`e}re and Guillaume Melquiond
and Florian Faissole",
title = "Slimmer Formal Proofs for Mathematical Libraries",
crossref = "IEEE:2023:PIS",
pages = "32--35",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00026",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Behavioral sciences; Codes; Coq proof
assistant; Costs; Digital arithmetic; Floating-point
arithmetic; Formal methods; Libraries; Mathematical
libraries; Writing",
}
@InProceedings{Desrentes:2023:EFD,
author = "Or{\'e}gane Desrentes and Beno{\^\i}t Dupont de
Dinechin and Florent de Dinechin",
title = "Exact Fused Dot Product Add Operators",
crossref = "IEEE:2023:PIS",
pages = "151--158",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00016",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; BF16; Computer architecture; Digital
arithmetic; dot product; FP32; FP64; Heuristic
algorithms; High dynamic range; Low latency
communication; three-term sum",
}
@Article{Eckert:2023:EMM,
author = "Charles Eckert and Arun Subramaniyan and Xiaowei Wang
and Charles Augustine and Ravishankar Iyer and
Reetuparna Das",
title = "{Eidetic}: an In-Memory Matrix Multiplication
Accelerator for Neural Networks",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "6",
pages = "1539--1553",
month = jun,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2022.3214151",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed May 17 10:34:15 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
abstract = "This paper presents the Eidetic architecture, which is
an SRAM-based ASIC neural network accelerator that
eliminates the need to continuously load weights from
off-chip, while also minimizing the need to go off chip
for intermediate results. Using in-situ arithmetic in
the SRAM arrays, this architecture can supports a
variety of precision types allowing for effective
inference. We also present different data mapping
policies for matrix-vector based networks (RNN and MLP)
on the Eidetic architecture and describe the tradeoffs
involved. With this architecture, multiple layers of a
network can be concurrently mapped, storing both the
layer weights and intermediate results on-chip,
removing the energy and latency penalty of off-chip
memory accesses. We evaluate Eidetic on Google's Neural
Machine Translation System (GNMT) encoder and
demonstrate a 17.20$ \times $ increase in throughput
and 7.77$ \times $ reduction in average latency over a
single TPUv2 chip.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Edamatsu:2023:FMP,
author = "Takuya Edamatsu and Daisuke Takahashi",
title = "Fast Multiple-Precision Integer Division Using {Intel
AVX-512}",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "11",
number = "1",
pages = "224--236",
month = jan # "\slash " # mar,
year = "2023",
DOI = "https://doi.org/10.1109/TETC.2022.3196147",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
abstract = "This paper reports on the implementation of a large
integer division method that uses Intel Advanced Vector
Extensions 512 (AVX-512), which is a 512-bit Single
Instruction Multiple Data (SIMD) instruction set, and
proposes a modification to a conventional division
algorithm that makes it more SIMD instruction-friendly.
More specifically, we use the Integer Fused
Multiply-Add AVX-512 (AVX-512IFMA) subset, which is an
instruction set that works well with large integer
multiplication, to compute large integer divisions via
a multiplication-based approach with a reciprocal. For
the division process, we apply the most basic algorithm
and divide-and-conquer methods and then use several
techniques to compute efficiently with SIMD
instructions in our implementation. We then combine
these techniques and methods to implement our division
function so that it can flexibly handle various sizes.
To evaluate the performance of our proposed
implementation, we executed our division program and
the GNU Multiple Precision Arithmetic Library (GMP) on
a Cannon Lake microarchitecture processor. A comparison
of the execution times for our division program and GMP
with various sizes showed that our method resulted in
performance improvements of 25\% to 35\% on average,
thus indicating that SIMD instructions are effective
for fast arbitrary precision integer divisions.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Edavoor:2023:DAP,
author = "Pranose J Edavoor and Aneesh Raveendran and David
Selvakumar and Vivian Desalphine and Dharani Shankar G
and Gopal Raut",
editor = "{IEEE}",
booktitle = "{2023 36th International Conference on VLSI Design and
2023 22nd International Conference on Embedded Systems
(VLSID)}",
title = "Design and Analysis of Posit Quire Processing Engine
for Neural Network Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "252--257",
year = "2023",
DOI = "https://doi.org/10.1109/VLSID57277.2023.00059",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{ElArar:2023:SRV,
author = "El-Mehdi {El Arar} and Devan Sohier and Pablo de
Oliveira Castro and Eric Petit",
title = "Stochastic Rounding Variance and Probabilistic Bounds:
a New Approach",
journal = j-SIAM-J-SCI-COMP,
volume = "45",
number = "5",
pages = "C255--C275",
month = oct,
year = "2023",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/22m1510819",
ISSN = "1095-7197",
ISSN-L = "1064-8275",
bibdate = "Thu May 30 10:22:20 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "error bounds; floating-point rounding; random
rounding; stochastic rounding",
}
@InProceedings{Fakhreddine:2023:ULT,
author = "Youssef Fakhreddine and Guillaume Revy",
title = "Using loop transformations for precision tuning in
iterative programs",
crossref = "IEEE:2023:PIS",
pages = "159--166",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00031",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; delta-debugging algorithm; Digital
arithmetic; dynamic precision tuning tool;
floating-point arithmetic; Instruction sets; Iterative
methods; loop splitting and unrolling; mixed-precision;
multiple-precision; Runtime; Tuning",
}
@Article{Fasi:2023:CCL,
author = "Massimiliano Fasi and Mantas Mikaitis",
title = "{CPFloat}: a {C} Library for Simulating Low-precision
Arithmetic",
journal = j-TOMS,
volume = "49",
number = "2",
pages = "18:1--18:??",
month = jun,
year = "2023",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3585515",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Jun 29 07:01:00 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3585515",
abstract = "One can simulate low-precision floating-point
arithmetic via software by executing each arithmetic
operation in hardware and then rounding the result to
the desired number of significant bits. For
IEEE-compliant formats, rounding requires only standard
mathematical library functions, but handling
subnormals, underflow, and overflow demands special
attention, and numerical errors can cause
mathematically correct formulae to behave incorrectly
in finite arithmetic. Moreover, the ensuing
implementations are not necessarily efficient, as the
library functions these techniques build upon are
typically designed to handle a broad range of cases and
may not be optimized for the specific needs of rounding
algorithms. CPFloat is a C library for simulating
low-precision arithmetics. It offers efficient routines
for rounding, performing mathematical computations, and
querying properties of the simulated low-precision
format. The software exploits the bit-level
floating-point representation of the format in which
the numbers are stored and replaces costly library
calls with low-level bit manipulations and integer
arithmetic. In numerical experiments, the new
techniques bring a considerable speedup (typically one
order of magnitude or more) over existing alternatives
in C, C++, and MATLAB. To our knowledge, CPFloat is
currently the most efficient and complete library for
experimenting with custom low-precision floating-point
arithmetic.",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@InProceedings{Filippas:2023:RPF,
author = "Dionysios Filippas and Christodoulos Peltekis and
Giorgos Dimitrakopoulos and Chrysostomos Nicopoulos",
booktitle = "2023 {IEEE 5th International Conference on Artificial
Intelligence Circuits and Systems (AICAS)}",
title = "Reduced-Precision Floating-Point Arithmetic in
Systolic Arrays with Skewed Pipelines",
publisher = pub-IEEE,
address = pub-IEEE:adr,
month = jun,
year = "2023",
DOI = "https://doi.org/10.1109/aicas57966.2023.10168556",
bibdate = "Thu Dec 7 11:54:15 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
pagecount = "5",
}
@InProceedings{Flatt:2023:MIA,
author = "Oliver Flatt and Pavel Panchekha",
title = "Making Interval Arithmetic Robust to Overflow",
crossref = "IEEE:2023:PIS",
pages = "44--47",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00022",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; computable reals; Digital arithmetic;
Interval arithmetic; Libraries; Mathematics computing;
multiple precision arithmetic; overflow",
}
@TechReport{Fog:2023:FPE,
author = "Agner Fog",
title = "Floating point exception tracking and {NAN}
propagation",
type = "Report",
institution = "Technical University of Denmark",
address = "Lyngby, Denmark",
pages = "10",
day = "27",
month = apr,
year = "2023",
bibdate = "Tue May 09 08:55:38 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.agner.org/optimize/nan_propagation.pdf",
abstract = "The most common methods for detecting floating point
errors are based on exception trapping or a global
status register. These methods are inefficient in
modern systems that use out-of-order parallelism and
single-instruction-multiple-data (SIMD) parallelism for
improving performance. It is argued that a method based
on NAN propagation is more efficient and deterministic.
Problems with NAN propagation in current systems are
discussed. Examples of implementation in the C++ vector
class library and in an experimental instruction set
named ForwardCom are presented. The IEEE-754 standard
for floating point arithmetic may need adjustment to
accommodate the needs of modern forms of parallelism.",
acknowledgement = ack-nhfb,
remark = "See also earlier \cite{Fog:2020:FPE} and later
revisions \cite{Fog:2024:FPE}.",
}
@InProceedings{Glint:2023:HSC,
author = "Tom Glint and Kailash Prasad and Jinay Dagli and
Krishil Gandhi and Aryan Gupta and Vrajesh Patel and
Neel Shah and Joycee Mekie",
editor = "{IEEE}",
booktitle = "{2023 28th Asia and South Pacific Design Automation
Conference (ASP-DAC)}",
title = "Hardware-Software Codesign of {DNN} Accelerators using
Approximate Posit Multipliers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "469--474",
year = "2023",
DOI = "",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gorodecky:2023:SAC,
author = "Danila Gorodecky and Leonel Sousa",
title = "Scalable architecture of constant division on {FPGA}",
crossref = "IEEE:2023:PIS",
pages = "16--23",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00025",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Boolean functions; Computer architecture;
Costs; Delays; Digital arithmetic; Field programmable
gate arrays; Hardware",
}
@InProceedings{Graillat:2023:PCH,
author = "Stef Graillat and Youness Ibrahimy and Clothilde
Jeangoudoux and Christoph Lauter",
title = "A parallel compensated {Horner} scheme for {SIMD}
architecture",
crossref = "IEEE:2023:PIS",
pages = "131--138",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00010",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; AVX; compensated algorithms; Computer
architecture; Computers; Costs; Digital arithmetic;
error-free transformations; Horner scheme; Limiting;
parallel algorithms; polynomial evaluation; Registers;
rounding errors; Scalability; SIMD",
}
@InProceedings{Grale:2023:IMM,
author = "Trenton J. Grale and Earl E. Swartzlander",
title = "Improved {Montgomery} Multiplication",
crossref = "IEEE:2023:PIS",
pages = "60--67",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00019",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Computational modeling; Computer
architecture; Costs; digit multiplication; Digital
arithmetic; Hardware; modular arithmetic; modular
multiplication; Parallel processing; Rescheduled
Montgomery Multiplier; Serial Montgomery Model;
Taxonomy",
}
@InProceedings{Gunaratne:2023:EUL,
author = "Thushara Kanchana Gunaratne",
title = "Evaluation of the Use of Low Precision Floating-Point
Arithmetic for Applications in Radio Astronomy",
crossref = "Gustafson:2023:NGA",
pages = "155--170",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_10",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Gustafson:2023:DFT,
author = "John L. Gustafson and Marco Cococcioni and Federico
Rossi and Emanuele Ruffaldi and Sergio Saponara",
title = "Decoding-Free Two-Input Arithmetic for Low-Precision
Real Numbers",
crossref = "Gustafson:2023:NGA",
pages = "61--76",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_4",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Hallman:2023:PAD,
author = "Eric Hallman and Ilse C. F. Ipsen",
title = "Precision-aware deterministic and probabilistic error
bounds for floating point summation",
journal = j-NUM-MATH,
volume = "155",
number = "1--2",
pages = "83--119",
month = oct,
year = "2023",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-023-01370-y",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Thu Sep 28 06:27:49 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/i/ipsen-ilse-c-f.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
URL = "https://link.springer.com/article/10.1007/s00211-023-01370-y",
acknowledgement = ack-nhfb,
ajournal = "Num. Math.",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "accurate floating-point summation",
}
@Misc{Harris:2023:UMR,
author = "David Harris",
title = "Unified minimally redundant radix 4 {DivSqrt}
selection intervals and constants",
howpublished = "Web document",
year = "2023",
bibdate = "Thu Dec 28 10:11:34 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://bit.ly/3fLR81z",
acknowledgement = ack-nhfb,
remark = "URL leads to undated Google Docs spreadsheet with
interleaved commentary. Cited in
\cite{Harris:2024:UDS}.",
}
@InProceedings{Ho:2023:BBE,
author = "Nhut-Minh Ho and Duy-Thanh Nguyen and John L.
Gustafson and Weng-Fai Wong",
title = "{Bedot}: Bit Efficient Dot Product for Deep Generative
Models",
crossref = "Gustafson:2023:NGA",
pages = "19--37",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_2",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Hoffmann:2023:ASE,
author = "Alexandre Hoffmann and Yves Durand and J{\'e}r{\^o}me
Fereyre",
title = "Accelerating spectral elements method with extended
precision: a case study",
journal = "International Journal of Applied Physics and
Mathematics",
volume = "14",
number = "2",
pages = "45--58",
year = "2023",
CODEN = "IJAPJ3",
DOI = "https://doi.org/10.17706/ijapm",
ISSN = "2010-362X",
ISSN-L = "2010-362X",
bibdate = "Wed Jun 12 16:34:44 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
ajournal = "Int. J. Appl. Phys. Math.",
remark = "In Proc. 12th Int. Conf. Pure Appl. Math. (ICPAM).",
}
@TechReport{Hubrecht:2023:TCRa,
author = "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
Zimmermann",
title = "Towards a correctly-rounded and fast power function in
binary64 arithmetic",
type = "Report",
institution = "DI-ENS --- D{\'e}partement d'informatique --- ENS
Paris",
address = "Paris, France",
day = "12",
month = jul,
year = "2023",
bibdate = "Mon May 13 12:00:21 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-04159652v1/",
abstract = "We design algorithms for the correct rounding of the
power function $ x^y $ in the binary64 IEEE 754 format,
for all rounding modes, modulo the knowledge of
hardest-to-round cases. Our implementation of these
algorithms largely outperforms previous
correctly-rounded implementations and is not far from
the efficiency of current mathematical libraries, which
are not correctly-rounded. Still, we expect our
algorithms can be further improved for speed. The
proofs of correctness are fully detailed in an extended
version of this paper, with the goal to enable a formal
proof of these algorithms. We hope this work will
motivate the next IEEE 754 revision committee to
require correct rounding for mathematical functions.",
acknowledgement = ack-nhfb,
remark = "This is a longer version of \cite{Hubrecht:2023:TCRb}
with proofs.",
}
@InProceedings{Hubrecht:2023:TCRb,
author = "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
Zimmermann",
title = "Towards a correctly-rounded and fast power function in
binary64 arithmetic",
crossref = "IEEE:2023:PIS",
pages = "111--118",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00028",
bibdate = "Fri Dec 08 15:03:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arith2023.arithsymposium.org/slides/S6_PaulZimmermannS6P1.pdf;
https://inria.hal.science/hal-04326201
https://inria.hal.science/hal-04159652v1/file/pow.pdf",
abstract = "We design algorithms for the correct rounding of the
power function $ x^y $ in the binary64 IEEE 754 format,
for all rounding modes, modulo the knowledge of
hardest-to-round cases. Our implementation of these
algorithms largely outperforms previous
correctly-rounded implementations and is not far from
the efficiency of current mathematical libraries, which
are not correctly-rounded. Still, we expect our
algorithms can be further improved for speed. The
proofs of correctness are fully detailed, with the goal
to enable a formal proof of these algorithms. We hope
this work will motivate the next IEEE 754 revision
committee to require correct rounding for mathematical
functions.",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; binary64 format; correct rounding; Digital
arithmetic; double precision; efficiency; Error
analysis; IEEE 754; Libraries; power function;
Prediction algorithms; Software; Software algorithms;
Switches",
remark = "See also longer versions
\cite{Hubrecht:2023:TCRa,Hubrecht:2024:TCR}.",
}
@InProceedings{Hulsmeier:2023:HSH,
author = "Nils H{\"u}lsmeier and Moritz B{\"a}rthel and Jochen
Rust and Steffen Paul",
title = "Hybrid {SORN} Hardware Accelerator for Support Vector
Machines",
crossref = "Gustafson:2023:NGA",
pages = "77--87",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_5",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{IEEE:2023:MIS,
author = "{IEEE}",
title = "Milestones: {IEEE Standard 754 for Binary
Floating-Point Arithmetic, 1985. (J. Coonen,
proposer)}",
howpublished = "Web site",
day = "3",
month = may,
year = "2023",
DOI = "https://ethw.org/Milestones:IEEE_Standard_754_for_Binary_Floating-Point_Arithmetic,_1985",
bibdate = "Wed Aug 07 15:36:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Misc{IEEE:2023:UWG,
author = "{IEEE}",
title = "{IEEE Working Group P3109} Interim Report on 8-bit
Binary Floating-point Formats",
howpublished = "Web document",
pages = "18",
day = "24",
month = nov,
year = "2023",
bibdate = "Sat Dec 16 10:36:07 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://github.com/P3109/Public/blob/main/Shared%20Reports/P3109%20WG%20Interim%20report.pdf",
acknowledgement = ack-nhfb,
remark = "Table 2 on page 4 contains a compact summary of
binary8p\{p\}, binary8p5, binary8p4, binary8p3,
binary16, binary32, and binary64 data layouts.",
}
@TechReport{Innocente:2023:AMF,
author = "Vincenzo Innocente and Paul Zimmermann",
title = "Accuracy of Mathematical Functions in Single, Double,
Double Extended, and Quadruple Precision",
institution = "????",
pages = "21",
day = "14",
month = feb,
year = "2023",
bibdate = "Fri Dec 08 08:28:52 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-03141101;
https://members.loria.fr/PZimmermann/papers/glibc237-20230214.pdf",
acknowledgement = ack-nhfb,
remark = "Tabular comparison of AMD, Apple, CUDA, GNU, Intel,
Musl, Newlib, OpenLibm, and RadeonOpenCompute (ROCm) lm
libraries for correct rounding, versus results from
MPFR.",
}
@InProceedings{Jaberipur:2023:MMF,
author = "Ghassem Jaberipur and Saeid Gorgin and Navid Ahamadian
and Jeong-A Lee",
title = "Modulo-($ 2^q - 3$) Multiplication with Fully Modular
Partial Product Generation and Reduction",
crossref = "IEEE:2023:PIS",
pages = "68--75",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00023",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Costs; Delays; Digital arithmetic; Energy
measurement; Fully modular multiplication; Market
research; Partial product reduction; Residue number
system; Software; Software algorithms",
}
@InProceedings{K:2023:DEE,
author = "Lakshmi Bhanuprakash Reddy K and Haripriya R S and
Keerthija Puli and Subba Ramkumar Reddy Annapalli and
Vikramkumar Pudi",
editor = "{IEEE}",
booktitle = "{2023 36th International Conference on VLSI Design and
2023 22nd International Conference on Embedded Systems
(VLSID)}",
title = "Design of Energy Efficient and Low Delay Posit
Multiplier",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2023",
DOI = "https://doi.org/10.1109/VLSID57277.2023.00042",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kapoor:2023:FVF,
author = "Ashish Kapoor and Warren Ferguson and Himanshu Jain
and Sudipta Kundu",
title = "Formal Verification of Floating-Point Division",
crossref = "IEEE:2023:PIS",
pages = "93--96",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00018",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; datapath verification; Digital arithmetic;
equivalence checking; floating-point division; Formal
verification; formal verification; Software",
}
@InProceedings{Kavvousanos:2023:IRL,
author = "E. Kavvousanos and V. Sakellariou and I. Kouretas and
V. Paliouras and T. Stouraitis",
title = "Improving Residue-Level Sparsity in {RNS-based} Neural
Network Hardware Accelerators via Regularization",
crossref = "IEEE:2023:PIS",
pages = "102--109",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00020",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Artificial neural networks; Computer
architecture; Degradation; Digital arithmetic; hardware
acceleration; Machine learning; Neural network
hardware; neural networks; residue number system;
sparsity; Training",
}
@InProceedings{Kellison:2023:LLF,
author = "Ariel E. Kellison and Andrew W. Appel and Mohit
Tekriwal and David Bindel",
title = "{LAProof}: a Library of Formal Proofs of Accuracy and
Correctness for Linear Algebra Programs",
crossref = "IEEE:2023:PIS",
pages = "36--43",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00021",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Error analysis; floating-point arithmetic;
formal verification; Libraries; Mathematical models;
program verification; rounding error analysis; Roundoff
errors; Sparse matrices; Stability analysis; Vectors",
}
@Article{Klwer:2023:POC,
author = "Milan Kl{\"o}wer and Peter V. Coveney and E. Adam
Paxton and Tim N. Palmer",
title = "Periodic orbits in chaotic systems simulated at low
precision",
journal = j-SCI-REP,
volume = "13",
number = "1",
publisher = pub-SV,
address = pub-SV:adr,
month = jul,
year = "2023",
CODEN = "SRCEC3",
DOI = "https://doi.org/10.1038/s41598-023-37004-4",
ISSN = "2045-2322",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Scientific Reports",
journal-URL = "http://www.nature.com/srep/",
keywords = "posit arithmetic",
}
@Misc{Krishna:2023:RNF,
author = "Bharath Krishna",
title = "Rounding Numbers in the Financial Domain!",
howpublished = "Web site",
day = "1",
month = jan,
year = "2023",
bibdate = "Tue Feb 27 14:40:22 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Includes important mention of financial regulatory
sites, with this text taken verbatim from the article,
because such information may be hard to find
elsewhere:
* International Financial Reporting Standards (IFRS):
IFRS is a set of accounting standards developed by the
International Accounting Standards Board (IASB). It
includes guidelines on rounding financial numbers in
financial statements, such as the requirement to round
amounts to the nearest whole number or the nearest
multiple of 10;
* Generally Accepted Accounting Principles (GAAP): GAAP
is a set of accounting standards used in the United
States. It includes similar guidelines on rounding
financial numbers as IFRS and requires that any
rounding errors should be immaterial and
insignificant.
* International Organization for Standardization (ISO):
ISO has a standard for Rounding off numerical values,
which is ISO 80000-1:2009. It provides guidelines on
rounding numerical values in general and not specific
to the finance domain, but it's widely used in
financial systems.
* The Federal Reserve Board (FRB): The FRB, the central
banking system of the United States, has guidelines on
rounding financial numbers for bank reporting and
financial statement preparation.
* The European Central Bank (ECB): The ECB, the central
banking system of the European Union, has similar
guidelines on rounding financial numbers as the FRB.",
URL = "https://www.foundingminds.com/rounding-numbers-in-the-financial-domain/",
acknowledgement = ack-nhfb,
keywords = "decimal floating-point arithmetic; rounding errors",
}
@InProceedings{Kurian:2023:PER,
author = "Ashley Kurian and M. Ramesh Kini",
booktitle = "Lecture Notes in Networks and Systems",
title = "Posit Extended {RISC-V} Processor and Its Enhancement
Using Data Type Casting",
publisher = "Springer Nature",
address = "Singapore",
pages = "571--586",
year = "2023",
DOI = "https://doi.org/10.1007/978-981-19-6634-7_40",
ISBN = "981-19663-4-6",
ISBN-13 = "978-981-19663-4-7",
ISSN = "2367-3389",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Laguna:2023:FIT,
author = "Ignacio Laguna and Anh Tran and Ganesh
Gopalakrishnan",
title = "Finding inputs that trigger floating-point exceptions
in heterogeneous computing via {Bayesian}
optimization",
journal = j-PARALLEL-COMPUTING,
volume = "117",
number = "??",
pages = "103042:1--103042:13",
month = sep,
year = "2023",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/j.parco.2023.103042",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Thu Sep 7 08:37:05 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167819123000480",
acknowledgement = ack-nhfb,
articleno = "103042",
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@Article{Leitersdorf:2023:AHT,
author = "Orian Leitersdorf and Dean Leitersdorf and Jonathan
Gal and Mor Dahan and Ronny Ronen and Shahar
Kvatinsky",
title = "{AritPIM}: High-Throughput In-Memory Arithmetic",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "11",
number = "3",
pages = "720--735",
month = jul # "\slash " # sep,
year = "2023",
DOI = "https://doi.org/10.1109/TETC.2023.3268137",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
abstract = "Digital processing-in-memory (PIM) architectures are
rapidly emerging to overcome the memory-wall bottleneck
by integrating logic within memory elements. Such
architectures provide vast computational power within
the memory itself in the form of parallel bitwise logic
operations. We develop novel algorithmic techniques for
PIM that, combined with new perspectives on computer
arithmetic, extend this bitwise parallelism to the four
fundamental arithmetic operations (addition,
subtraction, multiplication, and division), for both
fixed-point and floating-point numbers, and using both
bit-serial and bit-parallel approaches. We propose a
state-of-the-art suite of arithmetic algorithms,
demonstrating the first algorithm in the literature of
digital PIM for a majority of cases --- including cases
previously considered impossible for digital PIM, such
as floating-point addition. Through a case study on
memristive PIM, we compare the proposed algorithms to
an NVIDIA RTX 3070 GPU and demonstrate significant
throughput and energy improvements.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@InProceedings{Leong:2023:LFU,
author = "Siew Hoon Leong and John L. Gustafson",
title = "Lossless {FFTs} Using Posit Arithmetic",
crossref = "Gustafson:2023:NGA",
pages = "1--18",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_1",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2023:DEG,
author = "Xinyi Li and Ignacio Laguna and Bo Fang and Katarzyna
Swirydowicz and Ang Li and Ganesh Gopalakrishnan",
booktitle = "Proceedings of the {32nd International Symposium on
High-Performance Parallel and Distributed Computing}",
title = "Design and Evaluation of {GPU-FPX}: a Low-Overhead
tool for Floating-Point Exception Detection in {NVIDIA
GPUs}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "59--71",
month = aug,
year = "2023",
DOI = "https://doi.org/10.1145/3588195.3592991",
bibdate = "Thu Sep 7 09:13:15 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://dl.acm.org/doi/10.1145/3588195.3592991;
https://github.com/LLNL/GPU-FPX",
abstract = "Floating-point exceptions occurring during numerical
computations can be a serious threat to the validity of
the computed results if they are not caught and
diagnosed Unfortunately, on NVIDIA GPUs --- today's
most widely used types and which do not have hardware
exception traps --- this task must be carried out in
software. Given the prevalence of closed-source
kernels, efficient binary-level exception tracking is
essential. It is also important to know how exceptions
flow through the code, whether they alter the code
behavior and additionally whether these exceptions can
be detected at the program outputs or are killed inside
program flow-paths. In this paper, we introduce
GPU-FPX, a tool that has low overhead, allows for deep
understanding of the origin and flow of exceptions, and
also how exceptions are modified by code optimizations.
We measure GPU-FPX's performance over 151 widely used
GPU programs coming from HPC and ML, detecting 26
serious exceptions that were previously not reported.
Our results show that GPU-FPX is $ 16 \times $ faster
with respect to the geometric-mean runtime in relation
to the only comparable prior tool, while also helping
debug a larger class of codes more effectively.",
acknowledgement = ack-nhfb,
}
@Article{Li:2023:DSE,
author = "He Li and Jiawei Liang and Hongxiang Fan and Yongming
Tang",
title = "Design Space Exploration for Efficient Quantum
Most-Significant Digit-First Arithmetic",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "6",
pages = "1822--1829",
month = jun,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2022.3215891",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed May 17 10:34:15 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
abstract = "Quantum computing has been considered as an emerging
approach in addressing problems which are not easily
solvable using classical computers. In parallel to the
physical implementation of quantum processors, quantum
algorithms have been actively developed for real-life
applications to show quantum advantages, many of which
benefit from quantum arithmetic algorithms and their
efficient implementations. As one of the most important
operations, quantum addition has been adopted in Shor's
algorithm and quantum linear algebra algorithms.
Although various least-significant digit-first quantum
adders have been introduced in previous work, interest
in investigating the efficient implementation of
most-significant digit-first addition is growing. In
this work, we propose a novel design method for
most-significant digit-first addition with several
quantum circuit optimisations to reduce the number of
quantum bits (i.e. qubits), quantum gates, and circuit
depth. An open-source library of different arithmetic
operators based on our proposed method is presented,
where all circuits are implemented on IBM Qiskit SDK.
Extensive experiments demonstrate that our proposed
design, together with the optimisation techniques,
reduces T-depth by up-to 4.0$ \times $, T-count by 3.5$
\times $, and qubit consumption by 1.2$ \times $.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Li:2023:EEB,
author = "Ruiyuan Li and Zheng Li and Yi Wu and Chao Chen and Yu
Zheng",
title = "{Elf}: Erasing-Based Lossless Floating-Point
Compression",
journal = j-PROC-VLDB-ENDOWMENT,
volume = "16",
number = "7",
pages = "1763--1776",
month = mar,
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.14778/3587136.3587149",
ISSN = "2150-8097",
bibdate = "Tue May 9 09:08:30 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/vldbe.bib",
URL = "https://dl.acm.org/doi/10.14778/3587136.3587149",
abstract = "There are a prohibitively large number of
floating-point time series data generated at an
unprecedentedly high rate. An efficient, compact and
lossless compression for time series data is of great
importance for a wide range of scenarios. Most existing
lossless floating-point compression methods are based
on the XOR operation, but they do not fully exploit the
trailing zeros, which usually results in an
unsatisfactory compression ratio. This paper proposes
an Erasing-based Lossless Floating-point compression
algorithm, i.e., \pkg{Elf}. The main idea of \pkg{Elf}
is to erase the last few bits (i.e., set them to zero)
of floating-point values, so the XORed values are
supposed to contain many trailing zeros. The challenges
of the erasing-based method are three-fold. First, how
to quickly determine the erased bits? Second, how to
losslessly recover the original data from the erased
ones? Third, how to compactly encode the erased data?
Through rigorous mathematical analysis, \pkg{Elf} can
directly determine the erased bits and restore the
original values without losing any precision. To
further improve the compression ratio, we propose a
novel encoding strategy for the XORed values with many
trailing zeros. \pkg{Elf} works in a streaming fashion.
It takes only $ O(N) $ (where $N$ is the length of a
time series) in time and $ O(1)$ in space, and achieves
a notable compression ratio with a theoretical
guarantee. Extensive experiments using 22 datasets show
the powerful performance of \pkg{Elf} compared with 9
advanced competitors.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the VLDB Endowment",
journal-URL = "https://dl.acm.org/loi/pvldb",
}
@InProceedings{Li:2023:POS,
author = "Qiong Li and Chao Fang and Zhongfeng Wang",
editor = "{IEEE}",
booktitle = "{2023 IEEE International Symposium on Circuits and
Systems (ISCAS)}",
title = "{PDPU}: an Open-Source Posit Dot-Product Unit for Deep
Learning Applications",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2023",
DOI = "https://doi.org/10.1109/ISCAS46773.2023.10182007",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Liu:2023:CHR,
author = "Zixuan Liu and Xiaoyu Song and Zhuowei Wang and Yan
Wang and Jian-Tao Zhou",
title = "Constructing High Radix Quotient Digit Selection
Tables for {SRT} Division and Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "7",
pages = "2111--2119",
month = jul,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2023.3235978",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 1 10:59:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Livesay:2023:AFF,
author = "Neal Livesay and Gilbert Jonatan and Evelio Mora and
Kaustubh Shivdikar and Rashmi Agrawal and Ajay Joshi
and Jos{\'e} L. Abell{\'a}n and John Kim and David
Kaeli",
title = "Accelerating Finite Field Arithmetic for Homomorphic
Encryption on {GPUs}",
journal = j-IEEE-MICRO,
volume = "43",
number = "5",
pages = "55--63",
month = sep # "\slash " # oct,
year = "2023",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2023.3253052",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu Sep 14 06:42:28 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
}
@InProceedings{Malathi:2023:DRV,
author = "D Malathi and R Sneha and M Shanmugapriya and S
Sethurajan",
editor = "{IEEE}",
booktitle = "{2023 4th International Conference on Signal
Processing and Communication (ICSPC)}",
title = "Design of {RISC-V} Processing Unit Using Posit Number
System",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "427--431",
year = "2023",
DOI = "https://doi.org/10.1109/ICSPC57692.2023.10125646",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@Article{Mansfield:2023:MSR,
author = "Daniel F. Mansfield",
title = "{Mesopotamian} square root approximation by a sequence
of rectangles",
journal = j-BRITISH-J-HIST-MATH,
volume = "38",
number = "3",
pages = "175--188",
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.1080/26375451.2023.2215652",
ISSN = "1749-8430 (print), 1749-8341 (electronic)",
ISSN-L = "1749-8341",
bibdate = "Thu Apr 25 11:06:30 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bshm.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.tandfonline.com/doi/full/10.1080/26375451.2023.2215652",
acknowledgement = ack-nhfb,
ajournal = "BSHM Bull.",
fjournal = "BSHM Bulletin: Journal of the British Society for the
History of Mathematics",
journal-URL = "http://www.tandfonline.com/loi/tbsh20",
onlinedate = "09 Jun 2023",
}
@Article{Martin-Dorel:2023:EFP,
author = "{\'E}rik Martin-Dorel and Guillaume Melquiond and
Pierre Roux",
title = "Enabling Floating-Point Arithmetic in the {Coq} Proof
Assistant",
journal = j-J-AUTOM-REASON,
volume = "67",
number = "4",
pages = "??--??",
month = dec,
year = "2023",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-023-09679-x",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Mon Nov 27 10:14:54 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "https://link.springer.com/article/10.1007/s10817-023-09679-x",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
articleno = "33",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
}
@Article{Melquiond:2023:WFV,
author = "Guillaume Melquiond and Rapha{\"e}l Rieu-Helft",
title = "{WhyMP}, a formally verified arbitrary-precision
integer library",
journal = j-J-SYMBOLIC-COMP,
volume = "115",
number = "??",
pages = "74--95",
month = mar # "\slash " # apr,
year = "2023",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1016/j.jsc.2022.07.007",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Sat Sep 17 06:23:51 MDT 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0747717122000657",
abstract = "Arbitrary-precision integer libraries such as GMP are
a critical building block of computer algebra systems.
GMP provides state-of-the-art algorithms that are
intricate enough to justify formal verification. In
this paper, we present a C library that has been
formally verified using the Why3 verification platform
in about four person-years. This verification deals not
only with safety, but with full functional correctness.
It has been performed using a mixture of mechanically
checked handwritten proofs and automated theorem
proving. We have implemented and verified a nontrivial
subset of GMP's algorithms, including their
optimizations and intricacies. Our library provides the
same interface as GMP and is almost as efficient for
smaller inputs. We detail our verification methodology
and the algorithms we have implemented, and include
some benchmarks to compare our library with GMP.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
keywords = "Deductive program verification; Integer arithmetic;
Mathematical library",
}
@Article{Mezzarobba:2023:REA,
author = "Marc Mezzarobba",
title = "Rounding error analysis of linear recurrences using
generating series",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "58",
pages = "196--227",
year = "2023",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Jun 3 08:23:58 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/etna.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://etna.math.kent.edu/vol.58.2023/pp196-227.dir/pp196-227.pdf;
https://etna.math.kent.edu/volumes/2021-2030/vol58/abstract.php?vol=58&pages=196-227",
abstract = "We develop a toolbox for the error analysis of linear
recurrences with constant or polynomial coefficients,
based on generating series, Cauchy's method of
majorants, and simple results from analytic
combinatorics. We illustrate the power of the approach
by several nontrivial application examples. Among these
examples are a new worst-case analysis of an algorithm
for computing the Bernoulli numbers and a new algorithm
for evaluating differentially finite functions in
interval arithmetic while avoiding interval blow-up",
acknowledgement = ack-nhfb,
ajournal = "Electron. Trans. Numer. Anal.",
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@TechReport{Micikevicius:2023:OBF,
author = "Paulius Micikevicius and Stuart Oberman and Marius
Cornea Pradeep Dubey and Andres Rodriguez and Ian Bratt
and Richard Grisenthwaite and Chiachen Chou Norm Jouppi
and Amber Huffman and Michael Schulte and Ralph Wittig
and Dharmesh Jani and Summer Deng",
title = "{OCP} 8-bit floating point specification ({OFP8}):
Revision 1.0.",
type = "Technical report",
institution = "Open Compute Project",
address = "????",
pages = "16",
day = "20",
month = jun,
year = "2023",
bibdate = "Thu Nov 30 05:39:50 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.opencompute.org/documents/ocp-8-bit-floating-point-specification-ofp8-revision-1-0-2023-06-20-pdf",
acknowledgement = ack-nhfb,
}
@Article{Mikaitis:2023:MMT,
author = "Mantas Mikaitis",
title = "Monotonicity of Multi-Term Floating-Point Adders",
journal = "arxiv.org",
volume = "??",
number = "??",
pages = "1--13",
day = "3",
month = apr,
year = "2023",
bibdate = "Thu Apr 06 15:33:19 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
URL = "https://arxiv.org/pdf/2304.01407.pdf",
abstract = "In the literature on algorithms for performing the
multi-term addition $ s_n = \sum_{i = 1}^n x_i $ using
floating-point arithmetic it is often shown that a
hardware unit that has single normalization and
rounding improves precision, area, latency, and power
consumption, compared with the use of standard add or
fused multiply--add units. However, non-monotonicity
can appear when computing sums with a subclass of
multi-term addition units, which currently is not
explored in the literature. We demonstrate that common
techniques for performing multi-term addition with $ n
\geq 4 $, without normalization of intermediate
quantities, can result in non-monotonicity-increasing
one of the addends $ x_i $ decreases the sum sn.
Summation is required in dot product and matrix
multiplication operations, operations that have
increasingly started appearing in the hardware of
supercomputers, thus knowing where monotonicity is
preserved can be of interest to the users of these
machines. Our results suggest that non-monotonicity of
summation, in some of the commercial hardware devices
that implement a specific class of multi-term adders,
is a feature that may have appeared unintentionally as
a consequence of design choices that reduce circuit
area and other metrics. To demonstrate our findings, we
use formal proofs as well as a numerical simulation of
non-monotonic multi-term adders in MATLAB",
acknowledgement = ack-nhfb,
keywords = "dot product; floating-point arithmetic; matrix
multiply; monotonicity; multi-term addition",
remark = "arXiv:2304.01407v1",
}
@Article{Murillo:2023:GPB,
author = "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
Botella and Christian Pilato",
title = "Generating Posit-Based Accelerators With High-Level
Synthesis",
journal = j-IEEE-TRANS-CIRCUITS-SYST-1,
volume = "70",
number = "10",
pages = "4040--4052",
year = "2023",
DOI = "https://doi.org/10.1109/TCSI.2023.3299009",
ISSN = "1549-8328 (print), 1558-0806 (electronic)",
ISSN-L = "1549-8328",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems I: Regular
Papers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
}
@Article{Murillo:2023:HMP,
author = "Raul Murillo and Javier Hormigo and Alberto A. {Del
Barrio} and Guillermo Botella",
title = "{HUB} Meets Posit: Arithmetic Units Implementation",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
pages = "1--1",
year = "2023",
DOI = "https://doi.org/10.1109/TCSII.2023.3307488",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}
@InProceedings{Murillo:2023:PPL,
author = "Raul Murillo and David Mallas{\'e}n and Alberto A. Del
Barrio and Guillermo Botella",
title = "{PLAUs}: Posit Logarithmic Approximate Units to
Implement Low-Cost Operations with Real Numbers",
crossref = "Gustafson:2023:NGA",
pages = "171--188",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_11",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Murillo:2023:SDA,
author = "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
Botella",
editor = "{IEEE}",
booktitle = "2023 {IEEE 34th International Conference on
Application-specific Systems, Architectures and
Processors (ASAP): ASAP 2023, 19--21 July 2023, Porto,
Portugal}",
title = "A Suite of Division Algorithms for Posit Arithmetic",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "41--44",
year = "2023",
DOI = "https://doi.org/10.1109/ASAP57973.2023.00020",
ISBN-13 = "979-83-503-4686-2 (print), 979-83-503-4685-5
(e-book)",
bibdate = "Thu Nov 16 15:55:09 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Mushtak:2023:FNP,
author = "Noble Mushtak and Daniel Lemire",
title = "Fast number parsing without fallback",
journal = j-SPE,
volume = "53",
number = "7",
pages = "1467--1471",
month = jul,
year = "2023",
CODEN = "SPEXBL",
DOI = "https://doi.org/10.1002/spe.3198",
ISSN = "0038-0644 (print), 1097-024X (electronic)",
ISSN-L = "0038-0644",
bibdate = "Thu Jun 29 14:46:14 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/spe.bib",
note = "See original work \cite{Lemire:2021:NPG}.",
abstract = "In recent work, Lemire (2021) presented a fast
algorithm to convert number strings into binary
floating-point numbers. The algorithm has been adopted
by several important systems: for example, it is part
of the runtime libraries of GCC 12, Rust 1.55, and Go
1.16. The algorithm parses any number string with a
significand containing no more than 19 digits into an
IEEE floating-point number. However, there is a check
leading to a fallback function to ensure correctness.
This fallback function is never called in practice. We
prove that the fallback is unnecessary. Thus we can
slightly simplify the algorithm and its
implementation.",
acknowledgement = ack-nhfb,
ajournal = "Softw. Pract. Exp.",
fjournal = "Software --- Practice and Experience",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
onlinedate = "04 March 2023",
}
@Article{Nadalini:2023:RPF,
author = "Davide Nadalini and Manuele Rusci and Luca Benini and
Francesco Conti",
title = "Reduced precision floating-point optimization for
{Deep Neural Network On-Device Learning} on
microcontrollers",
journal = j-FUT-GEN-COMP-SYS,
volume = "149",
number = "??",
pages = "212--226",
month = dec,
year = "2023",
CODEN = "FGSEVI",
DOI = "https://doi.org/10.1016/j.future.2023.07.020",
ISSN = "0167-739X (print), 1872-7115 (electronic)",
ISSN-L = "0167-739X",
bibdate = "Thu Sep 21 08:18:51 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/futgencompsys2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167739X23002728",
acknowledgement = ack-nhfb,
fjournal = "Future Generation Computer Systems",
journal-URL = "http://www.sciencedirect.com/science/journal/0167739X",
}
@InProceedings{Nadalini:2023:TWR,
author = "Alessandro Nadalini and Georg Rutishauser and Alessio
Burrello and Nazareno Bruschi and Angelo Garofalo and
Luca Benini and Francesco Conti and Davide Rossi",
editor = "{IEEE}",
booktitle = "{2023 IEEE Computer Society Annual Symposium on VLSI
(ISVLSI)}",
title = "A 3 {TOPS\slash W RISC-V} Parallel Cluster for
Inference of Fine-Grain Mixed-Precision Quantized
Neural Networks",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2023",
DOI = "https://doi.org/10.1109/ISVLSI59464.2023.10238679",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@Book{Nazareth:2023:CGN,
author = "John Lawrence Nazareth",
title = "Concise Guide to Numerical Algorithmics: The
Foundations and Spirit of Scientific Computing",
publisher = pub-SV,
address = pub-SV:adr,
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-21762-3",
ISBN = "3-031-21762-4",
ISBN-13 = "978-3-031-21762-3",
ISSN = "2191-5776",
ISSN-L = "2191-5768",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "SpringerBriefs in Computer Science",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Noh:2023:FFD,
author = "Seock-Hwan Noh and Jahyun Koo and Seunghyun Lee and
Jongse Park and Jaeha Kung",
title = "{FlexBlock}: a Flexible {DNN} Training Accelerator
With Multi-Mode Block Floating Point Support",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "9",
pages = "2522--2535",
month = sep,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2023.3253050",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Thu Aug 10 06:30:56 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Misc{NVIDIA:2023:FPI,
author = "{NVIDIA Corporation}",
title = "Floating Point and {IEEE 754} Compliance for {NVIDIA
GPUs}",
howpublished = "NVIDIA Web site.",
month = oct,
year = "2023",
bibdate = "Fri Dec 01 12:26:53 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://docs.nvidia.com/cuda/floating-point/",
acknowledgement = ack-nhfb,
remark = "The document discusses IEEE 754 conformance, CUDA,
fused multiply-add, dot products, and GPU issues. It
also says: ``NVIDIA GPUs differ from the x86
architecture in that rounding modes are encoded within
each floating point instruction instead of dynamically
using a floating point control word. Trap handlers for
floating point exceptions are not supported. On the GPU
there is no status flag to indicate when calculations
have overflowed, underflowed, or have involved inexact
arithmetic.''",
}
@InProceedings{Oh:2023:RLR,
author = "Hyun Woo Oh and Seongmo An and Won Sik Jeong and Seung
Eun Lee",
editor = "{IEEE}",
booktitle = "{2023 IEEE/ACM International Symposium on Low Power
Electronics and Design (ISLPED)}",
title = "{RF2P}: a Lightweight {RISC} Processor Optimized for
Rapid Migration from {IEEE-754} to Posit",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2023",
DOI = "https://doi.org/10.1109/ISLPED58423.2023.10244582",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{P:2023:AOF,
author = "Gayathri G P and Jaya S and Krishnakumar Rao S",
editor = "{IEEE}",
booktitle = "{2023 International Conference on Control,
Communication and Computing (ICCC)}",
title = "An Area Optimized Floating-Point Coprocessor for
{RISC-V} Processor",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--5",
year = "2023",
DOI = "https://doi.org/10.1109/ICCC57789.2023.10165397",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{P:2023:ITO,
author = "Ponsuganth Ilangovan P. and Rohan Rayan and Vinay
Shankar Saxena",
title = "Improving the Stability of {Kalman} Filters with Posit
Arithmetic",
crossref = "Gustafson:2023:NGA",
pages = "134--154",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_9",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Park:2023:FDL,
author = "Jina Park and Kyuseung Han and Eunjin Choi and Sukho
Lee and Jae-Jin Lee and Woojoo Lee and Massoud Pedram",
editor = "{IEEE}",
booktitle = "{2023 {IEEE\slash ACM} International Symposium on Low
Power Electronics and Design (ISLPED)}",
title = "{Florian}: Developing a Low-Power {RISC-V} Multicore
Processor with a Shared Lightweight {FPU}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1--6",
year = "2023",
DOI = "https://doi.org/10.1109/ISLPED58423.2023.10244431",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Pasca:2023:ELP,
author = "Bogdan Pasca and Martin Langhammer",
title = "Extracting low-precision floating-point adders from
embedded hard {FP DSP} Blocks on {FPGAs}",
crossref = "IEEE:2023:PIS",
pages = "139--142",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00017",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "adder; Adders; ARITH-30; bfloat16; Computer
architecture; Costs; Digital arithmetic; DSP;
extraction; Field programmable gate arrays;
floating-point; FP-DSP; FPGA; half-precision; mapping",
}
@Article{Perez:2023:TIL,
author = "Sergio P. Perez and Yan Zhang and James Briggs and
Charlie Blake and Josh Levy-Kramer and Paul Balanca and
Carlo Luschi and Stephen Barlow and Andrew William
Fitzgibbon",
title = "Training and inference of large language models using
8-bit floating point",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--22",
day = "29",
month = sep,
year = "2023",
DOI = "https://doi.org/10.48550/arXiv.2309.17224",
bibdate = "Wed Aug 07 16:34:17 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2309.17224",
abstract = "FP8 formats are gaining popularity to boost the
computational efficiency for training and inference of
large deep learning models. Their main challenge is
that a careful choice of scaling is needed to prevent
degradation due to the reduced dynamic range compared
to higher-precision formats. Although there exists
ample literature about selecting such scalings for INT
formats, this critical aspect has yet to be addressed
for FP8. This paper presents a methodology to select
the scalings for FP8 linear layers, based on
dynamically updating per-tensor scales for the weights,
gradients and activations. We apply this methodology to
train and validate large language models of the type of
GPT and Llama 2 using FP8, for model sizes ranging from
111M to 70B. To facilitate the understanding of the FP8
dynamics, our results are accompanied by plots of the
per-tensor scale distribution for weights, activations
and gradients during both training and inference.",
acknowledgement = ack-nhfb,
}
@Article{Perotti:2023:YOS,
author = "Matteo Perotti and Matheus Cavalcante and Alessandro
Ottaviano and Jiantao Liu and Luca Benini",
title = "{Yun}: an Open-Source, 64-Bit {RISC-V}-Based Vector
Processor With Multi-Precision Integer and
Floating-Point Support in 65-nm {CMOS}",
journal = j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
volume = "70",
number = "10",
pages = "3732--3736",
year = "2023",
DOI = "https://doi.org/10.1109/TCSII.2023.3292579",
ISSN = "1549-7747 (print), 1558-3791 (electronic)",
ISSN-L = "1549-7747",
bibdate = "Sat Dec 16 15:51:40 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Circuits and Systems II: Express
Briefs",
journal-URL = "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}
@Misc{Pilipovic:2023:EEN,
author = "Ratko Pilipovi{\'c} and Patricio Buli{\'c} and
Uro{\v{s}} Lotri{\v{c}}",
title = "Energy-efficient neural network learning with
accuracy-adjustable floating-point multiplier",
howpublished = "TechRxiv preprint.",
day = "19",
month = feb,
year = "2023",
DOI = "https://doi.org/10.36227/techrxiv.22123127.v1",
bibdate = "Fri Sep 29 14:34:35 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.techrxiv.org/articles/preprint/Energy-efficient_neural_network_learning_with_accuracy-adjustable_floating-point_multiplier/22123127",
abstract = "This paper proposes a novel approximate bfloat16
multiplier with on-the-fly adjustable accuracy for
energy-efficient learning in deep neural networks. The
size of the proposed multiplier is only 62\% of the
size of the exact bfloat16 multiplier. Furthermore, its
energy footprint is up to five times smaller than the
footprint of the exact bfloat multiplier. We
demonstrate the advantages of the proposed multiplier
in deep neural network learning, where we successfully
train the ResNet-20 network on the CIFAR-10 dataset
from scratch.",
acknowledgement = ack-nhfb,
}
@Misc{Postpischil:2023:WDI,
author = "Eric Postpischil",
title = "Why does the integer representation of a floating
point number offer a piecewise linear approximation to
the logarithm?",
howpublished = "Stack Overflow Web site.",
year = "2023",
bibdate = "Wed Dec 20 06:59:51 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://stackoverflow.com/questions/75772363/why-does-the-integer-representation-of-a-floating-point-number-offer-a-piecewise",
acknowledgement = ack-nhfb,
remark = "Discusses Jim Blinn's approximate logarithm for the
IEEE 32-bit binary format \cite{Blinn:1997:JBC}.",
}
@InProceedings{Ren:2023:EAM,
author = "Pengchang Ren and Reiji Suda and Vorapong
Suppakitpaisarn",
title = "Efficient Additions and {Montgomery} Reductions of
Large Integers for {SIMD}",
crossref = "IEEE:2023:PIS",
pages = "48--59",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00034",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "additions; ARITH-30; arithmetic for cryptography;
AVX-512; Cryptography; Digital arithmetic; Montgomery
reduction; Pipelines; Program processors; SIMD;
Standards; SVE",
}
@Article{Robert:2023:FMM,
author = "Jean-Marc Robert and Pascal V{\'e}ron",
title = "Faster multiplication over {$ \mathbb {F}_2 [X] $}
using {AVX512} instruction set and {VPCLMULQDQ}
instruction",
journal = j-J-CRYPTO-ENG,
volume = "13",
number = "1",
pages = "37--55",
month = apr,
year = "2023",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-021-00278-3",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Fri Jun 2 12:32:10 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
URL = "https://link.springer.com/article/10.1007/s13389-021-00278-3",
acknowledgement = ack-nhfb,
ajournal = "J. Crypto. Eng.",
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@Article{Rump:2023:IPP,
author = "Siegfried M. Rump",
title = "{IEEE-754} Precision-$p$ base-$ \beta $ Arithmetic
Implemented in Binary",
journal = j-TOMS,
volume = "49",
number = "4",
pages = "32:1--32:??",
month = dec,
year = "2023",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3596218",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Dec 23 05:40:24 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3596218;
https://www.tuhh.de/ti3/paper/rump/Ru23b.pdf",
abstract = "We show how an IEEE-754 conformant precision-$p$
base-$ \beta $ arithmetic can be implemented based on
some binary floating-point and/or integer arithmetic.
This includes the four basic operations and square root
subject to the five IEEE-754 rounding modes, namely he
nearest roundings with roundTiesToEven and
roundTiesToAway, the directed roundings downwards and
upwards, as well as rounding towards zero. Exceptional
values like $ \infty $ or NaN are covered according to
the IEEE-754 arithmetic standard.
The results of the precision-$p$ base-$ \beta $
operations are computed using some underlying
precision-$q$ binary arithmetic. We distinguish two
cases. When using a precision-$q$ binary integer
arithmetic, the base-$ \beta $ precision $p$ is limited
for all operations by $ \beta^{2 p} \leq 2^q$, whereas
using a precision-$q$ binary floating-point arithmetic
imposes stronger limits on the base-$ \beta $
precision, namely $ \beta^{2p} \leq 2^q$ for addition
and multiplication, $ \beta^{2p} \leq 2^{q - 1}$ for
division and $ \beta^{2p} \leq 2^{q - 3}$ for the
square root. Those limitations cannot be improved.
The algorithms are implemented in a Matlab/Octave
flbeta-toolbox with the choice of using uint64 or
binary64 as underlying arithmetic. The former allows
larger precisions, the latter is advantageous for the
square root, whereas computing times are similar. The
flbeta-toolbox offers precision-$p$ base-$ \beta $
scalar, vector and matrix operations including sparse
matrices as well as corresponding interval operations.
The base $ \beta $ can be chosen in the range $ \beta $
[2,64]. The flbeta-toolbox will be part of Version 13
of INTLAB [18], the Matlab/Octave toolbox for reliable
computing.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "32",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
remark = "Received 6 December 2021; revised 10 October 2022;
accepted 30 March 2023.",
}
@InProceedings{Rydahl:2023:PPA,
author = "Anton Rydahl and Joseph Huber and Ethan Luis Mcdonough
and Johannes Doerfert",
booktitle = "Proceedings of the {SC 23 Workshops of The
International Conference on High Performance Computing,
Network, Storage, and Analysis}",
title = "Precision and Performance Analysis of {C} Standard
Math Library Functions on {GPUs}",
publisher = pub-ACM,
address = pub-ACM:adr,
month = nov,
year = "2023",
DOI = "https://doi.org/10.1145/3624062.3624166",
bibdate = "Fri Dec 8 12:56:08 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "With the advent of GPU computing, executing large
program sections on accelerators has become
increasingly important. Efforts are being made to
support the C standard library, LIBC, on GPUs via LLVM
machinery. Therefore, the C standard math library,
LIBM, must be supported on GPUs. So far, LLVM
frontends, such as Clang, have relied on GPU vendor
implementations of LIBM functionality wrapped into
(mostly) LIBM-compatible forwarding functions.\par
We propose a novel LIBM for GPUs reusing a collection
of LLVM target-agnostic implementations and built-ins
alongside vendor implementations of most single and
double-precision floating point math functions. Our
approach allows selecting between individual
implementations based on the GPU target as opposed to
the current approach, which serves only the single
third-party library implementation. Our extensive
numerical analysis highlights the various
implementations differences in performance and
precision. Our solution allows users to choose the
implementation that maximizes speed while meeting their
specific precision requirements.",
acknowledgement = ack-nhfb,
}
@InProceedings{Safieh:2023:EBR,
author = "Malek Safieh and Andreas Furch and Fabrizio {De
Santis}",
title = "An Efficient {Barrett} Reduction Algorithm for
{Gaussian} Integer Moduli",
crossref = "IEEE:2023:PIS",
pages = "76--83",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00011",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Barrett Reduction; Computational complexity;
Computational efficiency; Costs; Digital arithmetic;
Gaussian Integers; Modular Arithmetic; Modulo
Reduction",
}
@InProceedings{Sakellariou:2023:MFR,
author = "Vasilis Sakellariou and Vassilis Paliouras and Ioannis
Kouretas and Hani Saleh and Thanos Stouraitis",
title = "A multiplier-Free {RNS}-Based {CNN} accelerator
exploiting bit-Level sparsity",
crossref = "IEEE:2023:PIS",
pages = "101--101",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00037",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "Analytical models; ARITH-30; Benchmark testing;
Digital arithmetic; Encoding; Energy efficiency;
Throughput; Vectors",
}
@Article{Schilling:2023:BSR,
author = "Jonathan Schilling and Jakob Svensson and Udo
H{\"o}fel and Joachim Geiger and Henning Thomsen",
title = "{Biot--Savart} routines with minimal floating point
error",
journal = j-COMP-PHYS-COMM,
volume = "287",
number = "??",
pages = "Article 108692",
month = jun,
year = "2023",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2023.108692",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Mar 17 07:49:53 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465523000371",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@InProceedings{Seo:2023:DPHa,
author = "Jihee Seo and Dae Hyun Kim",
title = "Dual-Purpose Hardware Algorithms and Architectures.
{Part 1}: Floating-Point Division",
crossref = "IEEE:2023:PIS",
pages = "24--31",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00013",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Computer architecture; Costs; Digital
arithmetic; Divider; Energy consumption; Floating-Point
Arithmetic; Hardware; Online Division; Simulation;
Throughput",
}
@InProceedings{Seo:2023:DPHb,
author = "Jihee Seo and Dae Hyun Kim",
title = "Dual-Purpose Hardware Algorithms and Architectures.
{Part 2}: Integer Division",
crossref = "IEEE:2023:PIS",
pages = "1--8",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00014",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Computer architecture; Costs; Digital
arithmetic; Divider; Energy consumption; Hardware;
Integer Arithmetic; Online Division; Simulation",
}
@InProceedings{Shah:2023:DPU,
author = "Nimish Shah and Wannes Meert and Marian Verhelst",
booktitle = "Efficient Execution of Irregular Dataflow Graphs",
title = "{DAG} Processing Unit Version 1 {(DPU)}: Efficient
Execution of Irregular Workloads on a Multicore
Processor",
publisher = pub-SV,
address = pub-SV:adr,
pages = "69--88",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-33136-7_4",
ISBN = "3-031-33136-2",
ISBN-13 = "978-3-031-33136-7",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Book{Shah:2023:EEI,
author = "Nimish Shah and Wannes Meert and Marian Verhelst",
title = "Efficient Execution of Irregular Dataflow Graphs:
Hardware\slash Software Co-optimization for
Probabilistic {AI} and Sparse Linear Algebra",
publisher = pub-SV,
address = pub-SV:adr,
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-33136-7",
ISBN = "3-031-33136-2",
ISBN-13 = "978-3-031-33136-7",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Shah:2023:IWR,
author = "Nimish Shah and Wannes Meert and Marian Verhelst",
booktitle = "Efficient Execution of Irregular Dataflow Graphs",
title = "Irregular Workloads at Risk of Losing the Hardware
Lottery",
publisher = pub-SV,
address = pub-SV:adr,
pages = "1--21",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-33136-7_1",
ISBN = "3-031-33136-2",
ISBN-13 = "978-3-031-33136-7",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Shah:2023:SDR,
author = "Nimish Shah and Wannes Meert and Marian Verhelst",
booktitle = "Efficient Execution of Irregular Dataflow Graphs",
title = "Suitable Data Representation: A Study of Fixed-Point,
Floating-Point, and {PositTM} Formats for Probabilistic
{AI}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "23--41",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-33136-7_2",
ISBN = "3-031-33136-2",
ISBN-13 = "978-3-031-33136-7",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Shahbazi:2023:OHI,
author = "Karim Shahbazi and Seok-Bum Ko",
title = "An Optimized Hardware Implementation of Modular
Multiplication of Binary Ring {LWE}",
journal = j-IEEE-TRANS-EMERG-TOP-COMPUT,
volume = "11",
number = "3",
pages = "817--821",
month = jul # "\slash " # sep,
year = "2023",
DOI = "https://doi.org/10.1109/TETC.2023.3280470",
ISSN = "2168-6750 (print), 2376-4562 (electronic)",
bibdate = "Thu Sep 21 14:02:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Emerging Topics in Computing",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}
@Article{Sharma:2023:CQE,
author = "Niraj N. Sharma and Riya Jain and Mohana Madhumita
Pokkuluri and Sachin B. Patkar and Rainer Leupers and
Rishiyur S. Nikhil and Farhad Merchant",
title = "{CLARINET}: A quire-enabled {RISC-V}-based framework
for posit arithmetic empiricism",
journal = j-J-SYST-ARCH,
volume = "135",
pages = "102801",
year = "2023",
CODEN = "JSARFB",
DOI = "https://doi.org/10.1016/j.sysarc.2022.102801",
ISSN = "1383-7621 (print), 1873-6165 (electronic)",
ISSN-L = "1383-7621",
bibdate = "Wed May 22 14:56:32 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
URL = "https://www.sciencedirect.com/science/article/pii/S1383762122002867",
acknowledgement = ack-nhfb,
ajournal = "J. Syst. Arch.",
fjournal = "Journal of Systems Architecture",
journal-URL = "https://www.sciencedirect.com/journal/journal-of-systems-architecture",
keywords = "Posit-arithmetic, RISC-V, Open-source hardware,
Custom-instructions",
}
@InProceedings{Shekhawat:2023:PPH,
author = "Diksha Shekhawat and Jugal Gandhi and M. Santosh and
Jai Gopal Pandey",
title = "{PHAc}: Posit Hardware Accelerator for Efficient
Arithmetic Logic Operations",
crossref = "Gustafson:2023:NGA",
pages = "88--100",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_6",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Shen:2023:CCA,
author = "Shiyu Shen and Hao Yang and Yu Liu and Zhe Liu and
Yunlei Zhao",
title = "{CARM}: {CUDA-Accelerated RNS Multiplication} in
Word-Wise Homomorphic Encryption Schemes for {Internet
of Things}",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "7",
pages = "1999--2010",
month = jul,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2022.3227874",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 1 10:59:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Silva:2023:TAB,
author = "Himeshi De Silva and Hongshi Tan and Nhut-Minh Ho and
John L. Gustafson and Weng-Fai Wong",
title = "Towards a Better 16-Bit Number Representation for
Training Neural Networks",
crossref = "Gustafson:2023:NGA",
pages = "114--133",
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1_8",
bibdate = "Sat Dec 16 08:52:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sohn:2023:EFP,
author = "Jongwook Sohn and David K. Dean and Eric Quintana and
Wing Shek Wong",
title = "Enhanced Floating-Point Multiply-Add with Full
Denormal Support",
crossref = "IEEE:2023:PIS",
pages = "143--150",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00015",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Delays; Digital arithmetic; Encoding;
floating-point arithmetic; floating-point denormal
numbers; Floating-point multiply-add; high-speed
computer arithmetic; Logic arrays; Next generation
networking; Optimization",
}
@Misc{Sukop:2023:HDB,
author = "Juraj Sukop and Niels M{\"o}ller",
title = "On {HGCD-D} bounds",
type = "Report",
day = "7",
month = feb,
year = "2023",
bibdate = "Thu Feb 09 11:15:45 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.science/hal-03976898",
abstract = "An improved bound for one of the founding relations of
HGCD-D algorithm is presented. This allows to put a
lower limit on the iteration count of the first sdiv
loop, to impose a particular structure on the
accumulated quotients and to bound the size of the
largest matrix element. The matrix product M.M' is
proved to have its upper and lower size bound differ by
at most two bits",
acknowledgement = ack-nhfb,
}
@Article{Talpes:2023:MDT,
author = "Emil Talpes and Debjit Das Sarma and Doug Williams and
Sahil Arora and Thomas Kunjan and Benjamin Floering and
Ankit Jalote and Christopher Hsiong and Chandrasekhar
Poorna and Vaidehi Samant and John Sicilia and Anantha
Kumar Nivarti and Raghuvir Ramachandran and Tim Fischer
and Ben Herzberg and Bill McGee and Ganesh
Venkataramanan and Pete Banon",
title = "The Microarchitecture of {DOJO}, {Tesla}'s Exa-Scale
Computer",
journal = j-IEEE-MICRO,
volume = "43",
number = "3",
pages = "31--39",
month = may # "\slash " # jun,
year = "2023",
CODEN = "IEMIDZ",
DOI = "https://doi.org/10.1109/MM.2023.3258906",
ISSN = "0272-1732 (print), 1937-4143 (electronic)",
ISSN-L = "0272-1732",
bibdate = "Thu May 18 07:38:12 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/hot-chips.bib;
https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Micro",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
remark = "DOJO is based on RISC-V64 with instruction set
extensions. Its arithmetic supports 8-, 16-, 32-, and
64-bit integers, and IEEE 754 FP32 (1/8/23), plus FP16
(1/5/10), BFP16 (1/8/7), CFP8 (1/4/3), CFP8 (1/5/2),
and CFP16 (1/5/10) floating-point formats. The latter
is unusual having an external register that records the
exponent bias (0, 31, or 63), so that it supports three
different ranges of numbers. There is no support for
FP64 or longer formats. There is support for stochastic
rounding.",
}
@InProceedings{Tompazi:2023:ABT,
author = "Styliani Tompazi and Georgios Karakonstantis",
title = "{AI}-based Timing Error Modelling: a Case Study on a
Pipelined Floating-point Core",
crossref = "IEEE:2023:PIS",
pages = "110--110",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00035",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; Computational modeling; Digital arithmetic;
Machine learning; Nanoscale devices; Timing; Training",
}
@Article{Towhidy:2023:DIA,
author = "Ahmad Towhidy and Reza Omidi and Karim Mohammadi",
title = "On the Design of Iterative Approximate Floating-Point
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "6",
pages = "1623--1635",
month = jun,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2022.3216465",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed May 17 10:34:15 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
abstract = "Approximate multipliers provide power and area-saving
for error-resilient applications. In this paper, we
first propose two approximate floating-point
multipliers based on two-dimensional pseudo-Booth
encoding: floating-point pseudo-Booth (PB), and
floating-point iterative pseudo-Booth (IPB). The
accuracy of proposed multipliers can be tuned by three
parameters: iteration, encoder's radix (R), and word
length after truncation (W). Next, we developed the
conventional iterative multipliers with a simplified
steering circuit for their correction part to eliminate
the power consumption of multipliers. The proposed
iterative multipliers are compared with conventional
iterative integer multipliers implemented by a
simplified steering circuit for the floating-point
area. The results reveal that the proposed PB-R4-W4 and
IPB-R16-W19, compared to the exact floating-point
multiplier, provide up to 98.9\% and 67.5\% reductions
in power consumption, respectively, in TSMC 180nm CMOS
technology. Also, their MRED values are, respectively,
2.9\% and ($ 7.4 \times 10 {-4}$)\%. Finally, we
evaluated the functionality of the proposed multipliers
for real-life applications, including a hyper-plane
classifier and two image processing applications of
smoothing and sharpening.",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@InProceedings{Ullah:2023:DRE,
author = "Salim Ullah and Siva Satyendra Sahoo and Akash Kumar",
booktitle = "Embedded Machine Learning for Cyber-Physical, {IoT},
and Edge Computing",
title = "Designing Resource-Efficient Hardware Arithmetic for
{FPGA}-Based Accelerators Leveraging Approximations and
Mixed Quantizations",
publisher = pub-SV,
address = pub-SV:adr,
pages = "89--119",
month = oct,
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-19568-6_4",
ISBN = "3-031-19568-X",
ISBN-13 = "978-3-031-19568-6",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@InProceedings{Vollmer:2023:UHA,
author = "Morgane Vollmer and Karim Bigou and Arnaud Tisserand",
title = "Using Hierarchical Approach to Speed-up {RNS} Base
Extensions in Homomorphic Encryption Context",
crossref = "IEEE:2023:PIS",
pages = "84--87",
year = "2023",
DOI = "https://doi.org/10.1109/ARITH58626.2023.00030",
bibdate = "Wed May 8 09:17:31 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30; base extension; Costs; Digital arithmetic;
homomorphic encryption; Homomorphic encryption;
Multicore processing; Parallel processing; residue
number system; Software; Software algorithms",
}
@Manual{Whitehead:2023:FPI,
author = "Nathan Whitehead and Alex Fit-florea",
title = "Floating Point and {IEEE 754} Compliance for {NVIDIA
GPUs}",
organization = "NVIDIA",
address = "????",
pages = "28",
day = "24",
month = aug,
year = "2023",
bibdate = "Mon Sep 11 07:26:37 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://docs.nvidia.com/cuda/floating-point/;
https://docs.nvidia.com/cuda/pdf/Floating_Point_on_NVIDIA_GPU.pdf",
abstract = "A number of issues related to floating point accuracy
and compliance are a frequent source of confusion on
both CPUs and GPUs. The purpose of this white paper is
to discuss the most common issues related to NVIDIA
GPUs and to supplement the documentation in the CUDA
C++ Programming Guide",
acknowledgement = ack-nhfb,
tableofcontents = "1 Floating Point / 3 \\
1.1 Formats / 3 \\
1.2 Operations and Accuracy / 4 \\
1.3 The Fused Multiply-Add (FMA) / 5 \\
2 Dot Product: An Accuracy Example / 7 \\
2.1 Example Algorithms / 7 \\
2.2 Comparison / 8 \\
3 CUDA and Floating Point / 9 \\
3.1 Compute Capability 2.0 and Above / 9 \\
3.2 Rounding Modes / 9 \\
3.3 Controlling Fused Multiply-add / 10 \\
3.4 Compiler Flags / 11 \\
3.5 Differences from x86 / 11 \\
4 Considerations for a Heterogeneous World / 13 \\
4.1 Mathematical Function Accuracy / 13 \\
4.2 x87 and SSE / 14 \\
4.3 Core Counts / 14 \\
4.4 Verifying GPU Results / 14 \\
5 Concrete Recommendations / 17 \\
6 Acknowledgements / 19 \\
7 References / 21 \\
8 Notices / 23 \\
8.1 Notice / 23 \\
8.2 OpenCL / 24 \\
8.3 Trademarks / 24",
}
@Book{Wilkinson:2023:REA,
author = "J. H. (James Hardy) Wilkinson",
title = "Rounding Errors in Algebraic Processes",
volume = "89",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiii + 161",
year = "2023",
ISBN = "1-61197-751-7",
ISBN-13 = "978-1-61197-751-6",
LCCN = "QA275 .W64 2023",
bibdate = "Wed Aug 7 17:00:33 MDT 2024",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "New foreword by N. J. Higham.",
series = "Classics in applied mathematics",
abstract = "\booktitle{Rounding Errors in Algebraic Processes} was
the first book to give systematic analyses of the
effects of rounding errors on a variety of key
computations involving polynomials and matrices. A
detailed analysis is given of the rounding errors made
in the elementary arithmetic operations and inner
products, for both floating-point arithmetic and
fixed-point arithmetic. The results are then applied in
the error analyses of a variety of computations
involving polynomials as well as the solution of linear
systems, matrix inversion, and eigenvalue computations.
The conditioning of these problems is investigated. The
aim was to provide a unified method of treatment, and
emphasis is placed on the underlying concepts.",
acknowledgement = ack-nhfb,
author-dates = "James H. Wilkinson (27 September 1919--5 October
1986)",
remark = "``\ldots{}a republication originally published by Her
Majesty's Stationery Office under British Crown
copyright in 1963''-- title page verso.",
subject = "Roundoff errors; Erreurs d'arrondi; Roundoff errors",
tableofcontents = "The fundamental arithmetic operations \\
Computations involving polynomials \\
Matrix computations",
}
@Article{Wong:2023:KNS,
author = "Zheng-Yan Wong and Denis C.-K. Wong and Wai-Kong Lee
and Kai-Ming Mok and Wun-She Yap and Ayesha Khalid",
title = "{KaratSaber}: New Speed Records for {Saber} Polynomial
Multiplication Using Efficient {Karatsuba} {FPGA}
Architecture",
journal = j-IEEE-TRANS-COMPUT,
volume = "72",
number = "7",
pages = "1830--1842",
month = jul,
year = "2023",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2023.3238129",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sat Jul 1 10:59:22 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Yang:2023:ATF,
author = "Chun-Chieh Yang and Yi-Ru Chen and Hui-Hsin Liao and
Yuan-Ming Chang and Jenq-Kuen Lee",
title = "Auto-tuning Fixed-point Precision with {TVM} on
{RISC-V} Packed {SIMD} Extension",
journal = j-TODAES,
volume = "28",
number = "3",
pages = "33:1--33:??",
month = may,
year = "2023",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/3569939",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Wed May 17 08:06:20 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib;
https://www.math.utah.edu/pub/tex/bib/todaes.bib",
URL = "https://dl.acm.org/doi/10.1145/3569939",
abstract = "Today, as deep learning (DL) is applied more often in
daily life, dedicated processors such as CPUs and GPUs
have become very important for accelerating model
executions. With the growth of technology, people are
becoming accustomed to using edge devices, such as
mobile phones, smart watches, and VR devices in their
daily lives. A variety of technologies using DL are
gradually being applied to these edge devices. However,
there is a large number of computations in DL. It faces
a challenging problem how to provide solutions in the
edge devices. In this article, the proposed method
enables a flow with the RISC-V Packed extension (P
extension) in TVM. TVM, an open deep learning compiler
for neural network models, is growing as a key
infrastructure for DL computing. RISC-V is an open
instruction set architecture (ISA) with customized and
flexible features. The Packed-SIMD extension is a
RISC-V extension that enables subword
single-instruction multiple-data (SIMD) computations in
RISC-V architectures to support fallback engines in AI
computing. In the proposed flow, a fixed-point type
that is supported by an integer of 16-bit type and
saturation instructions is added to replace the
original 32-bit float type. In addition, an auto-tuning
method is proposed to use a uniform selector mechanism
(USM) to find the binary point position for fixed-point
type use. The tensorization feature of TVM can be used
to optimize specific hardware such as subword SIMD
instructions with RISC-V P extension. With our
experiment on the Spike simulator, the proposed method
with the USM can improve performance by approximately
2.54 to 6.15$ \times $ in terms of instruction counts
with little accuracy loss.",
acknowledgement = ack-nhfb,
articleno = "33",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems",
journal-URL = "https://dl.acm.org/loi/todaes",
}
@Article{Zhang:2023:EAP,
author = "Hao Zhang and Seok-Bum Ko",
title = "Efficient Approximate Posit Multipliers for Deep
Learning Computation",
journal = j-IEEE-J-EMERG-SEL-TOP-CIRCUITS-SYST,
volume = "13",
number = "1",
pages = "201--211",
year = "2023",
DOI = "https://doi.org/10.1109/JETCAS.2022.3231642",
ISSN = "2156-3357 (print), 2156-3365 (electronic)",
ISSN-L = "2156-3357",
bibdate = "Fri Dec 15 09:21:55 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Journal on Emerging and Selected Topics in
Circuits and Systems",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5503868",
}
@Article{Zlatopolski:2023:PAV,
author = "Dmitry Zlatopolski",
title = "{``Perfect Arithmetic'' by Vaclav Josef Pelikan}",
journal = j-HIST-MATH,
volume = "62",
number = "??",
pages = "40--50",
month = feb,
year = "2023",
CODEN = "HIMADS",
DOI = "https://doi.org/10.1016/j.hm.2022.09.002",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Mar 15 09:40:56 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0315086022000659",
abstract = "The present article describes for the first time the
book of Vaclav Josef Pelikan titled
\booktitle{Arithmeticus Perfectus Qui tria numerare
nescit. Seu Arithmetica dualis, In qua Numerando non
proceditur, nisi ad duo, \& tamen omnes quaestiones
Arithmeticae negotio facili enodari possunt}, published
in Prague in 1712. The book is written in Latin on 86
pages and consists of a dedication, a message to the
reader and four chapters. Operations in the binary
system, including the extraction of square and cube
roots, methods of converting numbers from the decimal
system to the binary system and vice versa, etc., are
given. In general, we may say that the book by Vaclav
Josef Pelikan is the first fully fledged and
methodologically sound textbook of arithmetic using the
binary number system as well as containing original
methods of solution.",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860",
keywords = "base conversion; binary arithmetic",
}
@Book{Alsuhli:2024:NSD,
author = "Ghada Alsuhli and Vasilis Sakellariou and Hani Saleh
and Mahmoud Al-Qutayri and Baker Mohammad and Thanos
Stouraitis",
title = "Number Systems for Deep Neural Network Architectures",
publisher = pub-SV,
address = pub-SV:adr,
year = "2024",
DOI = "https://doi.org/10.1007/978-3-031-38133-1",
ISBN = "3-031-38133-5",
ISBN-13 = "978-3-031-38133-1",
ISSN = "2690-0327",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Synthesis Lectures on Engineering, Science, and
Technology",
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
}
@Article{Angioli:2024:DIE,
author = "Marco Angioli and Marcello Barbirotta and Abdallah
Cheikh and Antonio Mastrandrea and Francesco Menichelli
and Saeid Jamili and Mauro Olivieri",
title = "Design, Implementation and Evaluation of a New
Variable Latency Integer Division Scheme",
journal = j-IEEE-TRANS-COMPUT,
volume = "73",
number = "7",
pages = "1767--1779",
month = jul,
year = "2024",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2024.3386060",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jun 12 15:57:24 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Benchmark testing; Clocks; computer arithmetic; Field
programmable gate arrays; Frequency conversion;
Hardware; high-speed arithmetic; integer division;
low-power design; real-time and embedded systems;
Registers; Signal processing algorithms;
Variable-latency divider",
}
@Article{Bandil:2024:HIU,
author = "Lalit Bandil and Bal Chand Nagar",
title = "Hardware Implementation of Unsigned Approximate Hybrid
Square Rooters for Error-Resilient Applications",
journal = j-IEEE-TRANS-COMPUT,
volume = "73",
number = "12",
pages = "2734--2746",
year = "2024",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2024.3457731",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Nov 20 07:36:48 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Accuracy; accuracy metrics; Approximate computing;
Arithmetic; Computers; Hardware; hardware
implementation; image processing; Image restoration;
low power; Measurement; Multiplexing; square rooter",
}
@Article{Benmaghnia:2024:CGN,
author = "Hanane Benmaghnia and Matthieu Martel and Yassamine
Seladji",
title = "Code Generation for Neural Networks Based on
Fixed-point Arithmetic",
journal = j-TECS,
volume = "23",
number = "5",
pages = "68:1--68:??",
month = sep,
year = "2024",
CODEN = "????",
DOI = "https://doi.org/10.1145/3563945",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Wed Sep 25 11:16:16 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
URL = "https://dl.acm.org/doi/10.1145/3563945",
abstract = "Over the past few years, neural networks have started
penetrating safety critical systems to make decisions
as, for example, in robots, rockets, and autonomous
driving cars. Neural networks based on floating-point
arithmetic are very time and memory consuming, which
are not compatible with embedded systems known to have
limited resources. They are also very sensitive to the
precision in which they have been trained, so changing
this precision generally degrades the quality of their
answers. To deal with that, we introduce a new
technique to generate a fixed-point code for a trained
neural network. This technique is based on fixed-point
arithmetic with mixed-precision. This arithmetic is
based on integer operations only, which are compatible
with small memory devices. The obtained neural network
has the same behavior as the initial one (based on the
floating-point arithmetic) up to an error threshold
defined by the user. The experimental results show the
efficiency of our tool SyFix in terms of memory saved
and the accuracy of the computations.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Embed. Comput. Syst.",
articleno = "68",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "https://dl.acm.org/loi/tecs",
}
@TechReport{Brisebarre:2024:CRE,
author = "Nicolas Brisebarre and Guillaume Hanrot and
Jean-Michel Muller and Paul Zimmermann",
title = "Correctly-rounded evaluation of a function: why, how,
and at what cost?",
type = "Report",
number = "hal-04474530",
institution = "CNRS --- Centre National de la Recherche Scientifique
and others",
address = "Paris, France",
pages = "29",
day = "23",
month = feb,
year = "2024",
bibdate = "Fri Feb 23 16:11:08 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.science/hal-04474530",
abstract = "The goal of this paper is to convince the reader that
a future standard for floating-point arithmetic should
require the availability of a correctly-rounded version
of a well-chosen core set of elementary functions. We
discuss the interest and feasibility of this
requirement. We also give answers to common objections
we have received over the last 10 years.",
acknowledgement = ack-nhfb,
keywords = "algorithmic number theory; approximation theory;
Computer arithmetic; elementary functions;
floating-point arithmetic; lattice basis reduction; LLL
algorithm; standardization",
}
@Article{Brogi:2024:FPP,
author = "F. Brogi and S. Bn{\`a} and G. Boga and G. Amati and
T. Esposti Ongaro and M. Cerminara",
title = "On floating point precision in computational fluid
dynamics using {OpenFOAM}",
journal = j-FUT-GEN-COMP-SYS,
volume = "152",
number = "??",
pages = "1--16",
month = mar,
year = "2024",
CODEN = "FGSEVI",
DOI = "https://doi.org/10.1016/j.future.2023.10.006",
ISSN = "0167-739X (print), 1872-7115 (electronic)",
ISSN-L = "0167-739X",
bibdate = "Sat Dec 16 07:26:57 MST 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/futgencompsys2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0167739X23003813",
acknowledgement = ack-nhfb,
fjournal = "Future Generation Computer Systems",
journal-URL = "http://www.sciencedirect.com/science/journal/0167739X",
}
@Article{Cai:2024:TEV,
author = "Luwei Cai and Fu Song and Taolue Chen",
title = "Towards Efficient Verification of Constant-Time
Cryptographic Implementations",
journal = "Proceedings of the ACM on Software Engineering",
volume = "1",
number = "FSE",
pages = "1019--1042",
month = jul,
year = "2024",
DOI = "https://doi.org/10.1145/3643772",
ISSN = "2994-970X",
bibdate = "Tue Aug 27 07:37:07 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Timing side-channel attacks exploit secret-dependent
execution time to fully or partially recover secrets of
cryptographic implementations, posing a severe threat
to software security. Constant-time programming
discipline is an effective software-based
countermeasure against timing side-channel attacks, but
developing constant-time implementations turns out to
be challenging and error-prone. Current verification
approaches/tools suffer from scalability and precision
issues when applied to production software in practice.
In this paper, we put forward practical verification
approaches based on a novel synergy of taint analysis
and safety verification of self-composed programs.
Specifically, we first use an IFDS-based lightweight
taint analysis to prove that a large number of
potential (timing) side-channel sources do not actually
leak secrets. We then resort to a precise taint
analysis and a safety verification approach to
determine whether the remaining potential side-channel
sources can actually leak secrets. These include novel
constructions of taint-directed semi-cross-product of
the original program and its Boolean abstraction, and a
taint-directed self-composition of the program. Our
approach is implemented as a cross-platform and fully
automated tool CT-Prover. The experiments confirm its
efficiency and effectiveness in verifying real-world
benchmarks from modern cryptographic and SSL/TLS
libraries. In particular, CT-Prover identify new,
confirmed vulnerabilities of open-source SSL libraries
(e.g., Mbed SSL, BearSSL) and significantly outperforms
the state-of-the-art tool",
acknowledgement = ack-nhfb,
keywords = "constant-time cryptographic implementation; Formal
security models; Formal software verification; formal
verification; Logic and verification; Program analysis;
Security and privacy; Software and its engineering;
taint analysis; Theory of computation; Timing
side-channel",
}
@Article{Cameron:2024:AHM,
author = "Thomas R. Cameron and Stef Graillat",
title = "Accurate {Horner} methods in real and complex
floating-point arithmetic",
journal = j-BIT-NUM-MATH,
volume = "64",
number = "2",
pages = "??--??",
month = jun,
year = "2024",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-024-01017-w",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Tue May 28 15:02:24 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/bit.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://link.springer.com/article/10.1007/s10543-024-01017-w",
acknowledgement = ack-nhfb,
ajournal = "Bit Num. Math.",
articleno = "17",
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@TechReport{Caprioli:2024:ACM,
author = "Paul Caprioli and Vincenzo Innocente and Paul
Zimmermann",
title = "Accuracy of Complex Mathematical Operations and
Functions in Single and Double Precision",
type = "Report",
number = "hal-04714173",
institution = "High Performance Kernels LLC",
address = "????",
pages = "8",
day = "30",
month = sep,
year = "2024",
bibdate = "Mon Sep 30 06:08:35 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-04714173v1",
acknowledgement = ack-nhfb,
}
@Misc{Demmel:2024:EDS,
author = "Jim Demmel",
title = "Exploring the Design Space of Exception Handling",
howpublished = "Posting to STDS-754 mailing list.",
pages = "42",
day = "22",
month = aug,
year = "2024",
bibdate = "Tue Aug 27 08:09:27 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Lecture slides on progress in research on
floating-point exception handling, notably in LAPACK
and the BLAS (Basic Linear Algebra Subroutines).",
URL = "ExceptionHandling_22Aug2024.pdf",
acknowledgement = ack-nhfb,
}
@Article{Deng:2024:FPE,
author = "Bobin Deng and Bhargava Nadendla and Kun Suo and Yixin
Xie and Dan Chia-Tien Lo",
title = "Fixed-point Encoding and Architecture Exploration for
Residue Number Systems",
journal = j-TACO,
volume = "21",
number = "3",
pages = "53:1--53:??",
month = sep,
year = "2024",
CODEN = "????",
DOI = "https://doi.org/10.1145/3664923",
ISSN = "1544-3566 (print), 1544-3973 (electronic)",
ISSN-L = "1544-3566",
bibdate = "Sat Sep 21 06:05:41 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/taco.bib",
URL = "https://dl.acm.org/doi/10.1145/3664923",
abstract = "Residue Number Systems (RNS) demonstrate the
fascinating potential to serve integer addition\slash
multiplication-intensive applications. The complexity
of Artificial Intelligence (AI) models has grown
enormously in recent years. From a computer system's
perspective, ensuring the training of these large-scale
AI models within an adequate time and energy
consumption has become a big concern. Matrix
multiplication is a dominant subroutine in many
prevailing AI models, with an addition\slash
multiplication-intensive attribute. However, the data
type of matrix multiplication within machine learning
training typically requires real numbers, which
indicates that RNS benefits for integer applications
cannot be directly gained by AI training. The
state-of-the-art RNS real-number encodings, including
floating-point and fixed-point, have defects and can be
further enhanced. To transform default RNS benefits to
the efficiency of large-scale AI training, we propose a
low-cost and high-accuracy RNS fixed-point
representation: Single RNS Logical Partition
(S-RNS-Logic-P) representation with Scaling-down
Postprocessing Multiplication (SD-Post-Mul). Moreover,
we extend the implementation details of the other two
RNS fixed-point methods: Double RNS Concatenation and
S-RNS-Logic-P representation with Scaling-down
Preprocessing Multiplication. We also design the
architectures of these three fixed-point multipliers.
In empirical experiments, our S-RNS-Logic-P
representation with SD-Post-Mul method achieves less
latency and energy overhead while maintaining good
accuracy. Furthermore, this method can easily extend to
the Redundant Residue Number System to raise the
efficiency of error-tolerant domains, such as improving
the error correction efficiency of quantum computing.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Archit. Code Optim.",
articleno = "53",
fjournal = "ACM Transactions on Architecture and Code Optimization
(TACO)",
journal-URL = "https://dl.acm.org/loi/taco",
}
@Article{ElArar:2024:BNE,
author = "E-M. {El Arar} and D. Sohier and P. {de Oliveira
Castro} and E. Petit",
title = "Bounds on Nonlinear Errors for Variance Computation
with Stochastic Rounding",
journal = j-SIAM-J-SCI-COMP,
volume = "46",
number = "5",
pages = "B579--B599",
month = "????",
year = "2024",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/23M1563001",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Mon Sep 30 10:38:50 MDT 2024",
bibsource = "http://epubs.siam.org/toc/sjoce3/46/5;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "https://epubs.siam.org/doi/10.1137/23M1563001",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "accurate floating-point summation; stochastic
rounding",
}
@Article{Faissole:2024:FVR,
author = "Florian Faissole",
title = "Formally-Verified Round-Off Error Analysis of
{Runge--Kutta} Methods",
journal = j-J-AUTOM-REASON,
volume = "68",
number = "1",
pages = "??--??",
month = mar,
year = "2024",
CODEN = "JAREEW",
DOI = "https://doi.org/10.1007/s10817-023-09686-y",
ISSN = "0168-7433 (print), 1573-0670 (electronic)",
ISSN-L = "0168-7433",
bibdate = "Fri May 24 08:31:25 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
URL = "https://link.springer.com/article/10.1007/s10817-023-09686-y",
acknowledgement = ack-nhfb,
ajournal = "J. Autom. Reason.",
articleno = "1",
fjournal = "Journal of Automated Reasoning",
journal-URL = "http://link.springer.com/journal/10817",
}
@TechReport{Fog:2024:FPE,
author = "Agner Fog",
title = "Floating point exception tracking and {NAN}
propagation",
type = "Report",
institution = "Technical University of Denmark",
address = "Lyngby, Denmark",
pages = "11",
day = "15",
month = aug,
year = "2024",
bibdate = "Wed Jan 15 10:06:11 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.agner.org/optimize/nan_propagation.pdf",
abstract = "The most common methods for detecting floating point
errors are based on exception trapping or a global
status register. These methods are inefficient in
modern systems that use out-of-order parallelism and
single-instruction-multiple-data (SIMD) parallelism for
improving performance. It is argued that a method based
on NAN propagation is more efficient and deterministic.
Problems with NAN propagation in current systems are
discussed. Examples of implementation in the C++ vector
class library and in an experimental instruction set
named ForwardCom are presented. The IEEE-754 standard
for floating point arithmetic may need adjustment to
accommodate the needs of modern forms of parallelism.",
acknowledgement = ack-nhfb,
remark = "Revision of \cite{Fog:2020:FPE} and
\cite{Fog:2023:FPE}.",
}
@Article{Giles:2024:REU,
author = "Michael B. Giles and Oliver Sheridan-Methven",
title = "Rounding Error Using Low Precision Approximate Random
Variables",
journal = j-SIAM-J-SCI-COMP,
volume = "46",
number = "4",
pages = "B502--B526",
month = "????",
year = "2024",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/23M1552814",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Sat Aug 24 16:22:17 MDT 2024",
bibsource = "http://epubs.siam.org/toc/sjoce3/46/4;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "https://epubs.siam.org/doi/10.1137/23M1552814",
acknowledgement = ack-nhfb,
ajournal = "SIAM J. Sci. Comput.",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@TechReport{Gladman:2024:AMFa,
author = "Brian Gladman and Vincenzo Innocente and John Mather
and Paul Zimmermann",
title = "Accuracy of Mathematical Functions in Single, Double,
Double Extended, and Quadruple Precision",
institution = "????",
pages = "25",
day = "15",
month = feb,
year = "2024",
bibdate = "Thu Feb 15 13:17:22 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://hal.inria.fr/hal-03141101;
https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
acknowledgement = ack-nhfb,
remark = "Tabular comparison of AMD, Apple, ARM, CUDA, FreeBSD,
GNU, Intel, LLVM, Microsoft Musl, Newlib, OpenLibm,
RadeonOpenCompute (ROCm), and RedHat -lm libraries for
correct rounding, versus results from MPFR.",
}
@TechReport{Gladman:2024:AMFb,
author = "Brian Gladman and Vincenzo Innocente and John Mather
and Paul Zimmermann",
title = "Accuracy of Mathematical Functions in Single, Double,
Double Extended, and Quadruple Precision",
institution = "????",
pages = "25",
day = "26",
month = aug,
year = "2024",
bibdate = "Thu Sep 19 14:49:38 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
acknowledgement = ack-nhfb,
remark = "Tabular comparison of AMD, Apple, ARM, CUDA, FreeBSD,
GNU, Intel, LLVM, Microsoft Musl, Newlib, OpenLibm,
RadeonOpenCompute (ROCm), and RedHat -lm libraries for
correct rounding, versus results from MPFR.",
}
@Article{Guthmuller:2024:XRV,
author = "Eric Guthmuller and C{\'e}sar Fuguet and Andrea Bocco
and J{\'e}r{\^o}me Fereyre and Riccardo Alidori and
Ihsane Tahir and Yves Durand",
title = "{Xvpfloat}: {RISC-V} {ISA} Extension for Variable
Extended Precision Floating Point Computation",
journal = j-IEEE-TRANS-COMPUT,
volume = "73",
number = "7",
pages = "1683--1697",
month = jul,
year = "2024",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2024.3383964",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jun 12 15:57:24 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "application specific processor; Arithmetic; Computer
architecture; Convergence; coprocessor; Field
programmable gate arrays; floating point arithmetic;
Hardware; high precision arithmetic; Instruction sets;
linear algebra; Open area test sites; RISC-V;
scientific computing; Software",
}
@Article{Haider:2024:DRA,
author = "Muhammad Hamis Haider and Hao Zhang and Seok-Bum Ko",
title = "Decoder Reduction Approximation Scheme for {Booth}
Multipliers",
journal = j-IEEE-TRANS-COMPUT,
volume = "73",
number = "3",
pages = "735--746",
month = mar,
year = "2024",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2023.3343093",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Feb 16 07:37:44 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; approximate computing; Booth multipliers;
Complexity theory; Computer architecture; convolutional
neural networks; Decoding; Error analysis; Filtration;
Hardware; leading one detection; logarithmic
multipliers",
}
@Article{Harris:2024:UDS,
author = "David Harris and James Stine and Milo Ercegovac and
Alberto Nannarelli and Katherine Parry and Cedar
Turek",
title = "Unified Digit Selection for Radix-4 Recurrence
Division and Square Root",
journal = j-IEEE-TRANS-COMPUT,
volume = "73",
number = "1",
pages = "292--300",
month = jan,
year = "2024",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2023.3305760",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Dec 27 15:37:27 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "division; minimally-redundant radix-4; RISC-V; square
root; SRT",
}
@Article{Harvey:2024:FTI,
author = "David Harvey",
title = "Faster truncated integer multiplication",
journal = j-MATH-COMPUT,
volume = "93",
number = "347",
pages = "1265--1296",
month = jul,
year = "2024",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/mcom/3939",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon May 27 15:56:44 MDT 2024",
bibsource = "https://www.ams.org/mcom/2024-93-347;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp2020.bib",
URL = "https://www.ams.org/journals/mcom/2024-93-347/S0025-5718-2024-03939-X",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "https://www.ams.org/mcom/",
pubdate = "2 February 2024",
}
@TechReport{Hubrecht:2024:TCR,
author = "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
Zimmermann and Laurence Rideau and Laurent Th{\'e}ry",
title = "Towards a correctly-rounded and fast power function in
binary64 arithmetic",
institution = "DI-ENS --- D{\'e}partement d'informatique --- ENS
Paris",
year = "2024",
type = "Report",
address = "Paris, France",
month = feb,
day = "8",
URL = "https://inria.hal.science/hal-04159652v2/",
acknowledgement = ack-nhfb,
bibdate = "Mon May 13 12:00:21 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "We design algorithms for the correct rounding of the
power function $x^y$ in the binary64 IEEE 754 format,
for all rounding modes, modulo the knowledge of
hardest-to-round cases. Our implementation of these
algorithms largely outperforms previous
correctly-rounded implementations and is not far from
the efficiency of current mathematical libraries, which
are not correctly-rounded. Still, we expect our
algorithms can be further improved for speed. The
proofs of correctness are fully detailed and have been
formally verified. We hope this work will motivate the
next IEEE 754 revision committee to require correct
rounding for mathematical functions.",
remark = "This is a longer version of \cite{Hubrecht:2023:TCRb}
with proofs and remarks by the final two authors on the
formal verification.",
}
@TechReport{Hubrecht:2024:UAC,
author = "Tom Hubrecht and Claude-Pierre Jeannerod and
Jean-Michel Muller",
title = "Useful applications of correctly-rounded operators of
the form $ a b + c d + e $",
type = "Report",
number = "hal-04461089",
institution = "DI-ENS (D{\'e}partment d'informatique --- ENS Paris)
and Universit{\'e} de Lyon",
address = "Paris, France and Lyon France",
day = "16",
month = feb,
year = "2024",
bibdate = "Thu Feb 22 05:37:30 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-04461089",
abstract = "We show that the availability of fused arithmetic
operators that evaluate expressions of the form $ a b +
c d $ (FD2 instruction) or $ a b + c d + e $ (FD2A
instruction) in floating-point arithmetic with one
final rounding only would significantly facilitate many
calculations that are hard to perform with high
accuracy at small cost using only the traditional
operations $+$, $-$, $ \div $, $ \times $, $ \sqrt {}
$, and fused multiply-add (FMA).",
acknowledgement = ack-nhfb,
}
@Article{Kim:2024:MCA,
author = "Kwang Ho Kim and Sihem Mesnager and Kyong Il Pak",
title = "{Montgomery} curve arithmetic revisited",
journal = j-J-CRYPTO-ENG,
volume = "14",
number = "2",
pages = "343--362",
month = jun,
year = "2024",
CODEN = "????",
DOI = "https://doi.org/10.1007/s13389-024-00353-5",
ISSN = "2190-8508 (print), 2190-8516 (electronic)",
ISSN-L = "2190-8508",
bibdate = "Thu Aug 8 07:34:12 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib
https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
note = "See \cite{Montgomery:1987:SPE}.",
URL = "https://link.springer.com/article/10.1007/s13389-024-00353-5",
acknowledgement = ack-nhfb,
ajournal = "J. Crypto. Eng.",
fjournal = "Journal of Cryptographic Engineering",
journal-URL = "http://link.springer.com/journal/13389",
}
@Article{Laudadio:2024:CIE,
author = "Teresa Laudadio and Nicola Mastronardi and Donatella
Occorsio",
title = "Computing integrals with an exponential weight on the
real axis in floating point arithmetic",
journal = j-APPL-NUM-MATH,
volume = "200",
number = "??",
pages = "309--317",
month = jun,
year = "2024",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2023.05.025",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Thu Apr 11 08:18:17 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0168927423001551",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Misc{Lefevre:2024:TMF,
author = "Vincent Lef{\`e}vre",
title = "Test of Mathematical Functions of the {Standard C
Library}",
howpublished = "Web site.",
day = "27",
month = sep,
year = "2024",
bibdate = "Mon Oct 21 11:32:37 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.vinc17.net/research/testlibm/;
https://www.vinc17.net/research/testlibm/hrcases/",
acknowledgement = ack-nhfb,
remark = "Contains link to collection of data files with
worst-case (or hard-to-round) arguments for common
elementary functions. See also
\cite{Lefevre:2003:WCC}.",
}
@Article{Lemire:2024:ESP,
author = "Daniel Lemire",
title = "Exact Short Products From Truncated Multipliers",
journal = j-COMP-J,
volume = "67",
number = "4",
pages = "1514--1520",
month = apr,
year = "2024",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxad077",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Apr 26 12:13:08 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/compj2020.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://academic.oup.com/comjnl/article/67/4/1514/7306807;
https://arxiv.org/abs/2303.14321v1",
abstract = "We sometimes need to compute the most significant
digits of the product of small integers with a
multiplier requiring much storage: e.g., a large
integer (e.g., $ 5^{100} $) or an irrational number ($
\pi $). We only need to access the most significant
digits of the multiplier --- as long as the integers
are sufficiently small. We provide an efficient
algorithm to compute the range of integers given a
truncated multiplier and a desired number of digits.",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Mackie:2024:RFM,
author = "Maximilien Mackie",
title = "Recursion-free modular arithmetic in the
lambda-calculus",
journal = j-INFO-PROC-LETT,
volume = "183",
number = "??",
pages = "Article 106408",
month = jan,
year = "2024",
CODEN = "IFPLAT",
DOI = "https://doi.org/10.1016/j.ipl.2023.106408",
ISSN = "0020-0190 (print), 1872-6119 (electronic)",
ISSN-L = "0020-0190",
bibdate = "Tue Sep 19 07:09:51 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/infoproc2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0020019023000510",
acknowledgement = ack-nhfb,
fjournal = "Information Processing Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00200190",
}
@Article{Mikaitis:2024:MMT,
author = "Mantas Mikaitis",
title = "Monotonicity of Multi-Term Floating-Point Adders",
journal = j-IEEE-TRANS-COMPUT,
volume = "??",
number = "??",
pages = "1--13",
month = "????",
year = "2024",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/tc.2024.3371783",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Mar 11 11:33:29 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "accurate floating-point summation",
remark = "Online on 11 March 2024, but not yet assigned to an
issue.",
}
@Misc{Muller:2024:SNC,
author = "Jean-Michel Muller",
title = "Some notes on correct rounding of functions",
howpublished = "Attachment to STDS-754 mailing list",
pages = "31",
day = "18",
month = sep,
year = "2024",
bibdate = "Thu Sep 19 15:27:07 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Article{Navimipour:2024:NSA,
author = "Nima Jafari Navimipour and Seyed-Sajad Ahmadpour and
Senay Yalcin",
title = "A nano-scale arithmetic and logic unit using a
reversible logic and quantum-dots",
journal = j-J-SUPERCOMPUTING,
volume = "80",
number = "1",
pages = "395--412",
month = jan,
year = "2024",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-023-05491-x",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Thu Feb 15 10:23:12 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-023-05491-x",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Noyez:2024:MMS,
author = "Louis Noyez and Nadia {El Mrabet} and Olivier Potin
and Pascal Veron",
title = "{Montgomery} Multiplication Scalable Systolic Designs
Optimized for {DSP48E2}",
journal = j-TRETS,
volume = "17",
number = "1",
pages = "9:1--9:??",
month = mar,
year = "2024",
CODEN = "????",
DOI = "https://doi.org/10.1145/3624571",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Wed Mar 20 07:25:09 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
URL = "https://dl.acm.org/doi/10.1145/3624571",
abstract = "This article describes an extensive study of the use
of DSP48E2 Slices in Ultrascale FPGAs to design
hardware versions of the Montgomery Multiplication
algorithm for the hardware acceleration of modular
multiplications. Our fully scalable systolic \ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Reconfigurable Technol. Syst.",
articleno = "9",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "https://dl.acm.org/loi/trets",
}
@Manual{Oracle:2024:SLR,
title = "{SQL} Language Reference",
organization = "{Oracle Corporation}",
publisher = pub-ORACLE,
address = pub-ORACLE:adr,
edition = "19c (E96310-27)",
month = jul,
year = "2024",
bibdate = "Tue Sep 10 15:24:10 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sqlbooks.bib",
note = "The Data Types section describes the (non-IEEE 754)
decimal number encoding. The precision is about 39
decimal digits, with a nonzero range of [1e-130,
1e126).",
URL = "https://docs.oracle.com/en/database/oracle/oracle-database/19/sqlrf/Data-Types.html#GUID-A3C0D836-BADB-44E5-A5D4-265BA5968483",
acknowledgement = ack-nhfb,
}
@Article{Perez:2024:HAF,
author = "J. Ayuso Perez",
title = "Hardware Addition Over Finite Fields Based On
{Booth--Karatsuba} Algorithm",
journal = j-COMP-J,
volume = "67",
number = "8",
pages = "2643--2666",
month = aug,
year = "2024",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxae034",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Mon Aug 19 11:43:29 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/compj2020.bib",
URL = "http://academic.oup.com/comjnl/article/67/8/2643/7667243",
acknowledgement = ack-nhfb,
fjournal = "Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Rashidi:2024:AFE,
author = "Bahram Rashidi",
title = "{APPAs}: fast and efficient approximate parallel
prefix adders and multipliers",
journal = j-J-SUPERCOMPUTING,
volume = "80",
number = "16",
pages = "24269--24296",
month = nov,
year = "2024",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-024-06356-7",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Thu Aug 22 13:34:29 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-024-06356-7",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Article{Sahoo:2024:ADF,
author = "Siva Satyendra Sahoo and Salim Ullah and Akash Kumar",
title = "{AxOMaP}: Designing {FPGA}-based Approximate
Arithmetic Operators using Mathematical Programming",
journal = j-TRETS,
volume = "17",
number = "2",
pages = "31:1--31:??",
month = jun,
year = "2024",
CODEN = "????",
DOI = "https://doi.org/10.1145/3648694",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Tue Jun 4 06:09:07 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
URL = "https://dl.acm.org/doi/10.1145/3648694",
abstract = "With the increasing application of machine learning
(ML) algorithms in embedded systems, there is a rising
necessity to design low-cost computer arithmetic for
these resource-constrained systems. As a result,
emerging models of computation, such as approximate and
stochastic computing, that leverage the inherent
error-resilience of such algorithms are being actively
explored for implementing ML inference on
resource-constrained systems. Approximate computing
(AxC) aims to provide disproportionate gains in the
power, performance, and area (PPA) of an application by
allowing some level of reduction in its behavioral
accuracy (BEHAV). Using approximate operators (AxOs)
for computer arithmetic forms one of the more prevalent
methods of implementing AxC. AxOs provide the
additional scope for finer granularity of optimization,
compared to only precision scaling of computer
arithmetic. To this end, the design of
platform-specific and cost-efficient approximate
operators forms an important research goal. Recently,
multiple works have reported the use of AI\slash
ML-based approaches for synthesizing novel FPGA-based
AxOs. However, most of such works limit the use of
AI/ML to designing ML-based surrogate functions that
are used during iterative optimization processes. To
this end, we propose a novel data analysis-driven
mathematical programming-based approach to synthesizing
approximate operators for FPGAs. Specifically, we
formulate mixed integer quadratically constrained
programs based on the results of correlation analysis
of the characterization data and use the solutions to
enable a more directed search approach for evolutionary
optimization algorithms. Compared to traditional
evolutionary algorithms-based optimization, we report
up to 21\% improvement in the hypervolume, for joint
optimization of PPA and BEHAV, in the design of signed
8-bit multipliers. Further, we report up to 27\% better
hypervolume than other state-of-the-art approaches to
DSE for FPGA-based application-specific AxOs.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Reconfigurable Technol. Syst.",
articleno = "31",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "https://dl.acm.org/loi/trets",
}
@Article{Scott:2024:ABI,
author = "Jennifer Scott and Miroslav Tuma",
title = "Avoiding Breakdown in Incomplete Factorizations in Low
Precision Arithmetic",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "9:1--9:25",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3651155",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3651155",
abstract = "The emergence of low precision floating-point
arithmetic in computer hardware has led to a resurgence
of interest in the use of mixed precision numerical
linear algebra. For linear systems of equations, there
has been renewed enthusiasm for mixed precision
variants of iterative refinement. We consider the
iterative solution of large sparse systems using
incomplete factorization preconditioners. The focus is
on the robust computation of such preconditioners in
half precision arithmetic and employing them to solve
symmetric positive definite systems to higher precision
accuracy; however, the proposed ideas can be applied
more generally. Even for well-conditioned problems,
incomplete factorizations can break down when small
entries occur on the diagonal during the factorization.
When using half precision arithmetic, overflows are an
additional possible source of breakdown. We examine how
breakdowns can be avoided and implement our strategies
within new half precision Fortran sparse incomplete
Cholesky factorization software. Results are reported
for a range of problems from practical applications.
These demonstrate that, even for highly ill-conditioned
problems, half precision preconditioners can
potentially replace double precision preconditioners,
although unsurprisingly this may be at the cost of
additional iterations of a Krylov solver.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "9",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Tosini:2024:AEI,
author = "Marcelo Tosini and Mart{\'\i}n V{\'a}zquez and Lucas
Leiva",
title = "Analysis and efficient implementation of {IEEE-754}
decimal floating point adders\slash subtractors in
{FPGAs} for {DPD} and {BID} encoding",
journal = j-J-SUPERCOMPUTING,
volume = "80",
number = "7",
pages = "9298--9326",
month = may,
year = "2024",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-023-05808-w",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Fri Apr 19 06:28:17 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-023-05808-w",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
keywords = "decimal floating-point arithmetic",
}
@Manual{Towner:2024:IAF,
author = "Daniel Towner and Steven Wood and Phoebe Wang and
Marius Cornea and Cristina Anderson and Amit
Gradstein",
title = "{Intel AVX-512} --- {FP16} Instruction Set for {Intel
Xeon} Processor Based Products Technology Guide",
organization = "Intel Corporation",
address = "????",
day = "12",
month = mar,
year = "2024",
bibdate = "Fri Apr 11 08:28:36 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://www.intel.com/content/www/us/en/content-details/669773/intel-avx-512-fp16-instruction-set-for-intel-xeon-processor-based-products-technology-guide.html",
acknowledgement = ack-nhfb,
}
@Article{Wu:2024:SAM,
author = "Ying Wu and Chuangtao Chen and Weihua Xiao and Xuan
Wang and Chenyi Wen and Jie Han and Xunzhao Yin and
Weikang Qian and Cheng Zhuo",
title = "A Survey on Approximate Multiplier Designs for Energy
Efficiency: From Algorithms to Circuits",
journal = j-TODAES,
volume = "29",
number = "1",
pages = "23:1--23:??",
month = jan,
year = "2024",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/3610291",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Mon Jan 15 11:14:18 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/todaes.bib",
URL = "https://dl.acm.org/doi/10.1145/3610291",
abstract = "Given the stringent requirements of energy efficiency
for Internet-of-Things edge devices, approximate
multipliers, as a basic component of many processors
and accelerators, have been constantly proposed and
studied for decades, especially in error-resilient
applications. The computation error and energy
efficiency largely depend on how and where the
approximation is introduced into a design. Thus, this
article aims to provide a comprehensive review of the
approximation techniques in multiplier designs ranging
from algorithms and architectures to circuits. We have
implemented representative approximate multiplier
designs in each category to understand the impact of
the design techniques on accuracy and efficiency. The
designs can then be effectively deployed in high-level
applications, such as machine learning, to gain energy
efficiency at the cost of slight accuracy loss.",
acknowledgement = ack-nhfb,
ajournal = "ACM Transact. Des. Automat. Electron. Syst.",
articleno = "23",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems",
journal-URL = "https://dl.acm.org/loi/todaes",
}
@Article{Xie:2024:FRO,
author = "Peichen Xie and Yanjie Gao and Jilong Xue",
title = "{FPRev}: Revealing the Order of Floating-Point
Summation by Numerical Testing",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "1--20",
day = "1",
month = nov,
year = "2024",
bibdate = "Tue Jan 28 06:36:44 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://arxiv.org/abs/2411.00442v1",
abstract = "The order of floating-point summation is a key factor
in numerical reproducibility. However, this critical
information is generally unspecified and unknown for
most summation-based functions in numerical libraries,
making it challenging to migrate them to new
environments reproducibly. This paper presents novel,
non-intrusive, testing-based algorithms that can reveal
the order of floating-point summation by treating
functions as callable black boxes. By constructing
well-designed input that can cause the swamping
phenomenon of floating-point addition, we can infer the
order of summation from the output. We introduce FPRev,
a tool that implements these algorithms, and validate
its efficiency through extensive experiments with
popular numerical libraries on various CPUs and GPUs
(including those with Tensor Cores). FPRev reveals the
varying summation orders across different libraries and
devices, and outperforms other methods in terms of time
complexity. The source code of FPRev is at this
article's URL.",
acknowledgement = ack-nhfb,
keywords = "accurate floating-point summation",
}
@Article{Zhang:2024:HSA,
author = "Zuoyan Zhang and Jinchen Xu and Jiangwei Hao and Yang
Qu and Haotian He and Bei Zhou",
title = "Hierarchical search algorithm for error detection in
floating-point arithmetic expressions",
journal = j-J-SUPERCOMPUTING,
volume = "80",
number = "1",
pages = "1183--1205",
month = jan,
year = "2024",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-023-05523-6",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Thu Feb 15 10:23:12 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-023-05523-6",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@TechReport{Zimmermann:2024:NVD,
author = "Paul Zimmermann",
title = "Note on the {Veltkamp\slash Dekker} Algorithms with
Directed Roundings",
type = "Report",
number = "hal-04480440",
institution = "Universit{\'e} de Lorraine, CNRS, Inria, LORIA",
address = "Metz, France",
day = "29",
month = feb,
year = "2024",
bibdate = "Thu Aug 01 17:14:10 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://inria.hal.science/hal-04480440",
abstract = "The Veltkamp\slash Dekker algorithms are very useful
for double-double arithmetic, when no fused
multiply-add is available in hardware. Their analysis
is well-known for rounding to nearest-even. We study
how they behave with directed roundings in radix 2.",
acknowledgement = ack-nhfb,
keywords = "CARAMBA --- Cryptology, arithmetic: algebraic methods
for better algorithms",
}
@Article{Zou:2024:PRE,
author = "Qinmeng Zou",
title = "Probabilistic Rounding Error Analysis of Modified
{Gram--Schmidt}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "45",
number = "2",
pages = "1076--1088",
month = may,
year = "2024",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/23m1585817",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri May 31 08:23:04 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
ajournal = "SIAM J. Matrix Anal. Appl.",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Allred:2025:FNT,
author = "Taylor Allred and Xinyi Li and Ashton Wiersdorf and
Ben Greenman and Ganesh Gopalakrishnan",
title = "{FlowFPX}: Nimble Tools for Debugging Floating-Point
Exceptions",
journal = "Proceedings of the {JuliaCon} Conferences",
volume = "7",
number = "67",
pages = "148:1--148:8",
year = "2025",
DOI = "https://doi.org/10.21105/jcon.00148",
bibdate = "Wed Jan 22 13:56:37 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/julia.bib",
abstract = "Reliable numerical computations are central to
scientific computing, but the floating-point arithmetic
that enables large-scale models is error-prone. Numeric
exceptions are a common occurrence and can propagate
through code, leading to flawed results. This paper
presents FlowFPX, a toolkit for systematically
debugging floating-point exceptions by recording their
flow, coalescing exception contexts, and fuzzing in
select locations. These tools help scientists discover
when exceptions happen and track down their origin,
smoothing the way to a reliable codebase.",
acknowledgement = ack-nhfb,
keywords = "debugging; floating-point; Julia",
ORCID-numbers = "Allred, Taylor/0009-0000-7238-1816; Li,
Xinyi/0009-0005-7276-7715; Wiersdorf,
Ashton/0000-0001-5524-7930; Greenman,
Ben/0000-0001-7078-9287; Gopalakrishnan,
Ganesh/0000-0002-4161-9278",
}
@Article{Cui:2025:PES,
author = "Mengqi Cui and Jinchen Xu and Yuchang Zhou and Hongru
Yang and Liguang Ji and Bei Zhou",
title = "{PESA}: error sensitivity analysis tool for
floating-point computational programs",
journal = j-J-SUPERCOMPUTING,
volume = "81",
number = "3",
pages = "??--??",
month = feb,
year = "2025",
CODEN = "JOSUED",
DOI = "https://doi.org/10.1007/s11227-025-06962-z",
ISSN = "0920-8542 (print), 1573-0484 (electronic)",
ISSN-L = "0920-8542",
bibdate = "Wed Feb 19 09:44:27 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
URL = "https://link.springer.com/article/10.1007/s11227-025-06962-z",
acknowledgement = ack-nhfb,
ajournal = "J. Supercomputing",
articleno = "477",
fjournal = "The Journal of Supercomputing",
journal-URL = "http://link.springer.com/journal/11227",
}
@Misc{Darcy:2025:FJ,
author = "Joseph Darcy",
title = "Float16.java",
howpublished = "Web site",
year = "2025",
bibdate = "Mon Mar 10 13:45:31 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://github.com/openjdk/jdk/blob/dbdbbd473061d7e8077ed07ccc6b03065a8c2ffc/src/jdk.incubator.vector/share/classes/jdk/incubator/vector/Float16.java#L1240",
acknowledgement = ack-nhfb,
remark = "The code comments provide an informal analysis that
Float16 fused multiply-add (FMA) can be correctly
implemented in IEEE 754 Binary64 arithmetic, including
for NaN, Infinity, and signed zero arguments.",
}
@TechReport{Gladman:2025:AMF,
author = "Brian Gladman and Vincenzo Innocente and John Mather
and Paul Zimmermann",
title = "Accuracy of Mathematical Functions in Single, Double,
Double Extended, and Quadruple Precision",
institution = "????",
pages = "27",
day = "10",
month = feb,
year = "2025",
bibdate = "Mon Feb 10 10:00:22 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
acknowledgement = ack-nhfb,
remark = "Tabular comparison of AMD, Apple, ARM, CUDA, FreeBSD,
GNU, Intel, LLVM, Microsoft Musl, Newlib, OpenLibm,
RadeonOpenCompute (ROCm), and RedHat -lm libraries for
correct rounding, versus results from MPFR.",
}
@Article{Imbach:2025:FER,
author = "R{\'e}mi Imbach and Guillaume Moroz",
title = "Fast evaluation and root finding for polynomials with
floating-point coefficients",
journal = j-J-SYMBOLIC-COMP,
volume = "127",
number = "??",
pages = "??--??",
month = mar # "\slash " # apr,
year = "2025",
CODEN = "JSYCEH",
DOI = "https://doi.org/10.1016/j.jsc.2024.102372",
ISSN = "0747-7171 (print), 1095-855X (electronic)",
ISSN-L = "0747-7171",
bibdate = "Fri Sep 6 08:44:41 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0747717124000762",
acknowledgement = ack-nhfb,
articleno = "102372",
fjournal = "Journal of Symbolic Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/07477171",
}
@Article{Kim:2025:SRF,
author = "Kevin Kim and Katherine Parry and David Harris and
Cedar Turek and Alessandro Maiuolo and Rose Thompson
and James Stine",
title = "Shared Recurrence Floating-Point Divide\slash Sqrt and
Integer Divide\slash Remainder With Early Termination",
journal = j-IEEE-TRANS-COMPUT,
volume = "74",
number = "2",
pages = "740--748",
month = feb,
year = "2025",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2024.3500380",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Mar 14 07:34:19 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Approximation algorithms; Art; Computer
architecture; Computers; Division; early termination;
Hardware; Logic; Optical wavelength conversion; Reduced
instruction set computing; remainder; RISC-V64
floating-point unit; square root; SRT; subnormal
arithmetic; Three-dimensional displays",
}
@Article{Ma:2025:STF,
author = "Dongyu Ma and Zeyu Liang and Luming Yin and Hongliang
Liang",
title = "Symbolic testing of floating-point bugs and
exceptions",
journal = j-J-SYST-SOFTW,
volume = "219",
number = "??",
pages = "??--??",
month = jan,
year = "2025",
CODEN = "JSSODM",
DOI = "https://doi.org/10.1016/j.jss.2024.112226;
https://doi.org/10.2139/ssrn.4797965",
ISSN = "0164-1212 (print), 1873-1228 (electronic)",
ISSN-L = "0164-1212",
bibdate = "Thu Nov 7 07:42:59 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/jsystsoftw2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S016412122400270X;
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4797965",
acknowledgement = ack-nhfb,
articleno = "112226",
fjournal = "Journal of Systems and Software",
journal-URL = "http://www.sciencedirect.com/science/journal/01641212",
keywords = "CVE (Common Vulnerabilities and Exposures) bug
reports; floating-point arithmetic; GNU Scientific
Library (GSL); interval arithmetic; LLVM/CLang compiler
system; MuPDF (viewing and converting PDF (Portable
Document Format) files); SoX (audio editing); symbolic
execution",
}
@Article{Mirzaei-Teshnizi:2025:PMM,
author = "Shahab Mirzaei-Teshnizi and Parviz Keshavarzi",
title = "Parallel Modular Multiplication Using Variable Length
Algorithms",
journal = j-IEEE-TRANS-COMPUT,
volume = "74",
number = "1",
pages = "143--154",
month = jan,
year = "2025",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2024.3475574",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Mar 14 07:34:19 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Canonic signed digit (CSD); Clocks; Computers;
Costs; Elliptic curve cryptography; Field programmable
gate arrays; FPGA; Hardware; high-speed arithmetic;
Interleaved modular multiplication; Montgomery
multiplication; Partitioning algorithms; Symbols;
Throughput",
}
@Article{Rathor:2025:AFE,
author = "Mahendra Rathor",
title = "{ALOHA-FP2I}: Efficient Algorithms and Hardware for
Multi-Mode Rounding of Floating Point to Integer",
journal = j-TECS,
volume = "24",
number = "1",
pages = "12:1--12:26",
month = jan,
year = "2025",
CODEN = "????",
DOI = "https://doi.org/10.1145/3701560",
ISSN = "1539-9087 (print), 1558-3465 (electronic)",
ISSN-L = "1539-9087",
bibdate = "Thu Jan 2 07:31:47 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/tecs.bib",
URL = "https://dl.acm.org/doi/10.1145/3701560",
abstract = "Modern technology is relying on hardware accelerators
to achieve enhanced performance of computing systems.
In the modern computing paradigm, floating point
representation of numbers has gained popularity owing
to its wide dynamic range. Rounding of floating point
numbers to integer is used in modern processor
architectures e.g., ARM and Intel's architecture (IA)
as well as in specific applications such as multimedia.
However, the academic literature lacks discussion on
hardware designs for rounding binary floating point
numbers to integer in different rounding modes. This
article presents novel efficient algorithms and
hardware architecture designs for rounding binary
floating point numbers to the integer for the following
rounding modes: round towards zero, round up (towards
positive infinity), round down (towards negative
infinity), round to the nearest integer, and round to
nearest even. The article also proposes an integrated
multi-mode rounding (IMR) algorithm and hardware design
which can be configured to a specific rounding mode
among the above-mentioned five modes. This article
proposes a mantissa bit of rounding (MBR) to determine
the condition of rounding for the various modes. The
MBR is identified on the basis of the dynamic range and
precision features of floating point representation. To
the best of our knowledge, we present the individual as
well as an integrated hardware design for the various
rounding modes for the first time in the literature.
The proposed designs have been implemented on an FPGA
platform to analyze the design metrics such as area,
delay, and power. The results imply that the proposed
designs are suitable to aid the intended hardware
accelerators as they are efficient in terms of the
design parameters. Moreover, this article presents the
integration of the proposed rounding hardware design
with the compression processor and evaluates the
integration overhead which is found to be nominal
(<1\%).",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Embed. Comput. Syst.",
articleno = "12",
fjournal = "ACM Transactions on Embedded Computing Systems",
journal-URL = "https://dl.acm.org/loi/tecs",
}
@Article{Vakili:2025:DFL,
author = "Shervin Vakili and Mobin Vaziri and Amirhossein Zarei
and J. M. Pierre Langlois",
title = "{DyRecMul}: Fast and Low-Cost Approximate Multiplier
for {FPGAs} using Dynamic Reconfiguration",
journal = j-TRETS,
volume = "18",
number = "1",
pages = "7:1--7:??",
month = mar,
year = "2025",
CODEN = "????",
DOI = "https://doi.org/10.1145/3663480",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Tue Mar 25 09:48:37 MDT 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
URL = "https://dl.acm.org/doi/10.1145/3663480",
abstract = "Multipliers are widely-used arithmetic operators in
digital signal processing and machine learning (ML)
circuits. Due to their relatively high complexity, they
can have high latency and be a significant source of
power consumption. One strategy to alleviate these
limitations is to use approximate computing. This
article thus introduces an original FPGA-based
approximate multiplier specifically optimized for ML
computations. It utilizes dynamically reconfigurable
lookup table (LUT) primitives in AMD-Xilinx technology
to realize the core part of the computations. The
article provides an in-depth analysis of the hardware
architecture, implementation outcomes, and accuracy
evaluations of the multiplier proposed in INT8
precision. The article also facilitates the
generalization of the proposed approximate multiplier
idea to other datatypes, providing analysis and
estimations for hardware cost and accuracy as a
function of multiplier parameters. Implementation
results on an AMD-Xilinx Kintex Ultrascale+ FPGA
demonstrate remarkable savings of 64\% and 67\% in LUT
utilization for signed multiplication and
multiply-and-accumulation configurations, respectively
when compared to the standard Xilinx multiplier core.
Accuracy measurements on four popular deep learning
(DL) benchmarks indicate a minimal average accuracy
decrease of less than 0.29\% during post-training
deployment, with the maximum reduction staying less
than 0.33\%. The source code of this work is available
on GitHub.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Reconfigurable Technol. Syst.",
articleno = "7",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "https://dl.acm.org/loi/trets",
}
@Article{Walczyk:2025:OAX,
author = "Cezary J. Walczyk and Leonid V. Moroz and Volodymyr
Samotyy and Jan L. Cie{\'s}li{\'n}ski",
title = "Optimal Approximation of the $ 1 / x $ Function using
{Chebyshev} Polynomials and Magic Constants",
journal = j-TOMS,
volume = "51",
number = "1",
pages = "2:1--2:??",
month = mar,
year = "2025",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3708472",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Thu Apr 10 08:03:40 MDT 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
abstract = "In this article we analyze low-cost accurate
approximation of the function $ 1 / x $ using Chebyshev
polynomials of the first kind and minimizing number of
elementary operations in computer codes (in particular,
by using the so-called magic constants). It is shown
that Newton-Raphson iterative method is not optimal and
a new approach is proposed. We prove that optimal
Chebyshev polynomials can be factorized in terms of
Chebyshev polynomials of lower order which leads to new
optimal iteration schemes. We also construct a family
of new algorithms by dividing the considered interval
into sub-intervals where different magic constants and
multiplicative factors are used (in order to increase
the accuracy). Theoretical considerations and proofs
are completed with numerical tests on three types of
microcontroller processors.",
accepted = "4 December 2024",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "2",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
received = "3 September 2022",
revised = "25 September 2024",
}
@Article{Wen:2025:PPW,
author = "Chenyi Wen and Haonan Du and Jiayi Wang and Zhengrui
Chen and Li Zhang and Qi Sun and Cheng Zhuo",
title = "{PACE}: a Piece-Wise Approximate Floating-Point
Divider with Runtime Configurability and High Energy
Efficiency",
journal = j-TODAES,
volume = "30",
number = "2",
pages = "21:1--21:??",
month = mar,
year = "2025",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/3706634",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Thu Feb 13 06:21:20 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/todaes.bib",
URL = "https://dl.acm.org/doi/10.1145/3706634",
abstract = "Approximate computing emerges as a viable solution to
enhance energy efficiency in applications sensitive to
human perception, particularly on edge devices. This
work introduces a novel piece-wise approximate
floating-point divider that boasts resource \ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Transact. Des. Automat. Electron. Syst.",
articleno = "21",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems",
journal-URL = "https://dl.acm.org/loi/todaes",
}
@Article{Wu:2025:TPM,
author = "Jiajun Wu and Mo Song and Jingmin Zhao and Yizhao Gao
and Jia Li and Hayden Kwok-Hay So",
title = "{TATAA}: Programmable Mixed-Precision Transformer
Acceleration with a Transformable Arithmetic
Architecture",
journal = j-TRETS,
volume = "18",
number = "1",
pages = "14:1--14:??",
month = mar,
year = "2025",
CODEN = "????",
DOI = "https://doi.org/10.1145/3714416",
ISSN = "1936-7406 (print), 1936-7414 (electronic)",
ISSN-L = "1936-7406",
bibdate = "Tue Mar 25 09:48:37 MDT 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/trets.bib",
URL = "https://dl.acm.org/doi/10.1145/3714416",
abstract = "Modern transformer-based deep neural networks present
unique technical challenges for effective acceleration
in real-world applications. Apart from the vast amount
of linear operations needed due to their sizes, modern
transformer models are increasingly reliance on precise
non-linear computations that make traditional
low-bitwidth quantization methods and fixed-dataflow
matrix accelerators ineffective for end-to-end
acceleration. To address this need to accelerate both
linear and non-linear operations in a unified and
programmable framework, this article introduces TATAA.
TATAA employs 8-bit integer (int8) arithmetic for
quantized linear layer operations through post-training
quantization, while it relies on bfloat16
floating-point arithmetic to approximate non-linear
layers of a transformer model. TATAA hardware features
a transformable arithmetic architecture that supports
both formats during runtime with minimal overhead,
enabling it to switch between a systolic array mode for
int8 matrix multiplications and a SIMD mode for
vectorized bfloat16 operations. An end-to-end compiler
is presented to enable flexible mapping from emerging
transformer models to the proposed hardware.
Experimental results indicate that our mixed-precision
design incurs only 0.14% to 1.16% accuracy drop when
compared with the pre-trained single-precision
transformer models across a range of vision, language,
and generative text applications. Our prototype
implementation on the Alveo U280 FPGA currently
achieves 2,935.2 GOPS throughput on linear layers and a
maximum of 189.5 GFLOPS for non-linear operations,
outperforming related works by up to in end-to-end
throughput and $ 2.29 \times $ in DSP efficiency, while
achieving $ 2.19 \times $ higher power efficiency than
modern NVIDIA RTX4090 GPU.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Reconfigurable Technol. Syst.",
articleno = "14",
fjournal = "ACM Transactions on Reconfigurable Technology and
Systems (TRETS)",
journal-URL = "https://dl.acm.org/loi/trets",
}
@Article{Xie:2025:FFL,
author = "Yujun Xie and Yuan Liu and Xin Zheng and Bohan Lan and
Dengyun Lei and Dehao Xiang and Shuting Cai and
Xiaoming Xiong",
title = "{FLALM}: a Flexible Low Area-Latency {Montgomery}
Modular Multiplication on {FPGA}",
journal = j-IEEE-TRANS-COMPUT,
volume = "74",
number = "1",
pages = "29--42",
month = jan,
year = "2025",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2024.3457739",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Fri Mar 14 07:34:19 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
acknowledgement = ack-nhfb,
ajournal = "IEEE Trans. Comput.",
fjournal = "IEEE Transactions on Computers",
journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Adders; Computers; Cryptography; Delays; Field
programmable gate arrays; finely integrated product
scanning; generic Montgomery modular multiplication;
Hardware acceleration; Hazards; Montgomery modular
multiplication; Schedules; square Montgomery modular
multiplication",
}
@Article{Zhao:2025:ISS,
author = "Gaoyang Zhao and Junzhong Shen and Rongzhen Lin and
Hua Li and Yaohua Wang",
title = "{ISOAcc}: In-situ Shift Operation-based Accelerator
For Efficient in-{SRAM} Multiplication",
journal = j-TODAES,
volume = "30",
number = "2",
pages = "22:1--22:??",
month = mar,
year = "2025",
CODEN = "ATASFO",
DOI = "https://doi.org/10.1145/3707205",
ISSN = "1084-4309 (print), 1557-7309 (electronic)",
ISSN-L = "1084-4309",
bibdate = "Thu Feb 13 06:21:20 MST 2025",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/todaes.bib",
URL = "https://dl.acm.org/doi/10.1145/3707205",
abstract = "Digital SRAM-based CIM architectures must balance
three critical factors: quantized neural network
bitwidth, accuracy loss, and computational efficiency,
each crucial to optimizing performance and efficiency.
In Domain Specific Accelerators (DSAs), flexible and
specific hardware design, when incorporated with
tailored Power-of-2 (P-2) quantization schemes,
addresses this issue. However, in CIMs, the absence of
flexible and specific hardware to support dynamic
switching between general and tailored quantization
schemes hinders the adoption of efficient quantization
methods. In this article, we propose the In-situ Shift
Operation based Accelerator (ISOAcc) for efficient
SRAM-based multiplication. The key idea is to introduce
transmission gates near the SRAM array to enable the
selection of bits from either the same or the neighbor
line when data flows from one row to another. This
functionally equals a shift operation. By configuring
the transmission gates array in a cascade manner,
ISOAcc can support 0 to 15-bit shift with a negligible
overhead. The ISOAcc can directly leverage P-2
quantization schemes in hardware, thereby greatly
reducing multiplication cycles. We have chosen five
well-known neural networks to evaluate ISOAcc. The
evaluations show that ISOAcc achieves an average
performance improvement of 3.24 $ \times $ and an
energy reduction of 75\%, compared with the
state-of-the-art (SOTA) SRAM-based CIM design,
Bit-Parallel.",
acknowledgement = ack-nhfb,
ajournal = "ACM Transact. Des. Automat. Electron. Syst.",
articleno = "22",
fjournal = "ACM Transactions on Design Automation of Electronic
Systems",
journal-URL = "https://dl.acm.org/loi/todaes",
}
@Misc{Anonymous:20xx:CMP,
author = "Anonymous",
title = "The {CORE-MATH} project",
howpublished = "Web site and code archive",
year = "20xx",
bibdate = "Mon Dec 04 07:10:51 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://core-math.gitlabpages.inria.fr/",
acknowledgement = ack-nhfb,
remark = "From the Web site: ``CORE-MATH Mission: provide
on-the-shelf high performance open-source mathematical
functions with correct rounding that can be integrated
into current mathematical libraries (GNU libc, Intel
Math Library, AMD Libm, Newlib, OpenLibm, Musl, Apple
Libm, llvm-libc, Microsoft libm, CUDA libm, ROCm)''",
}
@Misc{QinetiQ:20xx:QFP,
author = "{QinetiQ}",
title = "{Quixilica} floating point cores",
howpublished = "Web document",
year = "20xx",
bibdate = "Sat Oct 9 12:58:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.tekmicro.com/",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1948:PSL,
editor = "Anonymous",
booktitle = "Proceedings of a {Symposium on Large-Scale Digital
Calculating Machinery}: Jointly Sponsored by {The Navy
Department Bureau of Ordnance and Harvard University at
The Computation Laboratory 7--10 January 1947}",
title = "Proceedings of a {Symposium on Large-Scale Digital
Calculating Machinery}: Jointly Sponsored by {The Navy
Department Bureau of Ordnance and Harvard University at
The Computation Laboratory 7--10 January 1947}",
volume = "16",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "xxix + 302",
year = "1948",
LCCN = "QA75 .S96 1947",
bibdate = "Mon Nov 4 07:46:57 MST 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "The Annals of the Computation Laboratory of Harvard
University",
acknowledgement = ack-nhfb,
keywords = "calculators --- congresses; electronic digital
computers --- congresses",
remark = "Goldstine's paper is listed in the table of contents,
but is absent from the volume. The printed order of a
few papers differs from that shown in the table of
contents; the order has been corrected in the data in
this entry.",
tableofcontents = "Program of the Symposium on Large-Scale Digital
Calculating Machinery: 7--10 January 1947 \\
First Session: Tuesday, 7 January 1947 1O:00 a.m. \\
Opening Addresses \\
Mr. Edward Reynolds, Administrative Vice President of
Harvard University / 3--3 \\
Rear Admiral C. T. Joy, USN, Naval Proving Ground,
Dahlgren, Virginia / 4--6 \\
Professor Howard H. Aiken, Chairman, Harvard University
/ 7--7 \\
11:00 a.m. Inspection of the Computation Laboratory and
of Mark II Calculator \\
Second Session: Tuesday, 7 January 1947, 2:00 p.m. \\
Existing Calculating Machines / \\
Professor Willard E. Bleick, Chairman, Post Graduate
School, U.S. Naval Academy, Annapolis / \\
Mr. Richard H. Babbage, Montreal, Canada / The Work of
Charles Babbage / 13--22 \\
Mr. Richard M. Bloch, Harvard University / Mark I
Calculator / 23--30 \\
Dr. Lewis P. Tabor, University of Pennsylvania / Brief
Description and Operating Characteristics of the ENIAC
/ 31--40 \\
Mr. Samuel B. Williams, Consulting Electrical Engineer
/ Bell Telephone Laboratories' Relay Computing System /
41--68 \\
Mr. Robert V. D. Campbell, Harvard University / Mark II
Calculator / 69--79 \\
Third Session: Wednesday, 8 January 1947, 9:30 a.m. \\
The Logic of Large-Scale Calculating Machinery / \\
Professor \Vendell H. Furry, Chairman, Harvard
University \\
Dr. Alexander W. Wundheiler, Bureau of Ordnance /
Problems of Mathematical Analysis Involved in Machine
Computations / 83--90 \\
Dr. George R. Stibitz, University of Vermont / The
Organization of Large-Scale Calculating Machinery /
91--100 \\
Fourth Session: Wednesday, 8 January 1947, 2:00 p.m.
\\
Storage Devices \\
Dr. John H. Curtiss, Chairman / National Bureau of
Standards / \\
Dr. T. Kite Sharpless, University of Pennsylvania /
Mercury Delay Lines as a Memory Unit / 103--109 \\
Professor Leon Brillouin, Harvard University / Slow
Electromagnetic Waves / 110--124 \\
Dr. Jay W. Forrester, Massachusetts Institute of
Technology / High-Speed Electrostatic Storage /
125--129 \\
Dr. Benjamin L. Moore, Harvard University / Magnetic
and Phosphor Coated Discs / 130--132 \\
Dr. Jan Rajchman, Radio Corporation of America / The
Selectron --- A Tube for Selective Electrostatic
Storage / 133--145 \\
Dr. Arthur W. Tyler, Eastman Kodak Company / Optical
and Photographic Storage Techniques / 146--150 \\
Fifth Session: Thursday, 9 January 1947, 9:30 a.m. \\
Numerical Methods and Suggested Problems for Solution
\\
Dr. Mina Rees, Chairman, Office of Naval Research \\
Professor Richard Courant, New York University / Method
of Finite Differences for the Solution of Partial
Differential Equations / 153--156 \\
Dr. Raymond J. Seeger, Naval Ordnance Laboratory / On
Computational Techniques for Certain Problems in Fluid
Dynamics / 157--168 \\
Professor Wassily W. Leontief, Harvard University /
Computational Problems Arising in Connection with
Economic Analysis of interindustrial Relationships /
169--175 \\
Professor Hans A. Rademacher, University of
Pennsylvania / On the Accumulation of Errors in
Processes of Integration on High-Speed Calculating
Machines / 176--187 \\
Professor Howard W. Emmons, Harvard University / Fluid
Mechanics Computations / 188--193 \\
Dr. L. S. Dederick, Ballistic Research Laboratory,
Aberdeen, Maryland / Firing Tables / 194--199 \\
Sixth Session: Thursday, 9 January 1947, 2:00 p.m. \\
Sequencing, Coding, and Problem Preparation \\
Dr. Julius A. Stratton, Chairman, Massachusetts
Institute of Technology \\
Dr. John W. Mauchly, Electronic Control Company /
Preparation of Problems for EDVAC-Type Machines /
203--207 \\
Mr. Joseph 0. Harrison, Jr., Harvard University / The
Preparation of Problems for the Mark I Calculator /
208--210 \\
Dr. Herman H. Goldstine, Institute for Advanced Study /
Coding for Large-Scale Calculating Machinery / ??--??
\\
Seventh Session: Friday, 10 January 1947, 9:30 a.m. \\
Input and Output Devices \\
Professor E. Leon Chaffee, Chairman, Harvard University
\\
Mr. Frederick G. Miller, Harvard University /
Application of Printing Telegraph Techniques to
Large-Scale Calculating Machinery / 213--222 \\
Mr. Otto Kornei, The Brush Development Company / Survey
of Magnetic Recording / 223--237 \\
Mr. Harrison W. Fuller, Harvard University / The
Numeroscope / 238--247 \\
Dr. Samuel N. Alexander, National Bureau of Standards /
Input and Output Devices for Electronic Digital
Calculating Machinery / 248--253 \\
Dr. Morris Rubinoff, Harvard University / An Input
Device Using Multiple Gates / 254--259 \\
Dr. R. D. O'Neal, Eastman Kodak Company / Photographic
Methods of Handling Input and Output Data / 260--266
\\
Mr. C. Bradford Sheppard, Electronic Control Company /
Transfer Between External and Internal Memory /
267--273 \\
Eighth Session: Friday, 10 January 1947, 2:00 p.m. \\
Conclusions and Open Discussion \\
Professor Charles C. Bramble, Chairman, Post Graduate
School, U.S. Naval Academy, Annapolis / \\
Professor Samuel H. Caldwell, Massachusetts Institute
of Technology / Publication, Classification, and
Patents / 277--283 \\
Dr. Louis Couffignal (in absentia), Centre National de
la Recherche Scientifique / Le Domaine du Calcul
M{\'e}canique / 284--296 \\
Dr. Alan T. Waterman, Office of Naval Research / New
Vistas in Mathematics / 298--302",
}
@Proceedings{Householder:1951:MCM,
editor = "Alston S. Householder and George E. Forsythe and
Hallett-Hunt Germond",
booktitle = "{Monte Carlo method. Proceedings of a Symposium Held
June 29, 30 and July 1, 1949 in Los Angeles,
California}",
title = "{Monte Carlo method. Proceedings of a Symposium Held
June 29, 30 and July 1, 1949 in Los Angeles,
California}",
volume = "12",
publisher = pub-USGPO,
address = pub-USGPO:adr,
pages = "49",
year = "1951",
bibdate = "Tue Jan 31 06:36:58 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
series = ser-APPL-MATH-SER-NBS,
acknowledgement = ack-nhfb,
tableofcontents = "Preface / iii \\
Foreword / v \\
1. Showers produced by low-energy electrons and photons
/ Robert R. Wilson / 1 \\
2. An alignment chart for Monte Carlo solution of the
transport problem / B. I. Spinrad, G. H. Goertzel, W.
S. Snyder / 4 \\
3. Neutron age calculations in water, graphite, and
tissue / Alston S. Householder / 6 \\
4. Methods of probabilities in chains applied to
particle transmission through matter / Wendell C.
DeMarcus, Lewis Nelson / 9 \\
5. Stochastic methods in statistical mechanics / W.
Gilbert King / 12 \\
6. Report on a Monte Carlo calculation performed with
the Eniac / Maria Mayer / 19 \\
7. Calculation of shielding properties of water for
high energy neutrons / Preston C. Hammer / 21 \\
8. A Monte Carlo technique for estimating particle
attenuation in bulk matter / B. A. Shoor, Lewis Nelson,
Wendell DeMarcus, Robert L. Echols / 24 \\
9. Estimation of particle transmission by random
sampling / Herman Kahn, T. E. Harris / 27 \\
10. History of RAND's random digits --- Summary / W.
George Brown / 31 \\
11. The mid-square method of generating digits /
Preston C. Hammer / 33 \\
12. Generation and testing of random digits at the
National Bureau of Standards, Los Angeles / George E.
Forsythe / 34 \\
13. Various techniques used in connection with random
digits / John von Neumann / 36 \\
14. Round table discussion / H. H. Germond / 39",
}
@Book{Alt:1960:AC,
editor = "Franz L. Alt and Andrew Donald Booth and Robert Emmet
Meagher",
booktitle = "Advances in Computers",
title = "Advances in Computers",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 316",
year = "1960",
ISSN = "0065-2458",
LCCN = "QA76 .A3",
bibdate = "Sat Nov 29 11:05:31 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Taub:1961:JNCa,
editor = "A. H. Taub",
booktitle = "{John von Neumann}: Collected Works: {Volume I}:
{Logic}, Theory of Sets and Quantum Mechanics",
title = "{John von Neumann}: Collected Works: {Volume I}:
{Logic}, Theory of Sets and Quantum Mechanics",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "x + 654",
year = "1961",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also volumes II--VI
\cite{Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.",
ZMnumber = "0188.00102",
acknowledgement = ack-nhfb,
}
@Book{Taub:1961:JNCb,
editor = "A. H. Taub",
booktitle = "{John von Neumann}: Collected Works. {Volume II}:
{Operators}, Ergodic Theory and Almost Periodic
Functions in a Group",
title = "{John von Neumann}: Collected Works. {Volume II}:
{Operators}, Ergodic Theory and Almost Periodic
Functions in a Group",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "x + 568",
year = "1961",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also volumes I, III--VI
\cite{Taub:1961:JNCa,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.",
ZMnumber = "0188.00102",
acknowledgement = ack-nhfb,
}
@Book{Taub:1961:JNCc,
editor = "A. H. Taub",
booktitle = "{John von Neumann}: Collected Works. {Volume III}:
Rings of Operators",
title = "{John von Neumann}: Collected Works. {Volume III}:
Rings of Operators",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "ix + 574",
year = "1961--1963",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also volumes I--II, IV--VI
\cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.",
ZMnumber = "0188.00102",
acknowledgement = ack-nhfb,
}
@Proceedings{AFIPS:1962:APS,
editor = "AFIPS",
key = "AFIPS SJCC '62",
booktitle = "{AFIPS} Proceedings of the {Spring Joint Computer
Conference} 1962",
title = "{AFIPS} Proceedings of the {Spring Joint Computer
Conference} 1962",
volume = "21",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "??--??",
year = "1962",
LCCN = "????",
bibdate = "Wed Feb 14 17:16:30 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AFIPS conference proceedings",
acknowledgement = ack-nhfb,
}
@Book{Taub:1962:JNC,
editor = "A. H. Taub",
booktitle = "{John von Neumann}: Collected Works. {Volume IV}:
{Continuous} Geometry and Other Topics",
title = "{John von Neumann}: Collected Works. {Volume IV}:
{Continuous} Geometry and Other Topics",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "x + 516",
year = "1962",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also volumes I--III, V--VI
\cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1963:JNCa,Taub:1963:JNCb}.",
ZMnumber = "0188.00102",
acknowledgement = ack-nhfb,
}
@Proceedings{Metropolis:1963:PFS,
editor = "N. Metropolis and A. H. Taub and John Todd and C. B.
Tompkins",
booktitle = "{Experimental arithmetic, high speed computing and
mathematics: Proceedings of the fifteenth Symposium in
Applied Mathematics of the American Mathematical
Society held in Chicago, Illinois, April 12--14, 1962
and Atlantic City, New Jersey, April 16-19, 1962}",
title = "{Experimental arithmetic, high speed computing and
mathematics: Proceedings of the fifteenth Symposium in
Applied Mathematics of the American Mathematical
Society held in Chicago, Illinois, April 12--14, 1962
and Atlantic City, New Jersey, April 16-19, 1962}",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "ix + 396",
year = "1963",
LCCN = "QA297 .S987 1962",
bibdate = "Tue Mar 20 10:37:16 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Taub:1963:JNCa,
editor = "A. H. Taub",
booktitle = "{John von Neumann}: Collected Works. {Volume V}:
{Design} of Computers, Theory of Automata and Numerical
Analysis",
title = "{John von Neumann}: Collected Works. {Volume V}:
{Design} of Computers, Theory of Automata and Numerical
Analysis",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "ix + 784",
year = "1963",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See also volumes I--IV, VI
\cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCb}.",
ZMnumber = "0188.00102",
acknowledgement = ack-nhfb,
}
@Book{Taub:1963:JNCb,
editor = "A. H. Taub",
booktitle = "{John von Neumann}: Collected Works. {Volume VI}:
{Theory} of Games, Astrophysics, Hydrodynamics and
Meteorology",
title = "{John von Neumann}: Collected Works. {Volume VI}:
{Theory} of Games, Astrophysics, Hydrodynamics and
Meteorology",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "x + 538",
year = "1963",
LCCN = "????",
bibdate = "Wed Jun 01 16:58:29 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "See also volumes I--V
\cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa}.",
ZMnumber = "0188.00102",
acknowledgement = ack-nhfb,
}
@Book{Wilkinson:1963:REA,
author = "J. H. Wilkinson",
booktitle = "Rounding Errors in Algebraic Processes",
title = "Rounding Errors in Algebraic Processes",
volume = "32",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "vi + 161",
year = "1963",
ISBN = "0-486-67999-3 (Dover)",
ISBN-13 = "978-0-486-67999-0 (Dover)",
LCCN = "QA76.5 .W53 1964",
MRclass = "65.80",
MRnumber = "MR0161456 (28 \#4661)",
MRreviewer = "A. S. Householder",
bibdate = "Sat Feb 8 10:28:55 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also published by Prentice-Hall, Englewood Cliffs, NJ,
USA, 1964, translated into Polish as {\em Bledy
Zaokragle{\'n} w Procesach Algebraicznych\/} by PWW,
Warsaw, Poland, 1967 and translated into German as {\em
Rundungsfehler\/} by Springer-Verlag, Berlin, Germany,
1969. Reprinted by Dover Publications, New York,
1994.",
series = "Notes on Applied Science",
acknowledgement = ack-nhfb,
remark = "Cited in \cite{Sterbenz:1974:FPC}.",
tableofcontents = "1. The Fundamental Arithmetic Operations \\
Digital computation / 1 \\
Fixed-point and floating-point computation / 1 \\
Notational conventions / 2 \\
Rounding errors in fixed-point computation / 4 \\
Fixed-point accumulation of inner-products / 6 \\
Rounding errors in floating-point computation / 7 \\
Round-off with single-precision accumulator / 11 \\
Comparison of fixed-point and floating-point
computation / 14 \\
Common floating-point operations / 16 \\
More precise bounds / 19 \\
Floating-point accumulation of sums and inner-products
/ 23 \\
Statistical error bounds / 25 \\
Block-floating vectors and matrices / 26 \\
Fundamental limitations oft-digit computation / 27 \\
Ill-conditioned problems / 28 \\
Condition numbers / 29 \\
Rounding errors in the computation / 30 \\
Additional comments / 33 \\
2. Computations Involving Polynomials \\
Evaluation of power series / 34 \\
Fixed-point representation / 34 \\
Floating-point representation / 36 \\
Calculation of zeros of functions defined by power
series / 37 \\
Polynomials with arbitrary coefficients / 38 \\
Condition of a polynomial with respect to the
computation of its zeros / 38 \\
Some typical distributions of zeros / 41 \\
Linear distributions of zeros / 41 \\
Geometric distribution / 44 \\
Chebyshev polynomial / 46 \\
Significance of the condition of the zeros of
polynomials 4 / 7 \\
Determination of the zeros / 49 \\
Iterative methods / 52 \\
Effect of rounding errors on Newton's process / 53 \\
Simple examples / 54 \\
Polynomial deflation / 55 \\
Analysis of errors inherent in deflation / 56 \\
Examples of deflation / 59 \\
Deflation of ill-conditioned polynomials / 62 \\
General comments on iteration and deflation / 64 \\
Purification in the original polynomial / 65 \\
Other iterative methods / 66 \\
The root-squaring process / 67 \\
Forward error analysis of root-squaring / 69 \\
Relative error in computed coefficients / 71 \\
Numerical example / 72 \\
Deterioration of condition / 74 \\
General comments on the computation of zeros of
polynomials / 76 \\
Additional comments / 78 \\
3. Matrix Computations \\
Introduction / 79 \\
Vector and matrix norms / 80 \\
Error analysis of simple matrix operations / 82 \\
Matrix multiplication / 83 \\
Matrix operations in block-floating arithmetic / 85 \\
Matrices which are not infinity row standardized / 85
\\
Orthogonalization of vectors / 86 \\
Numerical example / 87 \\
General case / 89 \\
Solution of equations and matrix inversion / 91 \\
Rounding of matrix of coefficients / 93 \\
Error analysis of Gaussian elimination / 94 \\
Computational equations / 95 \\
Floating-point bounds / 96 \\
Gaussian elimination in fixed-point / 99 \\
Determinant evaluation / 99 \\
Solution of a triangular set of equations using
standard floating-point arithmetic / 99 \\
Accuracy of computed solution / 102 \\
Solution of triangular set of equations with
floating-point accumulation of inner-products / 103 \\
Inversion of a triangular matrix / 104 \\
High accuracy of solutions of triangular equations /
105 \\
Solution of a general set of equations / 107 \\
Inversion of a general matrix / 109 \\
Left-handed and right-handed inverses / 110 \\
Numerical example / 111 \\
Comments on example / 113 \\
Compact methods of triangular decomposition / 114 \\
Triangular decomposition with partial pivoting / 115
\\
Positive definite matrix / 117 \\
Numerical example / 118 \\
Comments on the solution / 119 \\
Residual corresponding to block-floating solution / 120
\\
Iterative refinement of the solution / 121 \\
Practical procedure / 122 \\
Analysis of the practical procedure / 124 \\
Assessment of accuracy of the computed solution / 126
\\
The use of an estimate for $||A^{-1}||$ / 126 \\
Assessment of a computed inverse / 127 \\
Use of the approximate inverse to solve equations / 128
\\
Iterative procedure based on use of the approximate
inverse / 130 \\
Numerical example / 131 \\
Sensitivity of the eigenvalues of a matrix / 134 \\
Sensitivity of individual eigenvalues / 137 \\
Example of ill-conditioned eigenvalues / 138 \\
A posteriori estimates for a computed eigenvalue and
eigenvector of a real symmetric matrix / 139 \\
Calculation of the eigenvectors of a symmetric
tri-diagonal matrix / 142 \\
Effect of rounding errors / 143 \\
Calculation of the eigenvalues of a lower Hessenberg
matrix / 147 \\
Calculation of $f(\lambda)$ using floating-point
accumulation / 149 \\
Perturbation of the eigenvalues / 150 \\
Numerical example / 151 \\
Additional comments / 155 \\
Bibliography / 157 \\
Index / 159",
}
@Proceedings{AFIPS:1965:FJC,
key = "AFIPS FJCC '65",
booktitle = "{1965 Fall Joint Computer Conference, 18--20 November,
1965, Las Vegas, Nevada}",
title = "{1965 Fall Joint Computer Conference, 18--20 November,
1965, Las Vegas, Nevada}",
volume = "27",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "????",
year = "1965",
LCCN = "????",
bibdate = "Fri Sep 16 10:42:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AFIPS conference proceedings",
acknowledgement = ack-nj,
}
@Book{Alt:1965:AC,
editor = "Franz L. Alt and Morris Rubinoff and Andrew Donald
Booth and Robert Emmet Meagher",
booktitle = "Advances in Computers",
title = "Advances in Computers",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiv + 310",
year = "1965",
ISSN = "0065-2458",
LCCN = "QA76 .A3",
bibdate = "Sat Nov 29 11:06:34 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Kalenich:1965:IPP,
editor = "Wayne A. Kalenich",
booktitle = "{Information processing 1965: proceedings of IFIP
congress 65; New York City May 24--29, 1965}",
title = "{Information processing 1965: proceedings of IFIP
congress 65; New York City May 24--29, 1965}",
publisher = "Spartan Books",
address = "Washington, DC, USA",
pages = "648",
year = "1965",
LCCN = "????",
bibdate = "Tue Mar 20 10:47:07 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
remark = "Third international conference on information
processing, organized by the International Federation
for Information Processing.",
}
@Proceedings{Rall:1965:EDCa,
editor = "L. B. Rall",
booktitle = "Error in Digital Computation",
title = "Error in Digital Computation",
volume = "1",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "338",
year = "1965",
MRclass = "65.80",
MRnumber = "MR0189284 (32 \#6711)",
MRreviewer = "J. M. Ortega",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Proceedings of an advanced seminar conducted by the
Mathematics Research Center, United States Army, at the
University of Wisconsin, Madison, October 5--7, 1964.",
acknowledgement = ack-nhfb,
tableofcontents = "1. The problem of error in digital computation /
Todd \\
2. Techniques for automatic error monitoring and
control / Ashenhurst \\
3. The automatic analysis and control of error in
digital computing based on the use of interval numbers
/ Moore \\
4. Error in digital solution of linear problems /
Albasiny \\
5. The propagation of error in the digital integration
of ordinary differential equations / Henrici \\
6. Bibliography on error in digital computation (114
pp.)",
}
@Proceedings{Rall:1965:EDCb,
editor = "L. B. Rall",
booktitle = "Error in Digital Computation",
title = "Error in Digital Computation",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "288",
year = "1965",
MRclass = "65.80",
MRnumber = "MR0189284 (32 \#6711)",
MRreviewer = "J. M. Ortega",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Proceedings of an advanced seminar conducted by the
Mathematics Research Center, United States Army, at the
University of Wisconsin, Madison, October 5--7, 1964.",
acknowledgement = ack-nhfb,
tableofcontents = "1. Experimental investigation of unnormalized
arithmetic / Ashenhurst \\
2. Error bounds for computations with continued
fractions / Henrici \\
3. Error bounds for asymptotic expansions of special
functions in the complex plane / Olver \\
4. Error analysis for transformations based on the use
of matrices of the form $I -2 w w^H$. / Wilkinson \\
5. Automatic local coordinate transformations to reduce
the growth of error bounds in interval computation of
solutions of ordinary differential equations / Moore
\\
6. Differential inequalities and error bounds /
Schroder \\
7. Discrete representations of partial differential
operators / Young and Dauwalder \\
8. Upper and lower bounds for solutions of integral
equations / Brown \\
9. Convergence ana error bounds for approximate
solutions of integral and operator equations / Anselone
\\
10. Applications of functional analysis to error
estimation / Collatz \\
11. Error in the solution of linear programming
problems / Wolfe",
}
@Book{Wilkinson:1965:AEP,
author = "J. H. Wilkinson",
booktitle = "The Algebraic Eigenvalue Problem",
title = "The Algebraic Eigenvalue Problem",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xviii + 662",
year = "1965",
ISBN = "0-19-853403-5",
ISBN-13 = "978-0-19-853403-7",
LCCN = "QA218 .W686 1965",
MRclass = "65.40",
MRnumber = "MR0184422 (32 \#1894)",
MRreviewer = "A. S. Householder",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
acknowledgement = ack-nhfb,
shorttableofcontents = "1. Theoretical Background \\
2. Perturbation Theory \\
3. Error Analysis \\
4. Solution of Linear Algebraic Equations \\
5. Hermitian Matrices \\
6. Reduction of a General Matrix to Condensed Form \\
7. Eigenvalues of Matrices of Condensed Forms \\
8. The $ L R $ and $ Q R $ Algorithms \\
9. Iterative Methods \\
Bibliography / 649 \\
Index / 657",
tableofcontents = "1. Theoretical Background \\
Introduction / 1 \\
Definitions / 2 \\
Eigenvalues and eigenvectors of the transposed matrix /
3 \\
Distinct eigenvalues / 4 \\
Similarity transformations / 6 \\
Multiple eigenvalues and canonical forms for general
matrices / 7 \\
Defective system of eigenvectors / 9 \\
The Jordan (classical) canonical form / 10 \\
The elementary divisors / 12 \\
Companion matrix of the characteristic polynomial of
$A$ / 12 \\
Non-derogatory matrices / 13 \\
The Frobenius (rational) canonical form / 15 \\
Relationship between the Jordan and Frobenius canonical
forms / 16 \\
Equivalence transformations / 17 \\
Lambda matrices / 18 \\
Elementary operations / 19 \\
Smith's canonical form / 19 \\
The highest common factor of $k$-rowed minors of a
$A$-matrix / 22 \\
Invariant factors of $ (A - \lambda M) $ / 22 \\
The triangular canonical form / 24 \\
Hermitian and symmetric matrices / 24 \\
Elementary properties of Hermitian matrices / 25 \\
Complex symmetric matrices / 26 \\
Reduction to triangular form by unitary transformations
/ 27 \\
Quadratic forms / 27 \\
Necessary and sufficient conditions for positive
definiteness / 28 \\
Differential equations with constant coefficients / 30
\\
Solutions corresponding to non-linear elementary
divisors / 31 \\
Differential equations of higher order / 32 \\
Second-order equations of special form / 34 \\
Explicit solution of $ B \ddot{y} = -A y$ / 35 \\
Equations of the form $(AB - \lambda I) x = 0$ / 35 \\
The minimum polynomial of a vector / 36 \\
The minimum polynomial of a matrix / 37 \\
Cayley--Hamilton theorem / 38 \\
Relation between minimum polynomial and canonical forms
/ 39 \\
Principal vectors / 42 \\
Elementary similarity transformations / 43 \\
Properties of elementary matrices / 45 \\
Reduction to triangular canonical form by elementary
similarity transformations / 46 \\
Elementary unitary transformations / 47 \\
Elementary unitary Hermitian matrices / 48 \\
Reduction to triangular form by elementary unitary
transformations / 50 \\
Normal matrices / 51 \\
Commuting matrices / 52 \\
Eigenvalues of $A B$ / 54 \\
Vector and matrix norms / 55 \\
Subordinate matrix norms / 56 \\
The Euclidean and spectral norms / 57 \\
Norms and limits / 58 \\
Avoiding use of infinite matrix series / 60 \\
2. Perturbation Theory \\
Introduction / 62 \\
Ostrowski's theorem on continuity of the eigenvalues /
63 \\
Algebraic functions / 64 \\
Numerical examples / 65 \\
Perturbation theory for simple eigenvalues / 66 \\
Perturbation of corresponding eigenvectors / 67 \\
Matrix with linear elementary divisors / 68 \\
First-order perturbations of eigenvalues / 68 \\
First-order perturbations of eigenvectors / 69 \\
Higher-order perturbations / 70 \\
Multiple eigenvalues / 70 \\
Gerschgorin's theorems / 71 \\
Perturbation theory based on Gerschgorin's theorems /
72 \\
Case 1. Perturbation of a simple eigenvalue $\lambda_1$
of a matrix having linear elementary divisors / 72 \\
Case 2. Perturbation of a multiple eigenvalue
$\lambda_1$ of a matrix having linear elementary
divisors / 75 \\
Case 3. Perturbation of a simple eigenvalue of a matrix
having one or more non-linear elementary divisors / 77
\\
Case 4. Perturbations of the eigenvalues corresponding
to a non-linear elementary divisor of a non-derogatory
matrix / 79 \\
Case 5. Perturbations of eigenvalues $\lambda_i$ when
there is more than one divisor involving $(\lambda_i -
\lambda_)$ and at least one of them is non-linear / 80
\\
Perturbations corresponding to the general distribution
of non-linear divisors / 81 \\
Perturbation theory for the eigenvectors from Jordan
canonical form / 81 \\
Perturbations of eigenvectors corresponding to a
multiple eigenvalue (linear elementary divisors) / 83
\\
Limitations of perturbation theory / 84 \\
Relationships between the $s_i$ / 85 \\
The condition of a computing problem / 86 \\
Condition numbers / 86 \\
Spectral condition number of A with respect to its
eigenproblem / 87 \\
Properties of spectral condition number / 88 \\
Invariant properties of condition numbers / 89 \\
Very ill-conditioned matrices / 90 \\
Perturbation theory for real symmetric matrices / 93
\\
Unsymmetric perturbations / 93 \\
Symmetric perturbations / 94 \\
Classical techniques / 94 \\
Symmetric matrix of rank unity / 97 \\
Extremal properties of eigenvalues / 98 \\
Minimax characterization of eigenvalues / 99 \\
Eigenvalues of the sum of two symmetric matrices / 101
\\
Practical applications / 102 \\
Further applications of minimax principle / 103 \\
Separation theorem / 103 \\
The Wielandt--Hoffman theorem / 104 \\
3. Error Analysis \\
Introduction / 110 \\
Fixed-point operations / 110 \\
Accumulation of inner-products / 111 \\
Floating-point operations / 112 \\
Simplified expressions for error bounds / 113 \\
Error bounds for some basic floating-point computations
/ 114 \\
Bounds for norms of the error matrices / 115 \\
Accumulation of inner-products in floating-point
arithmetic / 116 \\
Error bounds for some basic $\fl_2() $ computations /
117 \\
Computation of square roots / 118 \\
Block-floating vectors and matrices / 119 \\
Fundamental limitations oft-digit computation / 120 \\
Eigenvalue techniques based on reduction by similarity
transformations / 123 \\
Error analysis of methods based on elementary
non-unitary transformations / 124 \\
Error analysis of methods based on elementary unitary
transformations / 126 \\
Superiority of the unitary transformation / 128 \\
Real symmetric matrices / 129 \\
Limitations of unitary transformations / 129 \\
Error analysis of floating-point computation of plane
rotations / 131 \\
Multiplication by a plane rotation / 133 \\
Multiplication by a sequence of plane rotations / 134
\\
Error in product of approximate plane rotations / 139
\\
Errors in similarity transforms / 140 \\
Symmetric matrices / 141 \\
Plane rotations in fixed-point arithmetic / 143 \\
Alternative computation of $\sin \theta$ and $\cos
\theta$ / 145 \\
Pre-multiplication by an approximate fixed-point
rotation / 145 \\
Multiplication by a sequence of plane rotations
(fixed-point) / 147 \\
The computed product of an approximate set of plane
rotations / 148 \\
Errors in similarity transformations / 148 \\
General comments on the error bounds / 151 \\
Elementary Hermitian matrices in floating-point / 152
\\
Error analysis of the computation of an elementary
Hermitian matrix / 153 \\
Numerical example / 156 \\
Pre-multiplication by an approximate elementary
Hermitian matrix / 157 \\
Multiplication by a sequence of approximate elementary
Hermitians / 160 \\
Non-unitary elementary matrices analogous to plane
rotations / 162 \\
Non-unitary elementary matrices analogous to elementary
Hermitian matrices / 163 \\
Pre-multiplication by a sequence of non-unitary
matrices / 165 \\
A priori error bounds / 166 \\
Departure from normality / 167 \\
Simple examples / 169 \\
A posteriori bounds / 170 \\
A posteriori bounds for normal matrices / 170 \\
Rayleigh quotient / 172 \\
Error in Rayleigh quotient / 173 \\
Hermitian matrices / 174 \\
Pathologically close eigenvalues / 176 \\
Non-normal matrices / 178 \\
Error analysis for a complete eigensystem / 180 \\
Numerical example / 181 \\
Conditions limiting attainable accuracy / 181 \\
Non-linear elementary, divisors / 182 \\
Approximate invariant subspaces / 184 \\
Almost normal matrices / 187 \\
4. Solution of Linear Algebraic Equations \\
Introduction / 189 \\
Perturbation theory / 189 \\
Condition numbers / 191 \\
Equilibrated matrices / 192 \\
Simple practical examples / 193 \\
Condition of matrix of eigenvectors / 193 \\
Explicit solution / 194 \\
General comments on condition of matrices / 195 \\
Relation of ill-conditioning to near-singularity / 196
\\
Limitations imposed by t-digit arithmetic / 197 \\
Algorithms for solving linear equations / 198 \\
Gaussian elimination / 200 \\
Triangular decomposition / 201 \\
Structure of triangular decomposition matrices / 201
\\
Explicit expressions for elements of the triangles /
202 \\
Breakdown of Gaussian elimination / 204 \\
Numerical stability / 205 \\
Significance of the interchanges / 206 \\
Numerical example / 207 \\
Error analysis of Gaussian elimination / 209 \\
Upper bounds for the perturbation matrices using
fixed-point arithmetic / 211 \\
Upper bound for elements of reduced matrices / 212 \\
Complete pivoting / 212 \\
Practical procedure with partial pivoting / 214 \\
Floating-point error analysis / 214 \\
Floating-point decomposition without pivoting / 215 \\
Loss of significant figures / 217 \\
A popular fallacy / 217 \\
Matrices of special form / 218 \\
Gaussian elimination on a high-speed computer / 220 \\
Solutions corresponding to different right-hand sides /
221 \\
Direct triangular decomposition / 221 \\
Relations between Gaussian elimination and direct
triangular decomposition / 223 \\
Examples of failure and non-uniqueness of decomposition
/ 224 \\
Triangular decomposition with row interchanges / 225
\\
Error analysis of triangular decomposition / 227 \\
Evaluation of determinants / 228 \\
Cholesky decomposition / 229 \\
Symmetric matrices which are not positive definite /
230 \\
Error analysis of Cholesky decomposition in fixed-point
arithmetic / 231 \\
An ill-conditioned matrix / 233 \\
Triangularization using elementary Hermitian matrices /
233 \\
Error analysis of Householder triangularization / 236
\\
Triangularization by elementary stabilized matrices of
the type M1, / 236 \\
Evaluation of determinants of leading principal minors
/ 237 \\
Triangularization by plane rotations / 239 \\
Error analysis of Givens reduction / 240 \\
Uniqueness of orthogonal triangularization / 241 \\
Schmidt orthogonalization / 242 \\
Comparison of the methods of triangularization / 244
\\
Back-substitution / 247 \\
High accuracy of computed solutions of triangular sets
of equations / 249 \\
Solution of a general set of equations / 251 \\
Computation of the inverse of a general matrix / 252
\\
Accuracy of computed solutions / 253 \\
Ill-conditioned matrices which give no small pivots /
254 \\
Iterative improvements of approximate solution / 255
\\
Effect of rounding errors on the iterative process /
256 \\
The iterative procedure in fixed-point computation /
257 \\
Simple example of iterative procedure / 258 \\
General comments on the iterative procedure / 260 \\
Related iterative procedures / 261 \\
Limitations of the iterative procedure / 261 \\
Rigorous justification of the iterative method / 262
\\
5. Hermitian Matrices \\
Introduction / 265 \\
The classical Jacobi method for real symmetric matrices
/ 266 \\
Rate of convergence / 267 \\
Convergence to fixed diagonal matrix / 268 \\
Serial Jacobi method / 269 \\
The Gerschgorin discs / 269 \\
Ultimate quadratic convergence of Jacobi methods / 270
\\
Close and multiple eigenvalues / 271 \\
Numerical examples / 273 \\
Calculation of cos 8 and sin B / 274 \\
Simpler determination of the angles of rotation / 276
\\
The threshold Jacobi method / 277 \\
Calculation of the eigenvectors / 278 \\
Numerical example / 279 \\
Error analysis of the Jacobi method / 279 \\
Accuracy of the computed eigenvectors / 280 \\
Error bounds for fixed-point computation / 281 \\
Organizational problems / 282 \\
Givens' method / 282 \\
Givens' process on a computer with a two-level store /
284 \\
Floating-point error analysis of Givens' process / 286
\\
Fixed-point error analysis / 287 \\
Numerical example / 288 \\
Householder's method / 290 \\
Taking advantage of symmetry / 292 \\
Storage considerations / 293 \\
Householder's process on a computer with a two-level
store / 294 \\
Householder's method in fixed-point arithmetic / 294
\\
Numerical example / 296 \\
Error analyses of Householder's method / 297 \\
Eigenvalues of a symmetric tri-diagonal matrix / 299
\\
Sturm sequence property / 300 \\
Method of bisection / 302 \\
Numerical stability of the bisection method / 302 \\
Numerical example / 305 \\
General comments on the bisection method / 306 \\
Small eigenvalues / 307 \\
Close eigenvalues and small $\beta_i$ / 308 \\
Fixed-point computation of the eigenvalues / 312 \\
Computation of the eigenvectors of a tri-diagonal form
/ 315 \\
Instability of the explicit expression for the
eigenvector / 316 \\
Numerical examples / 319 \\
Inverse iteration / 321 \\
Choice of initial vector $b$ / 322 \\
Error analysis / 323 \\
Numerical example / 325 \\
Close eigenvalues and small $\beta_i$ / 327 \\
Independent vectors corresponding to coincident
eigenvalues / 328 \\
Alternative method for computing the eigenvectors / 330
\\
Numerical example / 331 \\
Comments on the eigenproblem for tri-diagonal matrices
/ 332 \\
Completion of the Givens and Householder methods / 333
\\
Comparison of methods / 334 \\
Quasi-symmetric tri-diagonal matrices / 335 \\
Calculation of the eigenvectors / 336 \\
Equations of the form $A x = \lambda B x$ and $A B x =
\lambda X $ / 337 \\
Numerical example / 339 \\
Simultaneous reduction of $A$ and $B$ to diagonal form
/ 340 \\
Tri-diagonal $A$ and $B$ / 340 \\
Complex Hermitian matrices / 342 \\
6. Reduction of a General Matrix to Condensed Form \\
Introduction / 345 \\
Givens' method / 345 \\
Householder's method / 347 \\
Storage considerations / 350 \\
Error analysis / 350 \\
Relationship between the Givens and Householder methods
/ 351 \\
Elementary stabilized transformations / 353 \\
Significance of the permutations / 355 \\
Direct reduction to Hessenberg form / 357 \\
Incorporation of interchanges / 359 \\
Numerical example / 360 \\
Error analysis / 363 \\
Related error analyses / 365 \\
Poor determination of the Hessenberg matrix / 368 \\
Reduction to Hessenberg form using stabilized matrices
of the type $ M^'_{ji} $ / 368 \\
The method of Krylov / 369 \\
Gaussian elimination by columns / 370 \\
Practical difficulties / 371 \\
Condition of O for some standard distributions of
eigenvalues / 372 \\
Initial vectors of grade less than n / 374 \\
Practical experience / 376 \\
Generalized Hessenberg processes / 377 \\
Failure of the generalized Hessenberg process / 378 \\
The Hessenberg method / 379 \\
Practical procedure / 380 \\
Relation between the Hessenberg method and earlier
methods / 381 \\
The method of Arnoldi / 382 \\
Practical considerations / 383 \\
Significance of re-orthogonalization / 385 \\
The method of Lanczos / 388 \\
Failure of procedure / 389 \\
Numerical example / 390 \\
The practical Lanczos process / 391 \\
Numerical example / 392 \\
General comments on the unsymmetric Lanczos process /
394 \\
The symmetric Lanczos process / 394 \\
Reduction of a Hessenberg matrix to a more compact form
/ 395 \\
Reduction of a lower Hessenberg matrix to tri-diagonal
form / 396 \\
The use of interchanges / 397 \\
Effect of a small pivotal element / 398 \\
Error analysis / 399 \\
The Hessenberg process applied to a lower Hessenberg
matrix / 402 \\
Relationship between the Hessenberg process and the
Lanczos process / 402 \\
Reduction of a general matrix to tri-diagonal form /
403 \\
Comparison with Lanczos method / 404 \\
Re-examination of reduction to tri-diagonal form / 404
\\
Reduction from upper Hessenberg form to Frobenius form
/ 405 \\
Effect of small pivot / 407 \\
Numerical example / 408 \\
General comments on the stability / 408 \\
Specialized upper Hessenberg form / 409 \\
Direct determination of the characteristic polynomial /
410 \\
7. Eigenvalues of Matrices of Condensed Forms \\
Introduction / 413 \\
Explicit polynomial form / 413 \\
Condition numbers of explicit polynomials / 416 \\
Some typical distributions of zeros / 417 \\
Final assessment of Krylov's method / 421 \\
General comments on explicit polynomials / 421 \\
Tri-diagonal matrices / 423 \\
Determinants of Hessenberg matrices / 426 \\
Effect of rounding errors / 427 \\
Floating-point accumulation / 428 \\
Evaluation by orthogonal transformations / 429 \\
Evaluation of determinants of general matrices / 431
\\
The generalized eigenvalue problem / 432 \\
Indirect determinations of the characteristic
polynomial / 432 \\
Le Verrier's method / 434 \\
Iterative methods based on interpolation / 435 \\
Asymptotic rate of convergence / 436 \\
Multiple zeros / 437 \\
Inversion of the functional relationship / 439 \\
The method of bisection / 440 \\
Newton's method / 441 \\
Comparison of Newton's method with interpolation / 442
\\
Methods giving cubic convergence / 443 \\
Laguerre's method / 443 \\
Complex zeros / 446 \\
Complex conjugate zeros / 447 \\
Bairstow's method / 449 \\
The generalized Bairstow method / 450 \\
Practical considerations / 452 \\
Effect of rounding errors on asymptotic convergence /
453 \\
The method of bisection / 453 \\
Successive linear interpolation / 455 \\
Multiple and pathologically close eigenvalues / 457 \\
Other interpolation methods / 458 \\
Methods involving the use of a derivative / 459 \\
Criterion for acceptance of a zero / 461 \\
Effect of rounding errors / 462 \\
Suppression of computed zeros / 464 \\
Deflation for Hessenberg matrices / 465 \\
Deflation of tri-diagonal matrices / 468 \\
Deflation by rotations or stabilized elementary
transformations / 469 \\
Stability of the deflation / 472 \\
General comments on deflation / 474 \\
Suppression of computed zeros / 474 \\
Suppression of computed quadratic factors / 475 \\
General comments on the methods of suppression / 476
\\
Asymptotic rates of convergence / 478 \\
Convergence in the large / 478 \\
Complex zeros / 481 \\
Recommendations / 482 \\
Complex matrices / 483 \\
Matrices containing an independent parameter / 483 \\
8. The $ L R $ and $ Q R $ Algorithms \\
Introduction / 485 \\
Real matrices with complex eigenvalues / 486 \\
The $ L R $ algorithm / 487 \\
Proof of the convergence of the $A_s$ / 489 \\
Positive definite Hermitian matrices / 493 \\
Complex conjugate eigenvalues / 494 \\
Introduction of interchanges / 498 \\
Numerical example / 499 \\
Convergence of the modified process / 501 \\
Preliminary reduction of original matrix / 501 \\
Invariance of upper Hessenberg form / 502 \\
Simultaneous row and column operations / 504 \\
Acceleration of convergence / 505 \\
Incorporation of shifts of origin / 506 \\
Choice of shift of origin / 507 \\
Deflation of the matrix / 509 \\
Practical experience of convergence / 510 \\
Improved shift strategy / 511 \\
Complex conjugate eigenvalues / 512 \\
Criticisms of the modified $ L R $ algorithm. / 515 \\
The $ Q R $ algorithm / 515 \\
Convergence of the $ Q R $ algorithm / 516 \\
Formal proof of convergence / 517 \\
Disorder of the eigenvalues / 519 \\
Eigenvalues of equal modulus / 520 \\
Alternative proof for the $ L R $ technique / 521 \\
Practical application of the $ Q R $ algorithm / 523
\\
Shifts of origin / 524 \\
Decomposition of A8 / 525 \\
Numerical example / 527 \\
Practical procedure / 527 \\
Avoiding complex conjugate shifts / 528 \\
Double $ Q R $ step using elementary Hermitians / 532
\\
Computational details / 534 \\
Decomposition of A8 / 535 \\
Double-shift technique for $ L R $ / 537 \\
Assessment of $ L R $ and $ Q R $ algorithms / 538 \\
Multiple eigenvalues / 540 \\
Special use of the deflation process / 543 \\
Symmetric matrices / 544 \\
Relationship between $ L R $ and $ Q R $ algorithms /
545 \\
Convergence of the Cholesky $ L R $ algorithm / 546 \\
Cubic convergence of the $ Q R $ algorithm / 548 \\
Shift of origin in Cholesky $ L R $ / 549 \\
Failure of the Cholesky decomposition / 550 \\
Cubically convergent $ L R $ process / 551 \\
Band matrices / 553 \\
$ Q R $ decomposition of a band matrix / 557 \\
Error analysis / 561 \\
Unsymmetric band matrices / 562 \\
Simultaneous decomposition and recombination in $ Q R $
algorithm / 565 \\
Reduction of band width / 567 \\
9. ITERATIVE METHODS \\
Introduction / 570 \\
The power method / 570 \\
Direct iteration with a single vector / 571 \\
Shift of origin / 572 \\
Effect of rounding errors / 573 \\
Variation of $p$ / 576 \\
{\em Ad hoc\/} choice of $p$ / 577 \\
Aitken's acceleration technique / 578 \\
Complex conjugate eigenvalues / 579 \\
Calculation of the complex eigenvector / 581 \\
Shift of origin / 582 \\
Non-linear divisors / 582 \\
Simultaneous determination of several eigenvalues / 583
\\
Complex matrices / 584 \\
Deflation / 584 \\
Deflation based on similarity transformations / 585 \\
Deflation using invariant subspaces / 587 \\
Deflation using stabilized elementary transformations /
587 \\
Deflation using unitary transformations / 589 \\
Numerical stability / 590 \\
Numerical example / 592 \\
Stability of unitary transformations / 594 \\
Deflation by non-similarity transformations / 596 \\
General reduction using invariant subspaces / 599 \\
Practical application / 601 \\
Treppen-iteration / 602 \\
Accurate determination of complex conjugate eigenvalues
/ 604 \\
Very close eigenvalues / 606 \\
Orthogonalization techniques / 606 \\
Analogue of treppen-iteration using orthogonalization /
607 \\
Bi-iteration / 609 \\
Numerical example / 610 \\
Richardson's purification process / 614 \\
Matrix squaring / 615 \\
Numerical stability / 616 \\
Use of Chebyshev polynomials / 617 \\
General assessment of methods based on direct iteration
/ 618 \\
Inverse iteration / 619 \\
Error analysis of inverse iteration / 620 \\
General comments on the analysis / 621 \\
Further refinement of eigenvectors / 622 \\
Non-linear elementary divisors / 626 \\
Inverse iteration with Hessenberg matrices / 626 \\
Degenerate cases / 627 \\
Inverse iteration with band matrices / 628 \\
Complex conjugate eigenvectors / 629 \\
Error analysis / 631 \\
Numerical example / 633 \\
The generalized eigenvalue problem / 633 \\
Variation of approximate eigenvalues / 635 \\
Refinement of eigensystems / 637 \\
Numerical example / 639 \\
Refinement of the eigenvectors / 641 \\
Complex conjugate eigenvalues / 643 \\
Coincident and pathologically close eigenvalues / 644
\\
Comments on the ACE programmes / 646 \\
Bibliography / 649 \\
Index / 657",
}
@Book{Ralston:1966:MMD,
editor = "Anthony Ralston and Herbert S. Wilf",
booktitle = "Mathematical Methods for Digital Computers",
title = "Mathematical Methods for Digital Computers",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "various",
year = "1966",
LCCN = "QA76.5 .R3",
bibdate = "Fri Dec 08 13:02:58 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Three volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{AFIPS:1967:ACP,
key = "AFIPS SJCC '67",
booktitle = "{1967 Spring Joint Computer Conference, April 18--20,
Atlantic City, NJ}",
title = "{1967 Spring Joint Computer Conference, April 18--20,
Atlantic City, NJ}",
volume = "30",
publisher = "Thompson Book Co.",
address = "Washington, DC, USA",
pages = "799",
year = "1967",
LCCN = "TK7885.A1 J6 1967",
bibdate = "Sat Sep 24 01:00:25 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AFIPS conference proceedings",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1968:PSA,
editor = "Anonymous",
booktitle = "Proc. Sixth Annual Allerton Conference on Circuit and
System Theory (Monticello, {IL, 1968)}",
title = "Proc. Sixth Annual Allerton Conference on Circuit and
System Theory (Monticello, {IL}, 1968)",
publisher = "University of Illinois at Urbana-Champaign",
address = "Urbana, IL, USA",
year = "1968",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0569-0552",
LCCN = "????",
bibdate = "Sat Nov 29 11:03:47 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{AFIPS:1969:ACPa,
key = "AFIPS SJCC '69",
booktitle = "{1967 Spring Joint Computer Conference, May 14--16,
1969, Boston, MA}",
title = "{1967 Spring Joint Computer Conference, May 14--16,
1969, Boston, MA}",
volume = "34",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "866",
year = "1969",
LCCN = "TK7885.A1 J6 1969",
bibdate = "Sat Sep 24 01:05:52 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AFIPS conference proceedings",
acknowledgement = ack-nj # " and " # ack-nhfb,
}
@Proceedings{AFIPS:1969:ACPb,
key = "AFIPS FJCC '69",
booktitle = "{1969 Fall Joint Computer Conference, November 18--20,
1969, Las Vegas, Nevada}",
title = "{1969 Fall Joint Computer Conference, November 18--20,
1969, Las Vegas, Nevada}",
volume = "35",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "807",
year = "1969",
LCCN = "????",
bibdate = "Fri Sep 16 10:42:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AFIPS conference proceedings",
acknowledgement = ack-nj,
}
@Proceedings{IEEE:1969:SCA,
editor = "{IEEE}",
booktitle = "Papers presented at a workshop sponsored by the {Logic
Design Subcommittee of the Systems Technical Committee
(IEEE Computer Group), 1969}",
title = "Papers presented at a workshop sponsored by the {Logic
Design Subcommittee of the Systems Technical Committee
(IEEE Computer Group), 1969}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "1969",
LCCN = "????",
bibdate = "Wed Apr 27 17:36:48 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Reprinted in IEEE Transactions on Computers, Special
issue on computer arithmetic (when??)",
xxnote = "Where was the conference?? Were the proceedings
published?? What was the conference title?? Is this the
proceedings of ARITH '69 (Minneapolis, MN, USA, June
16, 1969)?",
}
@Proceedings{Morrell:1969:IPP,
editor = "A. J. H. Morrell",
booktitle = "{Information processing 68: proceedings of IFIP
congress 1968, organized by the International
Federation for Information Processing, Edinburgh, 5--10
August 1968}",
title = "{Information processing 68: proceedings of IFIP
congress 1968, organized by the International
Federation for Information Processing, Edinburgh, 5--10
August 1968}",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "????",
year = "1969",
ISBN = "0-7204-2032-6",
ISBN-13 = "978-0-7204-2032-6",
LCCN = "QA76 .I578",
bibdate = "Fri Nov 11 07:22:32 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "Volume 1. Mathematics, software. Volume 2. Hardware,
applications.",
subject = "Electronic data processing; Congresses; Electronic
digital computers; Congresses; Machine theory;
Congresses",
}
@Proceedings{Morrell:1970:IPP,
editor = "A. J. H. Morrell",
booktitle = "Information Processing 68 (Proc. {IFIP} Congress,
Edinburgh, 1968), Vol. 1: Mathematics, Software",
title = "Information Processing 68 (Proc. {IFIP} Congress,
Edinburgh, 1968), Vol. 1: Mathematics, Software",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "various",
year = "1970",
ISBN = "0-7204-2032-6",
ISBN-13 = "978-0-7204-2032-6",
LCCN = "QA 75.5 I57 1968",
bibdate = "Thu Jan 18 13:48:59 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{AFIPS:1971:ACP,
key = "AFIPS SJCC '71",
booktitle = "1971 Spring Joint Computer Conference, May 18--20,
1971, Atlantic City, New Jersey",
title = "1971 Spring Joint Computer Conference, May 18--20,
1971, Atlantic City, New Jersey",
volume = "38",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "631",
year = "1971",
LCCN = "????",
bibdate = "Fri Sep 16 10:47:01 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "AFIPS conference proceedings",
acknowledgement = ack-nj,
}
@Proceedings{Freiman:1971:PIC,
editor = "C. V. Freiman and J. E. Griffith and J. L. Rosenfeld",
booktitle = "Information processing 71: proceedings of {IFIP}
Congress 71 organized by the International Federation
for Information Processing, Ljubljana, Yugoslavia,
August 23--28, 1971",
title = "Information processing 71: proceedings of {IFIP}
Congress 71 organized by the International Federation
for Information Processing, Ljubljana, Yugoslavia,
August 23--28, 1971",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
year = "1971",
ISBN = "0-7204-2063-6",
ISBN-13 = "978-0-7204-2063-0",
LCCN = "????",
bibdate = "Sat Nov 29 07:10:48 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Eight booklets in two volumes.",
acknowledgement = ack-nhfb,
}
@Book{Gear:1971:NIV,
author = "Charles William Gear",
booktitle = "Numerical Initial Value Problems in Ordinary
Differential Equations",
title = "Numerical Initial Value Problems in Ordinary
Differential Equations",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xvii + 253",
year = "1971",
ISBN = "0-13-626606-1 (hardcover)",
ISBN-13 = "978-0-13-626606-8 (hardcover)",
LCCN = "QA372 .G4",
bibdate = "Sat Dec 19 09:50:43 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Prentice-Hall series in automatic computation",
acknowledgement = ack-nhfb,
author-dates = "(1935-- \ldots{})",
remark-1 = "Foreword on page vii by series editor George Forsythe,
and the author's host during the sabbatical year when
he wrote this book.",
remark-2 = "The initial chapters contain multiple references to
work by Peter Henrici.",
remark-3 = "The initial chapters discuss the error amplification
from chopping arithmetic on the IBM 7090 series
machines on the solution of ODEs, and point out the
need for better rounding algorithms, and higher
numerical precision, for solving ODEs.",
subject = "Numerical integration; Data processing; Differential
equations; Mathematics; {\'y}Equations
diff{\'y}erentielles; Informatique; Int{\'y}egration
num{\'y}erique; Data processing.; Probl{\'y}emes aux
valeurs initiales; Analyse num{\'y}erique.;
Probl{\'y}emes et exercices.; Int{\'y}egration
num{\'y}erique.; Math{\'y}ematiques.",
tableofcontents = "1: Introduction \\
2: Higher order one-step methods \\
3: Systems of equations and equations of order greater
than one \\
4: Convergence, error bounds, and error estimates for
one-step methods \\
5: The choice of step size and order \\
6: Extrapolation methods \\
7: Multivalue or multistep methods --- introduction \\
8: General multistep methods, order and stability \\
9: Multivalue methods \\
10: Existence, convergence, and error estimates for
multivalue methods \\
11: Special methods for special problems [stiff
ODEs]\\
12: Choosing a method",
}
@Book{Rice:1971:MS,
editor = "John R. Rice",
booktitle = "Mathematical Software",
title = "Mathematical Software",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 515",
year = "1971",
ISBN = "0-12-587250-X",
ISBN-13 = "978-0-12-587250-8",
LCCN = "QA1 .M26",
bibdate = "Thu Sep 15 18:56:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Based on the proceedings of the Mathematical Software
Symposium held at Purdue University, Lafayette,
Indiana, USA, April 1--3, 1970.",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:1972:PAA,
editor = "{ACM}",
booktitle = "Proceedings of the {ACM} annual conference, August
1972, Boston, Massachusetts",
title = "Proceedings of the {ACM} annual conference, August
1972, Boston, Massachusetts",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiii + 1156",
year = "1972",
LCCN = "QA76; TK7885",
bibdate = "Fri Nov 28 11:28:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Book{Cardenas:1972:CS,
editor = "Alfonso F. Cardenas and Leon Presser and Miguel A.
Marin",
booktitle = "Computer Science",
title = "Computer Science",
publisher = pub-WILEY-INTERSCIENCE,
address = pub-WILEY-INTERSCIENCE:adr,
pages = "xii + 522",
year = "1972",
ISBN = "0-471-13468-6",
ISBN-13 = "978-0-471-13468-8",
LCCN = "QA76.5 .C365; TK7885 .C178c",
bibdate = "Sat Nov 29 11:09:31 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1972:IAD,
editor = "{IEEE}",
booktitle = "{Innovative architecture: digest of papers: COMPCON
72, 6. annual IEEE Computer Society International
Conference, Jack Tar Hotel, San Francisco, California,
September 12--14, 1972}",
title = "{Innovative architecture: digest of papers: COMPCON
72, 6. annual IEEE Computer Society International
Conference, Jack Tar Hotel, San Francisco, California,
September 12--14, 1972}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 340",
year = "1972",
LCCN = "TK7885.A1 C53 1972",
bibdate = "Wed Mar 21 09:29:22 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE order number 72CH0659-3C.",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1972:ITS,
editor = "{IEEE}",
booktitle = "{2nd IEEE-TCCA Symposium on Computer Arithmetic,
College Park, Maryland, May 15--16, Maryland}",
title = "{2nd IEEE-TCCA Symposium on Computer Arithmetic,
College Park, Maryland, May 15--16, Maryland}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "1972",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Apr 27 17:36:48 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-2",
remark = "Selected papers from this conference are reprinted in
a special issue on computer arithmetic in IEEE
Transactions on Computers, volume C-22, number 6, June
1973. Otherwise, the remaining papers appear not to
have been published, at least not in one location.",
}
@Proceedings{Zaremba:1972:ANT,
editor = "S. K. Zaremba",
booktitle = "Applications of Number Theory to Numerical Analysis =
{Applications} de la th{\'e}orie des nombres {\`a}
l'analyse num{\'e}rique. Proceedings of the symposium
at the {Centre for Research in Mathematics, University
of Montreal, September 9--14, 1971}",
title = "Applications of Number Theory to Numerical Analysis =
{Applications} de la th{\'e}orie des nombres {\`a}
l'analyse num{\'e}rique. Proceedings of the symposium
at the {Centre for Research in Mathematics, University
of Montreal, September 9--14, 1971}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xii + 489",
year = "1972",
ISBN = "0-12-775950-6",
ISBN-13 = "978-0-12-775950-0",
LCCN = "QA297 .A67",
bibdate = "Mon Aug 02 10:53:03 2004",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
language = "French and English",
}
@Proceedings{ACM:1974:CRS,
editor = "{ACM}",
booktitle = "Conference record of sixth annual {ACM} Symposium on
Theory of Computing: papers presented at the symposium,
Seattle, Washington, April 30--May 2, 1974",
title = "Conference record of sixth annual {ACM} Symposium on
Theory of Computing: papers presented at the symposium,
Seattle, Washington, April 30--May 2, 1974",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "iv + 347",
year = "1974",
LCCN = "QA76.6 .A13 1974",
bibdate = "Thu Dec 3 07:11:18 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "computational complexity --- congresses; electronic
digital computers --- programming --- congresses",
xxISBN = "none",
}
@Proceedings{Panagiotopoulos:1974:PCC,
editor = "Antonios Ch. Panagiotopoulos",
booktitle = "Proceedings of the C. Carath{\'e}odory International
Symposium (Athens, 1973)",
title = "Proceedings of the {C}. Carath{\'e}odory International
Symposium (Athens, 1973)",
publisher = "Greek Mathematical Society",
address = "Athens, Greece",
pages = "634",
year = "1974",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Dec 08 13:53:34 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1975:SCA,
key = "IEEE SCA '75",
booktitle = "3rd Symposium on Computer Arithmetic, November 19--20,
1975, Southern Methodist University, Dallas, Texas",
title = "3rd Symposium on Computer Arithmetic, November 19--20,
1975, Southern Methodist University, Dallas, Texas",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "viii + 249",
year = "1975",
LCCN = "QA76.6.S919 1975",
bibdate = "Fri Nov 28 18:13:53 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE order number CH1017-3C.",
acknowledgement = ack-nhfb,
keywords = "ARITH-3; Computer arithmetic and logic units ---
Congresses.; Electronic digital computers ---
Programming --- Congresses.; Floating-point arithmetic
--- Congresses",
xxISBN = "(none)",
}
@Book{Randell:1975:ODC,
editor = "Brian Randell",
booktitle = "The Origins of Digital Computers: Selected Papers",
title = "The Origins of Digital Computers: Selected Papers",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Second",
pages = "xvi + 464",
year = "1975",
DOI = "https://doi.org/10.1007/978-3-642-96242-4",
ISBN = "0-387-07114-8, 3-540-07114-8, 3-642-96244-0,
3-642-96242-4 (e-book)",
ISBN-13 = "978-0-387-07114-5, 978-3-540-07114-3,
978-3-642-96244-8, 978-3-642-96242-4 (e-book)",
LCCN = "?TK7888.3 .R36 1975",
bibdate = "Wed Oct 13 09:24:25 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Texts and monographs in computer science",
acknowledgement = ack-nhfb,
remark = "See also other editions
\cite{Randell:1973:ODC,Randell:1982:ODC}.",
subject = "Electronic digital computers; History; Calculators",
tableofcontents = "Front Matter / / i--xvi \\
Introduction / Brian Randell / 1--6 \\
Analytical Engines / Charles Babbage, Mr. C. W.
Merrifield, H. P. Babbage, Percy E. Ludgate, Leonardo
Torres y Quevedo, L. Couffignal/ 7--123 \\
Tabulating Machines / H. Hollerith, L. Couffignal,
H.-J. Dreyer, A. Walther / 125--153 \\
Zuse and Schreyer / Konrad Zuse, Helmut Schreyer /
155--186 \\
Aiken and IBM / Howard H. Aiken, Grace M. Hopper, W. J.
Eckert, John W. Sheldon, Liston Tatum / 187--235 \\
Bell Telephone Laboratories / G. R. Stibitz, O.
Cesareo, Joseph Juley, Franz L. Alt / 237--286 \\
The Advent of Electronic Computers / E. William
Phillips O.B.E., F.I.A., John V. Atanasoff, D. Michie,
John W. Mauchly, H. H. Goldstine, Adele Goldstine /
287--347 \\
Stored Program Electronic Computers / John von Neumann,
John W. Mauchly, Arthur W. Burks, Herman H. Goldstine,
F. C. Williams, T. Kilburn, M. V. Wilkes, W. Renwick /
349--401 \\
Back Matter / / 403--464",
}
@Proceedings{Swamy:1975:PEM,
editor = "M. N. S. Swamy",
booktitle = "Proceedings of the Eighteenth Midwest Symposium on
Circuits and Systems (Concordia University, Montreal,
Que., 1975)",
title = "Proceedings of the Eighteenth Midwest Symposium on
Circuits and Systems (Concordia University, Montreal,
Que., 1975)",
publisher = pub-WESTERN-PERIODICALS,
address = pub-WESTERN-PERIODICALS:adr,
pages = "xvi + 659",
year = "1975",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Dec 08 13:57:52 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Swartzlander:1976:CDD,
author = "Earl E. {Swartzlander, Jr.}",
booktitle = "Computer Design Development: Principal Papers",
title = "Computer Design Development: Principal Papers",
publisher = pub-HAYDEN-BOOK,
address = pub-HAYDEN-BOOK:adr,
pages = "310",
year = "1976",
ISBN = "0-8104-5988-4",
ISBN-13 = "978-0-8104-5988-5",
LCCN = "QA76.5 .C612565",
bibdate = "Wed Oct 13 08:14:58 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
tableofcontents = "0. Preface by Swartzlander \\
1: Logic Design \\
1.0 Introduction by Swartzlander \\
1.1 ``A Symbolic Analysis of Relay and Switching
Circuits'', Claude E. Shannon (1938) \\
1.2 ``The Map Method for Synthesis of Combinational
Logic Circuits'', M. Karnaugh (1953) \\
1.3 ``Minimization of Boolean Functions'', E. J.
McCluskey (1956) \\
1.4 ``A Method for Synthesizing Sequential Circuits'',
George H. Mealy (1955) \\
1.5 ``Hazards and Delays in Asynchronous Sequential
Switching Circuits'', S. H. Unger (1959) \\
1.6 ``Internal State Assignments for Asynchronous
Sequential Machines'', James H. Tracey \\
2: Arithmetic Algorithms \\
2.0 Introduction by Swartzlander \\
2.1 ``High-Speed Arithmetic in Binary Computers'', O. L
. MacSorley (1961) \\
2.2 ``A Signed Binary Multiplication Technique'',
Andrew D. Booth (1951) \\
2.3 ``Some Schemes for Parallel Multipliers'', L. Dadda
(1965) \\
2.4 ``The Residue Number System'', Harvey L. Garner
(1959) \\
2.5 ``The IBM System 360 Model 91: Floating-Point
Execution Unit'', S. F. Anderson, J. G. Earle, R. E.
Goldschmidt, and D. M. Powers (1967) \\
3: Computer Architecture \\
3.0 Introduction by Swartzlander \\
3.1 ''Preliminary Discussion of the Logical Design of
an Electronic Computing Instrument'', Arthur W. Burks,
Herman H. Goldstine, and John von Neumann (1946) \\
3.2 ''Symbolic Synthesis of Digital Computers'', Irving
S. Reed (1950) \\
3.3 ''The Best Way to Design an Automatic Calculating
Machine'', M. V. Wilkes (1951) \\
3.4 ''Structural Aspects of the System/360 Model 85
part II: The Cache'', J. S. Liptay (1968) \\
3.5 ''Parallel Operation in the Control Data 6600'',
James E. Thornton (1964) \\
3.6 ''The SOLOMON Computer'', Daniel L. Slotnick, W.
Borck, and R. McReynolds (1962) \\
4: Appendix \\
4.0 Introduction by Swartzlander \\
4.1 ``A Trigger Relay Utilizing Three-Electrode
Thermionic Vacuum Tubes'', W. H. Eccles and F. W.
Jordan (1919) \\
4.2 ``The CORDIC Trigonometric Computing Technique'',
Jack E. Bolder (1959)",
}
@Proceedings{Traub:1976:ACC,
editor = "J. F. (Joseph Frederick) Traub",
booktitle = "{Analytic computational complexity: Proceedings of the
Symposium on Analytic Computational Complexity, held by
the Computer Science Department, Carnegie-Mellon
University, Pittsburgh, Pennsylvania, on April 7--8,
1975}",
title = "{Analytic computational complexity: Proceedings of the
Symposium on Analytic Computational Complexity, held by
the Computer Science Department, Carnegie-Mellon
University, Pittsburgh, Pennsylvania, on April 7--8,
1975}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 239",
year = "1976",
ISBN = "0-12-697560-4",
ISBN-13 = "978-0-12-697560-4",
LCCN = "QA297.S9151 1975",
bibdate = "Mon Jan 13 10:18:33 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Cowell:1977:PMS,
editor = "Wayne Cowell",
booktitle = "{Portability of Numerical Software Workshop, Oak
Brook, Illinois, June 21--23, 1976}",
title = "{Portability of Numerical Software Workshop, Oak
Brook, Illinois, June 21--23, 1976}",
volume = "57",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 539",
year = "1977",
ISBN = "0-387-08446-0",
ISBN-13 = "978-0-387-08446-6",
LCCN = "QA297 .W65 1976",
bibdate = "Sat Sep 24 00:24:09 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1977:ICS,
editor = "{IEEE}",
booktitle = "{The IEEE Computer Society's First International
Computer Software \& Applications Conference, Chicago,
November 8--11, 1977: Proceedings}",
title = "{The IEEE Computer Society's First International
Computer Software \& Applications Conference, Chicago,
November 8--11, 1977: Proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxi + 834",
year = "1977",
ISBN = "????",
ISBN-13 = "????",
LCCN = "QA76.6",
bibdate = "Fri Nov 09 20:06:59 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Jacobs:1977:SAN,
editor = "D. Jacobs",
booktitle = "The state of the art in numerical analysis:
{Proceedings of the Conference held at The University
of York, Heslington, April 12th--15th, 1976}",
title = "The state of the art in numerical analysis:
{Proceedings of the Conference held at The University
of York, Heslington, April 12th--15th, 1976}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xix + 978",
year = "1977",
MRclass = "65-06",
MRnumber = "MR0440858 (55 \#13726)",
bibdate = "Thu Nov 8 19:02:54 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "With a foreword by R. A. Scriven",
acknowledgement = ack-nhfb,
}
@Proceedings{Rice:1977:MSI,
editor = "John R. Rice",
booktitle = "{Mathematical software III: Proceedings of a symposium
conducted by the Mathematics Research Center, the
University of Wisconsin--Madison, March 28--30, 1977}",
title = "{Mathematical software III: Proceedings of a symposium
conducted by the Mathematics Research Center, the
University of Wisconsin--Madison, March 28--30, 1977}",
number = "39",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 388",
year = "1977",
DOI = "https://doi.org/10.1016/C2013-0-11364-5",
ISBN = "0-12-587260-7",
ISBN-13 = "978-0-12-587260-7",
LCCN = "QA3 .U45 no. 39; QA297 .M36 1977",
bibdate = "Fri Dec 08 08:24:52 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/brandt-achi.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
series = "Publication of the Mathematics Research Center, the
University of Wisconsin, Madison",
URL = "https://www.sciencedirect.com/book/9780125872607/mathematical-software",
acknowledgement = ack-nhfb,
shorttableofcontents = "Contributors / / vii \\
Preface / / ix \\
Research, Development, and UNPACK / G. W. Stewart / 1
\\
A Technique that Gains Speed and Accuracy in the
Minimax Solution of Overdetermined Linear Equations /
M. J. Hopper and M. J. D. Powell / 15 \\
Infallible Calculation of Polynomial Zeros to Specified
Precision / G. E. Collins / 35 \\
Representation and Approximation of Surfaces / Robert
E. Barnhill / 69 \\
Simulation: Conflicts between Real-Time and Software /
C. W. Gear / 121 \\
Mathematical Software and Exploratory Data Analysis /
David C. Hoaglin / 139 \\
Software for $C^1$ Surface Interpolation / C. L. Lawson
/ 161 \\
Mathematical Software Production / W. R. Cowell and L.
D. Fosdick / 195 \\
Computational Aspects of the Finite Element Method / I.
Babuska and W. Rheinboldt / 225 \\
The Art of Writing a Runge-Kutta Code, Part I / L. F.
Shampine and H. A. Watts / 257 \\
Multi-Level Adaptive Techniques (MLAT) for Partial
Differential Equations: Ideas and Software / Achi
Brandt / 277 \\
ELLPACK: A Research Tool for Elliptic Partial
Differential Equations Software / John R. Rice / 319
\\
A Realistic Model of Floating-Point Computation / W. S.
Brown / 343 \\
The Block Lanczos Method for Computing Eigenvalues / G.
H. Golub and R. Underwood / 361 \\
Index / / 379",
tableofcontents = "Contributors \\
Preface \\
\\
1: Research, Development, and Linpack \\
Abstract \\
1. Introduction \\
2. Estimation of Condition Numbers \\
3. Stability of Least Squares Solutions \\
4. Scaling and Column Elimination \\
5. Downdating \\
6. Timing the BLAS \\
References \\
\\
2: A Technique That Gains Speed and Accuracy in the
Minimax Solution of Overdetermined Linear Equations \\
Abstract \\
1. Introduction \\
2. Numerical Instability in the Exchange Algorithm \\
3. The New Technique \\
4. Theory \\
5. Discussion \\
References \\
\\
3: Infallible Calculation Of Polynomial Zeros To
Specified Precision \\
Abstract \\
1. Introduction \\
2. Preliminaries \\
3. Sturm Sequences For Real Zeros \\
4. Sturm Sequences For Complex Zeros \\
5. Rolle's Theorem For Real Zeros \\
6. Descartes' Theorem For Real Zeros \\
7. Application of Interval Arithmetic \\
8. Complex Zeros Without Sturm Sequences \\
References \\
\\
4: Representation and Approximation of Surfaces \\
Abstract \\
1. Introduction \\
2. Interpolation Methods Defined Over Rectangles \\
3. Interpolation Schemes Defined Over Triangles \\
4. Interpolation Methods For Arbitrarily Placed Data 5.
Conclusions \\
References \\
Acknowledgements \\
\\
5: Simulation: Conflicts Between Real-Time And Software
\\
Abstract \\
1. Introduction \\
2. Simulation \\
3. Real-Time Operation \\
4. Numerical Integration in Real-Time \\
5. Errors in Numerical Integration \\
6. Methods For Reducing Delay and Improving Stability
\\
7. Conclusions \\
References \\
\\
6: Mathematical Software and Exploratory Data Analysis
\\
Abstract \\
1. Introduction \\
2. Overview of Exploratory Data Analysis \\
3. An Example: Timing Data \\
4. Software Needs of Exploratory Data Analysis \\
5. Summary \\
References \\
\\
7: Software For $C^1$ Surface Interpolation \\
1. Introduction \\
2. Problem Statement \\
3. Expected Applications \\
4. Published Work On Surface Interpolation To
Irregularly Located Data \\
5. Outline of the Algorithmic Approach Selected \\
6. Constructing a Triangular Grid \\
7. Estimating Partial Derivatives At the Grid Nodes \\
8. Lookup in the Triangular Grid \\
9. Interpolation in a Triangle \\
10. Examples \\
11. Three Criteria For Triangulation of a Strictly
Convex Quadrilateral \\
12. Global Consequences of the Local Optimization
Procedure \\
13. Mclain's Triangulation Method \\
14. Limits On Grid Changes When Adding a New Point \\
15. Conclusions \\
References \\
\\
8: Mathematical Software Production \\
Abstract \\
I. Introduction \\
II. The Evolution of Mathematical Software Production
\\
III. Intellectual Challenges \\
IV. Projects To Produce Mathematical Software \\
V. Trends in Mathematical Software Production \\
References \\
\\
9: Computational Aspects of the Finite Element Method
\\
1. Introduction \\
2. Goals of the Computational Analysis \\
3. The Principal Stages of the Computational Analysis
\\
4. Some Software Aspects \\
5. Some Computational Results \\
References",
}
@Proceedings{COMPSAC:1978:CPC,
key = "COMPSAC '78",
booktitle = "{COMPSAC} 78: Proceedings [conference held] November
13--16, 1978 [at] The Palmer House, Chicago, Illinois",
title = "{COMPSAC} 78: Proceedings [conference held] November
13--16, 1978 [at] The Palmer House, Chicago, Illinois",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 832",
year = "1978",
LCCN = "????",
bibdate = "Thu Sep 15 18:50:37 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{IEEE:1978:PSC,
key = "IEEE SCA '78",
booktitle = "Proceedings of the 4th Symposium on Computer
Arithmetic, Santa Monica, {CA}, {USA}, 25--27 October
1978",
title = "Proceedings of the 4th Symposium on Computer
Arithmetic, Santa Monica, {CA}, {USA}, 25--27 October
1978",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 274",
year = "1978",
ISSN = "1063-6889",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 78CH1412-6C.",
acknowledgement = ack-nhfb,
keywords = "ARITH-4; Computer arithmetic --- Congresses.;
Electronic digital computers --- Programming ---
Congresses.; Floating-point arithmetic ---
Congresses.",
xxISBN = "(none)",
xxLCCN = "(none)",
}
@Proceedings{ACM:1979:PSC,
editor = "{ACM}",
booktitle = "Proceedings of the {SIGNUM} Conference on the
Programming Environment for Development of Numerical
Software",
title = "Proceedings of the {SIGNUM} Conference on the
Programming Environment for Development of Numerical
Software",
publisher = pub-ACM,
address = pub-ACM:adr,
year = "1979",
bibdate = "Fri Nov 28 17:28:30 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1979:WCR,
editor = "Anonymous",
booktitle = "{WESCON} conference record",
title = "{WESCON} conference record",
publisher = "Electronic Conventions Management",
address = "Los Angeles, CA, USA",
year = "1979",
CODEN = "WCREDI",
ISSN = "1044-6036, 0083-8837",
LCCN = "TK7800",
bibdate = "Fri Nov 09 20:00:43 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "17 volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{Budach:1979:FCT,
editor = "L. (Lothar) Budach",
booktitle = "{Fundamentals of computation theory: FCT '79:
proceedings of the Conference on Algebraic, Arithmetic,
and Categorial Methods in Computation Theory held in
Berlin\slash Wendisch-Rietz (GDR), September 17--21,
1979}",
title = "{Fundamentals of computation theory: FCT '79:
proceedings of the Conference on Algebraic, Arithmetic,
and Categorial Methods in Computation Theory held in
Berlin\slash Wendisch-Rietz (GDR), September 17--21,
1979}",
volume = "2",
publisher = pub-AKADEMIE-VERLAG,
address = pub-AKADEMIE-VERLAG:adr,
pages = "576",
year = "1979",
ISBN = "????",
ISBN-13 = "????",
LCCN = "QA267 .C594 1979",
bibdate = "Sat Mar 31 10:25:37 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematical research",
acknowledgement = ack-nhfb,
meetingname = "Conference on Algebraic, Arithmetic, and Categorial
Methods in Computation Theory (1979 : Wendisch Rietz,
Germany)",
remark = "English or French.",
subject = "Machine theory; Congresses; Categories (Mathematics);
Computational complexity",
}
@Book{Linger:1979:SPT,
author = "R. C. Linger and H. D. Mills and B. I. Witt",
booktitle = "Structured Programming: Theory and Practice",
title = "Structured Programming: Theory and Practice",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xi + 402",
year = "1979",
ISBN = "0-201-14461-1",
ISBN-13 = "978-0-201-14461-1",
LCCN = "QA76.6 .L55",
bibdate = "Tue Jul 26 11:13:15 2022",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "No tableofcontents data found, and no online source
yet located. This book discussion multiword integer
division, but the treatment is later shown to be
inferior to that of subsequent work
\cite{BrinchHansen:1995:LDA}.",
}
@Proceedings{Meinardus:1979:ATP,
editor = "Gunther Meinardus",
booktitle = "{Approximation in Theorie und Praxis: e.
Symposiumsbericht} \toenglish {Approximation in Theory
and Practice: Symposium Proceedings} \endtoenglish",
title = "{Approximation in Theorie und Praxis: e.
Symposiumsbericht} \toenglish {Approximation in Theory
and Practice: Symposium Proceedings} \endtoenglish",
publisher = pub-BIB-INST,
address = pub-BIB-INST:adr,
pages = "304",
year = "1979",
ISBN = "3-411-01567-5",
ISBN-13 = "978-3-411-01567-2",
LCCN = "QA297.5 .A66",
bibdate = "Fri Sep 16 16:30:41 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Contributions in English or German from a meeting held
Jan. 31--Feb. 2, 1979, at the Gesamthochschule Siegen,
Forschungsinstitut fur Geistes- und
Sozialwissenschaften.",
acknowledgement = ack-nhfb,
}
@Proceedings{Ng:1979:SAC,
editor = "Edward W. Ng",
booktitle = "{Symbolic and algebraic computation: EUROSAM '79, an
International Symposium on Symbolic and Algebraic
Manipulation, Marseille, France, June 1979}",
title = "{Symbolic and algebraic computation: EUROSAM '79, an
International Symposium on Symbolic and Algebraic
Manipulation, Marseille, France, June 1979}",
volume = "72",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 557",
year = "1979",
ISBN = "0-387-09519-5",
ISBN-13 = "978-0-387-09519-6",
LCCN = "QA155.7.E4I57 1979",
bibdate = "Fri Dec 08 08:45:00 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:1980:CPA,
editor = "{ACM}",
booktitle = "{Conference Proceedings: 7th Annual Symposium on
Computer Architecture, La Baule, France, 6--8 May
1980}",
title = "{Conference Proceedings: 7th Annual Symposium on
Computer Architecture, La Baule, France, 6--8 May
1980}",
volume = "8(3)",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "333",
year = "1980",
CODEN = "CANED2, CPAADU",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0163-5964 (ACM), 0884-7495 (IEEE), 0149-7111",
bibdate = "Fri Sep 16 10:53:10 1994",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
http://portal.acm.org/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
series = j-COMP-ARCH-NEWS,
URL = "http://portal.acm.org/toc.cfm?id=800090",
acknowledgement = ack-nj,
}
@Proceedings{Alefeld:1980:FNC,
editor = "G. Alefeld and R. D. Grigorieff",
booktitle = "Fundamentals of Numerical Computation
(Computer-Oriented Numerical Analysis)",
title = "Fundamentals of Numerical Computation
(Computer-Oriented Numerical Analysis)",
volume = "2",
publisher = pub-SPRINGER-WIEN,
address = pub-SPRINGER-WIEN:adr,
pages = "v + 229",
year = "1980",
CODEN = "COSPDM",
ISBN = "0-387-81566-X",
ISBN-13 = "978-0-387-81566-4",
ISSN = "0344-8029",
LCCN = "QA297 .F84",
bibdate = "Wed Oct 13 18:45:11 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "In cooperation with R. Albrecht, U. Kulisch, and F.
Stummel.",
series = j-COMPUTING-SUPPLEMENTUM,
acknowledgement = ack-nhfb,
remark = "Collection of invited lectures which were given during
a conference held on June 5--8, 1979, on the occasion
of the centennial of the Technical University of
Berlin.",
}
@Proceedings{Anonymous:1980:CPA,
key = "COMPARCH '80",
booktitle = "Conference Proceedings 7th Annual Symposium on
Computer Architecture, La Baule, France, 6--8 May
1980",
title = "Conference Proceedings 7th Annual Symposium on
Computer Architecture, La Baule, France, 6--8 May
1980",
volume = "8(3)",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "333",
year = "1980",
CODEN = "CANED2",
ISSN = "0163-5964 (print), 1943-5851 (electronic)",
bibdate = "Fri Sep 16 10:53:10 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = j-COMP-ARCH-NEWS,
acknowledgement = ack-nj,
}
@Proceedings{Electro:1980:ECR,
key = "Electro '80",
booktitle = "Electro\slash 80 Conference Record: Sessions Presented
at {ELECTRO}\slash 80, Boston, {MA}, May 13--15, 1980",
title = "Electro\slash 80 Conference Record: Sessions Presented
at {ELECTRO}\slash 80, Boston, {MA}, May 13--15, 1980",
publisher = "Electronic Conventions, Inc.",
address = "El Segundo, CA, USA",
pages = "various",
year = "1980",
LCCN = "TK 7801 E375 1980",
bibdate = "Fri Dec 08 13:02:59 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{IEEE:1980:IIS,
key = "IEEE ISSCC '80",
booktitle = "1980 {IEEE} International Solid-State Circuits
Conference Digest of Technical Papers, Philadelphia,
{PA}, {USA}, 13--15 February 1980",
title = "1980 {IEEE} International Solid-State Circuits
Conference Digest of Technical Papers, Philadelphia,
{PA}, {USA}, 13--15 February 1980",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "??--??",
year = "1980",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Sep 16 10:55:14 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxnote = "NHFB: OCLC shows this conference in San Francisco, and
says 282 pages.",
}
@Proceedings{IEEE:1980:PMA,
key = "IEEE MICRO '80",
booktitle = "Proceedings: Microprocessor Applications in the 80's:
Arizona Technical Symposium, March 12--14, 1980,
Arizona State University, Tempe, Arizona",
title = "Proceedings: Microprocessor Applications in the 80's:
Arizona Technical Symposium, March 12--14, 1980,
Arizona State University, Tempe, Arizona",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "105",
year = "1980",
LCCN = "QA76.5 .P74",
bibdate = "Thu Sep 15 18:50:53 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Proceedings{Johnson:1980:MPA,
editor = "Gearold R. Johnson and Bruce E. Kittinger",
booktitle = "{MICRO 13: Proceedings of the 13th annual workshop on
Microprogramming 1980, Broadmoor Hotel, Colorado
Springs, United States, November 30--December 03,
1980}",
title = "{MICRO 13: Proceedings of the 13th annual workshop on
Microprogramming 1980, Broadmoor Hotel, Colorado
Springs, United States, November 30--December 03,
1980}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 192",
year = "1980",
bibdate = "Thu Aug 07 18:23:40 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Published in SIGMICRO newsletter, 11(3--4)
(Sept.--Dec. 1980). ACM Order no. 520800. IEEE Catalog
no. 80CH1599-0.",
acknowledgement = ack-nhfb,
}
@Proceedings{Lavington:1980:IPP,
editor = "Simon Hugh Lavington",
booktitle = "Information Processing 80: Proceedings of {IFIP}
Congress 80, Tokyo, Japan, October 6--9, 1980,
Melbourne, Australia, October 14--17, 1980",
title = "Information Processing 80: Proceedings of {IFIP}
Congress 80, Tokyo, Japan, October 6--9, 1980,
Melbourne, Australia, October 14--17, 1980",
publisher = pub-ENH,
address = pub-ENH:adr,
pages = "xiii + 1070",
year = "1980",
ISBN = "0-444-86034-7",
ISBN-13 = "978-0-444-86034-7",
LCCN = "QA 75.5 I57 1980",
bibdate = "Thu Sep 01 23:09:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Nickel:1980:IMP,
editor = "Karl L. E. Nickel",
booktitle = "{Interval mathematics 1980: proceedings of an
International Symposium on Interval Mathematics, held
at the Institut f{\"u}r Angewandte Mathematik,
Universit{\"a}t Freiburg i. Br., Germany, May 27--31,
1980}",
title = "{Interval mathematics 1980: proceedings of an
International Symposium on Interval Mathematics, held
at the Institut f{\"u}r Angewandte Mathematik,
Universit{\"a}t Freiburg i. Br., Germany, May 27--31,
1980}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 554",
year = "1980",
ISBN = "0-12-518850-1",
ISBN-13 = "978-0-12-518850-0",
LCCN = "QA297.75 .I57 1980",
bibdate = "Fri Dec 08 08:24:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{GAMM:1981:PAM,
key = "GAMM'81",
booktitle = "{Proceedings of the Annual Meeting of the Gesellschaft
f{\"u}r Angewandte Mathematik und Mechanik,
W{\"u}rzburg}",
title = "{Proceedings of the Annual Meeting of the Gesellschaft
f{\"u}r Angewandte Mathematik und Mechanik,
W{\"u}rzburg}",
publisher = "Gesellschaft f{\"u}r Angewandte Mathematik und
Mechanik",
address = "W{\"u}rzburg, Germany",
pages = "????",
year = "1981",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Dec 08 08:56:45 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Part II (W{\"u}rzburg, 1981)",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1981:PSC,
key = "IEEE CA5 '81",
booktitle = "Proceedings: 5th Symposium on Computer Arithmetic, May
18--19, 1981, University of Michigan, Ann Arbor,
Michigan",
title = "Proceedings: 5th Symposium on Computer Arithmetic: May
18--19, 1981, University of Michigan, Ann Arbor,
Michigan",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "vii + 278",
year = "1981",
LCCN = "QA 76.6 S985t 1981",
bibdate = "Sat Feb 24 15:01:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 81CH1630-C.",
acknowledgement = ack-nhfb,
keywords = "ARITH-5; Computer arithmetic and logic units ---
Congresses.; Electronic digital computers ---
Programming --- Congresses.; Floating-point arithmetic
Congresses.",
xxISBN = "(none)",
}
@Proceedings{Messina:1982:PMM,
editor = "P. C. Messina and A. Murli",
booktitle = "{Problems and Methodologies in Mathematical Software
Production: International Seminar held at Sorrento,
Italy, November 3--8, 1980}",
title = "{Problems and Methodologies in Mathematical Software
Production: International Seminar held at Sorrento,
Italy, November 3--8, 1980}",
volume = "142",
publisher = pub-SV,
address = pub-SV:adr,
pages = "271",
year = "1982",
ISBN = "0-387-11603-6 (New York), 3-540-11603-6 (Berlin)",
ISBN-13 = "978-0-387-11603-7 (New York), 978-3-540-11603-5
(Berlin)",
LCCN = "QA76.95 .P76 1982",
bibdate = "Sat Sep 24 00:30:07 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Lecture Notes in Computer Science",
acknowledgement = ack-nhfb,
}
@Book{Randell:1982:ODC,
editor = "Brian Randell",
booktitle = "The Origins of Digital Computers: Selected Papers",
title = "The Origins of Digital Computers: Selected Papers",
publisher = pub-SV,
address = pub-SV:adr,
edition = "Third",
pages = "xvi + 580",
year = "1982",
DOI = "https://doi.org/10.1007/978-3-642-61812-3",
ISBN = "0-387-11319-3, 3-540-11319-3",
ISBN-13 = "978-0-387-11319-7, 978-3-540-11319-5",
LCCN = "TK7885.A5 O741 1982",
bibdate = "Sun Nov 03 08:28:47 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
series = "Texts and monographs in computer science",
acknowledgement = ack-nhfb,
remark = "See also other editions
\cite{Randell:1973:ODC,Randell:1975:ODC}.",
tableofcontents = "Chapter I: Introduction / 1 \par
Chapter II: Analytical Engines / 9 \\
2.1. On the Mathematical Powers of the Calculating
Engine / C. Babbage (1837) / 19 \\
2.2. Report of the Committee \ldots{} appointed to
consider the advisability and to estimate the expense
of constructing Mr. Babbage's Analytical Machine, and
of printing tables by its means / C. W. Merrifield
(1879) / 55 \\
2.3. Babbage's Analytical Engine / H. P. Babbage (1910)
/ 67 \\
2.4. On a Proposed Analytical Machine / P. E. Ludgate
(1909) / 73 \\
2.5. Essays on Automatics -- Its Definition --
Theoretical Extent of its Applications / L. Torres Y
Quevedo 1914 / 89 \\
2.6. Electromechanical Calculating Machine / L. Torres
y Quevedo (1920) / 109 \\
2.7. Scheme of Assembly of a Machine Suitable for the
Calculations of Celestial Mechanics / L. Couffignal
(1938) / 121 \par
Chapter III: Tabulating Machines / 127 \\
3.1. An Electric Tabulating System / H. Hollerith
(1889) / 133 \\
3.2. Calculating Machines: Their Principles and
Evolution / L. Couffignal (1933) / 145 \\
3.3. The Automatic Calculator IPM / H.-J. Dreyer and A.
Walther (1946) / 155 \par
Chapter IV: Zuse and Schreyer / 159 \\
4.1. Method for Automatic Execution of Calculations
with the aid of Computers / K. Zuse 1936 / 163 \\
4.2. Technical Computing Machines / H. Schreyer (1939)
/ 171 \\
4.3. The Outline of a Computer Development from
Mechanics to Electronics / K. Zuse 1962 / 175
\par
Chapter V: Aiken and IBM / 191 \\
5.1. Proposed Automatic Calculating Machine / H. H.
Aiken (1937) / 195 \\
5.2. The Automatic Sequence Controlled Calculator / H.
H. Aiken and G. M. Hopper (1946) / 203 \\
5.3. Electrons and Computation / W. J. Eckert (1948) /
223 \\
5.4. The IBM Card-Programmed Electronic Calculator / J.
W. Sheldon and L. Tatum (1951) / 233 \par
Chapter VI: Bell Telephone Laboratories / 241 \\
6.1. Computer / G. R. Stibitz (1940) / 247 \\
6.2. The Relay Interpolator / O. Cesareo (1946) / 253
\\
6.3. The Ballistic Computer / J. Juley (1947) / 257 \\
6.4. A Bell Telephone Laboratories' Computing Machine /
F. L. Alt (1948) / 263 \par
Chapter VII: The Advent of Electronic Computers / 293
\\
7.1. Binary Calculation / E. W. Phillips (1936) / 303
\\
7.2. Computing Machine for the Solution of Large
Systems of Linear Algebraic Equations / J. V. Atanasoff
(1940) / 315 \\
7.3. Arithmetical Machine / V. Bush (1940) / 337 \\
7.4. Report on Electronic Predictors for Anti-Aircraft
Fire Control / J. A. Rajchman et al. (1942) / 345 \\
7.5. Colossus: Godfather of the Computer / B. Randell
(1977) / 349 \\
7.6. The Use of High Speed Vacuum Tube Devices for
Calculating / J. W. Mauchly (1942) / 355 \\
7.7. The Electronic Numerical Integrator and Computer.
(ENIAC) / H. H. Goldstine and A. Goldstine (1946) / 359
\par
Chapter VIII: Stored Program Electronic Computers / 375
\\
8.1. First Draft of a Report on the EDVAC / J. von
Neumann (1945) / 383 \\
8.2. Preparation of Problems for EDVAC-type Machines /
J. W. Mauchly (1947) / 393 \\
8.3. Preliminary Discussion of the Logical Design of an
Electronic Computing Instrument / A. W. Burks et al.
(1946) / 399 \\
8.4. Electronic Digital Computers / F. C. Williams and
T. Kilburn (1948) / 415 \\
8.5. The EDSAC / M. V. Wilkes and W. Renwick (1949) /
417 \\
8.6. The EDSAC Demonstration / B. H. Worsley (1949) /
423 \par
Bibliography / 431 \\
Index to Bibliography / 545 \\
Subject Index / 563",
}
@Proceedings{Reid:1982:RBN,
editor = "John K. Reid",
booktitle = "{The Relationship Between Numerical Computation and
Programming Languages: Proceedings of the IFIP TC2
Working Conference on the Relationship between
Numerical Computation and Programming Languages,
Boulder, Colorado, USA., 3--7 August, 1981}",
title = "{The Relationship Between Numerical Computation and
Programming Languages: Proceedings of the IFIP TC2
Working Conference on the Relationship between
Numerical Computation and Programming Languages,
Boulder, Colorado, USA., 3--7 August, 1981}",
publisher = pub-ENH,
address = pub-ENH:adr,
pages = "x + 377",
year = "1982",
ISBN = "0-444-86377-X",
ISBN-13 = "978-0-444-86377-5",
LCCN = "QA297 .I34 1981",
bibdate = "Tue Sep 06 22:34:51 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
tableofcontents = "PREFACE v\\
LIST OF CONTENTS vii\\
SESSION 1: INTRODUCTION. Chair: C. L. Lawson.
Discussant: B. Ford 1\\
Programming Languages: Power, Trends and Facilities for
Numerical Computation. J. R. Rice 3\\
Programming Languages for Numerical Subroutine
Libraries. J. J. Du Croz 17\\
Experience with the Olympus System. K. V. Roberts 33\\
SESSION 2: ARITHMETIC. 49 Chair: H. J. Stetter,
Discussant: R. P. Brent\\
Floating-point Parameters, Models and Standards. W. J.
Cody 51\\
The Use of Controlled Precision. T. E. Hull 71\\
A Synopsis of Interval Arithmetic for the Designer of
Programming Languages. C. Reinsch 85\\
SESSION 3: ARITHMETIC AND SYMBOLIC MATHEMATICS 101
Chair: W. Cowell, Discussant: W. S. Brown\\
The Near Orthogonality of Syntax, Semantics and
Diagnostics in Numerical Programming Environments. W.
Kahan and J. T. Coonen 103\\
Symbolic Manipulation Languages and Numerical
Computation: Trends. R. J. Fateman 117\\
Programming Languages for Symbolic Algebra and
Numerical Analysis. W. M. Gentleman 131\\
SESSION 4: DATA STRUCTURES. 143 Chair: M. Paul,
Discussant: P. Kemp\\
Data Structures for Numerical Quadrature. L. M. Delves
145\\
Data Structures for Sparse Matrices. J. K. Reid 153\\
Array Processing Features in the Next Fortran. B. T.
Smith 163\\
Examples of Array Processing in the Next Fortran. A.
Wilson 179\\
SESSION 5: PARALLELISM; LANGUAGE EVOLUTION. 185 Chair:
J. A. Nelder, Discussant: G. Paul\\
Exception Handling in Array Languages. T. W. Lake
187\\
A Framework for Language Evolution. J. L. Wagener
197\\
Languages and High-performance Computations. D. Kuck,
D. Padua, A. Sameh and M. Wolfe 205\\
SESSION 6: PROGRAM STRUCTURE. 223 Chair: J. C. Adams,
Discussant: E. L. Battiste\\
Numerical Packages in Ada. S. J. Hammarling and B. A.
wichmann 225\\
Tasking Features in Programming Languages. O. Roubine
245\\
Language Support for Floating Point. S. Feldman 263\\
OVERALL SESSION DISCUSSION. 275\\
SESSION 7: OPEN SESSION. 277 Chair: B. Einarsson,
Discussant: F. N. Fritsch\\
A Combined Lexical, Syntactic, and Semantic Approach
for Improving Notation. M. B. Wells 279\\
Program Transformation and Language Design. J. M. Boyle
285\\
Programming Parallel Numerical Algorithms in Ada. E. K.
Blum 297\\
Programming in Algol 68 (as a host) and the usage of
Fortran (program libraries). C. G. van der Laan 305\\
The Fortran of the Future. 317 F. N. Fritsch (ed.) -
Exception handling in Fortran (J. A. M. Snoek) 317 -
Conformity - towards a less permissive standard for
Fortran (D. T. Muxworthy) 318 - An alternative approach
to the evolution of Fortran (W. S. Brown, S. 1.
Feldman, N. L. Schryer, L. D. Fosdick) 320 - Notes on
Fortran evolution (E. L. Battiste) 322 - Discussion
324\\
SESSION 8: SOURCE TO SOURCE TRANSFORMATIONS AND
LANGUAGE COMPLEXITY. 329 Chair: J. M. Boyle,
Discussant: Th. J. Dekker\\
Specification Languages and Program Transformation. P.
Pepper 331\\
Tools for Numerical Programming. W. Miller 347\\
Languageless Programming. A. van Wijngaarden 361\\
LIST OF PARTICIPANTS. 373",
}
@Book{Rodrigue:1982:AC,
editor = "Garry Rodrigue",
booktitle = "Parallel computations",
title = "Parallel computations",
volume = "1",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xii + 408",
year = "1982",
ISBN = "0-12-592101-2",
ISBN-13 = "978-0-12-592101-5",
LCCN = "????",
bibdate = "Sat Nov 29 11:11:02 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Computational techniques",
acknowledgement = ack-nhfb,
}
@Proceedings{Ruschitzka:1982:IWC,
editor = "Manfred Ruschitzka and M. Christensen and W. F. Ames
and R. Vichnevetsky",
key = "IMACS '82",
booktitle = "{IMACS} World Congress on Systems Simulation and
Scientific Computation (10th: 1982: Montreal, Quebec).
Parallel and large-scale computers: performance,
architecture, applications",
title = "{IMACS} World Congress on Systems Simulation and
Scientific Computation (10th: 1982: Montreal, Quebec).
Parallel and large-scale computers: performance,
architecture, applications",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xii + 329",
year = "1982",
ISBN = "0-444-86608-6",
ISBN-13 = "978-0-444-86608-0",
LCCN = "QA76.5 .I414 1982",
bibdate = "Wed Sep 07 22:56:44 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{Seck:1981:WWS,
editor = "Friedrich Seck",
booktitle = "{Wissenschaftsgeschichte um Wilhelm Schickard:
Vortr{\"a}ge bei dem Symposion der Universit{\"a}t
T{\"u}bingen im 500. Jahr ihres Bestehens am 24.und 25.
Juni 1977}. ({German}) [{History of Science and William
Schickard Presentations at the Symposium of the
University of T{\"u}bingen in 500 Years of existence on
24th and 25th June 1977}]",
title = "{Wissenschaftsgeschichte um Wilhelm Schickard:
Vortr{\"a}ge bei dem Symposion der Universit{\"a}t
T{\"u}bingen im 500. Jahr ihres Bestehens am 24.und 25.
Juni 1977}. ({German}) [{History of Science and William
Schickard Presentations at the Symposium of the
University of T{\"u}bingen in 500 Years of existence on
24th and 25th June 1977}]",
volume = "26",
publisher = "J. C. B. Mohr",
address = "T{\"u}bingen, West Germany",
pages = "240",
year = "1981",
ISBN = "3-16-444151-7",
ISBN-13 = "978-3-515-08004-0",
LCCN = "QB29",
bibdate = "Sat Jul 27 11:16:04 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib;
z3950.gbv.de:20011/gvk",
series = "Contubernium",
acknowledgement = ack-nhfb,
language = "German",
subject = "Schickard, Wilhelm",
subject-dates = "1592--1635",
tableofcontents = "Richard A. Jarrell / Astronomy at the University of
T{\"u}bingen: The Work of Michael M{\"a}stlin / 9 \\
Matthias Schramm / Ans{\"a}tze zu einer darstellenden
Geometrie bei Schickard / 21 \\
Menso Folkerts / Sp{\"a}tmittelalterliche
Multiplikationsmethoden, Nepers Rhabdologie und
Schickards Rechenmaschine / 51 \\
Ludolf von Mackensen / Wilhelm Schickards technische
Entw{\"u}rfe und die Erfindung seines Handplanetariums
/ 67 \\
Manfred B{\"u}ttner / Johannes St{\"o}ffler und die
Beziehungen zwischen Geographie und Theologie im 16.
Jahrhundert / 81 \\
J{\"u}rgen H{\"u}bner / Johannes Kepler als Geograph im
Kontext des theologischen Denkens seiner Zeit /99 \\
Volker Bialas / Entwicklung und erste Anwendungen des
Triangulationsverfahrens in der Geod{\"a}sie des
fr{\"u}hen 17. Jahrhunderts / 115 \\
Martin Brecht / Kritik und Reform der Wissenschaften
bei Johann Valentin Andreae / 129 \\
Berthold Sutter / Wissenschaft und geistige
Str{\"o}mungen zwischen dem Augsburger Religionsfrieden
und dem Drei{\ss}igj{\"a}hrigen Krieg / 153",
}
@Proceedings{Southcon:1982:SCR,
key = "Southcon '82",
booktitle = "Southcon\slash 82 Conference Record: Sessions
Presented at Southcon\slash 82, Orlando, Florida, March
23--25, 1982",
title = "Southcon\slash 82 Conference Record: Sessions
Presented at Southcon\slash 82, Orlando, Florida, March
23--25, 1982",
publisher = "Electronic Conventions, Inc.",
address = "El Segundo, CA, USA",
pages = "various",
year = "1982",
LCCN = "TK 7801 S68 1982",
bibdate = "Fri Dec 08 13:03:00 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{Watson:1982:NAP,
editor = "George Alistair Watson",
booktitle = "{Numerical Analysis: Proceedings of the 9th Biennial
Conference, held at Dundee, Scotland, June 23--26,
1981}",
title = "{Numerical Analysis: Proceedings of the 9th Biennial
Conference, held at Dundee, Scotland, June 23--26,
1981}",
volume = "912",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xi + 245",
pages = "xi + 245",
year = "1982",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0093144",
ISBN = "0-387-11199-9 (softcover), 3-540-11199-9 (softcover),
3-540-39009-X (e-book)",
ISBN-13 = "978-0-387-11199-5 (softcover), 978-3-540-11199-3
(softcover), 978-3-540-39009-1 (e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L28 no. 912; QA1 .L471; QA297 .D915n 1981",
bibdate = "Sat Oct 29 15:16:39 1994",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1980.bib;
library.ox.ac.uk:210/ADVANCE;
melvyl.cdlib.org:210/CDL90",
series = ser-LECT-NOTES-MATH,
URL = "http://www.springerlink.com/content/978-3-540-39009-1",
acknowledgement = ack-nhfb,
subject = "Analisi numerica; Congressi; 1981; Dundee; Numerical
analysis; Congresses",
tableofcontents = "P. H. Calamai and A. R. Conn / A second-order
method for solving the continuous multifacility
location problem / 1--25 \\
M. P. Cullinan and M. J. D. Powell / Data smoothing by
divided differences / 26--37 \\
G. Dahlquist / On the control of the global error in
stiff initial value problems / 38--49 \\
L. M. Delves / Chebyshev methods for integral and
differential equations / 50--63 \\
J. Douglas, Jr. / Simulation of miscible displacement
in porous media by a modified method of characteristic
procedure / 64--70 \\
I. S. Duff / Full matrix techniques in sparse Gaussian
elimination / 71--84 \\
R. Fletcher / Second order corrections for
non-differentiable optimization / 85--114 \\
C. W. Gear and K. A. Gallivan / Automatic methods for
highly oscillatory ordinary differential equations /
115--124 \\
G. H. Golub and M. L. Overton / Convergence of a
two-stage Richardson iterative procedure for solving
systems of linear equations / 125--139 \\
J. G. Hayes: Curved knot lines and surfaces with ruled
segments / 140--156 \\
P. J. van der Houwen / On the time integration of
parabolic differential equations / 157--168 \\
T. E. Hull / Precision control, exception handling and
a choice of numerical algorithms / 169--178 \\
P. Lancaster / Generalized Hermitian matrices: a new
frontier for numerical analysis? / 179--189 \\
R. J. Y. McLeod / Some applications of geometry in
numerical analysis / 190--229 \\
L. B. Wahlbin / A quasioptimal estimate in piecewise
polynomial Galerkin approximation of parabolic problems
/ 230 --245 \\
Back matter / 249--251",
}
@Proceedings{Anonymous:1983:PSC,
editor = "Anonymous",
booktitle = "1983 proceedings of the statistical computing section:
papers presented at the annual meeting of the American
Statistical Association, Toronto, Canada, August
15--18, 1983",
title = "1983 proceedings of the statistical computing section:
papers presented at the annual meeting of the American
Statistical Association, Toronto, Canada, August
15--18, 1983",
publisher = "American Statistical Association",
address = "Washington, DC, USA",
year = "1983",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0149-9963",
LCCN = "QA276.4 .A43a",
bibdate = "Sat Nov 29 11:12:49 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Gentle:1983:CSS,
editor = "James E. Gentle",
booktitle = "Computer Science and Statistics: Proceedings of the
Fifteenth Symposium on the Interface, Houston, Texas,
March 1983",
title = "Computer Science and Statistics: Proceedings of the
Fifteenth Symposium on the Interface, Houston, Texas,
March 1983",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xi + 379",
year = "1983",
ISBN = "0-444-86688-4",
ISBN-13 = "978-0-444-86688-2",
LCCN = "QA276.4 .S95 1983",
bibdate = "Tue Sep 06 22:39:53 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1983:IEE,
key = "IEEE '83",
booktitle = "1983 International Electrical, Electronics Conference:
Proceedings, September 26--28, Automotive Building,
Exhibition Place, Toronto, Canada",
title = "1983 International Electrical, Electronics Conference:
Proceedings, September 26--28, Automotive Building,
Exhibition Place, Toronto, Canada",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1983",
LCCN = "TK 5 I6514 1983",
bibdate = "Fri Dec 08 13:03:01 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Proceedings{IEEE:1983:PII,
key = "IEEE CSO '83",
booktitle = "{IEEE} International Workshop on Computer Systems
Organization, March 29--31, 1983, Sheraton New Orleans
Hotel, New Orleans",
title = "{IEEE} International Workshop on Computer Systems
Organization, March 29--31, 1983, Sheraton New Orleans
Hotel, New Orleans",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "viii + 227",
year = "1983",
ISBN = "0-8186-0010-1",
ISBN-13 = "978-0-8186-0010-4",
LCCN = "QA 76.9 A73 I2 1983",
bibdate = "Wed Sep 07 23:43:15 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{IEEE:1983:PSC,
key = "IEEE SCA6 '83",
booktitle = "Proceedings: 6th Symposium on Computer Arithmetic,
June 20--22, 1983, Aarhus University, {\AA}rhus,
Denmark",
title = "Proceedings: 6th Symposium on Computer Arithmetic,
June 20--22, 1983, Aarhus University, {\AA}rhus,
Denmark",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 221",
year = "1983",
ISBN = "0-8186-4476-1 (paperback), 0-8186-8476-3 (hardcover),
0-8186-6476-2 (microfiche), 0-8186-0034-9 (hardcover)",
ISBN-13 = "978-0-8186-4476-4 (paperback), 978-0-8186-8476-0
(hardcover), 978-0-8186-6476-2 (microfiche),
978-0-8186-0034-0 (hardcover)",
LCCN = "QA 76.9 C62 S95 1983",
bibdate = "Fri Sep 02 00:35:28 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 83CH1892-9. IEEE Computer Society
order number 476.",
URL = "http://www.acsel-lab.com/arithmetic/arith6/papers/",
acknowledgement = ack-nhfb,
keywords = "ARITH-6",
}
@Proceedings{Kulisch:1983:NAS,
editor = "Ulrich Kulisch and Willard L. Miranker and Gerd
Bohlender",
booktitle = "A New Approach to Scientific Computation: Proceedings
of the {Symposium on a New Approach to Scientific
Computation (1982: IBM Thomas J. Watson Research
Center)}",
title = "A New Approach to Scientific Computation: Proceedings
of the {Symposium on a New Approach to Scientific
Computation (1982: IBM Thomas J. Watson Research
Center)}",
volume = "7",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 384",
year = "1983",
ISBN = "0-12-428660-7, 1-4832-7204-4",
ISBN-13 = "978-0-12-428660-3, 978-1-4832-7204-7",
LCCN = "QA297 .N49 1983; QA297 .S847 1982",
bibdate = "Mon Jan 08 10:57:28 1996",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Notes and Reports in Computer Science and Applied
Mathematics",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Data processing; Algebra; Computer
arithmetic; Electronic books; Analyse num{\'e}rique;
Informatique; Alg{\'e}bre; Arithm{\'e}tique interne des
ordinateurs; Data processing; Computer arithmetic",
tableofcontents = "Front Cover \\
A New Approach to Scientific Computation \\
Copyright Page \\
Dedication \\
Table of Contents \\
Contributors \\
Preface \\
Acknowledgments \\
1. A New Arithmetic For Scientific Computation \\
1. Introduction \\
2. The Spaces of Numerical Computations \\
3. Traditional Definition of Computer Arithmetic: The
Vertical Method \\
4. The New Definition of Computer Arithmetic: The
Horizontal Method \\
5. Computer Arithmetic and Programming Languages \\
6. Realization and Applications \\
References \\
2. Computer Demonstration Packages For Standard
Problems of Numerical Mathematics \\
Language Extension \\
Pascal-SC Computing Inclusions \\
Old and New \\
Precise Dot Product \\
Linear Systems \\
Inversion of a Matrix \\
Eigenproblems \\
Rounding Error and Cancellation \\
Evaluation of a Polynomial \\
Zero of a Polynomial \\
Polynomial Package \\
Arithmetic Expressions \\
Systems of Non-Linear Equations \\
Differential Equations \\
3. Solving Algebraic Problems With High Accuracy \\
Introduction \\
1. Computer Arithmetic \\
2. Linear Systems \\
3. Over- and Underdetermined Linear Systems \\
4. Linear Systems With Band Matrices \\
5. Sparse Linear Systems \\
6. Matrix Inversion \\
7. Non-Linear Systems \\
8. The Algebraic Eigenvalue Problem \\
9. Real and Complex Zeros of Polynomials \\
10. Linear, Quadratic and Convex Programming \\
11. Arithmetic Expressions \\
Conclusions \\
References \\
4. Evaluation of Arithmetic Expression Swith Maximum
Accuracy \\
Introduction \\
1. Evaluation of Polynomials \\
2. Evaluation of Arbitrary Arithmetic Expressions \\
3. Numerical Results \\
References \\
5. Solving Function Space Problems With Guaranteed
Close Bounds \\
1. Introduction \\
2. Mathematical Preliminaries \\
3. Practical Use of the Fixed Point Theorems \\
4. Functional Arithmetic and Roundings \\
5. Algorithmic Execution of Iterations \\
6. Applications to Differential and Integral Equations
\\
7. Some Examples \\
References \\
6. Ultra-Arithmetic: the Digital Computer Set In
Function Space \\
1. Introduction \\
2. A Review of Ultra-Arithmetic \\
3. Applications of Ultra-Arithmetic \\
4. The Arithmetic of Intervals of Polynomials \\
References \\
7. A Fortran Extension For Scientific Computation \\
1. Motivation \\
2. Notation of the Language Extension \\
3. Syntax and Semantics of the Extension \\
References \\
8. An Introduction to Matrix Pascal: A Pascal Extension
For Scientific Computation \\
a. Data Types \\
b. Expressions \\
C. Procedures, Functions, Operators \\
D. Universal Operator Concept \\
E. Expressions With Maximum Accuracy \\
F. Standard Functions \\
References \\
9. Realization of An Optimal Computer Arithmetic \\
1. Introduction \\
Mathematical Foundations \\
2. Organization of the Arithmetic \\
3. Implementation of the Elementary Operations \\
4. Operations In the Higher Spaces \\
5. Realization On a Micro Computer \\
References \\
10. Features of a Hardware Implementation of An Optimal
Arithmetic \\
1. Introduction \\
2. Implementation of Scalar Products",
}
@Proceedings{Mini-Micro:1983:MMN,
key = "Mini-Micro Northeast '83",
booktitle = "Mini\slash Micro Northeast\slash 83 Conference Record:
Sessions Presented at Mini\slash Micro Northeast-83,
New York, New York, April 18--20, 1983, in conjunction
with Electro\slash 83",
title = "Mini\slash Micro Northeast\slash 83 Conference Record:
Sessions Presented at Mini\slash Micro Northeast-83,
New York, New York, April 18--20, 1983, in conjunction
with Electro\slash 83",
publisher = "Electronic Conventions, Inc.",
address = "Los Angeles, CA, USA",
pages = "various",
year = "1983",
LCCN = "QA 76.5 M565 1983",
bibdate = "Fri Dec 08 13:03:05 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{Mini-Micro:1983:MMW,
key = "Mini-Micro West '83",
booktitle = "Mini\slash Micro West '83: Conference Record: Sessions
Presented at Mini\slash Micro West-83, San Francisco,
California, November 8--11, 1983",
title = "Mini\slash Micro West '83: Conference Record: Sessions
Presented at Mini\slash Micro West-83, San Francisco,
California, November 8--11, 1983",
publisher = "Electronic Conventions, Inc.",
address = "Los Angeles, CA, USA",
pages = "various",
year = "1983",
LCCN = "TK7885.A1 M56 1983",
bibdate = "Fri Dec 08 13:03:06 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{Ranocchia:1983:RFA,
editor = "Diane D. Ranocchia",
booktitle = "1983 Rochester {FORTH} Applications Conference, June
7--11, 1983",
title = "1983 Rochester {FORTH} Applications Conference, June
7--11, 1983",
publisher = "Institute for Applied FORTH Research",
address = "Rochester, NY, USA",
pages = "301",
year = "1983",
ISBN = "0-914593-00-5",
ISBN-13 = "978-0-914593-00-3",
LCCN = "QA76.73.F24 R59 1983",
bibdate = "Thu Sep 01 22:47:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1984:TFA,
editor = "Anonymous",
booktitle = "Transactions of the First Army Conference on Applied
Mathematics and Computing (Washington, {DC, 1983)}",
title = "Transactions of the First Army Conference on Applied
Mathematics and Computing (Washington, {DC}, 1983)",
volume = "84-1",
publisher = "ARO Rep. 84-1, U. S. Army Res. Office",
address = "Research Triangle Park, NC, USA",
pages = "xxii + 925",
month = feb,
year = "1984",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 11:40:45 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "ARO report",
acknowledgement = ack-nhfb,
}
@Book{Cowell:1984:SDM,
editor = "Wayne R. Cowell",
booktitle = "Sources and Development of Mathematical Software",
title = "Sources and Development of Mathematical Software",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xii + 404",
year = "1984",
ISBN = "0-13-823501-5",
ISBN-13 = "978-0-13-823501-7",
LCCN = "QA76.95 .S68 1984",
bibdate = "Tue Dec 14 22:44:45 1993",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Prentice-Hall Series in Computational Mathematics,
Cleve Moler, Advisor",
acknowledgement = ack-nhfb,
}
@Book{Evanczuk:1984:MSS,
editor = "Stephen Evanczuk",
booktitle = "Microprocessor systems: software and hardware
architecture",
title = "Microprocessor systems: software and hardware
architecture",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
bookpages = "vii + 389",
year = "1984",
ISBN = "0-07-019756-3, 0-07-606876-5 (paperback)",
ISBN-13 = "978-0-07-019756-5, 978-0-07-606876-0 (paperback)",
LCCN = "QA76.5 .M521955 1984",
bibdate = "Sat Nov 29 11:14:42 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Feilmeier:1984:PCP,
editor = "M. Feilmeier and G. Joubert and U. Schendel",
booktitle = "Parallel computing 83: proceedings of the
International Conference on Parallel Computing, held at
the Freie Universit{\"a}t Berlin, 26--28 September
1983",
title = "Parallel computing 83: proceedings of the
International Conference on Parallel Computing, held at
the Freie Universit{\"a}t Berlin, 26--28 September
1983",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xiii + 566",
year = "1984",
ISBN = "0-444-87528-X",
ISBN-13 = "978-0-444-87528-0",
LCCN = "QA76.6.I547 1983",
bibdate = "Mon Apr 14 17:58:44 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Ford:1984:TML,
editor = "B. Ford and J. C. Rault and F. Thomasset",
booktitle = "Tools, methods and languages for scientific and
engineering computation. Proc. of international
conference (Paris, France, May 17--19, 1983)",
title = "Tools, methods and languages for scientific and
engineering computation. Proc. of international
conference (Paris, France, May 17--19, 1983)",
publisher = pub-ENH,
address = pub-ENH:adr,
pages = "xvi + 458",
year = "1984",
ISBN = "0-444-87570-0",
ISBN-13 = "978-0-444-87570-9",
LCCN = "Q183.9 .I53 1983",
bibdate = "Sat Nov 29 07:20:57 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Golub:1984:SNA,
editor = "Gene H. Golub",
booktitle = "Studies in Numerical Analysis",
title = "Studies in Numerical Analysis",
volume = "24",
publisher = pub-MATH-ASSOC-AMER,
address = pub-MATH-ASSOC-AMER:adr,
pages = "x + 415",
year = "1984",
ISBN = "0-88385-126-1 (v. 1), 0-88385-100-8 (set)",
ISBN-13 = "978-0-88385-126-5 (v. 1), 978-0-88385-100-5 (set)",
LCCN = "QA297 .S83 1984",
MRclass = "65-06",
MRnumber = "88i:65007",
bibdate = "Sat Oct 22 17:16:36 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Studies in mathematics",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "numerical analysis",
tableofcontents = "Gene H. Golub / Preface \\
James H. Wilkinson / The perfidious polynomial \\
Jorge J. Mor{\'e} and D. C. Sorensen / Newton's method
\\
Iain S. Duff / Research directions in sparse matrix
computations \\
Walter Gautschi / Questions of numerical conditions
related to polynomials \\
Paul Concus, Gene H. Golub, and Dianne P. O'Leary / A
generalized conjugate gradient method for the numerical
solution of elliptic partial differential equations \\
J. Barkley Rosser / Solving differential equations on a
hand held programmable calculator \\
V. Pereyra / Finite difference solution of boundary
value problems in ordinary differential equations \\
Dennis C. Jespersen / Multigrid methods for partial
differential equations \\
Paul N. Swarztrauber / Fast Poisson solvers \\
Peter Henrici / Poisson's equation in a hypercube:
discrete Fourier methods, eigenfunction expansions,
Pad{\'e} approximation to eigenvalues",
}
@Proceedings{Griffiths:1984:NAP,
editor = "D. F. Griffiths",
booktitle = "{Numerical analysis: Proceedings of the 10th Dundee
biennial conference held at the University of Dundee,
Scotland, June 28--July 1, 1983}",
title = "{Numerical analysis: Proceedings of the 10th Dundee
biennial conference held at the University of Dundee,
Scotland, June 28--July 1, 1983}",
volume = "1066",
publisher = pub-SV,
address = pub-SV:adr,
pages = "various",
year = "1984",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0099514",
ISBN = "3-540-13344-5 (print), 3-540-38881-8 (e-book)",
ISBN-13 = "978-3-540-13344-5 (print), 978-3-540-38881-4
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3.L28 no.1066, QA 297 D915n 1983",
bibdate = "Fri Dec 08 13:03:21 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Lecture notes in mathematics",
URL = "http://link.springer.com/chapter/10.1007/BFb0099525/",
acknowledgement = ack-nhfb,
book-DOI = "https://doi.org/10.1007/BFb0099514",
book-URL = "http://www.springerlink.com/content/978-3-540-38881-4",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
tableofcontents = "Front Matter / / i--xi \\
Splines in interactive computer graphics / Richard H.
Bartels / 1--29 \\
Some methods for separating stiff components in initial
value problems / {\AA}. Bj{\"o}rck / 30--43 \\
Approximation order from smooth bivariate PP functions
/ C. de Boor / 44--49 \\
The numerical solution of integral equations with
weakly singular kernels / Hermann Brunner / 50--71 \\
A trust-region approach to linearly constrained
optimization / David M. Gay / 72--105 \\
Multigrid methods for problems with a small parameter
in the highest derivative / P. W. Hemker / 106--121 \\
Nonconvex minimization calculations and the conjugate
gradient method / M. J. D. Powell / 122--141 \\
Particle approximation of linear hyperbolic equations
of the first order / P.-A. Raviart / 142--158 \\
Global error estimation for stiff ODEs / Lawrence F.
Shampine / 159--168 \\
Numerical techniques for nonlinear multi-parameter
problems / A. Spence, A. Jepson / 169--185 \\
Sequential defect correction for high-accuracy
floating-point algorithms / Hans J. Stetter / 186--202
\\
Numerical experiments with partially separable
optimization problems / A. Griewank, Ph. L. Toint /
203--220 \\
The numerical solution of total lp approximation
problems / G. A. Watson / 221--238 \\
An implicit diffusive numerical procedure for a
slightly compressible miscible displacement problem in
porous media / Thom C. Potempa, Mary Fanett Wheeler /
239--263 \\
Singularities in three-dimensional elliptic problems
and their treatment with finite element methods / J. R.
Whiteman / 264--275 Back Matter / / 277--278",
}
@Proceedings{IEEE:1984:CPI,
key = "IEEE Southeastcon '84",
booktitle = "Conference proceedings: {IEEE} Southeastcon '84, the
Galt House, Louisville, Kentucky, April 8--11, 1984",
title = "Conference proceedings: {IEEE} Southeastcon '84, the
Galt House, Louisville, Kentucky, April 8--11, 1984",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "562",
year = "1984",
LCCN = "TK 7801 I117 1984",
bibdate = "Thu Sep 15 18:50:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Proceedings{IEEE:1984:ILD,
editor = "{IEEE}",
key = "IEEE COMPCON '84",
booktitle = "{Intellectual Leverage the Driving Technologies:
Digest of Papers, Compcon Spring 84, February 27--March
1, Twenty-eighth IEEE Computer Society International
Conference, Meridien Hotel, San Francisco,
California}",
title = "{Intellectual Leverage the Driving Technologies:
Digest of Papers, Compcon Spring 84, February 27--March
1, Twenty-eighth IEEE Computer Society International
Conference, Meridien Hotel, San Francisco,
California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxvi + 522",
year = "1984",
CODEN = "PCICDQ",
ISBN = "0-8186-0525-1 (paperback), 0-8186-8525-5 (hardcover)",
ISBN-13 = "978-0-8186-0525-3 (paperback), 978-0-8186-8525-5
(hardcover)",
LCCN = "QA75.5 .C58 1984, TK7885.A1 C53 1984",
bibdate = "Wed Sep 29 09:24:59 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/common-lisp.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 84CH2017-2.",
acknowledgement = ack-nhfb # "\slash " # ack-nj,
}
@Proceedings{Kirk:1984:CRE,
editor = "Donald E. Kirk",
booktitle = "Conference Record: Eighteenth Asilomar Conference on
Circuits, Systems and Computers: Papers Presented
November 5--7, 1984, Pacific Grove, California",
title = "Conference Record: Eighteenth Asilomar Conference on
Circuits, Systems and Computers: Papers Presented
November 5--7, 1984, Pacific Grove, California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 456",
year = "1984",
ISBN = "0-8186-0673-8 (paperback), 0-8186-8673-1 (hard),
0-8186-4673-X (microfiche)",
ISBN-13 = "978-0-8186-0673-1 (paperback), 978-0-8186-8673-3
(hard), 978-0-8186-4673-7 (microfiche)",
LCCN = "TK 7801 A83 1984",
bibdate = "Thu Sep 08 13:41:13 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Mini-Micro:1984:MMS,
key = "Mini-Micro Southwest '84",
booktitle = "Mini\slash Micro Southwest\slash 84 Conference Record:
Sessions Presented at Mini\slash Micro Southwest-84,
Dallas, Texas, September 11--13, 1984, in conjunction
with Midcon\slash 84",
title = "Mini\slash Micro Southwest\slash 84 Conference Record:
Sessions Presented at Mini\slash Micro Southwest-84,
Dallas, Texas, September 11--13, 1984, in conjunction
with Midcon\slash 84",
publisher = "Electronic Conventions Management",
address = "Los Angeles, CA, USA",
pages = "various",
year = "1984",
LCCN = "TK 7888.3 M566 1984",
bibdate = "Fri Dec 08 13:03:08 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{NCC:1984:ACP,
key = "AFIPS NCC '84",
booktitle = "{AFIPS} Conference Proceedings of the 1984 National
Computer Conference, Las Vegas, {NV}, {USA}, 9--12 July
1984",
title = "{AFIPS} Conference Proceedings of the 1984 National
Computer Conference, Las Vegas, {NV}, {USA}, 9--12 July
1984",
publisher = pub-AFIPS,
address = pub-AFIPS:adr,
pages = "xi + 734",
year = "1984",
ISBN = "0-88283-043-0",
ISBN-13 = "978-0-88283-043-8",
LCCN = "????",
bibdate = "Fri Sep 16 10:57:24 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{Buchberger:1985:PEE,
editor = "Bruno Buchberger and Bob F. Caviness",
booktitle = "Proceedings: {EUROCAL} '85, European Conference on
Computer Algebra, Linz, Austria, April 1--3, 1985",
title = "Proceedings: {EUROCAL} '85, European Conference on
Computer Algebra, Linz, Austria, April 1--3, 1985",
volume = "203, 204",
publisher = pub-SV,
address = pub-SV:adr,
pages = "various",
year = "1985",
CODEN = "LNCSD9",
ISBN = "0-387-15983-5 (v. 1), 0-387-15984-3 (v. 2)",
ISBN-13 = "978-0-387-15983-6 (v. 1), 978-0-387-15984-3 (v. 2)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA155.7.E4 E85 1985",
bibdate = "Fri Apr 12 07:14:49 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Vol. 2 edited by: Bob F. Caviness. ``Jointly organized
by the ACM Special Interest Group on Symbolic and
Algebraic Manipulation (SIGSAM) and by the Symbolic and
Algebraic Manipulation Group in Europe (SAME)''--Vol.
2, pref. Contents: v. 1. Invited lectures --- v. 2.
Research contributions.",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "algebra --- data processing --- congresses",
}
@Proceedings{Hwang:1985:PSC,
editor = "Kai Hwang",
booktitle = "Proceedings: 7th Symposium on Computer Arithmetic,
June 4--6, 1985, University of Illinois, Urbana,
Illinois",
title = "Proceedings: 7th Symposium on Computer Arithmetic,
June 4--6, 1985, University of Illinois, Urbana,
Illinois",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 343",
year = "1985",
ISBN = "0-8186-0632-0 (paperback), 0-8186-8632-4 (hard),
0-8186-4632-2 (microfiche)",
ISBN-13 = "978-0-8186-0632-8 (paperback), 978-0-8186-8632-0
(hard), 978-0-8186-4632-4 (microfiche)",
LCCN = "QA76.9.C62 S95 1985",
bibdate = "Thu Sep 08 00:11:41 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 85CH2146-9. IEEE Computer Society
order number 632.",
acknowledgement = ack-nj,
keywords = "ARITH-7",
}
@Proceedings{IEEE:1985:ERC,
key = "IEEE Region 5 '85",
booktitle = "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
Holiday Inn Civic Center, Lubbock, Texas",
title = "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
Holiday Inn Civic Center, Lubbock, Texas",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "vi + 71",
year = "1985",
LCCN = "TK 7801 N56 1985",
bibdate = "Thu Sep 15 18:50:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Proceedings{Meek:1985:PFM,
editor = "D. S. Meek and G. H. J. {van Rees}",
booktitle = "{Proceedings of the Fourteenth Manitoba Conference on
Numerical Mathematics and Computing held at the
University of Manitoba, September 27--29, 1984}",
title = "{Proceedings of the Fourteenth Manitoba Conference on
Numerical Mathematics and Computing held at the
University of Manitoba, September 27--29, 1984}",
volume = "46",
publisher = "Utilitas Mathematica Publishers",
address = "Winnipeg, Manitoba, Canada",
pages = "358",
year = "1985",
ISBN = "0-919628-46-X",
ISBN-13 = "978-0-919628-46-5",
LCCN = "QA1 C75",
bibdate = "Fri Dec 08 08:33:52 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Congressus numerantium",
acknowledgement = ack-nhfb,
}
@Proceedings{Miranker:1985:ASC,
editor = "Willard L. Miranker and Richard A. Toupin",
booktitle = "Accurate Scientific Computations: Symposium, Bad
Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
title = "Accurate Scientific Computations: Symposium, Bad
Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
volume = "235",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 205",
year = "1985",
DOI = "https://doi.org/10.1007/3-540-16798-6",
ISBN = "0-387-16798-6",
ISBN-13 = "978-0-387-16798-5",
LCCN = "QA76.95 .A231 1986",
bibdate = "Sat Sep 03 12:24:08 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Proceedings{USENIX:1985:SCP,
editor = "{USENIX Association}",
booktitle = "Summer conference proceedings, Portland 1985: June
11--14, 1985, Portland, Oregon {USA}",
title = "Summer conference proceedings, Portland 1985: June
11--14, 1985, Portland, Oregon {USA}",
publisher = pub-USENIX,
address = pub-USENIX-EL-CERRITO:adr,
pages = "viii + 612",
year = "1985",
LCCN = "QA76.8.U65 U8 1985",
bibdate = "Sun Feb 18 07:46:09 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "UNIX (Computer operating system) --- Congresses.",
remark = "Spine title: USENIX Conference proceedings.",
}
@Proceedings{Vrdoljak:1985:ICA,
editor = "B. Vrdoljak",
booktitle = "{IV} Conference on Applied Mathematics, University of
Split, May 28--30, 1984",
title = "{IV} Conference on Applied Mathematics, University of
Split, May 28--30, 1984",
publisher = "Faculty of Civil Engineering, University of Split",
address = "Split, Yugoslavia",
pages = "153",
year = "1985",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Dec 08 08:54:11 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1986:III,
editor = "{IEEE}",
booktitle = "{ICASSP '86: IEEE International Conference on
Acoustics, Speech, and Signal Processing, April 7--11,
1986, Keio Plaza Inter-Continental Hotel Tokyo,
Japan}",
title = "{ICASSP '86: IEEE International Conference on
Acoustics, Speech, and Signal Processing, April 7--11,
1986, Keio Plaza Inter-Continental Hotel Tokyo,
Japan}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "1986",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Aug 08 09:31:51 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 86CH2243-4.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8362",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1986:PII,
key = "IEEE ICCD '86",
booktitle = "Proceedings: {IEEE} International Conference on
Computer Design, {VLSI} in Computers: {ICCD} '86, Rye
Town Hilton, Port Chester, New York, October 6--9,
1986",
title = "Proceedings: {IEEE} International Conference on
Computer Design, {VLSI} in Computers: {ICCD} '86, Rye
Town Hilton, Port Chester, New York, October 6--9,
1986",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvi + 607",
year = "1986",
ISBN = "0-8186-0735-1 (paperback), 0-8186-8735-5 (hard),
0-8186-4735-3 (microfiche)",
ISBN-13 = "978-0-8186-0735-6 (paperback), 978-0-8186-8735-8
(hard), 978-0-8186-4735-2 (microfiche)",
LCCN = "TK 7888.4 I23 1986",
bibdate = "Thu Sep 08 10:29:35 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{Mini-Micro:1986:EMM,
key = "Mini-Micro Northeast '86",
booktitle = "Electro\slash 86 and Mini\slash Micro Northeast
Conference Record: Sessions Presented at Electro\slash
86 and Mini\slash Micro Northeast-86, Boston, {MA}, May
13--15, 1986",
title = "Electro\slash 86 and Mini\slash Micro Northeast
Conference Record: Sessions Presented at Electro\slash
86 and Mini\slash Micro Northeast-86, Boston, {MA}, May
13--15, 1986",
publisher = "Electronic Conventions Management",
address = "Los Angeles, CA, USA",
pages = "various",
year = "1986",
LCCN = "TK 7801 E375 1986",
bibdate = "Fri Dec 08 13:03:09 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{Unicom:1986:SQA,
key = "SQART'86",
booktitle = "Software Quality Assurance, Reliability, and Testing.
London, {UK, 9--10} December 1986",
title = "Software Quality Assurance, Reliability, and Testing.
London, {UK}, 9--10 December 1986",
publisher = "Unicom Seminars Ltd.",
address = "Uxbridge, Middlesex, UK",
pages = "xi + 149",
year = "1986",
ISBN = "0-291-39732-8",
ISBN-13 = "978-0-291-39732-4",
LCCN = "????",
bibdate = "Fri Dec 08 13:46:34 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "The Technical Press-Unicom applied information
technology reports",
acknowledgement = ack-nhfb,
}
@Proceedings{Wescon:1986:WCR,
key = "WESCON '86",
booktitle = "Wescon\slash 86 Conference Record: Sessions Presented
at Wescon\slash 86, Anaheim, {CA}, November 18--20,
1986",
title = "Wescon\slash 86 Conference Record: Sessions Presented
at Wescon\slash 86, Anaheim, {CA}, November 18--20,
1986",
publisher = "Electronic Conventions Management",
address = "Los Angeles, CA, USA",
pages = "various",
year = "1986",
LCCN = "TK 7801 W47 1986",
bibdate = "Fri Dec 08 13:03:18 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Book{Anbar:1987:CM,
editor = "Michael Anbar",
booktitle = "Computers in medicine",
title = "Computers in medicine",
publisher = "Computer Science Press, Inc.",
address = "Rockville, MD, USA",
pages = "314",
year = "1987",
ISBN = "0-88175-080-8",
ISBN-13 = "978-0-88175-080-5",
LCCN = "????",
bibdate = "Sat Nov 29 11:19:13 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$32.95",
series = "Applications of computer science series",
acknowledgement = ack-nhfb,
}
@Book{Aspray:1987:PJN,
editor = "William Aspray and Arthur Burks",
booktitle = "Papers of {John von Neumann} on Computing and Computer
Theory",
title = "Papers of {John von Neumann} on Computing and Computer
Theory",
volume = "12",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "xviii + 624",
year = "1987",
ISBN = "0-262-22030-X",
ISBN-13 = "978-0-262-22030-9",
LCCN = "QA76.5 .P31451 1987",
bibdate = "Mon Sep 16 16:40:48 2002",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "See \cite{Knuth:1970:VNF}.",
series = "Charles Babbage Institute reprint series for the
history of computing",
acknowledgement = ack-nhfb,
subject-dates = "John von Neumann (1903--1957)",
tableofcontents = "Preface xi\\
Biographical Notes xiii \\
I. Computer Architecture and Logical Design \\
Introduction 3 \\
1. First Draft of a Report on the EDVAC 17 \\
2. Donald Knuth---Von Neumann's First Computer Program
83 \\
3. Preliminary Discussion of the Logical Design of an
Electronic Computing Instrument (with Arthur W. Burks
and Herman H. Goldstine) 97 \\
II. Computer Programming and Flow Diagrams Introduction
145 \\
Planning and Coding of Problems for an Electronic
Computing Instrument (with Herman H. Goldstine) \\
4. Planning and Coding of Problems, vol. 1 151 \\
5. Planning and Coding of Problems, vol. 2 223 \\
6. Planning and Coding of Problems, vol. 3 286 \\
III. Large-Scale High-Speed Computing \\
Introduction 309 \\
7. On the Principles of Large Scale Computing Machines
(with Herman H. Goldstine) 317 \\
8 The Future of High-Speed Computing 349 \\
9. The NORC and Problems in High Speed Computing 350
\\
IV. Theory of Natural and Artificial Automata \\
Introduction 363 \\
10. The General and Logical Theory of Automata 391 \\
11. Theory and Organization of Complicated Automata 432
\\
First Lecture: Computing Machines in General 434 \\
Second Lecture: Rigorous Theories of Control and
Information 445 \\
Third Lecture: Statistical Theories of Information 460
\\
Fourth Lecture: The Role of High and of Extremely High
Complication 467 \\
Fifth Lecture: Re-evaluation of the Problems of
Complicated Automata-Problems of Hierarchy and
Evolution 477 \\
12. Von Neumann's Self-Reproducing Automata, edited by
Arthur W. Burks 491 \\
13. Probabilistic Logics and the Synthesis of Reliable
Organisms from Unreliable Components 553 \\
Bibliography 603 \\
References 611",
}
@Proceedings{Davis:1987:PAC,
editor = "Pat Davis and Vicki McClintock",
booktitle = "{Proceedings of the 15th annual conference on Computer
Science, St. Louis, Missouri, USA}",
title = "{Proceedings of the 15th annual conference on Computer
Science, St. Louis, Missouri, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "473",
year = "1987",
ISBN = "0-89791-218-7",
ISBN-13 = "978-0-89791-218-1",
LCCN = "????",
bibdate = "Sat Aug 22 09:09:51 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 404870.",
acknowledgement = ack-nhfb,
}
@Proceedings{Irwin:1987:PSC,
editor = "Mary Jane Irwin and Renato Stefanelli",
booktitle = "Proceedings: 8th Symposium on Computer Arithmetic, May
19--21, 1987, Villa Olmo, Como, Italy",
title = "Proceedings: 8th Symposium on Computer Arithmetic, May
19--21, 1987, Villa Olmo, Como, Italy",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "ix + 277",
month = may,
year = "1987",
ISBN = "0-8186-0774-2 (paperback), 0-8186-4774-4 (microfiche),
0-8186-8774-6 (case)",
ISBN-13 = "978-0-8186-0774-5 (paperback), 978-0-8186-4774-1
(microfiche), 978-0-8186-8774-7 (case)",
LCCN = "QA 76.9 C62 S95 1987",
bibdate = "Wed Sep 14 20:52:21 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-8",
}
@Proceedings{Iserles:1987:SAN,
editor = "A. Iserles and M. J. D. Powell",
booktitle = "The State of the Art in Numerical Analysis:
Proceedings of the Joint {IMA}\slash {SIAM} Conference
on the State of the Art in Numerical Analysis held at
the University of Birmingham, 14--18 April 1986",
title = "The State of the Art in Numerical Analysis:
Proceedings of the Joint {IMA}\slash {SIAM} Conference
on the State of the Art in Numerical Analysis held at
the University of Birmingham, 14--18 April 1986",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xiv + 719",
year = "1987",
ISBN = "0-19-853614-3",
ISBN-13 = "978-0-19-853614-7",
LCCN = "QA297 .S781 1987",
bibdate = "Thu Sep 08 00:41:24 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "UK\pounds55.00, US\$77.50",
acknowledgement = ack-nj,
}
@Book{Kaucher:1987:CAS,
editor = "Edgar Kaucher and Ulrich Kulisch and Christian
Ullrich",
booktitle = "Computer arithmetic: scientific computation and
programming languages",
title = "Computer arithmetic: scientific computation and
programming languages",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
pages = "456",
year = "1987",
ISBN = "3-519-02448-9",
ISBN-13 = "978-3-519-02448-4",
LCCN = "QA76.9.C62 C69 1987",
bibdate = "Mon Dec 18 09:51:44 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Lin:1987:DSP,
editor = "Kun-Shan Lin",
booktitle = "Digital signal processing applications with the
{TMS320} family: Vol. 1",
title = "Digital signal processing applications with the
{TMS320} family: Vol. 1",
publisher = pub-PH,
address = pub-PH:adr,
pages = "724",
year = "1987",
ISBN = "0-13-212466-1",
ISBN-13 = "978-0-13-212466-9",
LCCN = "????",
bibdate = "Sat Nov 29 11:16:25 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$30.67",
series = "Prentice-Hall and Texas Instruments digital signal
processing series",
acknowledgement = ack-nhfb,
}
@Proceedings{Losleben:1987:ARV,
editor = "Paul Losleben",
booktitle = "Advanced research in {VLSI}: proceedings of the 1987
Stanford Conference",
title = "Advanced research in {VLSI}: proceedings of the 1987
Stanford Conference",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "415",
month = mar,
year = "1987",
ISBN = "0-262-12121-2",
ISBN-13 = "978-0-262-12121-7",
LCCN = "TK7888.4 .A4 1987",
bibdate = "Sat Nov 29 07:24:40 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Mason:1987:AAB,
editor = "J. C. Mason and M. G. Cox",
booktitle = "{Algorithms for approximation: based on the
proceedings of the IMA Conference on Algorithms for the
Approximation of Functions and Data, held at the Royal
Military College of Science, Shrivenham, July 1985}",
title = "{Algorithms for approximation: based on the
proceedings of the IMA Conference on Algorithms for the
Approximation of Functions and Data, held at the Royal
Military College of Science, Shrivenham, July 1985}",
volume = "10",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "xvi + 694 + 8",
year = "1987",
ISBN = "0-19-853612-7",
ISBN-13 = "978-0-19-853612-3",
LCCN = "QA221 .A5361 1987; QA221 .I47 1985",
bibdate = "Fri Nov 8 18:01:57 MST 2002",
bibsource = "ACM Computing Archive CD-ROM database (1991);
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$90",
series = "The Institute of Mathematics and Its Applications
conference series, new series",
acknowledgement = ack-nhfb,
bibno = "39820",
catcode = "G.1.2; G.1.2",
CRclass = "G.1.2 Approximation; G.1.2 Approximation; G.1.2
Elementary function approximation",
descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS,
Approximation; Mathematics of Computing, NUMERICAL
ANALYSIS, Approximation, Elementary function
approximation",
genterm = "theory; algorithms",
guideno = "1987-16080",
meetingname = "IMA Conference on Algorithms for the Approximation of
Functions and Data (1985: Royal Military College of
Science, Shrivenham)",
procdate = "The Institute of mathematics and its applications
conference series; 10 July 1985",
procloc = "Shrivenham, UK",
sub = "Proceedings of the IMA Conference on Algorithms for
the approximation of functions",
subject = "Approximation theory; Data processing; Congresses; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
tableofcontents = "Preface / v \\
Contributors / xiii \\
\\
I Development of Algorithms \\
\\
1. Spline Approximation and Smoothing \\
\\
G. T. Anthony and M. G. Cox / The fitting of extremely
large data sets by bivariate splines / 5 \\
W. Dahmen / Subdivision algorithms --- recent results,
some extensions and further developments / 21 \\
P. Dierckx / Fast algorithms for smoothing data over a
disc or a sphere using tensor product splines / 51 \\
T. Lyche and K. M{\o}rken / A discrete approach to knot
removal and degree reduction algorithms for splines /
67 \\
R. H. J. Gmelig Meyling / On algorithms and
applications for bivariate B-splines / 83 \\
\\
2. Spline Interpolation and Shape Preservation \\
\\
R. E. Carlson / Shape preserving interpolation / 97 \\
M. G. Cox and H. M. Jones / Shape preserving spline
approximation in the $\ell_1$-norm / 115 \\
J. A. Gregory / A review of curve interpolation with
shape control / 131 \\
\\
3. Multivariate Interpolation \\
\\
M. J. D. Powell / Radial basis functions for
multivariable interpolation: a review / 143 \\
R. A. Lorentz / On the determinant of a bivariate
Birkhoff interpolation problem / 169 \\
A. Le Mehaute / Interpolation with piecewise
polynomials in more than one variable / 181 \\
\\
4. Least Square Methods \\
\\
R. Farwig / Multivariate interpolation of scattered
data by moving least squares methods / 193 \\
F. Yoshimoto / Least squares approximation by one-pass
methods with piecewise polynomials / 213 \\
\\
5. Rational Approximation \\
\\
L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable
Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227
\\
P. T. Breuer / A new method for real rational uniform
approximation / 265 \\
C. B. Dunham / Rationals with repeated poles / 285 \\
A. Iserles and S. P. N{\o}rsett / Error control of
rational approximation with a matrix argument / 293 \\
\\
6. Complex and Nonlinear Approximation \\
\\
K. Madsen / General algorithms for discrete non-linear
parameter estimation / 309 \\
G. Opfer / Complex rational approximation with
numerical experiments / 327 \\
G. A. Watson / Data fitting by positive sums of
exponentials / 337 \\
J. C. Mason and P. Owen / Some simple algorithms for
constrained complex and rational approximation / 357
\\
\\
7. Computer-Aided Design and Blending \\
\\
L. L. Schumaker / Numerical aspects of spaces of
piecewise polynomials on triangulations / 373 \\
M. V. Golitschek / The $H$-sets of the blending
functions / 407 \\
D. Levin / Multidimensional reconstruction by
set-valued approximations/ 421 \\
\\
II Applications \\
\\
8. Applications in Numerical Analysis \\
\\
H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the
behaviour of zeros of best approximating polynomials
and rational functions / 437 \\
J. Gilbert and W. A. Light / Multigrid methods and the
alternating algorithm / 447 \\
K. Jetter and J. St{\"o}ckler / On the computation of
Gauss--Birkhoff quadrature formulas / 459 \\
E. Schock / Error bounds for the solution of integral
equations by Galerkin-like methods / 471 \\
N. M. Temme / On the computation of the incomplete
gamma functions for large values of the parameters /
479 \\
\\
9. Applications in Partial Differential Equations \\
\\
J. R. Rice / Adaptive tensor product grids for singular
problems / 493 \\
W. Freeden / Harmonic splines for solving boundary
value problems of potential theory / 507 \\
D. C. Hanscomb / Recovery of fluid flow fields / 531
\\
L. Reichel / The selection of subspace and collocation
points in the boundary collocation method for some
plane elliptic boundary problems / 541 \\
\\
10. Applications in Other Disciplines \\
\\
L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex
formation constants --- a problem from solution
chemistry / 557 \\
D. E. Roberts and P. R. Graves-Morris / The application
of generalised inverse rational interpolants in the
model analysis of vibrating structures I / 573 \\
A. Daman and J. C. Mason / A generalised
cross-validation method for meteorological data with
gaps / 595 \\
K. P. Jackson and J. C. Mason / The approximation by
complex functions of stresses in cracked domains / 611
\\
J. H. McDonnell / Equally spaced cubic splines for
representing time histories / 623 \\
B. L. Rahimi and S. W. Ellacott / Dynamic phase
analysis of heart anomalies / 641 \\
\\
III Software \\
\\
J. G. Hayes / NAG algorithms for the approximation of
functions and data / 653 \\
G. T. Anthony and M. G. Cox / The National Physical
Laboratory's Data Approximation Subroutine Library /
669 \\
\\
M. G. Cox (editor) / Panel Discussion / 689",
}
@Proceedings{Zunde:1987:EFI,
editor = "Pranas Zunde and Jagdish C. Agrawal",
booktitle = "Proceedings of the Fourth Symposium on Empirical
Foundations of Information and Software Science, held
October 22--24, 1986 in Atlanta, Georgia",
title = "Proceedings of the Fourth Symposium on Empirical
Foundations of Information and Software Science, held
October 22--24, 1986 in Atlanta, Georgia",
publisher = pub-PLENUM,
address = pub-PLENUM:adr,
pages = "x + 533",
year = "1987",
ISBN = "0-306-42817-2",
ISBN-13 = "978-0-306-42817-3",
LCCN = "QA75.5 .S956 1986",
bibdate = "Mon Sep 12 07:44:06 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:1988:ICS,
editor = "{ACM}",
booktitle = "1988 International Conference on Supercomputing, July
4--8, 1988, St. Malo, France",
title = "1988 International Conference on Supercomputing, July
4--8, 1988, St. Malo, France",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiii + 679",
year = "1988",
ISBN = "0-89791-272-1",
ISBN-13 = "978-0-89791-272-3",
LCCN = "QA76.5 .I547 1988",
bibdate = "Sat Nov 29 07:52:15 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:1988:PAC,
key = "ACM LFP '88",
booktitle = "{Proceedings of the 1988 ACM Conference on LISP and
Functional Programming: Papers Presented at the
Conference, Snowbird, Utah, July 25--27, 1988}",
title = "{Proceedings of the 1988 ACM Conference on LISP and
Functional Programming: Papers Presented at the
Conference, Snowbird, Utah, July 25--27, 1988}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 351",
year = "1988",
ISBN = "0-89791-273-X",
ISBN-13 = "978-0-89791-273-0",
LCCN = "QA76.73.L23 A24 1988",
bibdate = "Thu Sep 01 23:12:58 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$27.00",
acknowledgement = ack-nhfb,
}
@Proceedings{Brodersen:1988:VSP,
editor = "Robert W. Brodersen and Howard S. Moscovitz",
booktitle = "{VLSI} Signal Processing, {III}",
title = "{VLSI} Signal Processing, {III}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 536",
year = "1988",
ISBN = "0-87942-248-3",
ISBN-13 = "978-0-87942-248-6",
LCCN = "TK5102.5 .V563 1988; TK5102.5 .V56 1988",
bibdate = "Fri Dec 8 10:50:52 MST 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "The chapters in this book are based on presentations
given at the IEEE Acoustics, Speech, and Signal
Processing Society Workshop on VLSI Signal Processing
held November 2--4, 1988 at the Monterey Plaza Hotel,
Monterey, California. Published under the sponsorship
of the IEEE Acoustics, Speech, and Signal Processing
Society.",
subject = "Signal processing; Digital techniques; Congresses;
Integrated circuits; Very large scale integration",
}
@Proceedings{Chen:1988:CRT,
editor = "Ray R. Chen",
key = "Asilomar CSSC '88",
booktitle = "Conference Record: Papers Presented October
31--November 2, 1988, Pacific Grove, California:
Twenty-second Asilomar Conference on Signals, Systems
and Computers",
title = "Conference Record: Papers Presented October
31--November 2, 1988, Pacific Grove, California:
Twenty-second Asilomar Conference on Signals, Systems
and Computers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1988",
ISBN = "0-929029-15-1",
ISBN-13 = "978-0-929029-15-3",
LCCN = "TK5102.5 .A74 1988",
bibdate = "Fri Dec 08 13:03:10 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nj,
}
@Proceedings{Electro:1988:ECR,
key = "Electro '88",
booktitle = "Electro\slash 88 Conference Record: Sessions Presented
at Electro\slash 88, Boston, {MA}, May 10--12, 1988",
title = "Electro\slash 88 Conference Record: Sessions Presented
at Electro\slash 88, Boston, {MA}, May 10--12, 1988",
publisher = "Electronic Conventions Management",
address = "Los Angeles, CA, USA",
pages = "various",
year = "1988",
ISBN = "(done)",
ISBN-13 = "(done)",
LCCN = "TK 7801 E375 1988",
bibdate = "Fri Dec 08 13:03:11 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{Harris:1988:PAI,
editor = "Gerald F. Harris and Cedric Frank Walker",
booktitle = "Proceedings of the Annual International Conference of
the {IEEE} Engineering in Medicine and Biology Society:
New Orleans, Louisiana, November 4--7, 1988",
title = "Proceedings of the Annual International Conference of
the {IEEE} Engineering in Medicine and Biology Society:
New Orleans, Louisiana, November 4--7, 1988",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1988",
LCCN = "R856.A2 I344 1988",
bibdate = "Fri Dec 08 13:03:12 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Four volumes.",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{IEEE:1988:IIS,
editor = "????",
key = "IEEE ISSCC '88",
booktitle = "1988 {IEEE} International Solid-State Circuits
Conference Digest of Technical Papers 31st {ISSCC}, San
Francisco, {CA}, {USA}, 17--19 February 1988",
title = "1988 {IEEE} International Solid-State Circuits
Conference Digest of Technical Papers 31st {ISSCC}, San
Francisco, {CA}, {USA}, 17--19 February 1988",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "??--??",
year = "1988",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 12 21:57:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxnote = "NHFB: OCLC says: ``AUTHOR: IEEE International
Solid-State Circuits Conference (35th: 1988: New York,
NY); TITLE: Digest of technical papers: 1988 IEEE
International Solid-State Circuits Conference; EDITION:
1st ed.; PLACE: Coral Gables, Fla.; FORMAT: 432 p.:
ill.; 28 cm.; OTHER: Winner, Lewis, 1906--''",
}
@Proceedings{IEEE:1988:PII,
key = "IEEE ICCD '88",
booktitle = "Proceedings: 1988 {IEEE} International Conference on
Computer Design, {VLSI} in Computers and Processors:
{ICCD} '88, Rye Town Hilton, Rye Brook, New York,
October 3--5, 1988",
title = "Proceedings: 1988 {IEEE} International Conference on
Computer Design, {VLSI} in Computers and Processors:
{ICCD} '88, Rye Town Hilton, Rye Brook, New York,
October 3--5, 1988",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvii + 168",
year = "1988",
ISBN = "0-8186-8872-6",
ISBN-13 = "978-0-8186-8872-0",
LCCN = "TK 7888.4 I23 1988",
bibdate = "Wed Sep 07 23:22:51 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{IEEE:1988:PSN,
editor = "{IEEE}",
booktitle = "Proceedings, Supercomputing '88: November 14--18,
1988, Orlando, Florida",
title = "Proceedings, Supercomputing '88: November 14--18,
1988, Orlando, Florida",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 458",
year = "1988",
ISBN = "0-8186-0882-X (v. 1; paper), 0-8186-8882-3 (v. 1;
case), 0-8186-4882-1 (v. 1: microfiche) 0-8186-8923-4
(v. 2), 0-8186-5923-X (v. 2: microfiche), 0-8186-8923-4
(v. 2: case)",
ISBN-13 = "978-0-8186-0882-7 (v. 1; paper), 978-0-8186-8882-9 (v.
1; case), 978-0-8186-4882-3 (v. 1: microfiche)
978-0-8186-8923-9 (v. 2), 978-0-8186-5923-2 (v. 2:
microfiche), 978-0-8186-8923-9 (v. 2: case)",
LCCN = "QA76.5 .S894 1988",
bibdate = "Fri Aug 23 13:34:23 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes. Available from IEEE Service Center
(Catalog number 88CH2617-9), Piscataway, NJ, USA.",
acknowledgement = ack-nhfb,
classification = "C5220 (Computer architecture); C5440 (Multiprocessor
systems and techniques); C5470 (Performance evaluation
and testing); C5540 (Terminals and graphic displays);
C6150C (Compilers, interpreters and other processors);
C6150J (Operating systems)",
keywords = "algorithms; architecture; benchmarking; compiler
evaluation; compiler technology; computer graphic
equipment; data-flow systems; Horizon superconducting
system; mass storage systems; operating systems;
operating systems (computers); parallel algorithms;
parallel architectures; parallel machines; performance
evaluation; program compilers; program development;
supercomputer performance; supercomputing center
management; visualization",
}
@Proceedings{IREE:1988:AMC,
editor = "{IREE}",
booktitle = "7th Australian Microelectronics Conference: May
16--18, 1988, Sydney University, {NSW}: proceedings",
title = "7th Australian Microelectronics Conference: May
16--18, 1988, Sydney University, {NSW}: proceedings",
publisher = "IREE",
address = "Edgecliff, NSW, Australia",
pages = "ix + 303",
year = "1988",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 07:57:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "16-18 May 1988",
conflocation = "Sydney, NSW, Australia",
confsponsor = "Inst. Radio and Electron. Eng. Australia; IEE;
University of Sydney; Inst, Eng. Australia; IEEE",
keywords = "Institution of Radio and Electronics Engineers
Australia (IREE)",
pubcountry = "Australia",
}
@Proceedings{Lacoume:1988:SPI,
editor = "J. L. Lacoume and A. Chehikian and N. Martin and J.
Malbos",
booktitle = "Signal Processing {IV}: Theories and Applications
Proceedings of {EUSIPCO-88}. Fourth European Signal
Processing Conference",
title = "Signal Processing {IV}: Theories and Applications
Proceedings of {EUSIPCO}-88. Fourth European Signal
Processing Conference",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xxxix + 1680",
year = "1988",
ISBN = "0-444-70516-3",
ISBN-13 = "978-0-444-70516-7",
LCCN = "????",
bibdate = "Sat Nov 29 08:01:22 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "5-8 Sept. 1988",
conflocation = "Grenoble, France",
pubcountry = "Netherlands",
}
@Proceedings{Martin:1988:SPN,
editor = "Joanne L. Martin and Stephen F. Lundstrom",
booktitle = "Supercomputing '88: proceedings, November 14--18,
1988, Orlando, Florida",
title = "Supercomputing '88: proceedings, November 14--18,
1988, Orlando, Florida",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "viii + 263",
year = "1988",
ISBN = "0-8186-0882-X (v. 1; paper), 0-8186-8882-3 (v. 1;
case), 0-8186-4882-1 (v. 1: microfiche) 0-8186-8923-4
(v. 2), 0-8186-5923-X (v. 2: microfiche), 0-8186-8923-4
(v. 2: case)",
ISBN-13 = "978-0-8186-0882-7 (v. 1; paper), 978-0-8186-8882-9 (v.
1; case), 978-0-8186-4882-3 (v. 1: microfiche)
978-0-8186-8923-9 (v. 2), 978-0-8186-5923-2 (v. 2:
microfiche), 978-0-8186-8923-9 (v. 2: case)",
LCCN = "QA76.5 .S894 1988",
bibdate = "Fri Aug 30 08:01:51 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/pi.bib",
note = "Two volumes. IEEE catalog number 88CH2617-9. IEEE
Computer Society Order Number 882.",
acknowledgement = ack-nhfb,
classification = "C5440 (Multiprocessor systems and techniques); C7300
(Natural sciences)",
keywords = "biology computing; chemistry; computational biology;
computational fluid dynamics; computational
mathematics; computational physics; flow simulation;
global change; mathematics computing; parallel
processing; physics computing; structural analysis;
structural engineering computing; supercomputers ---
congresses",
}
@Proceedings{Mason:1990:AAI,
editor = "J. C. Mason and M. G. Cox",
booktitle = "{Algorithms for approximation II: based on the
proceedings of the Second International Conference on
Algorithms for Approximation, held at Royal Military
College of Science, Shrivenham, July 1988}",
title = "{Algorithms for approximation II: based on the
proceedings of the Second International Conference on
Algorithms for Approximation, held at Royal Military
College of Science, Shrivenham, July 1988}",
publisher = pub-CHAPMAN-HALL,
address = pub-CHAPMAN-HALL:adr,
pages = "514",
year = "1990",
ISBN = "0-412-34580-3",
ISBN-13 = "978-0-412-34580-7",
LCCN = "QA221 .I54 1988",
bibdate = "Thu Sep 01 23:55:44 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Algorithms for
Approximation (2nd: 1988: Royal Military College of
Science, Shrivenham, England)",
subject = "Approximation theory; Data processing; Congresses",
tableofcontents = "Part One: Development of Algorithms / 1 \\
1. Spline Approximation / 3 \\
E. Arge, M. Dcehlen, T. Lyche and K. Morken /
Constrained spline approximation of functions and data
based on constrained knot removal / 4 \\
G. T. Anthony and M. G. Cox / Near real-time spline
fitting of long sequences of uniformly-spaced data / 21
\\
M. Bozzini and F. de Tisi / An algorithm for knot
location in bivariate least squares spline
approximation / 30 \\
M. G. Cox, P. M. Harris and H. M. Jones / A knot
placement strategy for least squares spline fitting
based on the use of local polynomial approximations /
37 \\
G. Opfer / An algorithm for nonlinear splines with
non-negativity constraints / 46 \\
C. Potier and C. Vercken / Spline curve fitting of
digitized contours / 54 \\
C. Rabut / A B-spline approximation algorithm for
quasi-interpolation or filtering / 62 \\
P. W. Smith / On knots and nodes for spline
interpolation / 72 \\
2. Polynomial and Piecewise Polynomial Approximation /
79 \\
W. Dahmen / A basis for certain spaces of multivariate
polynomials and exponentials / 80 \\
F. N. Fritschi / Monotone piecewise cubic data fitting
/ 99 \\
M. Heilmann and M. W. M{\"u}ller / Direct and converse
results on simultaneous approximation by the method of
Bernstein--Durrmeyer operators / 107 \\
A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M.
Sanz-Serna / Orthogonality and approximation in a
Sobolev space / 117 \\
M. A. Lachance / Piecewise polynomial approximation of
polynomial curves / 125 \\
E. Quak and L. L. Schumaker / Calculation of the energy
of a piecewise polynomial surface / 134 \\
3. Interpolation / 145 \\
M. D. Buhmann and M. J. D. Powell / Radial basis
function interpolation on an infinite regular grid /
146 \\
L. Brutman / The Fourier operator of even order and its
application to an extremum problem in interpolation /
170 \\
N. Dyn and A. Ron / On multivariate polynomial
interpolation / 177 \\
N. Dyn, D. Levin and S. Rippen / Algorithms for the
construction of data dependent triangulations / 185 \\
C. Rademacher and K. Scherer / Algorithms for computing
best parametric cubic interpolation / 193 \\
4. Smoothing and Constraint Methods / 209 \\
M. Von Golitschek and L. L. Schumaker / Data fitting by
penalized least squares / 210 \\
K. W. Bosworth / A semiinfinite programming algorithm
for constrained best approximation / 228 \\
M. Bozzini and L. Lenarduzzi / Inference region for a
method of local approximation by using the residuals /
236 \\
5. Complex Approximation / 245 \\
G. A. Watson / Numerical methods for Chebyshev
approximation of complex-valued functions / 246 \\
P. T. P. Tang / A fast algorithm for linear complex
Chebyshev approximation / 265 \\
Part Two: Applications / 275 \\
6. Computer Aided Design and Geometric Modelling / 277
\\
N. Dyn, J. A. Gregory and D. Levin / Uniform
subdivision algorithms for curves and surfaces / 278
\\
T. B. Boffey, M. G. Cox, L. M. Delves and C. J.
Pursglove / Approximation by spheres / 296 \\
T. A. Foley / Interpolation of scattered data on a
spherical domain / 303 \\
A. B. Forbes / Least squares best fit geometric
elements / 311 \\
W. Freeden and J. C. Mason / Uniform piecewise
approximation on the sphere / 320 \\
7. Applications in Numerical Analysis / 335 \\
L. N. Trefethen / Approximation theory and numerical
linear algebra / 336 \\
M. Frontini, G. Rodriguez and S. Seatzu / An algorithm
for computing minimum norm solutions of the finite
moment problem / 361 \\
R. H. J. Gmelig Meyling / Numerical solution of the
biharmonic equation using different types of bivariate
spline functions / 369 \\
G. O. Olaofe / Quadrature solution of integral
equations: a uniform treatment of Fredholm and Volterra
equations / 377 \\
G. Walz / Increasing the convergence modulus of an
asymptotic expansion: an algorithm for numerical
differentiation / 387 \\
J. Williams / Approximation and parameter estimation in
ordinary differential equations / 395 \\
8. Applications in Other Disciplines / 405 \\
C. Zala and I. Barrodale / Applications of discrete
$L_1$ methods in science and engineering / 406 \\
J. C. Mason, A. E. Trefethen and S. J. Wilde /
Constrained complex approximation algorithms in
communication engineering / 424 \\
R. W. Allen and J. G. Metcalfe / Integration of
absolute amplitude from a decibel B-spline fit / 449
\\
M. G. Cox and H. M. Jones / A nonlinear least squares
data fitting problem arising in microwave measurement /
458 \\
J. C. Mason and S. J. Wilde / A complex minimax
algorithm for phase-only adaptation in antenna arrays /
466 \\
Part Three: Catalogue of Algorithms / 477 \\
E. Grosse / A catalogue of algorithms for approximation
/ 479",
}
@Proceedings{Midcon:1988:MCP,
editor = "{Midcon}",
booktitle = "Midcon 88: Conference: Papers, August 30 -- September
1, 1998, Dallas, {TX}, {USA}",
title = "{Midcon} 88: Conference: Papers, August 30 --
September 1, 1998, Dallas, {TX}, {USA}",
publisher = "Electron. Conventions Manage",
address = "Ventura, CA, USA",
edition = "Midcon",
pages = "iv + 397",
year = "1988",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 07:30:24 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
availability = "Western Periodicals Co., 13000 Raymer Street, North
Hollywood, CA 91605, USA",
confdate = "30 Aug.-1 Sept. 1988",
conflocation = "Dallas, TX, USA",
confsponsor = "IEEE; ERA",
keywords = "Midwest Electronic Show and Convention (Midcon)",
}
@Book{Moore:1988:RCR,
editor = "Ramon E. Moore",
booktitle = "Reliability in Computing: the Role of Interval Methods
in Scientific Computing",
title = "Reliability in Computing: the Role of Interval Methods
in Scientific Computing",
volume = "19",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xv + 428",
year = "1988",
ISBN = "0-12-505630-3",
ISBN-13 = "978-0-12-505630-4",
LCCN = "QA76.9.E94 R45 1988",
bibdate = "Mon Dec 18 09:41:47 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Perspectives in computing",
ZMnumber = "0638.00033",
acknowledgement = ack-nhfb,
classmath = "00Bxx Conference proceedings and collections of
papers; 65-06 Proceedings of conferences (numerical
analysis)",
keywords = "Computing; Interval methods; Reliability; Scientific
computing",
tableofcontents = "Contributors / ix \\
Preface / xiii \\
Acknowledgments / xv \\
Part 1: Computer Arithmetic and Mathematical Software /
3 \\
Chapter 1. Arithmetic for Vector Processors / R.
Kirchner and U. Kulisch / 3 \\
Abstract \\
1. Introduction \\
2. The State of the Art \\
3. Fast Computation of Sums and Scalar Products \\
4. Summation with only One Row of Adders \\
5. Systems with Large Exponent Range and Further
Remarks \\
6. Application to Multiple Precision Arithmetic \\
7. Contemporary Floating-Point Arithmetic \\
8. Literature \\
Chapter 2. FORTRAN-SC, A FORTRAN Extension for
Engineering/Scientific Computation with Access to
ACRITH: Language Description with Examples / Wolfgang
Walter / 43 \\
Abstract \\
1. Introduction \\
2. Development of FORTRAN-SC \\
3. Main Language Concepts \\
4. Language Description with Examples \\
5. Implementation of FORTRAN-SC \\
References \\
Chapter 3. FORTRAN-SC, A FORTRAN Extension for
Engineering/Scientific Computation with Access to
ACRITH: Demonstration of the Compiler and Sample
Programs / Michael Metzger / 63 \\
Abstract \\
Introduction \\
Example 1: Interval Newton Method \\
Example 2: Automatic Differentiation \\
Example 3: Runge--Kutta Method \\
Example 4: Gaussian Elimination Method \\
Example 5: Verified Solution of a Linear System \\
References \\
Chapter 4. Reliable Expression Evaluation in PASCAL-SC
/ J{\"u}rgen Wolff von Gudenberg / 81 \\
Abstract \\
1. Floating-point arithmetic \\
2. Interval arithmetic \\
3. The optimal scalar product \\
4. Complex floating-point and complex interval
arithmetic \\
5. Matrix and vector arithmetic \\
6. Accurate Operations and Problem Solving Routines \\
7. Transformation of arithmetic expressions \\
8. Solution of nonlinear systems \\
9. The data type dotprecision \\
10. Dotproduct expressions \\
11. Conclusion \\
References \\
Chapter 5. Floating-Point Standards --- Theory and
Practice / W. J. Cody / 99 \\
1. Introduction \\
2. The Standards \\
3. Implementations \\
4. Software Support \\
5. Conclusions \\
References \\
Chapter 6. Algorithms for Verified Inclusions: Theory
and Practice / Siegfried M. Rump / 109 \\
Summary \\
0. Introduction \\
1. Basic theorems \\
2. Practical verification on the computer \\
3. Interactive Programming Environment \\
4. References \\
Chapter 7. Applications of Differentiation Arithmetic /
George F. Corliss / 127 \\
Abstract \\
1. Differentiation Arithmetic \\
Why, What, and How? \\
2. Why? \\
Motivation \\
3. What? \\
Component tools \\
4. Conditions on f \\
5. How to use it? \\
Applications \\
6. Acknowledgements \\
References \\
Part 2: Linear and Nonlinear Systems / 149 \\
Chapter 8. Interval Acceleration of Convergence / Karl
Nickel / 151 \\
Abstract \\
1. Introduction \\
2. Examples \\
3. Definitions and Notation \\
4. Interval Methods \\
5. How Can We Get Bounds on a Given Point-Sequence? \\
6. Acceleration of Convergence \\
References \\
Chapter 9. Solving Systems of Linear Interval Equations
/ J. Rohn / 171 \\
0. Introduction \\
1. Bounding the solutions \\
2. Computing the xy's \\
3. Explicit formulae for x, x \\
4. Inverse interval matrix \\
References \\
Chapter 10. Interval Least Squares --- a Diagnostic
Tool / David M. Gay / 183 \\
Introduction \\
Linearity \\
Interval Notation \\
Chapter 11. Existence of Solutions and Iterations for
Nonlinear Equations / G. Alefeld / 207 \\
Chapter 12. Interval Method for Algebraic Equations /
M. A. Wolfe / 229 \\
Chapter 13. Error Questions in the Computation of
Solution Manifolds of Parametrized Equations / Werner
C. Rheinbolt / 249 \\
Chapter 14. The Enclosure of Solutions of
Parameter-Dependent Systems of Equations / A. Neumaier
/ 269 \\
Part 3. Optimization / 287 \\
Chapter 15. An Overview of Global Optimization Using
Interval Analysis / Eldon Hansen / 289 \\
Chapter 16. Philosophy and Practicalities of Interval
Arithmetic / G. William Walster / 309 \\
Chapter 17. Some Recent Aspects of Interval Algorithms
for Global Optimization / Helmut Ratschek / 325 \\
Chapter 18. The Use of Interval Arithmetic in
Uncovering Structure of Linear Systems / Weldon A.
Lodwick / 341 \\
Part 4. Operator Equations / 355 \\
Chapter 19. The Role of Order in Computing / Garrett
Birkhoff / 357 \\
Chapter 20. Interval Methods for Operator Equations /
R. E. Moore and Shen Zuhe / 379 \\
Chapter 21. Boundary Implications for Stability
Properties: Present Status / J. Garloff and N. K. Bose
/ 391 \\
Chapter 22. Validating Computation in a Function Space
/ Edgar Kaucher and Willard L. Miranker / 403 \\
Epilogue: A Poem about My Life, by Daniel J. Langton /
427",
}
@Proceedings{Sakamura:1988:TPO,
editor = "Ken Sakamura",
booktitle = "{TRON} Project 1988. Open-Architecture Computer
Systems Proceedings of the Fifth {TRON} Project
Symposium",
title = "{TRON} Project 1988. Open-Architecture Computer
Systems Proceedings of the Fifth {TRON} Project
Symposium",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xi + 384",
year = "1988",
DOI = "https://doi.org/10.1007/978-4-431-68081-9",
ISBN = "0-387-70038-2 (New York), 3-540-70038-2 (Berlin),
4-431-70038-2 (Tokyo)",
ISBN-13 = "978-0-387-70038-0 (New York), 978-3-540-70038-8
(Berlin), 978-4-431-70038-8 (Tokyo)",
LCCN = "????",
bibdate = "Sat Nov 29 07:43:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{USENIX:1988:UPC,
editor = "{USENIX Association}",
booktitle = "{USENIX} proceedings: {C++} Conference, Denver, {CO},
October 17--21, 1988",
title = "{USENIX} proceedings: {C++} Conference, Denver, {CO},
October 17--21, 1988",
publisher = pub-USENIX,
address = pub-USENIX:adr,
pages = "362",
year = "1988",
bibdate = "Sun Feb 18 07:46:09 MST 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "C++ (Computer program language) --- Congresses.",
}
@Proceedings{Wescon:1988:WCR,
editor = "{Wescon}",
booktitle = "Wescon/88 conference record: sessions presented at
Wescon/88, Anaheim, Calif., November 15--17, 1988",
title = "Wescon/88 conference record: sessions presented at
Wescon/88, Anaheim, Calif., November 15--17, 1988",
volume = "32",
publisher = "Electronic Conventions Management",
address = "Ventura, CA, USA",
pages = "798",
year = "1988",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 07:37:36 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "15-17 Nov. 1988",
conflocation = "Anaheim, CA, USA",
confsponsor = "IEEE; ERA",
}
@Proceedings{ACM:1989:APT,
editor = "{ACM}",
booktitle = "{ASPLOS-III} Proceedings. Third International
Conference on Architectural Support for Programming
Languages and Operating Systems, Boston, {MA}, {USA},
April 3--6, 1989",
title = "{ASPLOS}-{III} Proceedings. Third International
Conference on Architectural Support for Programming
Languages and Operating Systems, Boston, {MA}, {USA},
April 3--6, 1989",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 303",
year = "1989",
ISBN = "0-89791-300-0",
ISBN-13 = "978-0-89791-300-3",
LCCN = "QA76.9.A73I565 1989",
bibdate = "Sun Sep 29 06:28:50 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 556890. Also published as Computer
architecture news, v. 17, no. 2 (Apr. 1989), Operating
systems review, v. 23, special issue (Apr. 1989), and
SIGPLAN notices, v. 24, special issue (May 1989).",
acknowledgement = ack-nhfb,
confsponsor = "IEEE; ACM",
}
@Proceedings{ACM:1989:PSN,
editor = "{ACM}",
booktitle = "Proceedings, Supercomputing '89: November 13--17,
1989, Reno, Nevada",
title = "Proceedings, Supercomputing '89: November 13--17,
1989, Reno, Nevada",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xviii + 849",
year = "1989",
ISBN = "0-89791-341-8",
ISBN-13 = "978-0-89791-341-6",
LCCN = "QA 76.5 S87 1989",
bibdate = "Wed Aug 28 06:48:31 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
University of California MELVYL catalog.",
note = "IEEE 89CH2802-7.",
acknowledgement = ack-nhfb,
classification = "A0130C (Conference proceedings); A0270
(Computational techniques); A0500 (Statistical physics
and thermodynamics); A4700 (Fluid dynamics); B0100
(General electrical engineering topics); B0290
(Numerical analysis); B1130B (Computer-aided circuit
analysis and design); C4100 (Numerical analysis); C4240
(Programming and algorithm theory); C5440
(Multiprocessor systems and techniques); C5470
(Performance evaluation and testing); C6110B (Software
engineering techniques); C6150J (Operating systems);
C7000 (Computer applications)",
keywords = "benchmarking; computer applications; parallel
algorithms; parallel processing; performance
evaluation; performance measurements; performance
tools; pipeline processing; software environments;
supercomputer architectures; supercomputers ---
congresses; technology integration; vector algorithms",
remark = "89CM2802-7. ACM Order Number 415892. IEEE 89CH2802-7.
IEEE Computer Society Order Number 2021.",
}
@Book{Carey:1989:PSM,
editor = "Graham F. Carey",
booktitle = "Parallel supercomputing: methods, algorithms and
applications",
title = "Parallel supercomputing: methods, algorithms and
applications",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "x + 287",
year = "1989",
ISBN = "0-471-92436-9",
ISBN-13 = "978-0-471-92436-4",
LCCN = "M89.E02452; QA76.6",
bibdate = "Mon Jan 2 15:42:42 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Wiley series in parallel computing",
acknowledgement = ack-nhfb,
subject = "Parallel programming (Computer science)",
}
@Proceedings{Chen:1989:TSA,
editor = "Ray R. Chen",
booktitle = "Twenty-second Asilomar Conference on Signals, Systems
\& Computers: October 31--November 2, 1988, Pacific
Grove, California",
title = "Twenty-second Asilomar Conference on Signals, Systems
\& Computers: October 31--November 2, 1988, Pacific
Grove, California",
publisher = "Maple Press",
address = "San Jose, CA, USA",
pages = "xviii + 985",
year = "1989",
ISBN = "0-929029-15-1",
ISBN-13 = "978-0-929029-15-3",
LCCN = "????",
bibdate = "Sat Nov 29 08:06:51 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes. IEEE catalog number 88CH2660-9. IEEE
catalog no. 88CH2835-7.",
acknowledgement = ack-nhfb,
confdate = "31 Oct.-2 Nov. 1988",
conflocation = "Pacific Grove, CA, USA",
confsponsor = "Naval Postgraduate School; San Jose State Univ",
xxnote = "Check differing IEEE catalog numbers??",
}
@Proceedings{Ercegovac:1989:PSC,
editor = "Milo{\v{s}} D. Ercegovac and Earl E. {Swartzlander,
Jr.}",
booktitle = "Proceedings: 9th Symposium on Computer Arithmetic:
September 6--8, 1989, Santa Monica, California, {USA}",
title = "Proceedings: 9th Symposium on Computer Arithmetic:
September 6--8, 1989, Santa Monica, California, {USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xv + 247",
year = "1989",
ISBN = "0-8186-8963-3 (case), 0-8186-5963-7 (microfiche)",
ISBN-13 = "978-0-8186-8963-5 (case), 978-0-8186-5963-8
(microfiche)",
LCCN = "QA 76.9 C62 S95 1989",
bibdate = "Thu Sep 01 22:36:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 89CH2757-3.",
acknowledgement = ack-nhfb,
confdate = "6-8 Sept. 1989",
conflocation = "Santa Monica, CA, USA",
confsponsor = "IEEE; IFIP; University of California",
keywords = "ARITH-9",
}
@Proceedings{IEE:1989:EEC,
editor = "{IEE}",
booktitle = "{ECCTD 89}: European Conference on Circuit Theory and
Design, 5--8 September 1989: venue, University of
Sussex, Brighton, United Kingdom",
title = "{ECCTD} 89: European Conference on Circuit Theory and
Design, 5--8 September 1989: venue, University of
Sussex, Brighton, United Kingdom",
publisher = "IEE",
address = "London, UK",
bookpages = "xviii + 680",
year = "1989",
ISBN = "0-85296-383-1",
ISBN-13 = "978-0-85296-383-8",
LCCN = "????",
bibdate = "Sat Nov 29 08:19:35 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Conference publication no. 308.",
acknowledgement = ack-nhfb,
confdate = "5-8 Sept. 1989",
conflocation = "Brighton, UK",
confsponsor = "IEE",
pubcountry = "UK",
}
@Proceedings{IEEE:1989:IISa,
key = "IEEE SCS '89",
booktitle = "1989 {IEEE} International Symposium on Circuits and
Systems: Portland Hilton, Portland, {OR}, May 8--11,
1989",
title = "1989 {IEEE} International Symposium on Circuits and
Systems: Portland Hilton, Portland, {OR}, May 8--11,
1989",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xl + 2246",
year = "1989",
LCCN = "TK 7801 I22 1989",
bibdate = "Thu Sep 15 18:50:54 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Three volumes.",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Proceedings{IEEE:1989:ISV,
editor = "{IEEE}",
booktitle = "{1989 International Symposium on VLSI Technology,
Systems and Applications: proceedings of technical
papers: VLSI: May 17--19, 1989\slash Taipei, Taiwan,
R.O.C.}",
title = "{1989 International Symposium on VLSI Technology,
Systems and Applications: proceedings of technical
papers: VLSI: May 17--19, 1989\slash Taipei, Taiwan,
R.O.C.}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 393",
year = "1989",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 08:32:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 89CH2631-0.",
acknowledgement = ack-nhfb,
confdate = "17-19 May 1989",
conflocation = "Taipei, Taiwan",
confsponsor = "IEEE; Nat. Sci. Council; Ind. Technol. Res. Inst",
}
@Proceedings{IEEE:1989:PII,
key = "IEEE ICCD '89",
booktitle = "Proceedings: 1989 {IEEE} International Conference on
Computer Design: {VLSI} in Computer and Processors,
{ICCD} '89, Hyatt Regency Cambridge, Cambridge,
Massachusetts, October 2--4, 1989",
title = "Proceedings: 1989 {IEEE} International Conference on
Computer Design: {VLSI} in Computer and Processors,
{ICCD} '89, Hyatt Regency Cambridge, Cambridge,
Massachusetts, October 2--4, 1989",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvii + 587",
year = "1989",
ISBN = "0-8186-1971-6 (paper), 0-8186-5971-8 (microfiche),
0-8186-8971-4 (case)",
ISBN-13 = "978-0-8186-1971-7 (paper), 978-0-8186-5971-3
(microfiche), 978-0-8186-8971-0 (case)",
LCCN = "TK 7888.4 I23 1989",
bibdate = "Wed Dec 13 18:26:58 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 89CH2794-6.",
acknowledgement = ack-nj,
confdate = "2-4 Oct. 1989",
conflocation = "Cambridge, MA, USA",
confsponsor = "IEEE",
}
@Proceedings{Turner:1989:NAP,
editor = "Peter R. Turner",
booktitle = "Numerical analysis and parallel processing: lectures
given at the {Lancaster Numerical Analysis Summer
School}, 1987",
title = "Numerical analysis and parallel processing: lectures
given at the {Lancaster Numerical Analysis Summer
School}, 1987",
volume = "1397",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 264",
year = "1989",
DOI = "https://doi.org/10.1007/BFb0085715",
ISBN = "0-387-51645-X, 0-387-13864-1",
ISBN-13 = "978-0-387-51645-5, 978-0-387-13864-0",
LCCN = "QA3 .L28 no. 1397",
bibdate = "Fri Dec 08 08:24:14 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.bibsys.no:2100/BIBSYS",
price = "US\$45.00",
series = "Lecture Notes in Mathematics",
acknowledgement = ack-nhfb,
}
@Proceedings{Wuorinen:1989:DTP,
editor = "J. H. Wuorinen",
booktitle = "Digest of technical papers: 1989 {IEEE} International
Solid-State Circuits Conference",
title = "Digest of technical papers: 1989 {IEEE} International
Solid-State Circuits Conference",
volume = "32",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "394",
month = feb,
year = "1989",
CODEN = "DTPCDE",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0193-6530",
LCCN = "TK7870 .I58 1989",
bibdate = "Wed Sep 29 07:47:11 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 89CH2684-9.",
acknowledgement = ack-nhfb,
confdate = "15-17 Feb. 1989",
conflocation = "New York, NY, USA",
confsponsor = "IEEE; University of Pennsylvania",
keywords = "analog to digital converters; audio equipment; charge
coupled devices; circuits; cmos; conferences; digital
electronics; Electronic circuits --- Congresses.;
floating point arithmetic; gates (circuits); image
processing; integrated circuits; ISSCC 89; memory
(computers); microprocessors; operational amplifiers;
semiconductor devices; Semiconductors --- Congresses.;
signal processing; solid state; Solid state electronics
--- Congresses.; video signals",
xxnote = "NHFB: OCLSC says ``PLACE: Castine, ME''",
xxpages = "400",
}
@Proceedings{ACM:1990:PAS,
editor = "{ACM}",
booktitle = "Proceedings of the {ACM SIGPLAN} '90 Conference on
Programming Language Design and Implementation, {White
Plains, New York}, {June} 20--22, 1990",
title = "Proceedings of the {ACM SIGPLAN} '90 Conference on
Programming Language Design and Implementation, {White
Plains, New York}, {June} 20--22, 1990",
volume = "25(6)",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 351",
month = jun,
year = "1990",
CODEN = "SINODQ",
ISBN = "0-89791-364-7",
ISBN-13 = "978-0-89791-364-5",
ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160
(electronic)",
ISSN-L = "0362-1340",
LCCN = "QA76.7.S53 1990",
bibdate = "Tue Nov 10 07:57:14 1998",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-SIGPLAN,
abstract = "This conference proceedings contains 30 papers. The
main subjects are code generation, code positioning,
register allocation, representing control, program
optimization, floating-point numbers accurately,
optimizing dynamically-typed object-oriented programs,
higher-order attribute grammars and editing
environments, program and data dependence,
demand-driven interpretation of imperative languages,
analysis of pointers and structures, and compact
representations for control dependence.",
acknowledgement = ack-nhfb,
classification = "722; 723",
conference = "Proceedings of the ACM SIGPLAN '90 Conference on
Programming Language Design and Implementation",
conferenceyear = "1990",
journalabr = "SIGPLAN Not",
keywords = "Code Generation; Computer Operating Systems; Computer
Programming --- Object Oriented Programming; Computer
Programming Languages --- Design; Computer Systems,
Digital --- Parallel Processing; Computers, Digital ---
Computational Methods; Data Abstraction; Data
Processing --- Data Structures; Object-Oriented
Languages; Optimizing Compilers; Program Compilers;
Register Allocation",
meetingaddress = "White Plains, NY, USA",
meetingdate = "Jun 20--22 1990",
meetingdate2 = "06/20--22/90",
pagecount = "351",
sponsor = "Assoc for Computing Machinery, Special Interest Group
on Programming Languages",
}
@Proceedings{ACM:1990:PDB,
editor = "{ACM}",
booktitle = "{Proceedings: December 3--7, 1990, Baltimore
Convention Center, Baltimore, MD}",
title = "{Proceedings: December 3--7, 1990, Baltimore
Convention Center, Baltimore, MD}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xxvi + 630",
year = "1990",
ISBN = "0-89791-409-0",
ISBN-13 = "978-0-89791-409-3",
LCCN = "QA76.73.A35",
bibdate = "Thu Aug 7 18:17:59 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.gbv.de:20011/gvk",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1990:PAN,
editor = "{Anonymous}",
booktitle = "Proceedings of the Annual National Conference of Ada
Technology (8th). Held in Atlanta, Georgia on March
5--8, 1990",
title = "Proceedings of the Annual National Conference of Ada
Technology (8th). Held in Atlanta, Georgia on March
5--8, 1990",
publisher = "U.S. Army Commun.-Electron. Command",
address = "Fort Monmouth, NJ, USA",
pages = "xiv + 669",
year = "1990",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 09:01:32 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "5-8 March 1990",
conflocation = "Atlanta, GA, USA",
confsponsor = "Ancost",
}
@Proceedings{Chen:1990:CRT,
editor = "Ray R. Chen",
booktitle = "Conference record: Twenty-fourth Asilomar Conference
on Signals, Systems and Computers: Papers Presented
November 5--7, 1990, Pacific Grove, California",
title = "Conference record: Twenty-fourth Asilomar Conference
on Signals, Systems and Computers: Papers Presented
November 5--7, 1990, Pacific Grove, California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxi + 1089",
year = "1990",
ISBN = "0-8186-2182-6",
ISBN-13 = "978-0-8186-2182-6",
LCCN = "TK 5102.5 A78 1990",
bibdate = "Wed Sep 07 21:55:08 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nj,
confdate = "5-7 Nov. 1990",
conflocation = "Pacific Grove, CA, USA",
confsponsor = "IEEE; Naval Post Graduate Sch",
}
@Proceedings{CUG:1990:PSC,
editor = "{CUG}",
key = "Cray UG '90",
booktitle = "Proceedings, 25th Semiannual Cray User Group Meeting,
Toronto, Ontario, June 1990",
title = "Proceedings, 25th Semiannual Cray User Group Meeting,
Toronto, Ontario, June 1990",
publisher = "Cray User Group",
address = "186 Mandela Road, Shepherdstown, WV 25443, USA",
pages = "????",
year = "1990",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Sep 08 08:56:01 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxnote = "Check: is this June or April 10 meeting??",
}
@Book{Feijen:1990:BOB,
editor = "W. H. J. Feijen and A. J. M. van Gasteren and David
Gries and J. Misra",
booktitle = "Beauty is our Business: a Birthday Salute to {Edsger
W. Dijkstra}",
title = "Beauty is our Business: a Birthday Salute to {Edsger
W. Dijkstra}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xix + 453",
year = "1990",
DOI = "https://doi.org/10.1007/978-1-4612-4476-9",
ISBN = "0-387-97299-4, 3-540-97299-4, 1-4612-8792-8 (print),
1-4612-4476-5 (online)",
ISBN-13 = "978-0-387-97299-2, 978-3-540-97299-0,
978-1-4612-8792-6 (print), 978-1-4612-4476-9 (online)",
ISSN = "0172-603X",
ISSN-L = "0172-603X",
LCCN = "QA76 .B326 1990",
bibdate = "Thu Mar 24 09:27:40 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hoare-c-a-r.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
note = "Contains important treatment of accurate
binary-to-decimal conversion
\cite{Gries:1990:BDO,Knuth:1990:SPW}.",
URL = "http://www.zentralblatt-math.org/zmath/en/search/?an=0718.68004",
acknowledgement = ack-nhfb,
tableofcontents = "Anonymous / Front Matter / i--xix \\
Krzysztof R. Apt, Frank S. de Boer, Ernst-R{\"u}diger
Olderog / Proving Termination of Parallel Programs /
1--6 / doi:10.1007/978-1-4612-4476-9_1 \\
Roland C. Backhouse / On a Relation on Functions /
7--18 / doi:10.1007/978-1-4612-4476-9_2 \\
F. L. Bauer / Efficient Solution of a Non--Monotonic
Inverse Problem / 19--26 /
doi:10.1007/978-1-4612-4476-9_3 \\
A. Bijlsma / Semantics of Quasi--Boolean Expressions /
27--35 / doi:10.1007/978-1-4612-4476-9_4 \\
Richard S. Bird / Small Specification Exercises /
36--43 / doi:10.1007/978-1-4612-4476-9_5 \\
Maarten Boasson / Architecture of Real--Time Systems /
44--53 / doi:10.1007/978-1-4612-4476-9_6 \\
Robert S. Boyer, Milton W. Green, J Strother Moore /
The Use of a Formal Simulator to Verify a Simple Real
Time Control Program / 54--66 /
doi:10.1007/978-1-4612-4476-9_7 \\
Donald W. Braben / Exploring the Future: Trends and
Discontinuities / 67--75 /
doi:10.1007/978-1-4612-4476-9_8 \\
Coen Bron / On a Renewed Visit to the Banker and a
Remarkable Analogy / 76--82 /
doi:10.1007/978-1-4612-4476-9_9 \\
Manfred Broy / On Bounded Buffers: Modularity,
Robustness, and Reliability in Reactive Systems /
83--93 / doi:10.1007/978-1-4612-4476-9_10 \\
K. Mani Chandy, Stephen Taylor / Examples in Program
Composition / 94--101 /
doi:10.1007/978-1-4612-4476-9_11 \\
Albert J. Dijkstra / On the Mechanism of the
Hydrogenation of Edible Oils / 102--111 /
doi:10.1007/978-1-4612-4476-9_12 \\
W. H. J. Feijen, A. J. M. van Gasteren, D. Gries, J.
Misra / The Problem of the Majority Network / 112--118
/ doi:10.1007/978-1-4612-4476-9_13 \\
W. H. J. Feijen / A Little Exercise in Deriving
Multiprograms / 119--126 /
doi:10.1007/978-1-4612-4476-9_14 \\
A. J. M. van Gasteren / Experimenting with a Refinement
Calculus / 127--134 / doi:10.1007/978-1-4612-4476-9_15
\\
Mohamed G. Gouda / Serializable Programs,
Parallelizable Assertions: A Basis for Interleaving /
135--140 / doi:10.1007/978-1-4612-4476-9_16 \\
David Gries / Binary to Decimal, One More Time /
141--148 / doi:10.1007/978-1-4612-4476-9_17 \\
A. N. Habermann / Rotate and Double / 149--162 /
doi:10.1007/978-1-4612-4476-9_18 \\
Eric C. R. Hehner / Beautifying G{\"o}del / 163--172 /
doi:10.1007/978-1-4612-4476-9_19 \\
G. Helmberg / A Striptease of Entropy / 173--175 /
doi:10.1007/978-1-4612-4476-9_20 \\
Ted Herman / On a Theorem of Jacobson / 176--181 /
doi:10.1007/978-1-4612-4476-9_21 \\
Wim H. Hesselink / Modalities of Nondeterminacy /
182--192 / doi:10.1007/978-1-4612-4476-9_22 \\
C. A. R. Hoare / A Theory for the Derivation of C-mos
Circuit Designs / 193--205 /
doi:10.1007/978-1-4612-4476-9_23 \\
Rob Hoogerwoord / On Mathematical Induction and the
Invariance Theorem / 206--211 /
doi:10.1007/978-1-4612-4476-9_24 \\
J. J. Horning / Formalizing Some Classic
Synchronization Primitives / 212--219 /
doi:10.1007/978-1-4612-4476-9_25 \\
Cliff B. Jones / Consequences / 220--225 /
doi:10.1007/978-1-4612-4476-9_26 \\
Anne Kaldewaij / Shortest and Longest Segments /
226--232 / doi:10.1007/978-1-4612-4476-9_27 \\
Donald E. Knuth / A Simple Program Whose Proof Isn't /
233--242 / doi:10.1007/978-1-4612-4476-9_28 \\
Vadim E. Kotov / Binding Structure and Behaviour in
``Whole Net'' Concurrency Semantics / 243--250 /
doi:10.1007/978-1-4612-4476-9_29 \\
F. E. J. Kruseman Aretz / Maximal Strong Components: An
Exercise in Program Presentation / 251--261 /
doi:10.1007/978-1-4612-4476-9_30 \\
Christian Lengauer, Duncan G. Hudson / A Systolic
Program for Gauss--Jordan Elimination / 262--273 /
doi:10.1007/978-1-4612-4476-9_31 \\
J. H. van Lint / Coding for Channels with Localized
Errors / 274--279 / doi:10.1007/978-1-4612-4476-9_32
\\
Johan J. Lukkien, Jan L. A. van de Snepscheut /
Topology-Independent Algorithms Based on Spanning Trees
/ 280--288 / doi:10.1007/978-1-4612-4476-9_33 \\
Zohar Manna, Amir Pnueli / An Exercise in the
Verification of Multi--Process Programs / 289--301 /
doi:10.1007/978-1-4612-4476-9_34 \\
Alain J. Martin / The Limitations to
Delay--Insensitivity in Asynchronous Circuits /
302--311 / doi:10.1007/978-1-4612-4476-9_35 \\
Jayadev Misra / A Simple Proof of a Simple Consensus
Algorithm / 312--318 / doi:10.1007/978-1-4612-4476-9_36
\\
Carroll Morgan / Of wp and {CSP} / 319--326 /
doi:10.1007/978-1-4612-4476-9_37 \\
Joseph M. Morris / Programming by Expression
Refinement: the {KMP} Algorithm / 327--338 /
doi:10.1007/978-1-4612-4476-9_38 \\
Greg Nelson / Methodical Competitive Snoopy--Caching /
339--345 / doi:10.1007/978-1-4612-4476-9_39 \\
Peter G. Neumann / Beauty and the Beast of Software
Complexity Elegance versus Elephants / 346--351 /
doi:10.1007/978-1-4612-4476-9_40 \\
W. Peremans / A Note on Feasibility / 352--355 /
doi:10.1007/978-1-4612-4476-9_41 \\
Karel A. Post / A Curious Property of Points and
Circles in the Plane / 356--357 /
doi:10.1007/978-1-4612-4476-9_42 \\
Paul Pritchard / A Problem Involving Subsequences /
358--364 / doi:10.1007/978-1-4612-4476-9_43 \\
Martin Rem / A Personal Perspective of the
Alpern--Schneider Characterization of Safety and
Liveness / 365--372 / doi:10.1007/978-1-4612-4476-9_44
\\
Fred B. Schneider / Simpler Proofs for Concurrent
Reading and Writing / 373--379 /
doi:10.1007/978-1-4612-4476-9_45 \\
Carel S. Scholten / Goodbye Junctivity? / 380--385 /
doi:10.1007/978-1-4612-4476-9_46 \\
Henk C. A. van Tilborg / An Assignment Problem for the
Vertices of a Cycle / 386--389 /
doi:10.1007/978-1-4612-4476-9_47 \\
D. A. Turner / Duality and De Morgan Principles for
Lists / 390--398 / doi:10.1007/978-1-4612-4476-9_48 \\
W. M. Turski / The Quest for Timeless Specifications
Leads to Non--Stepping Automata / 399--409 /
doi:10.1007/978-1-4612-4476-9_49 \\
Jan Tijmen Udding / The Maximum Length of a Palindrome
in a Sequence / 410--416 /
doi:10.1007/978-1-4612-4476-9_50 \\
Lincoln A. Wallen / On Form, Formalism and Equivalence
/ 417--426 / doi:10.1007/978-1-4612-4476-9_51 \\
N. Wirth / Drawing Lines, Circles, and Ellipses in a
Raster / 427--434 / doi:10.1007/978-1-4612-4476-9_52
\\
Jaap van der Woude / Calculations with Relations, an
Example / 435--441 / doi:10.1007/978-1-4612-4476-9_53
\\
Heinz Zemanek / Two Proofs for Pythagoras / 442--447 /
doi:10.1007/978-1-4612-4476-9_54 \\
Anonymous / Back Matter / 448--453",
}
@Book{Hennessy:1990:CAQ,
author = "John L. Hennessy and David A. Patterson",
booktitle = "Computer Architecture: a Quantitative Approach",
title = "Computer Architecture: a Quantitative Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xxviii + 594",
year = "1990",
ISBN = "1-55860-069-8, 1-55880-169-8",
ISBN-13 = "978-1-55860-069-0, 978-1-55880-169-1",
LCCN = "QA76.9.A73 P377 1990",
bibdate = "Mon Jan 31 08:47:46 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Fundamentals of Computer Design \\
Introduction \\
The Changing Face of Computing and the Task of the
Computer Designer \\
Technology Trends \\
Cost, Price, and their Trends \\
Measuring and Reporting Performance \\
Quantitative Principles of Computer Design \\
Putting It All Together: Performance and
Price-Performance \\
Another View: Power Consumption and Efficiency as the
Metric \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Instruction Set Principles and Examples \\
Introduction \\
Classifying Instruction Set Architectures \\
Memory Addressing \\
Addressing Modes for Signal Processing \\
Type and Size of Operands \\
Operands for Media and Signal Processing \\
Operations in the Instruction Set \\
Operations for Media and Signal Processing \\
Instructions for Control Flow \\
Encoding an Instruction Set \\
Crosscutting Issues: The Role of Compilers \\
Putting It All Together: The MIPS Architecture \\
Another View: The Trimedia TM32 CPU \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Instruction-Level Parallelism and its Dynamic
Exploitation \\
Instruction-Level Parallelism: Concepts and Challenges
\\
Overcoming Data Hazards with Dynamic Scheduling \\
Dynamic Scheduling: Examples and the Algorithm \\
Reducing Branch Costs with Dynamic Hardware Prediction
\\
High Performance Instruction Delivery \\
Taking Advantage of More ILP with Multiple Issue \\
Hardware Based Speculation \\
Studies of the Limitations of ILP \\
Limitations on ILP for Realizable Processors \\
Putting It All Together: The P6 Microarchitecture \\
Another View: Thread Level Parallelism \\
Crosscutting Issues: Using an ILP Datapath to Exploit
TLP \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Exploiting Instruction Level Parallelism with Software
Approaches \\
Basic Compiler Techniques for Exposing ILP \\
Static Branch Prediction \\
Static Multiple Issue: the VLIW Approach \\
Advanced Compiler Support for Exposing and Exploiting
ILP \\
Hardware Support for Exposing More Parallelism at
Compile-Time \\
Crosscutting Issues \\
Putting It All Together: The Intel IA-64 Architecture
and Itanium Processor \\
Another View: ILP in the Embedded and Mobile Markets
\\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Memory-Hierarchy Design \\
Introduction \\
Review of the ABCs of Caches \\
Cache Performance \\
Reducing Cache Miss Penalty \\
Reducing Miss Rate \\
Reducing Cache Miss Penalty or Miss Rate via
Parallelism \\
Reducing Hit Time \\
Main Memory and Organizations for Improving Performance
\\
Memory Technology \\
Virtual Memory \\
Protection and Examples of Virtual Memory \\
Crosscutting Issues in the Design of Memory Hierarchies
\\
Putting It All Together: Alpha 21264 Memory Hierarchy
\\
Another View: The Emotion Engine of the Sony
Playstation 2 \\
Another View: The Sun Fire 6800 Server \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Multiprocessors and Thread-Level Parallelism \\
Introduction \\
Characteristics of Application Domains \\
Symmetric Shared-Memory Architectures \\
Performance of Symmetric Shared-Memory Multiprocessors
\\
Distributed Shared-Memory Architectures \\
Performance of Distributed Shared-Memory
Multiprocessors \\
Synchronization \\
Models of Memory Consistency: An Introduction \\
Multithreading: Exploiting Thread-Level Parallelism
within a Processor \\
Crosscutting Issues \\
Putting It All Together: Sun's Wildfire Prototype \\
Another View: Multithreading in a Commercial Server \\
Another View: Embedded Multiprocessors \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises",
}
@Proceedings{IEE:1990:ICV,
editor = "{IEE}",
booktitle = "{IEE} Colloquium on {`VLSI} Signal Processing
Architectures' (Digest No.95)",
title = "{IEE} Colloquium on `{VLSI} Signal Processing
Architectures' (Digest No.95)",
publisher = "IEE",
address = "London, UK",
pages = "66",
year = "1990",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 09:05:00 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "31 May 1990",
conflocation = "London, UK",
pubcountry = "UK",
}
@Proceedings{IEEE:1990:MMM,
editor = "{IEEE}",
booktitle = "{MICRO 23}: microprogramming and microarchitecture:
23rd Annual workshop and symposium: Selected papers",
title = "{MICRO} 23: microprogramming and microarchitecture:
23rd Annual workshop and symposium: Selected papers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 299",
year = "1990",
ISBN = "0-8186-2124-9",
ISBN-13 = "978-0-8186-2124-6",
LCCN = "????",
bibdate = "Sat Nov 29 09:17:36 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 90TH0341-8.",
acknowledgement = ack-nhfb,
confdate = "27-29 Nov. 1990",
conflocation = "Orlando, FL, USA",
confsponsor = "IEEE; ACM",
}
@Proceedings{IEEE:1990:PII,
key = "IEEE ICCD '90",
booktitle = "Proceedings: 1990 {IEEE} International Conference on
Computer Design: {VLSI} in Computers and Processors:
{ICCD} '90, Hyatt Regency Cambridge, Cambridge,
Massachusetts, September 17--19, 1990",
title = "Proceedings: 1990 {IEEE} International Conference on
Computer Design: {VLSI} in Computers and Processors:
{ICCD} '90, Hyatt Regency Cambridge, Cambridge,
Massachusetts, September 17--19, 1990",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xx + 477",
year = "1990",
ISBN = "0-8186-9079-8 (case), 0-8186-6079-1 (microfiche),
0-8186-2079-X (paper)",
ISBN-13 = "978-0-8186-9079-2 (case), 978-0-8186-6079-5
(microfiche), 978-0-8186-2079-9 (paper)",
LCCN = "TK 7888.4 I23 1990",
bibdate = "Wed Sep 07 23:34:16 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Book{Patterson:1990:CAQ,
author = "David A. Patterson and John L. Hennessy",
booktitle = "Computer Architecture: a Quantitative Approach",
title = "Computer Architecture: a Quantitative Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
pages = "xxviii + 594",
year = "1990",
ISBN = "1-55860-069-8, 1-55880-169-8",
ISBN-13 = "978-1-55860-069-0, 978-1-55880-169-1",
LCCN = "QA76.9.A73 P377 1990",
bibdate = "Mon Jan 31 08:47:46 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/microchip.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Fundamentals of Computer Design \\
Introduction \\
The Changing Face of Computing and the Task of the
Computer Designer \\
Technology Trends \\
Cost, Price, and their Trends \\
Measuring and Reporting Performance \\
Quantitative Principles of Computer Design \\
Putting It All Together: Performance and
Price-Performance \\
Another View: Power Consumption and Efficiency as the
Metric \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Instruction Set Principles and Examples \\
Introduction \\
Classifying Instruction Set Architectures \\
Memory Addressing \\
Addressing Modes for Signal Processing \\
Type and Size of Operands \\
Operands for Media and Signal Processing \\
Operations in the Instruction Set \\
Operations for Media and Signal Processing \\
Instructions for Control Flow \\
Encoding an Instruction Set \\
Crosscutting Issues: The Role of Compilers \\
Putting It All Together: The MIPS Architecture \\
Another View: The Trimedia TM32 CPU \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Instruction-Level Parallelism and its Dynamic
Exploitation \\
Instruction-Level Parallelism: Concepts and Challenges
\\
Overcoming Data Hazards with Dynamic Scheduling \\
Dynamic Scheduling: Examples and the Algorithm \\
Reducing Branch Costs with Dynamic Hardware Prediction
\\
High Performance Instruction Delivery \\
Taking Advantage of More ILP with Multiple Issue \\
Hardware Based Speculation \\
Studies of the Limitations of ILP \\
Limitations on ILP for Realizable Processors \\
Putting It All Together: The P6 Microarchitecture \\
Another View: Thread Level Parallelism \\
Crosscutting Issues: Using an ILP Datapath to Exploit
TLP \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Exploiting Instruction Level Parallelism with Software
Approaches \\
Basic Compiler Techniques for Exposing ILP \\
Static Branch Prediction \\
Static Multiple Issue: the VLIW Approach \\
Advanced Compiler Support for Exposing and Exploiting
ILP \\
Hardware Support for Exposing More Parallelism at
Compile-Time \\
Crosscutting Issues \\
Putting It All Together: The Intel IA-64 Architecture
and Itanium Processor \\
Another View: ILP in the Embedded and Mobile Markets
\\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Memory-Hierarchy Design \\
Introduction \\
Review of the ABCs of Caches \\
Cache Performance \\
Reducing Cache Miss Penalty \\
Reducing Miss Rate \\
Reducing Cache Miss Penalty or Miss Rate via
Parallelism \\
Reducing Hit Time \\
Main Memory and Organizations for Improving Performance
\\
Memory Technology \\
Virtual Memory \\
Protection and Examples of Virtual Memory \\
Crosscutting Issues in the Design of Memory Hierarchies
\\
Putting It All Together: Alpha 21264 Memory Hierarchy
\\
Another View: The Emotion Engine of the Sony
Playstation 2 \\
Another View: The Sun Fire 6800 Server \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises \\
Multiprocessors and Thread-Level Parallelism \\
Introduction \\
Characteristics of Application Domains \\
Symmetric Shared-Memory Architectures \\
Performance of Symmetric Shared-Memory Multiprocessors
\\
Distributed Shared-Memory Architectures \\
Performance of Distributed Shared-Memory
Multiprocessors \\
Synchronization \\
Models of Memory Consistency: An Introduction \\
Multithreading: Exploiting Thread-Level Parallelism
within a Processor \\
Crosscutting Issues \\
Putting It All Together: Sun's Wildfire Prototype \\
Another View: Multithreading in a Commercial Server \\
Another View: Embedded Multiprocessors \\
Fallacies and Pitfalls \\
Concluding Remarks \\
Historical Perspective and References \\
Exercises",
}
@Proceedings{SHARE:1990:PSE,
editor = "{SHARE}",
booktitle = "Proceedings {SHARE} Europe Spring Meeting",
title = "Proceedings {SHARE} Europe Spring Meeting",
publisher = "SHARE Europe (SEAS)",
address = "Geneva, Switzerland",
pages = "969",
year = "1990",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0255-6464",
LCCN = "????",
bibdate = "Sat Nov 29 09:07:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "2 vol.",
acknowledgement = ack-nhfb,
confdate = "2-6 April 1990",
conflocation = "Berlin, Germany",
pubcountry = "Switzerland",
}
@Book{Swartzlander:1990:CAa,
author = "Earl E. {Swartzlander, Jr.}",
booktitle = "Computer Arithmetic",
title = "Computer Arithmetic",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 378",
year = "1990",
ISBN = "0-8186-8931-5 (hardcover), 0-8186-5931-9
(microfiche)",
ISBN-13 = "978-0-8186-8931-4 (hardcover), 978-0-8186-5931-7
(microfiche)",
LCCN = "QA76.6 .C633 1990",
bibdate = "Wed Dec 15 10:43:03 1993",
bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "IEEE Computer Society Press tutorial",
acknowledgement = ack-nj,
keywords = "Computer arithmetic; Electronic digital computers ---
Programming; Floating-point arithmetic.",
remark = "Vol. 1 is a reprint. Originally published:
Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980.
Originally published in series: Benchmark papers in
electrical engineering and computer science; 21. Vol 2
is a sequel to the earlier collection. Vol. 1: 2nd
ed.",
tableofcontents = "Series Editor's Foreword / v \\
Preface / vii \\
Contents by Author / xiii \\
Introduction / 1 \\
Part I: Overview / 6 \\
Editor's / Comments on Papers 1 and 2 / 7 \\
1: Shaw, R. F.: Arithmetic Operations in a Binary
Computer, Rev. Sci. Instrum. 21:687--693 (1950) / 7 \\
2: MacSorley, O. L: High-Speed Arithmetic in Binary
Computers, IRE Proc. 49:67--91 (1961) / 14 \\
Part II: Addition and Subtraction \\
Editor's Comments on Papers 3 Through 10 / 40 \\
3: Gilchrist, B., J. H. Pomerene, and S. Y. Wong: Fast
Carry Logic for Digital Computers, IRE Trans. Electron.
Comput. EC-4:133--136 (1955) / 43 \\
4: Weinberger, A., and J. L. Smith: A Logic for
High-Speed Addition, Nat. Bur. Stand. Circ. 591, pp.
3--12 (1958) / 47 \\
5: Sklansky J.: Conditional-Sum Addition Logic, IRE
Trans. Electron. Comput. EC-9:226--231 (1960) / 57 \\
6: Sklansky J.: An Evaluation of Several Two-Summand
Binary Adders / IRE Trans. Electron. Comput.
EC-9:213--226 (1960) / 63 \\
7: Svoboda, A.: Adder with Distributed Control, IEEE
Trans. Comput. C-19: 749--751 (1970) / 77 \\
8: Ho, I. T., and T. C. Chen: Multiple Addition by
Residue Threshold Functions and Their Representation by
Array Logic, IEEE Trans. Comput. C-22:762--767 (1973) /
80 \\
9: Foster, C C,, and F. D. Stockton: Counting
Responders in an Associative Memory, IEEE Trans.
Comput. C-20:1580--1583 (1971) / 86 \\
10: Swartzlander, E. E., Jr.: Parallel Counters, IEEE
Trans. Comput. C-22:1021--1024 (1973) / 90 \\
Editor's Comments on Papers 11 Through 20 / 96 \\
11: Booth, A, D.: A Signed Binary Multiplication
Technique, Q. J. Mech. Appl. Math. 4:236--240 (1951) /
100 \\
12: Ghest, C.: Multiplying Made Easy for Digital
Assemblies, Electronics 44:56--61 (Nov. 22, 1971) / 105
\\
13: Chen, T. C.: A Binary Multiplication Scheme Based
on Squaring, IEEE Trans. Comput. C-20:678--680 (1971) /
111 \\
14: Wallace, C. S.: A Suggestion for a Fast Multiplier,
IEEE Trans. Electron. Comput. EC-13:14--17 (1964) / 114
\\
15: Dadda, L.: Some Schemes for Parallel Multipliers,
Alta Freq. 34:349--356 (1965) / 118 \\
16: Dadda, L.: On Parallel Digital Multipliers, Alta
Freq. 45:574--580 (1976) / 126 \\
17: Stenzel, W. J., W. J. Kubitz, and G. H. Garcia: A
Compact High-Speed Parallel Multiplication Scheme, IEEE
Trans. Comput. C-26:948--957 (1977) / 133 \\
18A: Baugh, C. R., and B. A, Wooley: A Two's Complement
Parallel Array Multiplication Algorithm, IEEE Trans.
Comput. C-22:1045--1047 (1973) / 143 \\
18B: Blankenship, P. E.: Comments on ``A Two's
Complement Parallel Array Multiplication Algorithm'',
IEEE Trans. Comput. C-23:1327 (1974) / 146 \\
19: Swartzlander, E. E., Jr.: The Quasi-Serial
Multiplier, IEEE Trans. Comput. C-22:317--321 (1973) /
147 \\
20: McDaneld, T. G., and R. K. Guha: The Two's
Complement Quasi-Serial Multiplier, IEEE Trans. Comput.
C-24:1233--1235 (1975) / 152 \\
Part IV: Division \\
Editor's Comments on Papers 21 Through 26 / 156 \\
21: Robertson, J. E.: A New Class of Digital Division
Methods, IRE Trans. Electron. Comput. EC-7:218--222
(1958) / 159 \\
22: Wilson, J. B., and R. S. Ledley: An Algorithm for
Rapid Binary Division, IRE Trans. Electron. Comput.
EC-10:662--670 (1961) / 164 \\
23: Atkins, D. E.: Higher-Radix Division Using
Estimates of the Divisor and Partial Remainders, IEEE
Trans. Comput. C-17:925--934 (1968) / 173 \\
24: Svoboda, A.: An Algorithm for Division, Inf.
Process. Mach. 9:25--32 (1963) / 183 \\
25: Ferrari, D.: A Division Method Using a Parallel
Multiplier, IEEE Trans. Electron. Comput.
EC-16:224--226 (1967) / 191 \\
26: Flynn, M. J.: On Division by Functional Iteration,
IEEE Trans. Comput. C-19:702--706 (1970) / 194 \\
Part V: Logarithms \\
Editor's Comments on Papers 27 Through 31 / 200 \\
27: Combet, M., H. van Zonneveld, and L. Verbeek:
Computation of the Base Two Logarithm of Binary
Numbers, IEEE Trans. Electron. Comput. EC-14:863--867
(1965) / 202 \\
28: Marino, D.: New Algorithms for the Approximate
Evaluation in Hardware of Binary Logarithms and
Elementary Functions IEEE Trans. Comput. C-21:
1416--1421 (1972) / 207 \\
29: Majithia J. C., and D. Levan: A Note on Base-2
Logarithm Computations, IEEE Proc. 61:1519--1520 (1973)
/ 213 \\
30: Kingsbury N. G., and P. J. W. Rayner: Digital
Filtering Using Logarithmic Arithmetic, Electron. Lett.
7:56--58 (1971) / 215 \\
31: Swartzlander E. E., Jr., and A. G. Alexopoulos: The
Sign/Logarithm Number System, IEEE Trans. Comput.
C-24:1238--1242 (1975) / 218 \\
Part VI: Elementary Functions \\
Editor's Comments on Papers 32 Through 37 / 224 \\
32: Volder, J. E.: The CORDIC Trigonometric Computing
Technique, IRE Trans. Electron. Comput. EC-8:330--334
(1959) / 226 \\
33: Specker W. H.: A Class of Algorithms for Ln $x$,
Exp $x$, Sin $x$, Cos $x$, Tan$^{-1}$ $x$, and
Cot$^{-1}$ $x$, IEEE Trans. Electron. Comput.
EC-14:85--86 (1965) / 231 \\
34: Linhardt, R. J., and H. S. Muller: Digit-by-Digit
Transcendental-Function Computation RCA Rev. 30:20~247
(1969) / 233 \\
35: Walther J. S.: A Unified Algorithm for Elementary
Functions, Spring Joint Computer Conf., 1971, Proc.,
pp. 379--385 / 272 \\
36: Ramamoorthy, C. V., J. R. Goodman, and K. H. Kim:
Some Properties of Iterative Square-Rooting Methods
Using High-Speed Multiplication, IEEE Trans. Comput.
C-21: 837--847 (1972) / 279 \\
37: Ercegovac M. D.: Radix-16 Evaluation of Certain
Elementary Functions, IEEE Trans. Comput. C-22:561--566
(1973) / 290 \\
Part VII: Floating-Point Arithmetic \\
Editor's Comments on Papers 38 Through 42 / 298 \\
38: Hamming, R. W.: On the Distribution of Numbers,
Bell Syst. Tech. J. 49:1609--1625 (1970) / 300 \\
39: Sweeney D. W.: An Analysis of Floating-Point
Addition, IBM Syst. J. 4:31--42 (1965) / 317 \\
40: Anderson, S. F., J. G. Earler, R. E. Goldschmidt,
and D. M. Powers: The IBM System/360 Model 91:
Floating-Point Execution Unit, IBM J. Res. Dev.
11:34--53 (1967) / 329 \\
41: Gosling, J. B.: Design of Large High-Speed Floating
Point Arithmetic Units, IEE Proc. 118:493--498 (1971) /
349 \\
42: Kuck, D. J., D. S. Parker, Jr., and A. H. Sameh:
Analysis of Rounding Methods in Floating-Point
Arithmetic, IEEE Trans. Comput. C-26:643--650 (1977) /
355 \\
Bibliography / 363 \\
Author Citation Index / 373 \\
Subject Index / 377 \\
About the Editor / 379",
}
@Book{Swartzlander:1990:CAb,
author = "Earl E. {Swartzlander, Jr.}",
booktitle = "Computer Arithmetic",
title = "Computer Arithmetic",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "ix + 396",
year = "1990",
ISBN = "0-8186-8945-5",
ISBN-13 = "978-0-8186-8945-1",
LCCN = "QA76.9 .C62C66 1990",
bibdate = "Wed Dec 15 10:43:03 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
note = "This is part of a two-volume collection of influential
papers on the design of computer arithmetic. See also
\cite{Swartzlander:1990:CAa}.",
acknowledgement = ack-nhfb,
tableofcontents = "Preface / v \\
Chapter 1: Overview / E. E. Swartzlander, Jr. / 1 \\
Chapter 2: Error Tolerant Arithmetic / 15 \\
Error Detecting and Error Correcting Codes / R. W.
Hamming (Bell System Technical Journal, 1950, Pages
147--160) / 16 \\
Generalized Parity Checking / H. L. Garner (IRE
Transactions on Electronic Computers, 1958, Pages
207--213) / 30 \\
Error Checking Logic for Arithmetic Type Operations of
a Processor / T. R. N. Rao (IEEE Transactions on
Computers, 1968, Pages 845--849) / 37 \\
Arithmetic Algorithms for Error-Coded Operands / A.
Avizienis (IEEE Transactions on Computers, 1973, Pages
567--572) / 42 \\
Error Detection and Correction for Addition and
Subtraction, through Use of Higher Radix Extensions of
Hamming Codes / J. E. Robertson (Proceedings 8th
Symposium on Computer Arithmetic, 1987, Pages 226--229)
/ 48 \\
Chapter 3: On-Line Arithmetic / 53 \\
Signed-Digit Number Representations for Fast Parallel
Arithmetic / A. Avizienis (IRE Transactions on
Electronic Computers, 1961, Pages 389---400) / 54 \\
On-Line Arithmetic: A Design Methodology and
Applications in Digital Signal Processing / M. D.
Ercegovac and T. Lang (VLSI Signal Processing, III,
1988, Pages 252--263) / 66 \\
On-Line Algorithms for Division and Multiplication / K.
S. Trivedi and M. D. Ercegovac (IEEE Transactions on
Computers, 1977, Pages 681---687) / 78 \\
Error Analysis of Certain Floating-point On-Line
Algorithms / O. Watanuki and M. D. Ercegovac (IEEE
Transactions on Computers, 1983, Pages 352--358) / 85
\\
Improved Normalization Results for Digit On-Line
Arithmetic / R. J. Zaccone and J. L. Barlow
(Proceedings 7th Symposium on Computer Arithmetic,
1985, Pages 20--27) / 92 \\
Fully Digit On-Line Networks / M. J. Irwin and R. M.
Owens (IEEE Transactions on Computers, 1983, Pages
402---406) / 100 \\
On-Line Scheme for Computing Rotation Factors / M. D.
Ercegovac and T. Lang (Journal of Parallel and
Distributed Computing, 1988, Pages 209--227) / 104 \\
On-the-Fly Conversion of Redundant into Conventional
Representations / M. D. Ercegovac and T. Lang (IEEE
Transactions on Computers, 1987, Pages 895--897) / 123
\\
Chapter 4: VLSI Adder Implementations / 127 \\
Time-Component Complexity of Two Approaches to
Multioperand Binary Addition / D. E. Atkins and S. Ong
(IEEE Transactions on Computers, 1979, Pages 918--926)
/ 128 \\
Some Optimal Schemes for ALU Implementation in VLSI
Technology / V. G. Oklobdzija and E. R. Barnes
(Proceedings 7th Symposium on Computer Arithmetic,
1985, Pages 2--8) / 137 \\
A Regular Layout for Parallel Adders / R. P. Brent and
H. T. Kung (IEEE Transactions on Computers, 1982, Pages
260--264) / 144 \\
An Area-Time Efficient NMOS Adder / M. A. Bayoumi, G.
A. Jullien, and W. C. Miller (Integration, the VLSI
Journal, 1983, Pages 317--334) / 148 \\
Regular, Area-Time Efficient Carry-Lookahead Adders /
T.-F. Ngai, M. J. Irwin, and S. Rawat (Journal of
Parallel and Distributed Computing, 1986, Pages
92--105) / 166 \\
Efficient Use of Time and Hardware Redundancy for
Concurrent Error Detection in a 32-Bit VLSI Adder / B.
W. Johnson, J. H. Aylor, and H. H. Hana (IEEE Journal
of Solid-State Circuits, 1988, Pages 208--215) / 180
\\
Chapter 5: VLSI Multiplier Implementations / 189 \\
A Monolithic $16 \times 16$ Digital Multiplier / G. W.
McIver, R. W. Miller, and T. G. O'Shaughnessy (IEEE
International Solid-State Circuits Conference Digest of
Technical Papers, 1974, Pages 231--233) / 190 \\
Optimization of One-Bit Full Adders Embedded in Regular
Structures / K. Iwano and K. Steiglitz (IEEE
Transactions on Acoustics, Speech, and Signal
Processing, 1986, Pages 1289--1300) / 193 \\
A VLSI Layout for a Pipelined Dadda Multiplier / P. R.
Cappello and K. Steiglitz (ACM Transactions on Computer
Systems, 1983, Pages 157--174) / 205 \\
A Very Fast Multiplication Algorithm for VLSI
Implementation / J. Vuillemin (Integration, the VLSI
Journal, 1983, Pages 39--52) / 223 \\
A High-Speed Multiplier Using a Redundant Binary Adder
Tree / Y. Harata, Y. Nakamura, H. Nagase, M. Takigawa,
and N. Takagi (IEEE Journal of Solid-State Circuits,
1987, Pages 28--34) / 237 \\
A Sub-10-ns $16 \times 16$ Multiplier Using 0.6-$\mu$m
CMOS Technology / Y. Oowaaki, K. Numata, K. Tsuchiya,
K. Tsuda, H. Takato, N. Takenouchi, A. Nitayama, T.
Kobayashi, M. Chiba, S. Watanabe, K. Ohuchi, and A.
Rojo (IEEE Journal of Solid-State Circuits, 1987, Pages
762--767) / 244 \\
Chapter 6: Floating Point VLSI Chips / 251 \\
A High Performance Floating Point Coprocessor / G.
Wolrich, E. McLellan, L. Harada, J. Montanaro, and R.
A. J. Yodlowski (IEEE Journal of Solid-State Circuits,
1984, Pages 690--696) / 252 \\
64-Bit Monolithic Floating Point Processors / F. A.
Ware, W. H. McAllister, J. R. Carlson, D. K. Sun, and
R. J. Vlach (IEEE Journal of Solid-State Circuits,
1982, Pages 898--907) / 259 \\
A CMOS Floating Point Multiplier / M. Uya, K. Kaneko,
and J. Yasui (IEEE Journal of Solid-State Circuits,
1984, Pages 697--702) / 269 \\
A Single-Chip 80-Bit Floating Point Processor / K.
Takeda, F. Ishino, Y. Ito, R. Kasai, and T. Nakashima
(IEEE Journal of Solid-State Circuits, 1985, Pages
986--992) / 275 \\
VLSI Floating-Point Processors / J. Fandrianto and B.
Y. Woo (Proceedings 7th Symposium on Computer
Arithmetic, 1985, Pages 93--100) / 282 \\
Fast Multiply and Divide for a VLSI Floating-Point Unit
/ B. K. Bose, L. Pei, G. S. Taylor, and D. A. Patterson
(Proceedings 8th Symposium on Computer Arithmetic,
1987, Pages 87--94) / 290 \\
Chapter 7: Number Representation / 299 \\
A Formalization of Floating-Point Numeric Base
Conversion / D. W. Matula (IEEE Transactions on
Computers, 1970, Pages 681--692) / 300 \\
Analysis of Proposals for the Floating-Point Standard /
W. J. Cody (Computer, March 1987, Pages 63--68) / 312
\\
CADAC: A Controlled-Precision Decimal Arithmetic Unit /
M. S. Cohen, T. E. Hull, and V. C. Hamacher (IEEE
Transactions on Computers, 1983, Pages 370--377) / 317
\\
Finite Precision Rational Arithmetic: Slash Number
Systems / D. W. Matula and P. Kornerup (IEEE
Transactions on Computers, 1985, Pages 3--18) / 325 \\
Finite Precision Lexicographic Continued Fraction
Number Systerns / P. Kornerup and D. W. Matula
(Proceedings 7th Symposium on Computer Arithmetic,
1985, Pages 207--214) / 341 \\
An Overflow\slash Underflow Free Floating Point
Representation of Numbers / S. Matsui and M. lri
(Journal of Information Processing, 1981, Pages
123--133) / 349 \\
A Closed Computer Arithmetic / F. W. J. Olver
(Proceedings 8th Symposium on Computer Arithmetic,
1987, Pages 139--143) / 360 \\
Bibliography / 365 \\
Index / 393 \\
About the Editor / 397",
}
@Proceedings{Ullrich:1990:CCA,
editor = "Christian Ullrich",
booktitle = "Contributions to Computer Arithmetic and
Self-Validating Numerical Methods. (Proceedings of
{SCAN 89}, held in Basel, Oct. 2--6, 1989)",
title = "Contributions to Computer Arithmetic and
Self-Validating Numerical Methods. (Proceedings of
{SCAN} 89, held in Basel, Oct. 2--6, 1989)",
volume = "7",
publisher = pub-BALTZER,
address = pub-BALTZER:adr,
pages = "526",
year = "1990",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 08:36:57 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "IMACS annals on computing and applied mathematics",
acknowledgement = ack-nhfb,
xxbooktitle = "SCAN-89, International Symposium on Scientific
Computing, Computer Arithmetic, and Numeric Validation
[October 1989, Basel, Switzerland]",
}
@Proceedings{USENIX:1990:PWU,
key = "USENIX Winter '90",
booktitle = "Proceedings of the Winter 1990 {USENIX} Conference,
January 22--26, 1990, Washington, {DC}, {USA}",
title = "Proceedings of the Winter 1990 {USENIX} Conference,
January 22--26, 1990, Washington, {DC}, {USA}",
publisher = pub-USENIX,
address = pub-USENIX:adr,
pages = "xvi + 374",
year = "1990",
LCCN = "QA76.8.U65 U82 1990",
bibdate = "Thu Sep 15 18:50:55 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxISBN = "(none)",
}
@Proceedings{Wescon:1990:WCR,
editor = "{Wescon}",
booktitle = "Wescon/90 conference record, November 13--15, 1990,
Anaheim, California",
title = "Wescon/90 conference record, November 13--15, 1990,
Anaheim, California",
volume = "34",
publisher = "Electronic Conventions Management",
address = "Los Angeles, CA, USA",
pages = "xiv + 802",
year = "1990",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 08:57:03 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Wescon conference record",
acknowledgement = ack-nhfb,
confdate = "13-15 Nov. 1990",
conflocation = "Anaheim, CA, USA",
confsponsor = "IEEE; ERA",
}
@Proceedings{ASEE:1991:CCW,
editor = "{ASEE}",
booktitle = "Challenges of a changing world: proceedings, 1991
Annual Conference, June 16--19, 1991, University of New
Orleans",
title = "Challenges of a changing world: proceedings, 1991
Annual Conference, June 16--19, 1991, University of New
Orleans",
publisher = "American Society for Engineering Education (ASEE)",
address = "Washington, DC, USA",
pages = "xxi + 2026",
year = "1991",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 09:34:59 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "2 vol.",
acknowledgement = ack-nhfb,
confdate = "16-19 June 1991",
conflocation = "New Orleans, LA, USA",
}
@Proceedings{Griewank:1991:ADA,
editor = "Andreas Griewank and George F. Corliss",
booktitle = "{Automatic differentiation of algorithms: theory,
implementation, and application. Proceedings of the
first SIAM Workshop on Automatic Differentiation, held
in Breckenridge, Colorado, January 6--8, 1991}",
title = "{Automatic differentiation of algorithms: theory,
implementation, and application. Proceedings of the
first SIAM Workshop on Automatic Differentiation, held
in Breckenridge, Colorado, January 6--8, 1991}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "353",
year = "1991",
ISBN = "0-89871-284-x",
ISBN-13 = "978-0-89871-284-1",
LCCN = "QA304 1991",
bibdate = "Thu May 27 07:48:05 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.bibsys.no:2100/BIBSYS",
acknowledgement = ack-nhfb,
subject = "differential calculus; data processing congresses",
}
@Proceedings{IEEE:1991:PFC,
editor = "{IEEE}",
booktitle = "Proceedings / Fourth {CSI/IEEE} International
Symposium on {VLSI} Design, New Delhi, India, January
4--8, 1991: digest of papers",
title = "Proceedings / Fourth {CSI}/{IEEE} International
Symposium on {VLSI} Design, New Delhi, India, January
4--8, 1991: digest of papers",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 315",
year = "1991",
ISBN = "0-8186-2125-7",
ISBN-13 = "978-0-8186-2125-3",
LCCN = "????",
bibdate = "Sat Nov 29 09:25:08 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 91TH0340-0.",
acknowledgement = ack-nhfb,
confdate = "4-8 Jan. 1991",
conflocation = "New Delhi, India",
confsponsor = "IEEE; Comput. Soc. India",
}
@Proceedings{IEEE:1991:PIC,
key = "IEEE CICC '91",
booktitle = "Proceedings of the {IEEE} 1991 Custom Integrated
Circuits Conference: Town and Country Hotel, San Diego,
California, May 12--15, 1991",
title = "Proceedings of the {IEEE} 1991 Custom Integrated
Circuits Conference: Town and Country Hotel, San Diego,
California, May 12--15, 1991",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1991",
ISBN = "0-7803-0016-5",
ISBN-13 = "978-0-7803-0016-3",
LCCN = "TK 7874 C87 1991",
bibdate = "Fri Dec 08 13:03:13 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{IEEE:1991:PSA,
editor = "{IEEE}",
booktitle = "Proceedings, Supercomputing '91: Albuquerque, New
Mexico, November 18--22, 1991",
title = "Proceedings, Supercomputing '91: Albuquerque, New
Mexico, November 18--22, 1991",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxiii + 917",
year = "1991",
ISBN = "0-8186-9158-1 (IEEE case), 0-8186-2158-3 (IEEE paper),
0-8186-6158-5 (IEEE microfiche), 0-89791-459-7 (ACM)",
ISBN-13 = "978-0-8186-9158-4 (IEEE case), 978-0-8186-2158-1 (IEEE
paper), 978-0-8186-6158-7 (IEEE microfiche),
978-0-89791-459-8 (ACM)",
LCCN = "QA76.5 .S894 1991",
bibdate = "Fri Aug 30 08:01:51 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
University of California MELVYL catalog.",
note = "ACM order number 415913. IEEE Computer Society Press
order number 2158. IEEE catalog number 91CH3058-5.",
acknowledgement = ack-nhfb,
classification = "C5440 (Multiprocessor systems and techniques); C5470
(Performance evaluation and testing); C6110P (Parallel
programming)",
keywords = "combinatorial algorithms; data dependence; distributed
memory code generation; high school environment;
latency tolerance; memory access; numerical algorithms;
parallel processing; parallel programming; performance
evaluation; performance tools; processor design;
program analysis; storage hierarchy optimization;
supercomputer benchmarks; supercomputer congresses;
supercomputing; system issues",
}
@Proceedings{IEEE:1991:VCA,
key = "ICASSP'91",
booktitle = "{VLSI} Cell Architecture and Application to Signal
Processing. {ICASSP 91}: 1991 International Conference
on Acoustics, Speech and Signal Processing, May 14--17,
1991, The Sheraton Centre Hotel and Towers, Toronto,
Ontario, Canada",
title = "{VLSI} Cell Architecture and Application to Signal
Processing. {ICASSP} 91: 1991 International Conference
on Acoustics, Speech and Signal Processing, May 14--17,
1991, The Sheraton Centre Hotel and Towers, Toronto,
Ontario, Canada",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3732",
year = "1991",
ISBN = "0-7803-0003-3 (softbound), 0-7803-0004-1 (casebound),
0-7803-0005-X (microfiche)",
ISBN-13 = "978-0-7803-0003-3 (softbound), 978-0-7803-0004-0
(casebound), 978-0-7803-0005-7 (microfiche)",
LCCN = "TK 7882 S65 I16 1991",
bibdate = "Sat Dec 09 14:13:02 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Five volumes. IEEE catalog number 91CH2977-7.",
acknowledgement = ack-nhfb,
}
@Proceedings{Kaucher:1991:CAS,
editor = "Edgar W. Kaucher and S. M. (Svetoslav M.) Markov and
G. (Gunter) Mayer",
booktitle = "Computer Arithmetic, Scientific Computation and
Mathematical Modelling: Proceedings of the Second
International Conference on Computer Arithmetic,
Scientific Computation and Mathematical Modelling,
Albena, Bulgaria, September 24--28, 1990",
title = "Computer Arithmetic, Scientific Computation and
Mathematical Modelling: Proceedings of the Second
International Conference on Computer Arithmetic,
Scientific Computation and Mathematical Modelling,
Albena, Bulgaria, September 24--28, 1990",
volume = "12",
publisher = pub-BALTZER,
address = pub-BALTZER:adr,
pages = "498",
year = "1991",
ISSN = "1012-2435",
LCCN = "QA76.9.C62 I555 1990",
bibdate = "Thu Sep 15 20:51:47 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "IMACS Annals on Computing and Applied Mathematics",
acknowledgement = ack-nhfb,
confdate = "24-28 Sept. 1990",
conflocation = "Albena, Bulgaria",
pubcountry = "Switzerland",
xxISBN = "(none)",
}
@Proceedings{Koopman:1991:PST,
editor = "Philip J. {Koopman, Jr.}",
booktitle = "The proceedings of the second and third annual
workshops for the {ACM Special Interest Group on Forth:
SIGForth '90, February 16--18, 1990, Dallas, Texas
\ldots{} SIGForth '91, March 7--9, 1991, San Antonio,
Texas}",
title = "The proceedings of the second and third annual
workshops for the {ACM Special Interest Group on Forth:
SIGForth '90, February 16--18, 1990, Dallas, Texas
\ldots{} SIGForth '91, March 7--9, 1991, San Antonio,
Texas}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ii + 134",
year = "1991",
ISBN = "0-89791-462-7",
ISBN-13 = "978-0-89791-462-8",
LCCN = "QA 76.73 F24 S53 1991",
bibdate = "Tue May 04 07:39:28 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 817911.",
acknowledgement = ack-nhfb,
}
@Proceedings{Kornerup:1991:PIS,
editor = "Peter Kornerup and David W. Matula",
booktitle = "{Proceedings: 10th IEEE Symposium on Computer
Arithmetic: June 26--28, 1991, Grenoble, France}",
title = "{Proceedings: 10th IEEE Symposium on Computer
Arithmetic: June 26--28, 1991, Grenoble, France}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 282",
year = "1991",
ISBN = "0-8186-9151-4 (case), 0-8186-6151-8 (microfiche),
0-7803-0187-0 (library binding)",
ISBN-13 = "978-0-8186-9151-5 (case), 978-0-8186-6151-8
(microfiche), 978-0-7803-0187-0 (library binding)",
LCCN = "QA76.9.C62 S95 1991",
bibdate = "Thu Sep 01 23:18:52 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 91CH3015-5.",
acknowledgement = ack-nhfb,
confdate = "26-28 June 1991",
conflocation = "Grenoble, France",
confsponsor = "IEEE; CNRS; IMAG",
keywords = "ARITH-10",
}
@Proceedings{Meyer:1991:CAP,
editor = "Kenneth R. (Kenneth Ray) Meyer and Dieter S. Schmidt",
booktitle = "{Computer aided proofs in analysis}",
title = "{Computer aided proofs in analysis}",
volume = "28",
publisher = pub-SV,
address = pub-SV:adr,
pages = "251",
year = "1991",
DOI = "https://doi.org/10.1007/978-1-4613-9092-3",
ISBN = "0-387-97426-1, 3-540-97426-1",
ISBN-13 = "978-0-387-97426-2, 978-3-540-97426-0",
LCCN = "QA614.58 .I52 1989; QA297 .C638 1991",
bibdate = "Thu Feb 23 06:54:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/macsyma.bib;
library.mit.edu:9909/mit01",
series = "The IMA volumes in mathematics and its applications",
acknowledgement = ack-nhfb,
keywords = "Numerical analysis --- Data processing ---
Congresses.",
remark = "Proceedings of an IMA Participating Institutions (PI)
Conference held at the University of Cincinnati in
April 1989.",
subject = "Numerical analysis; Data processing; Congresses",
tableofcontents = "The conversion of a high order programming language
from floating-point arithmetic to range arithmetic /
Oliver Aberth \\
Sylvester's form of the resultant and the
matrix-triangularization subresultant PRS method /
Alkiviadis G. Akritas \\
Computing the Tsirelson space norm / Johnnie W. Baker,
Oberta A. Slotterbeck and Richard Aron \\
Floating-point systems for theorem proving / G.
Bohlender, J. Wolff von Gudenberg and W. L. Miranker
\\
Computer algebra and indefinite integrals / Manuel
Bronstein \\
A computer-assisted approach to small-divisors problems
arising in Hamiltonian mechanics / Alessandra Celletti
and Luigi Chierchia \\
On a computer algebra aided proof in bifurcation theory
/ Carmen Chicone and Marc Jacobs \\
MACSYMA program to implement averaging using elliptic
functions / Vincent T. Coppola and Richard H. Rand \\
Validated anti-derivatives / George F. Corliss \\
A toolbox for nonlinear dynamics / Shannon Coffey
\ldots{} [et al.] \\
Computer assisted proofs of stability of matter / R. de
la Llave \\
Accurate strategies for K.A.M. bounds and their
implementation / R. de la Llave and D. Rana \\
A software tool for analysis in function spaces / J.-P.
Eckmann, A. Malaspinas and S. Oliffson Kamphorst \\
Equation solving by symbolic computation / Anthony C.
Hearn \\
Deciding a class of Euclidean geometry theorems with
Buchberger's algorithm / Bernhard Kutzler \\
Lie transform tutorial : II / Kenneth R. Meyer \\
Interval tools for computer aided proofs in analysis /
Ramon E. Moore \\
Tools for mathematical computation / L. B. Rall \\
Shadowing trajectories of dynamical systems / Tim Sauer
and James A. Yorke \\
Transformation to versal normal form / Dieter S.
Schmidt \\
Computer assisted lower bounds for atomic energies /
Luis A. Seco",
}
@Proceedings{Morris:1991:RWP,
editor = "Joseph M. Morris and Roger C. Shaw",
booktitle = "4th Refinement Workshop: proceedings of the 4th
Refinement Workshop, 9--11 January 1991, Cambridge",
title = "4th Refinement Workshop: proceedings of the 4th
Refinement Workshop, 9--11 January 1991, Cambridge",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 478",
year = "1991",
DOI = "https://doi.org/10.1007/978-1-4471-3756-6",
ISBN = "3-540-19657-9",
ISBN-13 = "978-3-540-19657-0",
LCCN = "????",
bibdate = "Sat Nov 29 09:29:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "9-11 Jan. 1991",
conflocation = "Cambridge, UK",
pubcountry = "Germany",
}
@Proceedings{SPIE:1991:PSI,
editor = "Franklin T. Luk",
booktitle = "Advanced Signal Processing Algorithms, Architectures,
and Implementations {II}: 24--26 July 1991, San Diego,
California",
title = "Advanced Signal Processing Algorithms, Architectures,
and Implementations {II}: 24--26 July 1991, San Diego,
California",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "ix + 494",
year = "1991",
ISBN = "0-8194-0694-5",
ISBN-13 = "978-0-8194-0694-1",
LCCN = "TS510.S63 v.1566",
bibdate = "Wed Sep 07 23:38:20 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{Alley:1992:CRI,
editor = "Gary T. Alley",
booktitle = "Conference record of the 1992 {IEEE} Nuclear Science
Symposium and Medical Imaging Conference: October
25--31, 1992, Orlando, Florida {USA}",
title = "Conference record of the 1992 {IEEE} Nuclear Science
Symposium and Medical Imaging Conference: October
25--31, 1992, Orlando, Florida {USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xlix + 1362",
year = "1992",
ISBN = "0-7803-0884-0",
ISBN-13 = "978-0-7803-0884-8",
LCCN = "????",
bibdate = "Sat Nov 29 09:55:50 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes. IEEE catalog no. 92CH3232-6.",
acknowledgement = ack-nhfb,
confdate = "25-31 Oct. 1992",
conflocation = "Orlando, FL, USA",
confsponsor = "IEEE; Argonne Nat. Lab.; Brookhaven Nat. Lab.; United
States Dept. Energy; et al",
}
@Proceedings{Anonymous:1992:EAP,
editor = "Anonymous",
booktitle = "{Euro ASIC '92: proceedings, CNIT, Paris, June 1--5,
1992 in cooperation with IEEE Computer Society}",
title = "{Euro ASIC '92: proceedings, CNIT, Paris, June 1--5,
1992 in cooperation with IEEE Computer Society}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 423",
year = "1992",
ISBN = "0-8186-2845-6, 0-8186-2846-4, 0-8186-2847-2",
ISBN-13 = "978-0-8186-2845-0, 978-0-8186-2846-7,
978-0-8186-2847-4",
LCCN = "TK7874.6 .E87 1992",
bibdate = "Thu Mar 2 09:48:17 MST 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "IEEE catalog no. 92TH0442-4. IEEE Computer Society
Press order number 2845.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=416",
acknowledgement = ack-nhfb,
meetingname = "Euro ASIC (Conference) (6th: 1992: Paris, France)",
subject = "Application specific integrated circuits; Congresses",
}
@Proceedings{Atanassova:1992:CAE,
editor = "Lidiya Atanassova and J{\"u}rgen Herzberger",
booktitle = "Computer Arithmetic and Enclosure Methods: Proceedings
of the Third International {IMACS-GAMM} Symposium on
Computer Arithmetic and Scientific Computing
({SCAN}-91), Oldenburg, Germany, 1--4 October 1991",
title = "Computer Arithmetic and Enclosure Methods: Proceedings
of the Third International {IMACS-GAMM} Symposium on
Computer Arithmetic and Scientific Computing
({SCAN}-91), Oldenburg, Germany, 1--4 October 1991",
publisher = pub-ENH,
address = pub-ENH:adr,
pages = "x + 504",
year = "1992",
ISBN = "0-444-89834-4",
ISBN-13 = "978-0-444-89834-0",
LCCN = "QA76.9.C62 I559 1992",
bibdate = "Thu Sep 15 19:22:16 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1992:ASF,
editor = "{IEEE}",
booktitle = "{33rd Annual Symposium on Foundations of Computer
Science: October 24--27, 1992, Pittsburgh,
Pennsylvania: proceedings [papers]}",
title = "{33rd Annual Symposium on Foundations of Computer
Science: October 24--27, 1992, Pittsburgh,
Pennsylvania: proceedings [papers]}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 734",
year = "1992",
CODEN = "ASFPDV",
ISBN = "0-8186-2901-0 (microfiche), 0-8186-2900-2
(paperback)",
ISBN-13 = "978-0-8186-2901-3 (microfiche), 978-0-8186-2900-6
(paperback)",
ISSN = "0272-5428",
LCCN = "QA 76 S979 1992",
bibdate = "Thu Dec 3 07:11:18 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number 92CH3188-0. IEEE Computer Society
Press Order Number 2900.",
acknowledgement = ack-nhfb,
keywords = "electronic data processing --- congresses",
}
@Proceedings{IEEE:1992:GCG,
editor = "{IEEE}",
booktitle = "{GLOBECOM '92}. Communication for Global Users. {IEEE}
Global Telecommunications Conference. Conference
Record",
title = "{GLOBECOM} '92. Communication for Global Users. {IEEE}
Global Telecommunications Conference. Conference
Record",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xlviii + 1920",
year = "1992",
ISBN = "0-7803-0608-2, 0-7803-0609-0, 0-7803-0610-4
(microfiche)",
ISBN-13 = "978-0-7803-0608-0, 978-0-7803-0609-7,
978-0-7803-0610-3 (microfiche)",
LCCN = "????",
bibdate = "Sat Nov 29 09:41:22 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Three volumes. IEEE catalog no. 92CH3130-2.",
acknowledgement = ack-nhfb,
confdate = "6-9 Dec. 1992",
conflocation = "Orlando, FL, USA",
confsponsor = "IEEE",
}
@Proceedings{IEEE:1992:IIC,
key = "IEEE ICCD '92",
booktitle = "1992 {IEEE} International Conference on Computer
Design, {VLSI} in Computers and Processors:
Proceedings, Royal Sonesta Hotel, Cambridge,
Massachusetts, October 11--14, 1992",
title = "1992 {IEEE} International Conference on Computer
Design, {VLSI} in Computers and Processors:
Proceedings, Royal Sonesta Hotel, Cambridge,
Massachusetts, October 11--14, 1992",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvii + 605",
year = "1992",
ISBN = "0-8186-3110-4 (paper), 0-8186-3111-2 (microfiche),
0-8186-3112-0 (case)",
ISBN-13 = "978-0-8186-3110-8 (paper), 978-0-8186-3111-5
(microfiche), 978-0-8186-3112-2 (case)",
LCCN = "TK 7888.4 I23 1992",
bibdate = "Thu Sep 08 00:35:29 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
}
@Proceedings{IEEE:1992:PIC,
editor = "{IEEE}",
booktitle = "Proceedings of the {IEEE 1992} Custom Integrated
Circuits Conference: the Westin Copley Place Hotel,
Boston, Massachusetts, May 3--6, 1992",
title = "Proceedings of the {IEEE} 1992 Custom Integrated
Circuits Conference: the Westin Copley Place Hotel,
Boston, Massachusetts, May 3--6, 1992",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "1992",
ISBN = "0-7803-0246-X, 0-7803-0247-8, 0-7803-0248-6",
ISBN-13 = "978-0-7803-0246-4, 978-0-7803-0247-1,
978-0-7803-0248-8",
LCCN = "????",
bibdate = "Sat Nov 29 10:08:17 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 92CH3078-3.",
acknowledgement = ack-nhfb,
confdate = "3-6 May 1992",
conflocation = "Boston, MA, USA",
confsponsor = "IEEE",
}
@Proceedings{IEEE:1992:PIS,
editor = "{IEEE}",
booktitle = "Proceedings / {IEEE} Southeastcon '92, April 12--15,
1992, Birmingham, Alabama",
title = "Proceedings / {IEEE} Southeastcon '92, April 12--15,
1992, Birmingham, Alabama",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "lii + 846",
year = "1992",
ISBN = "0-7803-0494-2",
ISBN-13 = "978-0-7803-0494-9",
LCCN = "????",
bibdate = "Sat Nov 29 09:59:47 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes. IEEE catalog no. 92CH3094-0.",
acknowledgement = ack-nhfb,
confdate = "12-15 April 1992",
conflocation = "Birmingham, AL, USA",
confsponsor = "IEEE",
}
@Proceedings{Juj:1992:NCR,
editor = "Hardev Juj and Alvin Todd Moser",
booktitle = "Northcon\slash 92 Conference Record: Seattle,
Washington, October 19--21, 1992",
title = "Northcon\slash 92 Conference Record: Seattle,
Washington, October 19--21, 1992",
publisher = "Electronic Conventions Management",
address = "Los Angeles, CA, USA",
pages = "vii + 366",
year = "1992",
LCCN = "TK 7801 N67 1992",
bibdate = "Fri Dec 08 13:10:32 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nj,
xxISBN = "(none)",
}
@Proceedings{Katwijk:1992:AMT,
editor = "J. Katwijk",
booktitle = "{Ada: moving towards 2000: 11th Ada-Europe
International Conference, Zandvoort, The Netherlands,
June 1--5, 1992: proceedings}",
title = "{Ada: moving towards 2000: 11th Ada-Europe
International Conference, Zandvoort, The Netherlands,
June 1--5, 1992: proceedings}",
volume = "603",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 324",
year = "1992",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/3-540-55585-4",
ISBN = "3-540-55585-4 (Berlin), 0-387-55585-4 (New York)",
ISBN-13 = "978-3-540-55585-8 (Berlin), 978-0-387-55585-0 (New
York)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.73.A35 A24 1992",
bibdate = "Fri Apr 12 07:14:56 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t0603.htm;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=603",
acknowledgement = ack-nhfb,
keywords = "Ada (computer program language) --- congresses",
}
@Proceedings{Prinetto:1992:CHD,
editor = "Paolo Prinetto and Paolo Camurati",
booktitle = "Correct Hardware Design Methodologies. Proceedings of
the Advanced Research Workshop on Correct Hardware
Design Methodologies, Turin, Italy, June 12--14, 1991",
title = "Correct Hardware Design Methodologies. Proceedings of
the Advanced Research Workshop on Correct Hardware
Design Methodologies, Turin, Italy, June 12--14, 1991",
publisher = "North-Holland",
address = "Amsterdam, Netherlands",
pages = "ix + 470",
year = "1992",
ISBN = "0-444-89367-9",
ISBN-13 = "978-0-444-89367-3",
LCCN = "TK7874 .A3353 1991",
bibdate = "Sat Nov 29 09:58:12 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "12-14 June 1991",
conflocation = "Turin, Italy",
confsponsor = "Politecnico di Torino",
pubcountry = "Netherlands",
}
@Proceedings{Quinton:1992:APV,
editor = "Patrice Quinton and Yves Robert",
booktitle = "Proceedings of the International Workshop Algorithms
and Parallel {VLSI} Architectures {II}, Ch{\^a}teau de
Bonas, Gers, France, June 3--6, 1991",
title = "Proceedings of the International Workshop Algorithms
and Parallel {VLSI} Architectures {II}, Ch{\^a}teau de
Bonas, Gers, France, June 3--6, 1991",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "xvi + 388",
year = "1992",
ISBN = "0-444-89153-6",
ISBN-13 = "978-0-444-89153-2",
LCCN = "????",
bibdate = "Sat Nov 29 09:45:36 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "3-6 June 1991",
conflocation = "Gers, France",
confsponsor = "CNRS; French Minist. Res. Technol.; French Minist.
Defence",
pubcountry = "Netherlands",
}
@Proceedings{Singh:1992:CRT,
editor = "Avtar Singh",
booktitle = "Conference record of the Twenty-sixth Asilomar
Conference on Signals, Systems and Computers: October
26--28, 1992, Pacific Grove, California",
title = "Conference record of the Twenty-sixth Asilomar
Conference on Signals, Systems and Computers: October
26--28, 1992, Pacific Grove, California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xviii + 1156",
year = "1992",
ISBN = "0-8186-3162-7 (case), 0-8186-3160-0 (paper),
0-8186-3161-9 (microfiche)",
ISBN-13 = "978-0-8186-3162-7 (case), 978-0-8186-3160-3 (paper),
978-0-8186-3161-0 (microfiche)",
LCCN = "TK 5102.5 A78 1992",
bibdate = "Thu Sep 08 13:38:22 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nj,
confdate = "26-28 Oct. 1992",
conflocation = "Pacific Grove, CA, USA",
confsponsor = "IEEE",
}
@Book{Turing:1992:PM,
author = "A. M. Turing",
booktitle = "Pure mathematics",
title = "Pure mathematics",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "xxii + 287",
year = "1992",
ISBN = "0-444-88059-3",
ISBN-13 = "978-0-444-88059-8",
LCCN = "????",
MRclass = "01A75 (03-03 03D40 62-03 68-03)",
MRnumber = "MR1150052 (93k:01094)",
MRreviewer = "A. A. Mullin",
bibdate = "Sat Nov 19 13:23:32 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "Edited and with an introduction and postscript by J.
L. Britton and Irvine John Good. With a preface by P.
N. Furbank",
series = "Collected Works of A. M. Turing",
acknowledgement = ack-nhfb,
author-dates = "1912--1954",
subject = "Mathematics",
}
@Proceedings{Vandewalle:1992:SPV,
editor = "J. Vandewalle and R. Boite and M. Moonen and A.
Oosterlinck",
booktitle = "Signal processing {VI}: theories and applications;
proceedings of {EUSIPCO-92}, Sixth European Signal
Processing Conference, Brussels, Belgium, August
24--27, 1992",
title = "Signal processing {VI}: theories and applications;
proceedings of {EUSIPCO}-92, Sixth European Signal
Processing Conference, Brussels, Belgium, August
24--27, 1992",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "lvii + 1844",
year = "1992",
ISBN = "0-444-89587-6",
ISBN-13 = "978-0-444-89587-5",
LCCN = "TK5102.5 621.382/2",
bibdate = "Sat Nov 29 09:49:22 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "3 vol.",
acknowledgement = ack-nhfb,
confdate = "24-27 Aug. 1992",
conflocation = "Brussels, Belgium",
confsponsor = "Belgian Nat. Fund for Sci. Res.; CERA; LMS Int",
pubcountry = "Netherlands",
}
@Proceedings{Wang:1992:PII,
editor = "Paul S. Wang",
booktitle = "{Proceedings of ISSAC '92. International Symposium on
Symbolic and Algebraic Computation}",
title = "{Proceedings of ISSAC '92. International Symposium on
Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 406",
year = "1992",
ISBN = "0-89791-489-9 (soft cover), 0-89791-490-2 (hard
cover)",
ISBN-13 = "978-0-89791-489-5 (soft cover), 978-0-89791-490-1
(hard cover)",
LCCN = "QA76.95.I59 1992",
bibdate = "Thu Sep 26 05:51:45 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/issac.bib",
note = "ACM order number: 505920.",
abstract = "The following topics were dealt with: symbolic
computation; differential equations; differs-integral
software; algebraic algorithms; algebraic software;
real algebraics and root isolation; groups and number
theory; systems and interfaces.",
acknowledgement = ack-nhfb,
classification = "C6130 (Data handling techniques); C7310
(Mathematics)",
confdate = "27--29 July 1992",
conflocation = "Berkeley, CA, USA",
confsponsor = "ACM",
keywords = "Algebraic algorithms; Algebraic software; Differential
equations; Differs-integral software; Groups theory;
Interfaces; Number theory; Real algebraics; Root
isolation; Symbolic computation",
pubcountry = "USA",
thesaurus = "Differential equations; Mathematics computing; Symbol
manipulation",
}
@Proceedings{White:1992:IIS,
editor = "Stan White",
booktitle = "1992 {IEEE} International Symposium on Circuits and
Systems: San Diego {CA}, May 10--13, 1992",
title = "1992 {IEEE} International Symposium on Circuits and
Systems: San Diego {CA}, May 10--13, 1992",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3028",
year = "1992",
ISBN = "0-7803-0593-0",
ISBN-13 = "978-0-7803-0593-9",
LCCN = "????",
bibdate = "Sat Nov 29 09:52:25 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Six volumes. IEEE catalog no. 92CH3139-3.",
acknowledgement = ack-nhfb,
confdate = "10-13 May 1992",
conflocation = "San Diego, CA, USA",
confsponsor = "IEEE",
}
@Book{Adams:1993:SCA,
editor = "Ernst Adams and Ulrich Kulisch",
booktitle = "Scientific computing with automatic result
verification",
title = "Scientific computing with automatic result
verification",
volume = "189",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 612",
year = "1993",
ISBN = "0-12-044210-8",
ISBN-13 = "978-0-12-044210-2",
LCCN = "QA76 .S368 1993",
bibdate = "Sat Nov 29 11:22:09 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = "Mathematics in science and engineering",
URL = "http://lccn.loc.gov/92247371",
acknowledgement = ack-nhfb,
subject = "Electronic data processing; Computer science;
Mathematics",
}
@Proceedings{Anonymous:1993:IPF,
editor = "Anonymous",
booktitle = "{ICSPAT '93}: Proceedings of the Fourth International
Conference on Signal Processing Applications \&
Technology: Santa Clara, California, {USA}, September
28 -- October 1, 1993",
title = "{ICSPAT '93}: Proceedings of the Fourth International
Conference on Signal Processing Applications \&
Technology: Santa Clara, California, {USA}, September
28 -- October 1, 1993",
publisher = "DSP Associates",
address = "Newton, MA, USA",
pages = "1675",
year = "1993",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 10:11:01 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes",
acknowledgement = ack-nhfb,
confdate = "28 Sept.-1 Oct. 1993",
conflocation = "Santa Clara, CA, USA",
}
@Proceedings{Corliss:1993:AIC,
editor = "G. F. Corliss and R. B. Kearfott",
booktitle = "Abstracts for an International Conference on Numerical
Analysis with Automatic Result Verification:
Mathematics, Application and Software, February
25--March 1, 1993, Lafayette, {LA, 1993}",
title = "Abstracts for an International Conference on Numerical
Analysis with Automatic Result Verification:
Mathematics, Application and Software, February
25--March 1, 1993, Lafayette, {LA}, 1993",
volume = "3(3--4)",
publisher = "????",
address = "????",
pages = "????",
year = "1993",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0135-4868",
LCCN = "????",
bibdate = "Tue Oct 22 13:32:36 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = j-INTERVAL-COMP,
acknowledgement = ack-nhfb,
xxtitle = "Numerical analysis with automatic result verification:
International conference: Selected papers",
}
@Proceedings{Eggermont:1993:VSP,
editor = "Ludwig D. J. Eggermont and others",
booktitle = "{VLSI signal processing, VI. Proceedings of the 1993
IEEE workshop on VLSI signal processing, Veldhoven, The
Netherlands, October 20--22, 1993}",
title = "{VLSI signal processing, VI. Proceedings of the 1993
IEEE workshop on VLSI signal processing, Veldhoven, The
Netherlands, October 20--22, 1993}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xv + 527",
year = "1993",
DOI = "https://doi.org/10.1109/VLSISP.1993.404510",
ISBN = "0-7803-0996-0",
ISBN-13 = "978-0-7803-0996-8",
LCCN = "TK7874 .V5637 1993",
bibdate = "Sun Mar 4 21:10:43 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=3196",
acknowledgement = ack-nhfb,
remark = "Based on reviewed and accepted contributions to the
1993 IEEE Workshop on VLSI Signal Processing, which was
held in Veldhoven, The Netherlands, from October
20--22, 1993",
subject = "Integrated circuits; Very large scale integration;
Signal processing",
}
@Proceedings{IEEE:1993:PEC,
editor = "{IEEE}",
booktitle = "(1993) Proceedings The European Conference on Design
Automation with the European Event in {ASIC} Design",
title = "(1993) Proceedings The European Conference on Design
Automation with the European Event in {ASIC} Design",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxv + 601",
year = "1993",
ISBN = "0-8186-3410-3",
ISBN-13 = "978-0-8186-3410-9",
LCCN = "????",
bibdate = "Sat Nov 29 10:21:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "22-25 Feb. 1993",
conflocation = "Paris, France",
}
@Proceedings{IEEE:1993:PIP,
editor = "{IEEE}",
booktitle = "{Proceedings of the IEEE Pacific Rim Conference on
Communications, Computers, and Signal Processing (1993:
Victoria, BC)}",
title = "{Proceedings of the IEEE Pacific Rim Conference on
Communications, Computers, and Signal Processing (1993:
Victoria, BC)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "1993",
ISBN = "0-7803-0971-5 (softbound), 0-7803-1219-8 (casebound),
0-7803-0972-3 (microfiche)",
ISBN-13 = "978-0-7803-0971-5 (softbound), 978-0-7803-1219-7
(casebound), 978-0-7803-0972-2 (microfiche)",
LCCN = "TK5101.A1 I34 1993",
bibdate = "Sun Feb 20 10:56:48 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
subject = "telecommunication; congresses; computers; signal
processing",
}
@Proceedings{IEEE:1993:PMS,
editor = "{IEEE}",
booktitle = "Proceedings of the 36th Midwest Symposium on Circuits
and Systems",
title = "Proceedings of the 36th Midwest Symposium on Circuits
and Systems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxxv + 1565",
year = "1993",
ISBN = "0-7803-1760-2",
ISBN-13 = "978-0-7803-1760-4",
LCCN = "????",
bibdate = "Sat Nov 29 10:12:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes. IEEE catalog no. 93CH3381-1.",
acknowledgement = ack-nhfb,
confdate = "16-18 Aug. 1993",
conflocation = "Detroit, MI, USA",
confsponsor = "Wayne State University; IEEE Circuits and Syst. Soc",
}
@Proceedings{Lee:1993:MCM,
editor = "Thomas Lee",
booktitle = "Mathematical computation with Maple V: ideas and
applications: Proceedings of the Maple Summer Workshop
and Symposium, University of Michigan, Ann Arbor, June
28--30, 1993",
title = "Mathematical computation with Maple {V}: ideas and
applications: Proceedings of the Maple Summer Workshop
and Symposium, University of Michigan, Ann Arbor, June
28--30, 1993",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "viii + 199",
year = "1993",
ISBN = "0-8176-3724-9, 3-7643-3724-9",
ISBN-13 = "978-0-8176-3724-8, 978-3-7643-3724-7",
LCCN = "QA76.95.M36 1993",
bibdate = "Sat Dec 09 11:54:32 1995",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Lombardi:1993:PII,
editor = "F. Lombardi and M. Sami and Y. Savaria and R.
Stefanelli",
booktitle = "Proceedings / The {IEEE} International Workshop on
Defect and Fault Tolerance in {VLSI} Systems: October
27--29, 1993, Venice, Italy",
title = "Proceedings / The {IEEE} International Workshop on
Defect and Fault Tolerance in {VLSI} Systems: October
27--29, 1993, Venice, Italy",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 335",
year = "1993",
ISBN = "0-8186-3502-9 (case), 0-8186-3501-0 (microfiche)",
ISBN-13 = "978-0-8186-3502-1 (case), 978-0-8186-3501-4
(microfiche)",
LCCN = "????",
bibdate = "Sat Nov 29 10:22:50 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 93TH0571-0.",
acknowledgement = ack-nhfb,
confdate = "27-29 Oct. 1993",
conflocation = "Venice, Italy",
confsponsor = "IEEE Comput. Soc.; IEEE Comput. Soc. Tech. Committee
on Fault-Tolerant Comput.; Euromicro",
}
@Proceedings{Sincovec:1993:PSS,
editor = "Richard F. Sincovec and David E. Keyes and L. M. R.
and L. R. Petzold and D. A. Reed",
booktitle = "{Proceedings of the Sixth SIAM Conference on Parallel
Processing for Scientific Computing, held March 22--24,
1993, in Norfolk, VA, USA}",
title = "{Proceedings of the Sixth SIAM Conference on Parallel
Processing for Scientific Computing, held March 22--24,
1993, in Norfolk, VA, USA}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xix + 1041 + iv",
year = "1993",
ISBN = "0-89871-315-3",
ISBN-13 = "978-0-89871-315-2",
LCCN = "QA76.58 .S55 1993 v.1-2",
bibdate = "Tue Oct 11 12:21:40 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
xxnote = "Check authors: catalogs are incomplete",
}
@Proceedings{Swartzlander:1993:PSC,
editor = "Earl {Swartzlander, Jr.} and Mary Jane Irwin and
Graham Jullien",
booktitle = "Proceedings: 11th Symposium on Computer Arithmetic,
June 29--July 2, 1993, Windsor, Ontario",
title = "Proceedings: 11th Symposium on Computer Arithmetic,
June 29--July 2, 1993, Windsor, Ontario",
publisher = pub-IEEE,
address = pub-IEEE:adr,
bookpages = "xii + 284",
pages = "xii + 284",
year = "1993",
ISBN = "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound),
0-8186-3861-3 (microfiche)",
ISBN-13 = "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6
(casebound), 978-0-8186-3861-9 (microfiche)",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
LCCN = "QA 76.9 C62 S95 1993",
bibdate = "Thu Sep 01 22:58:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "IEEE Transactions on Computers {\bf 43(8)}, 1994.",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Proceedings{Swartzlander:1993:SCA,
editor = "Earl {Swartzlander, Jr.} and Mary Jane Irwin and
Graham Jullien",
booktitle = "Proceedings: 11th Symposium on Computer Arithmetic,
June 29--July 2, 1993, Windsor, Ontario",
title = "Proceedings: 11th Symposium on Computer Arithmetic,
June 29--July 2, 1993, Windsor, Ontario",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 284",
year = "1993",
ISBN = "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound),
0-8186-3861-3 (microfiche)",
ISBN-13 = "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6
(casebound), 978-0-8186-3861-9 (microfiche)",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
LCCN = "QA 76.9 C62 S95 1993",
bibdate = "Thu Sep 01 22:58:49 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Transactions on Computers {\bf 43(8)}, 1994",
acknowledgement = ack-nhfb,
keywords = "ARITH-11",
}
@Proceedings{Wah:1993:ICA,
editor = "Benjamin W. Wah and Luigi Dadda",
booktitle = "{The International Conference on Application-Specific
Array Processors: October 25--27, 1993, Venice, Italy:
proceedings}",
title = "{The International Conference on Application-Specific
Array Processors: October 25--27, 1993, Venice, Italy:
proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 594",
year = "1993",
ISBN = "0-8186-3492-8, 0-8186-3491-X",
ISBN-13 = "978-0-8186-3492-5, 978-0-8186-3491-8",
LCCN = "TK5102.5",
bibdate = "Sun Mar 4 21:08:02 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Application Specific Array
Processors (7th: 1993: Venice, Italy)",
remark = "Sponsored by Euromicro. IEEE Computer Society Press
order number 3492-02. IEEE catalog number 93TH0572-8",
subject = "Array processors; Congresses; Signal processing;
Digital techniques; Application-specific integrated
circuits",
}
@Proceedings{ACM:1994:AAW,
editor = "{ACM}",
booktitle = "{Ada in applications: WADAS '94: eleventh Annual
Washington Ada Symposium \& Summer ACM SIGAda Meeting:
featuring Working Group Product Development and
Delivery: June 27 -- July 1, 1994, McLean Hilton,
Tyson's Corner, McLean, Virginia: proceedings}",
title = "{Ada in applications: WADAS '94: eleventh Annual
Washington Ada Symposium \& Summer ACM SIGAda Meeting:
featuring Working Group Product Development and
Delivery: June 27 -- July 1, 1994, McLean Hilton,
Tyson's Corner, McLean, Virginia: proceedings}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "121",
year = "1994",
ISBN = "0-89791-684-0",
ISBN-13 = "978-0-89791-684-4",
LCCN = "????",
bibdate = "Sat Nov 29 06:48:28 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Proceedings{Ames:1994:IPI,
editor = "William F. Ames",
booktitle = "{IMACS '94: proceedings of the 14th IMACS World
Congress on Computation and Applied Mathematics: July
11--15, 1994, Georgia Institute of Technology, Atlanta,
Georgia, USA}",
title = "{IMACS '94: proceedings of the 14th IMACS World
Congress on Computation and Applied Mathematics: July
11--15, 1994, Georgia Institute of Technology, Atlanta,
Georgia, USA}",
publisher = pub-IMACS,
address = pub-IMACS:adr,
pages = "1572",
year = "1994",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Jun 14 16:37:46 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fazio-riccardo.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Three volumes.",
acknowledgement = ack-nhfb,
annote = "Accompanied by `Late papers volume' (101 p.).",
keywords = "Computer simulation -- Congresses.; Mathematical
models -- Congresses.; Numerical analysis --
Congresses.; Simulation methods -- Congresses.",
}
@Proceedings{Calmet:1994:RWC,
editor = "Jacques Calmet",
booktitle = "{Rhine Workshop on Computer Algebra. Proceedings}",
title = "{Rhine Workshop on Computer Algebra. Proceedings}",
publisher = "University of Karlsruhe",
address = "Karlsruhe, Germany",
pages = "v + 224",
year = "1994",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 10:35:47 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "22-24 March 1994",
conflocation = "Karlsruhe, Germany",
confsponsor = "University of Karlsruhe",
pubcountry = "Germany",
}
@Proceedings{Cappello:1994:PIC,
editor = "P. Cappello and R. M. Owens and E. E. {Swartzlander,
Jr.} and B. W. Wah",
booktitle = "Proceedings. The International Conference on
Application Specific Array Processors",
title = "Proceedings. The International Conference on
Application Specific Array Processors",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 452",
year = "1994",
ISBN = "0-8186-6517-3",
ISBN-13 = "978-0-8186-6517-2",
LCCN = "????",
bibdate = "Sat Nov 29 10:43:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 94TH0687-4.",
acknowledgement = ack-nhfb,
confdate = "22-24 Aug. 1994",
conflocation = "San Francisco, CA, USA",
confsponsor = "IEEE Comput. Soc. Tech. Committee on VLSI",
}
@Proceedings{Echtle:1994:PFI,
editor = "K. Echtle and D. Hammer and D. Powell",
booktitle = "Dependable Computing --- {EDCC-1}. First European
Dependable Computing Conference Proceedings",
title = "Dependable Computing --- {EDCC}-1. First European
Dependable Computing Conference Proceedings",
volume = "852",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvii + 618",
year = "1994",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/3-540-58426-9",
ISBN = "3-540-58426-9",
ISBN-13 = "978-3-540-58426-1",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "????",
bibdate = "Sat Nov 29 10:29:16 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = j-LECT-NOTES-COMP-SCI,
acknowledgement = ack-nhfb,
confdate = "4-6 Oct. 1994",
conflocation = "Berlin, Germany",
pubcountry = "Germany",
}
@Proceedings{Gautschi:1994:MCH,
editor = "Walter Gautschi",
booktitle = "{Mathematics of computation, 1943--1993: a
half-century of computational mathematics: Mathematics
of Computation 50th Anniversary Symposium, August
9--13, 1993, Vancouver, British Columbia}",
title = "{Mathematics of computation, 1943--1993: a
half-century of computational mathematics: Mathematics
of Computation 50th Anniversary Symposium, August
9--13, 1993, Vancouver, British Columbia}",
volume = "48",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xix + 643",
year = "1994",
ISBN = "0-8218-0291-7, 0-8218-0353-0 (pt. 1), 0-8218-0354-9
(pt. 2)",
ISBN-13 = "978-0-8218-0291-5, 978-0-8218-0353-0 (pt. 1),
978-0-8218-0354-7 (pt. 2)",
ISSN = "0160-7634",
LCCN = "QA1 .A56 v.48 1994; QA297.M385 1993",
MRclass = "00B25 (11-06 65-06)",
MRnumber = "95j:00014",
bibdate = "Mon Oct 24 11:37:20 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib;
https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1940.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
note = "See also SIAM Review, September 1995, {\bf 37}(3), p.
483.",
series = "Proceedings of Symposia in Applied Mathematics",
acknowledgement = ack-nhfb,
author-dates = "Frank William John Olver (15 December 1924--23 April
2013)",
tableofcontents = "Preface / xi \\
Mathematics of Computation: A brief history / Eugene
Isaacson / xvii \\
\\
Part I. Symposium on Numerical Analysis \\
\\
Invited Papers \\
\\
On the development of multigrid methods and their
analysis / James H. Bramble / 5 \\
An introduction to inverse problems / Margaret Cheney /
21 \\
Algorithms for unconstrained optimization: A review of
recent developments / Donald Goldfarb / 33 \\
A survey of componentwise perturbation theory in
numerical linear algebra / Nicholas J. Higham / 49 \\
Numerical evaluation of special functions / D. W.
Lozier and F. W. J. Olver / 79 \\
A survey of numerical cubature over triangles / J. N.
Lyness and Ronald Cools / 127 \\
New trends in the use and analysis of integral
equations / J. C. Nedelec / 151 \\
Applications of multivariate splines / Larry L.
Schumaker / 177 \\
Initial value problems for ordinary differential
equations: Development of ideas, techniques, and
implementation / Hans J. Stetter / 205 \\
Multiresolution methods for partial differential
equations / Roger Temam / 225 \\
\\
Contributed Papers \\
\\
A comparison of techniques for solving ill-conditioned
problems arising from the immersed boundary method /
Loyce Adams and Zhiyun Yang / 243 \\
A mixed spectral-collocation and operator splitting
method for the Wigner-Poisson equation / Anton Arnold /
249 \\
Finite volume methods for irregular one-dimensional
grids / M. J. Berger, R. J. Leveque, and L. G. Stern /
255 \\
Linear rational interpolation of continuous functions
over an interval / Jean-Paul Berrut / 261 \\
A von Neumann reflection for the 2-D Burgers equation /
M. Brio and J. K. Hunter / 265 \\
Slow evolution from the boundary: A new stabilizing
constraint in ill-posed continuation problems / Alfred
S. Carasso / 269 \\
A finite element method for the 2D drift-diffusion
semiconductor model / Zhangxin Chen / 275 \\
Splitting functions and numerical analysis of WR-type
methods for evolutionary and stationary problems / S.
De Marchi, M. Vianello, and R. Zanovello / 281 \\
Error estimates for a quadrature rule for Cauchy
principal value integrals / Kai Diethelm / 287 \\
A numerical radius approach to stable difference
schemes for parabolic systems / Moshe Goldberg / 293
\\
An extension of the Olver-Sookne method for the
solution of second-order linear difference equations /
Takemitsu Hasegawa and Tatsuo Torii / 297 \\
The Faber polynomials for circular arcs / Matthew He /
301 \\
Finite element approximation for optimal control of
electrically conducting fluid flows / L. S. Hou and S.
S. Ravindran / 305 \\
ADI methods for heat equations with discontinuities
along an arbitrary interface / Zhilin Li and Anita Mayo
/ 311 \\
Eigenvalue approximation of Fredholm integral operators
/ E. B. Lin / 317 \\
Spectral methods for singular perturbation problems /
Wenbin Liu and Tao Tang / 323 \\
A quaternion-Jacobi method for symmetric matrices /
Niloufer Mackey / 327 \\
On constructing Chebyshev series solutions of
differential equations / Allan J. MacLeod / 333 \\
Multiquadric collocation methods in the numerical
solution of Volterra integral and integro-differential
equations / Athena Makroglou / 337 \\
Methods for solving large eigenvalue problems
associated with configuration interaction electronic
structure calculations / Kristyn J. Maschhoff / 343 \\
Computing limiting normals to real surfaces / Donal
O'Shea and Les Wilson / 349 \\
Orthogonal spline collocation solution of nonlinear
Schr{\"o}dinger equations / Mark P. Robinson / 355 \\
Who invented the computer? The debate from the
viewpoint of computer architecture / Ra{\'u}l Rojas /
361 \\
Locking and boundary layer effects in the finite
element approximation of the Reissner--Mindlin plate
model / Christoph Schwab and Manil Suri / 367 \\
Efficient spectral Galerkin methods for some elliptic
problems / Jie Shen / 373 \\
Periodic solutions of higher-order difference equations
in two independent variables / Qin Sheng and Ravi P.
Agarwal / 377 \\
Front tracking based on high-resolution wave
propagation methods / Keh-Ming Shyue / 383 \\
Time-splitting methods for nonhomogeneous conservation
laws / Tao Tang and Zhen-Huan Teng / 389 \\
Numerical aspects of uniform Airy-type asymptotic
expansions / N. M. Temme / 395 \\
Local dynamics and bifurcation consistencies of
continuous-time dynamical systems and their numerical
discretizations / Xin Wang, Edward K. Blum, and Qingnan
Li / 399 \\
Computing integrals of the complex error function / J.
A. C. Weideman / 403 \\
Quadratures for improper integrals and their
applications in integral equations / Yuesheng Xu and
Yunhe Zhao / 409 \\
Spline harmonic analysis and wavelet bases / Valery A.
Zheludev / 415 \\
\\
Part II. Minisymposium on Computational Number Theory
Dedicated to the memory of Derrick Henry Lehmer \\
\\
Invited Papers \\
\\
Algorithms for quadratic orders / Ingrid Biehl and
Johannes Buchmann / 425 \\
Analytic computations in number theory / Andrew M.
Odlyzko / 451 \\
The number field sieve / Carl Pomerance / 465 \\
Factoring integers before computers / H. C. Williams
and J. O. Shallit / 481 \\
\\
Contributed Papers \\
\\
Explicit bounds for primes in residue classes / Eric
Bach and Jonathan Sorenson / 535 \\
Ramanujan and Euler's constant / Richard P. Brent / 541
\\
Congruential sieves on FPGA computers / Nathan D.
Bronson and Duncan A. Buell / 547 \\
Lehmer pairs of zeros and the Riemann $\xi$-function /
George Csordas, Wayne Smith, and Richard S. Varga / 553
\\
A record Aliquot sequence / Andrew W. P. Guy and
Richard K. Guy / 557 \\
Implications of computational mathematics for the
philosophy of mathematics / Andrew J. Lazarus / 561 \\
Square roots of products of algebraic numbers / Peter
L. Montgomery / 567 \\
A locally parameterized version of Lehmer's problem /
Gary A. Ray / 573 \\
A new method for finding amicable pairs / H. J. J. te
Riele / 577 \\
Generalized Fermat numbers / Hans Riesel and Anders
Bj{\"o}rn / 583 \\
Evaluation of $\zeta_K(2)$ for some totally real
algebraic number fields K of degree 9 / Kisao Takeuchi
/ 589 \\
The period of the Bell exponential integers modulo a
prime / Samuel S. Wagstaff, Jr. / 595 \\
Computing invariant polynomials of $p$-adic reflection
groups / Changsheng Xu / 599 \\
Author Index / 603 \\
Subject Index / 619",
}
@Proceedings{IEEE:1994:PFI,
editor = "{IEEE}",
booktitle = "Proceedings of the First International Conference on
Massively Parallel Computing Systems {(MPCS)}. The
Challenges of General-Purpose and Special-Purpose
Computing",
title = "Proceedings of the First International Conference on
Massively Parallel Computing Systems ({MPCS}). The
Challenges of General-Purpose and Special-Purpose
Computing",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 655",
year = "1994",
ISBN = "0-8186-6322-7",
ISBN-13 = "978-0-8186-6322-2",
LCCN = "????",
bibdate = "Sat Nov 29 10:25:52 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "2-6 May 1994",
conflocation = "Ischia, Italy",
}
@Proceedings{IEEE:1994:PTA,
editor = "{IEEE}",
booktitle = "Proceedings of the Third Asian Test Symposium",
title = "Proceedings of the Third Asian Test Symposium",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 392",
year = "1994",
ISBN = "0-8186-6690-0",
ISBN-13 = "978-0-8186-6690-2",
LCCN = "????",
bibdate = "Sat Nov 29 10:41:40 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 94TH8016.",
acknowledgement = ack-nhfb,
confdate = "15-17 Nov. 1994",
conflocation = "Nara, Japan",
confsponsor = "IEEE Comput. Soc. Test Technol. Tech. Committee; Tech.
Group on Fault Tolerant Syst. IEICE; Tech. Group on
VLSI Design Technol., IEICE; Special Interest Group on
Design Autom., IPS Japan; Japan Soc. Promotion of Sci.;
132nd Committee (Electron. and Ion Beam Sci. and
Technol.); Nara Inst. Sci. and Technol",
}
@Proceedings{Lea:1994:PSA,
editor = "R. M. Lea and S. Tewksbury",
booktitle = "1994 Proceedings. Sixth Annual {IEEE} International
Conference on Wafer Scale Integration",
title = "1994 Proceedings. Sixth Annual {IEEE} International
Conference on Wafer Scale Integration",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "ix + 404",
year = "1994",
ISBN = "0-7803-1850-1",
ISBN-13 = "978-0-7803-1850-2",
LCCN = "????",
bibdate = "Sat Nov 29 10:45:27 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 94CH3412-4.",
acknowledgement = ack-nhfb,
confdate = "19-21 Jan. 1994",
conflocation = "San Francisco, CA, USA",
confsponsor = "IEEE",
}
@Proceedings{Mudge:1994:PTS,
editor = "T. N. Mudge and B. D. Shriver",
booktitle = "Proceedings of the Twenty-Seventh Hawaii Internation
Conference on System Sciences Vol. I: Architecture",
title = "Proceedings of the Twenty-Seventh Hawaii Internation
Conference on System Sciences Vol. {I}: Architecture",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 621",
year = "1994",
ISBN = "0-8186-5050-8",
ISBN-13 = "978-0-8186-5050-5",
LCCN = "????",
bibdate = "Sat Nov 29 10:39:37 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 94TH0607-2.",
acknowledgement = ack-nhfb,
confdate = "4-7 Jan. 1994",
conflocation = "Wailea, HI, USA",
confsponsor = "IEEE; ACM; University of Hawaii; University of Hawaii
Coll. Bus. Admin",
}
@Proceedings{Pehrson:1994:IPP,
editor = "Bj{\"o}rn Pehrson and Imre Simon",
booktitle = "{Information processing '94: proceedings of the IFIP
13th World Computer Congress, Hamburg, Germany, 28
August--2 September, 1994: Technology and foundations:
Applications and impacts: Linkage and developing
countries}",
title = "{Information processing '94: proceedings of the IFIP
13th World Computer Congress, Hamburg, Germany, 28
August--2 September, 1994: Technology and foundations:
Applications and impacts: Linkage and developing
countries}",
volume = "A51--A53",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "????",
year = "1994",
ISBN = "0-444-81990-8 (set)",
ISBN-13 = "978-0-444-81990-1 (set)",
LCCN = "QA75.5 .I3785 1994",
bibdate = "Tue Nov 13 22:41:40 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "IFIP transactions. A, Computer science and
technology",
acknowledgement = ack-nhfb,
meetingname = "IFIP World Computer Congress (13th: 1994: Hamburg,
Germany)",
remark = "v. 1 Technology and foundations / edited by Bj{\"o}rn
Pehrson, Imre Simon\\
v. 2. Applications and impacts / edited by Klaus
Brunnstein, Eckart Raubold \\
v. 3. Linkage and developing countries / edited by
Karen Duncan, Karl Krueger.",
subject = "Computer industry; Developing countries; Congresses;
Information technology; Electronic data processing",
}
@Proceedings{Wuorinen:1994:IIS,
editor = "John H. Wuorinen and others",
booktitle = "{1994 IEEE International Solid-State Circuits
Conference Digest of Technical Papers}",
title = "{1994 IEEE International Solid-State Circuits
Conference Digest of Technical Papers}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "400",
year = "1994",
ISBN = "0-7803-1844-7, 0-7803-1845-5, 0-7803-1846-3
(microfiche)",
ISBN-13 = "978-0-7803-1844-1, 978-0-7803-1845-8,
978-0-7803-1846-5 (microfiche)",
LCCN = "TK 7867 1994",
bibdate = "Sat Nov 29 10:30:52 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 94CH3410-8.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=1111",
acknowledgement = ack-nhfb,
confdate = "16-18 Feb. 1994",
conflocation = "San Francisco, CA, USA",
confsponsor = "IEEE Solid-State Circuits Council; IEEE Bay Area
Council San Francisco Sect",
}
@Proceedings{ACM:1995:PEA,
editor = "{ACM}",
booktitle = "{Proceedings of the Eleventh Annual Symposium on
Computational Geometry: Vancouver, British Columbia,
Canada, June 5--7, 1995}",
title = "{Proceedings of the Eleventh Annual Symposium on
Computational Geometry: Vancouver, British Columbia,
Canada, June 5--7, 1995}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 389 + 51",
year = "1995",
ISBN = "0-89791-724-3",
ISBN-13 = "978-0-89791-724-7",
LCCN = "QA448.D38 S96 1995",
bibdate = "Tue Nov 13 22:49:06 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "Symposium on Computational Geometry (11th: 1995:
Vancouver, BC)",
subject = "Geometry; Data processing; Congresses",
}
@Proceedings{Anonymous:1995:HEI,
editor = "Anonymous",
booktitle = "{HOL95}: Eighth International Workshop on Higher-Order
Logic Theorem Proving and Its Applications, Aspen
Grove, {UT}, September 1995",
title = "{HOL95}: Eighth International Workshop on Higher-Order
Logic Theorem Proving and Its Applications, Aspen
Grove, {UT}, September 1995",
publisher = "Brigham Young University",
address = "Provo, UT, USA",
year = "1995",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 10:48:53 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://lal.cs.byu.edu/lal/hol95/Bprocs/indexB.html",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Proceedings{Athanas:1995:PIS,
editor = "Peter Athanas and Kenneth L. Pocek",
booktitle = "{Proceedings: IEEE Symposium on FPGAs for Custom
Computing Machines, April 19--21, 1995, Napa Valley,
California}",
title = "{Proceedings: IEEE Symposium on FPGAs for Custom
Computing Machines, April 19--21, 1995, Napa Valley,
California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "viii + 222",
year = "1995",
DOI = "https://doi.org/10.1109/FPGA.1995.477402",
ISBN = "0-8186-7086-X",
ISBN-13 = "978-0-8186-7086-2",
LCCN = "TK79.85 G36 I36 1995",
bibdate = "Sat Oct 9 15:10:55 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "field programmable gate arrays; congresses; computer
engineering",
tableofcontents = "A FCCM for Dataflow (Spreadsheet) Programs / A. Lew
and R. Halverson \\
MORRPH: A MOdular and Reprogrammable Real-time
Processing Hardware / T. H. Drayer, W. E. King, J. G.
Tront and R. W. Conners \\
Architecture of a FPGA-based Coprocessor: The PAR-1 /
J. M. Carrera, E. J. Martinez, S. A. Fernandez and J.
M. M. Chaus \\
Teramac - Configurable Custom Computing / R. Amerson,
R. J. Carter, W. B. Culbertson, P. Kuekes and G. Snider
\\
Common Processor Element Packaging for CHAMP / B. Box
and J. Nieznanski \\
Enable++: A Second Generation FPGA Processor / H. Hogl,
A. Kugel, J. Ludvig, R. Manner, K. H. Noffz and R. Zoz
\\
Design and Implementation of a Multicomputer
Interconnection Network Using FPGAs / C.-C. Yeh, C.-H.
Wu and J.-Y. Juang \\
Routability Improvement Using Dynamic Interconnect
Architecture / J. Li and C.-K. Cheng \\
Reconfigurable Real-Time Signal Transport System Using
Custom FPGAs / K. Hayashi, T. Miyazaki, K. Shirakawa,
K. Yamada and N. Ohta.",
}
@Proceedings{Bainov:1995:PTI,
editor = "D. (Dimitur) Bainov and Valery Covachev",
booktitle = "Proceedings of the Third International Colloquium on
Numerical Analysis: Plovdiv, Bulgaria, 13--17 August
1994",
title = "Proceedings of the Third International Colloquium on
Numerical Analysis: Plovdiv, Bulgaria, 13--17 August
1994",
publisher = "VSP",
address = "Utrecht, The Netherlands",
pages = "vi + 229",
year = "1995",
ISBN = "90-6764-193-6",
ISBN-13 = "978-90-6764-193-7",
LCCN = "QA297.I45 1994",
bibdate = "Sat Nov 29 10:53:15 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Cappello:1995:ICA,
editor = "Peter Cappello and Catherine Mongenet and Guy-Ren{\'e}
Perrin and Patrice Quinton and Yves Robert",
booktitle = "The International Conference on Application Specific
Array Processors: July 24--26, 1995, Strasbourg,
France: proceedings",
title = "The International Conference on Application Specific
Array Processors: July 24--26, 1995, Strasbourg,
France: proceedings",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 340",
year = "1995",
ISBN = "0-8186-7109-2",
ISBN-13 = "978-0-8186-7109-8",
ISSN = "1063-6862",
LCCN = "TK7874.6 .I57 1995",
bibdate = "Mon Oct 20 07:16:07 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society Press order number PR07109. EEE
catalog number 95TB8098.",
acknowledgement = ack-nhfb,
searchkey = "ti:interval computations or ti:interval arithmetic",
sponsor = "IEEE. Computer Society. Technical Committee on VLSI.",
}
@Proceedings{IEEE:1995:DPC,
editor = "{IEEE}",
booktitle = "{Digest of papers: Compcon '95: technologies for the
information superhighway: March 5--9, 1995, San
Francisco, CA, USA}",
title = "{Digest of papers: Compcon '95: technologies for the
information superhighway: March 5--9, 1995, San
Francisco, CA, USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 491",
year = "1995",
ISBN = "0-7803-2657-1 (hardcover), 0-8186-7029-0 (paperback),
0-7803-2658-X (microfiche)",
ISBN-13 = "978-0-7803-2657-6 (hardcover), 978-0-8186-7029-9
(paperback), 978-0-7803-2658-3 (microfiche)",
ISSN = "1063-6390",
LCCN = "QA 75.5 C58 1995",
bibdate = "Mon Aug 26 10:38:41 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society Press order number PR07029. IEEE
catalog number 95CH35737.",
acknowledgement = ack-nhfb,
sponsor = "IEEE; Computer Society.",
}
@Proceedings{IEEE:1995:IAI,
editor = "{IEEE}",
booktitle = "1995 {IEEE\slash} {ACM} International Conference on
Computer-Aided Design: digest of technical papers;
November 5--9, 1995, San Jose, California",
title = "1995 {IEEE}\slash {ACM} International Conference on
Computer-Aided Design: digest of technical papers;
November 5--9, 1995, San Jose, California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxviii + 743",
year = "1995",
ISBN = "0-8186-7213-7, 0-8186-7214-5",
ISBN-13 = "978-0-8186-7213-2, 978-0-8186-7214-9",
LCCN = "TA174 .I52 1995; TK7874 .I3235 1995",
bibdate = "Sat Nov 29 10:46:57 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 95CB35859. IEEE Computer Society
Press order number PR07213.",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1995:ISM,
editor = "{IEEE}",
booktitle = "{5th International Symposium on Multiple-Valued Logic,
Bloomington, Indiana, May 23--25, 1995: Proceedings}",
title = "{5th International Symposium on Multiple-Valued Logic,
Bloomington, Indiana, May 23--25, 1995: Proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 296",
year = "1995",
ISBN = "0-8186-7118-1, 0-7803-2764-0, 0-7803-2765-9",
ISBN-13 = "978-0-8186-7118-0, 978-0-7803-2764-1,
978-0-7803-2765-8",
LCCN = "????",
bibdate = "Sat Aug 22 08:44:56 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.bibsys.no:2100/BIBSYS",
acknowledgement = ack-nhfb,
}
@Proceedings{Jain:1995:PET,
editor = "L. C. Jain",
booktitle = "Proceedings. Electronic Technology Directions to the
Year 2000",
title = "Proceedings. Electronic Technology Directions to the
Year 2000",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 313",
year = "1995",
ISBN = "0-8186-7085-1",
ISBN-13 = "978-0-8186-7085-5",
LCCN = "TK7801 .E456 1995",
bibdate = "Sat Nov 29 10:51:35 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
confdate = "23-25 May 1995",
conflocation = "Adelaide, SA, Australia",
confsponsor = "Electron. Assoc. South Australia; Defence Sci. and
Technol. Organ. Australia; MFP Australia; Telecom
Australia; Knowledge-Based Eng. Syst. Group, University
of South Australia; IEEE South Australia Section; Inst.
Eng., Australia; Security Inst. South Australia; IEEE
Comput. Soc",
}
@Proceedings{Knowles:1995:PSC,
editor = "Simon Knowles and William H. McAllister",
booktitle = "{Proceedings of the 12th Symposium on Computer
Arithmetic, July 19--21, 1995, Bath, England}",
title = "{Proceedings of the 12th Symposium on Computer
Arithmetic, July 19--21, 1995, Bath, England}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvi + 252",
year = "1995",
ISBN = "0-8186-7089-4 (paperback), 0-8186-7089-4 (case),
0-8186-7149-1 (microfiche), 0-8186-7089-4 (softbound),
0-7803-2949-X (casebound)",
ISBN-13 = "978-0-8186-7089-3 (paperback), 978-0-8186-7089-3
(case), 978-0-8186-7149-4 (microfiche),
978-0-8186-7089-3 (softbound), 978-0-7803-2949-2
(casebound)",
LCCN = "QA 76.9 C62 S95 1995",
bibdate = "Sun Mar 29 08:48:20 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/xpl/conhome/3236/proceeding",
acknowledgement = ack-nhfb,
keywords = "ARITH-12",
}
@Proceedings{Seck:1995:GWS,
editor = "Friedrich Seck",
booktitle = "{Zum 400. Geburtstag von Wilhelm Schickard: Zweites
T{\"u}binger Schickard-Symposion, 25. bis 27. Juni
1992}. ({German}) [{On} the 400th Birthday of {Wilhelm
Schickard}: {Second Tubingen Schickard Symposium,
25--27 June 1992}]",
title = "{Zum 400. Geburtstag von Wilhelm Schickard: Zweites
T{\"u}binger Schickard-Symposion, 25. bis 27. Juni
1992}. ({German}) [{On} the 400th Birthday of {Wilhelm
Schickard}: {Second Tubingen Schickard Symposium,
25--27 June 1992}]",
volume = "41",
publisher = "Thorbecke",
address = "Sigmaringen, Germany",
pages = "319",
year = "1995",
ISBN = "3-7995-3235-8",
ISBN-13 = "978-3-7995-3235-8",
ISSN = "0340-6857",
ISSN-L = "0340-6857",
LCCN = "????",
bibdate = "Sat Jul 27 11:09:25 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/scicontext.bib;
z3950.gbv.de:20011/gvk",
price = "DM 76.00, sfr 76.00, S 600.00",
series = "Contubernium",
acknowledgement = ack-nhfb,
language = "German",
subject = "Schickard, Wilhelm",
subject-dates = "1592--1635",
tableofcontents = "Vorwort / 7 \\
Volker Sch{\"a}fer / Die Universit{\"a}t T{\"u}bingen
zur Zeit Schickards / 9 \\
Fran{\c{c}}ois-Joseph Fuchs / Matthias Bernegger und
die Anfange der Universit{\"a}t Stra{\ss}burg / 27 \\
Wilhelm K{\"u}hlmann / Wilhelm Schickard ---
Wissenschaft und Reformbegehren in der Zeit des
Konfessionalismus / 41 \\
Ulrich Bubenheimer / Wilhelm Schickard im Kontext einer
religi{\"o}sen Subkultur / 67 \\
Ulrich Neumann / ``Olim, da die Rosen Creutzerey noch
florirt, Theophilus Schweighart genant'': Wilhelm
Schickards Freund und Briefpartner Daniel M{\"o}gling
(1596--1635) / 93 \\
Claudia Ott / Schickard als Orientalist --- verkanntes
Genie oder interessierter Laie? / 117 \\
Wolfgang H{\"u}bner / Die Christianisierung der
Sternbilder in Schickards \booktitle{Astroscopium} \\
Horst Mauder / Die Kometenschriften von Schickard und
Kepler / 131 \\
Owen Gingerich / M{\"a}stlin's, Kepler's, and
Schickard's Copies of \booktitle{De revolutionibus} /
167 \\
Gerhard Betsch / Praxis geometrica und Kartographie an
der Universit{\"a}t T{\"u}bingen im 16 und fr{\"u}hen
17 Jahrhundert / 185 \\
G{\"u}nther Oestmann / Aus Wilhelm Schickards
\booktitle{Stuttgarter Skizzenbuch} / 227 \\
Friedrich Wilhelm Kistermann / Die Rechentechnik um
1600 und Wilhelm Schickards Rechenmaschine / 241 \\
N. Joachim Lehmann / Schickard und Leibniz als Erfinder
von Rechenmaschinen / 273 \\
Bruno Baron v. Freytag L{\"o}ringhoff / Zu Irrungen und
Verwirrungen um Wilhelm Schickard und seine /
Rechenmaschine von 1623 --- Ein Satyrspiel / 287 \\
Friedrich Seck / Zur Edition von Schickards
Briefwechsel / 297 \\
Anhang: Wilhelm Schickard und der N{\"u}rnberger
Trichter / 310 \\
Personenregister / 313",
}
@Proceedings{Singh:1995:CRT,
editor = "Avtar Singh",
booktitle = "Conference record of the Twenty-Ninth Asilomar
Conference on Signals, Systems \& Computers: October
30--November 1, 1995 Pacific Grove, California",
title = "Conference record of the Twenty-Ninth Asilomar
Conference on Signals, Systems \& Computers: October
30--November 1, 1995 Pacific Grove, California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "various",
year = "1995",
ISBN = "0-8186-7370-2",
ISBN-13 = "978-0-8186-7370-2",
LCCN = "TK7801 .A83 1995",
bibdate = "Sun Mar 29 08:51:26 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{Alefeld:1996:NME,
editor = "G{\"o}tz Alefeld and J{\"u}rgen Herzberger",
booktitle = "Numerical methods and error bounds: proceedings of the
{IMACS GAMM International Symposium on Numerical
Methods and Error Bounds held in Oldenburg, Germany,
July 9--12, 1995}",
title = "Numerical methods and error bounds: proceedings of the
{IMACS GAMM International Symposium on Numerical
Methods and Error Bounds held in Oldenburg, Germany,
July 9--12, 1995}",
volume = "89",
publisher = pub-AKADEMIE-VERLAG,
address = pub-AKADEMIE-VERLAG:adr,
pages = "302",
year = "1996",
ISBN = "3-05-501696-3",
ISBN-13 = "978-3-05-501696-7",
ISSN = "0138-3019",
LCCN = "QA297 .I455 1995",
bibdate = "Tue Nov 02 18:36:50 1999",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Mathematical Research",
acknowledgement = ack-nhfb,
}
@Proceedings{Alefeld:1996:SCV,
editor = "G{\"o}tz Alefeld and Andreas Frommer and Bruno Lang",
booktitle = "Scientific computing and validated numerics:
proceedings of the International Symposium on
Scientific Computing, Computer Arithmetic and Validated
Numerics {SCAN-95} held in Wuppertal, Germany,
September 26--29, 1995",
title = "Scientific computing and validated numerics:
proceedings of the International Symposium on
Scientific Computing, Computer Arithmetic and Validated
Numerics {SCAN}-95 held in Wuppertal, Germany,
September 26--29, 1995",
volume = "90",
publisher = "Akademie Verlag",
address = "Berlin, Germany",
pages = "340",
year = "1996",
ISBN = "3-05-501737-4",
ISBN-13 = "978-3-05-501737-7",
ISSN = "0138-3019",
LCCN = "QA76.95 .I575 1995",
bibdate = "Fri Mar 27 09:56:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Mathematical Research",
acknowledgement = ack-nhfb,
}
@Book{Bergin:1996:HPL,
author = "Thomas J. {Bergin, Jr.} and Richard G. {Gibson, Jr.}",
booktitle = "History of Programming Languages {II}",
title = "History of Programming Languages {II}",
publisher = pub-ACM # " and " # pub-AW,
address = pub-ACM:adr # " and " # pub-AW:adr,
pages = "xvi + 864",
year = "1996",
ISBN = "0-201-89502-1",
ISBN-13 = "978-0-201-89502-5",
LCCN = "QA76.7 .H558 1996",
bibdate = "Wed Nov 19 08:49:59 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Drawn from the Second ACM SIGPLAN History of
Programming Languages Conference.",
acknowledgement = ack-nhfb,
}
@Proceedings{Bouge:1996:EPP,
editor = "L. (Luc) Bouge",
booktitle = "{Euro-Par'96}: parallel processing: second
International {Euro-Par} Conference, Lyon, France,
August 26--29, 1996: proceedings",
title = "{Euro-Par'96}: parallel processing: second
International {Euro-Par} Conference, Lyon, France,
August 26--29, 1996: proceedings",
volume = "1123, 1124",
publisher = pub-SV,
address = pub-SV:adr,
pages = "various",
year = "1996",
DOI = "https://doi.org/10.1007/3-540-61626-8;
https://doi.org/10.1007/BFb0024677",
ISBN = "3-540-61626-8 (vol. 1), 3-540-61627-6 (vol. 2)",
ISBN-13 = "978-3-540-61626-9 (vol. 1), 978-3-540-61627-6 (vol.
2)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.58.I554 1996",
bibdate = "Sat Sep 7 08:18:27 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "Parallel processing (Electronic computers) ---
Congresses.",
}
@Book{Hennessy:1996:CAQ,
author = "John L. Hennessy and David A. Patterson",
booktitle = "Computer Architecture\emdash {A} Quantitative
Approach",
title = "Computer Architecture\emdash {A} Quantitative
Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
edition = "Second",
pages = "xxiii + 760 + A-77 + B-47 + C-26 + D-26 + E-13 + R-16
+ I-14",
year = "1996",
ISBN = "1-55860-329-8",
ISBN-13 = "978-1-55860-329-5",
LCCN = "QA76.9.A73P377 1995",
bibdate = "Mon May 20 10:01:59 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$69.95",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1996:DAC,
editor = "{IEEE}",
booktitle = "33rd Design Automation Conference: proceedings 1996,
Las Vegas Convention Center, Las Vegas, {NV}, June
3--7, 1996",
title = "33rd Design Automation Conference: proceedings 1996,
Las Vegas Convention Center, Las Vegas, {NV}, June
3--7, 1996",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxx + 839",
year = "1996",
ISBN = "0-7803-3294-6 (casebound), 0-7803-3364-0 (softbound),
0-7803-3295-4 (microfiche), 0-89791-779-0 (ACM)",
ISBN-13 = "978-0-7803-3294-2 (casebound), 978-0-7803-3364-2
(softbound), 978-0-7803-3295-9 (microfiche),
978-0-89791-779-7 (ACM)",
LCCN = "TA174 .D46 1996",
bibdate = "Sat Nov 29 10:54:23 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 47796. IEEE catalog number
96CH35932.",
acknowledgement = ack-nhfb,
}
@Proceedings{Kearfott:1996:AICa,
editor = "R. Baker Kearfott and Vladik Kreinovich",
booktitle = "Applications of interval computations: Papers
presented at an international workshop in El Paso,
Texas, February 23--25, 1995",
title = "Applications of interval computations: Papers
presented at an international workshop in El Paso,
Texas, February 23--25, 1995",
volume = "3",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "xvii + 425",
year = "1996",
ISBN = "0-7923-3847-2",
ISBN-13 = "978-0-7923-3847-5",
LCCN = "QA297.75.A66 1996",
bibdate = "Mon Oct 20 07:16:07 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "``Applications of Interval Computations'' contains
primarily survey articles of actual industrial
applications of numerical analysis with automatic
result verification and of interval representation of
data.
Underlying topics include: \begin{itemize} \item branch
and bound algorithms for global optimization, \item
constraint propagation, \item solution sets of linear
systems, \item hardware and software systems for
interval computations, and \item fuzzy logic.
\end{itemize}
Actual applications described in the book include:
\begin{itemize} \item economic input-output models,
\item quality control in manufacturing design, \item a
computer-assisted proof in quantum mechanics, \item
medical expert systems, \item and others.
\end{itemize}
A realistic view of interval computations is taken: the
articles indicate when and how overestimation and other
challenges can be overcome.
An introductory chapter explains the content of the
papers in terminology accessible to mathematically
literate graduate students. The style of the
individual, refereed contributions has been made
uniform and understandable, and there is an extensive
book-wide index.
Audience: Valuable to students and researchers
interested in automatic result verification.
Detailed information, including contents, contributors,
and an order form can be found: \begin{itemize} \item
on Kluwer homepage \path=http://www.wkap.nl=, or \item
on the Interval Computations homepage
\path=http://cs.utep.edu/interval-comp/main.html=, in
the ``Books'' section. \end{itemize} The information on
the Interval Computations homepage is basically a
mirror image of the Kluwer one (the only difference is
that the fonts are fancier).",
series = "Applied Optimization",
acknowledgement = ack-nhfb # " and " # ack-dgh,
}
@Proceedings{LakshmanYN:1996:IPI,
editor = "{Lakshman Y.N.}",
booktitle = "{ISSAC '96: Proceedings of the 1996 International
Symposium on Symbolic and Algebraic Computation, July
24--26, 1996, Zurich, Switzerland}",
title = "{ISSAC '96: Proceedings of the 1996 International
Symposium on Symbolic and Algebraic Computation, July
24--26, 1996, Zurich, Switzerland}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xvii + 313",
year = "1996",
ISBN = "0-89791-796-0",
ISBN-13 = "978-0-89791-796-4",
LCCN = "QA 76.95 I59 1996",
bibdate = "Thu Mar 12 08:00:14 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
sponsor = "ACM; Special Interest Group in Symbolic and Algebraic
Manipulation (SIGSAM). ACM; Special Interest Group on
Numerical Mathematics (SIGNUM).",
}
@Proceedings{Luk:1996:PSC,
editor = "Franklin T. Luk",
booktitle = "{Proceedings of the 1996 SPIE Conference on Advanced
Signal Processing Algorithms, Architectures, and
Implementations VI, 6--8 August, 1996, Denver,
Colorado}",
title = "{Proceedings of the 1996 SPIE Conference on Advanced
Signal Processing Algorithms, Architectures, and
Implementations VI, 6--8 August, 1996, Denver,
Colorado}",
volume = "2846",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "vii + 464",
year = "1996",
ISBN = "0-8194-2234-7",
ISBN-13 = "978-0-8194-2234-7",
LCCN = "????",
bibdate = "Tue Jun 14 18:19:43 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://spiedigitallibrary.org/proceedings/resource/2/psisdg/2846/1",
acknowledgement = ack-nhfb,
}
@Proceedings{Pellikaan:1996:AGC,
editor = "R. Pellikaan and M. Perret and S. G. Vladut",
booktitle = "Arithmetic, geometry, and coding theory: proceedings
of the international conference held at Centre
international de rencontres math{\'e}matiques {(CIRM),
Luminy, France, June 28--July 2, 1993}",
title = "Arithmetic, geometry, and coding theory: proceedings
of the international conference held at Centre
international de rencontres math{\'e}matiques {(CIRM),
Luminy, France, June 28--July 2, 1993}",
publisher = pub-GRUYTER,
address = pub-GRUYTER:adr,
pages = "xii + 288",
year = "1996",
ISBN = "3-11-014616-9",
ISBN-13 = "978-3-11-014616-5",
LCCN = "QA268 .A75 1996",
bibdate = "Wed Jan 16 09:27:31 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "UK\pounds 102.45",
acknowledgement = ack-nhfb,
keywords = "coding theory --- congresses; geometry, algebraic ---
congresses; number theory --- congresses",
}
@Proceedings{Pocek:1996:ISF,
editor = "Kenneth L. Pocek and Jeffrey M. Arnold",
booktitle = "{IEEE Symposium on FPGAs for Custom Computing
Machines: proceedings, April 17--19, 1996, Napa Valley,
California}",
title = "{IEEE Symposium on FPGAs for Custom Computing
Machines: proceedings, April 17--19, 1996, Napa Valley,
California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "viii + 235",
year = "1996",
ISBN = "0-8186-7548-9",
ISBN-13 = "978-0-8186-7548-5",
LCCN = "TK7895.G36 I35 1996",
bibdate = "Sat Oct 9 15:15:32 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 96TB100063.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4230",
acknowledgement = ack-nhfb,
subject = "field programmable gate arrays; congresses; computer
engineering; compilers (computer programs)",
}
@Proceedings{Srivas:1996:FMC,
editor = "Mandayam Srivas and Albert Camilleri",
booktitle = "Formal methods in computer-aided design: first
international conference, {FMCAD} '96, Palo Alto, {CA},
{USA}, November 6--8, 1996: proceedings",
title = "Formal methods in computer-aided design: first
international conference, {FMCAD} '96, Palo Alto, {CA},
{USA}, November 6--8, 1996: proceedings",
volume = "1166",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 470",
year = "1996",
ISBN = "3-540-61937-2",
ISBN-13 = "978-3-540-61937-6",
LCCN = "TK7874.65 .F53 1996",
bibdate = "Thu Nov 25 10:43:33 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNCS,
acknowledgement = ack-nhfb,
meetingname = "FMCAD '96 (1996: Palo Alto, Calif.)",
subject = "Digital integrated circuits; Computer-aided design;
Congresses; Automatic theorem proving; Congresses;
Integrated circuits; Verification; Congresses; Computer
engineering; Computer-aided design; Congresses; Formal
methods (Computer science); Congresses",
}
@Proceedings{Wuorinen:1996:DTP,
editor = "John H. Wuorinen",
booktitle = "Digest of technical papers: 1996 {IEEE} International
Solid-State Circuits Conference. San Francisco Marriott
Hotel, February 6--7, 1996",
title = "Digest of technical papers: 1996 {IEEE} International
Solid-State Circuits Conference. San Francisco Marriott
Hotel, February 6--7, 1996",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "512",
year = "1996",
ISBN = "0-7803-3137-0 (casebound), 0-7803-3136-2 (softbound),
0-7803-3138-9 (microfiche)",
ISBN-13 = "978-0-7803-3137-2 (casebound), 978-0-7803-3136-5
(softbound), 978-0-7803-3138-9 (microfiche)",
LCCN = "TK7870 .I58 1996",
bibdate = "Sun Mar 29 08:45:04 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Book{Zachary:1996:ISP,
author = "Joseph Zachary",
booktitle = "Introduction to scientific programming: computational
problem solving using {Maple} and {C}",
title = "Introduction to scientific programming: computational
problem solving using {Maple} and {C}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxiv + 380",
year = "1996",
DOI = "https://doi.org/10.1007/978-1-4612-2366-5",
ISBN = "0-387-94630-6, 1-4612-7518-0 (print), 1-4612-2366-0
(electronic)",
ISBN-13 = "978-0-387-94630-6, 978-1-4612-7518-3 (print),
978-1-4612-2366-5 (electronic)",
LCCN = "QA76.6 .Z32 1996",
bibdate = "Tue Mar 25 09:08:38 1997",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
acknowledgement = ack-nhfb,
annote = "System requirements for accompanying computer disk:
Maple V Release 3 or 4; ANSI C compiler; Macintosh;
Unix or DOS computer capable of reading DOS-formatted
high-density diskettes.",
keywords = "C (Computer program language); Computer programming;
Maple (Computer file)",
}
@Proceedings{Boisvert:1997:QNS,
editor = "Ronald F. Boisvert",
booktitle = "The Quality of Numerical Software: Assessment and
Enhancement: Proceedings of the {IFIP} {TC2}\slash {WG}
2.5 Working Conference on the Quality of Numerical
Software, Oxford, United Kingdon, 8--12 July 1996",
title = "The Quality of Numerical Software: Assessment and
Enhancement: Proceedings of the {IFIP} {TC2}\slash {WG}
2.5 Working Conference on the Quality of Numerical
Software, Oxford, United Kingdon, 8--12 July 1996",
publisher = "Chapman Hall on behalf of IFIP",
address = "London",
year = "1997",
ISBN = "0-412-80530-8",
ISBN-13 = "978-0-412-80530-1",
bibdate = "Tue Jul 21 11:17:29 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Fargues:1997:CRT,
editor = "Monique P. Fargues and Ralph D. Hippenstiel",
booktitle = "{Conference record of the Thirty-First Asilomar
Conference on Signals, Systems \& Computers: November
2--5, 1997, Pacific Grove, California}",
title = "{Conference record of the Thirty-First Asilomar
Conference on Signals, Systems \& Computers: November
2--5, 1997, Pacific Grove, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxiii + 1749",
year = "1997",
ISBN = "0-8186-8316-3, 0-8186-8317-1 (casebound),
0-8186-8318-X (microfiche)",
ISBN-13 = "978-0-8186-8316-9, 978-0-8186-8317-6 (casebound),
978-0-8186-8318-3 (microfiche)",
LCCN = "TK454.2; TK 7885",
bibdate = "Sat Jun 25 06:57:59 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes. IEEE order plan catalog number
97CB36163.",
URL = "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/;
http://ieeexplore.ieee.org/servlet/opac?punumber=5559",
acknowledgement = ack-nhfb,
}
@Proceedings{Lang:1997:ISC,
editor = "Tomas Lang and Jean-Michel Muller and Naofumi Takagi",
booktitle = "13th {IEEE} Symposium on Computer Arithmetic:
proceedings, July 6--9, 1997, Asilomar, California,
{USA}",
title = "13th {IEEE} Symposium on Computer Arithmetic:
proceedings, July 6--9, 1997, Asilomar, California,
{USA}",
volume = "13",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 291",
year = "1997",
ISBN = "0-8186-7846-1, 0-8186-7847-X, 0-8186-7848-8",
ISBN-13 = "978-0-8186-7846-2, 978-0-8186-7847-9,
978-0-8186-7848-6",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 1997",
bibdate = "Fri Mar 27 09:56:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society order number PR07846. IEEE Order
Plan catalog number 97CB36091.",
series = "Symposium on Computer Arithmetic",
acknowledgement = ack-nhfb,
keywords = "ARITH-13",
sponsor = "IEEE.",
}
@Proceedings{Pocek:1997:PAI,
editor = "Kenneth L. Pocek and Jeffrey M. Arnold",
booktitle = "{Proceedings, the 6th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines, April
16--18, 1998, Napa Valley, California}",
title = "{Proceedings, the 6th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines, April
16--18, 1998, Napa Valley, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 250",
year = "1997",
DOI = "https://doi.org/10.1109/FPGA.1998.707875",
ISBN = "0-8186-8900-5, 0-8186-8902-1 (microfiche)",
ISBN-13 = "978-0-8186-8900-0, 978-0-8186-8902-4 (microfiche)",
ISSN = "1082-3409",
LCCN = "TK7895.G36 I36 1998",
bibdate = "Sat Oct 9 15:17:05 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society order number PR08159. IEEE order
plan catalog number 97TB100186.",
acknowledgement = ack-nhfb,
subject = "Field programmable gate arrays; Congresses; Computer
engineering",
xxnote = "IEEE Web Xplore site says 15--17 April, 1998.
Check??",
}
@Proceedings{Thiele:1997:IIC,
editor = "Lothar Thiele and Jose Fortes and Kees Vissers and
Valerie Taylor and Tobias Noll and J{\"u}rgen Teich",
booktitle = "{IEEE International Conference on Application-Specific
Systems, Architectures and Processors: proceedings,
July 14--16, 1997, Z{\"u}rich, Switzerland}",
title = "{IEEE International Conference on Application-Specific
Systems, Architectures and Processors: proceedings,
July 14--16, 1997, Z{\"u}rich, Switzerland}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 540",
year = "1997",
DOI = "https://doi.org/10.1109/ASAP.1997.606806",
ISBN = "0-8186-7959-X, 0-8186-7960-3, 0-8186-7958-1",
ISBN-13 = "978-0-8186-7959-9, 978-0-8186-7960-5,
978-0-8186-7958-2",
LCCN = "TK7874.6 .I57 1997",
bibdate = "Sun Mar 4 21:13:29 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Application-Specific
Systems, Architectures, and Processors (11th: 1997:
Z{\"u}rich, Switzerland)",
remark = "IEEE Computer Society Press order number PR07958. IEEE
catalog number 97TB100177",
subject = "Array processors; Congresses; Signal processing;
Digital techniques; Application-specific integrated
circuits",
}
@Proceedings{ACM:1998:AWJ,
editor = "{ACM}",
booktitle = "{ACM 1998} Workshop on Java for High-Performance
Network Computing",
title = "{ACM} 1998 Workshop on Java for High-Performance
Network Computing",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "1998",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Apr 27 10:40:59 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Possibly unpublished, except electronically.",
URL = "http://www.cs.ucsb.edu/conferences/java98/program.html",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1998:PNI,
editor = "Anonymous",
booktitle = "The Proceedings of the Ninth International Conference
on Signal Processing Applications \& Technology:
September 13--16, 1998, Toronto, Canada",
title = "The Proceedings of the Ninth International Conference
on Signal Processing Applications \& Technology:
September 13--16, 1998, Toronto, Canada",
publisher = pub-MILLER-FREEMAN,
address = pub-MILLER-FREEMAN:adr,
pages = "1622",
year = "1998",
LCCN = "TK5102.5",
bibdate = "Sat Nov 29 11:01:38 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
xxISBN = "none",
}
@Proceedings{Chesneaux:1998:PCR,
editor = "Jean-Marie Chesneaux and others",
booktitle = "Proceedings of the 3rd Conference on Real Numbers and
Computers {(RNC3), 27--29} Avril, 1998, Paris, France",
title = "Proceedings of the 3rd Conference on Real Numbers and
Computers ({RNC3}), 27--29 Avril, 1998, Paris, France",
publisher = "????",
address = "Paris, France",
pages = "229",
year = "1998",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Mar 13 10:37:17 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Troisi{\`e}me conf{\'e}rence Nombres R{\'e}els et
Ordinateurs",
}
@Proceedings{Gloor:1998:IPI,
editor = "Oliver Gloor",
booktitle = "{ISSAC 98}: Proceedings of the 1998 International
Symposium on Symbolic and Algebraic Computation, August
13--15, 1998, University of Rostock, Germany",
title = "{ISSAC 98}: Proceedings of the 1998 International
Symposium on Symbolic and Algebraic Computation, August
13--15, 1998, University of Rostock, Germany",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xxii + 327",
year = "1998",
ISBN = "1-58113-002-3",
ISBN-13 = "978-1-58113-002-7",
LCCN = "????",
bibdate = "Wed Sep 16 17:13:58 1998",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Holub:1998:ILW,
editor = "Jan Holub and Radislav Smid",
booktitle = "1st International On-Line Workshop on Dithering in
Measurement: Theory and Applications, Prague, Czech
Republic, March 1--31, 1998",
title = "1st International On-Line Workshop on Dithering in
Measurement: Theory and Applications, Prague, Czech
Republic, March 1--31, 1998",
publisher = "CTU FEE Department of Measurement and TUT Measurement
and Information Technology",
address = "Prague, Czech Republic and Tampere, Finland",
pages = "105",
year = "1998",
ISBN = "80-01-01806-7",
ISBN-13 = "978-80-01-01806-4",
LCCN = "????",
bibdate = "Sat Nov 29 10:57:48 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Huijsing:1998:EPE,
editor = "Johan H. Huijsing and Arthur H. M. van Roermund and
Herbert Grunbacher",
booktitle = "{ESSCIRC '98}: proceedings of the 24th European
Solid-State Circuits Conference, The Hague, The
Netherlands, 22--24, 1998: Challenges for the next
millennium",
title = "{ESSCIRC} '98: proceedings of the 24th European
Solid-State Circuits Conference, The Hague, The
Netherlands, 22--24, 1998: Challenges for the next
millennium",
publisher = "Editions Fronti{\`e}res",
address = "Paris, France",
pages = "xii + 514",
year = "1998",
ISBN = "2-86332-235-4",
ISBN-13 = "978-2-86332-235-2",
LCCN = "TK7871.85 .E887 1998",
bibdate = "Sat Nov 29 11:23:20 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1998:HCC,
editor = "{IEEE}",
booktitle = "Hot chips 10: conference record: August 16--18, 1998,
Memorial Auditorium, Stanford University, Palo Alto,
California",
title = "Hot chips 10: conference record: August 16--18, 1998,
Memorial Auditorium, Stanford University, Palo Alto,
California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "1998",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Mon Jan 08 05:06:55 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1998:IIC,
editor = "{IEEE}",
booktitle = "{1998 IEEE International Conference on Computer
Design: VLSI in Computers and Processors: October 5--7,
1998 Austin, Texas: Proceedings}",
title = "{1998 IEEE International Conference on Computer
Design: VLSI in Computers and Processors: October 5--7,
1998 Austin, Texas: Proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xix + 644",
year = "1998",
ISBN = "0-8186-9099-2, 0-7803-5198-3, 0-8186-9101-8",
ISBN-13 = "978-0-8186-9099-0, 978-0-7803-5198-1,
978-0-8186-9101-0",
LCCN = "????",
bibdate = "Sat Aug 22 08:28:30 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.bibsys.no:2100/BIBSYS",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1998:IOM,
editor = "{IEEE}",
booktitle = "Proceedings of the 24th {EUROMICRO} Conference,
V{\"a}ster{\aa}s, Sweden, August 25--27, 1998",
title = "Proceedings of the 24th {EUROMICRO} Conference,
{V}{\"a}ster{\aa}s, Sweden, August 25--27, 1998",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "1998",
ISBN = "0-8186-8646-4, 0-8186-8647-2 (casebound),
0-8186-8648-0 (microfiche)",
ISBN-13 = "978-0-8186-8646-7, 978-0-8186-8647-4 (casebound),
978-0-8186-8648-1 (microfiche)",
LCCN = "QA76.5 .S97 1998; QA 76.5 .E9 1998",
bibdate = "Sat Jun 25 07:18:07 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
sirsi.library.utoronto.ca:2200/UNICORN",
note = "Two volumes. IEEE Computer Society Order Number
PR08646.",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1998:PGL,
editor = "{IEEE}",
booktitle = "{Proceedings of the 8th Great Lakes Symposium on VLSI:
Hotel Acadiana, Lafayette, Louisiana, February 19--21,
1998}",
title = "{Proceedings of the 8th Great Lakes Symposium on VLSI:
Hotel Acadiana, Lafayette, Louisiana, February 19--21,
1998}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvi + 460",
year = "1998",
ISBN = "0-8186-8409-7, 0-8186-8411-9",
ISBN-13 = "978-0-8186-8409-8, 978-0-8186-8411-1",
LCCN = "TK7874 .G689 1998",
bibdate = "Mon Mar 5 15:59:16 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "Great Lakes Symposium on VLSI (8th: 1998: Lafayette,
La.)",
remark = "IEEE Computer Society Order Number PR08409. IEEE Order
Plan Catalog Number 98TB100222.",
subject = "Integrated circuits; Very large scale integration;
Design and construction; Congresses; Computer-aided
design",
}
@Proceedings{MacKay:1998:PCT,
editor = "Stephen A. MacKay and J. Howard Johnson",
booktitle = "Proceedings of {CASCON'98}: Toronto, Ontario, Canada,
30 November--3 December 1998",
title = "Proceedings of {CASCON}'98: Toronto, Ontario, Canada,
30 November--3 December 1998",
publisher = "IBM Toronto Laboratory, Centre for Advanced Studies",
address = "Toronto, ON, Canada",
pages = "xiii + 322",
year = "1998",
LCCN = "TK 5105.5 .C36 1998",
bibdate = "Sat Nov 29 10:56:20 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
altbooktitle = "Meeting of minds: conference program / CASCON '98,
November 30--December 3, 1998, International Plaza
Hotel, Toronto, Ontario, Canada",
xxISBN = "none",
}
@Proceedings{Matthews:1998:CRT,
editor = "Michael B. Matthews and others",
booktitle = "{Conference record of the Thirty-Second Asilomar
Conference on Signals, Systems and Computers: November
1--4, 1998, Pacific Grove, California}",
title = "{Conference record of the Thirty-Second Asilomar
Conference on Signals, Systems and Computers: November
1--4, 1998, Pacific Grove, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "1998",
ISBN = "0-7803-5148-7, 0-7803-5149-5, 0-7803-5150-9",
ISBN-13 = "978-0-7803-5148-6, 978-0-7803-5149-3,
978-0-7803-5150-9",
LCCN = "TK5101.A1 A85 1998; TK454.2 .A8 1998",
bibdate = "Mon Mar 5 15:56:18 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "Asilomar Conference on Signals, Systems and Computers
(32nd: 1998: Pacific Grove, Calif.)",
remark = "IEEE Catalog Number 98CH36284.",
subject = "Signal processing; Digital techniques; Congresses;
Electronic digital computers",
}
@Proceedings{Pocek:1998:PIS,
editor = "Kenneth L. Pocek and Jeffrey M. Arnold",
booktitle = "{Proceedings, IEEE Symposium on FPGAs for Custom
Computing Machines, April 15--17, 1998, Napa Valley,
California}",
title = "{Proceedings, IEEE Symposium on FPGAs for Custom
Computing Machines, April 15--17, 1998, Napa Valley,
California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 344",
year = "1998",
DOI = "https://doi.org/10.1109/FPGA.1998.707875",
ISBN = "0-8186-8900-5, 0-8186-8902-1 (microfiche)",
ISBN-13 = "978-0-8186-8900-0, 978-0-8186-8902-4 (microfiche)",
ISSN = "1082-3409",
LCCN = "TK7895.G36 I33 1998",
bibdate = "Sat Oct 9 15:17:05 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5734",
acknowledgement = ack-nhfb,
subject = "field programmable gate arrays; congresses; computer
engineering",
}
@Proceedings{Sasao:1998:ISM,
editor = "Tsutomu Sasao and Bob Werner",
booktitle = "28th International Symposium on Multiple-Valued Logic
{(ISMVL '98)}, Fukuoka, Japan, May 26--29, 1998",
title = "28th International Symposium on Multiple-Valued Logic
({ISMVL} '98), Fukuoka, Japan, May 26--29, 1998",
volume = "28",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvi + 384",
year = "1998",
ISBN = "0-8186-8371-6 (paperback), 0-8186-8372-4 (casebound),
0-8186-8373-2 (microfiche)",
ISBN-13 = "978-0-8186-8371-8 (paperback), 978-0-8186-8372-5
(casebound), 978-0-8186-8373-2 (microfiche)",
ISSN = "0195-623X",
LCCN = "????",
bibdate = "Sat Jun 25 10:06:53 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 98CB36138.",
acknowledgement = ack-nhfb,
}
@Proceedings{Sohi:1998:YIS,
editor = "Gurindar Sohi",
booktitle = "25 years of the {International Symposia on Computer
architecture}",
title = "25 years of the {International Symposia on Computer
architecture}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiii + 546",
year = "1998",
ISBN = "1-58113-058-9",
ISBN-13 = "978-1-58113-058-4",
ISSN = "1063-6897",
LCCN = "QA76.9.A73 S944 1998",
bibdate = "Fri Nov 28 18:41:44 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-mfc # " and " # ack-nhfb,
}
@Proceedings{ACM:1999:PFA,
editor = "{ACM}",
booktitle = "Proceedings of the Fifteenth Annual Symposium on
Computational Geometry: June 13--16, 1999, Miami Beach,
Florida",
title = "Proceedings of the Fifteenth Annual Symposium on
Computational Geometry: June 13--16, 1999, Miami Beach,
Florida",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 432",
year = "1999",
ISBN = "1-58113-068-6",
ISBN-13 = "978-1-58113-068-3",
LCCN = "????",
bibdate = "Sat Apr 28 18:59:36 2001",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 429990.",
URL = "http://www.acm.org/pubs/contents/proceedings/compgeom/304893/",
acknowledgement = ack-nhfb,
}
@Proceedings{Begehr:1999:PSI,
editor = "Heinrich G. W. Begehr and Robert P. Gilbert and Joji
Kajiwara",
booktitle = "Proceedings of the Second {ISAAC} Congress:
Fukuoka-shi, Japan",
title = "Proceedings of the Second {ISAAC} Congress:
Fukuoka-shi, Japan",
volume = "7--8",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
year = "1999",
ISBN = "0-7923-6598-4, 0-7923-6754-5",
ISBN-13 = "978-0-7923-6598-3, 978-0-7923-6754-3",
LCCN = "QA299.6 .I58 1999",
bibdate = "Sat Nov 29 11:33:40 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "International Society for Analysis, Applications, and
Computation",
acknowledgement = ack-nhfb,
}
@Proceedings{Csendes:1999:DRC,
editor = "Tibor Csendes",
booktitle = "{Developments in Reliable Computing: Papers presented
at the International Symposium on Scientific Computing,
Computer Arithmetic, and Validated Numerics, SCAN-98,
in Szeged, Hungary}",
title = "{Developments in Reliable Computing: Papers presented
at the International Symposium on Scientific Computing,
Computer Arithmetic, and Validated Numerics, SCAN-98,
in Szeged, Hungary}",
volume = "5(3)",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "viii + 402",
year = "1999",
ISBN = "0-7923-6057-5",
ISBN-13 = "978-0-7923-6057-5",
LCCN = "QA76.9.E94 D48 1999",
bibdate = "Sat Nov 29 11:31:21 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = j-RELIABLE-COMPUTING,
acknowledgement = ack-nhfb,
}
@Proceedings{Hosticka:1999:EPE,
editor = "B. J. Hosticka and G. Zimmer and H. Grunbacher",
booktitle = "{ESSCIRC '99}: proceedings of the 25th European
Solid-State Circuits Conference, Duisburg, Germany,
21--23 September, 1999",
title = "{ESSCIRC} '99: proceedings of the 25th European
Solid-State Circuits Conference, Duisburg, Germany,
21--23 September, 1999",
publisher = "Editions Fronti{\`e}res",
address = "Paris, France",
pages = "ix + 446",
year = "1999",
ISBN = "2-86332-246-X",
ISBN-13 = "978-2-86332-246-8",
LCCN = "TK7871.85 .E887 1999",
bibdate = "Sat Nov 29 11:25:06 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1999:AAF,
editor = "{IEEE}",
booktitle = "{AP-ASIC '99: the First IEEE Asia Pacific Conference
on ASICs, Yonsei University, Seoul, Korea, August
23--25, 1999}",
title = "{AP-ASIC '99: the First IEEE Asia Pacific Conference
on ASICs, Yonsei University, Seoul, Korea, August
23--25, 1999}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxvi + 423",
year = "1999",
ISBN = "0-7803-5705-1",
ISBN-13 = "978-0-7803-5705-1",
LCCN = "TK7874.6 .I32 1999",
bibdate = "Sat Jun 25 07:40:16 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 99EX360.",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1999:IPI,
editor = "{IEEE}",
booktitle = "{ICECS '99: proceedings of ICECS '99, the 6th IEEE
International Conference on Electronics, Circuits, and
Systems: Pafos, Cyprus, 5--8 September, 1999}",
title = "{ICECS '99: proceedings of ICECS '99, the 6th IEEE
International Conference on Electronics, Circuits, and
Systems: Pafos, Cyprus, 5--8 September, 1999}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
year = "1999",
ISBN = "0-7803-5682-9",
ISBN-13 = "978-0-7803-5682-5",
LCCN = "TK7874 .I3236 1999",
bibdate = "Sat Nov 29 11:34:32 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Three volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:1999:PII,
editor = "{IEEE}",
booktitle = "{Proceedings: 1999 29th IEEE International Symposium
on Multiple-Valued Logic, May 20--22, 1999, Freiburg im
Breisgau, Germany}",
title = "{Proceedings: 1999 29th IEEE International Symposium
on Multiple-Valued Logic, May 20--22, 1999, Freiburg im
Breisgau, Germany}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 302",
year = "1999",
ISBN = "0-7695-0161-3, 0-7803-5684-5, 0-7695-0163-x",
ISBN-13 = "978-0-7695-0161-1, 978-0-7803-5684-9,
978-0-7695-0163-5",
LCCN = "????",
bibdate = "Sat Aug 22 08:56:51 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.bibsys.no:2100/BIBSYS",
acknowledgement = ack-nhfb,
}
@Proceedings{Koren:1999:ISC,
editor = "Israel Koren and Peter Kornerup",
booktitle = "{14th IEEE Symposium on Computer Arithmetic:
proceedings: April 14--16, 1999, Adelaide, Australia}",
title = "{14th IEEE Symposium on Computer Arithmetic:
proceedings: April 14--16, 1999, Adelaide, Australia}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 274",
year = "1999",
DOI = "https://doi.org/10.1109/ARITH.1999.762854",
ISBN = "0-7803-5609-8, 0-7695-0116-8, 0-7695-0118-4",
ISBN-13 = "978-0-7803-5609-2, 978-0-7695-0116-1,
978-0-7695-0118-5",
ISSN = "1063-6889",
LCCN = "QA76.6 .S887 1999",
bibdate = "Mon Feb 7 07:28:26 MST 2000",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society Order Number PR00116. IEEE Order
Plan Catalog Number 99CB36336.",
URL = "http://computer.org/conferen/home/arith/;
http://www.ecs.umass.edu/ece/arith14/program.html",
acknowledgement = ack-nhfb,
keywords = "ARITH-14",
remark = "Also known as ARITH-14.",
source = "Computer arithmetic",
sponsor = "IEEE.",
}
@Proceedings{Luk:1999:PSA,
editor = "Franklin T. Luk",
booktitle = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations IX:
19--21 July, 1999, Denver, Colorado}",
title = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations IX:
19--21 July, 1999, Denver, Colorado}",
volume = "3807",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "ix + 648",
year = "1999",
ISBN = "0-8194-3293-8",
ISBN-13 = "978-0-8194-3293-3",
LCCN = "TK5102.5 .A3325 1999; TK5102.5 .A3173 1999; TK5102.9
.A37 1999",
bibdate = "Mon Mar 5 07:43:43 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
subject = "Signal processing; Digital techniques; Congresses;
Algorithms; Computer architecture",
}
@Proceedings{Matthews:1999:CRT,
editor = "Michael B. Matthews and others",
booktitle = "{Conference record of the Thirty-Third Asilomar
Conference on Signals, Systems and Computers: October
24--27, 1999, Pacific Grove, California}",
title = "{Conference record of the Thirty-Third Asilomar
Conference on Signals, Systems and Computers: October
24--27, 1999, Pacific Grove, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxv + 1689 + 7 (two volumes)",
year = "1999",
DOI = "https://doi.org/10.1109/ACSSC.1999.831824",
ISBN = "0-7803-5700-0 (softbound), 0-7803-5701-9 (casebound),
0-7803-5702-7 (microfiche)",
ISBN-13 = "978-0-7803-5700-6 (softbound), 978-0-7803-5701-3
(casebound), 978-0-7803-5702-0 (microfiche)",
LCCN = "TK5101.A1 A85 1999; TK454.2 .A8 1999",
bibdate = "Sun Mar 4 21:19:53 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "IEEE Catalog Number 99CH37020.",
subject = "Signal processing; Congresses; Electronic digital
computers; Digital techniques",
}
@Proceedings{Mazumder:1999:NGL,
editor = "Pinaki Mazumder and Ronald J. Lomax",
booktitle = "{Ninth Great Lakes Symposium on VLSI: proceedings:
Ypsilanti Marriott at Eagle Court, Ypsilanti, Michigan,
March 4--6, 1999}",
title = "{Ninth Great Lakes Symposium on VLSI: proceedings:
Ypsilanti Marriott at Eagle Court, Ypsilanti, Michigan,
March 4--6, 1999}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 400",
year = "1999",
ISBN = "0-7695-0104-4, 0-7695-0106-0",
ISBN-13 = "978-0-7695-0104-8, 978-0-7695-0106-2",
LCCN = "TK7874 .G689 1999",
bibdate = "Sun Mar 4 21:21:39 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "IEEE Computer Society Order Number PR0 0104",
subject = "Integrated circuits; Very large scale integration;
Design and construction; Congresses; Computer-aided
design",
}
@Proceedings{Piuri:1999:IAV,
editor = "Vincenzo Piuri",
booktitle = "{IEEE Alessandro Volta Memorial Workshop on Low-Power
Design: proceedings: March 4--5, 1999, Como, Italy}",
title = "{IEEE Alessandro Volta Memorial Workshop on Low-Power
Design: proceedings: March 4--5, 1999, Como, Italy}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 203",
year = "1999",
ISBN = "0-7695-0019-6, 0-7695-0021-8",
ISBN-13 = "978-0-7695-0019-5, 978-0-7695-0021-8",
LCCN = "TK7874.66 .I34 1999",
bibdate = "Sun Mar 4 21:18:14 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "IEEE Alessandro Volta Memorial Workshop on Low-Power
Design (1999: Como, Italy)",
subject = "Low voltage integrated circuits; Design and
construction; Congresses; Volta, Alessandro",
subject-dates = "1745--1827",
}
@Proceedings{Shiratori:1999:PIC,
editor = "Norio Shiratori and Dhabaleswar Panda",
booktitle = "{Proceedings, 1999 International Conference on
Parallel Processing: Aizu-Wakamatsu City, Japan, 21--24
September 1999}",
title = "{Proceedings, 1999 International Conference on
Parallel Processing: Aizu-Wakamatsu City, Japan, 21--24
September 1999}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxi + 561",
year = "1999",
ISBN = "0-7695-0350-0, 0-7695-0352-7",
ISBN-13 = "978-0-7695-0350-9, 978-0-7695-0352-3",
ISSN = "0190-3918",
LCCN = "QA76.58 .I55 1999",
bibdate = "Sun Feb 20 14:02:52 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "IEEE Computer Society Order Number PR00350.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=6466",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Parallel Processing (28th:
1999: Aizuwakamatsu-shi, Japan)",
subject = "parallel processing (electronic computers);
congresses",
}
@Proceedings{Wuorinen:1999:IIS,
editor = "John H. Wuorinen",
booktitle = "1999 {IEEE} International Solid-State Circuits
Conference, San Francisco, {CA}: digest of technical
papers",
title = "1999 {IEEE} International Solid-State Circuits
Conference, San Francisco, {CA}: digest of technical
papers",
volume = "42",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "508",
year = "1999",
ISBN = "0-7803-5126-6, 0-7803-5127-4, 0-7803-5128-2,
0-7803-5129-0",
ISBN-13 = "978-0-7803-5126-4, 978-0-7803-5127-1,
978-0-7803-5128-8, 978-0-7803-5129-5",
LCCN = "????",
bibdate = "Sat Nov 29 11:26:12 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog no. 99CH36278 and 99CB36278.",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2000:PIC,
editor = "{ACM}",
booktitle = "Proceedings of the {International Conference on
Compilers, Architectures and Synthesis for Embedded
Systems, San Jose, California, November 17--19, 2000}",
title = "Proceedings of the {International Conference on
Compilers, Architectures and Synthesis for Embedded
Systems, San Jose, California, November 17--19, 2000}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "200 (est.)",
year = "2000",
ISBN = "1-58113-338-3",
ISBN-13 = "978-1-58113-338-7",
LCCN = "????",
bibdate = "Mon Mar 05 14:51:40 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:2000:DPX,
editor = "Anonymous",
booktitle = "{DCIS '2000: Proceedings of the XV Conference on
Design of Circuits and Integrated Systems, Le Corum,
Montpellier, November 21--24, 2000}",
title = "{DCIS '2000: Proceedings of the XV Conference on
Design of Circuits and Integrated Systems, Le Corum,
Montpellier, November 21--24, 2000}",
publisher = "????",
address = "????",
year = "2000",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Jun 25 10:35:13 2005",
bibsource = "http://www.lirmm.fr/DCIS2000/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Library catalogs suggest that this appeared only on
CD-ROM.",
}
@Proceedings{IEEE:2000:EPI,
editor = "{IEEE}",
booktitle = "{EDOC '00: Proceedings of the 4th International
Conference on Enterprise Distributed Computing, 25-28
September 2000, Makuhari, Japan}",
title = "{EDOC '00: Proceedings of the 4th International
Conference on Enterprise Distributed Computing, 25-28
September 2000, Makuhari, Japan}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 264",
year = "2000",
ISBN = "0-7695-0865-0",
ISBN-13 = "978-0-7695-0865-8",
LCCN = "????",
bibdate = "Thu Aug 7 17:51:05 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2000:IGP,
editor = "{IEEE}",
booktitle = "{ISCAS 2000 Geneva: proceedings of the 2000 IEEE
International Symposium on Circuits and Systems,
Emerging technologies for the 21st century: May 28--31,
2000, International Conference Center (CICG) of Geneva,
Switzerland}",
title = "{ISCAS 2000 Geneva: proceedings of the 2000 IEEE
International Symposium on Circuits and Systems,
Emerging technologies for the 21st century: May 28--31,
2000, International Conference Center (CICG) of Geneva,
Switzerland}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2000",
ISBN = "0-7803-5482-6, 0-7803-5483-4, 0-7803-5484-2",
ISBN-13 = "978-0-7803-5482-1, 978-0-7803-5483-8,
978-0-7803-5484-5",
LCCN = "TK7801 .I22 2000",
bibdate = "Mon Mar 5 07:46:37 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "IEEE International Symposium on Circuits and Systems
(2000: Geneva, Switzerland)",
remark = "IEEE Catalog Number: 00CH36353. Hosted by Swiss
Federal Institute of Technology, Lausanne.",
subject = "Electronics; Congresses; Electronic circuits; Neural
networks (Computer science); Integrated circuits; Very
large scale integration; Signal processing; Digital
techniques",
}
@Proceedings{IEEE:2000:IPI,
editor = "{IEEE}",
booktitle = "{IMTC\slash 2000}: Proceedings of the 17th {IEEE}
Instrumentation and Measurement Technology Conference:
Smart connectivity: integrating measurement and
control, Hilton Hotel and Towers, Baltimore, Maryland,
{USA}, May 1--4, 2000",
title = "{IMTC}\slash 2000: Proceedings of the 17th {IEEE}
Instrumentation and Measurement Technology Conference:
Smart connectivity: integrating measurement and
control, Hilton Hotel and Towers, Baltimore, Maryland,
{USA}, May 1--4, 2000",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xliv + 1615",
year = "2000",
ISBN = "0-7803-5891-0, 0-7803-5890-2, 0-7803-5892-9",
ISBN-13 = "978-0-7803-5891-1, 978-0-7803-5890-4,
978-0-7803-5892-8",
ISSN = "1091-5281",
LCCN = "TK7878 .I3295 2000",
bibdate = "Sat Nov 29 11:35:38 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Three volumes. IEEE catalog number 00CH3706.",
acknowledgement = ack-nhfb,
}
@Proceedings{Luk:2000:PSA,
editor = "Franklin T. Luk",
booktitle = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations X: 2--4
August 2000, San Diego, California, USA}",
title = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations X: 2--4
August 2000, San Diego, California, USA}",
volume = "4116",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "vii + 484",
year = "2000",
ISBN = "0-8194-3761-1",
ISBN-13 = "978-0-8194-3761-7",
LCCN = "TK5102.5 .A3325 2000; TK5102.9 .A382 2000; TK5102.9
.A38 2000",
bibdate = "Mon Mar 5 07:55:22 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
subject = "Signal processing; Digital techniques; Congresses;
Computer algorithms; Computer architecture",
}
@Proceedings{Matthews:2000:CRT,
editor = "Michael B. Matthews and others",
booktitle = "{Conference record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers: October
29--November 1, 2000, Pacific Grove, California}",
title = "{Conference record of the Thirty-Fourth Asilomar
Conference on Signals, Systems and Computers: October
29--November 1, 2000, Pacific Grove, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2000",
ISBN = "0-7803-6514-3 (softbound), 0-7803-6515-1 (casebound),
0-7803-6516-X (microfiche)",
ISBN-13 = "978-0-7803-6514-8 (softbound), 978-0-7803-6515-5
(casebound), 978-0-7803-6516-2 (microfiche)",
LCCN = "TK5101.A1 A85 2000",
bibdate = "Sun Mar 4 21:30:52 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "Asilomar Conference on Signals, Systems and Computers
(34th: 2000: Pacific Grove, Calif.)",
remark = "IEEE Catalog Number 99CH37020.",
subject = "Signal processing; Congresses; Electronic digital
computers; Digital techniques",
}
@Proceedings{Reynders:2000:IPI,
editor = "John Reynders and Alexander V. Veidenbaum",
booktitle = "{ICS '00: Proceedings of the 14th international
conference on Supercomputing: Santa Fe, New Mexico,
USA, May 8--11, 2000}",
title = "{ICS '00: Proceedings of the 14th international
conference on Supercomputing: Santa Fe, New Mexico,
USA, May 8--11, 2000}",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "xi + 509",
pages = "xi + 509",
year = "2000",
DOI = "https://doi.org/10.1145/335231",
ISBN = "1-58113-270-0",
ISBN-13 = "978-1-58113-270-0",
LCCN = "QA76.88 .I573 2000",
bibdate = "Fri Jul 27 05:22:06 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/supercomputing/335231/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/java2000.bib;
https://www.math.utah.edu/pub/tex/bib/pvm.bib",
URL = "https://dl.acm.org/doi/proceedings/10.1145/335231",
acknowledgement = ack-nhfb,
keywords = "AS/400; ESA/390; IA-64; Java Virtual Machine (JVM);
RS/6000",
}
@Proceedings{Sprague:2000:PAH,
editor = "Ralph H. Sprague",
booktitle = "{Proceedings of the 33rd Annual Hawaii International
Conference on System Sciences: abstracts and CD-ROM of
full papers: January 4--7, 2000, Maui, Hawaii}",
title = "{Proceedings of the 33rd Annual Hawaii International
Conference on System Sciences: abstracts and CD-ROM of
full papers: January 4--7, 2000, Maui, Hawaii}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "liv + 259",
year = "2000",
ISBN = "0-7695-0493-0, 0-7695-0494-9, 0-7695-0495-7",
ISBN-13 = "978-0-7695-0493-3, 978-0-7695-0494-0,
978-0-7695-0495-7",
LCCN = "TA168 .H37 2000",
bibdate = "Sun Mar 4 21:23:42 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "Hawaii International Conference on System Sciences
(33rd: 2000: Maui, Hawaii)",
remark = "IEEE Computer Society Order Number: PR00493",
subject = "Systems engineering; Congresses; Information theory;
Electronic data processing; System design",
}
@Proceedings{Swartzlander:2000:IIC,
editor = "Earl E. Swartzlander and Graham Jullien and Michael
Joseph Schulte",
booktitle = "{IEEE International Conference on Application-Specific
Systems, Architectures and Processors: proceedings,
July 10--12, 2000; Boston, Massachusetts}",
title = "{IEEE International Conference on Application-Specific
Systems, Architectures and Processors: proceedings,
July 10--12, 2000; Boston, Massachusetts}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 360",
year = "2000",
ISBN = "0-7695-0716-6, 0-7695-0718-2",
ISBN-13 = "978-0-7695-0716-3, 978-0-7695-0718-7",
LCCN = "TK7874.6 .I572 2000",
bibdate = "Sun Mar 4 21:28:08 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Application Specific
Systems, Architectures and Processors (12th: 2000:
Boston, Mass.)",
remark = "IEEE Computer Society order number PR00716. IEEE order
plan catalog number 97TB100177.",
subject = "Array processors; Congresses; Signal processing;
Digital techniques; Application specific integrated
circuits",
}
@Proceedings{Traverso:2000:IAU,
editor = "Carlo Traverso",
booktitle = "{ISSAC 2000}: 7--9 August 2000, University of St.
Andrews, Scotland: proceedings of the 2000
International Symposium on Symbolic and Algebraic
Computation",
title = "{ISSAC} 2000: 7--9 August 2000, University of St.
Andrews, Scotland: proceedings of the 2000
International Symposium on Symbolic and Algebraic
Computation",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 309",
year = "2000",
ISBN = "1-58113-218-2",
ISBN-13 = "978-1-58113-218-2",
LCCN = "QA76.95.I59 2000",
bibdate = "Tue Apr 17 09:12:53 2001",
bibsource = "http://www.acm.org/pubs/contents/proceedings/series/issac/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 505000.",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/345542/",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2001:PSA,
editor = "ACM",
booktitle = "{Proceedings of the seventeenth annual Symposium on
Computational Geometry (SCG'01): June 3--5, 2001,
Medford, Massachusetts, USA}",
title = "{Proceedings of the seventeenth annual Symposium on
Computational Geometry (SCG'01): June 3--5, 2001,
Medford, Massachusetts, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 334",
year = "2001",
ISBN = "1-58113-357-X",
ISBN-13 = "978-1-58113-357-8",
LCCN = "????",
bibdate = "Fri Jan 6 12:10:47 MST 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
library.ox.ac.uk:210/ADVANCE",
acknowledgement = ack-nhfb,
remark = "ACM order number 429010.",
subject = "Geometry; Data processing; Congresses",
}
@Proceedings{Anonymous:2001:JJ,
editor = "Anonymous",
booktitle = "{JavaOne 2001, June 7, 2001}",
title = "{JavaOne 2001, June 7, 2001}",
publisher = "????",
address = "????",
year = "2001",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Nov 29 11:36:43 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Boulton:2001:TPH,
editor = "Richard J. Boulton and Paul B. Jackson",
booktitle = "Theorem Proving in Higher Order Logics: 14th
International Conference, {TPHOLs 2001, Edinburgh,
Scotland, UK, September 3--6, 2001}: Proceedings",
title = "Theorem Proving in Higher Order Logics: 14th
International Conference, {TPHOLs 2001, Edinburgh,
Scotland, UK, September 3--6, 2001}: Proceedings",
volume = "2152",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 393",
year = "2001",
ISBN = "3-540-42525-X (paperback)",
ISBN-13 = "978-3-540-42525-0 (paperback)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.9.A96 T655 2001",
bibdate = "Thu Nov 25 11:01:06 MST 2004",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNCS,
acknowledgement = ack-nhfb,
meetingname = "TPHOLs 2001 (2001: Edinburgh, Scotland)",
subject = "Automatic theorem proving; Congresses",
}
@Proceedings{Brebner:2001:FLA,
editor = "Gordon Brebner and Roger Woods",
booktitle = "{Field-programmable logic and applications: 11th
International Conference, FPL 2001, Belfast, Northern
Ireland, UK, August 27--29, 2001: Proceedings}",
title = "{Field-programmable logic and applications: 11th
International Conference, FPL 2001, Belfast, Northern
Ireland, UK, August 27--29, 2001: Proceedings}",
volume = "2147",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 665",
year = "2001",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/3-540-44687-7",
ISBN = "3-540-42499-7 (softcover)",
ISBN-13 = "978-3-540-42499-4 (softcover)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "TK7895.G36 I48 2001; QA267.A1 L43 no.2147",
bibdate = "Thu Jan 17 11:49:19 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2147",
acknowledgement = ack-nhfb,
keywords = "field programmable gate arrays --- congresses;
programmable array logic --- congresses",
}
@Proceedings{Burgess:2001:ISC,
editor = "N. Burgess and L. Ciminiera",
booktitle = "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
title = "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 285",
year = "2001",
ISBN = "0-7695-1150-3; 0-7695-1152-X",
ISBN-13 = "978-0-7695-1150-4; 978-0-7695-1152-8",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2001",
bibdate = "Fri May 03 14:20:49 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE order no. PR01150.",
price = "US\$145",
acknowledgement = ack-nhfb,
keywords = "ARITH-15",
xxnote = "Check dates: 11--13 or 11--17??",
xxtitle = "Computer Arithmetic: Papers presented at the {15th
IEEE Symposium on Computer Arithmetic (Arith-15 2001),
11--17 June, 2001, Vail, CO}",
}
@Proceedings{IEEE:2001:IPI,
editor = "{IEEE}",
booktitle = "{ICCAD '01: Proceedings of the 2001 IEEE\slash ACM
International Conference on Computer-Aided Design, San
Jose, California}",
title = "{ICCAD '01: Proceedings of the 2001 IEEE\slash ACM
International Conference on Computer-Aided Design, San
Jose, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2001",
ISBN = "0-7803-7249-2",
ISBN-13 = "978-0-7803-7249-8",
LCCN = "????",
bibdate = "Fri Aug 08 09:19:44 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2001:PES,
editor = "{IEEE}",
booktitle = "{Proceedings of the Euromicro Symposium on Digital
Systems Design, Architectures, Methods and Tools (DSD
2001), Warsaw, Poland, 4--6 September 2001}",
title = "{Proceedings of the Euromicro Symposium on Digital
Systems Design, Architectures, Methods and Tools (DSD
2001), Warsaw, Poland, 4--6 September 2001}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 476",
year = "2001",
ISBN = "0-7695-1239-9",
ISBN-13 = "978-0-7695-1239-6",
LCCN = "TK7868.D5 E93 2001",
bibdate = "Sat Jun 25 08:26:26 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2001:PII,
editor = "{IEEE}",
booktitle = "Proceedings of the {IEEE} International Conference on
Computer Design, September 23--26, 2001, Austin, {TX}",
title = "Proceedings of the {IEEE} International Conference on
Computer Design, September 17--20, 2001, Austin, {TX}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxii + 559",
year = "2001",
ISBN = "0-7695-1200-3 (paperback), 0-7695-1202-X
(microfiche)",
ISBN-13 = "978-0-7695-1200-6 (paperback), 978-0-7695-1202-0
(microfiche)",
LCCN = "TK7885.A1 .I24 2001; TK 7885 .A1I24 2001",
bibdate = "Sat Jun 25 08:16:29 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxnote = "Check dates: one source says 17--10 September, LC and
Melvyl say 23--26 September??",
}
@Proceedings{Kraemer:2001:SCV,
editor = "W. Kr{\"a}mer and J{\"u}rgen Wolff von Gudenberg",
booktitle = "Scientific Computing, Validated Numerics, Interval
Methods",
title = "Scientific Computing, Validated Numerics, Interval
Methods",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "ix + 398",
year = "2001",
ISBN = "0-306-46706-2",
ISBN-13 = "978-0-306-46706-6",
LCCN = "????",
bibdate = "Thu Mar 21 10:21:57 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Scan 2000, the GAMM--IMACS International Symposium on
Scientific Computing, Computer Arithmetic, and
Validated Numerics and Interval 2000, the International
Conference on Interval Methods in Science and
Engineering were jointly held in Karlsruhe, September
19--22, 2000.",
price = "09.00 EUR / 95.00 USD / 66.50 GBP",
URL = "http://www.wkap.nl/prod/b/0-306-46706-2",
acknowledgement = ack-nhfb,
author-dates = "1952--2014 (WK)",
}
@Proceedings{Kulisch:2001:PEM,
editor = "Ulrich Kulisch and Rudolf Lohner and Axel Facius",
booktitle = "Perspectives on enclosure methods: {GAMM--IMACS}
international symposium on scientific computing,
computer arithmetic and validated numerics, September
2000, Karlsruhe, Germany",
title = "Perspectives on enclosure methods: {GAMM}-{IMACS}
international symposium on scientific computing,
computer arithmetic and validated numerics, September
2000, Karlsruhe, Germany",
publisher = "????",
pages = "xii + 345",
year = "2001",
ISBN = "3-211-83590-3",
ISBN-13 = "978-3-211-83590-6",
LCCN = "QA76.9.C62 P47 2001",
bibdate = "Mon May 20 07:08:20 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Held jointly with INTERVAL 2000 International
conference on interval methods in science and
engineering, on the occasion of the 60th birthday of
Professor Gotz Alefeld. Also known as SCAN2000",
abstract = "????",
acknowledgement = ack-nhfb,
keywords = "Alefeld; computer arithmetic; enclosure methods; GAMM;
IMACS; interval methods; SCAN; scientific computing;
validated numerics",
}
@Proceedings{Luk:2001:ASP,
editor = "Franklin T. Luk",
booktitle = "{Advanced signal processing algorithms, architectures,
and implementations XI: 1--3 August, 2001, San Diego,
CA, USA}",
title = "{Advanced signal processing algorithms, architectures,
and implementations XI: 1--3 August, 2001, San Diego,
CA, USA}",
volume = "4474",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "x + 536",
year = "2001",
CODEN = "PSISDG",
ISBN = "0-8194-4188-0",
ISBN-13 = "978-0-8194-4188-1",
ISSN = "0277-786X (print), 1996-756X (electronic)",
LCCN = "TK5102.5 .A332 2001",
bibdate = "Sat Jun 25 11:05:11 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = j-PROC-SPIE,
acknowledgement = ack-nhfb,
}
@Proceedings{Matthews:2001:CRT,
editor = "Michael B. Matthews",
booktitle = "Conference record of the Thirty-Fifth Asilomar
Conference on Signals, Systems \& Computers: November
4--7, 2001, Pacific Grove, California",
title = "Conference record of the Thirty-Fifth Asilomar
Conference on Signals, Systems \& Computers: November
4--7, 2001, Pacific Grove, California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2001",
ISBN = "0-7803-7147-X (paperback), 0-7803-7148-8
(microfiche)",
ISBN-13 = "978-0-7803-7147-7 (paperback), 978-0-7803-7148-4
(microfiche)",
LCCN = "????",
bibdate = "Sat Nov 29 07:02:41 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes. IEEE catalog number 01CH37256.",
acknowledgement = ack-nhfb,
}
@Proceedings{Oliveira:2001:FFM,
editor = "Jose N. Oliveira and Pamela Zave",
booktitle = "{FME 2001}: formal methods for increasing software
productivity: [10th] International Symposium of Formal
Methods Europe, Berlin, Germany, March 12--16, 2001:
Proceedings",
title = "{FME 2001}: formal methods for increasing software
productivity: [10th] International Symposium of Formal
Methods Europe, Berlin, Germany, March 12--16, 2001:
Proceedings",
volume = "2021",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 628",
year = "2001",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/3-540-45251-6",
ISBN = "3-540-41791-5 (softcover)",
ISBN-13 = "978-3-540-41791-0 (softcover)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.76.D47 I593 2001; QA267.A1 L43 no.2021",
bibdate = "Thu Jan 17 11:49:19 MST 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2021.htm",
acknowledgement = ack-nhfb,
keywords = "computer software -- development -- congresses",
}
@Proceedings{Tang:2001:ICA,
editor = "Ting-Ao Tang and others",
booktitle = "{2001 4th International Conference on ASIC:
proceedings: Hotel Equatorial, Shanghai, China, October
23--25, 2001}",
title = "{2001 4th International Conference on ASIC:
proceedings: Hotel Equatorial, Shanghai, China, October
23--25, 2001}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "42 + 887 + viii",
year = "2001",
ISBN = "0-7803-6677-8, 7-900081-59-3",
ISBN-13 = "978-0-7803-6677-0, 978-7-900081-59-9",
LCCN = "TK7874.6 .I55 2001; TK7874.6 .I64 2001",
bibdate = "Mon Mar 5 08:06:40 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Conference on ASIC (4th: 2001: Shanghai,
China)",
remark = "IEEE Catalog Number: 01TH8549",
subject = "Application-specific integrated circuits; Design and
construction; Congresses; Computer-aided design;
Testing",
}
@Proceedings{Babuska:2002:MMN,
editor = "Ivo Babu{\v{s}}ka and Philippe G. Ciarlet and
Tetsuhiko Miyoshi",
booktitle = "{Mathematical Modeling and Numerical Simulation in
Continuum Mechanics: Proceedings of the International
Symposium on Mathematical Modeling and Numerical
Simulation in Continuum Mechanics, September
29--October 3, 2000 Yamaguchi, Japan}",
title = "{Mathematical Modeling and Numerical Simulation in
Continuum Mechanics: Proceedings of the International
Symposium on Mathematical Modeling and Numerical
Simulation in Continuum Mechanics, September
29--October 3, 2000 Yamaguchi, Japan}",
volume = "19",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "viii + 301",
pages = "viii + 301",
year = "2002",
CODEN = "LNCSA6",
DOI = "https://doi.org/10.1007/978-3-642-56288-4",
ISBN = "3-540-42399-0 (print), 3-642-56288-4 (e-book)",
ISBN-13 = "978-3-540-42399-7 (print), 978-3-642-56288-4
(e-book)",
ISSN = "1439-7358",
ISSN-L = "1439-7358",
LCCN = "QA808.2 .I59 2000",
bibdate = "Thu Dec 20 14:36:13 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncse.bib",
series = ser-LNCSE,
URL = "http://link.springer.com/book/10.1007/978-3-642-56288-4;
http://www.springerlink.com/content/978-3-642-56288-4",
acknowledgement = ack-nhfb,
series-URL = "http://link.springer.com/bookseries/3527",
}
@Proceedings{Borrione:2002:TIW,
editor = "Dominique Borrione",
booktitle = "{Third International Workshop on the ACL2 Theorem
Prover and its Applications (ACL2-2002), April 8--9,
2002, in Grenoble, France. Presentations, affiliated
with ETAPS 2002}",
title = "{Third International Workshop on the ACL2 Theorem
Prover and its Applications (ACL2-2002), April 8--9,
2002, in Grenoble, France. Presentations, affiliated
with ETAPS 2002}",
publisher = "????",
address = "????",
pages = "????",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Jun 25 12:28:18 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.cs.utexas.edu/users/moore/acl2/workshop-2002/",
acknowledgement = ack-nhfb,
}
@Proceedings{Cohen:2002:MSP,
editor = "Arjeh M. Cohen and Xiao-Shan Gao and Nobuki Takayama",
booktitle = "{Mathematical software: proceedings of the first
International Congress of Mathematical Software:
Beijing, China, 17--19 August 2002}",
title = "{Mathematical software: proceedings of the first
International Congress of Mathematical Software:
Beijing, China, 17--19 August 2002}",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xiii + 514",
year = "2002",
ISBN = "981-238-048-5",
ISBN-13 = "978-981-238-048-7",
LCCN = "QA76.95 .I5654 2002",
bibdate = "Sat Jun 25 12:12:34 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Mathematics; Data processing; Congresses; Computer
software; Congresses",
}
@Book{Hennessy:2002:CAQ,
author = "John L. Hennessy and David A. Patterson",
booktitle = "Computer Architecture\emdash {A} Quantitative
Approach",
title = "Computer Architecture\emdash {A} Quantitative
Approach",
publisher = pub-MORGAN-KAUFMANN,
address = pub-MORGAN-KAUFMANN:adr,
edition = "Third",
pages = "xxi + 883 + A-87 + B-42 + C-1 + D-1 + E-1 + F-1 + G-1
+ H-1 + I-1 + R-22 + I-44",
year = "2002",
ISBN = "1-55860-596-7",
ISBN-13 = "978-1-55860-596-1",
LCCN = "????",
bibdate = "Fri May 31 15:46:29 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "US\$89.95",
URL = "http://www.mkp.com/books_catalog/catalog.asp?ISBN=1-55860-596-7;
http://www.mkp.com/CA3",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2002:IIC,
editor = "{IEEE}",
booktitle = "{2002 IEEE International Conference on Computer
Design: VLSI in computers and processors: proceedings:
September 16--18, 2002, Freiburg, Germany}",
title = "{2002 IEEE International Conference on Computer
Design: VLSI in computers and processors: proceedings:
September 16--18, 2002, Freiburg, Germany}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xx + 533",
year = "2002",
ISBN = "0-7695-1700-5 (paperback), 0-7695-1701-3 (casebound),
0-7695-1702-1 (microfiche)",
ISBN-13 = "978-0-7695-1700-1 (paperback), 978-0-7695-1701-8
(casebound), 978-0-7695-1702-5 (microfiche)",
LCCN = "TK7888.3 .I25 2002",
bibdate = "Sat Jun 25 12:20:07 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "IEEE catalog number PR01700.",
URL = "http://www.computer.org/cspress/CATALOG/pr01700.htm",
acknowledgement = ack-nhfb,
meetingname = "IEEE International Conference on Computer Design
(2002: Freiburg im Breisgau, Germany)",
}
@Proceedings{IEEE:2002:IRA,
editor = "{IEEE}",
booktitle = "{IEEE Reconfigurable Architecture Workshop,
International Parallel and Distributed Symposium, Fort
Lauderdale, Florida, April 15--19, 2002}",
title = "{IEEE Reconfigurable Architecture Workshop,
International Parallel and Distributed Symposium, Fort
Lauderdale, Florida, April 15--19, 2002}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xlvii + 270",
year = "2002",
ISBN = "0-7695-1573-8 (paperback), 0-7695-1574-6 (casebound),
0-7695-1575-4 (microfiche)",
ISBN-13 = "978-0-7695-1573-1 (paperback), 978-0-7695-1574-8
(casebound), 978-0-7695-1575-5 (microfiche)",
ISSN = "1530-2075",
LCCN = "QA76.58 .I583 2002",
bibdate = "Sat Jun 25 12:07:25 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society Order Number PR01573",
URL = "http://www.computer.org/cspress/CATALOG/pr01573.htm",
acknowledgement = ack-nhfb,
keywords = "IPDPS '2002",
}
@Proceedings{IEEE:2002:IWS,
editor = "{IEEE}",
booktitle = "{IEEE Workshop on Signal Processing Systems:
(SIPS'02): San Diego, California, USA, October 16--18,
2002}",
title = "{IEEE Workshop on Signal Processing Systems:
(SIPS'02): San Diego, California, USA, October 16--18,
2002}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "viii + 287",
year = "2002",
ISBN = "0-7803-7587-4",
ISBN-13 = "978-0-7803-7587-1",
LCCN = "TK7874 .V5637 2002",
bibdate = "Sun Mar 4 21:36:39 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "IEEE Workshop on Signal Processing Systems (2002: San
Diego, Calif.)",
remark = "Published under the sponsorship of the IEEE Signal
Processing Society, IEEE Circuits and Systems Society.
IEEE Catalog Number 02TH8638",
subject = "Integrated circuits; Very large scale integration;
Congresses; Signal processing; Digital techniques",
}
@Proceedings{IEEE:2002:STI,
editor = "{IEEE}",
booktitle = "{SC2002}: From Terabytes to Insight. Proceedings of
the {IEEE ACM SC 2002 Conference, November 16--22,
2002, Baltimore, MD, USA}",
title = "{SC2002}: From Terabytes to Insight. Proceedings of
the {IEEE ACM SC 2002 Conference, November 16--22,
2002, Baltimore, MD, USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2002",
ISBN = "0-7695-1524-X",
ISBN-13 = "978-0-7695-1524-3",
LCCN = "????",
bibdate = "Thu Feb 21 18:29:36 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Li:2002:PIC,
editor = "Daqian Li",
booktitle = "Proceedings of the [24th] International Congress of
Mathematicians: Beijing 2002, August 20--28",
title = "Proceedings of the [24th] International Congress of
Mathematicians: Beijing 2002, August 20--28",
publisher = "Higher Education Press",
address = "Beijing, China",
pages = "672 (vol. 1) + 832 (vol. 2) + 968 (vol. 3)",
year = "2002",
ISBN = "7-04-008690-5 (three volumes), 7-900135-82-0
(CD-ROM)",
ISBN-13 = "978-7-04-008690-4 (three volumes), 978-7-900135-82-7
(CD-ROM)",
LCCN = "QA1 .I82 2002",
bibdate = "Tue Apr 26 10:26:26 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "Editor name also transcribed and cataloged as Tatsien
Li.",
}
@Proceedings{Luk:2002:PSA,
editor = "Franklin T. Luk",
booktitle = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations XII:
9--11 July, 2002, Seattle, Washington, USA}",
title = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations XII:
9--11 July, 2002, Seattle, Washington, USA}",
volume = "4791",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "viii + 468",
year = "2002",
ISBN = "0-8194-4558-4",
ISBN-13 = "978-0-8194-4558-2",
LCCN = "TK5102.5 .A3324 2002",
bibdate = "Sat Jun 25 11:59:48 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Signal processing; Digital techniques; Congresses;
Algorithms; Congresses; Computer architecture;
Congresses",
}
@Proceedings{Matthews:2002:PTS,
editor = "Michael B. Matthews",
booktitle = "Proceedings of the Thirty Sixth Asilomar Conference on
Signals, Systems, and Computers: November 3--6, 2002,
Pacific Grove, California",
title = "Proceedings of the Thirty Sixth Asilomar Conference on
Signals, Systems, and Computers: November 3--6, 2002,
Pacific Grove, California",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxiv + 1950 (est.)",
year = "2002",
DOI = "https://doi.org/10.1109/ACSSC.2002.1196928",
ISBN = "0-7803-7576-9",
ISBN-13 = "978-0-7803-7576-5",
LCCN = "TK5102.5 A78 2002",
bibdate = "Thu Mar 24 14:54:07 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes. IEEE catalog number 02CH37387.",
price = "UK\pounds 265.00",
acknowledgement = ack-nhfb,
subject = "signals; systems; computers; Asilomar",
}
@Proceedings{Pocek:2002:FAI,
editor = "Kenneth L. Pocek and Jeffrey Arnold",
booktitle = "{FCCM 2002: 10th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines:
proceedings: 22--24 April, 2002, Napa, California}",
title = "{FCCM 2002: 10th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines:
proceedings: 22--24 April, 2002, Napa, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 322",
year = "2002",
DOI = "https://doi.org/10.1109/FPGA.2002.1106655",
ISBN = "0-7695-1801-X",
ISBN-13 = "978-0-7695-1801-5",
ISSN = "1082-3409",
LCCN = "TK7895.G36 I36 2002",
bibdate = "Sat Oct 9 14:03:54 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8168",
acknowledgement = ack-nhfb,
subject = "Field programmable gate arrays; Congresses; Computer
engineering",
}
@Proceedings{Schulte:2002:PII,
editor = "Michael Joseph Schulte",
booktitle = "{Proceedings / The IEEE International Conference on
Application-Specific Systems, Architectures and
Processors: 17--19 July 2002, San Jose, California}",
title = "{Proceedings / The IEEE International Conference on
Application-Specific Systems, Architectures and
Processors: 17--19 July 2002, San Jose, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 404",
year = "2002",
ISBN = "0-7695-1712-9 (paperback), 0-7695-1713-7 (casebound),
0-7695-1714-5 (microfiche)",
ISBN-13 = "978-0-7695-1712-4 (paperback), 978-0-7695-1713-1
(casebound), 978-0-7695-1714-8 (microfiche)",
LCCN = "TK7874.6",
bibdate = "Sat Jun 25 11:53:24 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number PR01712.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8009;
http://www.cse.lehigh.edu/~asap/",
acknowledgement = ack-nhfb,
}
@Proceedings{Trimberger:2002:FTA,
editor = "Stephen Trimberger and Martine Schlag",
booktitle = "{FPGA 2002: Tenth ACM International Symposium on
Field-Programmable Gate Arrays, Monterey, California,
USA: February 24--26, 2002}",
title = "{FPGA 2002: Tenth ACM International Symposium on
Field-Programmable Gate Arrays, Monterey, California,
USA: February 24--26, 2002}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 258",
year = "2002",
ISBN = "1-58113-452-5",
ISBN-13 = "978-1-58113-452-0",
LCCN = "TK7895.G36 A36 2002",
bibdate = "Sat Oct 9 15:21:41 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 480020.",
URL = "http://portal.acm.org/toc.cfm?id=503048",
acknowledgement = ack-nhfb,
subject = "gate array circuits; congresses; field programmable
gate arrays; programmable array logic",
}
@Proceedings{Vladimirova:2002:TMA,
editor = "Tanya Vladimirova and Richard Katz",
booktitle = "{Third Military and Aerospace Programmable Logic
Devices International Conference (MAPLD 2000)}",
title = "{Third Military and Aerospace Programmable Logic
Devices International Conference (MAPLD 2000)}",
volume = "39(4)",
publisher = "AIAA",
address = "Reston, VA, USA",
pages = "474--500",
year = "2002",
LCCN = "????",
bibdate = "Sat Oct 9 14:09:02 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.gbv.de:20011/gvk",
series = "Journal of spacecraft and rockets",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:2003:CRN,
editor = "Anonymous",
booktitle = "5th Conference on Real Numbers and Computers 2003 ---
{RNC5}, Lyon, France, September 2003",
title = "5th Conference on Real Numbers and Computers 2003 ---
{RNC5}, Lyon, France, September 2003",
publisher = "????",
address = "????",
pages = "????",
year = "2003",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Jun 25 14:57:33 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Bajard:2003:ISC,
editor = "Jean Claude Bajard and Michael Schulte",
booktitle = "{16th IEEE Symposium on Computer Arithmetic: ARITH-16
2003: proceedings: Santiago de Compostela, Spain, June
15--18, 2003}",
title = "{16th IEEE Symposium on Computer Arithmetic: ARITH-16
2003: proceedings: Santiago de Compostela, Spain, June
15--18, 2003}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 282",
year = "2003",
ISBN = "0-7695-1894-X",
ISBN-13 = "978-0-7695-1894-7",
ISSN = "1063-6889",
LCCN = "QA76.6 .S919 2003",
bibdate = "Sat Jul 20 17:45:12 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society order number PR01894. Selected
papers republished in {\em IEEE Transactions on
Computers}, {\bf 54}(3) (2005)
\cite{Schulte:2005:GEI}.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8582;
http://www.dec.usc.es/arith16/",
acknowledgement = ack-nhfb,
keywords = "ARITH-16",
}
@Proceedings{Cheung:2003:FPL,
editor = "Peter Y. K. Cheung and George A. Constantinides and
Jos{\'e} T. de Sousa",
booktitle = "Field-Programmable Logic and Applications: 13th
International Conference, {FPL 2003}, Lisbon, Portugal,
September 1--3, 2003: Proceedings",
title = "Field-Programmable Logic and Applications: 13th
International Conference, {FPL 2003}, Lisbon, Portugal,
September 1--3, 2003: Proceedings",
volume = "2778",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxvi + 1179",
year = "2003",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/b12007",
ISBN = "3-540-40822-3 (softcover)",
ISBN-13 = "978-3-540-40822-2 (softcover)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "TK7895.G36 I48 2003",
bibdate = "Sat Jul 16 16:49:02 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2778.htm;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2778;
http://www.springerlink.com/openurl.asp?genre=volume&id=doi:10.1007/b12007",
acknowledgement = ack-nhfb,
meetingname = "International Workshop on Field-Programmable Logic and
Applications (13th: 2003: Lisbon, Portugal)",
subject = "Field programmable gate arrays; Congresses;
Programmable array logic; Congresses",
}
@Proceedings{Deprettere:2003:IIC,
editor = "Ed F. Deprettere",
booktitle = "{IEEE International Conference on Application-Specific
Systems, Architectures and Processors: proceedings:
ASAP 2003: 24-26 June, 2003, The Hague, The
Netherlands}",
title = "{IEEE International Conference on Application-Specific
Systems, Architectures and Processors: proceedings:
ASAP 2003: 24-26 June, 2003, The Hague, The
Netherlands}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 470",
year = "2003",
ISBN = "0-7695-1992-X",
ISBN-13 = "978-0-7695-1992-0",
ISSN = "1063-6862",
LCCN = "TK7874.6 .I58 2003",
bibdate = "Fri Mar 25 05:59:41 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society Order Number PR01992.",
acknowledgement = ack-nhfb,
}
@Proceedings{Dietz:2003:LCP,
editor = "Henry G. Dietz",
booktitle = "{Languages and Compilers for Parallel Computing: 14th
International Workshop, LCPC 2001, Cumberland Falls,
KY, USA, August 1--3, 2001: Revised Papers}",
title = "{Languages and Compilers for Parallel Computing: 14th
International Workshop, LCPC 2001, Cumberland Falls,
KY, USA, August 1--3, 2001: Revised Papers}",
volume = "2624",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 444",
year = "2003",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/3-540-35767-X",
ISBN = "3-540-04029-3 (paperback)",
ISBN-13 = "978-3-540-04029-3 (paperback)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.58 .W656 2001",
bibdate = "Thu Aug 21 09:09:03 MDT 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "The 14th workshop on Languages and Compilers for
Parallel Computing, LCPC 2001, was organized and hosted
by the Electrical and Computer Engineering Department
of the University of Kentucky, Lexington, KY, USA.",
series = ser-LNCS,
URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2624.htm;
http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2624",
acknowledgement = ack-nhfb,
keywords = "compilers (computer programs); parallel processing
(electronic computers); programming languages
(electronic computers)",
}
@Proceedings{IEEE:2003:IICa,
editor = "{IEEE}",
booktitle = "{2003 IEEE International Conference on Acoustics,
Speech, and Signal Processing: proceedings: April
6--10, 2003, Hong Kong Exhibition and Convention
Centre, Hong Kong (ICASSP '03)}",
title = "{2003 IEEE International Conference on Acoustics,
Speech, and Signal Processing: proceedings: April
6--10, 2003, Hong Kong Exhibition and Convention
Centre, Hong Kong (ICASSP '03)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2003",
ISBN = "0-7803-7663-3",
ISBN-13 = "978-0-7803-7663-2",
LCCN = "TK7882.S65 I16 2003",
bibdate = "Thu Mar 24 21:28:32 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "IEEE catalog number 03CH37404.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8535",
acknowledgement = ack-nhfb,
subject = "speech processing systems; congresses;
electro-acoustics; underwater acoustics; integrated
circuits; very large scale integration; signal
processing",
}
@Proceedings{IEEE:2003:IICb,
editor = "{IEEE}",
booktitle = "{2003 IEEE International Conference on
Field-Programmable Technology (FPT): proceedings:
15--17 December, 2003, the University of Tokyo}",
title = "{2003 IEEE International Conference on
Field-Programmable Technology (FPT): proceedings:
15--17 December, 2003, the University of Tokyo}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xv + 457",
year = "2003",
DOI = "https://doi.org/10.1109/FPT.2003.1275723",
ISBN = "0-7803-8320-6",
ISBN-13 = "978-0-7803-8320-3",
LCCN = "TK7895.G36 I143 2003",
bibdate = "Sat Oct 9 14:16:28 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8988",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2003:PCI,
editor = "{IEEE}",
booktitle = "{Proceedings of the 2003 CGO: the International
Symposium on Code Generation and Optimization; March
23--26, 2003, Fisherman's Wharf, San Francisco, CA,
with special emphasis on feedback-directed and runtime
optimization}",
title = "{Proceedings of the 2003 CGO: the International
Symposium on Code Generation and Optimization; March
23--26, 2003, Fisherman's Wharf, San Francisco, CA,
with special emphasis on feedback-directed and runtime
optimization}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xv + 347",
year = "2003",
ISBN = "0-7695-1913-X",
ISBN-13 = "978-0-7695-1913-5",
LCCN = "????",
bibdate = "Thu Jun 09 18:51:49 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM Order No. 530033.",
acknowledgement = ack-nhfb,
keywords = "EPIC; Intel IA-64; Itanium",
}
@Proceedings{Luk:2003:PSA,
editor = "Franklin T. Luk",
booktitle = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations XIII:
6--8 August, 2003, San Diego, California, USA}",
title = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations XIII:
6--8 August, 2003, San Diego, California, USA}",
volume = "5205",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "x + 620",
year = "2003",
ISBN = "0-8194-5078-2",
ISBN-13 = "978-0-8194-5078-4",
LCCN = "TK5102.5 .A3322 2003; TK5102.5 .A3325 2003; TK5102.9
.A38 2003; TK5102.5; TS510 .S63; TK5102.5 .A3173
2003eb",
bibdate = "Sun Mar 4 21:42:57 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
subject = "Signal processing; Digital techniques; Congresses;
Algorithms; Computer architecture",
}
@Proceedings{Matthews:2003:PTS,
editor = "Michael B. Matthews",
booktitle = "{Proceedings of the Thirty-Seventh Asilomar Conference
on Signals, Systems \& Computers: November 9--12, 2003,
Pacific Grove, California}",
title = "{Proceedings of the Thirty-Seventh Asilomar Conference
on Signals, Systems \& Computers: November 9--12, 2003,
Pacific Grove, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2003",
ISBN = "0-7803-8104-1",
ISBN-13 = "978-0-7803-8104-9",
LCCN = "????",
bibdate = "Sat Jun 25 12:39:08 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 03CH37493.",
acknowledgement = ack-nhfb,
}
@Proceedings{Senda:2003:IPI,
editor = "J. Rafael Senda",
booktitle = "{ISSAC 2003: Proceedings of the 2003 International
Symposium on Symbolic and Algebraic Computation, August
3--6, 2003, Drexel University, Philadelphia, PA, USA}",
title = "{ISSAC 2003: Proceedings of the 2003 International
Symposium on Symbolic and Algebraic Computation, August
3--6, 2003, Drexel University, Philadelphia, PA, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "x + 273",
year = "2003",
ISBN = "1-58113-641-2",
ISBN-13 = "978-1-58113-641-8",
LCCN = "QA76.95",
bibdate = "Sat Dec 13 18:18:22 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 505030.",
acknowledgement = ack-nhfb,
}
@Book{Warren:2003:HD,
author = "Henry S. Warren",
booktitle = "Hacker's delight",
title = "Hacker's delight",
publisher = pub-AW,
address = pub-AW:adr,
pages = "xiv + 306",
year = "2003",
ISBN = "0-201-91465-4",
ISBN-13 = "978-0-201-91465-8",
LCCN = "QA76.6 .W375 2003",
bibdate = "Tue Jan 03 18:20:34 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
note = "While this book does not specifically address
computational aspects of floating-point arithmetic
(apart from the nine-page Chapter 15), it has extensive
coverage of, and clever algorithms for, integer
arithmetic operations that are fundamental for
implementing hardware floating-arithmetic and software
multiple-precision arithmetic.",
URL = "http://www.awprofessional.com/bookstore/product.asp?isbn=0201914654;
http://www.hackersdelight.org/;
http://www.hackersdelight.org/hackerTOC.pdf;
http://www.informit.com/content/images/chap3_0201914654/elementLinks/0201914654.pdf",
acknowledgement = ack-nhfb,
keywords = "DEC PDP-10; division by constants; Gray code; Hilbert
curves; IEEE 754 floating-point arithmetic; integer
cube root; integer division; integer exponentiation;
integer logarithm; integer square root; prime numbers;
unusual number bases",
remark = "Foreword by Guy L. Steele, Jr., who begins ``When I
first got a summer job at MIT's Project MAC almost 30
years ago, I was delighted to be able to work with the
DEC PDP-10 computer, which was more fun to program in
assembly language than any other computer, bar none,
because of its rich yet tractable set of instructions
for performing bit tests, bit masking, field
manipulation, and operations on integers. Though the
PDP-10 has not been manufactured for quite some years,
there remains a thriving cult of enthusiasts who keep
old PDP-10 hardware running and who run old PDP-10
software---entire operating systems and their
applications---by using personal computers to simulate
the PDP-10 instruction set.''",
subject = "Computer programming; Computer hackers",
tableofcontents = "Preface\par
1. Introduction\par
Notation\par
Instruction Set and Execution Time Model\par
2. Basis\par
Manipulating Rightmost Bits \\
Addition Combined with Logical Operations \\
Inequalities among Logical and Arithmetic Expressions
\\
Absolute Value Function \\
Sign Extension \\
Shift Right Signed from Unsigned \\
Sign Function \\
Three-Valued Compare \\
Transfer of Sign \\
Decoding a `Zero Means 2**n' Field \\
Comparison Predicates \\
Overflow Detection \\
Condition Code Result of Add, Subtract, and Multiply
\\
Rotate Shifts \\
Double-Length Add/Subtract \\
Double-Length Shifts \\
Multibyte Add, Subtract, Absolute Value \\
Doz, Max, Min \\
Exchanging Registers \\
Alternating among Two or More Values\par
3. Power-of-2 Boundaries\par
Rounding Up/Down to a Multiple of a Known Power of 2
\\
Rounding Up/Down to the Next Power of 2 \\
Detecting a Power-of-2 Boundary Crossing\par
4. Arithmetic Bounds\par
Checking Bounds of Integers \\
Propagating Bounds through Adds and Subtracts \\
Propagating Bounds through Logical Operations \\
Signed Bounds\par
5. Counting Bits\par
Counting 1-bits \\
Parity \\
Counting Leading 0's \\
Counting Trailing 0's\par
6. Searching Words\par
Find First 0-Byte \\
Find First String of 1-Bits of a Given Length\par
7. Rearranging Bits and Bytes\par
Reversing Bits and Bytes \\
Shuffling Bits \\
Transposing a Bit Matrix \\
Compress, or Generalized Extract \\
General Permutations, Sheep and Goats Operation \\
Rearrangements and Index Transformations\par
8. Multiplication\par
Multiword Multiplication \\
High-Order Half of 64-Bit Product \\
High-Order Product Signed from/to Unsigned \\
Multiplication by Constants\par
9. Integer Division\par
Preliminaries \\
Multiword Division \\
Unsigned Short Division from Signed Division \\
Unsigned Long Division\par
10. Integer Division by Constants\par
Signed Division by a Known Power of 2 \\
Signed Remainder from Division by a Known Power of 2
\\
Signed Division and Remainder by Non-powers of 2 \\
Signed Division by Divisors >= 2 \\
Signed Division by Divisors <= -2 \\
Incorporation into a Compiler \\
Miscellaneous Topics \\
Unsigned Division \\
Unsigned Division by Divisors >= 1 \\
Incorporation into a Compiler (Unsigned) \\
Miscellaneous Topics (Unsigned) \\
Applicability to Modulus and Floor Division \\
Similar Methods \\
Sample Magic Numbers \\
Exact Division by Constants \\
Test for Zero Remainder after Division by a
Constant\par
11. Some Elementary Functions\par
Integer Square Root \\
Integer Cube Root \\
Integer Exponentiation \\
Integer Logarithm\par
12. Unusual Bases for Number Systems\par
Base -2 \\
Base -1 + i \\
Other Bases \\
What is the Most Efficient Base?\par
13. Gray Code \\
Gray Code \\
Incrementing a Gray Coded Integer \\
Negabinary Gray Code \\
Brief History and Applications\par
14. Hilbert's Curve\par
A Recursive Algorithm for Generating the Hilbert Curve
\\
Coordinates from Distance along the Hilbert Curve \\
Distance from Coordinates on the Hilbert Curve \\
Incrementing the Coordinates on the Hilbert Curve \\
Non-recursive Generating Algorithms \\
Other Space-Filling Curves \\
Applications\par
15. Floating-Point\par
IEEE Format \\
Comparing Floating-Point Numbers Using Integer
Operations \\
The Distribution of Leading Digits \\
Table of Miscellaneous Values\par
16. Formulas for Primes\par
Introduction \\
Willans's Formulas \\
Wormell's Formula \\
Formulas for Other Difficult Functions\par
Appendix A. Arithmetic Tables for a 4-Bit
Machine\par
Appendix B. Newton's Method\par
Bibliography.",
}
@Proceedings{Frougny:2004:RCR,
editor = "Christiane Frougny and Vasco Brattka and Norbert
M{\"u}ller",
booktitle = "{RNC'6, 6th Conference on Real Numbers and Computers:
Nov 15--17, 2004, Dagstuhl, Germany}",
title = "{RNC'6, 6th Conference on Real Numbers and Computers:
Nov 15--17, 2004, Dagstuhl, Germany}",
publisher = "Universita{\"a}t Trier, Fachbereich IV, Mathematik,
Informatik",
address = "Trier, Germany",
bookpages = "216 + i",
pages = "216 + i",
year = "2004",
ISSN = "0944-0488",
ISSN-L = "0944-0488",
bibdate = "Thu Apr 28 05:55:01 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Forschungsbericht Nr. 04-8.",
URL = "http://www.informatik.uni-trier.de/Reports/TR-08-2004;
http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6-complete.pdf",
acknowledgement = ack-nhfb,
keywords = "base conversion; correct rounding; decimal
floating-point arithmetic",
tableofcontents = "Introduction / Christiane Frougny / 1--4 \\
Invited Lecture: New ideas and results for solving
Differential equations symbolically [abstract only] /
Benno Fuchssteiner / 5--5 \\
Invited Lecture: A survey of Integer Relations
algorithms and rational numbers [abstract only] / Simon
Plouffe / 6--6 \\
Invited Lecture: Real Numbers and Robustness in
Computational Geometry / Stefan Schirra / 7--21 \\
Bridging the gap between formal specification and
bit-level floating-point arithmetic / Sylvie Boldo /
22--36 \\
Automata, Borel functions and real numbers in Pisot
base / B. Cagnard, P. Simonnet / 37--54 \\
Generating formally certified bounds on values and
round-off errors / Marc Daumas, Guillaume Melquiond /
55--70 \\
A proven correctly rounded logarithm in
double-precision / Florent de Dinechin, Catherine
Loirat, Jean-Michel Muller / 71--85 \\
A comparison of polynomial evaluation schemes / L.
Fousse, S. Schmitt / 86--102 \\
A comparison of real and complex pseudozero sets for
polynomials with real coefficients / Stef Graillat,
Philippe Langlois / 103--112 \\
On Intermediate Precision Required for
Correctly-Rounding Decimal-to-Binary Floating-Point
Conversion / Michel Hack / 113--134 \\
The Generic Multiple-Precision Floating-Point Addition
With Exact Rounding (as in the MPFR Library) / Vincent
Lef{\`e}vre / 135--145 \\
Software Division and Square Root Using Goldschmidt's
Algorithms / Peter Markstein / 146--157 \\
A Fast Algorithm for Julia Sets of Hyperbolic Rational
Functions / R. Rettinger / 158--171 \\
An extension of Chaitin's halting probability $\Omega$
to measurement operator in infinite dimensional quantum
system / Kohtaro Tadaki / 172--191 \\
On the Hierarchy of $\Delta_2^0$-Real Numbers / Xizhong
Zheng / 192--215 \\
Trierer Forschungsberichte Mathematik / Informatik [one
page list of reports] / 1--1 (216--216)",
}
@Proceedings{ACM:2004:FAS,
editor = "{ACM}",
booktitle = "{FPGA 2004: ACM\slash SIGDA Twelfth ACM International
Symposium on Field-Programmable Gate Arrays, Monterey
Beach Hotel, Monterey, California, USA: February
22--24, 2004}",
title = "{FPGA 2004: ACM\slash SIGDA Twelfth ACM International
Symposium on Field-Programmable Gate Arrays, Monterey
Beach Hotel, Monterey, California, USA: February
22--24, 2004}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "vi + 260",
year = "2004",
ISBN = "1-58113-829-6",
ISBN-13 = "978-1-58113-829-0",
LCCN = "TK7895.G36 A26 2004",
bibdate = "Sat Oct 9 15:25:33 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM order number 480040.",
URL = "http://portal.acm.org/toc.cfm?id=968280",
acknowledgement = ack-nhfb,
subject = "Gate array circuits; Congresses; Field programmable
gate arrays; Programmable array logic",
}
@Proceedings{ACM:2004:GVN,
editor = "{ACM}",
booktitle = "{GLSVLSI '04: VLSI in the nanometer era: proceedings
of the 2004 ACM Great Lakes Symposium on VLSI, Radisson
Hotel, Boston, MA, USA, April 26-28, 2004}",
title = "{GLSVLSI '04: VLSI in the nanometer era: proceedings
of the 2004 ACM Great Lakes Symposium on VLSI, Radisson
Hotel, Boston, MA, USA, April 26-28, 2004}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiii + 467",
year = "2004",
ISBN = "1-58113-853-9",
ISBN-13 = "978-1-58113-853-5",
LCCN = "????",
bibdate = "Thu Aug 7 18:09:26 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.gbv.de:20011/gvk",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2004:YAS,
editor = "ACM",
booktitle = "20 Years of the {ACM/SIGPLAN} Conference on
Programming Language Design and Implementation
(1979--1999): A Selection",
title = "20 Years of the {ACM}/{SIGPLAN} Conference on
Programming Language Design and Implementation
(1979--1999): a Selection",
volume = "39(4)",
publisher = pub-ACM,
address = pub-ACM:adr,
year = "2004",
ISBN = "1-58113-623-4",
ISBN-13 = "978-1-58113-623-4",
LCCN = "????",
bibdate = "Sat Nov 29 11:38:05 2003",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:2004:ICM,
editor = "Anonymous",
booktitle = "{6th International Conference on Mathematics in Signal
Processing: Cirencester, December 14--16, 2004}",
title = "{6th International Conference on Mathematics in Signal
Processing: Cirencester, December 14--16, 2004}",
publisher = "????",
address = "????",
year = "2004",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Dec 4 10:10:18 MST 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Arnold:2004:PAI,
editor = "Jeffrey Arnold",
booktitle = "{Proceedings / 12th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines, FCCM
2004: 20--23 April 2004, Napa Valley, California}",
title = "{Proceedings / 12th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines, FCCM
2004: 20--23 April 2004, Napa Valley, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 346",
year = "2004",
ISBN = "0-7695-2230-0",
ISBN-13 = "978-0-7695-2230-2",
LCCN = "????",
bibdate = "Sat Jun 25 12:49:50 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
}
@Proceedings{Druin:2004:IDC,
editor = "Allison Druin and Juan Pablo Hourcade and Sharmon
Kollet",
booktitle = "{Interactive Design \& Children 2004: Building a
Community}",
title = "{Interactive Design \& Children 2004: Building a
Community}",
publisher = "College Park IDC",
address = "College Park, MD, USA",
pages = "190",
year = "2004",
ISBN = "1-58113-791-5",
ISBN-13 = "978-1-58113-791-0",
LCCN = "QA76.9.H85 C746 2004",
bibdate = "Fri Aug 08 09:07:40 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Hilledt:2004:AME,
editor = "James M. Hill and Ross R. Moore",
booktitle = "{Applied mathematics entering the 21st Century:
invited talks from the ICIAM 2003 Congress}",
title = "{Applied mathematics entering the 21st Century:
invited talks from the ICIAM 2003 Congress}",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xv + 413",
year = "2004",
ISBN = "0-89871-559-8",
ISBN-13 = "978-0-89871-559-0",
LCCN = "QA7 .A6665 2004; QA7 .A67 2004; QA1 .I57 2004",
bibdate = "Thu Nov 8 19:52:42 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "Papers appearing in this volume are the Invited Talks
given at ICIAM 2003, the 5th International Congress of
Industrial and Applied Mathematics, held in Sydney over
the period July 7 to 11, 2003.",
subject = "Mathematics; Congresses; Applied mathematics",
}
@Proceedings{IEEE:2004:IICa,
editor = "{IEEE}",
booktitle = "{IEEE} International Conference on Computer Design:
{VLSI} in Computers and Processors, 2004. {ICCD 2004}.
Proceedings. 11--13 October 2004",
title = "{IEEE} International Conference on Computer Design:
{VLSI} in Computers and Processors, 2004. {ICCD} 2004.
Proceedings. 11--13 October 2004",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xviii + 578",
year = "2004",
ISBN = "0-7695-2231-9",
ISBN-13 = "978-0-7695-2231-9",
LCCN = "TK7888.4 .I23 2004",
bibdate = "Fri Mar 25 05:56:18 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
price = "UK\pounds 121.00",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2004:IICb,
editor = "{IEEE}",
booktitle = "{15th IEEE International Conference on
Application-Specific Systems, Architectures and
Processors: proceedings: September 2--29, 2004,
Galveston, Texas}",
title = "{15th IEEE International Conference on
Application-Specific Systems, Architectures and
Processors: proceedings: September 2--29, 2004,
Galveston, Texas}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 412",
year = "2004",
ISBN = "0-7695-2226-2",
ISBN-13 = "978-0-7695-2226-5",
LCCN = "TK7874.6 .I58 2004",
bibdate = "Sun Mar 4 21:48:24 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Application-Specific
Systems, Architectures, and Processors (15th: 2004:
Galveston, Tex.)",
remark = "IEEE Computer Society Order Number P2226.",
subject = "Signal processing; Digital techniques; Congresses;
Array processors; Application-specific integrated
circuits",
}
@Proceedings{IEEE:2004:IICc,
editor = "{IEEE}",
booktitle = "{2004 IEEE International Conference on Acoustics,
Speech, and Signal Processing: proceedings: May 17--21,
2004, Fairmont Queen Elizabeth Hotel, Montreal, Quebec,
Canada (ICASSP '04)}",
title = "{2004 IEEE International Conference on Acoustics,
Speech, and Signal Processing: proceedings: May 17--21,
2004, Fairmont Queen Elizabeth Hotel, Montreal, Quebec,
Canada (ICASSP '04)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2004",
ISBN = "0-7803-8484-9",
ISBN-13 = "978-0-7803-8484-2",
LCCN = "TK7882.S65 I61 2004",
bibdate = "Sun Feb 20 11:05:28 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number: 04CH37568",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=9248",
acknowledgement = ack-nhfb,
remark = "Vol. 1. Speech processing. Vol. 2. Sensor array and
Multichannel signal processing; signal processing
theory and methods. Vol. 3. Image and multidimensional
processing; special sessions. Vol. 4. Audio and
electroacoustics signal processing for communications.
Vol. 5. Design and implementation of signal processing
systems; industry technology tracks; machine learning
for signal processing; multimedia signal processing;
signal processing for education",
subject = "speech processing systems; congresses; signal
processing systems; electro-acoustics; underwater
acoustics; integrated circuits; very large scale
integration",
}
@Proceedings{IEEE:2004:IIS,
editor = "{IEEE}",
booktitle = "{2004 IEEE International Symposium on Computer-Aided
Control System Design: September 2--4, 2004, the Grand
Hotel, Taipei, Taiwan}",
title = "{2004 IEEE International Symposium on Computer-Aided
Control System Design: September 2--4, 2004, the Grand
Hotel, Taipei, Taiwan}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xv + 377 + 3 + 3",
year = "2004",
DOI = "https://doi.org/10.1109/CACSD.2004.1393830",
ISBN = "0-7803-8636-1",
ISBN-13 = "978-0-7803-8636-5",
LCCN = "TJ212.2 .I32495 2004",
bibdate = "Mon Nov 1 10:36:39 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "IEEE Catalog Number 04TH8770.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=9600",
acknowledgement = ack-nhfb,
subject = "Automatic control; Data processing; Congresses;
Computer-aided design",
}
@Proceedings{IEEE:2004:PJC,
editor = "{IEEE}",
booktitle = "{Proceedings of the 2003 Joint Conference of the
Fourth International Conference on Information,
Communications and Signal Processing, 2003 and the
Fourth Pacific Rim Conference on Multimedia, 15--18
December 2003, Meritus Mandarin Singapore Hotel,
Singapore}",
title = "{Proceedings of the 2003 Joint Conference of the
Fourth International Conference on Information,
Communications and Signal Processing, 2003 and the
Fourth Pacific Rim Conference on Multimedia, 15--18
December 2003, Meritus Mandarin Singapore Hotel,
Singapore}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2004",
ISBN = "0-7803-8185-8",
ISBN-13 = "978-0-7803-8185-8",
LCCN = "TK5102.9 .J65 2003",
bibdate = "Sun Feb 20 11:01:10 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 03EX758.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=9074",
acknowledgement = ack-nhfb,
}
@Proceedings{Luk:2004:ASP,
editor = "Franklin T. Luk",
booktitle = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations XIV:
4--6 August 2004, Denver, Colorado, USA}",
title = "Proceedings of {SPIE: Advanced signal processing
algorithms, architectures, and implementations XIV:
4--6 August 2004, Denver, Colorado, USA}",
volume = "5559",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "viii + 464",
year = "2004",
ISBN = "0-8194-5497-4",
ISBN-13 = "978-0-8194-5497-3",
ISSN = "0277-786X (print), 1996-756X (electronic)",
LCCN = "TK5102.5 .A3173 2004; TK5102.5 .A3322 2004",
bibdate = "Sun Mar 4 21:50:40 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
series = "SPIE proceedings series",
acknowledgement = ack-nhfb,
subject = "Algorithms; Congresses; Signal processing; Digital
techniques; Computer architecture",
}
@Proceedings{Selvaraj:2004:PES,
editor = "Henry Selvaraj",
booktitle = "{Proceedings of the EUROMICRO System on Digital System
Design: 31 August--3 September 2004, Rennes, France}",
title = "{Proceedings of the EUROMICRO System on Digital System
Design: 31 August--3 September 2004, Rennes, France}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 631",
year = "2004",
ISBN = "0-7695-2203-3",
ISBN-13 = "978-0-7695-2203-6",
LCCN = "QA76.9.S88 E97 2004; QA76.9.S88",
bibdate = "Sun Mar 4 21:45:21 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "Euromicro Symposium on Digital Systems Design (2004:
Rennes, France)",
subject = "Digital electronics; Congresses; System design;
Computer architecture",
}
@Proceedings{Smailagic:2004:ETV,
editor = "Asim Smailagic and Magdy A. Bayoumi",
booktitle = "Emerging trends in {VLSI} systems design: proceedings:
{IEEE} Computer Society Annual Symposium on {VLSI,
19--20} February 2004, Lafayette, Louisiana {[ISVLSI
2004]}",
title = "Emerging trends in {VLSI} systems design: proceedings:
{IEEE} Computer Society Annual Symposium on {VLSI},
19--20 February 2004, Lafayette, Louisiana [{ISVLSI}
2004]",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 324",
year = "2004",
ISBN = "0-7695-2097-9",
ISBN-13 = "978-0-7695-2097-1",
LCCN = "TK7874 .I122 2004",
bibdate = "Wed May 04 07:54:20 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society order number P2097.",
acknowledgement = ack-nhfb,
}
@Book{Wahdan:2004:IHE,
editor = "Abdel-Moniem Wahdan",
booktitle = "{ICEEC'04: 2004 International Conference on
Electrical, Electronic and Computer Engineering:
proceedings: 5--7 September, 2004, Cairo, Egypt}",
title = "{ICEEC'04: 2004 International Conference on
Electrical, Electronic and Computer Engineering:
proceedings: 5--7 September, 2004, Cairo, Egypt}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xlv + 954",
year = "2004",
bibdate = "Tue Jul 19 08:01:02 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "IEEE catalog number 04EX893.",
acknowledgement = ack-nhfb,
subject = "Electric engineering; Congresses; Electronics;
Congresses; Computer engineering; Congresses",
}
@Proceedings{ACM:2005:ASI,
editor = "{ACM}",
booktitle = "{ASSETS 2005: the Seventh International ACM SIGACCESS
Conference on Computers and Accessibility: October
9--12, 2005, Baltimore, Maryland, USA}",
title = "{ASSETS 2005: the Seventh International ACM SIGACCESS
Conference on Computers and Accessibility: October
9--12, 2005, Baltimore, Maryland, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "ix + 223",
year = "2005",
ISBN = "1-59593-159-7",
ISBN-13 = "978-1-59593-159-7",
LCCN = "????",
bibdate = "Thu Aug 7 18:45:20 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.gbv.de:20011/gvk",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2005:FAS,
editor = "{ACM}",
booktitle = "{FPGA 2005: ACM\slash SIGDA Thirteenth ACM
International Symposium on Field-Programmable Gate
Arrays, Monterey Beach Resort, Monterey, California,
USA: February 20--22, 2005}",
title = "{FPGA 2005: ACM\slash SIGDA Thirteenth ACM
International Symposium on Field-Programmable Gate
Arrays, Monterey Beach Resort, Monterey, California,
USA: February 20--22, 2005}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "vi + 282",
year = "2005",
ISBN = "1-59593-029-9",
ISBN-13 = "978-1-59593-029-3",
LCCN = "TK7895.G36 A26 2005",
bibdate = "Sat Oct 9 14:32:27 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "ACM order number 480050.",
acknowledgement = ack-nhfb,
subject = "gate array circuits; congresses; field programmable
gate arrays; programmable array logic",
}
@Proceedings{Bein:2005:PIS,
editor = "Wolfgang Bein",
booktitle = "{Proceedings: 8th International Symposium on Parallel
Architectures, Algorithms, and Networks: December 7--9,
2005, Las Vegas Nevada, USA: ISPAN 2005}",
title = "{Proceedings: 8th International Symposium on Parallel
Architectures, Algorithms, and Networks: December 7--9,
2005, Las Vegas Nevada, USA: ISPAN 2005}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 548",
year = "2005",
DOI = "https://doi.org/10.1109/ISPAN.2005.2",
ISBN = "0-7695-2509-1",
ISBN-13 = "978-0-7695-2509-9",
ISSN = "1087-4089",
LCCN = "QA76.58 .I5673 2005",
bibdate = "Sat Oct 9 14:43:16 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society Order Number P2509.",
acknowledgement = ack-nhfb,
subject = "parallel processing (electronic computers);
congresses; computer algorithms; computer networks;
computer architecture",
}
@Book{Copeland:2005:ATA,
editor = "B. Jack Copeland",
booktitle = "{Alan Turing}'s {Automatic Computing Engine}: the
master codebreaker's struggle to build the modern
computer",
title = "{Alan Turing}'s {Automatic Computing Engine}: the
master codebreaker's struggle to build the modern
computer",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xx + 553",
year = "2005",
ISBN = "0-19-856593-3 (hardcover)",
ISBN-13 = "978-0-19-856593-2 (hardcover)",
LCCN = "QA75 .A43 2005",
MRclass = "01A80 (01-06 01A60 68-03 94-03)",
MRnumber = "2164870 (2006g:01020)",
MRreviewer = "A. D. Booth",
bibdate = "Sat Nov 19 18:33:05 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
URL = "http://ukcatalogue.oup.com/product/9780198565932.do;
http://www.oxfordscholarship.com/oso/public/content/maths/9780198565932/toc.html",
abstract = "The mathematical genius Alan Turing (1912--1954) was
one of the greatest scientists and thinkers of the 20th
century. Now well known for his crucial wartime role in
breaking the ENIGMA code, he was the first to conceive
of the fundamental principle of the modern computer ---
the idea of controlling a computing machine's
operations by means of coded instructions, stored in
the machine's `memory'. In 1945, Turing drew up his
revolutionary design for an electronic computing
machine --- his Automatic Computing Engine (`ACE'). A
pilot model of the ACE ran its first programme in 1950
and the production version, the `DEUCE', went on to
become a cornerstone of the fledgling British computer
industry. The first `personal' computer was based on
Turing's ACE. This book describes Turing's struggle to
build the modern computer. It contains first-hand
accounts by Turing and by the pioneers of computing who
worked with him. The book describes the hardware and
software of the ACE and contains chapters describing
Turing's path-breaking research in the fields of
Artificial Intelligence (AI) and Artificial Life
(A-Life).",
acknowledgement = ack-nhfb,
remark = "Originally published: New York; London: Springer,
2003",
subject = "Turing, Alan Mathison; Computers; Great Britain;
History; Computer engineering; Great Britain; History",
tableofcontents = "Foreword / Donald W. Davies \\
Introduction / B. Jack Copeland \par
Part I: The National Physical Laboratory and the ACE
Project \\
A Century of Measurement and Computation at the
National Physical Laboratory, 1900--2000 / Eileen
Magnello \\
The Creation of the NPL Mathematics Division / Mary
Croarken \\
The Origins and Development of the ACE Project / B.
Jack Copeland \\
The Pilot ACE at the National Physical Laboratory,
James H. Wilkinson \par
Part II: Turing and the History of Computing \\
The ACE and the Shaping of British Computing / Martin
Campbell-Kelly \\
Computer Architecture and the ACE Computers / Robert
Doran \\
Turing and the Computer / B. Jack Copeland and Diane
Proudfoot \\
From Turing Machine to ``Electronic Brain'' / Teresa
Numerico \par
Part III: The ACE Computers \\
The Pilot ACE Instruction Format / Henry John Norton
\\
Programming the Pilot ACE / J.G. Hayes \\
The Pilot ACE: from Concept to Reality / Robin A.
Vowels \\
The DEUCE --- a User's View / Robin A. Vowels \\
Applications of the Pilot ACE and the DEUCE / Tom
Vickers \\
The ACE Test Assembly, the Pilot ACE, the Big ACE, and
the Bendix G15 / Harry D. Huskey \\
The ACE Simulator and the Cybernetic Model / Michael
Woodger \\
The Pilot Model and the Big ACE on the Web / Benjamin
Wells \par
Part IV: Electronics \\
How Valves Work / David O. Clayden \\
Recollections of Early Vacuum Tube Circuits / Maurice
Wilkes \\
Circuit Design of the Pilot ACE and the Big ACE / David
O. Clayden \par
Part V: Technical Reports and Lectures on the ACE and
the Pilot ACE, 1945--1951 \\
Proposed Electronic Calculator (1945) / Alan M. Turing
\\
Notes on Memory (1945) / Alan M. Turing \\
The Turing--Wilkinson Lecture Series (1946--1947) /
Alan M. Turing and James H. Wilkinson \\
The State of the Art in Electronic Digital Computing in
Britain and the United States (1947) / Harry D.
Huskey",
}
@Proceedings{IEEE:2005:DAT,
editor = "{IEEE}",
booktitle = "{Design, Automation, and Test in Europe: proceedings:
Munich, Germany, March 7--11, 2005}",
title = "{Design, Automation, and Test in Europe: proceedings:
Munich, Germany, March 7--11, 2005}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2005",
ISBN = "0-7695-2288-2",
ISBN-13 = "978-0-7695-2288-3",
LCCN = "TK7870 .D467 2005",
bibdate = "Sun Feb 20 11:17:37 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "IEEE Computer Society Order Number P2288.",
acknowledgement = ack-nhfb,
meetingname = "Design, Automation, and Test in Europe Conference and
Exhibition (2005 : Munich, Germany)",
subject = "Electronic systems; Design and construction;
Congresses; Electronic circuit design; Data processing;
Computer-aided design; Electronic industries;
Automation",
}
@Proceedings{IEEE:2005:ICS,
editor = "{IEEE}",
booktitle = "{IEEE Computer Society Annual Symposium on VLSI
(ISVLSI 2005)}",
title = "{IEEE Computer Society Annual Symposium on VLSI
(ISVLSI 2005)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "332 (est.)",
year = "2005",
ISBN = "0-7695-2365-X",
ISBN-13 = "978-0-7695-2365-1",
LCCN = "????",
bibdate = "Sat Jun 25 13:00:07 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.computer.org/cspress/CATALOG/p2365.htm",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2005:IIS,
editor = "{IEEE}",
booktitle = "{IEEE International Symposium on Circuits and Systems
(ISCAS): May 23--26, 2005, International Conference
Center, Kobe, Japan: conference proceedings}",
title = "{IEEE International Symposium on Circuits and Systems
(ISCAS): May 23--26, 2005, International Conference
Center, Kobe, Japan: conference proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2005",
ISBN = "0-7803-8834-8",
ISBN-13 = "978-0-7803-8834-5",
LCCN = "TK454.2 .I22 2005",
bibdate = "Mon Mar 5 08:19:11 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "IEEE International Symposium on Circuits and Systems
(2005: Kobe-shi, Japan)",
remark = "IEEE Catalog Number: 05CH37618.",
subject = "Electronics; Congresses; Signal processing; Digital
techniques; Electronic circuits; Neural networks
(Computer science); Integrated circuits; Very large
scale integration",
}
@Proceedings{IEEE:2005:MSC,
editor = "{IEEE}",
booktitle = "{2005 48th Midwest Symposium on Circuits and Systems:
[conference proceedings: Cincinnati, Ohio, August
7--10, 2005]}",
title = "{2005 48th Midwest Symposium on Circuits and Systems:
[conference proceedings: Cincinnati, Ohio, August
7--10, 2005]}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2005",
ISBN = "0-7803-9197-7",
ISBN-13 = "978-0-7803-9197-0",
LCCN = "TK3226 .M55 2005eb",
bibdate = "Sun Feb 20 11:11:21 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=10622",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2005:PII,
editor = "{IEEE}",
booktitle = "{Proceedings of the IEEE 16th International Conference
on Application-specific Systems, Architectures and
Processors, Samos, Greece, July 23--25, 2005 (ASAP
2005)}",
title = "{Proceedings of the IEEE 16th International Conference
on Application-specific Systems, Architectures and
Processors, Samos, Greece, July 23--25, 2005 (ASAP
2005)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2005",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Jun 25 13:09:23 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ece.uvic.ca/asap2005/",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2005:PIS,
editor = "{IEEE}",
booktitle = "{Proceedings of the 17th IEEE Symposium on Computer
Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
Massachusetts, USA}",
title = "{Proceedings of the 17th IEEE Symposium on Computer
Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
Massachusetts, USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2005",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Jun 21 19:02:16 2005",
bibsource = "http://arith17.polito.it/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
xxnote = "Not yet published: check editor??",
}
@Proceedings{IEEE:2005:PWE,
editor = "{IEEE}",
booktitle = "{Proceedings of the 2005 3rd Workshop on Embedded
Systems for Real Time Multimedia, 22--23 September
2005, New York Metropolitan Area}",
title = "{Proceedings of the 2005 3rd Workshop on Embedded
Systems for Real Time Multimedia, 22--23 September
2005, New York Metropolitan Area}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "140",
year = "2005",
DOI = "https://doi.org/10.1109/ESTMED.2005.1518044",
ISBN = "0-7803-9347-3",
ISBN-13 = "978-0-7803-9347-9",
LCCN = "QA76.575 .W67 2005",
bibdate = "Sat Oct 9 14:35:29 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "IEEE catalog number 5EX1149.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=10172",
acknowledgement = ack-nhfb,
subject = "Multimedia systems; Congresses; Embedded computer
systems",
}
@Proceedings{Luk:2005:ASP,
editor = "Franklin T. Luk",
booktitle = "{Advanced Signal Processing Algorithms, Architectures,
and Implementations XV, August, San Diego, CA, USA}",
title = "{Advanced Signal Processing Algorithms, Architectures,
and Implementations XV, August, San Diego, CA, USA}",
volume = "5910",
publisher = pub-SPIE,
address = pub-SPIE:adr,
pages = "????",
year = "2005",
CODEN = "PSISDG",
ISBN = "????",
ISBN-13 = "????",
ISSN = "0277-786X (print), 1996-756X (electronic)",
LCCN = "????",
bibdate = "Sat Jun 25 12:56:26 2005",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = j-PROC-SPIE,
acknowledgement = ack-nhfb,
}
@Proceedings{Montuschi:2005:PIS,
editor = "Paolo Montuschi and Eric (Eric Mark) Schwarz",
booktitle = "{Proceedings of the 17th IEEE Symposium on Computer
Arithmetic, ARITH-17 2005, June 27--29, 2005, Cape Cod,
Massachusetts, USA}",
title = "{Proceedings of the 17th IEEE Symposium on Computer
Arithmetic, ARITH-17 2005, June 27--29, 2005, Cape Cod,
Massachusetts, USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 298",
year = "2005",
ISBN = "0-7695-2366-8",
ISBN-13 = "978-0-7695-2366-8",
LCCN = "QA76.9.C62 .S95 2005",
bibdate = "Thu Sep 14 12:30:26 2006",
bibsource = "http://arith17.polito.it/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-17",
}
@Proceedings{Tang:2005:AIC,
editor = "Ting-Ao Tang and Yumei Huang and others",
booktitle = "{ASICON 2005: 2005, 6th International Conference on
ASIC proceedings, Shanghai, China, October 24--27,
2005}",
title = "{ASICON 2005: 2005, 6th International Conference on
ASIC proceedings, Shanghai, China, October 24--27,
2005}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2005",
ISBN = "0-7803-9210-8",
ISBN-13 = "978-0-7803-9210-6",
LCCN = "TK7874.6 2005",
bibdate = "Sun Feb 20 11:20:06 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number 05TH8820.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=10726",
acknowledgement = ack-nhfb,
meetingname = "International Conference on ASIC (6th : 2005 :
Shanghai, China)",
subject = "application specific integrated circuits; design and
construction; congresses; computer-aided design;
testing",
}
@Proceedings{Vassiliadis:2005:IIC,
editor = "Stamatis Vassiliadis and Nikitas J. Dimopoulos and
Sanjay Vishnu Rajopadhye",
booktitle = "{16th IEEE International Conference on
Application-Specific Systems, Architectures, and
Processors: ASAP 2005: 23--25 July 2005, Samos,
Greece}",
title = "{16th IEEE International Conference on
Application-Specific Systems, Architectures, and
Processors: ASAP 2005: 23--25 July 2005, Samos,
Greece}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 419",
year = "2005",
ISBN = "0-7695-2407-9",
ISBN-13 = "978-0-7695-2407-8",
LCCN = "TK7874.6 .I58 2005",
bibdate = "Sun Mar 4 21:53:56 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Application-Specific
Systems, Architectures, and Processors (16th: 2005:
Samos, Greece)",
subject = "Array processors; Congresses; Signal processing;
Digital techniques; Application specific integrated
circuits",
}
@Proceedings{ACM:2006:SCH,
editor = "{ACM}",
booktitle = "{SC'06: Conference on High Performance Networking and
Computing: proceedings of the 2006 ACM/IEEE conference
on Supercomputing, November 11--17, 2006, Tampa
Convention Center, Tampa, Florida, USA}",
title = "{SC'06: Conference on High Performance Networking and
Computing: proceedings of the 2006 ACM/IEEE conference
on Supercomputing, November 11--17, 2006, Tampa
Convention Center, Tampa, Florida, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2006",
ISBN = "0-7695-2700-0",
ISBN-13 = "978-0-7695-2700-0",
LCCN = "????",
bibdate = "Thu Nov 8 20:03:51 MST 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.bibsys.no:2100/BIBSYS",
note = "Contains one CD-ROM.",
acknowledgement = ack-nhfb,
meetingname = "Conference on High Performance Networking and
Computing 2006. Tampa, Florida",
}
@Proceedings{Anonymous:2006:PCR,
editor = "Anonymous",
booktitle = "{Proceedings of the 7th Conference on Real Numbers and
Computers (RNC 7) LORIA, Nancy, France, July 10--12,
2006}",
title = "{Proceedings of the 7th Conference on Real Numbers and
Computers (RNC 7) LORIA, Nancy, France, July 10--12,
2006}",
publisher = "????",
address = "????",
pages = "????",
year = "2006",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Jun 27 10:26:43 2006",
bibsource = "http://rnc7.loria.fr/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Bertels:2006:FPI,
editor = "Koen Bertels and Philip Leong and Eduardo Boemo",
booktitle = "{FPL 2006: Proceedings of the 16th International
Conference on Field-Programmable Logic and Applications
Meli{\'a} Madrid Princesa, Madrid, Spain: August
28--30, 2006}",
title = "{FPL 2006: Proceedings of the 16th International
Conference on Field-Programmable Logic and Applications
Meli{\'a} Madrid Princesa, Madrid, Spain: August
28--30, 2006}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xl + 975",
year = "2006",
DOI = "https://doi.org/10.1109/FPL.2006.311178",
ISBN = "1-4244-0312-X (softbound)",
ISBN-13 = "978-1-4244-0312-7 (softbound)",
LCCN = "TK7895.G36 I48 2006",
bibdate = "Sat Oct 9 15:27:53 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 06EX1349. Two volumes.",
acknowledgement = ack-nhfb,
subject = "Field programmable gate arrays; Congresses;
Programmable array logic",
}
@Proceedings{Cimatti:2006:FMH,
editor = "Alessandro Cimatti and Marco Bernardo",
booktitle = "{Formal methods for hardware verification: 6th
International School on Formal Methods for the Design
of Computer, Communication, and Software Systems, SFM
2006, Bertinoro, Italy, May 22--27, 2006: advanced
lectures}",
title = "{Formal methods for hardware verification: 6th
International School on Formal Methods for the Design
of Computer, Communication, and Software Systems, SFM
2006, Bertinoro, Italy, May 22--27, 2006: advanced
lectures}",
volume = "3965",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 242",
year = "2006",
DOI = "https://doi.org/10.1007/11757283",
ISBN = "3-540-34304-0",
ISBN-13 = "978-3-540-34304-2",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.9.F67 I586 2006",
bibdate = "Wed Nov 26 22:41:02 MST 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNCS,
URL = "http://www.loc.gov/catdir/enhancements/fy0661/2006925529-d.html;
http://www.loc.gov/catdir/toc/fy0705/2006925529.html",
acknowledgement = ack-nhfb,
subject = "formal methods (computer science); congresses;
integrated circuits; verification",
}
@Proceedings{Dimopoulos:2006:IIC,
editor = "Nikitas J. Dimopoulos and others",
booktitle = "{IEEE 17th International Conference on
Application-Specific Systems, Architectures, and
Processors: Steamboat Springs, Colorado, USA: September
11--13, 2006 [ASAP 2006]}",
title = "{IEEE 17th International Conference on
Application-Specific Systems, Architectures, and
Processors: Steamboat Springs, Colorado, USA: September
11--13, 2006 [ASAP 2006]}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 369",
year = "2006",
ISBN = "0-7695-2682-9",
ISBN-13 = "978-0-7695-2682-9",
ISSN = "1063-6862",
LCCN = "TK7874.6 .I57 2006",
bibdate = "Mon Mar 19 10:57:59 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "IEEE Computer Society Order Number P2682.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4019472",
acknowledgement = ack-nhfb,
meetingname = "IEEE International Conference on Application-Specific
Systems, Architectures, and Processors (17th: 2006:
Steamboat Springs, Colorado, USA)",
remark = "IEEE Computer Society Order Number P2682.",
subject = "Array processors; Congresses; Signal processing;
Digital techniques; Application specific integrated
circuits",
}
@Proceedings{Haddad:2006:ACP,
editor = "Hisham M. Haddad",
booktitle = "{Applied computing 2006: proceedings of the 2006 ACM
Symposium on Applied Computing, Dijon, France, April
23--27, 2006}",
title = "{Applied computing 2006: proceedings of the 2006 ACM
Symposium on Applied Computing, Dijon, France, April
23--27, 2006}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xliv + 1--938 + 939--1929 (2 volumes)",
year = "2006",
ISBN = "1-59593-108-2",
ISBN-13 = "978-1-59593-108-5",
LCCN = "QA76.76.A65 S95 2006",
bibdate = "Sat Feb 26 18:22:17 MST 2011",
bibsource = "catalog.princeton.edu:7090/voyager;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://portal.acm.org/toc.cfm?id=1141277",
acknowledgement = ack-nhfb,
remark = "Hosted by Bourgogne University, Dijon, France.",
subject = "Application software; Congresses; Electronic data
processing",
}
@Proceedings{Hess:2006:ANT,
editor = "Florian Hess and Sebastian Pauli and Michael Pohst",
booktitle = "Algorithmic number theory: {7th international
symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006:
proceedings}",
title = "Algorithmic number theory: {7th international
symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006:
proceedings}",
volume = "4076",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 598",
year = "2006",
DOI = "https://doi.org/10.1007/11792086",
ISBN = "3-540-36075-1 (paperback)",
ISBN-13 = "978-3-540-36075-9 (paperback)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA241 .A43 2006",
bibdate = "Mon May 31 12:35:41 MDT 2021",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
URL = "http://link.springer.com/10.1007/11792086;
http://springerlink.metapress.com/openurl.asp?genre=issue%26issn=0302-9743%26volume=4076",
acknowledgement = ack-nhfb,
meetingname = "Algorithmic Number Theory Symposium (7th : 2006).
Auteur.",
subject = "Number theory; Congresses; g{\'y}eom{\'y}etrie
alg{\'y}ebrique; courbe elliptique; algorithmique;
th{\'y}eorie nombre; Th{\'y}eorie des nombres;
Congr{\'y}es; Number theory.; Nombres, Th{\'y}eorie
des; Congr{\'y}es.; Th{\'y}eorie des nombres.; nombres
(math{\'y}ematiques); th{\'y}eorie; congr{\'y}es.;
algorithmique.; th{\'y}eorie.",
tableofcontents = "Invited Talks \\
Computing Pro-P Galois Groups \\
The Elliptic Curve Database for Conductors to 130000
\\
On the Computation of the Coefficients of a Modular
Form \\
Cohen--Lenstra Heuristics of Quadratic Number Fields
\\
Algebraic Number Theory \\
An Algorithm for Computing $p$-Class Groups of Abelian
Number Fields \\
Computation of Locally Free Class Groups \\
Numerical Results on Class Groups of Imaginary
Quadratic Fields \\
Cyclic Polynomials Arising from Kummer Theory of Norm
Algebraic Tori \\
The Totally Real Primitive Number Fields of
Discriminant at Most 109 \\
A Modular Method for Computing the Splitting Field of a
Polynomial \\
Analytic and Elementary Number Theory \\
On the Density of Sums of Three Cubes \\
The Mertens Conjecture Revisited \\
Fast Bounds on the Distribution of Smooth Numbers \\
Use of Extended Euclidean Algorithm in Solving a System
of Linear Diophantine Equations with Bounded Variables
\\
The Pseudosquares Prime Sieve \\
Doubly-Focused Enumeration of Pseudosquares and
Pseudocubes \\
Lattices \\
Practical Lattice Basis Sampling Reduction \\
LLL on the Average \\
On the Randomness of Bits Generated by Sufficiently
Smooth Functions \\
Curves and Varieties over Fields of Characteristic Zero
\\
Computing a Lower Bound for the Canonical Height on
Elliptic Curves over ? \\
Points of Low Height on Elliptic Curves and Surfaces I:
Elliptic Surfaces over with Small d \\
Shimura Curves for Level-3 Subgroups of the (2,3,7)
Triangle Group, and Some Other Examples \\
The Asymptotics of Points of Bounded Height on Diagonal
Cubic and Quartic Threefolds \\
Testing Equivalence of Ternary Cubics \\
Classification of Genus 3 Curves in Special Strata of
the Moduli Space \\
Heegner Point Computations Via Numerical $p$-Adic
Integration \\
Symmetric Powers of Elliptic Curve $L$-Functions \\
Determined Sequences, Continued Fractions, and
Hyperelliptic Curves \\
Computing CM Points on Shimura Curves Arising from
Cocompact Arithmetic Triangle Groups \\
Arithmetic of Generalized Jacobians \\
Hidden Pairings and Trapdoor DDH Groups \\
Constructing Pairing-Friendly Elliptic Curves with
Embedding Degree 10 \\
Fast Bilinear Maps from the Tate--Lichtenbaum Pairing
on Hyperelliptic Curves \\
High Security Pairing-Based Cryptography Revisited \\
Efficiently Computable Endomorphisms for Hyperelliptic
Curves \\
Construction of Rational Points on Elliptic Curves over
Finite Fields \\
20 Years of ECM \\
Discrete Logarithms \\
An Index Calculus Algorithm for Plane Curves of Small
Degree \\
Signature Calculus and Discrete Logarithm Problems \\
Spectral Analysis of Pollard Rho Collisions \\
Hard Instances of the Constrained Discrete Logarithm
Problem",
}
@Proceedings{IEEE:2006:ICV,
editor = "{IEEE}",
booktitle = "{19th International Conference on VLSI Design: held
jointly with the 5th International Conference on
Embedded Systems Design: proceedings: 3--7 January,
2005 [2006], Hyderabad, India}",
title = "{19th International Conference on VLSI Design: held
jointly with the 5th International Conference on
Embedded Systems Design: proceedings: 3--7 January,
2005 [2006], Hyderabad, India}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xli + 837",
year = "2006",
ISBN = "0-7695-2502-4 (paperback)",
ISBN-13 = "978-0-7695-2502-0 (paperback)",
LCCN = "TK7874 .I4728 2006",
bibdate = "Mon Mar 19 11:04:16 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
meetingname = "International Conference on VLSI Design (19th: 2006:
Hyderabad, India)",
remark = "Sister Conference IEEE/ACM Design Automation
Conference. IEEE Computer Society Order Number P2502.",
subject = "Integrated circuits; Very large scale integration;
Design and construction; Congresses; Signal processing;
Digital techniques; Circuits",
}
@Proceedings{IEEE:2006:PIW,
editor = "{IEEE}",
booktitle = "{Proceedings of the 2006 IEEE Workshop on Design and
Diagnostics of Electronic Circuits and Systems: April
18--21, 2006, Prague, Czech Republic}",
title = "{Proceedings of the 2006 IEEE Workshop on Design and
Diagnostics of Electronic Circuits and Systems: April
18--21, 2006, Prague, Czech Republic}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "x + 291",
year = "2006",
ISBN = "1-4244-0184-4 (softbound)",
ISBN-13 = "978-1-4244-0184-0 (softbound)",
LCCN = "TK7874 .I32745 2005",
bibdate = "Mon Mar 19 11:08:48 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "IEEE catalog number: 06EX1307",
acknowledgement = ack-nhfb,
meetingname = "IEEE Workshop on Design and Diagnostics of Electronic
Circuits and Systems (9th: 2006: Prague, Czech
Republic)",
subject = "Integrated circuits; Testing; Congresses; Design",
}
@Proceedings{Menezes:2006:PAS,
editor = "Ronaldo Menezes",
booktitle = "{Proceedings of the 44th annual Southeast Regional
Conference 2006: Melbourne, Florida, March 10--12,
2006}",
title = "{Proceedings of the 44th annual Southeast Regional
Conference 2006: Melbourne, Florida, March 10--12,
2006}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "823",
year = "2006",
ISBN = "1-59593-315-8 (print)",
ISBN-13 = "978-1-59593-315-7 (print)",
LCCN = "QA75.5 A184 2006 E",
bibdate = "Sat Oct 9 15:04:24 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
subject = "Computer-assisted instruction; Congresses; Database
management; Electronic data processing",
}
@Proceedings{Mohanty:2006:IIC,
editor = "Saraju P. Mohanty and Anirudha Sahoo",
booktitle = "{ICIT 2006: 9th International Conference on
Information Technology: proceedings: 18-21 December,
2006, Bhubaneswar, India}",
title = "{ICIT 2006: 9th International Conference on
Information Technology: proceedings: 18-21 December,
2006, Bhubaneswar, India}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xviii + 308",
year = "2006",
ISBN = "0-7695-2635-7",
ISBN-13 = "978-0-7695-2635-5",
LCCN = "QA76.575 .I25 2006",
bibdate = "Thu Aug 7 18:14:32 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Information Technology
(9th : 2006 : Bhubaneswar, India)",
remark = "IEEE Computer Society Order Number P2635.",
subject = "Multimedia systems; Congresses; Information
technology; Computer networks; Coding theory",
}
@Proceedings{Pocek:2006:FAI,
editor = "Kenneth L. Pocek and Duncan A. Buell",
booktitle = "{FCCM 2006: 14th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines:
proceedings: 24--26 April, 2006, Napa, California}",
title = "{FCCM 2006: 14th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines:
proceedings: 24--26 April, 2006, Napa, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 355",
year = "2006",
DOI = "https://doi.org/10.1109/FCCM.2006.2",
ISBN = "0-7695-2661-6",
ISBN-13 = "978-0-7695-2661-4",
LCCN = "TK7895.G36 .I36 2006",
bibdate = "Sat Oct 9 14:57:20 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4020883",
acknowledgement = ack-nhfb,
remark = "IEEE Computer Society Order Number P2661.",
subject = "Field programmable gate arrays; Congresses; Computer
engineering",
}
@Proceedings{Yi:2006:SAI,
editor = "Kwangkeun Yi",
booktitle = "{Static Analysis: 13th International Symposium, SAS
2006, Seoul, Korea, August 29--31, 2006. Proceedings}",
title = "{Static Analysis: 13th International Symposium, SAS
2006, Seoul, Korea, August 29--31, 2006. Proceedings}",
volume = "4134",
publisher = pub-SV,
address = pub-SV:adr,
pages = "317 (est.)",
year = "2006",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/11823230",
ISBN = "3-540-37756-5 (print), 3-540-37758-1 (e-book)",
ISBN-13 = "978-3-540-37756-6 (print), 978-3-540-37758-0
(e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "????",
bibdate = "Wed Dec 19 15:20:21 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
series = ser-LNCS,
URL = "http://www.springerlink.com/content/978-3-540-37758-0",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2007:SPA,
editor = "{ACM}",
booktitle = "{STOC '07: proceedings of the 39th Annual ACM
Symposium on Theory of Computing, San Diego,
California, USA, June 11--13, 2007}",
title = "{STOC '07: proceedings of the 39th Annual ACM
Symposium on Theory of Computing, San Diego,
California, USA, June 11--13, 2007}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xv + 718",
year = "2007",
ISBN = "1-59593-631-9",
ISBN-13 = "978-1-59593-631-8",
LCCN = "????",
bibdate = "Fri Jun 20 18:35:01 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.bibsys.no:2100/BIBSYS",
acknowledgement = ack-nhfb,
}
@Proceedings{Alefeld:2007:SCC,
editor = "G{\"o}tz Alefeld and Mitsuhiro T. Nakao and Siegfried
M. Rump",
booktitle = "Scientific computing, computer arithmetic, and
validated numerics: {(SCAN 2004)} [Fukuoka, Japan,
October 4--8, 2004]",
title = "Scientific computing, computer arithmetic, and
validated numerics: ({SCAN} 2004) [Fukuoka, Japan,
October 4--8, 2004]",
volume = "199(2)",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "194--453",
day = "15",
month = feb,
year = "2007",
CODEN = "JCAMDI",
ISSN = "0771-050X; 0377-0427",
LCCN = "????",
bibdate = "Thu Dec 28 20:59:33 2006",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Journal of computational and applied mathematics",
acknowledgement = ack-nhfb,
}
@Proceedings{Becker:2007:EVT,
editor = "J{\"u}rgen Becker",
booktitle = "{Emerging VLSI technologies and architectures:
proceedings; IEEE Computer Society Annual Symposium on
VLSI, ISVLSI 2007; Porto Alegre, Brazil, 9-11 May
2007}",
title = "{Emerging VLSI technologies and architectures:
proceedings; IEEE Computer Society Annual Symposium on
VLSI, ISVLSI 2007; Porto Alegre, Brazil, 9-11 May
2007}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xv + 251",
year = "2007",
ISBN = "0-7695-2896-1",
ISBN-13 = "978-0-7695-2896-0",
LCCN = "????",
bibdate = "Thu Aug 7 18:55:20 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
}
@Proceedings{Bertels:2007:PIC,
editor = "Koen Bertels and Walid Najjar and Arjan van Genderen
and Stamatis Vassiliadis",
booktitle = "{Proceedings of the International Conference on Field
Programmable Logic and Applications (FPL 2007),
Amsterdam, The Netherlands, August 27--29, 2007}",
title = "{Proceedings of the International Conference on Field
Programmable Logic and Applications (FPL 2007),
Amsterdam, The Netherlands, August 27--29, 2007}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2007",
ISBN = "1-4244-1060-6",
ISBN-13 = "978-1-4244-1060-6",
LCCN = "TK7895.G36 2007",
bibdate = "Thu Mar 24 21:23:04 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number 07EX1708C.",
acknowledgement = ack-nhfb,
}
@Proceedings{Brown:2007:PIS,
editor = "C. W. Brown",
booktitle = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
title = "{Proceedings of the 2007 International Symposium on
Symbolic and Algebraic Computation, July 29--August 1,
2007, University of Waterloo, Waterloo, Ontario,
Canada}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2007",
ISBN = "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
ISBN-13 = "978-1-59593-743-8 (print), 978-1-59593-742-1
(CD-ROM)",
LCCN = "QA76.5 S98 2007",
bibdate = "Fri Jun 20 08:53:37 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
note = "ACM order number 505070.",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2007:ACP,
editor = "{IEEE}",
booktitle = "{ASAP 07: conference proceedings: IEEE 18th
International Conference on Application-Specific
Systems, Architectures, and Processors: Montr{\'e}al,
Canada: July 8--11, 2007}",
title = "{ASAP 07: conference proceedings: IEEE 18th
International Conference on Application-Specific
Systems, Architectures, and Processors: Montr{\'e}al,
Canada: July 8--11, 2007}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2007",
ISBN = "1-4244-1027-4",
ISBN-13 = "978-1-4244-1027-9",
LCCN = "TK7874.6 .I57a 2007",
bibdate = "Sun Feb 20 17:46:31 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4429947",
acknowledgement = ack-nhfb,
meetingname = "IEEE International Conference on Application-Specific
Systems, Architectures, and Processors (18th : 2007 :
Montr{\'e}al, Qu{\'e}bec)",
subject = "array processors; congresses; signal processing;
digital techniques; application-specific integrated
circuits",
}
@Proceedings{IEEE:2007:API,
editor = "{IEEE}",
booktitle = "{ADCOM '07: Proceedings of the 15th International
Conference on Advanced Computing and Communications}",
title = "{ADCOM '07: Proceedings of the 15th International
Conference on Advanced Computing and Communications}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2007",
ISBN = "0-7695-3059-1",
ISBN-13 = "978-0-7695-3059-8",
LCCN = "????",
bibdate = "Thu Aug 7 18:34:32 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2007:ICC,
editor = "{IEEE}",
booktitle = "{25th International Conference on Computer Design,
2007 (ICCD 2007), 7--10 October 2007, Resort at Squaw
Creek, Lake Tahoe, California}",
title = "{25th International Conference on Computer Design,
2007 (ICCD 2007), 7--10 October 2007, Resort at Squaw
Creek, Lake Tahoe, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2007",
ISBN = "1-4244-1258-7",
ISBN-13 = "978-1-4244-1258-7",
LCCN = "TK7888.4 .I35 2007eb",
bibdate = "Sat Dec 4 11:01:31 MST 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4591423",
acknowledgement = ack-nhfb,
subject = "Microcomputers; Design and construction; Congresses;
Electronic digital computers; Circuits; Integrated
circuits; Very large scale integration; Computer
engineering",
}
@Proceedings{IEEE:2007:ICI,
editor = "{IEEE}",
booktitle = "{International Symposium on Integrated Circuits, 2007.
ISIC '07. 26--28 Sept. 2007}",
title = "{International Symposium on Integrated Circuits, 2007.
ISIC '07. 26--28 Sept. 2007}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "207",
year = "2007",
ISBN = "1-4244-0797-4",
ISBN-13 = "978-1-4244-0797-2",
LCCN = "TK7874 2007",
bibdate = "Sun Feb 20 11:23:35 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4441779",
acknowledgement = ack-nhfb,
meetingname = "International Symposium on Integrated Circuits
(2007)",
subject = "integrated circuits; congresses; very large scale
integration; microprocessors; radio frequency
identification systems; computer-aided design",
}
@Proceedings{IEEE:2007:ICV,
editor = "{IEEE}",
booktitle = "{20th International Conference on VLSI Design:
technology challenges in the nanoelectronics era: held
jointly with 6th International Conference on Embedded
Systems: proceedings: 6--10 January, 2007, Bangalore,
India}",
title = "{20th International Conference on VLSI Design:
technology challenges in the nanoelectronics era: held
jointly with 6th International Conference on Embedded
Systems: proceedings: 6--10 January, 2007, Bangalore,
India}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxxviii + 951",
year = "2007",
ISBN = "1-4244-3079-8",
ISBN-13 = "978-1-4244-3079-6",
LCCN = "TK7874 .I4728 2007",
bibdate = "Sun Feb 20 11:26:54 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society Order Number P2762.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4091978",
acknowledgement = ack-nhfb,
meetingname = "International Conference on VLSI Design (20e : 2007 :
Bangalore, Inde)",
subject = "circuits int\'egr\'es \`a tr\`es grande \'echelle;
conception et construction; congr\`es; traitement du
signal; techniques num\'eriques; ordinateurs;
circuits",
}
@Proceedings{IEEE:2007:IPI,
editor = "{IEEE}",
booktitle = "{ISMVL'07: Proceedings of the 37th International
Symposium on Multiple-Valued Logic, May 13--16, 2007}",
title = "{ISMVL'07: Proceedings of the 37th International
Symposium on Multiple-Valued Logic, May 13--16, 2007}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2007",
ISBN = "0-7695-2831-7",
ISBN-13 = "978-0-7695-2831-1",
ISSN = "0195-623X",
LCCN = "????",
bibdate = "Thu Aug 07 17:34:51 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Kornerup:2007:PIS,
editor = "Peter Kornerup and Jean-Michel Muller",
booktitle = "{Proceedings of the 18th IEEE Symposium on Computer
Arithmetic, June 25--27, 2007, Montpellier, France}",
title = "{Proceedings of the 18th IEEE Symposium on Computer
Arithmetic, June 25--27, 2007, Montpellier, France}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 269",
year = "2007",
ISBN = "0-7695-2854-6",
ISBN-13 = "978-0-7695-2854-0",
ISSN = "1063-6889",
LCCN = "QA76.9.C62",
bibdate = "Tue Jun 27 10:26:43 2006",
bibsource = "http://www.lirmm.fr/arith18/;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
odin2.bib.sdu.dk:210/Horizon",
URL = "http://www.lirmm.fr/arith18/",
acknowledgement = ack-nhfb,
keywords = "ARITH-18",
}
@Proceedings{Luther:2007:GII,
editor = "W. Luther and W. Otten",
booktitle = "{12th GAMM--IMACS International Symposium on
Scientific Computing, Computer Arithmetic and Validated
Numerics: SCAN 2006: conference post-proceedings:
September 26--29, 2006, Duisburg, Germany}",
title = "{12th GAMM--IMACS International Symposium on
Scientific Computing, Computer Arithmetic and Validated
Numerics: SCAN 2006: conference post-proceedings:
September 26--29, 2006, Duisburg, Germany}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2007",
ISBN = "0-7695-2821-X",
ISBN-13 = "978-0-7695-2821-2",
LCCN = "QA297.I5 2007",
bibdate = "Wed Nov 26 18:03:28 MST 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.loc.gov:7090/Voyager",
note = "IEEE Computer Society Order Number E2821.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4402381",
acknowledgement = ack-nhfb,
}
@Proceedings{Morales:2007:TRT,
editor = "Linda Morales and Debra Howard",
booktitle = "{TAPIA '07: Richard Tapia Celebration of Diversity in
Computing Conference: October 14--17, 2007, Orlando,
Florida: passion in computing, diversity in innovation:
proceedings of the Richard Tapia Celebration of
Diversity in Computing Conference 2007 }",
title = "{TAPIA '07: Richard Tapia Celebration of Diversity in
Computing Conference: October 14--17, 2007, Orlando,
Florida: passion in computing, diversity in innovation:
proceedings of the Richard Tapia Celebration of
Diversity in Computing Conference 2007 }",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "????",
year = "2007",
ISBN = "1-59593-866-4",
ISBN-13 = "978-1-59593-866-4",
LCCN = "????",
bibdate = "Fri Aug 08 08:53:53 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Pocek:2007:PAI,
editor = "Kenneth L. Pocek and Duncan A. Buell",
booktitle = "{Proceedings, 15th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines: FCCM
2007: 23--25 April, 2007, Napa, California}",
title = "{Proceedings, 15th Annual IEEE Symposium on
Field-Programmable Custom Computing Machines: FCCM
2007: 23--25 April, 2007, Napa, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 358",
year = "2007",
DOI = "https://doi.org/10.1109/FCCM.2007.65",
ISBN = "0-7695-2940-2",
ISBN-13 = "978-0-7695-2940-0",
LCCN = "TK7895.G36 2007",
bibdate = "Sat Oct 9 15:05:33 MDT 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Computer Society order number P2940.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4297231",
acknowledgement = ack-nhfb,
subject = "Field programmable gate arrays; Congresses; Computer
engineering",
}
@Proceedings{Simos:2007:CMS,
editor = "Theodore E. Simos and George Maroulis",
booktitle = "{Computation in Modern Science and Engineering:
Proceedings of the International Conference on
Computational Methods in Science and Engineering 2007
(ICCMSE 2007), Corfu, Greece, 25--30 September 2007}",
title = "{Computation in Modern Science and Engineering:
Proceedings of the International Conference on
Computational Methods in Science and Engineering 2007
(ICCMSE 2007), Corfu, Greece, 25--30 September 2007}",
volume = "2A",
publisher = pub-AIP,
address = pub-AIP:adr,
pages = "xxvi + 730 + 10 (vol. 2A)",
year = "2007",
ISBN = "0-7354-0476-3 (set), 0-7354-0477-1 (vol. 1),
0-7354-0478-X (vol. 2)",
ISBN-13 = "978-0-7354-0476-2 (set), 978-0-7354-0477-9 (vol. 1),
978-0-7354-0478-6 (vol. 2)",
LCCN = "Q183.9 2007",
bibdate = "Thu Feb 21 14:15:15 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2008:GPA,
editor = "{ACM}",
booktitle = "{GLSVLSI 2008: Proceedings of the 18th ACM Great Lakes
symposium on VLSI, Orlando, Florida, USA, May 4--6,
2008}",
title = "{GLSVLSI 2008: Proceedings of the 18th ACM Great Lakes
symposium on VLSI, Orlando, Florida, USA, May 4--6,
2008}",
publisher = pub-ACM,
address = pub-ACM:adr,
year = "2008",
ISBN = "1-59593-999-7",
ISBN-13 = "978-1-59593-999-9",
LCCN = "????",
bibdate = "Thu Aug 07 17:43:02 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "ACM Order Number 477088.",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2008:SPA,
editor = "{ACM}",
booktitle = "{STOC '08: proceedings of the 39th Annual ACM
Symposium on Theory of Computing, Victoria, British
Columbia, Canada, May 17--20, 2008}",
title = "{STOC '08: proceedings of the 39th Annual ACM
Symposium on Theory of Computing, Victoria, British
Columbia, Canada, May 17--20, 2008}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xv + 797 (est.)",
year = "2008",
ISBN = "1-60558-047-3",
ISBN-13 = "978-1-60558-047-0",
LCCN = "????",
bibdate = "Fri Jun 20 18:35:01 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
z3950.bibsys.no:2100/BIBSYS",
acknowledgement = ack-nhfb,
}
@Proceedings{Hertling:2008:RIR,
editor = "Peter Hertling and Christoph M. Hoffmann and Wolfram
Luther and Nathalie Revol",
booktitle = "{Reliable Implementation of Real Number Algorithms:
Theory and Practice: International Seminar Dagstuhl
Castle, Germany, January 8--13, 2006 Revised Papers}",
title = "{Reliable Implementation of Real Number Algorithms:
Theory and Practice: International Seminar Dagstuhl
Castle, Germany, January 8--13, 2006 Revised Papers}",
volume = "5045",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xi + 239",
pages = "xi + 239",
year = "2008",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-540-85521-7",
ISBN = "3-540-85520-3 (print), 3-540-85521-1 (e-book)",
ISBN-13 = "978-3-540-85520-0 (print), 978-3-540-85521-7
(e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "????",
bibdate = "Wed Dec 19 15:22:53 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
series = ser-LNCS,
URL = "https://link.springer.com/book/10.1007/978-3-540-85521-7",
acknowledgement = ack-nhfb,
tableofcontents = "Front Matter \\
Ekaterina Auer, Andreas Rauh, Eberhard P. Hofer,
Wolfram Luther / Validated Modeling of Mechanical
Systems with SmartMOBILE: Improvement of Performance by
ValEncIA-IVP / 1--27 \\
George F. Corliss, R. Baker Kearfott, Ned Nedialkov,
John D. Pryce, Spencer Smith / Interval Subroutine
Library Mission / 28--43 \\
Eva Dyllong / Convex Polyhedral Enclosures of
Interval-Based Hierarchical Object Representations /
44--56 \\
Ioannis Z. Emiris, Bernard Mourrain, Elias P.
Tsigaridas / Real Algebraic Numbers: Complexity
Analysis and Experimentation / 57--82 \\
Sebastian Kempken, Wolfram Luther / Verified Methods in
Stochastic Traffic Modelling / 83--101 \\
Branimir Lambov / Interval Arithmetic Using SSE-2 /
102--113 \\
Vincent Lef{\`e}vre, Damien Stehl{\'e}, Paul Zimmermann
/ Worst Cases for the Exponential Function in the IEEE
754r decimal64 Format / 114--126 \\
Dominique Michelucci, Jean Michel Moreau, Sebti Foufou
/ Robustness and Randomness / 127--148 \\
Lance Edward Miller, Edward L. F. Moore, Thomas J.
Peters, Alexander Russell / Topological Neighborhoods
for Spline Curves: Practice \& Theory / 149--161 \\
Vadim Shapiro / Homotopy Conditions for Tolerant
Geometric Queries / 162--180 \\
Neil F. Stewart, Malika Zidani / Transfinite
Interpolation for Well-Definition in Error Analysis in
Solid Modelling / 181--192 \\
Chee Yap / Theory of Real Computation According to EGC
/ 193--237 \\
Back Matter",
}
@Proceedings{IEEE:2008:ICA,
editor = "{IEEE}",
booktitle = "{2008 International Conference on Application-Specific
Systems, Architectures and Processors: Leuven, Belgium,
2--4 July 2008}",
title = "{2008 International Conference on Application-Specific
Systems, Architectures and Processors: Leuven, Belgium,
2--4 July 2008}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiv + 309 + 12",
year = "2008",
ISBN = "1-4244-1897-6 (paperback), 1-4244-1898-4",
ISBN-13 = "978-1-4244-1897-8 (paperback), 978-1-4244-1898-5",
LCCN = "????",
bibdate = "Mon Feb 10 07:31:38 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
note = "IEEE catalog number CFP08063-PRT.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=4569858;
http://www.gbv.de/dms/tib-ub-hannover/631855815.pdf",
acknowledgement = ack-nhfb,
remark = "Kongress auch zitiert als: ASAP 08. Parallel als
Online-Ausg. erschienen. ASAP 08.",
tableofcontents = "ASAP08 Conference proceedings / c1--c1 / doi:
10.1109/ASAP.2008.4580199 \\
ASAP08 Conference proceedings / c2--c2 / doi:
10.1109/ASAP.2008.4580200 \\
Frontmatter and table of contents / c1--xiii / doi:
10.1109/ASAP.2008.4580202 \\
ASAP Organizing and Steering Committees / ix \\
ASAP Technical Technical Program Committee / x \\
Keynote 1: Security and Opportunities for
Application-Specific Processors / Ruby B. Lee / xii \\
Keynote 2: Art of of Application-Specific Processor
Design: Great Artists use Good Tools / Gert Goossens /
xiv \\
Session 1: Application-Specific Processor Instruction
Sets / 1 \\
Copyright notice / i--i / doi:
10.1109/ASAP.2008.4580197 \\
Copyright notice / ii--ii / doi:
10.1109/ASAP.2008.4580198 \\
K. Atasu, O. Mencer, W. Luk, C. Ozturan and G. Dundar /
Fast custom instruction identification by convex
subgraph enumeration / 1--6 / doi:
10.1109/ASAP.2008.4580145 \\
Y. Hilewitz, C. Lauradoux and R. B. Lee / Bit matrix
multiplication in commodity processors / 7--12 / doi:
10.1109/ASAP.2008.4580146 \\
M. Alle et al. / Synthesis of application accelerators
on Runtime Reconfigurable Hardware / 13--18 / doi:
10.1109/ASAP.2008.4580147 \\
A. Amaricai, M. Vladutiu, M. Udrescu, L. Prodan and O.
Boncalo / Floating point multiplication rounding
schemes for interval arithmetic / 19--24 / doi:
10.1109/ASAP.2008.4580148 \\
S. Balasubramanian, H. W. Carter, A. Bogdanov, A. Rupp
and Jintai Ding / Fast multivariate signature
generation in hardware: The case of rainbow / 25--30 /
doi: 10.1109/ASAP.2008.4580149 \\
M. Hosseinabady and J. Nunez-Yanez / Fault-tolerant
dynamically reconfigurable NoC-based SoC / 31--36 /
doi: 10.1109/ASAP.2008.4580150 \\
T. Lorunser et al. / Security Processor with Quantum
Key Distribution / 37--42 / doi:
10.1109/ASAP.2008.4580151 \\
P. K. Meher and J. C. Patra / Fully-pipelined efficient
architectures for FPGA realization of discrete Hadamard
transform / 43--48 / doi: 10.1109/ASAP.2008.4580152 \\
R. Rajore, G. Garga, H. S. Jamadagni and S. K. Nandy /
Reconfigurable Viterbi decoder on mesh connected
multiprocessor architecture / 49--54 / doi:
10.1109/ASAP.2008.4580153 \\
T. Ramdas, G. K. Egan, D. Abramson and K. K. Baldridge
/ Run-time thread sorting to expose data-level
parallelism / 55--60 / doi: 10.1109/ASAP.2008.4580154
\\
S. Jovanovic, C. Tanougast and S. Weber / A New
High-Performance Scalable Dynamic Interconnection for
FPGA-based Reconfigurable Systems / 61--66 / doi:
10.1109/ASAP.2008.4580155 \\
D. Dickin and L. Shannon / Extending the SIMPPL SoC
architectural framework to support application-specific
architectures on multi-FPGA platforms / 67--72 / doi:
10.1109/ASAP.2008.4580156 \\
A. E. Kiasari, S. Hessabi and H. Sarbazi-Azad / PERMAP:
A performance-aware mapping for application-specific
SoCs / 73--78 / doi: 10.1109/ASAP.2008.4580157 \\
A. C. Atici, L. Batina, Junfeng Fan, I. Verbauwhede and
S. Berna Ors Yalcin / Low-cost implementations of NTRU
for pervasive security / 79--84 / doi:
10.1109/ASAP.2008.4580158 \\
M. Knezzevic, K. Sakiyama, Y. K. Lee and I. Verbauwhede
/ On the high-throughput implementation of RIPEMD-160
hash algorithm / 85--90 / doi:
10.1109/ASAP.2008.4580159 \\
Wang Haixin, Bai Guoqiang and Chen Hongyi / Zodiac:
System architecture implementation for a
high-performance Network Security Processor / 91--96 /
doi: 10.1109/ASAP.2008.4580160 \\
P. K. Meher / Efficient systolization of cyclic
convolution for systolic implementation of sinusoidal
transforms / 97--101 / doi: 10.1109/ASAP.2008.4580161
\\
D. B. Thomas and W. Luk / Resource efficient generators
for the floating-point uniform and exponential
distributions / 102--107 / doi:
10.1109/ASAP.2008.4580162 \\
I. L. Dalal, D. Stefan and J. Harwayne-Gidansky / Low
discrepancy sequences for Monte Carlo simulations on
reconfigurable platforms / 108--113 / doi:
10.1109/ASAP.2008.4580163 \\
Y. Vanderperren and W. Dehaene / A subsampling pulsed
UWB demodulator based on a flexible complex SVD /
114--119 / doi: 10.1109/ASAP.2008.4580164 \\
J. Divyasree, H. Rajashekar and K. Varghese /
Dynamically reconfigurable regular expression matching
architecture / 120--125 / doi:
10.1109/ASAP.2008.4580165 \\
J. Khan, S. Niar, A. Menhaj, Y. Elhillali and J. L.
Dekeyser / An MPSoC architecture for the Multiple
Target Tracking application in driver assistant system
/ 126--131 / doi: 10.1109/ASAP.2008.4580166 \\
Wangyuan Zhang and Tao Li / Managing multi-core
soft-error reliability through utility-driven cross
domain optimization / 132--137 / doi:
10.1109/ASAP.2008.4580167 \\
S. Braganza and M. Leeser / An efficient implementation
of a phase unwrapping kernel on reconfigurable hardware
/ 138--143 / doi: 10.1109/ASAP.2008.4580168 \\
H. Flatt, S. Blume, S. Hesselbarth, T. Schunemann and
P. Pirsch / A parallel hardware architecture for
connected component labeling based on fast label
merging / 144--149 / doi: 10.1109/ASAP.2008.4580169 \\
Yuki Kobayashi, M. Jayapala, P. Raghavan, F. Catthoor
and Masaharu Imai / Operation shuffling over cycle
boundaries for low energy L0 clustering / 150--155 /
doi: 10.1109/ASAP.2008.4580170 \\
V. Kundeti, Yunsi Fei and S. Rajasekaran / An efficient
digital circuit for implementing Sequence Alignment
algorithm in an extended processor / 156--161 / doi:
10.1109/ASAP.2008.4580171 \\
B. K. Mohanty and P. K. Meher / Concurrent systolic
architecture for high-throughput implementation of
3-dimensional discrete wavelet transform / 162--166 /
doi: 10.1109/ASAP.2008.4580172 \\
S. Mirzaei, A. Irturk, R. Kastner, B. T. Weals and R.
E. Cagley / Design space exploration of a cooperative
MIMO receiver for reconfigurable architectures /
167--172 / doi: 10.1109/ASAP.2008.4580173 \\
Mao Nakajima and Minoru Watanabe / Dynamic holographic
reconfiguration on a four-context ODRGA / 173--178 /
doi: 10.1109/ASAP.2008.4580174 \\
F. Pardo, P. Lopez and D. Cabello / FPGA-based hardware
accelerator of the heat equation with applications on
infrared thermography / 179--184 / doi:
10.1109/ASAP.2008.4580175 \\
M. Rahmati, M. S. Sadri and M. A. Naeini / FPGA based
singular value decomposition for image processing
applications / 185--190 / doi:
10.1109/ASAP.2008.4580176 \\
A. Jacob, J. Buhler and R. D. Chamberlain /
Accelerating Nussinov RNA secondary structure
prediction with systolic arrays on FPGAs / 191--196 /
doi: 10.1109/ASAP.2008.4580177 \\
J. Lee, L. Shannon, M. J. Yedlin and G. F. Margrave / A
multi-FPGA application-specific architecture for
accelerating a floating point Fourier Integral Operator
/ 197--202 / doi: 10.1109/ASAP.2008.4580178 \\
K. F. C. Yiu, Chun Hok Ho, N. Grbric, Yao Lu, Xiaoxiang
Shi and W. Luk / Reconfigurable acceleration of
microphone array algorithms for speech enhancement /
203--208 / doi: 10.1109/ASAP.2008.4580179 \\
Yang Sun, Yuming Zhu, M. Goel and J. R. Cavallaro /
Configurable and scalable high throughput turbo decoder
architecture for multiple 4G wireless standards /
209--214 / doi: 10.1109/ASAP.2008.4580180 \\
M. B. S. Tavares, S. Kunze, E. Matus and G. P. Fettweis
/ Architecture and VLSI realization of a high-speed
programmable decoder for LDPC convolutional codes /
215--220 / doi: 10.1109/ASAP.2008.4580181 \\
D. Llorente, K. Karras, T. Wild and A. Herkersdorf /
Buffer allocation for advanced packet segmentation in
Network Processors / 221--226 / doi:
10.1109/ASAP.2008.4580182 \\
A. Vazquez and E. Antelo / New insights on Ling adders
/ 227--232 / doi: 10.1109/ASAP.2008.4580183 \\
N. Brisebarre, F. de Dinechin and J. Muller / Integer
and floating-point constant multipliers for FPGAs /
239--244 / doi: 10.1109/ASAP.2008.4580184 \\
N. Brisebarre, S. Chevillard, M. D. Ercegovac, J.
Muller and S. Torres / An efficient method for
evaluating polynomial and rational function
approximations / 233--238 / doi:
10.1109/ASAP.2008.4580185 \\
A. Garcia, M. Berekovic and T. Vander Aa / Mapping of
the AES cryptographic algorithm on a Coarse-Grain
reconfigurable array processor / 245--250 / doi:
10.1109/ASAP.2008.4580186 \\
J. Nimmy et al. / RECONNECT: A NoC for polymorphic
ASICs using a low overhead single cycle router /
251--256 / doi: 10.1109/ASAP.2008.4580187 \\
M. Mbaye, N. Belanger, Y. Savaria and S. Pierre /
Loop-oriented metrics for exploring an
application-specific architecture design-space /
257--262 / doi: 10.1109/ASAP.2008.4580188 \\
S. K. Dash and T. Srikanthan / Rapid estimation of
instruction cache hit rates using loop profiling /
263--268 / doi: 10.1109/ASAP.2008.4580189 \\
Xuan Guan and Yunsi Fei / Reducing power consumption of
embedded processors through register file partitioning
and compiler support / 269--274 / doi:
10.1109/ASAP.2008.4580190 \\
A. Tumeo, M. Monchiero, G. Palermo, F. Ferrandi and D.
Sciuto / Lightweight DMA management mechanisms for
multiprocessors on FPGA / 275--280 / doi:
10.1109/ASAP.2008.4580191 \\
P. de Langen and B. Juurlink / Memory copies in
multi-level memory systems / 281--286 / doi:
10.1109/ASAP.2008.4580192 \\
R. Adrsha, Mythri, S. K. Nandy and R. Narayan /
Architecture of a polymorphic ASIC for interoperability
across multi-mode H.264 decoders / 287--292 / doi:
10.1109/ASAP.2008.4580193 \\
R. R. Osorio and J. D. Bruguera / An FPGA architecture
for CABAC decoding in manycore systems / 293--298 /
doi: 10.1109/ASAP.2008.4580194 \\
A. Guntoro and M. Glesner / Novel approach on
lifting-based DWT and IDWT processor with multi-context
configuration to support different wavelet filters /
299--304 / doi: 10.1109/ASAP.2008.4580195 \\
B. K. Mohanty and P. K. Meher / Throughput-scalable
hybrid-pipeline architecture for multilevel lifting 2-D
DWT of JPEG 2000 coder / 305--309 / doi:
10.1109/ASAP.2008.4580196 \\
Author index / 310--321 / doi:
10.1109/ASAP.2008.4580201",
}
@Proceedings{Matthews:2008:CRF,
editor = "Michael B. Matthews",
booktitle = "{Conference Record of the Forty-first Asilomar
Conference on Signals, Systems and Computers: November
4--7, 2007, Pacific Grove, California. ACSSC 2007}",
title = "{Conference Record of the Forty-first Asilomar
Conference on Signals, Systems and Computers: November
4--7, 2007, Pacific Grove, California. ACSSC 2007}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxix + 421",
year = "2008",
DOI = "https://doi.org/10.1109/ACSSC.2007.4487144",
ISBN = "1-4244-2109-8",
ISBN-13 = "978-1-4244-2109-1",
ISSN = "1058-6393",
LCCN = "TK7801 .A83 2007eb",
bibdate = "Sat Dec 4 10:31:40 MST 2010",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=4483515",
acknowledgement = ack-nhfb,
subject = "Electronics; Congresses; Signal processing; Computers;
Automatic control; Electrical engineering; System
theory",
}
@Book{Patterson:2008:COD,
author = "David A. Patterson and John L. Hennessy",
booktitle = "Computer Organization and Design: the Hardware\slash
Software Interface",
title = "Computer Organization and Design: the Hardware\slash
Software Interface",
publisher = pub-ELSEVIER-MORGAN-KAUFMANN,
address = pub-ELSEVIER-MORGAN-KAUFMANN:adr,
edition = "Fourth",
bookpages = "xxv + 703 + A-77 + B-83 + I-26",
pages = "xxv + 703 + A-77 + B-83 + I-26",
year = "2008",
ISBN = "0-12-374493-8",
ISBN-13 = "978-0-12-374493-7",
LCCN = "QA76.9.C643",
bibdate = "Mon Nov 17 13:31:21 MST 2008",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
z3950.gbv.de:20011/gvk",
acknowledgement = ack-nhfb,
subject = "computer organization; computer engineering; computer
interfaces",
tableofcontents = "1: Computer Abstractions and Technology \\
2: Instructions: Language of the Computer \\
3: Arithmetic for Computers \\
4: The Processor \\
5: Large and Fast: Exploiting Memory Hierarchy \\
6: Storage and Other I /O Topics \\
7: Multicores, Multiprocessors, and Clusters \\
Appendix A: Graphics and Computing GPUs \\
Appendix B: Assemblers, Linkers, and the SPIM Simulator
\\
Appendix C: The Basics of Logic Design \\
Appendix D: Mapping Control to Hardware \\
Appendix E: A Survey of RISC Architectures for Desktop,
Server, and Embedded Computers",
}
@Proceedings{Abraham:2009:WCN,
editor = "Ajith Abraham and Andre Carvalho and Francisco Herrera
and Vijayalakshmi Pai and Andr{\'e} Coelho and Ronaldo
Menezes",
booktitle = "{2009 World Congress on Nature and Biologically
Inspired Computing: 9--11 December 2009, Coimbatore,
India: proceedings [NaBIC 2009]}-",
title = "{2009 World Congress on Nature and Biologically
Inspired Computing: 9--11 December 2009, Coimbatore,
India: proceedings [NaBIC 2009]}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2009",
ISBN = "1-4244-5612-6, 1-4244-5053-5",
ISBN-13 = "978-1-4244-5612-3, 978-1-4244-5053-4",
LCCN = "QA76.887 2009",
bibdate = "Thu Feb 17 13:33:02 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number CFP0995H",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5377996",
acknowledgement = ack-nhfb,
meetingname = "World Congress on Nature and Biologically Inspired
Computing (2009: Coimbatore, India)",
subject = "biologically-inspired computing; congresses; natural
computation",
}
@Proceedings{Bouajjani:2009:CAV,
editor = "Ahmed Bouajjani and Oded Maler",
booktitle = "Computer Aided Verification: {21st International
Conference, CAV 2009, Grenoble, France, June 26--July
2, 2009, Proceedings}",
title = "Computer Aided Verification: {21st International
Conference, CAV 2009, Grenoble, France, June 26--July
2, 2009, Proceedings}",
volume = "5643",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 722",
year = "2009",
DOI = "https://doi.org/10.1007/978-3-642-02658-4",
ISBN = "3-642-02657-5 (paperback), 3-642-02658-3",
ISBN-13 = "978-3-642-02657-7 (paperback), 978-3-642-02658-4",
LCCN = "QA76.76.V47 .C38 2009",
bibdate = "Fri Dec 8 13:33:33 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
}
@Proceedings{Bruguera:2009:PIS,
editor = "Javier D. Bruguera and Marius Cornea and Debjit
DasSarma and John Harrison",
booktitle = "{Proceedings of the 19th IEEE Symposium on Computer
Arithmetic, June 8--10, 2009, Portland, Oregon, USA}",
title = "{Proceedings of the 19th IEEE Symposium on Computer
Arithmetic, June 8--10, 2009, Portland, Oregon, USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xi + 235",
year = "2009",
ISBN = "0-7695-3670-0, 1-4244-4329-6",
ISBN-13 = "978-0-7695-3670-5, 978-1-4244-4329-1",
ISSN = "1063-6889",
LCCN = "QA76.6 .S887 2009",
bibdate = "Fri Jun 12 12:24:37 2009",
bibsource = "http://www.ac.usc.es/arith19/;
https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://www.ac.usc.es/arith19/",
acknowledgement = ack-nhfb,
keywords = "ARITH-19",
tableofcontents = "Keynote Talk \\
Anton: A Specialized Machine for Millisecond-Scale
Molecular Dynamics Simulations of Proteins / David E.
Shaw / 3 \\
Session 1: Algorithms and Number Systems \\
Efficient Data Structure and Algorithms for Sparse
Integers, Sets and Predicates / Jean E. Vuillemin / 7
\\
A Dual-Purpose Real/Complex Logarithmic Number System
ALU / Mark G. Arnold and Sylvain Collange / 15 \\
Selected RNS Bases for Modular Multiplication / J. C.
Bajard, M. Kaihara, and T. Plantard / 25 \\
Invited Talk \\
A Historical Perspective on Computer Arithmetic /
Stanley Mazor / 35 \\
Session 2: Arithmetic Hardware \\
Higher Radix Squaring Operations Employing
Left-to-Right Dual Recoding / David W. Matula / 39 \\
Advanced Clockgating Schemes for
Fused-Multiply-Add-Type Floating-Point Units / Jochen
Preiss, Maarten Boersma, and Silvia Melitta Mueller /
48 \\
Unified Approach to the Design of Modulo-$(2^n \pm 1)$
Adders Based on Signed-LSB Representation of Residues /
Ghassem Jaberipur and Behrooz Parhami / 57 \\
Session 3: Finite Fields and Cryptography \\
Subquadratic Space Complexity Multiplier for a Class of
Binary Fields Using Toeplitz Matrix Approach / M. A.
Hasan and C. Negre / 67 \\
Hybrid Binary-Ternary Joint Form and Its Application in
Elliptic Curve / Cryptography / Jithra Adikari, Vassil
Dimitrov, and Laurent Imbert / 76 \\
Polynomial Multiplication over Finite Fields Using
Field Extensions and Interpolation / Murat Cenk, Cetin
Kaya Koc, and Ferruh Ozbudak / 84 \\
Session 4: Mathematical Software \\
A New Binary Floating-Point Division Algorithm and Its
Software Implementation on the ST231 Processor /
Claude-Pierre Jeannerod, Herve Knochel, Christophe
Monat, Guillaume Revy, and Gilles Villard / 95 \\
Fast and Accurate Bessel Function Computation / John
Harrison / 104 \\
Implementation Specific Verification of Divide and
Square Root Instructions / Elena Guralnik, Ariel J.
Birnbaum, Anatoly Koyfinan, and Avi Kaplan / 114 \\
Session 5: Decimal Hardware \\
A Decimal Floating-Point Adder with Decoded Operands
and a Decimal Leading-Zero Anticipator / Liang-Kai Wang
and Michael J. Schulte / 125 \\
A High-Performance Significand BCD Adder with IEEE
754-2008 Decimal Rounding / Alvaro Vazquez and Elisardo
Antelo / 135 \\
Fully Redundant Decimal Arithmetic / Saeid Gorgin and
Ghassem Jaberipur / 145 \\
Session 6: Floating-Point Techniques \\
On the Computation of Correctly-Rounded Sums / P.
Kornerup, V. Lefevre, N. Louvet, and Jean-Michel Muller
/ 155 \\
Multi-operand Floating-Point Addition / Alexandre F.
Tenca / 161 \\
Certified and Fast Computation of Supremum Norms of
Approximation Errors / Sylvain Chevillard, Mioara
Jolde{\c{s}}, and Christoph Lauter / 169 \\
Session 7: Decimal Transcendentals \\
Computation of Decimal Transcendental Functions Using
the CORDIC Algorithm / {\'A}lvaro V{\'a}zquez, Julio
Villalba, and Elisardo Antelo / 179 \\
Decimal Transcendentals via Binary / John Harrison /
187 \\
A 32-bit Decimal Floating-Point Logarithmic Converter /
Dongdong Chen, Yu Zhang, Younhee Choi, Moon Ho Lee, and
Seok-Bum Ko / 195 \\
Special Session on Automated Synthesis of Arithmetic
Operations \\
Datapath Synthesis for Standard-Cell Design / Reto
Zimmermann / 207 \\
Design Space Exploration for Power-Efficient
Mixed-Radix Ling Adders / Chung-Kuan Cheng / 212 \\
Challenges in Automatic Optimization of Arithmetic
Circuits / Ajay K. Verma, Philip Brisk, and Paolo Ienne
/ 213 \\
Panel on Decimal Arithmetic in Industry \\
Energy and Delay Improvement via Decimal Floating Point
Units / Hossam A. H. Fahmy, Ramy Raafat, Amira M.
Abdel-Majeed, Rodina Samy, Torek ElDeeb, and Yasmin
Farouk / 221 \\
IEEE 754-2008 Decimal Floating-Point for Intel
Architecture Processors / Marius Cornea / 225 \\
Special Session on Interval Arithmetic \\
IEEE Interval Standard Working Group --- P1788: Current
Status / William Edmonson and Guillaume Melquiond / 231
\\
Author Index",
}
@Proceedings{Cumplido:2009:RPI,
editor = "Ren{\'e} Cumplido and Lionel Torres and V. K.
{Prasanna Kumar}",
booktitle = "{ReConFig 2009: proceedings: 2009 [5th] International
Conference on Reconfigurable Computing and FPGAs: 9--11
December 2009: Cancun, Mexico}",
title = "{ReConFig 2009: proceedings: 2009 [5th] International
Conference on Reconfigurable Computing and FPGAs: 9--11
December 2009: Cancun, Mexico}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2009",
ISBN = "1-4244-5293-7, 0-7695-3917-3",
ISBN-13 = "978-1-4244-5293-4, 978-0-7695-3917-1",
LCCN = "TK7895.G36 2009",
bibdate = "Thu Feb 17 13:43:12 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5379688",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Reconfigurable Computing
and FPGAs (5th : 2009 : Canc\'un, Mexico)",
subject = "adaptive computing systems; congresses; field
programmable gate arrays",
}
@Proceedings{ICCIT:2009:ICC,
editor = "{ICCIT}",
booktitle = "{2009 12th International Conference on Computer and
Information Technology: ICCIT 2009: December 21-23,
Independent University, Bangladesh}",
title = "{2009 12th International Conference on Computer and
Information Technology: ICCIT 2009: December 21-23,
Independent University, Bangladesh}",
publisher = "ICCIT 2009 Conference Secretariat",
address = "Dhaka, Bangladesh",
pages = "702",
year = "2009",
ISBN = "1-4244-6281-9, 1-4244-6284-3",
ISBN-13 = "978-1-4244-6281-0, 978-1-4244-6284-1",
LCCN = "T58.5 2009",
bibdate = "Thu Feb 17 13:46:21 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5398764",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Computer and Information
Technology (1998-) (12th: 2009: Independent University,
Bangladesh)",
subject = "information technology; congresses; computer science",
}
@Proceedings{IEEE:2009:ICF,
editor = "{IEEE}",
booktitle = "{International Conference on Field Programmable Logic
and Applications, Prague, Czech Republic, August 31
2009--September 2, 2009 (FPL 2009)}",
title = "{International Conference on Field Programmable Logic
and Applications, Prague, Czech Republic, August 31
2009--September 2, 2009 (FPL 2009)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2009",
ISBN = "1-4244-3892-6",
ISBN-13 = "978-1-4244-3892-1",
LCCN = "????",
bibdate = "Fri Dec 03 15:38:12 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2009:IICa,
editor = "{IEEE}",
booktitle = "20th {IEEE} International Conference on
Application-specific Systems, Architectures and
Processors, Boston, {MA, 7-9} July 2009 {(ASAP 2009)}",
title = "20th {IEEE} International Conference on
Application-specific Systems, Architectures and
Processors, Boston, {MA}, 7-9 July 2009 ({ASAP} 2009)",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2009",
ISBN = "0-7695-3732-4",
ISBN-13 = "978-0-7695-3732-0",
ISSN = "1063-6862",
LCCN = "????",
bibdate = "Fri Dec 03 15:06:48 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "There are several papers from this that MUST be
included in this file.??!!",
}
@Proceedings{IEEE:2009:IICb,
editor = "{IEEE}",
booktitle = "{2009 IEEE International Conference on Computer
Design: October 4--7, 2009, Resort at Squaw Creek, Lake
Tahoe, CA: ICCD 2009}",
title = "{2009 IEEE International Conference on Computer
Design: October 4--7, 2009, Resort at Squaw Creek, Lake
Tahoe, CA: ICCD 2009}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
year = "2009",
ISBN = "1-4244-5028-4",
ISBN-13 = "978-1-4244-5028-2",
LCCN = "TK7888.3 2009",
bibdate = "Thu Feb 17 08:53:42 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "IEEE Catalog Number: CFP09ICD",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5406656",
acknowledgement = ack-nhfb,
meetingname = "IEEE International Conference on Computer Design
(2009: Lake Tahoe, Calif.)",
subject = "computer engineering; congresses; embedded computer
systems; integrated circuits; very large scale
integration; electronic digital computers; circuits;
microcomputers; design and construction",
}
@Proceedings{IEEE:2009:IIS,
editor = "{IEEE}",
booktitle = "{2009 IEEE International Symposium on Circuits and
Systems: circuits and systems for human centric smart
living technologies, conference program, Taipei
International Convention Center, Taipei, Taiwan, May
24--May 27, 2009}",
title = "{2009 IEEE International Symposium on Circuits and
Systems: circuits and systems for human centric smart
living technologies, conference program, Taipei
International Convention Center, Taipei, Taiwan, May
24--May 27, 2009}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2009",
ISBN = "1-4244-3827-6 (print)",
ISBN-13 = "978-1-4244-3827-3 (print)",
LCCN = "TK454 .I15 2009",
bibdate = "Thu Feb 17 13:29:04 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5076158",
acknowledgement = ack-nhfb,
meetingname = "IEEE International Symposium on Circuits and Systems
(2009: Taipei, Taiwan)",
subject = "electronics; congresses; signal processing; digital
techniques; electronic circuits; neural networks
(computer science); integrated circuits; very large
scale integration",
}
@Proceedings{IEEE:2009:PDR,
editor = "{IEEE}",
booktitle = "{Ph.D. Research in Microelectronics and Electronics
(PRIME 2009), 12--17 July 2009, Cork, Ireland}",
title = "{Ph.D. Research in Microelectronics and Electronics
(PRIME 2009), 12--17 July 2009, Cork, Ireland}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
year = "2009",
ISBN = "1-4244-3733-4",
ISBN-13 = "978-1-4244-3733-7",
LCCN = "TK7874 2009",
bibdate = "Thu Mar 24 21:42:23 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Matthews:2009:CRF,
editor = "Michael B. Matthews",
booktitle = "{Conference Record of the Forty-Third Asilomar
Conference on Signals, Systems and Computers, 1--4
November 2009, Pacific Grove, California}",
title = "{Conference Record of the Forty-Third Asilomar
Conference on Signals, Systems and Computers, 1--4
November 2009, Pacific Grove, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2009",
ISBN = "1-4244-5825-0",
ISBN-13 = "978-1-4244-5825-7",
LCCN = "????",
bibdate = "Thu Feb 17 13:40:37 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5465900",
acknowledgement = ack-nhfb,
}
@Proceedings{Sezer:2009:IIS,
editor = "Sakir Sezer and Andrew Marshall and Thomas Buechner",
booktitle = "{IEEE International SOC Conference: September 9--11,
2009, Wellington Park Hotel, Belfast, Northern Ireland,
UK (SOCC 2009)}",
title = "{IEEE International SOC Conference: September 9--11,
2009, Wellington Park Hotel, Belfast, Northern Ireland,
UK (SOCC 2009)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2009",
DOI = "https://doi.org/10.1109/SOCCON.2009.5398119",
ISBN = "1-4244-4940-5, 1-4244-4941-3",
ISBN-13 = "978-1-4244-4940-8, 978-1-4244-4941-5",
LCCN = "TK7874.6 .I59 2009",
bibdate = "Sun Feb 20 11:34:39 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5379508",
acknowledgement = ack-nhfb,
meetingname = "IEEE International SOC Conference (22nd: 2009:
Belfast, Northern Ireland)",
subject = "integrated circuits; very large scale integration;
design and construction; congresses; systems on a chip;
electronic digital computers; circuits",
}
@Proceedings{Charot:2010:API,
editor = "Fran{\c{c}}ois Charot and Frank Hannig and J{\"u}rgen
Teich and Christophe Wolinski",
booktitle = "{ASAP 2010: proceedings: 21st IEEE International
Conference on Application-Specific Systems,
Architectures, and Processors: July 7--9, 2010, Rennes,
France}",
title = "{ASAP 2010: proceedings: 21st IEEE International
Conference on Application-Specific Systems,
Architectures, and Processors: July 7--9, 2010, Rennes,
France}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2010",
ISBN = "1-4244-6965-1, 1-4244-6966-X, 1-4244-6967-8",
ISBN-13 = "978-1-4244-6965-9, 978-1-4244-6966-6,
978-1-4244-6967-3",
LCCN = "TK7874.6 2010",
bibdate = "Thu Feb 17 13:54:41 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number CFP10063ART",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5523683",
acknowledgement = ack-nhfb,
meetingname = "IEEE International Conference on Application-Specific
Systems, Architectures, and Processors (21st: 2010:
Rennes, France)",
subject = "array processors; congresses; signal processing;
digital techniques; application-specific integrated
circuits",
}
@Proceedings{Delgado-Frias:2010:IIM,
editor = "Jose G. Delgado-Frias and Rogelio Palomera-Garcia and
Jabulani Nyathi",
booktitle = "{53nd IEEE International Midwest Symposium on Circuits
and Systems, 2010: MWSCAS 2010, 1--4 August 2010,
Seattle, Washington}",
title = "{53nd IEEE International Midwest Symposium on Circuits
and Systems, 2010: MWSCAS 2010, 1--4 August 2010,
Seattle, Washington}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2010",
ISBN = "1-4244-7771-9",
ISBN-13 = "978-1-4244-7771-5",
LCCN = "????",
bibdate = "Thu Feb 17 16:34:42 MST 2011",
bibsource = "alpha.lib.uwo.ca:210/INNOPAC;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5542407",
acknowledgement = ack-nhfb,
meetingname = "Midwest Symposium on Circuits and Systems (53nd: 2010:
Seattle, Washington)",
subject = "electronics; congresses; electronic circuits",
}
@Proceedings{Fukuda:2010:MSI,
editor = "Komei Fukuda and Joris van der Hoeven and Michael
Joswig and Nobuki Takayama",
booktitle = "{Mathematical software --- ICMS 2010: third
International Congress on Mathematical Software,
K{\=o}be, Japan, September 13--17, 2010: proceedings}",
title = "{Mathematical software --- ICMS 2010: third
International Congress on Mathematical Software,
K{\=o}be, Japan, September 13--17, 2010: proceedings}",
volume = "6327",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 368",
year = "2010",
DOI = "https://doi.org/10.1007/978-3-642-15582-6",
ISBN = "3-642-15581-2 (paperback), 3-642-15582-0 (e-book)",
ISBN-13 = "978-3-642-15581-9 (paperback), 978-3-642-15582-6
(e-book)",
LCCN = "QA76.95 .I5654 2010",
bibdate = "Sat Aug 9 14:06:27 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
z3950.loc.gov:7090/Voyager",
series = ser-LNCS,
URL = "http://link.springer.com/book/10.1007/978-3-642-15582-6",
acknowledgement = ack-nhfb,
subject = "Mathematics; Data processing; Congresses; Computer
software",
tableofcontents = "Plenary \\
Computational Discrete Geometry / Thomas C. Hales /
1--3 \\
Exploiting Structured Sparsity in Large Scale
Semidefinite Programming Problems / Masakazu Kojima /
4--9 \\
Reliable and Efficient Geometric Computing / Kurt
Mehlhorn / 10--11 \\
The Sage Project: Unifying Free Mathematical Software
to Create a Viable Alternative to Magma, Maple,
Mathematica and MATLAB / Bur{\c{c}}in Er{\"o}cal,
William Stein / 12--27 \\
Computation of Special Functions (Invited) \\
Sollya: An Environment for the Development of Numerical
Codes / Sylvain Chevillard, Mioara Jolde , Christoph
Lauter / 28--31 \\
Validated Special Functions Software / Annie Cuyt,
Franky Backeljauw, Stefan Becuwe, Joris Van Deun /
32--34 \\
The Dynamic Dictionary of Mathematical Functions (DDMF)
/ Alexandre Benoit, Fr{\'e}d{\'e}ric Chyzak, Alexis
Darrasse, Stefan Gerhold, Marc Mezzarobba, Bruno Salvy
/ 35--41 \\
Reliable Computing with GNU MPFR / Paul Zimmermann /
42--45 \\
Computational Group Theory (Invited) \\
Simplicial Cohomology of Smooth Orbifolds in GAP /
Mohamed Barakat, Simon G{\"o}rtzen / 46--49 \\
Computing Polycyclic Quotients of Finitely
(L-)Presented Groups via Groebner Bases / Bettina Eick,
Max Horn / 50--53 \\
Constructive Membership Testing in Black-Box Classical
Groups / Sophie Ambrose, Scott H. Murray, Cheryl E.
Praeger, Csaba Schneider / 54--57 \\
Computational Group Theory (Contributed) \\
Towards High-Performance Computational Algebra with GAP
/ Reimer Behrends, Alexander Konovalov, Steve Linton,
Frank L{\"u}beck, Max Neunh{\"o}effer / 58--61 \\
An Improvement of a Function Computing Normalizers for
Permutation Groups / Izumi Miyamoto / 62--68 \\
A GAP Package for Computation with Coherent
Configurations / Dmitrii V. Pasechnik, Keshav Kini /
69--72 \\
Computer Algebra (Invited) \\
CoCoALib: A C++ Library for Computations in Commutative
Algebra \ldots{} and Beyond / John Abbott, Anna M.
Bigatti / 73--76 \\
LinBox Founding Scope Allocation, Parallel Building
Blocks, and Separate Compilation / Jean-Guillaume
Dumas, Thierry Gautier, Cl{\'e}ment Pernet, B. David
Saunders / 77--83 \\
FGb: A Library for Computing Gr{\"o}bner Bases /
Jean-Charles Faug{\`e}re / 84--87 \\
Fast Library for Number Theory: An Introduction /
William B. Hart / 88--91 \\
Exact Numeric Computation for Algebraic and Geometric
Computation (Invited) \\
Controlled Perturbation for Certified Geometric
Computing with Fixed-Precision Arithmetic / Dan
Halperin / 92--95 \\
Exact Numeric Computation for Algebraic and Geometric
Computation (Invited) \\
Exact Geometric and Algebraic Computations in CGAL /
Menelaos I. Karavelas / 96--99 \\
On Solving Systems of Bivariate Polynomials / Fabrice
Rouillier / 100--104 \\
Accurate and Reliable Computing in Floating-Point
Arithmetic / Siegfried M. Rump / 105--108 \\
Exact Numeric Computation for Algebraic and Geometric
Computation (Contributed) \\
Deferring Dag Construction by Storing Sums of Floats
Speeds-Up Exact Decision Computations Based on
Expression Dags / Marc M{\"o}rig / 109--120 \\
The Design of Core 2: A Library for Exact Numeric
Computation in Geometry and Algebra / Jihun Yu, Chee
Yap, Zilin Du, Sylvain Pion, Herv{\'e} Br{\"o}nnimann /
121--141 \\
Formal Proof (Invited) \\
Introducing HOL Zero / Mark Adams / 142--143 \\
Euler's Polyhedron Formula in mizar / Jesse Alama /
144--147 \\
Building a Library of Mechanized Mathematical Proofs:
Why Do It? and What Is It Like to Do? / R. D. Arthan /
148--148 \\
Linear Programs for the Kepler Conjecture / Thomas C.
Hales / 149--151 \\
A Formal Proof of Pick's Theorem / John Harrison /
152--154 \\
Formal Proof (Contributed) \\
Evaluation of Automated Theorem Proving on the Mizar
Mathematical Library / Josef Urban, Krystof Hoder,
Andrei Voronkov / 155--166 \\
Geometry and Visualization (Invited) \\
On Local Deformations of Planar Quad-Meshes / Tim
Hoffmann / 167--169 \\
Construction of Harmonic Surfaces with Prescribed
Geometry / Matthias Weber / 170--173 \\
Geometry and Visualization (Contributed) \\
A Library of OpenGL-Based Mathematical Image Filters /
Martin von Gagern, Christian Mercat / 174--185 \\
MD-jeep: An Implementation of a Branch and Prune
Algorithm for Distance Geometry Problems / Antonio
Mucherino, Leo Liberti, Carlile Lavor / 186--197 \\
TADD: A Computational Framework for Data Analysis Using
Discrete Morse Theory / Jan Reininghaus, David
G{\"u}nther, Ingrid Hotz, Steffen Prohaska,
Hans-Christian Hege / 198--208 \\
Groebner Bases and Applications (Invited) \\
Introduction to Normaliz 2.5 / Winfried Bruns, Bogdan
Ichim, Christof S{\"o}ger / 209--212 \\
Computer Algebra Methods in Tropical Geometry / Thomas
Markwig / 213--216 \\
Groebner Bases and Applications (Contributed) \\
A New Desingularization Algorithm for Binomial
Varieties in Arbitrary Characteristic / Roc{\'\i}o
Blanco / 217--220 \\
An Algorithm of Computing Inhomogeneous Differential
Equations for Definite Integrals / Hiromasa Nakayama,
Kenta Nishiyama / 221--232 \\
Groebner Bases and Applications (Contributed) \\
New Algorithms for Computing Primary Decomposition of
Polynomial Ideals / Masayuki Noro / 233--244 \\
An Automated Confluence Proof for an Infinite Rewrite
System Parametrized over an Integro-Differential
Algebra / Loredana Tec, Georg Regensburger, Markus
Rosenkranz, Bruno Buchberger / 245--248 \\
Operadic Gr{\"o}bner Bases: An Implementation /
Vladimir Dotsenko, Mikael Vejdemo-Johansson / 249--252
\\
Number Theoretical Software (Invited) \\
Magma - A Tool for Number Theory / John Cannon, Steve
Donnelly, Claus Fieker, Mark Watkins / 253--255 \\
Number Theoretical Software (Contributed) \\
Enumerating Galois Representations in Sage / Craig
Citro, Alexandru Ghitza / 256--259 \\
NZMATH 1.0 / Satoru Tanaka, Naoki Ogura, Ken Nakamula,
Tetsushi Matsui, Shigenori Uchiyama / 260--269 \\
Software for Optimization and Polyhedral Computation
(Invited) \\
Removing Redundant Quadratic Constraints / David
Adjiashvili, Michel Baes, Philipp Rostalski / 270--281
\\
Traversing Symmetric Polyhedral Fans / Anders
Nedergaard Jensen / 282--294 \\
C++ Tools for Exploiting Polyhedral Symmetries / Thomas
Rehn, Achill Sch{\"u}rmann / 295--298 \\
isl: An Integer Set Library for the Polyhedral Model /
Sven Verdoolaege / 299--302 \\
Software for Optimization and Polyhedral Computation
(Contributed) \\
The Reformulation-Optimization Software Engine / Leo
Liberti, Sonia Cafieri, David Savourey / 303--314 \\
Generating Smooth Lattice Polytopes / Christian Haase,
Benjamin Lorenz, Andreas Paffenholz / 315--328 \\
Reliable Computation (Invited) \\
Mathemagix: Towards Large Scale Programming for
Symbolic and Certified Numeric Computations /
Gr{\'e}goire Lecerf / 329--332 \\
Complex Inclusion Functions in the CoStLy C++ Class
Library / Markus Neher / 333--336 \\
Standardized Interval Arithmetic and Interval
Arithmetic Used in Libraries / Nathalie Revol /
337--341 \\
Reliable Computation (Contributed) \\
Efficient Evaluation of Large Polynomials / Charles E.
Leiserson, Liyun Li, Marc Moreno Maza, Yuzhen Xie /
342--353 \\
Communicating Functional Expressions from Mathematica
to C-XSC / Evgenija D. Popova, Walter Kr{\"a}mer /
354--365 \\
Author Index / 367--368",
}
@Proceedings{IEEE:2010:CCE,
editor = "{IEEE}",
booktitle = "23rd Canadian Conference on Electrical and Computer
Engineering {(CCECE)}, Calgary, {AB, 2--5} May, 2010",
title = "23rd Canadian Conference on Electrical and Computer
Engineering ({CCECE}), Calgary, {AB}, 2--5 May, 2010",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2010",
ISBN = "1-4244-5376-3",
ISBN-13 = "978-1-4244-5376-4",
LCCN = "????",
bibdate = "Fri Dec 03 15:46:10 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2010:ICC,
editor = "{IEEE}",
booktitle = "2010 2nd International Conference on Computer
Engineering and Technology {(ICCET)}",
title = "2010 2nd International Conference on Computer
Engineering and Technology ({ICCET}), 16--18 April
2010, Chengdu, China",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2010",
ISBN = "1-4244-6347-5",
ISBN-13 = "978-1-4244-6347-3",
LCCN = "????",
bibdate = "Fri Dec 03 15:22:32 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{IEEE:2010:ICM,
editor = "{IEEE}",
booktitle = "{2010 27th International Conference on
Microelectronics: proceedings: Ni{\v{s}}, MIEL 2010,
Ni{\v{s}}, Serbia: 16--19 May 2010}",
title = "{2010 27th International Conference on
Microelectronics: proceedings: Ni{\v{s}}, MIEL 2010,
Ni{\v{s}}, Serbia: 16--19 May 2010}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2010",
ISBN = "1-4244-7200-8, 1-4244-7201-6",
ISBN-13 = "978-1-4244-7200-0, 978-1-4244-7201-7",
LCCN = "TK7874 2010",
bibdate = "Thu Feb 17 13:49:56 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number CFP10432-ART.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5483038",
acknowledgement = ack-nhfb,
meetingname = "International Conference on Microelectronics (27th :
2010 : Ni{\v{s}}, Serbia)",
subject = "Microelectronics; Congresses",
}
@Proceedings{IEEE:2010:ICV,
editor = "{IEEE}",
booktitle = "{23rd International Conference on VLSI Design:
proceedings, held jointly with 9th International
Conference on Embedded Systems: Bangalore, India, 3--7
January 2010}",
title = "{23rd International Conference on VLSI Design:
proceedings, held jointly with 9th International
Conference on Embedded Systems: Bangalore, India, 3--7
January 2010}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xl + 469",
year = "2010",
ISBN = "1-4244-5541-3, 0-7695-3928-9, 1-4244-5541-3",
ISBN-13 = "978-1-4244-5541-6, 978-0-7695-3928-7,
978-1-4244-5541-6",
LCCN = "TK7874.75 2010",
bibdate = "Sun Feb 20 14:14:26 MST 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
melvyl.cdlib.org:210/CDL90",
note = "IEEE Computer Society Order Number E3928.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5400049",
acknowledgement = ack-nhfb,
meetingname = "International Conference on VLSI Design (23rd : 2010 :
Bangalore, India)",
subject = "electronic digital computers; circuits; congresses;
signal processing; digital techniques; integrated
circuits; very large scale integration; design and
construction",
}
@Book{Knuth:2010:SPD,
author = "Donald E. Knuth",
booktitle = "Selected Papers on Design of Algorithms",
title = "Selected Papers on Design of Algorithms",
volume = "191",
publisher = pub-CSLI,
address = pub-CSLI:adr,
pages = "xvi + 453",
year = "2010",
ISBN = "1-57586-582-3 (paperback), 1-57586-583-1 (hardcover)",
ISBN-13 = "978-1-57586-582-9 (paperback), 978-1-57586-583-6
(hardcover)",
LCCN = "QA9.58 KNU 2010",
MRclass = "01A75 (01-06 05B35 05C85 68-03)",
MRnumber = "2572388 (2011c:01022)",
bibdate = "Mon Jul 05 16:25:34 2010",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
library.ox.ac.uk:210/ADVANCE",
price = "US\$48.50",
series = "CSLI Lecture Notes",
acknowledgement = ack-nhfb,
subject = "Algorithms; Computer algorithms; Computer
programming",
tableofcontents = "1. Robert W. Floyd, in Memoriam / 1 \\
2. The Bose--Nelson Sorting Problem / 19 \\
3. A One-Way, Stackless Quicksort Algorithm / 31 \\
4. Optimum Binary Search Trees / 35 \\
5. Dynamic Huffman Coding / 51 \\
6. Inhomogeneous Sorting / 71 \\
7. Lexicographic Permutations with Restrictions / 79
\\
8. Nested Satisfiability / 91 \\
9. Fast Pattern Matching in Strings / 99 \\
10. Addition Machines / 137 \\
11. A Simple Program Whose Proof Isn't / 155 \\
12. Verification of Link-Level Protocols / 167 \\
13. A Problem in Concurrent Programming Control / 175
\\
14. Optimal Prepaging and Font Caching / 181 \\
15. A Generalization of Dijkstra's Algorithm / 209 \\
16. Two-Way Rounding / 219 \\
17. Matroid Partitioning / 235 \\
18. Irredundant Intervals / 245 \\
19. Simple Word Problems in Universal Algebras / 275
\\
20. Efficient Representation of Perm Groups / 315 \\
21. An Algorithm for Brownian Zeros / 329 \\
22. Semi-Optimal Bases for Linear Dependencies / 337
\\
23. Evading the Drift in Floating-Point Addition / 341
\\
24. Deciphering a Linear Congruential Encryption / 349
\\
25. Computation of Tangent, Euler, and Bernoulli
Numbers / 359 \\
26. Euler's Constant to 1271 Places / 373 \\
27. Evaluation of Polynomials by Computer / 383 \\
28. Minimizing Drum Latency Time / 397 \\
Index / 437",
}
@Proceedings{Santos:2010:PVS,
editor = "E. J. P. (Edval J. P.) Santos and Hor{\'a}cio C. Neto
and El{\'\i}as Todorovich",
booktitle = "{Proceedings of the VI Southern Programmable Logic
Conference: Ipojuca, Porto de Galinhas Beach, Brazil,
March 24th--26th, 2010}",
title = "{Proceedings of the VI Southern Programmable Logic
Conference: Ipojuca, Porto de Galinhas Beach, Brazil,
March 24th--26th, 2010}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2010",
ISBN = "1-4244-6309-2, 1-4244-7089-7",
ISBN-13 = "978-1-4244-6309-1, 978-1-4244-7089-1",
LCCN = "TK7895.G36 2010",
bibdate = "Thu Feb 17 13:58:15 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number CFPI021B-PRT.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5473892",
acknowledgement = ack-nhfb,
meetingname = "Southern Conference on Programmable Logic (6th: 2010:
Ipojuca, Pernambuco, Brazil)",
subject = "Field programmable gate arrays; Congresses;
Programmable array logic",
}
@Proceedings{Watt:2010:IPI,
editor = "Stephen M. Watt",
booktitle = "{ISSAC 2010: Proceedings of the 2010 International
Symposium on Symbolic and Algebraic Computation, July
25--28, 2010, Munich, Germany}",
title = "{ISSAC 2010: Proceedings of the 2010 International
Symposium on Symbolic and Algebraic Computation, July
25--28, 2010, Munich, Germany}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiv + 363",
year = "2010",
ISBN = "1-4503-0150-9",
ISBN-13 = "978-1-4503-0150-3",
LCCN = "QA76.95 .I59 2010",
bibdate = "Fri Jun 17 08:11:01 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2011:SSP,
editor = "{ACM}",
booktitle = "{SC '11 State of the Practice Reports}",
title = "{SC '11 State of the Practice Reports}",
publisher = pub-ACM,
address = pub-ACM:adr,
year = "2011",
ISBN = "1-4503-1139-3",
ISBN-13 = "978-1-4503-1139-7",
LCCN = "????",
bibdate = "Fri Dec 16 11:20:09 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/supercomputing2011.bib",
acknowledgement = ack-nhfb,
}
@Book{IEEE:2011:ICC,
author = "{IEEE}",
booktitle = "{2011 IEEE COOL Chips XIV: Yokohama Joho Bunka Center,
Yokohama, Japan, April 20--22, 2011}",
title = "{2011 IEEE COOL Chips XIV: Yokohama Joho Bunka Center,
Yokohama, Japan, April 20--22, 2011}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2011",
ISBN = "1-61284-884-2",
ISBN-13 = "978-1-61284-884-6",
LCCN = "????",
bibdate = "Wed Dec 21 14:21:28 MST 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE Catalog Number CFP11COL-ART.",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5871805",
acknowledgement = ack-nhfb,
meetingname = "IEEE Symposium on Low-Power and High-Speed Chips (14th
: 2011 : Yokohama-shi, Japan)",
subject = "Low voltage systems; Congresses; Electronic circuit
design",
}
@Proceedings{Impagliazzo:2011:PSR,
editor = "John Impagliazzo and Eduard Proydakov",
booktitle = "Perspectives on {Soviet} and {Russian} Computing:
{First IFIP WG 9.7 Conference, SoRuCom
2006Petrozavodsk, Russia, July 3--7, 2006. Revised
Selected Papers}",
title = "Perspectives on {Soviet} and {Russian} Computing:
{First IFIP WG 9.7 Conference, SoRuCom
2006Petrozavodsk, Russia, July 3--7, 2006. Revised
Selected Papers}",
volume = "357",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxi + 272",
year = "2011",
DOI = "https://doi.org/10.1007/978-3-642-22816-2",
ISBN = "3-642-22815-1 (print), 3-642-22816-X (e-book)",
ISBN-13 = "978-3-642-22815-5 (print), 978-3-642-22816-2
(e-book)",
ISSN = "1868-422X (print), 1868-4238 (electronic)",
ISSN-L = "1868-4238",
LCCN = "QA75.5 .C66 2011",
bibdate = "Sun Aug 16 19:31:45 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "IFIP Advances in Information and Communication
Technology",
URL = "http://link.springer.com/openurl?genre=book%26isbn=978-3-642-22815-5",
abstract = "This book contains a collection of thoroughly refereed
papers derived from the First IFIP WG 9.7 Conference on
Soviet and Russian Computing, held in Petrozavodsk,
Russia, in July 2006. The 32 revised papers were
carefully selected from numerous submissions; many of
them were translated from Russian. They reflect much of
the shining history of computing activities within the
former Soviet Union from its origins in the 1950s with
the first computers used for military decision-making
problems up to the modern period where Russian ICT grew
substantially, especially in the field of custom-made
programming.",
acknowledgement = ack-nhfb,
tableofcontents = "The Work of Sergey Alekseevich Lebedev in Kiev and
Its Subsequent Influence on Further Scientific Progress
There / Zinoviy L. Rabinovich / 1 \\
History of the Creation of BESM: The First Computer of
S / A / Lebedev Institute of Precise Mechanics and
Computer Engineering / Vera B. Karpova and Leonid E.
Karpov / 6 \\
Some Hardware Aspects of the BESM-6 Design / V. I.
Smirnov / 20 \\
Computer Architecture Development: From the BESM-6
Computer to Supercomputers / Yuri I. Mitropolski / 26
\\
Operating System of the Multi-machine Computer AS-6 /
I. B. Bourdonov, V. P. Ivannikov, A. S. Kossatchev, S.
D. Kuznetsov, and A. N. Tomilin / 31 \\
Distributed Systems for Data Handling / Vladislav P.
Shirikov / 36 \\
Automatic Digital Computer M-1 of the I. S. Brook
Laboratory / T. M. Alexandridi and U. V. Rogachov / 46
\\
Conception of New Generation Computer Systems --- The
Last Large-Scale Initiative in Computers of the COMECON
Countries: A Glance after Twenty Years / Victor
Zakharov and Yuri Lavrenjuk / 50 \\
SM EVM Control Computer Development / N. L. Prokhorov
and G. A. Egorov / 64 \\
Ternary Computers: The Setun and the Setun 70 / Nikolay
Petrovich Brusentsov and Jos{\'e} Ramil Alvarez / 74
\\
Ternary Dialectical Informatics / Nikolay Petrovich
Brusentsov and Julia Sergeevna Vladimirova / 81 \\
Establishing a Computer Industry in the Soviet
Socialist Republic of Belarus / Yuri Vladimirovich
Karpilovitch, Viktor Vladimirovich Przhijalkovskiy, and
Gennadiy Dmitrievich Smirnov / 89 \\
Some Aspects on Computing Means Development Philosophy
/ Jaroslav Khetagourov / 98 \\
The Algorithmic ``Computer'' / Zoya Alekseeva / 103 \\
Academician Andrei Ershov and His Archive / Irina
Kraineva and Natalia Cheremnykh / 117 \\
The START Project / Alexander Gurievich Marchuk / 126
\\
The MRAMOR Workstation / A. A. Baehrs / 134 \\
Mixed Computation in Novosibirsk / Mikhail Bulyonkov /
142 \\
The Zelenograd Centerof Microelectronics / B. M.
Malashevich and D. B. Malashevich / 152 \\
Modular: The Super Computer / B. M. Malashevich and D.
B. Malashevich / 164 \\
The Microprocessors, Mini- and Micro-computers with
Architecture``Electronics NC'' in Zelenograd / B. M.
Malashevich / 174 \\
Fund Collection: ``Electronic Digital Computing
Machines'' at the Polytechnic Museum / Marina
Smolevitskaya / 187 \\
An Open Adaptive Virtual Museum of Informatics History
in Siberia / Victor N. Kasyanov / 194 \\
The History of Computers and Computing in Virtual
Museums / Yuri Polak / 201 \\
Computer Development in the Socialist Countries:
Members of the Council for Mutual Economic Assistance
(CMEA) / A. Y. Nitusov / 208 \\
On the History of Computer Algebra at the Keldysh
Institute of Applied Mathematics / G. B. Efimov, I. B.
Tshenkov, and E. Yu. Zueva / 220 \\
Novosibirsk Young Programmers School: A Way to Success
and Future Development / Alexander Gurievich Marchuk,
Tatyana Ivanovna Tikhonova, and Lidiya Vasilyevna
Gorodnyaya / 228 \\
``Lions --- Marchuk'': The Soviet--French Cooperation
in Computing / Ksenia Tatarchenko / 235 \\
Information and Communication Technology Education
Based on the Russian State Educational Standard of
``Applied Mathematics and Informatics'' / Iurii A.
Bogoiavlenskii / 243 \\
Cooperation among Institutions of the Soviet Union and
Cuba:Accomplishments between 1972 and 1990 / Tom{\'a}s
L{\'o}pez Jim{\e}nez / 251 \\
Teaching Computer Science in Moscow Universities:
Evolution for Forty Years / Olga Parakhina and Yuri
Polak / 258 \\
Kronos: Processor Family for High-Level Languages /
Dmitry N. Kuznetsov, Alexey E. Nedorya, Eugene V.
Tarassov, Vladimir E. Philippov, and Marina Ya
Philippova / 266 \\
Author Index / / 273",
}
@Proceedings{Schwarz:2011:PIS,
editor = "Eric Schwarz and Vojin G. Oklobdzija",
booktitle = "{Proceedings of the 20th IEEE Symposium on Computer
Arithmetic, July 25--27, 2011, T{\"u}bingen, Germany}",
title = "{Proceedings of the 20th IEEE Symposium on Computer
Arithmetic, July 25--27, 2011, T{\"u}bingen, Germany}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xix + 253",
year = "2011",
DOI = "https://doi.org/10.1109/ARITH17396.2011",
ISBN = "0-7695-4318-9, 1-4244-9457-5",
ISBN-13 = "978-0-7695-4318-5, 978-1-4244-9457-6",
LCCN = "QA76.6",
bibdate = "Sat Aug 20 09:19:17 2011",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-20; correct rounding; floating-point
arithmetic",
tableofcontents = "Foreword / ix \\
Dedication / x \\
Steering Committee / xv \\
Symposium Committee / xvi \\
Program Committee / xvii \\
Additional Reviewers / xviii \\
Corporate Sponsors / xix \\
Session 1: Keynote Talk: Chair: Eric Schwarz and Vojin
G. Oklobdzija \\
High Intelligence Computing: The New Era of High
Performance Computing / Ralf Fischer / 3 \\
Session 2: Multiple-Precision Algorithms: Chair: Marius
Cornea \\
Short Division of Long Integers / David Harvey and Paul
Zimmermann / 7 \\
High Degree Toom'n'Half for Balanced and Unbalanced
Multiplication / Marco Bodrato / 15 \\
Augmented Precision Square Roots and 2-D Norms, and
Discussion on Correctly Rounding sqrt($x^2 + y^2$) /
Nicolas Brisebarre, Mioara Jolde{\c{s}}, Peter
Kornerup, Erik Martin-Dorel, and Jean-Michel Muller /
23 \\
Session 3: Transcendental Methods: Chair: Naofumi
Takagi \\
Towards a Quaternion Complex Logarithmic Number System
/ Mark G. Arnold, John Cowles, Vassilis Paliouras, and
Ioannis Kouretas / 33 \\
ROM-less LNS / R. Che Ismail and J. N. Coleman / 43 \\
Composite Iterative Algorithm and Architecture for q-th
Root Calculation / Alvaro Vazquez and Javier D.
Bruguera / 52 \\
On the Fixed-Point Accuracy Analysis and Optimization
of FFT Units with CORDIC Multipliers / Omid Sarbishei
and Katarzyna Radecka / 62 \\
Session 4: Special Session on Industrial Practices:
Chair: Mike Schulte \\
Self Checking in Current Floating-Point Units / Daniel
Lipetz and Eric Schwarz / 73 \\
How to Square Floats Accurately and Efficiently on the
ST231 Integer Processor/ Claude-Pierre Jeannerod,
Jingyan Jourdan-Lu, Christophe Monat, and Guillaume
Revy / 77 \\
A 1.5 Ghz VLIW DSP CPU with Integrated Floating Point
and Fixed Point Instructions in 40 nm CMOS / Timothy
Anderson, Due Bui, Shriram Moharil, Soujanya Narnur,
Mujibur Rahman, Anthony Lell, Eric Biscondi, Ashish
Shrivastava, Peter Dent, Mingjian Yan, and Hasan
Mahmood / 82 \\
The POWER7 Binary Floating-Point Unit / Maarten
Boersma, Michael Kroner, Christophe Layer, Petra Leber,
Silvia M. Muller, and Kerstin Schelm / 87 \\
Session 5: Addition: Chair: Alberto Nannarelli \\
Accelerating Computations on FPGA Carry Chains by
Operand Compaction / Thomas B. Preus{\ss}er, Martin
Zabel, and Rainer G. Spallek / 95 \\
Fast Ripple-Carry Adders in Standard-Cell CMOS VLSI /
Neil Burgess / 103 \\
A Family of High Radix Signed Digit Adders / Saeid
Gorgin and Ghassem Jaberipur / 112 \\
Session 6: Floating-Point Units: Chair: Javier Bruguera
\\
Fused Multiply-Add Microarchitecture Comprising
Separate Early-Normalizing Multiply and Add Pipelines /
David R. Lutz / 123 \\
Latency Sensitive FMA Design / Sameh Galal and Mark
Horowitz / 129 \\
The IBM zEnterprise-196 Decimal Floating-Point
Accelerator / Steven Carlough, Adam Collura, Silvia
Mueller, and Michael Kroener / 139 \\
Session 7: Division, Square-Root and Reciprocal
Square-Root: Chair: Peter Kornerup \\
Radix-8 Digit-by-Rounding: Achieving High-Performance
Reciprocals, Square Roots, and Reciprocal Square Roots
/ J. Adam Butts, Ping Tak Peter Tang, Ron O. Dror, and
David E. Shaw / 149 \\
Tight Certification Techniques for Digit-by-Rounding
Algorithms with Application to a New 1/sqrt(x) Design /
Ping Tak Peter Tang, J. Adam Butts, Ron O. Dror, and
David E. Shaw / 159 \\
Radix-16 Combined Division and Square Root Unit /
Alberto Nannarelli / 169 \\
A Prescale-Lookup-Postscale Additive Procedure for
Obtaining a Single Precision Ulp Accurate Reciprocal /
David W. Matula and Mihai T. Panu / 177 \\
Session 8: Special Session on High Performance
Arithmetic for FPGA's: Chair: Martin Langhammer \\
Teraflop FPGA Design / Martin Langhammer / 187 \\
The Arithmetic Operators You Will Never See in a
Microprocessor / Florent de Dinechin / 189 \\
Accelerating Large-Scale HPC Applications Using FPGAs /
Rob Dimond, Sebastien Racaniere, and Oliver Pell / 191
\\
Session 9: Arithmetic Algorithms for Cryptography:
Chair: David Matula \\
A General Approach for Improving RNS Montgomery
Exponentiation Using Pre-processing / Filippo Gandino,
Fabrizio Lamberti, Paolo Montuschi, and Jean-Claude
Bajard / 195 \\
Bit-Sliced Binary Normal Basis Multiplication / Billy
Bob Brumley and Dan Page / 205 \\
Efficient SIMD Arithmetic Modulo a Mersenne Number /
Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra, and
Peter L. Montgomery / 213 \\
Session 10: Tools for Formal Certified Code: Chair:
Martin Schmookler \\
Automatic Generation of Code for the Evaluation of
Constant Expressions at Any Precision with a Guaranteed
Error Bound / Sylvain Chevillard / 225 \\
Automatic Generation of Fast and Certified Code for
Polynomial Evaluation / Christophe Mouilleron and
Guillaume Revy / 233 \\
Flocq: A Unified Library for Proving Floating-Point
Algorithms in Coq / Sylvie Boldo and Guillaume
Melquiond / 243 \\
Author Index / 253",
}
@Book{Hennessy:2012:CAQ,
author = "John L. Hennessy and David A. Patterson",
booktitle = "Computer Architecture: a Quantitative Approach",
title = "Computer Architecture: a Quantitative Approach",
publisher = pub-MORGAN-KAUFMANN-ELSEVIER,
address = pub-MORGAN-KAUFMANN-ELSEVIER:adr,
edition = "Fifth",
pages = "xxvii + 493 + 325",
year = "2012",
ISBN = "0-12-383872-X (paperback)",
ISBN-13 = "978-0-12-383872-8 (paperback)",
LCCN = "QA76.9.A73 P377 2012",
bibdate = "Wed Feb 15 07:46:38 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
z3950.loc.gov:7090/Voyager",
note = "With contributions by Krste Asanovi{\'c}, Jason D.
Kabos, Robert P. Colwell, Thomas M. Conte, Jos{\'e}
Duato, Diana Franklin, David Goldberg, Norman P.
Jouppi, Sheng Li, Naveen Muralimanohar, Gregory D.
Peterson, Timothy M. Pinkston, Parthasarathy
Ranganthan, David A. Wood, and Amr Zaky.",
URL = "http://booksite.mkp.com/9780123838728",
acknowledgement = ack-nhfb,
subject = "Computer architecture",
tableofcontents = "1: Fundamentals of Quantitative Design and Analysis
\\
2: Memory Hierarchy Design \\
3: Instruction-Level Parallelism and Its Exploitation
\\
4: Data-Level Parallelism in Vector, SIMD, and GPU
Architectures \\
5: Thread-Level Parallelism \\
6: Warehouse-Scale Computers to Exploit Request-Level
and Data-Level Parallelism \\
A: Instruction Set Principles \\
B: Review of Memory Hierarchy \\
C: Pipelining: Basic and Intermediate Concepts \\
D: Storage Systems \\
E: Embedded Systems \\
F: Interconnection Networks \\
G: Vector Processors in More Depth \\
H: Hardware and Software for VLIW and EPIC \\
I: Large-Scale Multiprocessors and Scientific
Applications \\
J: Computer Arithmetic \\
K: Survey of Instruction Set Architectures \\
L: Historical Perspective and References \\
References \\
Index",
}
@Proceedings{Jonasson:2012:APSb,
editor = "Kristj{\'a}n J{\'o}nasson",
booktitle = "{Applied Parallel and Scientific Computing: 10th
International Conference, PARA 2010, Reykjav{\'\i}k,
Iceland, June 6--9, 2010, Revised Selected Papers, Part
II}",
title = "{Applied Parallel and Scientific Computing: 10th
International Conference, PARA 2010, Reykjav{\'\i}k,
Iceland, June 6--9, 2010, Revised Selected Papers, Part
II}",
volume = "7134",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxviii + 477",
year = "2012",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/978-3-642-28145-7",
ISBN = "3-642-28144-3 (print), 3-642-28145-1 (e-book)",
ISBN-13 = "978-3-642-28144-0 (print), 978-3-642-28145-7
(e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "????",
bibdate = "Wed Dec 19 15:24:47 MST 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib",
series = ser-LNCS,
URL = "http://www.springerlink.com/content/978-3-642-28145-7",
acknowledgement = ack-nhfb,
tableofcontents = "Free Energy Monte Carlo Simulations on a
Distributed Network \\
Numerical Investigation of the Cumulant Expansion for
Fourier Path Integrals \\
Optimization of Functionals of Orthonormal Functions in
the Absence of Unitary Invariance \\
Simulated Annealing with Coarse Graining and
Distributed Computing \\
Path Optimization with Application to Tunneling \\
Shallow Water Simulations on Multiple GPUs \\
High Performance Computing Techniques for Scaling Image
Analysis Workflows \\
Parallel Computation of Bivariate Polynomial Resultants
on Graphics Processing Units \\
Accelerating Model Reduction of Large Linear Systems
with Graphics Processors \\
Fast GPU-Based Fluid Simulations Using SPH \\
Toward Techniques for Auto-tuning GPU Algorithms \\
An Interval Version of the Crank-Nicolson Method \\
The First Approach \\
Parallel Detection of Interval Overlapping \\
Using the Second-Order Information in Pareto-set
Computations of a Multi-criteria Problem \\
Comments on Fast and Exact Accumulation of Products \\
An Interval Finite Difference Method of Crank-Nicolson
Type for Solving the One-Dimensional Heat Conduction
Equation with Mixed Boundary Conditions \\
Using C-XSC for High Performance Verified Computing \\
Efficient Implementation of Interval Matrix
Multiplication \\
The Computing Framework for Physics Analysis at LHCb
\\
Taming the Raven \\
Testing the Random Access, Visualization and
Exploration Network RAVEN \\
RAVEN \\
Boosting Data Analysis for the LHC Experiments \\
Bridging HPC and Grid File I/O with IOFSL \\
Fine Granularity Sparse QR Factorization for Multicore
Based Systems \\
Mixed Precision Iterative Refinement Methods for Linear
Systems: Convergence Analysis Based on Krylov Subspace
Methods \\
An Implementation of the Tile QR Factorization for a
GPU and Multiple CPUs \\
Efficient Reduction from Block Hessenberg Form to
Hessenberg Form Using Shared Memory \\
Cache-Oblivious Algorithms and Matrix Formats for
Computations on Interval Matrices \\
Parallel Solution of Narrow Banded Diagonally Dominant
Linear Systems \\
An Approach for Semiautomatic Locality Optimizations
Using OpenMP \\
Memory-Efficient Sierpinski-Order Traversals on
Dynamically Adaptive, Recursively Structured Triangular
Grids \\
Fast Wavelet Transform Utilizing a Multicore-Aware
Framework \\
Direct Sparse Factorization of Blocked Saddle Point
Matrices \\
Multi-Target Vectorization with MTPS C++ Generic
Library \\
Analysis of Gravitational Wave Signals on Heterogeneous
Architectures \\
Towards Efficient Execution of Erasure Codes on
Multicore Architectures \\
Communication-Efficient Algorithms for Numerical
Quantum Dynamics \\
Efficiently Implementing Monte Carlo Electrostatics
Simulations on Multicore Accelerators \\
Algebraic Multigrid Solver on Clusters of CPUs and GPUs
\\
Solution of Identification Problems in Computational
Mechanics \\
Parallel Processing Aspects \\
ScalaTrace: Tracing, Analysis and Modeling of HPC Codes
at Scale \\
A Lightweight Library for Building Scalable Tools \\
MATE: Toward Scalable Automated and Dynamic Performance
Tuning Environment \\
Improving the Scalability of Performance Evaluation
Tools \\
Automatic Performance Analysis of OpenMP Codes on a
Scalable Shared Memory System Using Periscope \\
Further Improving the Scalability of the Scalasca
Toolset",
}
@Proceedings{IEEE:2013:PIS,
editor = "{IEEE}",
booktitle = "{Proceedings of the 21st IEEE Symposium on Computer
Arithmetic, Austin, Texas, USA, 8--10 April 2013}",
title = "{Proceedings of the 21st IEEE Symposium on Computer
Arithmetic, Austin, Texas, USA, 8--10 April 2013}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xvi + 229",
year = "2013",
ISBN = "0-7695-4957-8",
ISBN-13 = "978-0-7695-4957-6",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2013",
bibdate = "Sat Aug 01 08:03:11 2013",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-21; computer arithmetic units; correctness
proofs; cryptography; domain specific designs; error
analysis; exascale computing; floating point
arithmetic; floating-point error analysis; formal
verification; function approximation; modular
arithmetic; theorem proving; verification",
}
@Proceedings{Butler:2015:FMS,
editor = "Michael Butler and Sylvain Conchon and Fatiha
Za{\"i}di",
booktitle = "{Formal Methods and Software Engineering: 17th
International Conference on Formal Engineering Methods,
ICFEM 2015, Paris, France, November 3--5, 2015,
Proceedings}",
title = "{Formal Methods and Software Engineering: 17th
International Conference on Formal Engineering Methods,
ICFEM 2015, Paris, France, November 3--5, 2015,
Proceedings}",
volume = "9407",
publisher = "Springer International Publishing",
address = "Cham, Switzerland",
pages = "xxv + 436 + 150",
year = "2015",
DOI = "https://doi.org/10.1007/978-3-319-25423-4",
ISBN = "3-319-25422-7 (paperback), 3-319-25423-5 (e-book)",
ISBN-13 = "978-3-319-25422-7 (paperback), 978-3-319-25423-4
(e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.758",
bibdate = "Fri Jan 31 15:45:10 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/java2010.bib",
series = ser-LNCS,
URL = "http://link.springer.com/10.1007/978-3-319-25423-4",
abstract = "This book constitutes the refereed proceedings of the
17th International Conference on Formal Engineering
Methods, ICFEM 2015, held in Paris, France, in November
2015. The 27 revised full papers presented were
carefully reviewed and selected from 82 submissions.
The papers cover a wide range of topics in the area of
formal methods and software engineering and are devoted
to advancing the state of the art of applying formal
methods in practice. They focus in particular on
combinations of conceptual and methodological aspects
with their formal foundation and tool support.",
acknowledgement = ack-nhfb,
subject = "Computer science; Computer networks; Computer
programming; Software engineering; Programming
languages (Electronic computers); Algorithms; Logic,
Symbolic and mathematical; Algorithms; Computer
networks; Computer programming; Computer science;
Logic, Symbolic and mathematical; Programming languages
(Electronic computers); Software engineering;
Computers; Programming; General; Programming Languages;
Algorithms; Mathematics; Logic; Hardware; Network
Hardware; software development; Programming and
scripting languages: general; Algorithms and data
structures; Mathematical theory of computation; Network
hardware; Software Development and Engineering;
Software Engineering",
tableofcontents = "Intro \\
Preface \\
Organization \\
Invited Talks \\
Can Java Ever Be Safe? The hiJaC Project Abstract \\
Specification and Analysis of SoC Flows (Abstract) \\
Algorithmic Analysis for Asynchronous Programs \\
Contents \\
Domain-Specific Languages with Scala \\
1 Introduction \\
2 External DSLs \\
2.1 The Parser Library Approach \\
2.2 The Parser Tool Approach \\
3 Internal DSLs \\
3.1 Annotations \\
3.2 Shallow Embedding \\
3.3 Deep Embedding \\
4 Discussion \\
5 Conclusions \\
References \\
Formal Verification of Programs Computing the
Floating-Point Average \\
1 Introduction \\
2 Basics About Floating-Point Arithmetic \\
3 Methodology and Desired Specification \\
3.1 Methodology \\
3.2 Desired Specification \\
4 Formal Proof of the Algorithms \\
4.1 The average1 Function \\
4.2 The average3 Function \\
4.3 The average2 Function \\
4.4 Putting All Parts Together: The Average Functions
\\
5 Specifications and Formal Verification of the
Programs \\
5.1 Absolute Value \\
5.2 Accurate Average \\
5.3 Correct Average \\
6 Conclusion and Perspectives \\
References \\
Formalization and Verification of Declarative Cloud
Orchestration \\
1 Introduction \\
2 TOSCA: Topology and Orchestration Specification for
Cloud Application \\
3 Model of Automation of Topologies \\
4 CafeOBJ Specification of Model \\
5 Verification of Setup Operation \\
5.1 Proof Score for Condition (1) \\
5.2 Cyclic Dependency \\
5.3 Proof Score for Condition (2) \\
5.4 Proof Scores for Condition (3), (4), (5) and (6)
\\
6 Related Work and Conclusion \\
References \\
Consistency Verification of Specification Rules \\
1 Introduction \\
2 Background \\
2.1 Constraints Satisfiability \\
2.2 Rules Consistency \\
3 Relationship Between MISes and MUSes \\
4 An Efficient Algorithm for Enumerating MUSes \\
4.1 The MARCO algorithm \\
4.2 The MUSesHunter Algorithm \\
4.3 Comparing MARCO and MUSesHunter \\
5 Empirical Analysis \\
5.1 MUSesHunter vs. MARCO \\
5.2 MISes Finder \\
6 Conclusion \\
References \\
Applying Automata Learning to Embedded Control Software
\\
1 Introduction \\
2 Engine Status Manager \\
2.1 ESRA \\
2.2 ESM and Connected Components \\
2.3 Rational Rose RealTime \\
2.4 The ESM State Diagram \\
3 Learning the ESM \\
3.1 Experimental Set-Up \\
3.2 Test Selection Strategies \\
3.3 Results \\
4 Verification \\
4.1 Approach \\
4.2 Model Transformations \\
4.3 Results \\
5 Conclusions and Future Work \\
References \\
A 3-Valued Contraction Model Checking Game: Deciding on
the World of Partial Information \\
1 Introduction \\
2 Computation Tree Logic and Kripke Structures \\
2.1 Kripke Modal Transition System \\
2.2 KMTS as a Set of Kripke Structures \\
3 Semantics of CTL with Respect to KMTS \\
4 KMTS Operations \\
4.1 Dealing with Sets of KMTSs \\
4.2 Tree Partition Set \\
5 The Contraction Model Checking \\
6 Conclusions \\
References \\
Supporting Requirements Analysis Using Pattern-Based
Formal Specification Construction \\
1 Introduction \\
2 Major Ideas of PBFSRA \\
2.1 Principle of PBFSRA \\
2.2 Procedure of Applying PBFSRA",
}
@Book{Higham:2015:PCA,
editor = "Nicholas J. Higham and Mark R. Dennis and Paul
Glendinning and Paul A. Martin and Fadil Santosa and
Jared Tanner",
booktitle = "The {Princeton} Companion to Applied Mathematics",
title = "The {Princeton} Companion to Applied Mathematics",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "994 (est.)",
year = "2015",
ISBN = "0-691-15039-7 (hardcover)",
ISBN-13 = "978-0-691-15039-0 (hardcover)",
LCCN = "QA155 .P75 2015",
bibdate = "Wed Sep 9 05:32:49 MDT 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Algebra; Mathematics; Mathematical models",
tableofcontents = "Preface / ix \\
Contributors / xiii \\
Part I: Introduction to Applied Mathematics \\
I.1 What Is Applied Mathematics? / 1 \\
I.2 The Language of Applied Mathematics / 8 \\
I.3 Methods of Solution / 27 \\
I.4 Algorithms / 40 \\
I.5 Goals of Applied Mathematical Research / 48 \\
I.6 The History of Applied Mathematics / 55 \\
Part II: Concepts \\
II.1 Asymptotics / 81 \\
II.2 Boundary Layer / 82 \\
II.3 Chaos and Ergodicity / 82 \\
II.4 Complex Systems / 83 \\
II.5 Conformal Mapping / 84 \\
II.6 Conservation Laws / 86 \\
II.7 Control / 88 \\
II.8 Convexity / 89 \\
II.9 Dimensional Analysis and Scaling / 90 \\
II.10 The Fast Fourier Transform / 94 \\
II.11 Finite Differences / 95 \\
II.12 The Finite-Element Method / 96 \\
II.13 Floating-Point Arithmetic / 96 \\
II.14 Functions of Matrices / 97 \\
II.15 Function Spaces / 99 \\
II.16 Graph Theory / 101 \\
II.17 Homogenization / 103 \\
II.18 Hybrid Systems / 103 \\
II.19 Integral Transforms and Convolution / 104 \\
II.20 Interval Analysis / 105 \\
II.21 Invariants and Conservation Laws / 106 \\
II.22 The Jordan Canonical Form / 112 \\
II.23 Krylov Subspaces / 113 \\
II.24 The Level Set Method / 114 \\
II.25 Markov Chains / 116 \\
II.26 Model Reduction / 117 \\
II.27 Multiscale Modeling / 119 \\
II.28 Nonlinear Equations and Newton's Method / 120 \\
II.29 Orthogonal Polynomials / 122 \\
II.30 Shocks / 122 \\
II.31 Singularities / 124 \\
II.32 The Singular Value Decomposition / 126 \\
II.33 Tensors and Manifolds / 127 \\
II.34 Uncertainty Quantification / 131 \\
II.35 Variational Principle / 134 \\
II.36 Wave Phenomena / 134 \\
Part III: Equations, Laws, and Functions of Applied
Mathematics \\
III.1 Benford's Law / 135 \\
III.2 Bessel Functions / 137 \\
III.3 The Black--Scholes Equation / 137 \\
III.4 The Burgers Equation / 138 \\
III.5 The Cahn--Hilliard Equation / 138 \\
III.6 The Cauchy--Riemann Equations / 139 \\
III.7 The Delta Function and Generalized Functions /
139 \\
III.8 The Diffusion Equation / 142 \\
III.9 The Dirac Equation / 142 \\
III.10 Einstein's Field Equations / 144 \\
III.11 The Euler Equations / 146 \\
III.12 The Euler--Lagrange Equations / 147 \\
III.13 The Gamma Function / 148 \\
III.14 The Ginzburg--Landau Equation / 148 \\
III.15 Hooke's Law / 149 \\
III.16 The Korteweg--de Vries Equation / 150 \\
III.17 The Lambert $W$ Function / 151 \\
III.18 Laplace's Equation / 155 \\
III.19 The Logistic Equation / 156 \\
III.20 The Lorenz Equations / 158 \\
III.21 Mathieu Functions / 159 \\
III.22 Maxwell's Equations / 160 \\
III.23 The Navier--Stokes Equations / 162 \\
III.24 The Painlev{\'e} Equations / 163 \\
III.25 The Riccati Equation / 165 \\
III.26 Schr{\"o}dinger's Equation / 167 \\
III.27 The Shallow-Water Equations / 167 \\
III.28 The Sylvester and Lyapunov Equations / 168 \\
III.29 The Thin-Film Equation / 169 \\
III.30 The Tricomi Equation / 170 \\
III.31 The Wave Equation / 171 \\
Part IV: Areas of Applied Mathematics \\
IV.1 Complex Analysis / 173 \\
IV.2 Ordinary Differential Equations / 181 \\
IV.3 Partial Differential Equations / 190 \\
IV.4 Integral Equations / 200 \\
IV.5 Perturbation Theory and Asymptotics / 208 \\
IV.6 Calculus of Variations / 218 \\
IV.7 Special Functions / 227 \\
IV.8 Spectral Theory / 236 \\
IV.9 Approximation Theory / 248 \\
IV.10 Numerical Linear Algebra and Matrix Analysis /
263 \\
IV.11 Continuous Optimization (Nonlinear and Linear
Programming) / 281 \\
IV.12 Numerical Solution of Ordinary Differential
Equations / 293 \\
IV.13 Numerical Solution of Partial Differential
Equations / 306 \\
IV.14 Applications of Stochastic Analysis / 319 \\
IV.15 Inverse Problems / 327 \\
IV.16 Computational Science / 335 \\
IV.17 Data Mining and Analysis / 350 \\
IV.18 Network Analysis / 360 \\
IV.19 Classical Mechanics / 374 \\
IV.20 Dynamical Systems / 383 \\
IV.21 Bifurcation Theory / 393 \\
IV.22 Symmetry in Applied Mathematics / 402 \\
IV.23 Quantum Mechanics / 411 \\
IV.24 Random-Matrix Theory / 419 \\
IV.25 Kinetic Theory / 428 \\
IV.26 Continuum Mechanics / 446 \\
IV.27 Pattern Formation / 458 \\
IV.28 Fluid Dynamics / 467 \\
IV.29 Magnetohydrodynamics / 476 \\
IV.30 Earth System Dynamics / 485 \\
IV.31 Effective Medium Theories / 500 \\
IV.32 Mechanics of Solids / 505 \\
IV.33 Soft Matter / 516 \\
IV.34 Control Theory / 523 \\
IV.35 Signal Processing / 533 \\
IV.36 Information Theory / 545 \\
IV.37 Applied Combinatorics and Graph Theory / 552 \\
IV.38 Combinatorial Optimization / 564 \\
IV.39 Algebraic Geometry / 570 \\
IV.40 General Relativity and Cosmology / 579 \\
Part V: Modeling \\
V.1 The Mathematics of Adaptation (Or the Ten Avatars
of Vishnu) / 591 \\
V.2 Sport / 598 \\
V.3 Inerters / 604 \\
V.4 Mathematical Biomechanics / 609 \\
V.5 Mathematical Physiology / 616 \\
V.6 Cardiac Modeling / 623 \\
V.7 Chemical Reactions / 627 \\
V.8 Divergent Series: Taming the Tails / 634 \\
V.9 Financial Mathematics / 640 \\
V.10 Portfolio Theory / 648 \\
V.11 Bayesian Inference in Applied Mathematics / 658
\\
V.12 A Symmetric Framework with Many Applications / 661
\\
V.13 Granular Flows / 665 \\
V.14 Modern Optics / 673 \\
V.15 Numerical Relativity / 680 \\
V.16 The Spread of Infectious Diseases / 687 \\
V.17 The Mathematics of Sea Ice / 694 \\
V.18 Numerical Weather Prediction / 705 \\
V.19 Tsunami Modeling / 712 \\
V.20 Shock Waves / 720 \\
V.21 Turbulence / 724 \\
Part VI: Example Problems \\
VI.1 Cloaking / 733 \\
VI.2 Bubbles / 735 \\
VI.3 Foams / 737 \\
VI.4 Inverted Pendulums / 741 \\
VI.5 Insect Flight / 743 \\
VI.6 The Flight of a Golf Ball / 746 \\
VI.7 Automatic Differentiation / 749 \\
VI.8 Knotting and Linking of Macromolecules / 752 \\
VI.9 Ranking Web Pages / 755 \\
VI.10 Searching a Graph / 757 \\
VI.11 Evaluating Elementary Functions / 759 \\
VI.12 Random Number Generation / 761 \\
VI.13 Optimal Sensor Location in the Control of
Energy-Efficient Buildings / 763 \\
VI.14 Robotics / 767 \\
VI.15 Slipping, Sliding, Rattling, and Impact:
Nonsmooth Dynamics and Its Applications / 769 \\
VI.16 From the $N$-Body Problem to Astronomy and Dark
Matter / 771 \\
VI.17 The $N$-Body Problem and the Fast Multipole
Method / 775 \\
VI.18 The Traveling Salesman Problem / 778 \\
Part VII: Application Areas \\
VII.1 Aircraft Noise / 783 \\
VII.2 A Hybrid Symbolic--Numeric Approach to Geometry
Processing and Modeling / 787 \\
VII.3 Computer-Aided Proofs via Interval Analysis / 790
\\
VII.4 Applications of Max-Plus Algebra / 795 \\
VII.5 Evolving Social Networks, Attitudes, and Beliefs
--- and Counterterrorism / 800 \\
VII.6 Chip Design / 804 \\
VII.7 Color Spaces and Digital Imaging / 808 \\
VII.8 Mathematical Image Processing / 813 \\
VII.9 Medical Imaging / 816 \\
VII.10 Compressed Sensing / 823 \\
VII.11 Programming Languages: An Applied Mathematics
View / 828 \\
VII.12 High-Performance Computing / 839 \\
VII.13 Visualization / 843 \\
VII.14 Electronic Structure Calculations (Solid State
Physics) / 847 \\
VII.15 Flame Propagation / 852 \\
VII.16 Imaging the Earth Using Green's Theorem / 857
\\
VII.17 Radar Imaging / 860 \\
VII.18 Modeling a Pregnancy Testing Kit / 864 \\
VII.19 Airport Baggage Screening with X-Ray Tomography
/ 866 \\
VII.20 Mathematical Economics / 868 \\
VII.21 Mathematical Neuroscience / 873 \\
VII.22 Systems Biology / 879 \\
VII.23 Communication Networks / 883 \\
VII.24 Text Mining / 887 \\
VII.25 Voting Systems / 891 \\
Part VIII: Final Perspectives \\
VIII.1 Mathematical Writing / 897 \\
VIII.2 How to Read and Understand a Paper / 903 \\
VIII.3 How to Write a General Interest Mathematics Book
/ 906 \\
VIII.4 Workflow / 912 \\
VIII.5 Reproducible Research in the Mathematical
Sciences / 916 \\
VIII.6 Experimental Applied Mathematics / 925 \\
VIII.7 Teaching Applied Mathematics / 933 \\
VIII.8 Mediated Mathematics: Representations of
Mathematics in Popular Culture and Why These Matter /
943 \\
VIII.9 Mathematics and Policy / 953 \\
Index / 963",
}
@Proceedings{IEEE:2015:ISS,
editor = "{IEEE}",
booktitle = "{2015 IEEE Symposium on Security and Privacy (SP 2015)
San Jose, California, USA, 18--20 May 2015}",
title = "{2015 IEEE Symposium on Security and Privacy (SP 2015)
San Jose, California, USA, 18--20 May 2015}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xix + 952",
year = "2015",
ISBN = "1-4673-6949-7 (print), 1-4673-6950-0 (e-book)",
ISBN-13 = "978-1-4673-6949-7, 978-1-4673-6950-3 (e-book)",
ISSN = "1081-6011 (print), 2375-1207 (electronic)",
ISSN-L = "1081-6011",
LCCN = "QA76.9.A25",
bibdate = "Mon Feb 10 08:59:08 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.gbv.de/dms/tib-ub-hannover/836112652.pdf",
acknowledgement = ack-nhfb,
}
@Proceedings{Muller:2015:ISC,
editor = "Jean-Michel Muller and Arnaud Tisserand and Julio
Villalba",
booktitle = "{2015 IEEE 22nd Symposium on Computer Arithmetic
(ARITH 2015) Lyon, France, 22--24 June 2015}",
title = "{2015 IEEE 22nd Symposium on Computer Arithmetic
(ARITH 2015) Lyon, France, 22--24 June 2015}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 176",
year = "2015",
ISBN = "1-4799-8665-8, 1-4799-8663-1",
ISBN-13 = "978-1-4799-8665-1, 978-1-4799-8663-7",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2015",
bibdate = "Sat Aug 01 08:03:11 2015",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7193754",
acknowledgement = ack-nhfb,
keywords = "ARITH-22; computer arithmetic units; correctness
proofs; cryptography; domain specific designs; error
analysis; exascale computing; floating point
arithmetic; floating-point error analysis; formal
verification; function approximation; modular
arithmetic; theorem proving; verification",
}
@Book{Swartzlander:2015:CAa,
editor = "Earl E. {Swartzlander, Jr.}",
booktitle = "Computer Arithmetic",
title = "Computer Arithmetic",
volume = "1",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "????",
year = "2015",
DOI = "https://doi.org/10.1142/9476",
ISBN = "981-4651-56-7 (vol. 1; hardcover), 981-4651-57-5,
981-4641-47-2 (e-book)",
ISBN-13 = "978-981-4651-56-1 (vol. 1; hardcover),
978-981-4651-57-8, 978-981-4641-47-0 (e-book)",
LCCN = "QA76.6 .C633 2015 vol. 1",
bibdate = "Tue Aug 7 07:57:49 MDT 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This is the new edition of the classic book
\booktitle{Computer Arithmetic} in three volumes
published originally in 1990 by IEEE Computer Society
Press. As in the original, the book contains many
classic papers treating advanced concepts in computer
arithmetic, which is very suitable as stand-alone
textbooks or complementary materials to textbooks on
computer arithmetic for graduate students and research
professionals interested in the field. Told in the
words of the initial developers, this book conveys the
excitement of the creators, and the implementations
provide insight into the details necessary to realize
real chips. This second volume presents topics on error
tolerant arithmetic, digit on-line arithmetic, number
systems, and now in this new edition, a topic on
implementations of arithmetic operations, all wrapped
with an updated overview and a new introduction for
each chapter.",
acknowledgement = ack-nhfb,
}
@Book{Swartzlander:2015:CAb,
editor = "Earl E. {Swartzlander, Jr.}",
booktitle = "Computer Arithmetic",
title = "Computer Arithmetic",
volume = "2",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xxxviii + 446",
year = "2015",
DOI = "https://doi.org/10.1142/9422;
https://doi.org/10.1142/9789814641470",
ISBN = "981-4641-46-4 (hardcover), 981-4641-47-2 (e-book)",
ISBN-13 = "978-981-4641-46-3 (hardcover), 978-981-4641-47-0
(e-book)",
LCCN = "QA76.6 .C633 2015 vol. 2",
bibdate = "Tue Aug 7 07:57:49 MDT 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "This is the new edition of the classic book
\booktitle{Computer Arithmetic} in three volumes
published originally in 1990 by IEEE Computer Society
Press. As in the original, the book contains many
classic papers treating advanced concepts in computer
arithmetic, which is very suitable as stand-alone
textbooks or complementary materials to textbooks on
computer arithmetic for graduate students and research
professionals interested in the field. Told in the
words of the initial developers, this book conveys the
excitement of the creators, and the implementations
provide insight into the details necessary to realize
real chips. This second volume presents topics on error
tolerant arithmetic, digit on-line arithmetic, number
systems, and now in this new edition, a topic on
implementations of arithmetic operations, all wrapped
with an updated overview and a new introduction for
each chapter.",
acknowledgement = ack-nhfb,
tableofcontents = "About the Editor \\
Preface \\
Contents by Author \\
Overview of Computer Arithmetic \\
Part I: ERROR TOLERANT ARITHMETIC \\
Editors' Comments on Papers 1 Through 5 \\
Error Detecting and Error Correcting Codes \\
Generalized Parity Checking \\
Error-Checking Logic for Arithmetic-Type Operations of
a Processor \\
Arithmetic Algorithms for Error-Coded Operands \\
Error Detection and Correction for Addition and
Subtraction, Through Higher Radix Extensions of Hamming
Codes \\
Part II: ON-LINE ARITHMETIC \\
Editor's Comments on Papers 6 Through 13 \\
Signed-Digit Number Representations for Fast Parallel
Arithmetic \\
On-Line Arithmetic: A Design Methodology and
Applications in Digital Signal Processing \\
On-Line Algorithms for Division and Multiplication \\
Error Analysis of Certain Floating-Point On-Line
Algorithms \\
Improved Normalization Results for Digit On-Line
Arithmetic \\
Fully Digit On-Line Networks \\
On-Line Scheme for Computing Rotation Factors \\
On-the-Fly Conversion of Redundant into Conventional
Representations \\
Part III: VLSI ADDER IMPLEMENTATIONS \\
Editor's Comments on Papers 14 Through 18 \\
Time-Component Complexity of Two Approaches to
Multioperand Binary Addition \\
Some Optimal Schemes for ALU Implementation in VLSI
Technology \\
An Area-Time Efficient NMOS Adder \\
Regular, Area-Time Efficient Carry-Lookahead Adders \\
Efficient Use of Time and Hardware Redundancy for
Concurrent Error Detection in a 32-bit VLSI Adder \\
Part IV: VLSI MULTIPLIER IMPLEMENTATIONS \\
Editor's Comments on Papers 19 Through 24 \\
A Monolithic $16 \times 16$ Digital Multiplier \\
Optimization of One-Bit Full Adders Embedded in Regular
Structures \\
A VLSI Layout for a Pipelined Dadda Multiplier \\
A Very Fast Multiplication Algorithm for VLSI
Implementation \\
A High-Speed Multiplier Using a Redundant Binary Adder
Tree \\
A Sub-10-ns $16 \times 16$ Multiplier Using 0.6-m CMOS
Technology \\
Part V: FLOATING-POINT VLSI CHIPS \\
Editor's Comments on Papers 25 Through 30 \\
A High Performance Floating Point Coprocessor \\
64 Bit Monolithic Floating Point Processors \\
A CMOS Floating Point Multiplier \\
A Single-Chip 80-Bit Floating Point Processor \\
VLSI Floating-Point Processors \\
Fast Multiply and Divide for a VLSI Floating-Point Unit
\\
Part VI: NUMBER REPRESENTATION \\
Editor's Comments on Papers 31 Through 37 \\
The Residue Number System \\
A Formalization of Floating-Point Numeric Base
Conversion \\
CADAC: A Controlled-Precision Decimal Arithmetic Unit
\\
Finite Precision Rational Arithmetic: Slash Number
Systems \\
Finite Precision Lexicographic Continued Fraction
Number Systems \\
An Overflow/Underflow-Free Floating-Point
Representation of Numbers \\
A Closed Computer Arithmetic \\
Part VII: IMPLEMENTATIONS \\
Editor's Comments on Papers 38 Through 40 \\
Applications of Distributed Arithmetic to Digital
Signal Processing: A Tutorial Review \\
Designing Low-Power Circuits: Practical Recipes \\
The European Logarithmic Microprocessor \\
Bibliography",
}
@Book{Swartzlander:2015:CAc,
editor = "Earl E. {Swartzlander, Jr.}",
booktitle = "Computer Arithmetic",
title = "Computer Arithmetic",
volume = "3",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xvii + 451",
year = "2015",
DOI = "https://doi.org/10.1142/9467",
ISBN = "981-4651-13-3 (hardcover), 981-4641-47-2 (e-book)",
ISBN-13 = "978-981-4651-13-4 (hardcover), 978-981-4641-47-0
(e-book)",
LCCN = "QA76.6 .C633 2015 vol. 3",
bibdate = "Tue Aug 7 07:57:49 MDT 2018",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "\booktitle{Computer Arithmetic}, Volume III, is a
compilation of key papers in computer arithmetic on
floating-point arithmetic and design. The intent is to
show progress, evolution, and novelty in the area of
floating-point arithmetic. This field has made
extraordinary progress since the initial software
routines on mainframe computers have evolved into
hardware implementations in processors spanning a wide
range of performance. Nevertheless, these papers pave
the way to the understanding of modern day processors
design where computer arithmetic are supported by
floating-point units. The goal of Volume III is to
collect the defining document for floating-point
arithmetic and many of the key papers on the
implementation of both binary and decimal
floating-point arithmetic into a single volume.
Although fewer than forty papers are included, their
reference lists will direct the interested reader to
other excellent work that could not be included here.
Volume III is specifically oriented to the needs of
designers and users of both general-purpose computers
and special-purpose digital processors. The book should
also be useful to systems engineers, computer
architects, and logic designers. It is also intended to
serve as a primary text for a course on floating-point
arithmetic, as well as a supplementary text for courses
in digital arithmetic and high-speed signal
processing.",
acknowledgement = ack-nhfb,
tableofcontents = "Part I. Overview \\
1. IEEE standard for floating-point arithmetic \\
Part II. Floating-point addition \\
2. Delay-optimized implementation of IEEE
floating-point addition / P. M. Seidel and G. Even \\
3. Using the reverse-carry approach for double datapath
floating-point addition / J. D. Bruguera and T. Lang
\\
4. Reduced latency IEEE floating-point standard adder
architectures / A. Beaumont-Smith [et al.] \\
5. Leading-zero anticipatory logic for high-speed
floating-point addition / H. Suzuki [et al.] \\
6. Leading zero anticipation and detection - A
comparison of methods / M. Schmookler and K. Nowka \\
7. S/370 sign-magnitude floating-point adder / S.
Vassiliadis, D. S. Lemon and M. Putrino \\
Part III. Floating-point multiplication \\
8. A quadruple precision and dual double precision
floating-point multiplier / A. Akkas and M. J. Schulte
\\
9. A dual mode IEEE multiplier / G. Even, S. M. Mueller
and P. M. Seidel \\
10. 167 MHz radix-4 floating-point multiplier / R. K.
Yu and G. B. Zyner \\
Part IV. Rounding \\
11. Rounding algorithms for IEEE multipliers / M. R.
Santoro, G. Bewick and M. A. Horowitz \\
12. ``Systematic IEEE rounding method for high-speed
floating-point multipliers / N. T. Quach, N. Takagi,
and M. J. Flynn \\
13. A comparison of three rounding algorithms for IEEE
floating-point multiplication / G. Even and P. M.
Seidel \\
14. Prenormalization rounding in IEEE floating-point
operations using a flagged prefix adder / N. Burgess
\\
Part V. Fused multiply add \\
15. Design of the IBM RISC system/6000 floating-point
execution unit / R. K. Montoye, E. Hokenek and S. L.
Runyon \\
16. A 17 x 69 bit multiply and add unit with redundant
binary feedback and single cycle latency / W. S. Briggs
and D. Matula \\
17. Comparison of single- and dual-pass multiply-add
fused floating-point units / R. Jessani and M. Putrino
\\
18. Floating-point fused multiply-add with reduced
latency / T. Lang and J. D. Bruguera \\
19. Floating-point fused multiply-add architectures /
E. Quinnell, E. E. Swartzlander, Jr. and C. Lemonds \\
Part VI. Floating-point division \\
20. Floating-point division and square root algorithms
and implementation in the AMD-K7 microprocessor / S. F.
Oberman \\
21. High performance floating-point unit with 116 bit
wide divider / G. Gerwig [et al.] \\
22. High-speed double-precision computation of
reciprocal, division, square root, and inverse square
root / J. A. Pineiro and J. D. Bruguera \\
23. 167 MHz radix-8 floating-point divide and square
root using overlapped radix-2 stages / J. Prabhu and G.
Zyner \\
24. Division algorithms and implementations / S. F.
Oberman and M. J. Flynn \\
25. Faithful interpolation in reciprocal tables / D.
Das Sarma and D. W. Matula \\
Part VII. Elementary functions \\
26. Computation of elementary functions on the IBM RISC
system/6000 processor / P. W. Markstein \\
27. Accurate and monotone approximations of some
transcendental functions / W. Ferguson and T. Brightman
\\
28. The K5 transcendental functions / T. Lynch [et al.]
\\
29. Hardware designs for exactly rounded elementary
functions / M. J. Schulte and E. E. Swartzlander, Jr.
\\
30. Toward correctly rounded transcendentals / V.
Lefevre, Jean-Michel Muller and A. Tisserand \\
31. Reciprocation, square root, inverse square root and
some elementary functions using small multipliers / M.
Ercegovac [et al.] \\
32. Multipartite table methods / F. Dinechin and A.
Tisserand \\
Part VIII. Decimal floating-point arithmetic \\
33. A decimal floating-point specification / M. F.
Cowlishaw [et al.] \\
34. Decimal floating-point: Algorism for computers / M.
F. Cowlishaw \\
35. A software implementation of the IEEE 754R decimal
floating-point arithmetic using the binary encoded
format / M. Cornea [et al.] \\
36. Decimal floating-point multiplication, / M. A.
Erle, B. J. Hickmann and M. J. Schulte \\
37. A survey of hardware designs for decimal arithmetic
/ L.-K. Wang [et al.]",
}
@Proceedings{Montuschi:2016:ISC,
editor = "Paolo Montuschi and Michael Schulte and Javier Hormigo
and Stuart Oberman and Nathalie Revol",
booktitle = "{2016 IEEE 23nd Symposium on Computer Arithmetic
(ARITH 2016), Santa Clara, California, USA, 10--13 July
2016}",
title = "{2016 IEEE 23nd Symposium on Computer Arithmetic
(ARITH 2016), Santa Clara, California, USA, 10--13 July
2016}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxi + 182",
year = "2016",
ISBN = "1-5090-1615-5",
ISBN-13 = "978-1-5090-1615-0",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2016",
bibdate = "Fri Dec 16 15:16:45 2016",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7562813",
acknowledgement = ack-nhfb,
keywords = "ARITH-23; computer arithmetic units; correctness
proofs; cryptography; domain specific designs; error
analysis; exascale computing; floating point
arithmetic; floating-point error analysis; formal
verification; function approximation; modular
arithmetic; theorem proving; verification",
}
@Proceedings{Burgess:2017:ISC,
editor = "Neil Burgess and Javier Bruguera and Florent de
Dinechin",
booktitle = "{24th IEEE Symposium on Computer Arithmetic (ARITH
24), London, UK, 24--26 July 2017}",
title = "{2017 IEEE 24th Symposium on Computer Arithmetic
(ARITH 24), London, UK, 24--26 July 2017}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xii + 198",
year = "2017",
ISBN = "1-5386-1966-0 (print), 1-5386-1965-2, 1-5386-1964-4",
ISBN-13 = "978-1-5386-1966-7 (print), 978-1-5386-1965-0,
978-1-5386-1964-3",
ISSN = "1063-6889",
LCCN = "QA76.9.C62 S95 2017",
bibdate = "Fri Nov 17 10:14:11 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8019911",
acknowledgement = ack-nhfb,
keywords = "ARITH-24; computer arithmetic units; correctness
proofs; cryptography; domain specific designs; error
analysis; exascale computing; floating point
arithmetic; floating-point error analysis; formal
verification; function approximation; modular
arithmetic; theorem proving; verification",
}
@Proceedings{Desprez:2017:EPP,
editor = "Fr{\'e}d{\'e}ric Desprez and Pierre-Fran{\c{c}}ois
Dutot and Christos Kaklamanis and Loris Marchal and
Korbinian Molitorisz and Laura Ricci and Vittorio
Scarano and Miguel A. Vega-Rodr{\'i}guez and Ana Lucia
Varbanescu and Sascha Hunold",
booktitle = "{Euro-Par 2016: Euro-Par 2016 International Workshops,
Grenoble, France, August 24--26, 2016, Revised Selected
Papers}",
title = "{Euro-Par 2016: Euro-Par 2016 International Workshops,
Grenoble, France, August 24--26, 2016, Revised Selected
Papers}",
volume = "10104",
publisher = "Springer",
address = "Cham, Switzerland",
pages = "xxxix + 829",
year = "2017",
DOI = "https://doi.org/10.1007/978-3-319-58943-5",
ISBN = "3-319-58943-1 (e-book), 3-319-58943-1 (hardcover)",
ISBN-13 = "978-3-319-58943-5 (e-book), 978-3-319-58943-5
(hardcover)",
LCCN = "QA76.9.E94; QA76.758TK",
bibdate = "Mon Feb 10 06:29:59 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
abstract = "This book constitutes the proceedings of the workshops
of the 23rd International Conference on Parallel and
Distributed Computing, Euro-Par 2016, held in Grenoble,
France in August 2016. The 65 full papers presented
were carefully reviewed and selected from 95
submissions. The volume includes the papers from the
following workshops: Euro-EDUPAR (Second European
Workshop on Parallel and Distributed Computing
Education for Undergraduate Students); HeteroPar 2016
(the 14th International Workshop on Algorithms, Models
and Tools for Parallel Computing on Heterogeneous
Platforms); IWMSE (5th International Workshop on
Multicore Software Engineering); LSDVE (Fourth Workshop
on Large-Scale Distributed Virtual Environments) -
PADABS (Fourth Workshop on Parallel and Distributed
Agent-Based Simulations); PBio (Fourth International
Workshop on Parallelism in Bioinformatics); PELGA
(Second Workshop on Performance Engineering for
Large-Scale Graph Analytics); REPPAR (Third
International Workshop on Reproducibility in Parallel
Computing); Resilience (9th Workshop in Resilience in
High Performance Computing in Clusters, Clouds, and
Grids); ROME (Fourth Workshop on Runtime and Operating
Systems for the Many-Core Era); UCHPC (9th Workshop on
UnConventional High-Performance Computing).",
acknowledgement = ack-nhfb,
meetingname = "Euro-Par (2016 : Grenoble)",
tableofcontents = "Parallel and distributed computing education for
undergraduate students.\\
Algorithms, models and tools for parallel computing on
heterogeneous platforms \\
Multicore software engineering \\
Large-scale distributed virtual environments \\
Parallel and distributed agent-based simulations \\
Parallelism in bioinformatics \\
Performance engineering for large-scale graph analytics
\\
Reproducibility in parallel computing \\
Resilience in high performance computing in clusters,
clouds, and grids \\
Runtime and operating systems for the many-core era \\
UnConventional high-performance computing",
}
@Proceedings{Matthews:2017:CRF,
editor = "Michael B. Matthews",
booktitle = "{Conference record of the Fifty-First Asilomar
Conference on Signals, Systems and Computers, October
29--November 1, 2017 Pacific Grove, California}",
title = "{Conference record of the Fifty-First Asilomar
Conference on Signals, Systems and Computers, October
29--November 1, 2017 Pacific Grove, California}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xxx + 2058",
year = "2017",
ISBN = "1-5386-1824-9 (print), 1-5386-0666-6, 1-5386-1823-0
(e-book)",
ISBN-13 = "978-1-5386-1824-0 (print), 978-1-5386-0666-7,
978-1-5386-1823-3 (e-book)",
LCCN = "TK7801",
bibdate = "Mon Feb 10 08:40:43 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=8330843",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2018:CNG,
editor = "{ACM}",
booktitle = "Conference for Next Generation Arithmetic ({Resorts
World Convention Centre, Singapore}): ({CoNGA '18})",
title = "Conference for Next Generation Arithmetic ({Resorts
World Convention Centre, Singapore}): ({CoNGA '18})",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "37",
year = "2018",
bibdate = "Sun Dec 10 14:24:09 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
remark = "No ISBN seems to have been assigned.",
tableofcontents = "1: A Matrix-Multiply Unit for Posits in
Reconfigurable Logic Using (OPEN)CAPI / Jianyu Chen,
Zaid Al-Ars \\
2: Provably Correct Posit Arithmetic with Fixed-Point
Big Integer / Shin Yee Chung \\
3: The Slide Number Format / Ignaz Kohlbecker \\
4: High-level .NET Software Implementations of Unum
Type I and Posit with Simultaneous FPGA Implementation
Using Hastlayer / Zolt{\'a}n Leh{\'o}czky, Andr{\'a}s
Retzler, Rich{\'a}rd T{\'o}th, {\'A}lmos Szab{\'o},
Benedek Farkas and Kriszti{\'a}n Somogyi \\
5: Universal Coding of the Reals: Alternatives to IEEE
Floating Point / Peter Lindstrom, Scott Lloyd and
Jeffrey Hittinger",
}
@Proceedings{Tenca:2018:PIS,
editor = "Alexandre Tenca and Naofumi Takagi",
booktitle = "Proceedings of the {25th International Symposium on
Computer Arithmetic, 25--27 June 2018 Amherst, MA,
USA}",
title = "Proceedings of the {25th International Symposium on
Computer Arithmetic, 25--27 June 2018 Amherst, MA,
USA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "17 + 152",
month = jun,
year = "2018",
DOI = "https://doi.org/10.1109/ARITH.2018.8464697",
ISBN = "1-5386-2612-8 (USB), 1-5386-2665-9",
ISBN-13 = "978-1-5386-2612-2 (USB), 978-1-5386-2613-9,
978-1-5386-2665-8",
ISSN = "2576-2265",
LCCN = "QA76.9.C62",
bibdate = "Fri Jan 31 08:05:31 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "IEEE catalog number CFP18121-USB.",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
subject = "ARITH-25; Computer arithmetic; Congresses; Computer
programming; Floating-point arithmetic; Computer
arithmetic and logic units",
}
@Proceedings{Gustafson:2019:CPC,
editor = "John Gustafson and Vassil Dimitrov",
booktitle = "{CoNGA'19: Proceedings of the Conference for Next
Generation Arithmetic 2019, Singapore, March 2019}",
title = "{CoNGA'19: Proceedings of the Conference for Next
Generation Arithmetic 2019, Singapore, March 2019}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "66",
year = "2019",
ISBN = "1-4503-7139-6",
ISBN-13 = "978-1-4503-7139-1",
LCCN = "????",
bibdate = "Mon Feb 10 12:06:51 MST 2020",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "ICPS",
acknowledgement = ack-nhfb,
meetingname = "Conference for Next Generation Arithmetic (2019 :
Singapore)",
subject = "Computer arithmetic; Congresses; Computer algorithms;
Computer algorithms.; Computer arithmetic.",
tableofcontents = "Milan Kl{\"o}wer and Peter D. D{\"u}ben and Tim N.
Palmer / Posits as an Alternative to Floats for Weather
and Climate Models /
https://doi.org/10.1145/3316279.3316281 / 1:1--1:8 \\
Andrea Bocco and Yves Durand and Florent de Dinechin /
SMURF: Scalar Multiple-precision Unum RISC-V
Floating-point Accelerator for Scientific Computing /
https://doi.org/10.1145/3316279.3316280 / 1:1--1:8 \\
Zachariah Carmichael and Hamed F. Langroudi and Char
Khazanov and Jeffrey Lillie and John L. Gustafson and
Dhireesha Kudithipudi / Performance-Efficiency
Trade-off of Low-Precision Numerical Formats in Deep
Neural Networks /
https://doi.org/10.1145/3316279.3316282 / 3:1--3:9 \\
Bill Zorn and Dan Grossman and Zach Tatlock / Sinking
Point: Dynamic Precision Tracking for Floating-Point /
https://doi.org/10.1145/3316279.3316283 / 4:1--4:8 \\
Laurens van Dam and Johan Peltenburg and Zaid Al-Ars
and H. Peter Hofstee / An Accelerator for Posit
Arithmetic Targeting Posit Level 1 BLAS Routines and
Pair-HMM / https://doi.org/10.1145/3316279.3316284 /
5:1--5:10 \\
Florent de Dinechin and Luc Forget and Jean-Michel
Muller and Yohann Uguen / Posits: The Good, the Bad and
the Ugly / https://doi.org/10.1145/3316279.3316285 /
6:1--6:10 \\
Peter Lindstrom / Universal Coding of the Reals Using
Bisection / https://doi.org/10.1145/3316279.3316286 /
7:1--7:10",
}
@Proceedings{Takagi:2019:ISC,
editor = "Naofumi Takagi and Sylvie Boldo and Martin
Langhammer",
booktitle = "{2019 IEEE 26th Symposium on Computer Arithmetic
ARITH-26 (2019), Kyoto, Japan, 10--12 June 2019}",
title = "{2019 IEEE 26th Symposium on Computer Arithmetic
ARITH-26 (2019), Kyoto, Japan, 10--12 June 2019}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "15 + 220",
month = jun,
year = "2019",
DOI = "https://doi.org/10.1109/ARITH.2019.00001",
ISBN = "1-72813-366-1",
ISBN-13 = "978-1-72813-366-9",
ISSN = "1063-6889",
ISSN-L = "1063-6889",
bibdate = "Fri Jan 31 08:18:07 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
abstract = "Presents the title page of the proceedings record.",
acknowledgement = ack-nhfb,
keywords = "ARITH-26",
}
@Proceedings{Cornea:2020:ISC,
editor = "Marius Cornea and Weiqiang Liu and Arnaud Tisserand",
booktitle = "{2020 27th IEEE Symposium on Computer Arithmetic:
ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
June 2020}",
title = "{2020 27th IEEE Symposium on Computer Arithmetic:
ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
June 2020}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
year = "2020",
DOI = "https://doi.org/10.1109/ARITH48897.2020",
ISBN = "1-72817-120-2, 1-72817-121-0",
ISBN-13 = "978-1-72817-120-3, 978-1-72817-121-0",
LCCN = "????",
bibdate = "Wed Jul 7 06:23:45 MDT 2021",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://ieeexplore.ieee.org/servlet/opac?punumber=9146973",
acknowledgement = ack-nhfb,
keywords = "ARITH-27",
}
@Proceedings{IEEE:2020:SPI,
editor = "{IEEE}",
booktitle = "{SC'20: Proceedings of the International Conference
for High Performance Computing, Networking, Storage and
Analysis (Atlanta, Georgia, November 9--19, 2020)}",
title = "{SC'20: Proceedings of the International Conference
for High Performance Computing, Networking, Storage and
Analysis (Atlanta, Georgia, November 9--19, 2020)}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2020",
DOI = "https://doi.org/10.1109/SC41405.2020",
ISBN = "1-72819-998-0, 1-72819-999-9 (printondemand)",
ISBN-13 = "978-1-72819-998-6, 978-1-72819-999-3 (printondemand)",
LCCN = "QA76.88",
bibdate = "Mon Sep 11 06:40:11 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/python.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Krzhizhanovskaya:2020:CSI,
editor = "Valeria V. Krzhizhanovskaya and G{\'a}bor
Z{\'a}vodszky and Michael H. Lees and Jack J. Dongarra
and Peter M. A. Sloot and S{\'e}rgio Brissos and
Jo{\~a}o Teixeira",
booktitle = "{Computational Science --- ICCS 2020 20th
International Conference, Amsterdam, The Netherlands,
June 3--5, 2020, Proceedings, Part II}",
title = "{Computational Science --- ICCS 2020 20th
International Conference, Amsterdam, The Netherlands,
June 3--5, 2020, Proceedings, Part II}",
volume = "12138",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xix + 697",
year = "2020",
DOI = "https://doi.org/10.1007/978-3-030-50417-5",
ISBN = "3-030-50416-6, 3-030-50417-4 (e-book)",
ISBN-13 = "978-3-030-50416-8, 978-3-030-50417-5 (e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
bibdate = "Thu Jun 25 08:21:10 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/julia.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/prng.bib",
series = ser-LNCS,
URL = "https://link.springer.com/book/10.1007/978-3-030-50417-5",
acknowledgement = ack-nhfb,
tableofcontents = "Front Matter / / i--xix \\
Modified Binary Tree in the Fast PIES for 2D Problems
with Complex Shapes / Andrzej Ku{\.z}elewski, Eugeniusz
Zieniuk, Agnieszka Bo{\l}tu{\'c}, Krzystof Szersze{\'n}
/ 1--14 \\
Generating Random Floating--Point Numbers by Dividing
Integers: A Case Study / Fr{\'e}d{\'e}ric Goualard /
15--28 \\
An Effective Stable Numerical Method for Integrating
Highly Oscillating Functions with a Linear Phase /
Leonid A. Sevastianov, Konstantin P. Lovetskiy, Dmitry
S. Kulyabov / 29--43 \\
Fitting Penalized Logistic Regression Models Using QR
Factorization / Jacek Klimaszewski, Marcin Korze{\'n} /
44--57 \\
Uncertainty Quantification in Fractional Stochastic
Integro--Differential Equations Using Legendre Wavelet
Collocation Method / Abhishek Kumar Singh, Mani Mehra /
58--71 \\
A Direct High--Order Curvilinear Triangular Mesh
Generation Method Using an Advancing Front Technique /
Fariba Mohammadi, Shusil Dangi, Suzanne M. Shontz,
Cristian A. Linte / 72--85 \\
Data--Driven Partial Differential Equations Discovery
Approach for the Noised Multi--dimensional Data /
Mikhail Maslyaev, Alexander Hvatov, Anna Kalyuzhnaya /
86--100 \\
Preconditioning Jacobian Systems by Superimposing
Diagonal Blocks / M. Ali Rostami, H. Martin B{\"u}cker
/ 101--115 \\
NURBS Curves in Parametric Integral Equations System
for Modeling and Solving Boundary Value Problems in
Elasticity / Marta Kapturczak, Eugeniusz Zieniuk,
Andrzej Ku{\.z}elewski / 116--123 \\
Parameterizations and Lagrange Cubics for Fitting
Multidimensional Data / Ryszard Kozera, Lyle Noakes,
Magdalena Wilko{\l}azka / 124--140 \\
Loop Aggregation for Approximate Scientific Computing /
June Sallou, Alexandre Gauvain, Johann Bourcier, Benoit
Combemale, Jean--Raynald de Dreuzy / 141--155 \\
Numerical Computation for a Flow Caused by a
High--Speed Traveling Train and a Stationary Overpass /
Shotaro Hamato, Masashi Yamakawa, Yongmann M. Chung,
Shinichi Asao / 156--169 \\
B{\'e}zier Surfaces for Modeling Inclusions in PIES /
Agnieszka Bo{\l}tu{\'c}, Eugeniusz Zieniuk, Krzysztof
Szersze{\'n}, Andrzej Ku{\.z}elewski / 170--183 \\
Impact of Water on Methane Adsorption in Nanopores: A
Hybrid GCMC--MD Simulation Study / Ji Zhou, Wenbin
Jiang, Mian Lin, Lili Ji, Gaohui Cao / 184--196 \\
A Stable Discontinuous Galerkin Based Isogeometric
Residual Minimization for the Stokes Problem / Marcin
{\L}o{\'s}, Sergio Rojas, Maciej Paszy{\'n}ski, Ignacio
Muga, Victor M. Calo / 197--211 \\
Numerical Modeling of the Two--Phase Flow of Water with
Ice in the Tom River / Vladislava Churuksaeva,
Alexander Starchenko / 212--224 \\
Remarks on Kaczmarz Algorithm for Solving Consistent
and Inconsistent System of Linear Equations / Xinyin
Huang, Gang Liu, Qiang Niu / 225--236 \\
Investigating the Benefit of FP16--Enabled
Mixed--Precision Solvers for Symmetric Positive
Definite Matrices Using GPUs / Ahmad Abdelfattah, Stan
Tomov, Jack Dongarra / 237--250 \\
Simulation Versus an Ordered Fuzzy--Numbers--Driven
Approach to the Multi--depot Vehicle Cyclic Routing and
Scheduling Problem / Grzegorz Bocewicz, Zbigniew
Banaszak, Czeslaw Smutnicki, Katarzyna Rudnik, Marcin
Witczak, Robert W{\'o}jcik / 251--266 \\
Epigenetic Modification of Genetic Algorithm / Kornel
Chrominski, Magdalena Tkacz, Mariusz Boryczka /
267--278 \\
ITP--KNN: Encrypted Video Flow Identification Based on
the Intermittent Traffic Pattern of Video and
$K$-Nearest Neighbors Classification / Youting Liu, Shu
Li, Chengwei Zhang, Chao Zheng, Yong Sun, Qingyun Liu /
279--293 \\
DeepAD: A Joint Embedding Approach for Anomaly
Detection on Attributed Networks / Dali Zhu, Yuchen Ma,
Yinlong Liu / 294--307 \\
SciNER: Extracting Named Entities from Scientific
Literature / Zhi Hong, Roselyne Tchoua, Kyle Chard, Ian
Foster / 308--321 \\
GPU--Embedding of kNN--Graph Representing Large and
High--Dimensional Data / Bartosz Minch, Mateusz Nowak,
Rafa{\l} Wcis{\l}o, Witold Dzwinel / 322--336 \\
Evolving Long Short--Term Memory Networks / Vicente
Coelho Lobo Neto, Leandro Aparecido Passos, Jo{\~a}o
Paulo Papa / 337--350 \\
Personality Recognition from Source Code Based on
Lexical, Syntactic and Semantic Features / Miko{\l}aj
Biel, Marcin Kuta, Jacek Kitowski / 351--363 \\
Data Fitting by Exponential Sums with Equal Weights /
Petr Chunaev, Ildar Safiullin / 364--371 \\
A Combination of Moment Descriptors, Fourier Transform
and Matching Measures for Action Recognition Based on
Shape / Katarzyna Go{\'s}ciewska, Dariusz Frejlichowski
/ 372--386 \\
Improving Accuracy and Speeding Up Document Image
Classification Through Parallel Systems / Javier
Ferrando, Juan Luis Dom{\'\i}nguez, Jordi Torres,
Ra{\'u}l Garc{\'\i}a, David Garc{\'\i}a, Daniel Garrido
et al. / 387--400 \\
Computation of the Airborne Contaminant Transport in
Urban Area by the Artificial Neural Network / Anna
Wawrzynczak, Monika Berendt--Marchel / 401--413 \\
Exploring Musical Structure Using Tonnetz Lattice
Geometry and LSTMs / Manuchehr Aminian, Eric Kehoe,
Xiaofeng Ma, Amy Peterson, Michael Kirby / 414--424 \\
Modeling of Anti--tracking Network Based on
Convex--Polytope Topology / Changbo Tian, Yongzheng
Zhang, Tao Yin / 425--438 \\
A Workload Division Differential Privacy Algorithm to
Improve the Accuracy for Linear Computations / Jun Li,
Huan Ma, Guangjun Wu, Yanqin Zhang, Bingnan Ma, Zhen
Hui et al. / 439--452 \\
On the Automated Assessment of Open--Source Cyber
Threat Intelligence Sources / Andrea Tundis, Samuel
Ruppert, Max M{\"u}hlh{\"a}user / 453--467 \\
Malicious Domain Detection Based on K--means and SMOTE
/ Qing Wang, Linyu Li, Bo Jiang, Zhigang Lu, Junrong
Liu, Shijie Jian / 468--481 \\
Microservice Disaster Crash Recovery: A Weak Global
Referential Integrity Management / Maude Manouvrier,
Cesare Pautasso, Marta Rukoz / 482--495 \\
Hashing Based Prediction for Large--Scale Kernel
Machine / Lijing Lu, Rong Yin, Yong Liu, Weiping Wang /
496--509 \\
Picking Peaches or Squeezing Lemons: Selecting
Crowdsourcing Workers for Reducing Cost of Redundancy /
Paulina Adamska, Marta Ju{\'z}win, Adam Wierzbicki /
510--523 \\
Are $n$-gram Categories Helpful in Text Classification?
/ Jakub Kruczek, Paulina Kruczek, Marcin Kuta /
524--537 \\
Calculating Reactive Power Compensation for
Large--Scale Street Lighting / Sebastian Ernst, Leszek
Kotulski, Tomasz Lerch, Micha{\l} Rad, Adam
S{\k{e}}dziwy, Igor Wojnicki / 538--550 \\
Developing a Decision Support App for Computational
Agriculture / Andrew Lewis, Marcus Randall, Ben
Stewart--Koster / 551--561 \\
Optimal Location of Sensors for Early Detection of
Tsunami Waves / Angelie R. Ferrolino, Jose Ernie C.
Lope, Renier G. Mendoza / 562--575 \\
A Novel Formulation for Inverse Distance Weighting from
Weighted Linear Regression / Leonardo Ramos
Emmendorfer, Gra{\c{c}}aliz Pereira Dimuro / 576--589
\\
Addressing the Robustness of Resource Allocation in the
Presence of Application and System Irregularities via
PEPA Based Modeling / Srishti Srivastava, Ioana
Banicescu, William S. Sanders / 590--603 \\
An Adaptive Computational Network Model for Strange
Loops in Political Evolution in Society / Julia Anten,
Jordan Earle, Jan Treur / 604--617 \\
Joint Entity Linking for Web Tables with Hybrid
Semantic Matching / Jie Xie, Yuhai Lu, Cong Cao,
Zhenzhen Li, Yangyang Guan, Yanbing Liu / 618--631 \\
A New Coefficient of Rankings Similarity in
Decision--Making Problems / Wojciech Sa abun, Karol
Urbaniak / 632--645 \\
Innovativeness Analysis of Scholarly Publications by
Age Prediction Using Ordinal Regression / Pavel Savov,
Adam Jatowt, Radoslaw Nielek / 646--660 \\
Advantage of Using Spherical over Cartesian Coordinates
in the Chromosome Territories 3D Modeling / Magdalena
A. Tkacz, Kornel Chromi{\'n}ski / 661--673 \\
Adaptive and Efficient Transfer for Online Remote
Visualization of Critical Weather Applications / Preeti
Malakar, Vijay Natarajan, Sathish S. Vadhiyar /
674--693 \\
Back Matter / / 695--697",
}
@Proceedings{Wyrzykowski:2020:PPA,
editor = "Roman Wyrzykowski and Ewa Deelman and Jack Dongarra
and Konrad Karczewski",
booktitle = "Parallel Processing and Applied Mathematics: {13th
International Conference, PPAM 2019, Bialystok, Poland,
September 8--11, 2019, Revised Selected Papers, Part
I}",
title = "Parallel Processing and Applied Mathematics: {13th
International Conference, PPAM 2019, Bialystok, Poland,
September 8--11, 2019, Revised Selected Papers, Part
I}",
publisher = pub-SV,
address = pub-SV:adr,
year = "2020",
DOI = "https://doi.org/10.1007/978-3-030-43229-4",
ISBN = "3-030-43229-7",
ISBN-13 = "978-3-030-43229-4",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
tableofcontents = "Front Matter / i--xxiii \\
Numerical Algorithms and Parallel Scientific Computing
== Front Matter / 1--1 \\
Matthias Korch, Tim Werner / Multi-workgroup Tiling to
Improve the Locality of Explicit One-Step Methods for
ODE Systems with Limited Access Distance on GPUs /
3--12 \\
Davor Davidovi{\'c}, Enrique S. Quintana-Ort{\'\i} /
Structure-Aware Calculation of Many-Electron Wave
Function Overlaps on Multicore Processors / 13--24 \\
Charles D. Murray, Tobias Weinzierl / Lazy Stencil
Integration in Multigrid Algorithms / 25--37 \\
Filip Paw{\l}owski, Bora U{\c{c}}ar, Albert-Jan Yzelman
/ High Performance Tensor Vector Multiplication on
Shared-Memory Systems / 38--48 \\
Pawe{\l} Augustynowicz, Andrzej Paszkiewicz / Efficient
Modular Squaring in Binary Fields on CPU Supporting AVX
and GPU / 49--57 \\
Carl Christian Kjelgaard Mikkelsen, Mirko Myllykoski /
Parallel Robust Computation of Generalized Eigenvectors
of Matrix Pencils / 58--69 \\
Mirko Myllykoski, Carl Christian Kjelgaard Mikkelsen /
Introduction to StarNEig A Task-Based Library for
Solving Nonsymmetric Eigenvalue Problems / 70--81 \\
Angelika Schwarz, Carl Christian Kjelgaard Mikkelsen /
Robust Task-Parallel Solution of the Triangular
Sylvester Equation / 82--92 \\
Beata Dmitruk, Przemys{\l}aw Stpiczy{\'n}ski /
Vectorized Parallel Solver for Tridiagonal Toeplitz
Systems of Linear Equations / 93--103 \\
Carola Kruse, Masha Sosonkina, Mario Arioli, Nicolas
Tardieu, Ulrich R{\"u}de / Parallel Performance of an
Iterative Solver Based on the Golub-Kahan
Bidiagonalization / 104--116 \\
Linus Seelinger, Anne Reinarz, Robert Scheichl / A
High-Performance Implementation of a Robust
Preconditioner for Heterogeneous Problems / 117--128
\\
Viviana Arrigoni, Annalisa Massini / Hybrid Solver for
Quasi Block Diagonal Linear Systems / 129--140 \\
Michal Krav{\v{c}}enko, Jan Zapletal, Xavier Claeys,
Michal Merta / Parallel Adaptive Cross Approximation
for the Multi-trace Formulation of Scattering Problems
/ 141--150 \\
Daisuke Takahashi / Implementation of Parallel 3-D Real
FFT with 2-D Decomposition on Intel Xeon Phi Clusters /
151--161 \\
Doru Thom Popovici, Devangi N. Parikh, Daniele G.
Spampinato, Tze Meng Low / Exploiting Symmetries of
Small Prime-Sized DFTs / 162--173 \\
Victor Gergel, Evgeny Kozinov / Parallel Computations
for Various Scalarization Schemes in Multicriteria
Optimization Problems / 174--184 \\
Emerging HPC Architectures \\
Front Matter / 185--185 \\
Enrico Calore, Alessandro Gabbana, Fabio Rinaldi,
Sebastiano Fabio Schifano, Raffaele Tripiccione / Early
Performance Assessment of the ThunderX2 Processor for
Lattice Based Simulations / 187--198 \\
Emerging HPC Architectures \\
Mate Cobrnic, Alen Duspara, Leon Dragic, Igor Piljic,
Hrvoje Mlinaric, Mario Kovac / An Area Efficient and
Reusable HEVC 1D-DCT Hardware Accelerator / 199--208
\\
Performance Analysis and Scheduling in HPC Systems \\
Front Matter / 209--209 \\
M. Yusuf {\"O}zkaya, Anne Benoit, {\"U}mit V.
{\c{C}}ataly{\"u}rek / Improving Locality-Aware
Scheduling with Acyclic Directed Graph Partitioning /
211--223 \\
Maciej Drozdowski, Gaurav Singh, J{\k{e}}drzej M.
Marsza{\l}kowski / Isoefficiency Maps for Divisible
Computations in Hierarchical Memory Systems / 224--234
\\
Environments and Frameworks for
Parallel/Distributed/Cloud Computing \\
Front Matter / 235--235 \\
Tim Cramer, Manoel R{\"o}mmer, Boris Kosmynin, Erich
Focht, Matthias S. M{\"u}ller / OpenMP Target Device
Offloading for the SX-Aurora TSUBASA Vector Engine /
237--249 \\
Camille Coti, Allen D. Malony / On the Road to DiPOSH:
Adventures in High-Performance OpenSHMEM / 250--260 \\
Roman Wiatr, Vladyslav Lyutenko, Mi{\l}osz Demczuk,
Renata S{\l}ota, Jacek Kitowski / Click-Fraud Detection
for Online Advertising / 261--271 \\
Adam Smyk, Marek Tudruj, Lukasz Grochal / Parallel
Graph Partitioning Optimization Under PEGASUS DA
Application Global State Monitoring / 272--286 \\
Bartosz Balis, Michal Orzechowski, Krystian Pawlik,
Maciej Pawlik, Maciej Malawski / Cloud Infrastructure
Automation for Scientific Workflows / 287--297 \\
Applications of Parallel Computing \\
Front Matter / 299--299 \\
Steven W. D. Chien, Ivy B. Peng, Stefano Markidis /
Posit NPB: Assessing the Precision Improvement in HPC
Scientific Applications / 301--310 \\
Lukas Krenz, Leonhard Rannabauer, Michael Bader / A
High-Order Discontinuous Galerkin Solver with Dynamic
Adaptive Mesh Refinement to Simulate Cloud Formation
Processes / 311--323 \\
Evgeny Kuznetsov, Nikolay Kondratyuk, Mikhail Logunov,
Vsevolod Nikolskiy, Vladimir Stegailov / Performance
and Portability of State-of-Art Molecular Dynamics
Software on Modern GPUs / 324--334 \\
Iosif Meyerov, Alexander Panov, Sergei Bastrakov,
Aleksei Bashinov, Evgeny Efimenko, Elena Panova, Igor
Surmin, Valentin Volokitin, and Arkady Gonoskov /
Exploiting Parallelism on Shared Memory in the QED
Particle-in-Cell Code PICADOR with Greedy Load
Balancing / 335--347 \\
Michael Quell, Paul Manstetten, Andreas H{\"o}ssinger,
Siegfried Selberherr, Josef Weinbub / Parallelized
Construction of Extension Velocities for the Level-Set
Method / 348--358 \\
Marcin Czajkowski, Krzysztof Jurczuk, Marek Kretowski /
Relative Expression Classification Tree. A Preliminary
GPU-Based Implementation / 359--369 \\
Kamil Halbiniak, Lukasz Szustak, Adam Kulawik, Pawel
Gepner / Performance Optimizations for Parallel
Modeling of Solidification with Dynamic Intensity of
Computation / 370--381 \\
Parallel Non-numerical Algorithms \\
Front Matter / 383--383 \\
Joel Fuentes, Wei-yu Chen, Guei-yuan Lueh, Arturo
Garza, Isaac D. Scherson / SIMD-node Transformations
for Non-blocking Data Structures / 385--395 \\
Parallel Non-numerical Algorithms \\
Hironobu Kobayashi, Yasuaki Ito, Koji Nakano / Stained
Glass Image Generation Using Voronoi Diagram and Its
GPU Acceleration / 396--407 \\
Anna Sasak-Oko{\'n} / Modifying Queries Strategy for
Graph-Based Speculative Query Execution for RDBMS /
408--418 \\
Soft Computing with Applications \\
Front Matter / 419--419 \\
Krzysztof Jurczuk, Marcin Czajkowski, Marek Kretowski /
Accelerating GPU-based Evolutionary Induction of
Decision Trees --- Fitness Evaluation Reuse / 421--431
\\
Hatem Khalloof, Phil Ostheimer, Wilfried Jakob, Shadi
Shahoud, Clemens Duepmeier, Veit Hagenmeyer / A
Distributed Modular Scalable and Generic Framework for
Parallelizing Population-Based Metaheuristics /
432--444 \\
Danuta Rutkowska, Krzysztof Wiaderek / Parallel
Processing of Images Represented by Linguistic
Description in Databases / 445--456 \\
Wojciech Kwedlo, Micha{\l} {\L}ubowicz / An OpenMP
Parallelization of the K-means Algorithm Accelerated
Using KD-trees / 457--466 \\
W{\l}odzimierz Funika, Pawe{\l} Koperek / Evaluating
the Use of Policy Gradient Optimization Approach for
Automatic Cloud Resource Provisioning / 467--478 \\
{\L}ukasz Karbowiak / Improving Efficiency of Automatic
Labeling by Image Transformations on CPU and GPU /
479--490 \\
Special Session on GPU Computing \\
Front Matter / 1--1 \\
Takahiro Inoue, Hiroki Tokura, Koji Nakano, Yasuaki Ito
/ Efficient Triangular Matrix Vector Multiplication on
the GPU / 493--504 \\
Dominik Ernst, Georg Hager, Jonas Thies, Gerhard
Wellein / Performance Engineering for a Tall & Skinny
Matrix Multiplication Kernels on GPUs / 505--515 \\
Daichi Mukunoki, Takeshi Ogita, Katsuhisa Ozaki /
Reproducible BLAS Routines with Tunable Accuracy Using
Ozaki Scheme for Many-Core Architectures / 516--527 \\
Tao Chang, Emeric Brun, Christophe Calvin / Portable
Monte Carlo Transport Performance Evaluation in the
PATMOS Prototype / 528--539 \\
Special Session on Parallel Matrix Factorizations \\
Front Matter / 541--541 \\
Piyush Sao, Ramakrishnan Kannan / Multifrontal
Non-negative Matrix Factorization / 543--554 \\
Martin Be{\v{c}}ka, Gabriel Ok{\v{s}}a /Preconditioned
Jacobi SVD Algorithm Outperforms PDGESVD / 555--566 \\
Marek Parfieniuk / A Parallel Factorization for
Generating Orthogonal Matrices / 567--578 \\
Back Matter / 579--581",
}
@Proceedings{IEEE:2021:ISC,
editor = "{IEEE}",
booktitle = "{2021 IEEE 28th Symposium on Computer Arithmetic:
ARITH 2021: virtual conference, 14--16 June 2021:
proceedings}",
title = "{2021 IEEE 28th Symposium on Computer Arithmetic:
ARITH 2021: virtual conference, 14--16 June 2021:
proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2021",
DOI = "https://doi.org/10.1109/ARITH51176.2021",
ISBN = "1-66542-293-9 (print), 1-66544-648-X (e-book)",
ISBN-13 = "978-1-66542-293-2 (print), 978-1-66544-648-8
(e-book)",
LCCN = "????",
bibdate = "Thu Sep 21 10:36:52 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-28",
meetingname = "IEEE International Symposium on Computer Arithmetic
28. 2021",
remark = "The 28th IEEE Symposium on Computer Arithmetic ---
ARITH 2021 --- originally scheduled in Turin, Italy, is
held in June 2021 as a virtual conference due to the
uncertainty of the world health and travel situation.",
}
@Proceedings{Gustafson:2022:NGA,
author = "John Gustafson and Vassil Dimitrov",
booktitle = "Next Generation Arithmetic: {Third International
Conference, CoNGA 2022, Singapore, March 1--3, 2022,
Revised Selected Papers}",
title = "Next Generation Arithmetic: {Third International
Conference, CoNGA 2022, Singapore, March 1--3, 2022,
Revised Selected Papers}",
volume = "13253",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "vii + 135",
pages = "vii + 135",
year = "2022",
DOI = "https://doi.org/10.1007/978-3-031-09779-9",
ISBN = "3-031-09778-5, 3-031-09779-3 (e-book)",
ISBN-13 = "978-3-031-09778-2, 978-3-031-09779-9 (e-book)",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
LCCN = "QA76.9.C62",
bibdate = "Fri Dec 15 07:04:06 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
tableofcontents = "Moritz B{\"a}rthel, Nils H{\"u}lsmeier, Jochen
Rust, and Steffen Paul / On the Implementation of Edge
Detection Algorithms with SORN Arithmetic / 1 \\
Or{\'e}gane Desrentes, Diana Resmerita, and Beno{\^\i}t
Dupont de Dinechin / A Posit8 Decompression Operator
for Deep Neural Network Inference / 14 \\
Nhut-Minh Ho, Himeshi De Silva, John L. Gustafson, and
Weng-Fai Wong / Qtorch+: Next Generation Arithmetic for
Pytorch Machine Learning / 31 \\
Hamed F. Langroudi, Vedant Karia, Tej Pandit, Becky
Mashaido, and Dhireesha Kudithipudi / ACTION: Automated
Hardware-Software Codesign Framework for Low-precision
Numerical Format SelecTION in TinyML / 50 \\
Peter Lindstrom / MultiPosits: Universal Coding of
$\mathbb{R}^n$ / 66 \\
Raul Murillo, David Mallas{\'e}n, Alberto A. Del
Barrio, and Guillermo Botella / Comparing Different
Decodings for Posit Arithmetic / 84 \\
E. Theodore L. Omtzigt and James Quinlan / Universal:
Reliable, Reproducible, and Energy-Efficient Numerics /
100 \\
Marco Cococcioni, Federico Rossi, Emanuele Ruffaldi,
and Sergio Saponara / Small Reals Representations for
Deep Learning at the Edge: A Comparison / 117 \\
Author Index / 135",
}
@Proceedings{IEEE:2022:ISC,
editor = "{IEEE}",
booktitle = "{2022 IEEE 29th Symposium on Computer Arithmetic:
ARITH 2022: virtual conference, 12--14 September 2022:
proceedings}",
title = "{2022 IEEE 29th Symposium on Computer Arithmetic:
ARITH 2022: virtual conference, 12--14 September 2022:
proceedings}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "????",
year = "2022",
DOI = "https://doi.org/10.1109/ARITH54963.2022",
ISBN = "1-66547-827-6, 1-66547-828-4",
ISBN-13 = "978-1-66547-827-4, 978-1-66547-828-1",
LCCN = "????",
bibdate = "Thu Sep 21 10:14:25 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-29",
meetingname = "IEEE Symposium on Computer Arithmetic 29. 2022",
}
@Proceedings{Gustafson:2023:NGA,
editor = "John Gustafson and Siew Hoon Leong and Marek
Michalewicz",
booktitle = "Next Generation Arithmetic: {4th International
Conference, CoNGA 2023, Singapore, March 1--2, 2023,
Proceedings}",
title = "Next Generation Arithmetic: {4th International
Conference, CoNGA 2023, Singapore, March 1--2, 2023,
Proceedings}",
publisher = pub-SV,
address = pub-SV:adr,
year = "2023",
DOI = "https://doi.org/10.1007/978-3-031-32180-1",
ISBN = "3-031-32180-4",
ISBN-13 = "978-3-031-32180-1",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Dec 15 11:31:31 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "posit arithmetic",
tableofcontents = "Front Matter / i--x \\
Siew Hoon Leong, John L. Gustafson / Lossless FFTs
Using Posit Arithmetic / 1--18 \\
Nhut-Minh Ho, Duy-Thanh Nguyen, John L. Gustafson,
Weng-Fai Wong / Bedot: Bit Efficient Dot Product for
Deep Generative Models / 19--37 \\
Moritz Beutel, Robert Strzodka / A Paradigm for
Interval-Aware Programming / 38--60 \\
John L. Gustafson, Marco Cococcioni, Federico Rossi,
Emanuele Ruffaldi, Sergio Saponara / Decoding-Free
Two-Input Arithmetic for Low-Precision Real Numbers /
61--76 \\
Nils H{\"u}lsmeier, Moritz B{\"a}rthel, Jochen Rust,
Steffen Paul / Hybrid SORN Hardware Accelerator for
Support Vector Machines / 77--87 \\
Diksha Shekhawat, Jugal Gandhi, M. Santosh, Jai Gopal
Pandey / PHAc: Posit Hardware Accelerator for Efficient
Arithmetic Logic Operations / 88--100 \\
Moritz B{\"a}rthel, Chen Yuxing, Nils H{\"u}lsmeier,
Jochen Rust, Steffen Paul / Fused Three-Input SORN
Arithmetic / 101--113 \\
Himeshi De Silva, Hongshi Tan, Nhut-Minh Ho, John L.
Gustafson, Weng-Fai Wong / Towards a Better 16--Bit
Number Representation for Training Neural Networks /
114--133 \\
Ponsuganth Ilangovan P., Rohan Rayan, Vinay Shankar
Saxena / Improving the Stability of Kalman Filters with
Posit Arithmetic / 134--154 \\
Thushara Kanchana Gunaratne / Evaluation of the Use of
Low Precision Floating-Point Arithmetic for
Applications in Radio Astronomy / 155--170 \\
Raul Murillo, David Mallas{\'e}n, Alberto A. Del
Barrio, Guillermo Botella / PLAUs: Posit Logarithmic
Approximate Units to Implement Low-Cost Operations with
Real Numbers / 171--188 \\
Back Matter / 189--189",
}
@Proceedings{IEEE:2023:PIS,
editor = "{IEEE}",
booktitle = "Proceedings: {2023 IEEE 30th Symposium on Computer
Arithmetic: ARITH 2023, 4--6 September 2023 Portland,
United States}",
title = "Proceedings: {2023 IEEE 30th Symposium on Computer
Arithmetic: ARITH 2023, 4--6 September 2023 Portland,
United States}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "167",
year = "2023",
ISBN-13 = "979-83-503-1923-1 (print), 979-83-503-1922-4 (electronic)",
LCCN = "????",
bibdate = "Wed May 08 09:18:10 2024",
acknowledgement = ack-nhfb,
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
acknowledgement = ack-nhfb,
keywords = "ARITH-30",
}
